JEE Main 2019 Previous Year Question Paper with Solutions

Which of the following tests cannot be used for identifying amino acids ?

Which of the following compounds is notaromatic ?

0.27 g of a long chain fatty acid was dissolved in 100 of hexane. 10 mL of this solution was added dropwise to the surface of water in a round watch glass. Hexane evaporates and a monolayer is formed.

Which of the following is NOT a correct method if the preparation of benzylamine from cyanobenzene ?

Maltose on treatment with dilute HCI gives:

The major product of the following reaction is:

Heat treatment of muscular pain involves radiation of wavelength of about 900 nm. Which spectral line of H-atom is suitable for this purpose ? [ = 1 × 105 , h = 6.6 × Js, c = 3 × 108 ]

The increasing order of nucleophilicity of the following nucleophiles is : a) b) c) d)

When the first electron gain enthalpy ( H) of oxygen is - 141 kJ/mol, its second electron gain enthalpy is :

In chromatography, which of the following statements is INCORRECT for ?

The decreasing order of ease of alkalinehydrolysis for the following esters is :

The entropy change associated with the conversion of 1 kg of ice at 273 K to water vapours at 383 K is : (Specific heat of water liquid and water vapour are 4.2 kJ and 2.0 kJ ; heat of liquid fusion a

Consider the bcc unit cells of the solids 1 and 2 with the position of atoms as shown below. The radius of atom B is twice that of atom A. The unit cell edge length is 50% more in solid 2 than in 1. W

Which of the following statements is not true about RNA?

The one that will show optical activity is: (en = ethane – 1,2, -diamine)

The correct order of the atomic radii of C, Cs, Al and S is :

The highest value of the calculated spin only magnetic moment (in BM) among all the transition metal complexs is : [9-Jan-2019 Shift 1]

Correct statements among a to d regarding silicones are : (a) They are polymers with hydrophobic character (b) They are biocompatible. (c) In general, they have high thermal stability and low dielectr

The total number of isomers for a square planar complex [M(F)(Cl)(SCN)( )] is :

The correct match between items - I and II is : Item-I (mixture) Item-II (Separation method) (A) : sugar (P) Sublimation(B) : Aniline (Q) Recrystallization (C) : Toluene (R) Steam distillation (S) Dif

An element has a face – centred cubic (fcc) structure with a cell edge of a. The distance between the centres of two nearest tetrahedral voids in the lattice is:

The chloride that CANNOT get hydrolysed is :

For the reaction 2A + B → C, the values of initial rate at different reactant concentrations are given in the table below. The rate law for the reaction is: Initial Rate 0.05 0.05 0.045 0.10 0.05 0.09

Among the following four aromatic compounds,which one will have the lowest melting point ?

Among the following molecules/ ions, Which one is diamagnetic and has the shortest bond length?

An organic compound is estimated through Dumus method and was found to evolve 6 moles of . 4 moles of and 1 mole of nitrogen gas. The formula of the compound is :

Which of the graphs shown below does notrepresent the relationship between incident lightand the electron ejected form metal surface ?

The major product in the following reaction is:

For a reaction consider the plot of ln k versus 1/T given in the figure. If the rate constant of this reaction at 400 K is , then the rate constant at 500 K is :

The major product of the following reaction is :

The degenerate orbitals of are

The major product ‘Y’ in the following reaction is :

The increasing order of the reactivity of thefollowing with is :

For the following reactions, equilibrium constans are given: The equilibrium constant for the reaction,

The reaction, MgO(s) + C(s)®Mg(S) + CO(g), for which = + 491.1 kJ and = 198.0 , is not feasible at 298 K. Temperature above which reaction will be feasible is :-

The correct order of the oxidation states of nitrogen in and is

Consider the hydrated ions of and The correct order of their spinonly magnetic moments is :

For diatomic ideal gas in a closed system, whichof the following plots does not correctly describethe relation between various thermodynamicquantities ?

In the following reaction Aldehyde + Alcohol Acetal Aldehyde Alcohol HCHO MeOH The best combinations is :

The reaction 2X → B is a zeroth order reaction. If the initial concentration of X is 0.2 M, the half-life is 6 h. When the initial concentration of X is 0.5 M, the time required to reach its final con

According to molecular orbital theory, which of the following is true with respect to and ? [9-Jan-2019 Shift 1]

The percentage composition of carbon by mole in methane is :

20 mL of 0.1 solution is added to 30 mL of 0.2 M solution. The pH of the resulatant mixture is : [ of = 4.7]. [9-Jan-2019 Shift 1]

A reaction of cobalt(III) chloride and ethylenediamine in a 1 : 2 mole ratio generates two isomeric products A (violet coloured) B (green coloured). A can show optial actively, B is optically inactive

A solution containing 62 g ethylene glycol in 250 g water is cooled to - 10°C. If for water is 1.86 K kg , the amount of water (in g) separated as ice is :

The increasing order of reactivity of the following compounds towards aromatic electrophilic substitution reaction is

Arrange the following amines in the decreasingorder of basicity: [9-Jan-2019 Shift 1]

For a reaction, : identify dihydrogen as a limiting reagent in the following reaction mixtures.

Given:

Consider the given plot of enthalpy of the following reaction between A and B. . Identify the incorrect statement.

The major product of the following reaction is

Which of the following amines can be prepared by Gabriel phthalimide reaction ?

Enthalpy of sublimation of iodine is 24 at . If specific heat of and are 0.055 and 0.031 respectively, then enthalpy of sublimation of iodine at 250°C in is:

The correct IUPAC name of following compound is

The major producer of the following reaction is

Which one of the following statements regarding Henry's law not correct ? [9-Jan-2019 Shift 1]

Among the following, the molecule expected to be stabilized by anion formation is:

Elevation in the boiling point for 1 molal solution of glucose is 2 K. The depression in the freezing point of 2 molal solutions of glucose in the same solvent is 2 K. The relation between and is:

Consider the following reversible chemicalreactions : (g) + (g) 2AB (g) ... (1) 6AB (g) (g) + (g) ... (2) The relation between and is :

For a reaction scheme , if the rate of formation of B is set to be zero then the concentration of B is given by:

The volume of gas A is twice than that of gas B. The compressibility factor of gas A is thrice than that of gas B at same temperature. The pressures of the gases for equal number of moles are :

Increasing order of reactivity of the following compounds for substitution is:

cannot be prepared by :

An aromatic compound 'A' having molecular formula on treating with aqueous ammonia and heating forms compound 'B'. The compound 'B' on reaction with molecular bromine and potassium hydroxide provides

If the de Broglie wavelength of the electron in nth Bohr orbit in a hydrogenic atom is equal to 1.5 ( is Bohr radius), then the value of n/z is :

The number of 2-centre-2-electron and 3- centre-2-electron bonds in , respectively, are :

In general, the properties that decrease and increase down a group in the periodic table, respectively, are : [9-Jan-2019 Shift 1]

Which one of the following is likely to give a precipitate with solution?

