JEE Main 2020 Previous Year Question Paper with Solutions

Which one of the following statements not true?

The atomic number of the element unnilennium is :

Reaction of ammonia with excess gives:

Consider the following reactions: The order of the above reactions are and d, respectively. The following graph is obtained when log [rate] vs. log[conc] are plotted: Among the following, the correct

For a dimerization reaction, at then the will be _______ J.

The theory that can com pletely/properly explain the nature of bonding in is : [7-Jan-2020 Shift 1]

The rate of a reaction decreased by 3.555 times when the temperature was changed from to . The activation energy (in ) of the reaction is ____________. Take; ,

'X’ melts at low temperature and is a bad conductor of electricity in both liquid and solid state. X is :

If molecule is a polar molecule, a possible geometry of is :

The difference between the radii of and orbits of is . The difference between theradii of and orbits of is . Ratio is :

Which of the following derivatives of alcohols is unstable in an aqueous base ?

Which of the following compounds will showretention in configuration on nucleophicsubstitution by ion

The final major product of the following reaction is :

The correct order of the calculated spin-only magnetic moments of complexs (A) to (D) is:(A) (B) (C) (D)

The volume (in mL) of 0.1 N NaOH required to neutralise 10 mL of 0.1 N phosphinic acid is _________ .

The increasing order of the boiling points of the major products and of the following reactions will be :

In general, the property (magnitudes only) thatshows an opposite trend in comparison to otherproperties across a period is

If you spill a chemical toilet cleaning liquid onyour hand, your first aid would be :

The total number of coordination sites in ethylenediaminetetraacetate (EDTA ) is _______.

The correct observation in the following reactions is : Sucrose A + B

A solution of two components containing moles of the component and moles of the component is prepared. and are the molecular weights of component 1 and 2 respectively. If is the density of the solutio

The redox reaction among the following is :

The correct match between Item-I (starting material) and Item-II (reagent) for the preparation of benzaldehyde is : Item-IItem-II(I) Benzene(P) and (II) Benzonitrile (Q) and quinoline (III) Benzoyl Ch

108 g of silver (molar mass 108 g mol ) is deposited at cathode from (aq) solution by a certain quantity of electricity. The volume (in L) of oxygen gas produced at 273 K and 1 bar pressure from water

The strength of an aqueous NaOH solution is most accurately determined by titrating : (Note : consider that an appropriate indicator is used)

The increasing order of the reactivity of the following compound in nucleophilic addition reaction is : Propanal, Benzaldehyde, Propanone, Butanone

In the following reaction sequence, [C] is :-

Two compounds A and B with same molecular formula undergo Grignard's reaction with methylmagnesium bromide to give products and . products and show following chemical tests. Test C D Cericammoniumnitr

Given that the standard potentials (E°) of Cu /Cu and Cu /Cu are 0.34 V and 0.522 V respectively, the E° of Cu /Cu is : [7-Jan-2020 Shift 1]

The flucculation value of HCl for arsenic sulphide sol. is 30 m mole . If is used for the flocculation of arsenic sulphide, the amount, in grams, of in 250 ml required for the above purpose is _______

CHEM ISTRYA flask contains a mixture of isohexane and 3- methylphentane. One of the liquids boils at 63°C while the other boils at 60°C. What is the best way to seprate the two liquids and which one w

For the following Assertion and Reason, thecorrect option is Assertion (A) : When Cu (II) and sulphide ions are mixed, they react together extremely quickly to give a solid. Reason (R) : The equilibri

The increasing order of the following compoundstowards HCN addition is :

Which of the following compounds produces an optically inactive compound on hydrogenation ?

Among the statements , the correct ones are: (I) Be has smaller atomic radius compared to (II) Be has higher ionization enthalpy than Al. (III) Charge/radius ratio of Be is greater than that of Al. (I

Hydrogen has three isotopes (A), (B) and (C). If the number of neutron(s) in (A), (B) and (C) respectively, are (x), (y) and (z), the sum of (x), (y) an (z) is :

On heating, lead(II) nitrate gives a brown gas (A). The gas (A) on cooling changes to a colourless solid/liquid (B). (B) on heating with NO changes to a blue solid (C). The oxidation number of nitroge

The hardness of a water sample containing M expressed as equivalents (in ppm) is ______ .(molar mass of is 120.37 g/mol)

The molecular geometry of is octahedral. What is the geometry of (including lone pair(s) of electrons, if any) ?

Among the compounds A and B with molecular formula , A is having higher boiling point then B. The possible structures of A and B are :

Three isomers and formula ) give the following results: A and C P + Q R(product of A) + S(product of C) R has lower boiling point than S B alkali-insoluble product A, B and C, respectively are :

If the solubility product of is then the solubility of in pure water is ________ [Assuming that neither kind of ion reacts with water]

Consider the following reactions,The compound [P] is :

Arrange the following bonds according to their average bond energies in descending order : C-Cl, C-Br, C-F, C-I

The de Broglie wavelength of an electron in the 4th Bohr orbit is :

At constant volume, 4 mol of an ideal gas when heated from 300 K to 500K changes its internal energy by 5000 J. The molar heat capacity a constant volume is ______ .

The decreasing order of reactivity towards dehydrohalogenation reaction of the following compounds is :

The molarity of in a sample which has density 1.4 g/mL and mass percentage of 63% is _____ . (Molecular Weight of )

The correct electronic configuration and spinonly magnetic moment (BM) of Gd (Z = 64), respectively, are

Which of the following has the shortest C-Cl bond?

250 mL of a waste solution obtained from the workshop of a goldsmith contains 0.1 M and 0.1 M AuCl. The solution was electrolyzed at 2 V by passing a current of 1 A for 15 minutes. The metal/metals el

The predominant intermolecular forces present in ethyl acetate, a liquid, are :

The number of chiral carbon(s) present in peptide, Ile-Arg-Pro, is ______.

The solubility product of at 298 K is . The concentration of hydroxide ions in a saturated solution of will be :

The photoelectric current from Na (work function, ) is stopped by the output voltage of the cell The pH of aq. HCl required to stop thephotoelectric current from all other conditions remaining the sam

A solution of m-chloroaniline, m-chlorophenol and m-chlorobenzoic acid in ethyl acetate was extracted initially with a saturated solution of to give fraction A. The left over organic phase was extract

The internal energy change (in ) when ofwater undergoes complete evaporation at is ____. (Given: for water at

The decreasing order of reactivity of the following compounds towards nucleophilic substitution is :

The increasing order of basicity of the following compounds is

When neopentyl alcohol is heated with an acid, it slowly converted into an 85: 15 mixture of alkenes A and B, respectively. What are these alkenes?

The correct statement about probability density (except at infinite distance from nucleus) is :

The major product [C] of the following reaction sequence will be :-

The number of chiral centres present in threonine is _________.

The dipole moments of , and are in the order : [7-Jan-2020 Shift 1]

Among the following compounds, geometrical isomerism is exhibited by :

Consider the following equations: (in basic medium) (in acidic medium) The sum of the stoichiometric coefficients and for products and E, respectively, is _______.

If enthalpy of atomisation for is x kJ/mol and bond enthalpy for is y kJ/mol, the relation between them :

What is the product of following reaction ? [7-Jan-2020 Shift 1]

The number of subshells associated with and quantum numbers is :

The size of a raw mango shrinks to a muchsmaller size when kept in a concentrated saltsolution. Which one of the following processescan explain this?

A mixture of one mole each of He and each are enclosed in a cylinder of volume attemperature . If the partial pressure of is2 atm, the total pressure of the gases in the cylinder is :

The species that has a spin only magnetic moment of is -

The incorrect statement is:

Two monomers in maltose are :

The major product in the following reaction is :

The increasing order of values of the following compounds is -

The compound that has the largest H–M–H bond angle (M=N, O, S, C), is :

The true statement amongst the following is:

The electron gain enthalpy (in kJ/mol) of fluorine, chlorine, bromine and iodine, respectively are : [7-Jan-2020 Shift 1]

In the following reaction sequence the major products B is -

A solution was made by adding of The normality of the solution is 0.1 N. The value of is_____. (The atomic mass of Na is ) :-

Consider that a metal ion forms acomplex with aqua ligands, and the spin onlymagnetic moment of the complex is . Thegeometry and the crystal field stabilization energyof the complex is:

Consider the reaction sequence given below :Which of the following statements is true:

The major products A and B in the following reactions are :

A sample of milk splits after 60 min. at 300 K and after 40 min. at 400 K when the population of lactobacillus acidophilus in it doubles. The activation energy (in kJ/ mol) for this process is closest

The major product obtained from -elimination of 3 -bromo- 2 -fluoropentaneis:

For the disproportionation reaction at ln (where is the equilibrium constant) is _____ Given

The major aromatic product in the following reaction sequence will be :

Two open beakers one containing a solvent and the other containing a mixture of that solvent with a non volatile solute are together sealed in a container. Over time -

The process that is NOT endothermic in nature is :-

The major product obtained from the following reaction is -

The decreasing order of reactivity of the following organic molecules towards AgNO solution is :

The lanthanoid that does NOT show +4 oxidation state is

The number of orbitals associated with quantum 1 numbers , is : [7-Jan-2020 Shift 1]

The increasing order of the acidity of the α-hydrogen of the following compounds is :

The mass percentage of nitrogen in histamine is ________.

Identify the incorrect statement from the options below for the above cell:

Reaction of an inorganic sulphite with dilute generates compound Y. Reaction of with gives . Further, the reaction of with and water affords compound . Y and Z, respectively, are:

The heat of combustion of ethanol into carbondioxides and water is -327 kcal at constantpressure. The heat evolved (in cal) at constantvolume and (if all gases behave ideally)is cal

Kjeldahl's method cannot be used to estimate nitrogen for which of the following compounds?

The compound A in the following reaction is :

The number of hybrid orbitals in a molecule of benzene is :

In a molecule of pyrophosphoric acid, thenumber of and bonds moiety(ies) respectivey are:

The figure that is not a direct manifestation of the quantum nature of atoms is :

Consider the following reactions The mass percentage of carbon in A is_____.

Complex X of com position has a spin only magnetic moment of 3.83 BM. It reacts with and shows geometrical isomerism . The IUPAC nomenclature of X is :

For the reaction; , , at . Hence in kcal is___________ . [7-Jan-2020 Shift 1]

Identify the correct labels o f A, B and C in the following graph from the options given below: Root mean square speed ; most probable speed ; Average speed

The atomic radius of Ag is closest to : [7-Jan-2020 Shift 1]

The oxidation states of iron atoms in compounds(A), (B) and (C), respectively, are , y and z. Thesum of and is ______. (A) (B) (C)

The strengths of 5.6 volume hydrogen peroxide (of density ) in terms of mass percentageand molarity (M), respectively, are: (Take molar mass of hydrogen peroxide as

Consider the complex ions, trans - and cis . The correct statement regarding them is :

The volume (in mL) of 0.125 M , required to quantitatively precipitate chloride ions in 0.3 g of is ________. = 267.46 g/mol = 169.87 g/mol

If the equilibrium constant for is and that of is the equilibrium constant for is :-

Consider the hypothetical situation where the azimuthal quantum number, , takes values 0 , where is the principalquantum number. Then, the element with atomic number :

For a metal ion in an octahedral field, the correct electronic configuration is:

The correct order of heat of combustion for following alkadienes is :

The number of bonds between sulphur and oxygen atoms in and the number of bonds between sulphur and sulphur atoms in rhombic sulphur, respectively, are :

The correct order of the spin-only magnetic moments of the following complexes is : (I) (II) (III) (IV)

Consider the following plots of rate constant versus for four different reactions. Which of the following orders is correct for the activation energies of these reactions?

In the figure shown below reactant A (represented by square) is in equilibrium with product B (represented by circle). The equilibrium constant is :

Which of the following compounds is likely to show both Frenkel and Schottky defects in its crystalline form?