The following results were obtained duringkinetic studies of the reaction : 2A + B → Products Experiment [A] (in mol ) [B] (in mol )Initial Rate of reaction (in mol ) (I)0.100.20 6.93 × (II) 0.10 0.25

The decreasing order of electrical conductivity of the following aqueous solutions is 0.1 M Formic acid (A) 0.1 M Acetic acid (B) 0.1 M Benzoic acid (C)

The statement that is INCORRECT about the interstitial compounds is :

5.1g is introduced in 3.0 L evacuated flask at 327°C. 30% of the solid decomposed to and as gases. The of the reaction at 327°C is (R = 0.082 L atm , Molar mass of S = 32 g mol/01, molar mass of N = 1

Ethylamine can be obtained from N- ethyiphthalimide on treatment with :

Homoleptic octahedral complexes of a metal ion ' ' with three monodentate ligands and absorb wavelengths in the region of green, blue and red respectively. The increasing order of the ligand strength

The correct order for acid strength of compounds CH ≡ CH, – C ≡ CH and is as follows :

The major product ‘Y’ in the following reaction is :

The osmotic pressure of a dilute solution of an ionic compound XY in water is four times that of a solution of 0.01 M in water. Assuming complete dissociation of the given ionic compounds is water, th

The organic compound that gives following qualitative analysis is: Test Inference a) Dil. HCl Insoluble b) NaOH solution Soluble c) water Decolourization

A solid having density of 9 × forms face centred cubic crystals of edge length 200 pm. What is the molar mass of the solid ? (Avogadro constant ~ 6 × , π ~ 3)

A process will be spontaneous at all temperatures if :

Which is the most suitable reagent for thefollowing transformation ? - CH = CH -

The number of bridging CO ligand (s) and Co- Co bond (s) in (CO)g, respectively are :-

Chlorine on reaction with hot and concentrated sodium hydroxide gives :

is 40% ionised in aqueous solution. The value of its van't Hoff factor (i) is :-

The element that usually does not show variable oxidation states is :

The major product of the following addition reaction is

What would be the molality of 20% (mass / mass) aqueous solution of KI? (molar mass of )

The basic structural unit of feldspar, zeolites, mica, and asbestos is:

The IUPAC symbol for the element with atomic number 119 would be:

The major product obtained in the following conversion is :-

Liquid ‘M’ and liquid ‘N’ form an ideal solution. The vapour pressures of pure liquids ‘M’ and ‘N’ are 450 and 700mmHg, respectively, at the same temperature. Then correct statement is: ( = Mole fract

What is the IUPAC name of the followingcompound ?

An organic compound neither reacts with neutral ferric chloride solution nor with Fehling solution. It however, reacts with Grignard reagent and gives positive iodoform test. The compound is :

A mixture of 100 m mol of and 2g of sodium sulphate was dissolved in water and the volume was made up to 100 mL. The mass of calcium sulphate formed and the concentration of in resulting solution, res

Compound shows positive iodoform test. Oxidation of A with given acid . Anhydride of is used for the preparation of phenolphthalein. Compound is:

The combination of plots which does notrepresent isothermal expansion of an ideal gasis:

Which of the these factors does not govern the stability of a conformation in acyclic compounds

The magnetic moment of an octahedral homoleptic Mn(II) complex is 5.9 BM. The suitable ligand for this complex is :

The correct match between item 'I' and item 'II' is : Item 'I' (compound) Item 'II' (reagent) (A) Lysine (P) 1-naphthol (B) Furfural (Q) ninhydrin (C) Benzyl alcohol (R) (D) Styrene (S) Ceric ammonium

The correct statement about and is:

The maximum possible denticities of a ligand given below towards a common transition and inner-transition metal ion, respectively, are :

The major product in the following conversionis :

The major product obtained in the following reaction is:

25 g of an unknown hydrocarbon upon burning produces 88 g of and 9 g of .This unknown hydrocarbon contains.

Hinsberg’s reagent is:

Which of the following graphs between molar conductivity versus is Correct ?

Which of the following potential energy (PE) diagrams represents the reaction?

The increasing order of pKa of the following amino acids in aqueous solution is : Gly Asp Lys Arg [9-Jan-2019 Shift 1]

The major product of the following reaction is :

The compounds A and B in the followingreaction are, respectively: [9-Jan-2019 Shift 1]

The anodic half-cell of lead-acid battery is recharged unsing electricity of 0.05 Faraday. The amount of electrolyzed in g during the process in : (Molar mass of = 303 g ) [9-Jan-2019 Shift 1]

In a chemical reaction, A + 2B 2C + D, the initial concentration of B was 1.5 times of theconcentration of A, but the equilibriumconcentrations of A and B were found to be equal.The equilibrium consta

The increasing order of reactivity of the followingcompounds towards reaction with alkyl halidesdirectly is :

50 mL of 0.5 M oxalic acid is needed to neutralize 25 mL of sodium hydroxide solution. The amount of NaOH in 50 mL of the given sodium hydroxide solution is :

Molecules of benzoic acid ( ) dimerise in benzene. 'w' g of the acid dissolved in 30 g of benzene shows a depression in freezing point equal to 2K. If the percentage association of the acid to form di

Which of the following compounds will show the maximum ‘enol’ content ?

The number of pentagons in and trigons (triangles ) in white phosphours, respectively ,are :

Iodine reacts with concentrated to yield Y along with other products. The oxidation state of iodine in Y, is :-

The INCORRECT match in the following is

The ratio of number of atoms present in a simple cubic ,body centered cubic and face centered cubic structure are respectively

Element ‘B’ forms ccp structure and ‘A’ occupies half of the octahedral voids, while oxygen atoms occupy all the tetrahedral voids. The structure of bimetallic oxide is:

The correct sequence of amino acids presentin the tripeptide given below is :

In the following reaction: xA → yB ‘A’ and ‘B’ respectively can be:

The pH of a 0.02 solution will be [given and log 2 = 0.301]

A 10 mg effervescent tablet contianing sodium bicarbonate and oxalic acid releases 0.25 ml of at T = 298.15 K and p = 1 bar. If molar volume of is 25.0 L under such condition, what is the percentage o

The pair that has similar atomic radii is :

The mole fraction of a solvent in aqueous solution of a solute is 0.8. The molality in mol of the aqueous solution is:

The pair that contains two P–H bonds in each of the oxoacids is :

For emission line of atomic hydrogen from to the plot of wave number against will be (The Rydberg constant, is in wave number unit) [9-Jan-2019 Shift 1]

The ratio of the shortest wavelength of two spectral series of hydrogen spectrum is found to be about 9. The spectral series are

The major product of the following reaction is:

Consider the statement S1 snd S2: S1: Conductivity always increases with decreases in the concentraction of electrolyte S2: Molar Conductivity always increase with decreases in the concentration of El

The major product of the following reactionis :-

p-Hydroxybenzophenone upon reaction with bromine in carbon tetrachloride gives:

The oxoacid of sulphur that does not contain bond between sulphur atoms is :

The size of the iso-electronic species , Ar and is affected by:

A solution is prepared by dissolving 0.6 g of urea ( molar mass =60 g mol ) and 1 .8 g of glucose (molar mass =180 g mol ) in 100 mL of water at 27°C . The osmotic pressure of the solution is :

Coupling of benzene diazonium chloride with 1-naphthol in alkaline medium will give:

Which one of the following alkenes when treated with HCl yields majorly an anti Markovnikov product?

Consider the given plots for a reaction obeying Arrhenius equation (0°C < T < 300°C) : (k and are rate constant and activation energy, respectively) Choose the correct option :

moles of weigh and 10 moles of weigh . The molar mass of and molar mass of in are:

HF has highest boiling point among hydrogen halides, because it has:

The major product of the following reaction is :

Complete removal of both the axial ligands (along the z – axis) from an octahedral complex leads to which of the following splitting patterns? (relative orbital energies not on scale).

Points I, II and III in the following plot respectively correspond to

The increasing order of the pKa values of thefollowing compounds is :

Which of the following compounds willproduce a precipitate with ?

The major product obtained in the following reaction is :

If dichloromethane (DCM) and water ( ) are used for differential extraction, which one of the following statements is correct ?

The correct decreasing order for acid strengthis :- [9-Jan-2019 Shift 1]

Given : (i) C(graphite) + (g) → (g) ;ΔrH° = x kJ (ii) C(graphite) + (g) → (g) ; ΔrH° = y kJ (iii) CO (g) + (g) → (g) ; ΔrH° = z kJ Based on the above thermochemical equations,find out which one of the

Consider the reaction (g) + (g) (g). The equilibrium constant of the above reaction is . If pure ammonia is left to dissociate, the partial pressure of ammonia at equilibrium is given by (Assume that

required for a reaction is produced by the decomposition of in as per the equation The initial concentration of is 3.00 mol and it is 2.75 mol after 30 minutes the rate of formation of is

The pair of metal ions that can give a spinonly magnetic moment of 3.9 BM for the complex , is :

If solubility product of is denoted by and its molar solubility is denoted by S, then which of the following relation between S and is correct ?

Heating of 2-chloro-1-phenylbutane with EtOK/EtOH gives as the major product. Reaction of with followed by gives as the major product. is :

Three complexes , and absorb light in the visible region . the correct order of the wavelength of lightabsorbed by them is :

In the following reaction . Rate of the reaction is the highest for:

The coordination number of Th in is :- ( = Oxolato)

The major product 'X' formed in the followingreaction is

The hardness of a water sample (in terms of equivalents of ) containing M is : (molar mass of CaSO4 = 136 g )

In the reaction of oxalate with permaganate in acidic medium, the number of electrons involved in producing one molecule of is :

In which of the following processes, the bondorder has increased and paramagnetic characterhas changed to diamagnetic ?

which of the given statements is INCORRECT about glycogen?

25 ml of the given HCl solution requires 30 mL of 0.1 M sodium carbonate solution. What is the volume of this HCl solution required to titrate 30 mL of 0.2 M aqueous NaOH solution?

For the solution of the gases w, x, y and z in water at 298 K, the Henrys law constants are 0.5, 2, 35 and 40 kbar, respectively. The correct plot for the given data is :

In which one of the following equilibria , ?

For the cell Zn(s) | (aq) || (aq) | M(s),different half cells and their standard electrodepotentials are given below : (aq) / M(s) (aq) / Ag (s) (aq) / Ag (s) (aq) / (s) (aq) / Fe (s) 1.400.80 0.77- 0

Diborane reacts independently with and to produce, respectively:

for NaCl, HCl and NaA are 126.4, 425.9 and 100.5 S , respectively. If the conductivity of 0.001 M HA is 5 × S , degree of dissociation of HA is :

The covalent alkaline earth metal halide (X = Cl, Br, I) is :

In the following reactions, products A and B are :

The amount of sugar ( ) required to prepare 2 L of its 0.1 M aqueous solution is :

For the reaction, 2A + B → products, when the concentrations of A and B both were doubled, the rate of the reaction increased from 0.3 mol to 2.4 mol . When the concentration of A alone is doubled, th

The major product of following reaction is : ? [9-Jan-2019 Shift 1]

the following compound the favourable site/s for protonation is/are :

The major product of the following reaction is : [9-Jan-2019 Shift 1]

The major product of the following reaction is:

The isoelectronic set of ions is :

The increasing basicity order of the following compounds is :