What would be the electrode potential for the given half cell reaction at pH = 5 ?_______ ; ( ; Temp = 298 K; oxygen under std. atm. pressure of 1 bar)

For a reaction, the free energy change is plotted as a function of temperature. The temperature below which the oxide is stable could be inferred from the plot as the point at which :

A diatomic molecule has a body-centred cubic (bec) structure with a cell edge of . The density of the molecule is . The number of molecules present in of is (Avogadro constant

Simplified absorption spectra of three complexes ((i), (ii) and (iii)) of ion are provided below; their values are marked as and respectively. The correct match between the complexes and their values

The major products of the following reaction are :

How much amount of NaCl should be added to 600 g of water (ρ = 1.00 g/mL) to decrease the freezing point of water to - 0.2 °C ? _______ . (The freezing point depression constant for water = 2K kg mol

The compound that cannot act both as oxidising and reducing agent is :

In the sixth period, the orbitals that are filled are

Consider the following reaction . For each of the following cases the direction in which the equilibrium shifts is: (a) Temperature is decreased (b) Pressure is increased by adding at constant T

The complex that can show optical activity is:

Which one of the following compounds possesses the most acidic hydrogen ?

Amongst the following statements, that whichwas not proposed by Dalton was : [7-Jan-2020 Shift 1]

The number of molecules with energy greater than the threshold energy for a reaction increases five fold by a rise of temperature from to Its energy of activation in is __________. ( Take

The increasing order of boiling points of the following compounds is :

If of an aqueous solution containing of a protein is isotonic with one litre of another aqueous solution containing of a protein at the ratio of the molecular mases of and is (to the nearest integer).

The region in the electromagnetic spectrum where the Balmer series lines appear is

The electronic spectrum of shows a single broad peak with a maximum at 20,300 cm . The crystal field stabilization energy (CFSE) of the complex ion, in kJ mol , is :

The pair in which both the species have the same magnetic moment (spin only) is :

The correct order of the ionic radii of and

Five moles of an ideal gas at 1 bar and is expanded into vacuum to double the volume. The work done is :-

The major product (Y) in the following reactions is :

A set of solutions is prepared using of water as a solvent and of different non-volatile solutes and . The relative lowering of vapour pressure in the presence of these solutes are in the order [Given

The mass of ammonia in grams produced when of dinitrogen quantitatively reacts with of dihydrogen is ______.

Within each pair of elements of F & Cl , S & Se, and Li & Na, respectively, the elements that release more energy upon an electron gain are-

Consider the following molecules and statements related to them : (a) (B) is more likely to be crystalline than (A) (b) (B) has higher boiling point than (A) (c) (B) dissolves more readily than (A) in

The rate of a certain biochemical reaction at physiological temperature (T) occurs times faster with enzyme than without. The change in the activation energy upon adding enzyme is :

An unsaturated hydrocarbon X absorbs two hydrogen molecules on catalytic hydrogenattion, and also gives following reaction : X will be:

The major product in the following reaction is :

For the following reactions it was found that is decreased by 30 kJ/mol in the presence of catalyst. If the rate remains unchanged, the activation energy for catalysed reaction is (Assume pre exponent

The reaction in which the hybridisation of the underlined atom is affected is :-

The number of bonds in perchloric acid is, "_________"

Consider the following reactions : (i) Glucose + ROH Acetal acetyl derivative (i) Glucose A acetyl derivative (i) Glucose + acetyl derivative 'x', 'y' and 'z' in these reactions are respectively.

If the magnetic moment of a dioxygen species is 1.73 B.M, it may be :

If of a first order reaction was completed in 90 minutes, of the same reaction would be completed in approximately (in minutes) ______. (Take

For the following reactions : and , are, respectively, the rate constants for the substitution and elimination, and , the correct options is -

The major product [B] in the following sequence of reactions is

The stoichiometry and solubility product of a salt with the solubility curve given below is, respectively :

An acidic solution of dichromate is electrolyzed for 8 minutes using current. As per the following equation The amount of obtained was . Theefficiency of the process(in\%) is (Take : , At. mass of chr

molecules are present in of a substance 'x'. The molarity of a solution containing 5 g of substance 'x' in 2 L solution is ______ .

Which of the following compound shows geometrical isomerism

For the reaction whichstatement is correct?

In the following reaction squence, structures of A and B, respectively will be :

For an electrochemical cell the ratio when this cell attains equilibrium is __________ . (Given , )

The shortest wavelength of atom is the Lyman series is The longest wavelength in the Balmer series of is :-

An organic compound 'A' whentreated with conc. HI undergoes cleavage toyield compounds 'B' and 'C'. 'B' gives yellowprecipitate with where as 'C' tautomerizes to 'D'. 'D' gives positive idoform test.

The equation that is incorrect is -

B has a smaller first ionization enthalpy than Be. Consider the following statements : (I) It is easier to remove 2d electron than 2s electron (II) 2p electron of B is more shielded from the nucleus b

A spherical balloon of radius containing helium gas has a pressure of bar. At the same temperature, the pressure, of a spherical balloon of radius containing the same amount of gas will be _________ b

For octahedral Mn(II) and tetrahedral Ni(II) complexes, consider the following statements: (I) both the complexes can be high spin (II) complex can very rarely be low spin. (III) with strong field lig

The rate constant (k) of a reaction is measured at different temperatures (T), and the data are plotted in the given figure. The activation energy of the reaction in is : (R is gas constant)

On heating compound (A) gives a gas (B) whichis constituent of air. This gas when treated with in the presence of a catalyst gives another gas(C) which is basic in nature. (A) should not be:

Match the following (i) Riboflavin (a) Beriberi (ii) Thiamine (b) Scurvy (iii) Pyridoxin (c) Cheilosis (iv) Ascorbic acid (d) Convulsions [7-Jan-2020 Shift 1]

A graph of vapour pressure and temperature for three different liquids X, Y and Z is shown below :The following inferences are made :(A) X has higher intermolecular interactions compared to Y.(B) X ha

The isomer(s) of that has/have a Cl-Co-Cl angle of 90°, is/are :

The variation of equilibrium constant with temperature is given below : Temperature Equilibrium constant The values of at and at (inkJ mol ) respectively, are close to [Use

For the following Assertion and Reason, the correct option is :Assertion : The pH of water increases with increase in temperature.Reason : The dissociation of water into and is an exothermic reaction.

Which o f the following statements is correct-

The number of chiral carbons present in the molecule given below is ______.

The volume strength of 8.9 M solution calculated at 273 K and 1 atm is _____. (R=0.0821 L atm K mol ) (rounded off to thenearest integer)

Chlorine reacts with hot and concentrated NaOH and produces compounds (X) and (Y). Compound (X) gives white precipitate with silver nitrate solution. The average bond order between Cl and O atoms in (

The Gibbs energy change (in ) for the given reaction at and is: Take

The major product of the following reaction is:

In an estimation of bromine by Carius method, 1.6 g of an organic compound gave 1.88 g of AgBr. The mass percentage of bromine in the compound is _________ . (Atomic mass,

Arrange the following solutions is the decreasing order of : (A) 0.01 M (B) 0.01 M (C) 0.01 M (D)

The for the following dissociation is Which of the following choices is correct for a mixture of 300 mL 0.134 M and 100 mL 0.4 M NaCl ?

The third ionization enthalpy is minimum for :

Which of these will produce the highest yield in Friedel Crafts reaction?

For a reaction of mol of Y and of were taken in a 1 L vessel and allowed to react. At equilibrium, the concentration of was . The equilibrium constant of the reaction is ______ The value of x is _____

The first and second ionisation enthalpies of a metal are 496 and 4560 kJ , respectively. How many moles of HCl and , respectively, will be needed to react completely with 1 mole of the metal hydroxid

The acidic, basic and amphoteric oxides, respectively, are :

The most suitable reagent for the given conversion is :

Glycerol is separated in soap industries by :

Among (a) - (d) the complexes that can display geometrical isomerism are :(a) (b) (c) (d)

Among the statements(a)-(d), the incorrect ones are- (a) Octahedral Co(III) complexes with strong field ligands have very high magnetic moments (b) When , the d-electron configuration of Co(III) in an

A soft drink was bottled with a partial pressure of of 3 bar over the liquid at room temperature. The partial pressure of over the solution approaches a value of 30 bar when of is dissolved in of wate

The relative strength of interionic/ intermolecular forces in decreasing order is : [7-Jan-2020 Shift 1]

The d-electron configuration of and respectively are :

The ionic radii of and are in the order :

The com plex that can show fac-and mer-isomers is :

The IUPAC name for the following compound is :

Which of the following is not an essential amino acid:

Potassium chlorate is prepared by the electrolysis of in basic solution If only of the current is utilized in the reaction, the time (rounded to the nearest hour) required to produce of using a curren

The atomic number of Unnilunium is _______

The variation of molar conductivity with concentration of an electrolyte (X) in aqueous solution is shown in the given figure. The electrolyte X is :

The magnitude of work done by a gas that undergoes a reversible expansion along the path ABC shown in the figure is ______ .

The correct statement with respect to dinitrogen is :

The mechanism of reaction is given as : A student writes general characteristics based on the given mechanism as : (a) The reaction is favoured by weak nucleophiles (b) would be easily formed if the s

The average molar mass of chlorine is . The ratio of to in naturally occurring chlorine is close to :

What are the functional groups present in the structure of maltose ?

In the following reaction A is :

An organic compound (A) (molecular formula ) was hydrolysed with dil. togive a carboxylic acid (B) and an alcohol (C). 'C' give white turbidity immediately when treated with anhydrous and conc. HCl. T

The sum of the total number of bonds betweenchromium and oxygen atoms in chromate anddichromate ions is _____________ .

The increasing order of basicity for the following intermediates is (from weak to (Atomic number B = 5, Be = 4) strong)

Which of the following reactions will not produce a racemic product ?

The elevation of boiling point of aqueous solution is two times that of aqueous solution. The value of is [Assume ionisation of the complex and coordination number of as and that all molecules are pre

The major product [B] in the following reactions is :-

For the reaction rate expression is, rate = , The rate expression of the reverse reaction is :

The minimum number of moles of required for complete combustion of 1 mole of propane and 2 moles of butane is ______.

The set that contains atomic number of only transition element is -

The total number of monohalogenated organic products in the following (including stereoisomers) reaction is _____.

For the Balmer series in the spectrum of Hatom, the correct statements among (I) and (IV) are : (I) As wavelength decreases, the lines in the series converge (II) The integer n, is equal to 2 (III) Th

The number of isomers possible for is :

Henry's constant (in kbar) for four gases and in water at is given below: α β γ δ 50 2 0.5(density of water at ) This table implies that :

In the following reactions products(A) and (B), respectively , are :

The major product Z obtained in the following reaction scheme is :

An element with molar mass forms a cubic unit cell with edge length . If its density is the radius of theelement is approximately ______ (to thenearest integer).

Which of the following statement is not true for glucose?

The electronic configurations of bivalent europium and trivalent cerium are (atomic number : Xe = 54, Ce = 58, Eu = 63)

A chromatography column, packed with silica gel as stationary phase, was used to separate a mixture of compounds consisting of (A) benzanilide (B) aniline and (C) acetophenone. When the column is elut

Consider the following reactions : Which of these reactions are possible ?

At 300 K, the vapour pressure of a solution containing 1 mole of n-hexane and 3 moles of n-heptane is 550 mm of Hg. At the same temperature, if one more mole of n-heptane is added to this solution, th

For the reaction

The radius of the second Bohr orbit, in terms of the Bohr radius, , in is :

The ammonia released on quantitative reaction of 0.6 g urea with sodium hydroxide (NaOH) can be neutralized by :

10.30 mg of is dissolved into a liter of sea water of density 1.03 g/mL. The concentration of in ppm is__________ .

In the following reaction sequence the major products A and B are :

The number of chiral centres present in [B] is _______.