Aluminium is usually found in +3 oxidation stagte. In contarast, thallium exists in +1 and +3 oxidation states. This is due to : [9-Jan-2019 Shift 1]

Liquids A and B form an ideal solution in the entire composition range. At 350 K, the vapor pressures of pure A and pure B are 7 × Pa and 12 × Pa, respectively. The composition of the vapor in equilib

In the cell Pt(s)| (g, 1bar|HCl(aq)|Ag(s)|Pt(s) the cell potential is 0.92 when a molal HCl solution is used. The standard electrode potential of (AgCl/Ag, ) electrode is : [given , = 0.06 V at 298 K]

A process has ΔH = 200 and ΔS = 40 . Out of the values given below, choose the minimum temperature above which the process will be spontaneous :

For any given series of spectral lines of atomic hydrogen, let be the difference in maximum and minimum frequencies in . The ratio of is:

The major product obtained in the given reaction is

For the following reaction, the mass of water produced from 445 g of is : (s) → (g) → 114 (g) + 110 (1)

The major product obtained in the following reaction is

The correct order of catenation is

Given the equilibrium constant : KC of the reaction : Cu (s) + (aq) → (aq) + 2Ag (s) is 10 × , calculate the of this reaction at 298 K

Wilkinson catalyst is : (Et =

The correct match between Item I and Item II is:- Item I Item II (A) Ester test(P) Tyr (B) Carbylamine test (Q) Asp (C) Phthalein dyetest (R) Ser (S) Lys

Major products of the following of the reaction are

The major product of the following reaction is

The element having greatest difference between its first and second ionization energies, is

The increasing order of the b pK of the following compound is:

If p is the momentum of the fastest electron ejected from a metal surface after the irradiation of light having wavelength λ , then for 1.5 p momentum of the photoelectron, the wavelength of the light

The correct statements among I to III regarding group 13 element oxides are, (I) Boron trioxide is acidic II) Oxides of aluminium and gallium are amphoteric III) Oxides of indium and thallium are basi

The correct order of the first ionization enthalpies is :

Which of the following compounds reacts withethylmagnesium bromide and alsodecolourizes bromine water solution :-

The type of hybridisation and number of lone pair(s) of electrons of Xe in , respectively, are :

An ideal gas is allowed to expand from 1L to 10 L against a constant external pressure of 1 bar. The work done is kJ is:

An ideal gas undergoes isothermal compression from 5 against a constant external pressure of 4 . Heat released in this process is used to increase the temperature of 1 mole of Al. If molar heat capaci

The complex ion that will lose its crystal field stabilization energy upon oxidation of its metal to +3 state is:

10 mL of 1 mM surfactant solution forms a monolayer covering on a polar substrate. If the polar head is approximated as a cube, what is its edge length?

The coordination numbers of and ion and respectively, are ( en = ethane 1,2-diamine)

The ground state energy of hydrogen atom is –13.6 eV. The energy of second excited state ion in eV is :

Among the following reactions of hydrogen with halogens, the one that requires a catalyst is :

If the standard electrode potential for a cell is2 V at 300 K, the equilibrium constant (K) forthe reaction Zn (s) + (aq) ⇌ (aq) + Cu (s) at 300 K is approximately (R = 8 , F = 96000 C )

5 moles of an ideal gas at 100 K are allowed to undergo reversible compression till its temperature becomes 200 K. If , calcuIate ΔU and ΔPV for this process.

But – 2 – ene on reaction with alkaline at elevated temperature followed by acidification will give:

The graph between and r(radial diatance) is shown below . This represents

A 2B (Green) + 3B 2C (Purple) + 2B 2A + 2KOH + D In the above sequence of reactions,A and D respectively, are :-

The ion that has hybridization for the central atom, is:

The value of for the following reactionsat 300K are respectively : (At 300 K , RT = 24.62 atm ) (g) + (g) ⇌ 2NO (g) (g) ⇌ (g) (g) + (g) ⇌ (g)

The upper stratosphere consisting of the ozone layer protects us from the sun's radiation that falls in the wavelength region of :

At , copper has unit cell structure with cell edge length of . What is the approximate density of (in ) at this temperature? [Atomic Mass of

The complex that has highest cry splittingenergy (Δ), is :

Thermal decomposition of a Mn compound (X) at 513 K results in compound Y , and a gaseous product. reacts with and concentrated to give a pungent gas Z. X, Y and Z respectively are

The metal d-orbitals that are directly facing the ligands in are :

The correct structure of histidine in a stronglyacidic solution (pH = 2) is

For the reaction of with , the rate constant is at and 1.0 at . The activation energy for the reaction, in

At 300k and 1 atmospheric pressure 10ml of a hydrocarbon required 55mL of for complete combustion and 40mL of is formed. The formula of the hydrocarbon is:

The noble gas that does NOT occur in the atmosphere is :

A solution of is electrolysed between platinum electrodes using 0.1 Faraday electricity. How many mole of Ni will be deposited at the cathode?

An organic compound ‘X’ showing the following solubility profile is:

Consider the following reactions 'A' is :

If a reaction follows the Arrhenius equation, theplot lnk vs gives straight line with agradient (–y) unit. The energy required toactivate the reactant is :

The species that can have a trams-isomer (en=ethane-1,2-diamine,ox=oxalate)

Which dicarboxylic acid in presence of adehydrating agent is least reactive to give ananhydride :

A baclerial infection in an initial wound grows , where the time t is in hours A dose of antibiotic, taken orally , needs 1 hour to reach the wound. Once it reaches there , the bacterial Population go

The highest possible oxidation states of uranium plutonium , respectively are

The major product of the following reaction is:

The molar solubility of is in water. The expected solubility of in a buffer solution of is :

The standard electrode potential and itstemperature coefficient for a cell are 2V and - 5 × at 300 K respectively. Thecell reaction is Zn(s) + (aq) → (aq) + Cu (s) The standard reaction enthalpy at 30

The calculated spin–only magnetic moments (BM) of the anionic and cationic species of and , respectively, are :

is an organometallic compound due to the presence of :

Calculate the standard cell potential (in V) of the cell in which following reaction takes place : Given that

Which of the following statement is not true about sucrose?

The minimum amount of consumed per gram of reactant is for the reaction : (Given atomic mass : Fe = 56, O=16, Mg=24, P= 31, C=12, H=1)

Among the following species, the diamagnetic molecule is:

If of is 8 × , the molar solubility of in 0.1M is :

The major product formed in the following reaction is:

The difference between and , when the combustion of one mole heptane (I) is carried out a temperature T, is equal to :

An example of a disproportionation reaction is:

The electrons are more likely to be found:

An ‘Assertion’ and a ‘Reasaon’ are given below Choose the correct answer from the following options : Assertion (A) : Vinyl halides do not undergo nucleophilic substitution easily. Reasaon (R) : Even

A solution of sodium sulfate contains 92 g of ions per kilogram of water. The molality of ions in that solution in mol is: [9-Jan-2019 Shift 1]

The lanthanide ion that would show colour is :

Given that The strongest oxidizing agent is:

Which one of the following equations does not correctly represent the first law of thermodynamics for the given processes involving an ideal gas? (Assume nonexpansion work is zero)

The pH of rain water, is approximately :

What is the work function of the metal if the light of wavelength 4000 Å generates photoelectrons of velocity 6 × 105 form it ? (Mass of electron = 9 × kg Velocity of light = 3 × Planck's constant = 6

Among the following, the set of parameters that represents path functions, is: A) q+w B) q C) w D) H-TS

Two pi and half sigma bonds are present in:

The aldehydes which will not form Grignardproduct with one equivalent Grignard reagentsare :

Consider the following reduction processes : → Zn(s); E° = – 0.76 V → Ca(s); E° = – 2.87 V → Mg(s); E° = – 2.36 V → Ni(s); E° = – 0.25 V The reducing power of the metals increases inthe order :

Increasing rate of reaction in the following compounds is :

The process with negative entropy change is :

The correct match between Item I and Item IIis : Item I Item II (A) Benzaldehyde(P) Mobile phase (B) Alumina (Q) Adsorbent (C) Acetonitrile(R) Adsorbate

For silver, . If the temperature (T) of 3 moles of silver is raised from 300 K to 1000 K at 1 atm pressure, the value of ΔH will be close to :

The correct statement among I to III are: I) Valence bond theory cannot explain the color exhibited by transition metal complexes II) Valence bond theory can predict quantitatively the magnetic proper

The quantum number of four electrons are given below: I. II. III. IV.

The amorphous form of silica is:

The compound that inhibits the growth of tumors is:

In the following compounds, the decreasing order of basic strength will be:

Which hydrogen in compound (E) is easilyreplaceable during bromination reaction inpresence of light : - - =

Fructose and glucose can be distinguished by :

Match the metals (Column I) with the coordinationcompound(s) / enzyme(s) (Column II) Column-I Metals Column-II Coordinationcompound(s) / Enzyme(s) (A) Co (i) Wilkinson catalyst (B) Zn (ii) Chlorophyll

Among the following , the energy of orbital is lowest in :

An open vessel at 27°C is heated until two fifth of the air (assumed as an ideal gas) in it has escaped from the vessel. Assuming that the volume of the vessel remains constant, the temperature at whi

Which premitive unit cell has unequal edge lenghs (a ≠ b ≠ c) and all axial angles differetn from 90° ?

The element with Z = 120 (not yet discovered) will be an/a :

The major product(s) obtained in the following reaction is/are:

During compression of a spring the work done is 10 kJ and 2 kJ escaped to the surroundings as heat. The change in internal energy, (in kJ) is:

The principle of Column Chromatography is

For an elementary chemical reaction, , the expression for is :

Freezing point of a 4% aqueous solution of X is equal to freezing point of 12% aqueous solution of Y. If molecular weight of X is A, then molecular weight of Y is :-

The product formed in the reaction of cumene with followed by treatment with dil. HCl are :

The element that does NOT show catenation is:

Which compound(s) out of the following is/are notaromatic ?

The correct statement among the following is :

Which one of the following about an electron occupying the 1s orbital in a hydrogen atom is incorrect? (The Bohr radius is represented by ).

Which amongst the following is the strongest acid ? [9-Jan-2019 Shift 1]

The element that shows greater ability to form pπ - pπ multiple bonds, is :

An organic compound ‘A’ is oxidized with followed by boiling with . The resultant solution is then treated with ammonium molybdate to yield a yellow precipitate. Based on above observation, the elemen

The relative stability of +1 oxidation state of group 13 elements follows the order :-

The correct option with respect to the Pauling electronegativity values of the elements is :-

Decomposition of X exhibits a rate constant of 0.05 mg/year. How many years are required for the decomposition of 5 mg of X into 2.5 µg ?

The peptide that gives positive ceric ammonium nitrate and carbylamines tests is:

The major products of the following reaction are:

The major product formed in the reaction givenbelow will be :

1 g of a non-volatile non – electrolyte solute is dissolved in 100 g of two different solvents A and B whose ebulliscopic constants are in the ratio of 1:5. The ratio of the elevation in their boiling

What is the molar solubility of in 0.2 M NaOH solution? Given that, solubility product of

The IUPAC name of the following compound is:

Which of the following combination of statements is true regarding the interpretation of the atomic orbitals ? (a) An electron in an orbital of high angular momentum stays away from the nucleus than a

At a given temperature T, gases Ne, Ar, Xe and Kr are found to deviate from ideal gas behaviour. Their equation of state is given as at T. Here, be is the van der Waals constant. Which gas will exhibi

Among the following compounds most basic amino acid is :

Amylopectin is composed of

The correct order of the spin-only magnetic moment of metal ions in the following low- spin complexes, and is

At room temperature a dilute solution of urea is prepared by dissolving 0.60g of urea in 360g of water . If the vapour pressure of pure water at this temperature is 35mmHg , Lowering of vapour pressur

Glucose and Galactose are having identical configuration in all the positions except position.