The most appropriate reagent for conversion of into is

The mole fraction of glucose in anaqueous binary solution is The masspercentage of water in it, to the nearest integer,is _______.

The correct order of stability for the following alkoxides is :

Consider the following reactions: 'A' is -

The ratio of the mass percentages of 'C \& H' and 'C O' of a saturated acyclic organiccompound 'X' are 4: 1 and 3: 4 respectively. Then,the moles of oxygen gas required for completecombustion of two m

An element crystallises in a face-centred cubic (fcc) unit cell with cell edge a. The distance between the centres of two nearest octahedral voids in the crystal lattice is

The Kjeldahl method of Nitrogen estimation fails for which of the following reaction products ?

Match the type of interaction in Column A with the distance dependence of their interaction energy in Column B： A B (I) iron - ion (a) (II) dipole - dipole (b) (III) London dispersion (c) (a)

5 g of zinc is treated separately with an excess of(a) dilute hydrochloric acid and(b) aqueous sodium hydroxide.The ratio of the volumes of evolved in these two reactions is :

A crystal is made up of metal ions ana and oxide ions. Oxide ions form a ccp lattice structure. The cation occupies of octahedral voids and the cation occupies of tetrahedral voids of oxide lattice. T

Among the following compounds, which one has the shortest bond

Three elements and are in the period of the periodic table. The oxides of and Z, respectively, are basic, amphoteric and acidic. The correct order of the atomic numbers of and is :

The reaction of with at gives :

on treatment with in produced a single isomer . Br while heating [P] with sodalime gave toluene. The compound [P] is :

While titrating dilute solution with aqueous which of the following will not berequired?

The number of possible optical isomers for the complexes with and hybridised metal atom, respectively, is : Note : A and B are unidentate neutral and unidentate monoanionic ligands, respectively

Consider the following reaction :The product ’X’ is used : [7-Jan-2020 Shift 1]

The one that is not expected to show isomerismis :

The osmotic pressure of a solution of is 0.10 atm and that of a glucose solution is 0.20 atm. The osmotic pressure of a solution formed by mixing of the sodium chloride solution with of the glucose so

The results given in the below table were obtained during kinetic studies of the following reaction: Experiment [A]/molL [B]/molL Initialrate/molL min I 0.1 0.1 II 0.1 0.2 III 0.2 0.1 IV X 0.2 V 0.3 Y

Two solutions A and B, each o f 100 L was made by dissolving 4g of NaOH and 9.8 g of in water, respectively. The pH of the resultant solution obtained from mixing 40 L of solution A and 10 L of soluti

The work function of sodium metal is If the photons of wavelength are incident on the metal, the kinetic energy of the ejected electrons will be _____

Conside the following reactions : (Conc.) → (A) + Side products(A) + NaOH → (B) + Side product(B) + (dilute) + (C) + Side productThe sum of the total number of atoms in one molecule each of (A), (B) a

For the given cell ; change in Gibbs energy ( ) is negative, if :

At 35°C, the vapour pressure of is 512 mm Hg and that of acetone is 344 mm Hg. A solution of in acetone has a total vapour pressure of 600 mm Hg. The false statement amongst the following is : [7-Jan-

In Carius method of estimation of halogen, of an organic compound showed presence of of bromine. Which of these is the correct structureof the compound :

The reaction of (A) with in tetrahydrofuran gives inorganic benzene (B). Further, the reaction of (A) with (C) leads to . Compounds (B) and (C) respectively, are:

1-methyl ethylene oxide when treated with an excess of HBr produces : [7-Jan-2020 Shift 1]

Complexes of metals Ni and Fe have ideal square pyramidal and trigonal bipyramidal grometries, respectively. The sum of the 90°, 120° and 180° L-M L angles in the two complexes i s _________ .

A solution containing impure reacts completely with of in acid solution. The purity of (in ) is ______ (mol. wt. of mol. wt. of

The potential energy curve for the molecule as a function of internuclear distance is :

The major product formed in the following reaction is :

The first ionization energy (in kJ/mol) of Na, Mg, Al and Si respectively, are :

A solution of phenol in chloroform when treated with aqueous NaOH gives compound as a major product. The mass percentage of carbon in is __________. (to the nearest integer) (Atomic mass :

White Phosphorus on reaction with concentrated NaOH solution in an inert atmosphere of gives phosphine and compound (X). (X) on acidification with HCl gives compound (Y). The basicity of compound (Y)

During the nuclear explosion, one of the products is with half life of 6.93 years, if 1 µg of was absorbed in the bones of a newly bom baby in place of Ca, how much time, in years , is required to red

The increasing order of for the following compounds will be : [7-Jan-2020 Shift 1]

The values of the crystal field stabilization energies for a high spin metal ion in octahedral and tetrahedral fields, respectively, are :

Lattice enthalpy and enthalpy of solution of are and respectively. The hydration enthalpy of is :

Considering that the magnetic moment (in BM) of would be ______.

The volume, in of solutionrequired to react with 0.288 g of ferrous oxalate in acidic medium is ______. (Molar mass of )

Let and be the conductances (in ) measured for saturated aqueous solutions of and respectively, at a temperatureT. Which of the following is false?

Aqua regia is used for dissolving noble metals (Au, Pt, etc). The gas evolved in this process is :

The increasing order of the atomic radii of the following elements is :-(a) C (b) O (c) F (d) Cl(e) Br

An open beaker of water in equilibrium with watervapour is in a sealed container. When a few gramsof glucose are added to the beaker of water, therate at which water molecules:

The number of chiral carbons present in sucrose is_______ .

The structure of in the solid state is

3g of acetic acid is added to 250 mL of 0.1 M HCl and the solution made up to 500 mL. To 20 mL of this solution mL of 5 M is added. The pH of the solution is _____ . [Given : of acetic acid = 4.75, mo

of is taken in a beaker and to it of is added in steps of and the is continuously measured. Which of the following graphs correctly depicts the change in pH?

Consider the following reaction :The product 'P' gives positive ceric ammonium nitrate test. This is because of the presence of which of these group

Arrange the following compounds in increasing order of C-OH bond length :methanol, phenol, p-ethoxyphenol

The one that can exhibit highest paramagnetic behaviour among the following is :- gly = glycinato; bpy = 2, 2'-bipyridine

is used, even in spacecrafts, to produce . The daily consumption of pure by a person is 492L at 1 atm, 300K. How much amount of , in grams, is required to produce for the daily consumption of a person

Ferrous sulphate heptahydrate is used to fortify foods with iron. The amount (in grams) of the salt required to achieve 10 ppm of iron in 100 kg of wheat is _____ . A tomic weight : Fe = 55.85 ; S = 3

Oxidation number of potassium in , respectively, is : [7-Jan-2020 Shift 1]

The oxidation states of transition metal atoms in and respectively, are and The sum of and is _____.

Of the species, NO, NO , NO , NO , the one with minimum bond strength is :

The five successive ionization enthalpies of an element are 800,2427,3658,25024 and 32824 . The number of valence electrons in the element is :

Which of the following compounds will form the precipitate with aq. solution most readily?

A metal (A) on heating in nitrogen gas gives compound B. B on treatment with gives a colourless gas which when passed through solution gives a dark blue-violet coloured solution. A and B respectively,

Identify (A) in the following reaction sequence:

has n number of geometrical isomers. Then, the spin-only magnetic moment and crystal field stabilisation energy [CFSE] of , respectively, are: [Note : Ignore the pairing energy]

An acidic buffer is obtained on mixing :

Which of the following compounds can be prepared in good yield by Gabriel phthalimide synthesis?

The incorrect statement(s) among (a) - (c) is (are) :- (a) W(VI) is more stable than Cr(VI). (b) in the presence of HCl, permanganate titrations provide satisfactory results. (c) some lanthanoid oxide

A flask contains a mixture of compounds A and B. Both compounds decompose by first-order kinetics. The half-lives for A and are and , respectively. If the concentrations of and are equal initially, th

The intermolecular potential energy for the molecules A, B, C and D given below suggests that :

The crystal Field stabilization Energy (CFSE)of is :-

The major product [R] in the following sequence of reactions is :-

For one mole of an ideal gas, which of these statements must be true ? (a) U and H each depends only on temperature (b) Compressibility factor z is not equal to 1 (c) (d) for any process

The IUPAC name of the complex is : [7-Jan-2020 Shift 1]

A cylinder containing an ideal gas (0.1 mol of 1.0 ) is in thermal equilibrium with a large volume of 0.5 molal aqueous solution of ethylene glycol at its freezing point. If the stoppers and (as shown

Complex A has a composition of If the complex on treatment with conc. loses 13.5% of its original mass, the correct molecular formula of A is : [Given : atomic mass of Cr = 52 amu and Cl = 35 amu]

For the equilibrium the variation of the rate of the forward (a) and reverse (b) reaction with time is given by

The bond order and the magnetic characteristics of are :

A, B and C are three biomolecules. The results of the tests performed on them are given below: Molisch's Test BarfoedTest BiuretTest A Positive Negative Negative B Positive Positive Negative C Negativ

The elements with atomic numbers 101 and 104 belong to, respectively:

The shape/structure of and respectively, are :

an oxidation-reduction reaction in which 3 electrons are transferred has a of at . The value of in is ________.

Arrange the following labelled hydrogens in decreasing order of acidity :

An organic compound [A], molecular formula was hydrolyzed with dilute sulphuricacid to give a carboxylic acid [B] and alcohol[C]. Oxidation of [C] with produced [B]. Which of the following structuresa

The decreasing order of basicity of the following amines is :

In the following sequence of reactions the maximum number of atoms present in molecule 'C' in one plane is __________ (A is a lowest molecular weight alkyne)

Which one of the following graphs is not correctfor ideal gas?

Test/MethodReagent(i) Lucas Test (a) (ii) Dumas method(b) (iii) Kjeldahl's method(c) (iv) Hinsberg Test(d) Conc. HCl and (e)

The standard heat of formation of ethane in (kJ/mol), if the heat of combustion of ethane, hydrogen and graphite are -1560, -393.5 and -286 kJ/mol, respectively is _____ .

It is true that:

The molecule in which hybrid MOs involve only one d-orbital of the central atom is :-

Mischmetal is an alloy consisting mainly of:

Which of the following will react with alc.

The major product of the following reaction is :

The value of is 64 at for the reaction The value of for the following reaction is :

Boron and silicon of very high purity can be obtained through :

The number of words, with or without meaning, that can be formed by taking 4 letters at a time from the letters of the word 'SYLLABUS' such that two letters are distinct and two letters are alike, is

If and then is equal to

he number of ordered pairs (r, k) for which where k is an integer, is :

Suppose a differentiable function satisfies the identity for all real and If then is equal to _______.

Let be a function defined by Let denote the set of all points in where is not differentiable. Then :

Let be the solution of the differentialequation, and at is then the ordered pair(a, b) is equal to :

If where then at is :

If the surface area of a cube is increasing at a rate of 3.6 cm /sec, retaining its shape; then the rate of change of its volume (in cm /sec), when the length of a side of the cube is 10 cm, is :

Let f : (1,3) → R be a function defined by , where [x] denotes the greatest integer ≤ x. Then the range of f is

Consider a region If a line divides the area of region into two equal parts, then which of the following is true?

Out of 11 consecutive natural numbers if three numbers are selected at random (without repetition), then the probability that they are in A.P. with positive common difference, is :

Let f(x) be a polynomial of degree 5 such that are its critical points. If then which one of the following is not true?

The plane which bisects the line joining the points (4,-2,3) and (2,4,-1) at right angles also passes through the point:

If then :

The inverse function of is

The mean and variance of 8 observations are 10 and 13.5, respectively. If 6 of these observations are 5, 7, 10, 12, 14, 15, then the absolute difference of the remaining two observations is :

Let and be two 3 × 3 real matrices such that , where . If the determinant of B is 81, then the determinant of A is :

Let If and then is equal to

The foot of the perpendicular drawn from thepoint (4,2,3) to the line joining the points(1,-2,3) and (1,1,0) lies on the plane :

The equation of the normal to the curve at is :

The integral is equal to : (where is a constant of integration)

Consider the two sets: both the roots of are real and . Which of the following is not true?