The radius of the largest sphere which fits properly at the centre of the edge of body centred cubic unit cell is : (Edge length is represented by 'a') :-

The de Broglie wavelength (λ) associated witha photoelectron varies with the frequency (v)of the incident radiation as, [ is thersholdfrequency] :

The major products A and B for the following reactions are, respectively:

A compound 'X' on treatment with /NaOH, provided , which gives positive carbylamine test. Compound 'X' is :-

Consider the van der walls constants, a and b, for the following gases Gas Ar Ne Kr Xe / ( ) 1.3 0.2 5.1 4.1 / 3.2 1.7 1.0 5.0 Which gas is expected to have the highest critical temperature

The effect of lanthanoid contraction in the lanthanoid series of elements by and large means :

The difference in the number of unpaired electrons of a metal ion in its high-spin and low-spin octahedral complexes is two. The metal ion is :

, an allotrope of carbon contains:

The IUPAC name for the following compound is:

What will be the major product in the following mono nitration reaction ?

In order to oxidise a mixture of one mole of each of , and in acidic medium, the number of moles of required is:

The major product of the following reaction is :

0.5 moles of gas A and x moles of gas B exert a pressure of 200 Pa in a a container of volume 10 at 1000 K. given R is the gas constant in m, x is : [9-Jan-2019 Shift 1]

The freezing point of a diluted milk sample is found to be –0.2°C, while it should have been –0.5°C for pure milk. How much water has been added to pure milk to make the diluted sample ?

The following ligand is

The hydride that is NOT electron deficient is:-

The one that is extensively used as a piezoelectric material is : [9-Jan-2019 Shift 1]

Consider the following statements a) The pH of a mixture containing 400mL of 0.1M H2SO4 and 400 mL of 0.1M NaOH will be approximately 1.3 b) Ionic product of water is temperature dependent c) A monoba

Number of stereo centers present in linear and cyclic structures of glucose are respectively

In comparison to boron, beryllium has

What will be the major product when m- cresol is reacted with propargyl bromide in presence of in acetone?

The vapour pressures of pure liquids A and B are 400 and 600 mmHg, respectively at 298 K. On mixing the two liquids, the sum of their initial volumes is equal to the volume of the final mixture. The m

Two complexes (A) and (B) are violet and yellowcoloured, respectively. The incorrect statementregarding them is : [9-Jan-2019 Shift 1]

The major product the following reaction is : [9-Jan-2019 Shift 1]

The given plots represent the variation of the concentration of a reactant R with time for two different reactions (i) and (ii). The respective orders of the reactions are

The correct order of atomic radii is :

The 71st electron of an element X with an atomic number of 71 enters into the orbital :

Benzene diazonium chloride on reaction with aniline in the presence of dilute hydrochloric acid gives

Consider the reversible isothermal expansion of an ideal gas in a closed system at two different temperatures and ( < ). The correct graphical depiction of the dependence of work done (w) on the final

The group number, number of valence electrons, and valencey of an element with atomic number 15, respectively, are:

The correct structure of product 'P' in thefollowing reaction is : Asn-Ser + P

Aniline dissolved in dilute HCl is reacted with sodium nitrite at 0°C. this solution was added dropwise to a solution containing equimolar mixture of aniline and phenol in dil. HCl. The structure of t

A compound of formula has the hcplattice. Which atom forms the hcp lattice andwhat fraction of tetrahedral voids is occupiedby the other atoms :

The standard Gibbs energy for the given cell reaction in kJ at 298 K is: at 298 K

Two solids dissociate as follows A (s) ⇌ B (g) + C (g) ; = x D (s) ⇌ C (g) + E (g) ; = y The total pressure when both the solids dissociatesimultaneously is :-

The transition element that has lowest enthalpy of atomisation, is :

8g of NaOH is dissolved in 18g of . Mole fraction of NaOH in solution and molality (in mol ) of the solutions respectively are :

The maximum number of possible oxidation states of actionoides are shown by:

In the following skew conformation of ethane H' - C - C - H" dihedral angle is

Polysubstitution is a major drawback in

For the chemical reaction X ⇌ Y , thestandard reaction Gibbs energy depends ontemperature T (in K) as : G° (in kJ ) = 120 - T The major component of the reaction mixture atT is :

The standard reaction Gibbs energy for achemical reaction at an absolute temperature Tis given by = A - Bt Where A and B are non-zero constants. Whichof the following is TRUE about this reaction ?

The INCORRECT statement is :

For the reaction , and .Which of the following statement is INCORRECT ?

The correct statement(s) among I to III with respect to potassium ions that are abundant within the cell fluids is/are : I. They activate many enzymes II. They participate in the oxidation of glucose

Consider the following table Gas A. 642.32 0.05196 B. 155.21 0.04136 C. 431.91 0.05196 D. 155.21 0.4382And b are vander walls contants . The correct statement a Bout the gases is :

Molal depression constant for a solvent is 4.0 K kg . The depression in thefreezing point of the solvent for 0.03 mol solution of is : (Assumecomplete dissociation of the electrolyte).

The compound use in the treatment of lead poisoning is

The major product obtained in the followingreaction is :

The crystal field stabilization energy (CFSE) of and respectively are:

Two blocks of the same metal having same mass and at temperature and , respectively. are brought in contact with each other and allowed to attain thermal equilibrium at constant pressure. The change i

In an acid-base titration, 0.1 M HCl solution was added to the NaOH solution of unknown strength. Which of the following correctly shows the change of pH of the titration mixture in this experiment ?

lood reducing nature of ttributed to the presence of:

For the equilibrium, ⇌ + , the value of ΔG° at 298 K is approximately :-

The major product of the following reaction is :

The C-C bond length is maximum in

Among the following compound which one is foundin RNA ?