Let a, b ∈ R, a ≠ 0 be such that the equation, has a repeated root a, which is also a root of the equation, . If P is the other root of this equation, then is equal to :

Let where andthen the set A:

Consider the data on x taking the values 0,2 , with frequencies respectively. If the mean of this data is then is equal to ___________ .

Let [t] denote the greatest integer ≤ t and . Then the function, is discontinuous, when x is equal to :

Let be the solution curve of the differential equation, , satisfying . This curve intersects the x-axis at a point whose abscissa is :

Let f and g be differentiable functions on R such that fog is the identity function. If for some a, b ∈ R, g'(a) = 5 and g(a) = b, then f'(b) is equal to :

The length of the perpendicular from the origin, on the normal to the curve, at the point (2,2) is

If the tangent to the curve at a poin(a, b) is parallel to the line joining anc then :

If the value of the integral is then is equal to

The integral is equal to :(where C is a constant of integration)

If a curve passing through the point (1,2), is the solution of the differential equation, then is equal to :

A plane meets the coordinate axes at and C respectively. The centroid of is given to be Then the equation of the line through this centroid and perpendicular to the plane is :

The solution of the differential equation is :- (where is a constant of integration.)

If the distance between the plane, 23x - 10y - 2z + 48 = 0 and the plane containing the lines and is equal to , then k is equal to _______.

If the four complex numbers and represent the vertices of a square of side 4 units in the Argand plane, then is equal to : :

Let f be any function continuous on [a, b] and twice differentiable on (a, b). If for all x ∈ (a, b), f'(x) > 0 and f"(x) < 0, then for any c ∈ (a,b), is greater than :

The area (in sq. units) of the region is :

The number of real roots of the equation, is :

Let be a twice differentiable function on If and for all then :

In a game two players A and B take turns in throwing a pair of fair dice starting with player A and total of scores on the two dice, in each throw is noted. A wins the game if he throws a total of 6 b

A survey shows that 73% of the persons working in an office like coffee, whereas 65% like tea. If x denotes the percentage of them, who like both coffee and tea, then x cannot be:

If where C is a constant of integration, then the ordered pair (λ, f(θ)) is equal to :

If ; then a value of x satisfying y(x) = e is :

Let f(x) be a polynomial of degree 3 such that f(-1) = 10, f(1) = -6, f(x) has a critical point at x = -1 and f'(x) has a critical point at x = 1. Then f(x) has a local minima at x = ______ .

If be respectively the smallest and the largest values of θ in which satisfy the equation, , then is equai to :

If and then is equal to

In a workshop, there are five machines and the probability of any one of them to be out of service on a day is . If the probability that at most two machines will be out of service on the same day is

Set A has elements and Set has elements. If the total number of subsets of A is 112 more than the total number of subsets of then the value of m.n is

An unbiased coin is tossed 5 times. Suppose that a variable X is assigned the value k when k consecutive heads are obtained for k = 3, 4, 5 otherwise X takes the value –1. Then the expected value of X

For a > 0, let the curves and intersect at origin O and a point P. Let the line x = b(0 < b < a) intersect the chord OP and the x-axis at points Q and R, respectively. If the line bisects the area bou

The value of is :

If thenthe value of is equal to ______.

If for some the lines and are coplanar, then the line passes through the point

If is the solution of the differential equation, such that y(0) = 0, then y(1) is equal to : [7-Jan-2020 Shift 1]

If the system of equations has infinitely many solutions, then :

The distance of the point (1,-2,3) from theplane measured parallel to the line is :

The area (in sq. units) of the region is :

Let and be the roots of and and be the roots of If form a geometric progression. Then ratio is :

In a box, there are 20 cards, out of which 10 are lebelled as A and the remaining 10 are labelled as B. Cards are drawn at random, one after the other and with replacement, till a second A-card is obt

is equal to :

Let where each contains 10elements and each contains 5 elements. Ifeach element of the set is an element ofexactly 20 of sets 's and exactly 6 of sets then is equal to :

The least positive value of 'a' for which the equation has real roots is

Let and If the curve represented by intersects the -axis at the points and where then the value of is :

Let be all non-zero and satisfy If the matrix satisfies then a value of abc can be :

If then is equal to :

Let the normal at a point P on the curve intersect the y-axis at . If m is the slope of the tangent at P to the curve, then is equal to

If the system of linear equations has a non-zero solution for some then is equal to :

If is the sum of the first 10 terms of the series then is equal to :

The mean and the standard deviation (s.d.) of 10 observations are 20 and 2 resepectively. Each of these 10 observations is multiplied by p and then reduced by q, where p ≠ 0 and q ≠ 0. If the new mean

If is a critical point of the function then :

Let and . Then is equal to :

is equal to :

The function, isincreasing for all x lying in :

The plane passing through the points (1,2,1)(2,1,2) and parallel to the line, also passes through the point:

If the equation, (b ∈ R) has conjugate complex roots and they satisfy , then

The integral is equal to ______.

Suppose the vectors and are the solutions of the system of linear equations, when the vector on the right side is equal to and respectively. If and then the determinant of A is equal to :-

Let denote the greatest integer . If for some then isequal to :

The area of the region, enclosed by the circle which is not common to the region bounded by the parabola and the straight line , is : [7-Jan-2020 Shift 1]

Let be a differentiable function such that and If then is equal to :

Let z be complex number such that and . Then the value of |z + 3i| is :

If and then the standard deviation of n observations is

Let [t] denote the greatest integer . Then the equation in has :

The imaginary part of can be :

Let P be a plane passing through the points (2, 1, 0), (4, 1, 1) and (5, 0, 1) and R be any point (2, 1, 6). Then the image of R in the plane P is : [7-Jan-2020 Shift 1]

Let and be the roots of the equation If then

is equal to

If is a relation on the set of integers then the domain of is :

If the system of equations has infinitely many solutions, then is equalto _______.

Four fair dice are thrown independently 27 times. Then the expected number of times, at least two dice show up a three or a five, is ______.

is equal to____ . [7-Jan-2020 Shift 1]

Let be the set of all for which the systemof linear equations has no solution. Then the set

Let be a solution of the differential equation, . If then is equal to

The mirror image of the point (1,2,3) in a plane is Which of the following points lies on this plane ?

If , where , then the point (x,y) lies on a : [7-Jan-2020 Shift 1]

If and then is equal to :

The value of a for which is:

Let for where denotes the greatest integer function. Then the number of points of discontinuity of is equal to _______.

Let S be the set of all functions , which are continuous on [0,1] and differentiable on (0,1). Then for every f in S, there exists a , depending on /f, such that

If a and b are real numbers such that where then is equal to :

The area (in sq. units) of the region enclosed by the curves and is equal to :

If where c is a constant o f integration, then is equal to

is equal to :

If where is a constant of integration, then is equal to :

The values of and for which the system of linear equations has infinitely many solutions are, respectively

If , then at is : [7-Jan-2020 Shift 1]

If z be a complex number satisfying |Re(z)| + |Im(z)| = 4, then |z| cannot be

Let a - 2b + c = 1.If then :

Let be a point on the curve nearest to the line, . Then the equationof the normal to the curve at is :

If the equation of a plane P, passing through the intesection of the planes, and is for some then the distance of the point -1 ) from the plane is ______.

Let iy be a non-zero complex number such that where then lies on the :

Let be a quadratic polynomial such that If one of the roots of is then its other root lies in :

The total number of 3-digit numbers, whose sum of digits is 10, is _______.

If c is a point at which Rolle's theorem holds for the function, in the interval [3,4], where , then is equal to

Let S be the set of all real roots of the equation, Then S :

Let α and β be the roots of the equation . If , then which one of the following statements is not true ?

Let A and B be two independent events such that and Then, which of the following is TRUE ?

There are 3 sections in a question paper and each section contains 5 questions. A candidate has to answer a total of 5 questions, choosing at least one question from each section. Then the number of w

The area (in sq. units) of the largest rectangle ABCD whose vertices A and B lie on the x-axis and vertices and lie on the parabola, below the -axis, is :

The domain of the function is Then a is equal to :

Let be defined by and Then the function

The set of all real values of for which thequadratic equations, always have exactly one root in the interval (0,1) is :

If the foot of the perpendicular drawn from the point (1, 0, 3) on a line passing through (α, 7, 1) is then α is equal to _______ .

The shortest distance between the lines and is :

If is a real number, then an argument of sinθ + icosθ is :

A plane passing through the point (3,1,1) contains two lines whose direction ratios are and respectively. If this plane also passes through the point then is equal to:

Let a plane contain two lines and If is the foot of the perpendicular drawn from the point to then equals _______.

If a,b and c are the greatest value of and respectively, then

The probabilities of three events and are given by and If , , , and where then lies in the interval:

If then at is _____.

The position of a moving car at time is given by where and are real numbers greater than Then the average speed of the car over the time interval is attained at the point :

If the system of linear equations2x + 2ay + az = 02x + 3by + bz = 02x + 4cy + cz = 0,where a, b, c ∈ R are non-zero and distinct; has a non-zero solution, then : [7-Jan-2020 Shift 1]

If and are the roots of the equation, then the value of is equal to :

Let be the set of all integer solutions, of the system of equations such that Then, the number of elements in the set is equal to _______.

Let . The system of linear equations is inconsistent for :

If is continuous at x = 0, then a + 2b is equal to :

If , where is a constant of integration, then can be :

If a function defined by be continuous for some and then the value of is :

is equal to

A test consists of 6 multiple choice questions, each having 4 alternative answers of which only one is correct. The number of ways, in which a candidate answers all six questions such that exactly fou

If then

Let A be a real matrix with entries from and Consider the following twostatements: If then (Q) If then , where denotes identity matrix and denotes the sum of the diagonal entries of A. Then:

Let a function be continuous f(1) = 3 and F be defined as : , where Then for the function F, the point x = 1 is :

Let be a function which satisfies If and then the value of forwhich is :

A die is thrown two times and the sum of the scores appearing on the die is observed to be a multiple of Then the conditional probability that the score 4 has appeared atleast once is :

Box I contains 30 cards numbered 1 to 30 and Box II contains 20 cards numbered 31 to A boxis selected at random and a card is drawn fromit. The number on the card is found to be anon-prime number. The

If for some α and β in R, the intersection of the following three places x + 4y - 2z = 1 x + 7y - 5z = β x + 5y + az = 5 is a line in , then is equal to :

Let and denote the fractional part of and the greatest integer respectively of a real number x. If and are three consecutive terms of a G.P., then is equal to ______.

Let and and If meanand variance of elements of are 17 and 216respectively then is equal to :

If where is a constant of integration, then the ordered pair can be :

A survey shows that 63% of the people in a city read newspaper A whereas 76% read newspaper B. If x% of the people read both the newspapers, then a possible value of x can be:

The value of is equal to :

Let A and B be two events such that the probability that exactly one of them occurs is and the probability that A or B occurs is , then the probability of both of them occur together is

If the mean and variance of eight numbers 3, 7, 9, 12, 13, 20, x and y be 10 and 25 respectively, then is equal to____ .

The sum of distinct values of for which the system of equations has non-zero solutions, is ___________.

The solution curve of the differential equation, which passesthrough the point is :

If A = {x ∈ R:|x| 3}; then :

The differential equation of the family of curves, , b ∈ R, is

Let and be respectively the minimum and maximum values of Then the ordered pair is equal to

If be a polynomial of degree three that hasa local maximum value 8 at and a localminimum value 4 at then is equal to:

The value of is

For the frequency distribution: where and the standard deviation cannot be :

Two families with three members each and one family with four members are to be seated in a row. In how many ways can they be seated so that the same family members are not separated ?