During the change of to ,the incoming electron goes to the orbital:

The increasing order of the reactivity of the following compounds towards electrophilic aromatic substitution reactions is :

The electronegativity of aluminium is similar to :

A committee of 11 members is to be formed from 8 males and 5 females. If m is the number of ways the committee is formed with at least 6 males and n is the number of ways the committee is formed with

If mean and standard deviation of 5 observations are 10 and 3, respectively, then the variance of 6 observations , .... , and –50 is equal to :

A group of students comprises of 5 boys and n girls. If the number of ways, in which a team of 3 students can randomly be selected from this group such that there is at least one boy and at least one

The domain of the definition of the function is

Let and If attains maximum value at and attains minimum value at then is equal to

The number of functions f from {1, 2, 3, ..., 20} onto {1, 2, 3, ....., 20} such that f(k) is a multiple of 3, whenever k is a multiple of 4, is :-

If the system of linear equations x–4y+7z = g 3y – 5z = h –2x + 5y – 9z = k is consistent, then :

If the line, meets the plane, at a point P, then the distance of P from the origin is:

The mean of five observations is 5 and their variance is 9.20. If three of the given five observations are 1, 3 and 8, then a ratio of other two observations is :

Let Then the set of all values of x, at which the function, is not differentiable, is:

Let a function f : (0, ∞) → (0, ∞) be defined by f (x) = |1 - | . The f is :

+ + + ... + is equal to :

A plane which bisects the angle between the two given planes and , passes through the point

The value of dx [9-Jan-2019 Shift 1]

If three of the six vertices of a regular hexagon are chosen at random, then the probability that the triangle formed with these chosen vertices is equailateral is:

The direction ratios of normal to the plane through the points (0, –1, 0) and (0, 0, 1) and making an angle with the plane y–z+5=0 are:

On which of the following lines lies the pointof intersection of the line, = = and the plane, x + y + z = 2 ?

A person throws two fair dice. He wins Rs. 15 for throwing a doublet (same numbers on the two dice), wins Rs. 12 when the throw results in the sum of 9, and loses Rs. 6 for any other outcome on the th

If an angle between the line, = = - and the plane, x – 2y – kz = 3 is , then a value of k is:

equals:

Let α and β be the roots of the quadratic equation sin θ – x (sin θ cos θ + 1) + cos θ = 0 (0 < θ < 45°), and α < β. Then is equal to :-

Let where g is a non–zero even function. If f(x+5)=g(x), then equals:

Let f be a differentiable function such that f

In a class of 140 students numbered 1 to 140, all even numbered students opted mathematics course, those whose number is divisible by 3 opted Physics course and theose whose number is divisible by 5 o

An unbiased coin is tossed. If the outcome isa head then a pair of unbiased dice is rolled andthe sum of the numbers obtained on them isnoted. If the toss of the coin results in tail thena card from a

The shortest distance between the point and the curve y = , (x > 0) is :

If is the inverse of a matrix A, then the sum of all values of for which det (A) + 1 = 0, is:

The area (in sq.units ) of the region bounded by the curves and in the first quadrant is:

Minimum number of times a fair coin must be tossed so that the probability of getting at least 0ne head is more than 99% is:

Suppose that 20 pillars of the same height have been erected along the boundary of a circular stadium if the top of each pillar has been connected by beams with the top of all its non –adjacent pillar

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

Let the numbers 2, b, c be in an A.P. and . If det(A) ∈ [2,16],then c lies in the interval:

For let and . If then is equal to:

The number of values of θ ∊ (0,π) for which the system of linear equations x + 3y + 7z = 0 –x + 4y + 7z = 0 (sin 3θ)x + (cos 2θ) y + 2z = 0 has a non-trivial solution, is :

If the function is continuous at x = 5, then the value of a-b is

A helicopter is flying along the curve given byy – = 7, (x ≥ 0). A soldier positioned at thepoint wants to shoot down the helicopterwhen it is nearest to him. Then this nearestdistance is :

Let A and B be two non-null events such that A ⊂ B . Then, which of the following statements is always correct?

A tetrahedron has vertices P(1, 2, 1),Q(2, 1, 3), R(-1,1,2) and O(0, 0, 0). The anglebetween the faces OPQ and PQR is :

Let A and B be two invertible matrices of order3 × 3. If det( ) = 8 and det( ) = 8, thendet ( ) is equal to :-

is equal to :

Let = (i = ) , where x and y are real numbers, then y – x equals :

If z and w are two complex numbers such that then:

Given that the slope of the tangent to a curve at any point is If the curve passes through the centre of the circle , then its equation is :

If and then for all :

The number of real roots of the equation is :

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

Two integers are selected at random from theset {1, 2,...., 11}. Given that the sum of selectednumbers is even, the conditional probabilitythat both the numbers are even is :

If and then the value of the integral is:

A student scores the following marks in five tests : 45, 54, 41, 57, 43. His score is not known for the sixth test. If the mean score is 48 in the six tests, then the standard deviation of the marks i

If is the image of in the plane and R is the point . then the area (in sq.units) of ΔPQR is :

Let such that then a value of is

A bag contains 30 white balls and 10 red balls. 16balls are drawn one by one randomly from the bagwith replacement. If X be the number of white ballsdrawn, the is equal to :

If and are respectively the sets of local minimum and local maximum points of the function, , then:

For an initial screening of an admission test, a candidate is given fifty problems to solve. If the probability that the candidate can solve any problem is , then the probability that he is unable to

If a cuver passes through the point (1, –2) and hasslope of the tangent at any point (x, y) on it as , then the curve also passes through thepoint :

For each t ∊ R, let [t] be the greatest integer lessthan or equal to t. Then

Let f and g be continuous functions on [0, a]such that f(x) = f(a-x) and g(x)+g(a-x)=4, then f (x) g (x) dx is equal to :

Let and Then the set of all , where the function h(x)=(fog)(x) is increasing, is:

If the function f defined on by is continuous, then k is equal to:

The value of is: dx is:

The plane through the intersection of the planes x + y + z = 1 and 2x + 3y - z = 4 = 0 and parallel to y-axis also passes through the point : [9-Jan-2019 Shift 1]

The plane containing the line = = and also containing its projection on the plane2x + 3y – z = 5, contains which one of thefollowing points ?