If and are the roots of the equation and and are the roots of the equation then is equal to:

The area (in sq. units) of the region is :

If where are non-zero distinct real numbers, then is equal to :

If and , where is the set of all natural numbers, thenthe value of is

The function is :

If the point on the curve, is farthest from the point then is equal to :

Let and If then is equal to _____.

If the variance of the following frequency distribution : Class : 10–20 20–30 30–40 Frequency : 2 x 2is 50, then x is equal to ____.

Total number of 6-digit numbers in which only and all the five digits 1, 3, 5, 7 and 9 appear, is : [7-Jan-2020 Shift 1]

Suppose is a polynomial of degree four, having critical points at If then the sum of squares of all the elements of is :

If are complex numbers such that and then is equal to:

The mean and variance of 20 observations are found to be 10 and 4, respectively. On rechecking, it was found that an observation 9 was incorrect and the correct observation was 11. Then the correct va

If is the positive root of the equation, then is equal to

Let be the solution of the differential equation, If then is equal to :

If and then is equal to [7-Jan-2020 Shift 1]

The set of all real values of for which the function has exactly one maxima and exactly one minima, is :

The shortest distance between the lines and is

The value of is :

If the letters of the word 'MOTHER' be permuted and all the words so formed (with or without meaning) be listed as in a dictionary, then the position of the word 'MOTHER' is ______.

Suppose that a function satisfies for all and If then is equal to

An urn contains 5 red marbles, 4 black marbles and 3 white marbles. Then the number of ways in which 4 marbles can be drawn so that at the most three of them are red is ....

If and where , then which one of the following is not true?

Let be a function of x satisfying where k is a constant and . Then at , is equal to

is equal to :

If for all real triplets (a, b, c), ; the is equal to :

For all twice differentiable functions with

Let be defined as The value of for which f"(0) exists, is ______.

The derivative of with respect to at is :

The integral equal :

If the matrices B = adj A and C = 3A, then is equal to

Let the function, f : [–7, 0] → R be continuous on [–7, 0] and differentiable on (–7, 0). If f(–7) = –3 and f' (x) ≤ 2, for all x ∈ (–7, 0), then for all such functions f, f(–1) + f (0) lies in the in

Let [t] denote the greatest integer less than or equal to t. Then the value of is ______.

If the number of five digit numbers with distinctdigits and 2 at the 10th place is 336 k, then kis equal to :

If then thegreatest common divisor of the least values of and is ______.

If the mean and the standard deviation of the data are 5 and 2 respectively, then a and are the roots of the equation :

Let denote the complement of an event . Let and be any pairwise independent events with and Then is equal to

Area (in sq. units) of the region outside and inside the ellipse is :

Let and Then the number of elements in the set and is not one-one is ________.

The area (in sq. units) of the region where [t] denotes the greatest integer function, is :

Which of the following points lies on thetangent to the curve at thepoint (1,0)

Let A be a matrix such that and B = adj (adj A). If and then the ordered pair is equal to :

If the system of linear equations,x + y + z = 6x + 2y + 3z = 103x + 2y + λz = µhas more two solutions, then is equal to _____ .

The mean and variance of 7 observations are 8 and respectively. If five observations are then the absolute difference of the remaining two observations is :

If and are the roots of the equation then is equal to :

If and be two roots of the equation Then the value of is

If for x ≥ 0, y = y(x) is the solution of the differential equation , ,then y(3) is equal to _________ .

In a bombing attack, there is 50% chance that a bomb will hit the target. At least two independent hits are required to destroy the target completely. Then the minimum number of bombs, that must be dr

Let be ten observations of a random variable X. If and where then the standard deviation of these observations is:

Let and be two relations defined as follows: and ,where is the set of all rational numbers. Then:

If is the image of the point (1,2,-3)in the line, then is equal to

The general solution of the differential equation is (where is a constant of integration)

The number of words (with or without meaning) that can be formed from all the letters of the word "LETTER" in which vowels never come together is __________.

If is the solution of the differential equation satisfying then a value of is :

The area (in sq. units) of the region {(x,y) ∈ : } is

For a suitably chosen real constant a, let a function, be defined by Further suppose that for any real number and Then is equal to :

Let Then is equal to :

For which of the following ordered pairs , the system of linear equations is inconsistent ?

The following system of linear equations7x + 6y - 2z = 03x + 4y + 2z = 0x - 2y - 6z = 0, has

If the function is twice differentiable, then the ordered pair is equal to :

If then the value of is ________.

Let be in If and are the roots of the equation, and and arethe roots of the equation, then is equal to :

If and . θ ∈ [0, 2π], then at θ = π is

If the lines and touch the curve at the points where the curve intersects the -axis, then is equal to _____.

Let X = {n ∈ N : 1 ≤ n ≤ 50}. If A = {n ∈ X : n is a multiple of 2} and B = {n ∈ X : n is a multiple of 7}, then the number of elements in the smallest subset of X containing both A and B is_____

The probability that a randomly chosen 5 -digit number is made from exactly two digits is :

Let S be the set of points where the function, , is not differentiable.Then is equal to __________. [7-Jan-2020 Shift 1]

The probability of a man hitting a target is . The least number of shots required, so that the probability of his hitting the target at least once is greater than is ______.

If the variance of the first n natural numbers is 10 and the variance of the first m even natural numbers is 16, then m + n is equal to ________. [7-Jan-2020 Shift 1]

A spherical iron ball of 10 cm radius is coated with a layer of ice of uniform thickness the melts at a rate of 50 /min. When the thickness of ice is 5 cm, then the rate (in cm/min.) at which of the t

If and such that then equals to

The number of all 3 × 3 matrices A, with enteries from the set {-1,0,1} such that the sum of the diagonal elements of is 3, is

If the function f defined on by is continuous, then k is equal to____ .

Let . If and , then a and b are the roots of the quadratic equation :

The system of linear equationsλx + 2y + 2z = 52λx + 3y + 5z = 84x + λy + 6z = 10 has

Let the observations satisfy the equations, and . If µ and λ are the mean and the variance of the observations, , then the ordered pair (µ, A,) isequal to :

A random variable X has the following probability distribution : Then P(X > 2) is equal to :

Let which of the following is true ?

The product of the roots of the equation is

If , for all x, where a and b are fixed positive real numbers, then is equal to : [7-Jan-2020 Shift 1]

If the variance of the terms in an increasing A.P., is then the commondifference of this A.P. is _____.

is equal to:

The number of 4 letter words (with or without meaning) that can be formed from the eleven letters of the word 'EXAMINATION' is __________.

If the tangent to the curve, at a point is parallel to the line - segment joining the points (1,0) and , then is equal to :

The region represented by is also given by the inequality : i :

The projection of the line segment joining the points (1, -1, 3) and (2, -4, 11) on the line joining the points (-1, 2, 3) and (3, -2, 10) is _________.

Let and . If then

The value of up to term up to term is equal to :

Given and . Then the area (in sq. units) of the region bounded by the curves, y = f(x) and y = g(x) between the lines, 2x = 1 and ,

The value of c in the Lagrange's mean value theorem for the function , when is :

If the minimum and the maximum values of thefunction defined by : are and respectively, then the ordered pair is equal to :

If 10 different balls are to be placed in 4 distinct boxes at random, then the probability that two of these boxes contain exactly 2 and 3 balls is :

Let be the solution of the differential equation , If then is equal to :

Let n > 2 be an integer. Suppose that there are n Metro stations in a city located along a circular path. Each pair of stations is connected by a straight track only. Further, each pair of nearest sta

Let and , then k is : [7-Jan-2020 Shift 1]

A quantity f is given by where c is speed of light, G universal gravitational constant and h is the Planck's constant. Dimension of f is that of :[9 Jan 2020 Shift 1]

Two particles of equal mass have respective initial velocities and . They collide completely inelastically. The energy lost in the process is:

A wire bent in the shape of an arc of a circle, carrying a current of and having radius and another wire also bent in the shape of arc of a circle, carrying a current of and having radius of are place

A series L-R circuit is connected to a battery of . If the circuit is switched on at ,then the time at which the energy stored in the inductor reaches times of its maximum value, is :

Two infinite planes each with uniform surface charge density are kept in such a way that the angle between them is 30°. The electric field in the region shown between them is given by: [7-Jan-2020 Shi

A non-isotropic solid metal cube has coefficients of linear expansion as : 5 × 10 along the x-axis and 5 × 10 along the y and the z-axis. If the coefficient of volume expansion of the solid is C × 10

Consider a force . The work done by this force in moving a particle from point to along the line segment is: (all quantities are in SI units)

A square loop of side and carrying current is kept in XZ plane with its centre at origin. A long wire carrying the same current is placed parallel to the z-axis and passing through the point The magni

A galvanometer is used in laboratory for detecting the null point in electrical experiments. If, on passing a current of it produces a deflection of its figure of merit is close to :

A simple pendulum is being used to determine th value of gravitational acceleration g at a certain place. Th length of the pendulum is 25.0 cm and a stop watch with Is resolution measures the time tak

A vector lies in the plane of the vectros and . If bisects the angle between and , then: [7-Jan-2020 Shift 1]

Two sources of light emit X-rays of wavelength and visible light of wavelength respectively. Both the sources emit light of the same power 200 W. The ratio of the number density of photons of X-rays t

Speed of a transverse wave on a straight wire (mass 6.0 g, length 60 cm and area of cross-section 1.0 mm ) is 90 ms . If the Young's modulus of wire is 16 × Nm , the extension of wire over its natural

In the circuit shown, charge on the capacitor is :

If the screw on a screw -gauge is given six rotations, it moves by 3 mm on the main scale. If there are 50 divisions on the circular scale the least count of the screw gauge is :[9 Jan 2020 Shift 1]

A thin lens made of glass (refractive index = 1.5) of focal length cm is immersed in a liquid of refractive index 1.42. If its focal length in liquid is , then the ratio is closest to the integer :

A Tennis ball is released from a height h and after freely falling on a wooden floor it rebounds and reaches height The velocity versus height of the ball during its motion may be represented graphica

Shown in the figure is rigid and uniform one meter long rod AB held in horizontal position by two strings tied to its ends and attached to the ceiling. The rod is of mass 'm' and has another weight of

There is a small source of light at some depth below the surface of water (refractive index = ) in a tank of large cross sectional surface area. Neglecting any reflection from the bottom and absorptio

Let be the point of local maxima of where , and Then the value of at is :

If the magnetic field in a plane electromagnetic wave is given by , then what will be expression for electric field? [7-Jan-2020 Shift 1]

A square loop of side and carrying current is kept in xz plane with its centre at origin. A long wire carrying the same current is placed parallel to z-axis and passing through point , . The magnitude

A beam of electrons of energy scatters from a target having atomic spacing of . The first maximum intensity occurs at . Then (in eV) is _______. (Planck constant , , electron mass )

The least count of the main scale of a verniercallipers is Its vernier scale is divided into 10 divisions and coincide with 9 divisionsof the main scale. When jaws are touching each other, the divisio

The density of a solid metal sphere is determined by measuring its mass and its diameter. The maximum error in the density of the sphere is If the relative errors in measuring the mass and the diamete

An ideal cell of emf is connected in circuitshown in figure. Each resistance is Thepotential difference (in ) across the capacitorwhen it is fully charged is _____.

Consider a sphere of radius which carries a uniform charge density . If a sphere of radius is carved out of it, as shown, the ratio of magnitude of electric field and , respectively, at points A and B

ABC is a plane lamina of the shape of an equilateral triagnle. D, E are mid points of AB, and is the centroid of the lamina. Moment of inertia of the lamina about an axis passing through and perpendic

An object is gradually moving away from the focal point of a concave mirror along the axis of the mirror. The graphical representation of the magnitude of linear magnification (m) versus distance of t

A particle of mass m and charge q is released from rest in a uniform electric field. If there is no other force on the particle, the dependence of its speed v on the distance x travelled by it is corr

A one metre long (both ends open) organ pipe is kept in a gas that has double the density of air at STP. Assuming the speed of sound in air at STP is 300 m/s, the frequency difference between the fund

An electron gun is placed inside a long solenoid of radius R on its axis. The solenoid has n turns/length and carries a current I. The electron gun shoots an electron along the radius of the solenoid

A light ray enters a solid glass sphere of refractive index at an angle of incidence . The ray is both reflected and refracted at the farther surface of the sphere. The angle (in degrees) between the

Visible light of wavelength falls normally on a single slit and produces a diffraction pattern. It is found that the second diffraction minimum is at from the central maximum. If the first minimum is

A calorimeter of water equivalent contains of water at 'm' grams of steam at is mixed in it till the temperature of the mixure is . The value of 'm' is close to (Latent heat of water cal specific heat

Four resistances , , and make the arms of a quadrilateral ABCD. Across AC is a battery of emf and internal resistance negligible. The potential difference across BD is is ________.

In a building there are 15 bulbs of 45 W, 15 bulbs of 100 W, 15 small fans of 10 W and 2 heaters of 1 kW. The voltage of electric main is 220 V. The minimum fusecapacity (rated value) of the building

A fluid is flowing through a horizontal pipe of varying cross-section, with speed at a point where the pressure is Pascal. At another point where pressure is Pascal its speed is . If the density of th

In the given circuit diagram, a wire is joining points B and D. The current in this wire is :

The change in the magnitude of the volume of an ideal gas when a small additional pressure is applied at a constant temperature, is the same as the change when the temperature is reduced by a small qu

A parallel plate capacitor has plates of area A separated by distance 'd' between them. It is filled with a dielectric which has a dielectric constant that varies as k(x) = K(1 + αx) where 'x' is the

Let the vectors be such that and If the projection of on is equal to the projection of on and is perpendicular to then the value of is ______.

If a semiconductor photodiode can detect a photon with a maximum wavelength of then its band gap energy is:

The distance between an object and a screen is 100 cm. A lens can produce real image of the object on the screen for two different positions between the screen and the object. The distance between the

Starling at temperature 300 K, one mole of an ideal diatomic gas is first compressed V, adiabatically from volume to . It is then allowed to expand isobarically to volume . If all the processes are th

The distance x covered by a particle in one dimensional motion varies with time t as . If the acceleration of the particle depends on as , where n is an integer, the value of n is[9 Jan 2020 Shift 1]

Radiation, with wavelength 6561 A falls on a metal surface to produce photoelectrons. The electrons are made to enter a uniform magnetic field of T. If the radius of the largest circular path followed

When the wavelength of radiation falling on a metal is changed from to , the maximum kinetic energy of the photoelectrons becomes three times larger. The work function of the metal is close to :

A beam of protons with speed enters a uniform magnetic field of at anangle of to the magnetic field. The pitch of the resulting helical path of protons is close to: (Mass of the proton , chargeof the

The circuit shown below is working as a 8 V dc regulated voltage source. When 12 V is used as input, the power dissipated (in mW) in each diode is; (considering both zener diodes are identical) ______

A (rms) source is connected to a resistance of an inductance of and a capacitance of all in series. The time in which the resistance (heat capacity ) will get heated by . (assume no loss of heat to th

On the x-axis and a dsitance from the origin, the gravitational field due to a mass distribution is given by in the -direction. The magnitude of gravitational potential on the -axis at a distance taki

A plane electromagnetic wave, has frequencyof and its energy density is in vacuum. The amplitude ofthe magnetic field of the wave is close to and speed of light = :

An electric field passes through the box shown in figure. The flux of the electric field through surfaces ABCD and BCGF are marked as and respectively. The difference between is (in )____________.

The coordinates of centre of mass of a uniform flag shaped lamina (thin flat plate) of mass 4kg. (The coordinates of the same are shown in figure) are :

Which of the following will NOT be observed when a multimeter (operating in resistance measuring mode) probes connected across a component, are just reversed?

In the given circuit, value of Y is :

For the given input voltage waveform , the output voltage waveform across the capacitor is correctly depicted by:

An ideal fluid flows (laminar flow) through a pipe of non-uniform diameter. The maximum and minimum diameters of the pipes are 6.4 cm and 4.8 cm, respectively. The ratio of the minimum and the maximum

The activity of a radioactive sample falls from 700 s to 500 s in 30 minutes. Its half life is close to :

In a fluorescent lamp choke (a small transformer) 100 V of reverse voltage is produced when the choke current changes uniformly from 0.25 A to 0 in a duration of 0.025 ms. The self-inductance of the c

When a diode is forward biased, it has a voltage drop of . The safe limit of current through the diode is . If a battery of emf is used in the circuit, the value of minimum resistance to be connected

A block of mass slides with velocity on a frictionless horizontal surfaceand collides with a uniform vertical rod andsticks to it as shown. The rod is pivoted about and swings as a result of the colli

A particle of charge and mass is moving with a velocity towards a large screen placed in the Y-Z plane at a distance d. If there is a magnetic field the minimum value of for which the particle will no

Identify the correct output signal Y in the given combination of gates (as shown) for the given inputs A and B.

Photon with kinetic energy of 1 MeV moves from south to north. It gets an acceleration of by an applied magnetic field (west to east). The value of magnetic field : (Rest mass of proton is kg) :

The current in the network is :

Two identical cylindrical vessels are kept on the ground and each contain the same liquid of density d. The area of the base of both vessels is but the height of liquid in one vessel is and in the oth

Two moles of an ideal gas with are mixed with 3 moles of another ideal gas with The value of for the mixture is : [7-Jan-2020 Shift 1]

A perfectly dimagnetic sphere has a small spherical cavity at its centre, which is filled with a paramagnetic substance. The whole system is placed in a uniform magnetic field . Then the field inside

In an adiabatic process, the density of a diatomic gas becomes 32 times its initial value. The final pressure of the gas is found to be times the initial pressure. The value of is:

In a dilute gas at pressure and temperature , the mean time between successive collisions of a molecule varies with T as:

Consider a uniform rod o f mass M = 4m and length l pivoted about its centre. A mass moving with velocity v making angle to the rod's long axis collides with one end of the rod and sticks to it. The a

A gas mixture consists of 3 moles of oxygen and 5 moles of argon at temperature T. Assuming the gases to be ideal and the oxygen bond to be rigid, the total internal energy (in units of ) of the mixtu

If minimum possible work is done by a refrigerator in converting 100 grams of water at to ice, how much heat (in calories) is released to the surrounding at temperature (Latent heat of ice to the near

In a meter bridge experiment S is a standard resistance. R is a resistance wire. It Is found that balancing length is cm. If R is replaced by a wire of half length and half diameter that of R of same

A thin rod of mass and length is suspended, at rest, from one end so that it can freely oscillate in the vertical plane. A particle of move moving in a straight line with velocity hits the rod at its

A small ball of mass is thrown upward with velocity u from the ground. The ball experiences a resistive force where is its speed. The maximum height attained by the ball is :

A double convex lens has power and same radii of curvature of both the surfaces. The radius of curvature of a surface of a plano-convex lens made of the same material with power is:

Consider two ideal diatomic gases A and B at some temperature T. Molecules of the gas A are rigid, and have a mass m. Molecules of the gas B have an additional vibrational mode, and m have a mass . Th

A student measuring the diameter of a pencil of circular cross-section with the help of a vernier scale records the following four readings The average of these four readings is and the standard devia

A camot engine having an efficiency of is being used as a refrigerator. If the work done on the refrigerator is 10 J, the amount of heat absorbed from the reservoir at lower temperature is :

A block of mass is at rest at the edge of a table, of height . A bullet of mass collides with the block and sticks to it. If the velocity of the bullet is in the horizontal direction just before the c

An electrical power line, having a total resistance of delivers at . The efficiency of the transmission line is approximately:

A hollow spherical shell at outer radius floats just submerged under the water surface. The inner radius of the shell is r. If the specific gravity of the shell material is w.r.t. water, the value of

A small circular loop of conducting wire has radius a and carries current I. It is placed in a uniform magnetic field B perpendicular to its plane such that when rotated slightly about its diameter an

A circular coil of radius is placed in a uniform magnetic field of with its plane perpendicular to the field initially. It is rotated at constant angular speed about an axis along the diameter of coil

A spaceship in space sweeps stationary interplanetary dust. As a result, its mass increases at a rate where is its instantaneous velocity. The instantaneous acceleration of the satellite is:

As shown in the figure, a bob of mass m is tied by a massless string whose other end portion is wound on a fly wheel (disc) of radius r and mass m. When released from rest the bob starts falling verti

Particle A of mass moving along the x-axis with velocity collides elastically with another particle B at rest having mass . If both particles move along the x-axis after the collision, the change in d

A wire of density is stretched between two clamps apart. The resulting strain in the wire is . The lowest frequency of the transverse vibrations in the wire is (Young's modulus of wire (to the nearest

An elliptical loop having resistance of semi major axis a, and semi minor axis b is placed in a magnetic field as shown in the figure. If the loop is rotated about the x-axis with angular frequency th

The magnetic field of a plane electromagnetic wave is Where is the speed of light. The corresponding electric field is:

A plane electromagnetic wave is propagating along the direction , with its polarization along the direction . The correct form of the magnetic field of the wave would be (here is an appropriate consta

In an experiment to verify Stokes law, a small spherical ball of radius and density falls under gravity through a distance in air before entering a tank of water. If the terminal velocity of the ball

A charged particle of mass 'm' and charge 'q' moving under the influence of uniform electric field and a uniform magnetic field follows a trajectory from point P to Q as shown in figure. The velocitie

An emf of 20 V is applied at time to a circuit containing in series 10 mH inductor and 5 Ω resistor. The ratio of the currents at time and at is close to : (Take )

Three containers and have water at different temperatures. The table below shows the final temperature T when different amounts of water (given in litres) are taken from each containers and mixed (ass

Both the diodes used in the circuit shown are assumed to be ideal and have negligible resistance when these are forward biased. Built in potential in each diode is 0.7 V. For the input voltages shown

When a car is at rest, its driver sees rain drops falling on it vertically. When driving the car with speed , he sees that rain drops are coming at an angle from the horizontal. On further increasing

Three harmonic waves having equal frequency v and same intensity , have phase angles and respectively . When they are superimposed the intensity of the resultant wave is close to :

A point object in air is in front of the curved surface of a plano-convex lens. The radius of curvature of the curved surface is 30 cm and the refractive index of the lens material is 1.5, then the fo

Three charged particle A, B and C with charges -4q, 2q and -2q are present on the circumference of a circle of radius d. the charged particles A, C and centre O of the circle formed an equilateral tri

A ball is dropped from the top of a 100 m high 1 tower on a planet. In the last s before hitting the ground, it covers a distance of 19 m. Acceleration due to gravity (in ms ) near the surface on that

A box weighs 196 N on a spring balance at the north pole. Its weight recorded on the same balance if it is shifted to the equator is close to (Take g = 10 ms at the north pole and the radius of the ea

A screw gauge has 50 divisions on its circular scale. The circular scale is 4 units ahead of the pitch scale marking, prior to use. Upon one complete rotation of the circular scale, a displacement of

A leak proof cylinder of length 1 m , made of a metal which has very low coefficient of expansion is floating vertically in water at 0°C such that its height above the water surface is 20 cm. When the

A galvanometer coil has 500 turns and each turnhas an average area of . If a torqueof is required to keep this coil parallelto magnetic field when a current of is flowing through it, the strength of t

M grams of steam at 100°C is mixed with 200 g of ice at its melting point in a thermally insulated container. If it produces liquid water at 40°C [heat of vaporization of water is 540 cal/ g and heat