Let z be a complex number such that|z| + z = 3 + i (where i = ). Then |z| is equalto :-

The equation of the plane containing the straightline = = and perpendicular to the planecontaining the straight lines = = and = = is :

For x ∊ R - {0 , 1} , let (x) = , (x) = 1 - x and (x) = be three given functions. If a function, J(x) satisfies (x) = (x) then J (x) is equal to : [9-Jan-2019 Shift 1]

All the points in the set lie on a:

Let [x] denote the greatest integer less than orequal to x. Then :-

Four persons can hit a target correctly with probabilities and respectively. If all hit at the target independently, then the probability that the target would be hit, is:

If the probability of hitting a target by a shooter,in any shot, is 1/3, then the minimum numberof independent shots at the target required byhim so that the probability of hitting the targetat least

The integral

If the lines x = ay + b , z = cy + d and x = a'z + b', y = c'z + d' are perpendicular, then:

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

The values of λ such that sum of the squaresof the roots of the quadratic equation, + (3 – λ) x + 2 = λ has the least value is :

Let N be the set of natural numbers and twofunctions f and g be defined as f,g : N → Nsuch that : f (n) = and g (n) = n - . The fog is :

If x = 3 tan t and y = 3 sec t , then the value of at t = , is :

If ∫ dx = A (x) + C , for a suitable chosen integer m and a functionA(x), where C is a constant of integration then equals :

The area (in sq. units) of the region boundedby the curve = 4y and the straight linex = 4y – 2 :-

The area (in sq. units) in the first quadrant boundedby the parabola, y = + 1, the tangent to it at thepoint (2, 5) and the coordinate axes is :-

Let be such that If then:

The plane which bisects the line segment joining the points (–3,–3,4) and (3,7,6) at right angles, passes through which one of the following points ?

The number of natural numbers less than 7,000 which can be formed by using the digits 0,1,3,7,9 (repitition of digits allowed) is equal to :

Let A = where b > 0. Then the minimum value of is :

If the plane has the distances and units from the planes and ,respectively then the maximum value of

Assume that each born child is equally likely to be a boy or a girl. If two families have two children each, then the conditional probability that all children are girls given that at least two are gi

If the system of equations x+y+z = 5 x+2y+3z = 9 x+3y+αz = b has infinitely many solutions, then b–a equals:

The system of linear equations , x + y + z = 2 2x + 3y + 2z = 5 2x + 3y + ( – 1)z = a + 1 [9-Jan-2019 Shift 1]

is equal to

Two lines = = and = = intersect at the point R. Thereflection of R in the xy-plane has coordinates :-

If α and β be the roots of the equation , then the least value of n for which is:

Let S = {1, 2, ...... , 20}. A subset B of S is saidto be "nice", if the sum of the elements of B is 203.Then the probability that a randomly chosen subsetof S is "nice" is :-

Let f be a differentiable function from R to R suchthat |f (x) - f (y)| ≤ , for x , y , ∊ R. If f (0) = 1 then (x) dx is equal to

If both the mean and the standard deviation of 50 observations are equal to 16, then the mean of IS :

If the function defined by , is surjective, then A is equal to:

Let z = . If R(z) and I[z]respectively denote the real and imaginary partsof z, then :

Let S be the set of all values of x for which the tangent to the curve at is parallel to the line segment joining the points (1,f (1 )),and (- 1,f (- 1 )) then S is equal to:

The length of the perpendicular from the point on the straight line, is:

If + = then x is equal to : [9-Jan-2019 Shift 1]

If + y = , x ∊ and y = , then y equals :

The curve amongst the family of curves, represented by the differential equation, dx + 2xy dy = 0 which passes through (1,1) is :

All possible numbers are formed using the digits 1,1,2,2,2,2,3,4,4, taken all at a time. The number of such numbers in which the odd digits occupy even places is:

The number of ways of choosing 10 objects out of 31 objects of which 10 are identical and the remaining 21 are distinct, is:

Let If is a root of the quadratic equation, , then :

Let S be the set of all real values of λ such that a plane passing through the points (– , 1, 1), (1, – , 1) and (1, 1, – ) also passes through the point (–1, –1, 1). Then S is equal to :

The value of cot is :

The tangent to the curve y = – 5x + 5, parallelto the line 2y = 4x + 1, also passes through the point.

The solution of the differential equation, = , when y (1) = 1 , is :

Lety = y(x) be the solution of the differentialequation, x + y = x x , (x > 1). If 2y (2) = , then y (e) is equal to :

The value of , where [t] denotes the greatest integer less than or equalto t, is :

If where C is a constant of integration, then the function f(x) is equal to :

All x satisfying the inequality – 7 + 10 > 0, lie in the interval:-

The length of the perpendicular drawn from the point to the plane containing the lines and is

Let f be a differentiable function such that f' (x) = 7 - , (x > 0) and f (1) ≠ 4 Then x f :

If is the solution of the differential equation , such that then is equal to

The number of four–digit numbers strictly greater than 4321 that can be formed using the digits 0, 1, 2, 3, 4, 5 (repetition of digits is allowed) is :

If the line intersects the plane at a point P and the plane at a point Q, then PQ is equal to:

If the system of equation and has a non – trivial solution (x, y, z) , then is equal to

If then is equal to:

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

Let be written as where is an even function and is an odd function. Then equals:

Let A be a point on the line = (1 - 3µ) + (µ - 1) + (2 + 5µ) and B(3 , 2 , 6) be a point in the space. Then the value of μ forwhich the vector is parallel to the planex - 4y + 3z =1 is :

If is a non-zero polynomial of degree four, having local extreme points at ; Then the set contains exactly:

If ∫ dx = f (x) + C , where C is aconstant of integration, then f(x) is equal to :

The outcome of each of 30 items was observed;10 items gave an outcome -d each, 10 itemsgave outcome each and the remaining10 items gave outcome + d each. If thevariance of this outcome data is then |d

For x > 1 , if , then is equal to :

The perpendicular distance from the origin to the plane containing the two lines, = = and = = , is :

The area (in sq. units) of the region boundedby the parabola, y = + 2 and the lines,y = x + 1, x = 0 and x = 3, is :

If the area (in sq. units) bounded by the parabola and the line , is , then is equal to

Let P = and Q = be two 3 × 3 matrices such that Q - = . Then is equal to :

Let .if is a positive real number such that a ,then:

If f (x) = ∫ dx , (x ≥ 0) and f (0) = 0 , then the value of f (1) is :

If A = , then the matrix when θ = , is equal to : [9-Jan-2019 Shift 1]

A perpendicular is drawn from a point on a line to the plane such that the foot of the perpendicular Q also lies on the plane . Then the coordinates of Q are:

is :

The maximum value of the function f(x) = + 27x – 40 on the set S = {x ∊ R : + 30 ≤ 11x} is :