The quantities and are defined where -capacitance -Resistance, -length, -Electric field, -magnetic field and -free space permittivity and permeability respectively. Then :[5 Sep 2020 Shift 2]

An electron is moving along direction with a velocity of It enters a region of uniform electric field of pointing along direction. The magnitude and direction of the magnetic field set up in this regi

A circular disc of mass and radius isrotating about its axis with angular speed . If another stationary disc having radius and same mass is dropped co-axially on to the rotating disc. Gradually both d

An AC circuit has and connected in series. The quality factor of the circuit is :

An object of mass is suspended at the end of a massless wire of length and area of cross-section, A. Young modulus of the material of the wire is . If the mass is pulled down slightly its frequency of

In the figure shown, the current in the battery is close to :

The plot that depicts the behavior of the mean free time t (time between two successive collisions) for the molecules of an ideal gas, as a function of temperature (T), qualitatively, is: (Graphs are

The surface of a metal is illuminated alternately with photons of energies and respectively. The ratio of maximum speeds of the photoelectrons emitted in the two cases is 2. The work function of the m

The value of current flowing from to in the circuit diagram is :

Moment of inertia of a cylinder of mass M, length and radius about an axis passing through its centre and perpendicular to the axis of the cylinder is If such a cylinder is to be made for a given mass

A capacitor is charged fully by a supply. It is then disconnected from the supplyand is connected in series to another uncharged capacitor. If the energy change duringthe charge redistribution is then

Consider a solid sphere of radius R and mass density The minimum density of a liquid in which it will float is :

If speed area and force are chosen asfundamental units, then the dimension ofYoung's modulus will be : [2 Sep 2020 Shift 1]

In a reactor, of fuel is fully used upin 30 days. The energy released per fission is . Given that the Avogadro number, per kilo mole and The power output of thereactor is close to :

For a plane electromagnetic wave, the magnetic field at a point xxx and time ttt is . The instantaneous electric field corresponding to is : (speed of light )

A force acts at a point Then the magnitude of torque about the point will be The value of is _______.

The velocity (v) and time (t) graph of a body in a straight line motion is shown in the figure. The point is at 4.333 seconds. The total distance covered by the body in 6 s is : [5 Sep 2020 Shift 2]

Nitrogen gas is at temperature. The temperature (in ) at which the speed of a molecule would be equal to the rms speed of a nitrogen molecule, is _____. (Molar mass of gas )

Two coherent sources of sound, and , produce sound waves of the same wavelength, , in phase. and are placed apart (see fig.) A listener, located at L, directly in front of finds that the intensity is

Magnitude of magnetic field (in SI units) at thecentre of a hexagonal shape coil of side ,50 turns and carrying current (Ampere) inunits of is :

A battery of is connected to a resistor dissipating of power. If the terminal voltage of the battery is the power dissipated within the internal resistance is :

An observer can see through a small hole onthe side of a jar (radius ) at a point atheight of from the bottom (see figure). The hole is at a height of . When the jaris filled with a liquid up to a hei

Consider two uniform discs of the samethickness and different radii and made of the same material. If the ratio of their moments of inertia and , respectively, about their axes is then the value of is

A cube of metal is subjected to a hydrostatic pressure of 4 GPa. The percentage change in the length of the side of the cube is close to : (Given bulk modulus of metal, )

In a Young's double slit experiment, 16 fringesare observed in a certain segment of the screenwhen light of wavelength is used. Ifthe wavelength of light is changed to ,the number of fringes observed

A balloon is moving up in air vertically above a point A on the ground. When it is at a height a girl standing at a distance (point ) from A (see figure) sees it at an angle with respect to the vertic

An asteroid is moving directly towards the centre of the earth. When at a distance of 10R (R is the radius of the earth) from the earths centre, it has a speed of 12 km/s. Neglecting the effect of ear

Assume that the displacement(s) of air is proportional to the pressure difference created by a sound wave. Displacement(s) further depends on the speed of sound , density of air and the frequency . If

A bullet of mass , travelling with a speed of , strikes a fixed wooden target. One half of its kinetic energy is converted into heat in the bullet while the other half is converted into heat in the wo

The energy required to ionise a hydrogen like ion in its ground state is 9 Rydbergs. What is the wavelength of the radiation emitted when the electron in this ion jumps from the second excited state t

A particle moving in the xy plane experiences a velocity dependent force where and are the and components of its velocity . If Ls the acceleration of the particle, then which of the following statemen

For the four sets of three measured physical quantities as given below. Which of the following options is correct ?(i) (ii) (iii) (iv) [9 Jan 2020 Shift 2]

In the line spectra of hydrogen atom, difference between the largest and the shortest wavelengths of the Lyman series is . Thecorresponding difference for the Paschan series in is : _______.

Charges and arc at points and of a right angle triangle OAB (see figure). The resultant electric field at point is perpendicular to the hypotenuse, then is proportional to :

The radius of gyration of a uniform rod of length , about an axis passing through a point away from the centre of the rod, and perpendicular to it, is : [7-Jan-2020 Shift 1]

A particle of mass collides with a hydrogen atom at rest. Soon after the collision the particle comes to rest, and the atom recoils and goes to its first excited state. The initial kinetic energy of t

A part of a complete circuit is shown in the figure. At some instant, the value of current I is and it is decreasing at a rate of . The value of the potential difference , (in volts) at that instant,

Boolean relation at the output stage-Y for the following circuit is :

An engine operates by taking a monatomic ideal gas through the cycle shown in the figure. The percentage efficiency of the engine is close to ________.

An electron, a doubly ionized helium ion ( ) and a proton are having the same kinetic energy. The relation between their respective de-Broglie wavelengths , and is:

A mass of 10 kg is suspended by a rope of length 4 m, from the ceiling. A force F is applied horizontally at the mid-point of the rope such that the top half of the rope makes an angle of 45° with the

Molecules of an ideal gas are known to have three translational degrees of freedom and two rotational degrees of freedom. The gas is maintained at a temperature of T. The total internal energy, U of a

The series combination of two batteries, both of the same emf 10 V, but different internal resistance of 20Ω and 5Ω, is connected to the parallel combination of two resistors 30 Ω and R Ω. The voltage

An electron is constrained to move along the y-axis with a speed of 0.1 c (c is the speed of light) in the presence of electromagnetic wave, whose electric field is . The maximum magnetic force experi

The electric field of a plane electromagnetic wave is given by Its magnetic field will be given by :

Given the masses of various atomic particles where proton, neutron, electron, antineutrino and deuteron. Which of the following process is allowed by momentum and energy conservation?

Two ideal Carnot engines operate in cascade (all heat given up by one engine is used by the other engine to produce work) between temperatures, and . The temperature of the hot reservoir of the first

In LC circuit the inductance L = 40 mH and capacitance C = 100 µF. If a voltage V(t) = 10sin(314 t) is applied to the circuit, the current in the circuit is given as :

A uniform magnetic field exists in a direction perpendicular to the plane of a square loop made of a metal wire. The wire has a diameter of and a total length of . The magnetic field changes with time

A capillary tube made of glass of radius is dipped vertically in a beaker filledwith methylene iodide (surfacetension density which rises to height h in the tube. It is observedthat the two tangents d

A parallel plate capacitor has plate of length 'l', width 'w' and separation of plates is 'd'. It is connected to a battery of emf . A dielectric slab of the same thickness 'd' and of dielectric const

Let and be three units vectors such that . If and , then the ordered pair, is equal to :

A thermodynamic cycle xyzx is shown on a V-T diagram.The P-V diagram that best describes this cycle is : (Diagrams are schematic and not to scale)

Under an adiabatic process, the volume of an ideal gas gets doubled. Consequently the mean collision time between the gas molecule changes from to . If for this gas then a good estimate for is given b

An electron (mass ) with initial velocity is in an electric field . If is initial de-Broglie wavelength of electron, its de-Broglie wave length at time is given by :

For a transverse wave travelling along a straight line, the distance between two peaks (crests) is while the distance between one crest and one trough is . The possible wavelengths (in ) of the waves

The linear mass density of a thin rod of length varies from to as where is the distance from A. If is the mass of the rod then its moment of inertia about an axis passing through A and perpendicular t

Two capacitors of capacitances and are charged to potential differences and respectively. These are then connected in parallel in such a manner that the positive terminal of one is connected to the ne

Consider the force on a charge 'q' due to a uniformly charged spherical shell of radius carrying charge Q distributed uniformly over it. Which one of the following statements is true for if 'q' is pla

A body is moving in a low circular orbit about a planet of mass and radius The radius of the orbit can be taken to be itself. Then the ratio of the speed of this body in the orbit to the escape veloci

For a uniform rectangular sheet shown in the figure, the ratio of moments of inertia about the axes perpendicular to the sheet and passing through (the centre of mass) and O' (corner point) is :

A particle of mass m is dropped from a height h above the ground. At the same time another particle of the same mass is thrown vertically upwards from the ground with a speed of . If they collide head

The speed verses time graph for a particle is shown in the figure. The distance travelled (in ) by the particle during the time interval to will be _________ :[4 Sep 2020 Shift 2]

An elevator in a building can carry a maximum of 10 persons, with the average mass of each person being 68 kg. The mass of the elevator itself is 920 kg and it moves with a constant speed 3 m/s. The f

A particle (m = 1 kg) slides down a frictionless track (AOC) starting from rest at a point A (height 2 m). After reaching C, the particle continues to move freely in air as a projectile. When it reach

Interference fringes are observed on a screen by illuminating two thin slits apart with a light source The distance between the screen and the slits is Ifa bright fringe is observed on a screen at a d

Consider a uniform cubical box of side a on a rough floor that is to be moved by applying minimum possible force F at a point b above its centre of mass (see figure). If the coefficient of friction is

When an object is kept at a distance of from a concave mirror, the image is formed at a distance of from the mirror. If the object is moved with a speed of , the speed (in ) with which image moves at

A compound microscope consists of an objective lens of focal length and an eye piece of focal length with a separation of The distance between an object and the objective lens, at which the strain on

A body A, of mass m = 0.1 kg has an initial velocity of . It collides elastically with another body, B of the same mass which has an initial velocity of . After collision, A moves with a velocity . Th

A litre of dry air at STP expands adiabatically to a volume of 3 litres. If , the work done by air is : [Take air to be an ideal gas] [7-Jan-2020 Shift 1]

If and are unit vectors, then the greatest value of is ______.

The radius of of a nucleus of massnumber A can be estimated by the formula It follows that the massdensity of a nucleus is of the order of:

Match the thermodynamic processes taking place in a system with the correct conditions. In the table : is the heat supplied, is the work done and is change in internal energy of the system : Process C

In a compound microscope, the magnified virtual image is formed at a distance of from the eye-piece. The focal length of its objective lens is . If the magnification is 100 and the tube length of the

Ten charges are placed on the circumference of a circle of radius with constant angular separation between successive charges. Alternate charges 1,3,5,7,9 have charge each, while 2,4,6,8,10 have charg

The specific heat of water and the latent heat of ice 100 grams of ice at is placed in of water at . The amount of ice that will melt as the temperature of water reaches is close to (in grams):

A bead of mass stays at point on a wire bent in the shape of a parabola and rotating with angular speed (see figure). The value of is (neglect friction):

A paramagnetic sample shows a net magnetisation of when it is placed in an external magnetic field of at a temperature of . When the sample is placed in an external magnetic field of at a temperature

Let and be three vectors such that , , and the angle between and is . If is perpendicular to the vector , then is equal to _____.

Mass per unit area of a circular disc of radius a depends on the distance r from its centre as σ (r) = A + Br. The moment of inertia of the disc about the the axis, perpendicular to the plane and pass

The length of a potentiometer wire is 1200 cm and it carries a current of 60 mA. For a cell of emf 5V and internal resistance of 20Ω, the null point on it is found to be a 1000cm. The resistance of wh

A metallic sphere cools from to in 300 s. If atmospheric temperature around is then the sphere's temperature after the next 5 minutes will be close to :

A shown in the figure, a battery of emf ε is connected to an inductor L and resistance R in series. The switch is closed at t = 0. The total charge that flows from the battery, between and ( is the ti

You are given that Mass of ,Mass of and Mass of . When of is converted into by proton capture, the energy liberated, (in ), is: [Mass of nudeon

In the circuit shown in the figure, the total charge in and the voltage across capacitor is . Then the charge on capacitor is :

Four resistances o f 15Ω, 12Ω, 4Ω and 10Ω respectively in cyclic order to form Wheatstone's network. The resistance that is to be connected in parallel with the resistance of 10Q to balance the networ

Concentric metallic hollow spheres of radii and hold charges and respectively. Given that surface charge densities of the concentric spheres are equal, the potential difference is :

A particle of mass m and charge q has an initial velocity . If an electric field and magnetic field act on the particle, its speed will double after a time:

An electric dipole of moment is at the origin (0, 0, 0). The electric field due to this dipole at (note that ) is parallel to:

Three different processes that can occur in an ideal monoatomic gas are shown in the vs diagram. The paths are labelled as and The change ininternal energies during these process are taken as and and

PHYSICS In the circuit, given in the figure currents in different branches and value of one resistor are shown. Then potential at point B with respect to the point is :

Two gases-argon (atomic radius 0.07 nm, atomic weight 40) and xenon (atomic radius 0.1 nm, atomic weight 140) have the same number density and are at the same temperature. The raito of their respectiv

A small point mass carrying some positive charge on it, is released from the edge of a table. There is a uniform electric field in this region in the horizontal direction. Which of thefollowing option

A particle of mass is projected with a speed from the ground at an angle w.r.t. horizontal ( -axis). When it has reached its maximum height, it collides completely inelastically with another particle

Effective capacitance of parallel combination of two capacitors and is 10 µF. When these capacitors are individually connected to a voltage source of 1V, the energy stored in the capacitor is 4 times

When a long glass capillary tube of radius is dipped in a liquid, the liquid rises to a heightof within it. If the contact angle betweenthe liquid and glass to close to the surface tension of the liqu

The current (in A) flowing through 1 Ω resistor in the following circuit is : [7-Jan-2020 Shift 1]

A stationary observer receives sound from two identical tuning forks, one of which approaches and the other one recedes with the same speed (much less than the speed of sound). The observer hears 2 be

A capacitor is fully charged with voltage . After disconnecting the voltage source, it is connected in parallel with another uncharged capacitor of capacitance The energy loss in the process after the

A loop ABCDEFA of straight edges has six corner points A(0,0,0), B(5,0,0), C(5,5,0), D(0, 5, 0), E(0, 5, 5) and F(0, 0, 5). The magnetic field in this region is . The quantity of flux through the loop

A beam of plane polarised light of large cross sectional area and uniform intensity of falls normally on a polariser (cross sectional area ) which rotates about its axis with an angular speed of . The

A heat engine is involved with exchange ofheat of and duringone cycle achieving an efficiency of . The value of is:

A particle of charge q and mass is subjected to an electric field in the -direction, where a and are constants. Initially the particle was at rest at Other than the initial position the kinetic energy

Take the breakdown voltage of the zener diode used in the given circuit as . For the input voltage shown in figure below, the time variation of the output voltage is : (Graphs drawn are schematic and

The correct match between the entries in column I and column II are : I II Radiation Wavelength (a) Microwave (i) (b) Gamma rays (ii) (c) A.M. radio waves (iii) (d) X-rays (iv)

The driver of a bus approaching a big wall notices that the frequency of his bus's horn changes from to when he hears it after it gets reflected from the wall. Find the speed of the bus if speed of th

A galvanometer of resistance is converted into a voltmeter of range by connecting a resistance in series with it. The additional resistance that should be connected in series with to increase the rang

When radiation of wavelength is used to illuminate a metallic surface, the stopping potential is V. When the same surface is illuminated with radiation of wavelength , thestopping potential is . If th

A satellite of mass m is launched vertically upwards with an initial speed u from the surface of the earth. After it reaches height R (R = radius of the earth), it ejects a rocket of mass so that subs

When photon of energy 4.0 eV strikes the surface of a metal A, the ejected photoelectrons have maximum kinetic energy eV end de-Broglie wavelength . The maximum kinetic energy of photoelectrons libera

A particle is moving along the x-axis with its coordinate with the time 't' given be . Another particle is moving the y-axis with its coordinate as a function of time given by . At , the speed of the

Two steel wires having same length are suspended from a ceiling under the same load. If the ratio of their energy stored per unit volume is 1 : 4, the ratio of their diameters is :

The value of the acceleration due to gravity is at a height radius of the earth from the surface of the earth. It is again equal to at a depth below the surface of the earth. The ratio equals

Let the volume of a parallelopiped whose coterminous edges are given by , and be 1 cu. unit. If θ be the angle between the edges and , then cosθ can be

The graph which depicts the results of Rutherform gold foil experiment with α-particales is :0 : Scattering angleY : Number of scattered α-particles detected (Plots are schematic and not to scale)

A charged particle going around in a circle can be considered to be a current loop. A particle of mass m carrying charge q is moving in a plane with speed under the influence of magnetic field . The m

A circuit to verify Ohm's law uses ammeter and voltmeter in series or parallel connected correctly to the resistor. In the circuit :

The lines and

Three point particles of masses 1.0 kg, 1.5 kg and 2.5 kg are placed at three corners of a right angle triangle of sides 4.0 cm, 3.0 cm and 5.0 cm as shown in the figure. The center of mass of the sys

Amount of solar energy received on the earth's surface per unit area per unit time is defined a solar constant. Dimension of solar constant is:[3 Sep 2020 Shift 2]

A wire carrying current I is bent in the shape ABCDEFA as shown, where rectangle ABCDA and ADEFA are perpendicular to each other. If the sides of the rectangles are of lengths and , then the magnitude

A body of mass m = 10 kg is attached to one end of a wire of length 0.3 m. The maximum angular speed (in rad s ) with which it can be rotated about its other end in space station is (Breaking stress o

In a Young's double slit experiment, light of is used to produce an interference pattern. When the distance between the slits is the angular width (in degree) of the fringes formed on the distance scr

The magnifying power of a telescope with tube 60 cm is 5. What is the focal length of its eye piece ?

If then the value of is equal to _______.

Starting from the origin at time , with initialvelocity , a particle moves in the plane with a constant acceleration of . At time , its coordinates are . The values of and , are respectively:[4 Sep 20

In a Young's double slit experiment 15 fringes are observed on a small portion of the screen when light of wavelength 500 nm is used. Ten fringes are observed on the same section of the screen when an

Using screw gauge of pitch and 50 divisions on its circular scale, the thickness of an object is measured. It should correctly be recorded as:[3 Sep 2020 Shift 1]

A vessel of depth 2h is half filled with a liquid of refractive index and the upper half with another liquid of refractive index . The liquids are immiscible. The apparent depth of the inner surface o

Suppose that intensity of a laser is . The rms electric field, in units of associated with this source is close to the nearest integer is ( ; )

An inductance coil has a reactance of . When an AC signal of frequency is applied to the coil, the applied voltage leads the current by The self-inductance of the coil is :

Water flows in a horizontal tube (see figure). The pressure of water changes by between A and B where the area of cross section are and , respectively. Find the rate of flow of water through the tube.

Two identical electric point dipoles have dipole moments and and are held on the axis at distance 'a' from each other. When released, they move along the -axis with the direction of their dipole momen

Three solid spheres each of m ass m and diameter d are stuck together such that the lines connecting the centres form an equilateral triangle of side of length d. The ratio of moment of inertia of the

A plane electrom agnetic wave of frequency 25 GHz is propagating in vacuum along the z-direction. At a particular point in space and time, the magnetic field is given by . The corresponding electric f

In finding the electric field using Gauss Law the formula is applicable. In the formula is permittivity of free space, A is the area of Gaussian surface and is charge enclosed by the Gaussian surface.

Two isolated conducting spheres and ofradius and have and charges, respectively, and are at a large distancefrom each other. They are now connected bya conducting wire. A long time after this is donet

If the volume of a parallelopiped, whose coterminus edges are given by the vectors and is units, then :

Shown in the figure is a hollow icecream cone (it is open at the top). If its mass is radius of its top, and height, then its moment of inertia about its axis is:

Two liquids of densities an are filled up behind a square wall of side 10 m as shown in figure. Each liquid has a height of 5 m. The ratio of the forces due to these liquids exerted on upper part MN t

A small bar magnet placed with its axis at with an external field of 0.06 T experiences a torque of 0.018 Nm. The minimum work required to rotate it from its stable to unstable equilibrium position is

Two different wires having lengths and , and respective temperature coefficient of linear expansion and are joined end-to-end. Then the effective temperature coefficient of linear expansion is :

In the figure below, PPP and QQQ are two equally intense coherent sources emitting radiation of wavelength . The separation between PPP and QQQ is and the phase of PPP is ahead of that of QQQ by . A,

A driver in a car, approaching a vertical wall notices that the frequency of his car horn, has changed from to when it gets reflected from the wall. If the speed of sound in air is then the speed of t

A closed vessel contains of a monoatomic ideal gas at 200 K. If 0.05 mole of the same gas at is added to it, the final equilibrium temperature (in ) of the gas in the vessel will be closed to ______.

Activities of three radioactive substances and are represented by the curves and C, in the figure. Then their half-lives are in the ratio :

Consider a gas of triatomic molecules. Themolecules are assumed to the triangular andmade of massless rigid rods whose vertices areoccupied by atoms. The internal energy of a mole of the gas at temper

In a Young's double slit experiment, the separation between the slits is 0.15 mm. In the experiment, a source of light of wavelength 589 nm is used and the interference pattern is observed on a screen

In the figure, potential difference between A and B is :

The aperture diameter of a telescope is 5m. The separation between the moon and the earth is km. With light of wavelength of , the minimum separation between objects on the surface of moon, so that th

Consider two solid spheres of radii , and masses and , respectively. The gravitational field due to sphere (1) and (2) are shown. The value of is :

Train A and train are running on parallel tracks in the opposite directions with speeds of hour and hour, respectively. A person is walking in train A in the direction opposite to its motion with a sp

Particle A of mass moving with velocity collides with another particle of mass which is at rest initially. Let and be the velocities of particles A and B after collision respectively. If and after col

The centre of mass of a solid hemisphere of radius is from the centre of the flat surface. Then value of is

An iron rod of volume and relative permeability 1000 is placed as core in a solenoid with 10 turns/cm. If a current of 0.5 A is passed through the solenoid, then the magnetic moment of the rod will be

Find the bindng energy per nucleon for . Mass of proton mass of neutron and mass of tin nucleus U. (take

The dimension of stopping potential in photoelectric effect in units of Planck's constant 'h', speed of light 'c' and Gravitational constant 'G' and ampere A is :[8 Jan 2020 Shift 1]

The displacement time graph of a particle executing S.H.M. is given in figure : (sketch is schematic and not to scale)Which of the following statements is/are true for this motion? (A) The force is ze

A 60 pF capacitor is fully charged by a 20 V supply. It is then disconnected from the supply and is connected to another uncharged 60 pF capactior is parallel. The electrostatic energy that is lost in

To raise the temperature of a certain mass of gas by at a constant pressure, 160 calories of heat is required. When the same mass of gas is cooled by at constant volume, 240 calories of heat is releas

PHYSICS A satellite is in an elliptical orbit around a planet P. It is observed that the velocity of the satellite when it is farthest from the planet is 6 times less than that when it is closest to t

If we need a magnification of 375 from a compound microscope of tube length 150 mm and an objective of focal length 5 mm, the focal length of the eye-piece, should be close to : [7-Jan-2020 Shift 1]

Two resistors and are connected in series across a battery. The potential difference measured by a voltmeter of across resistor is close to: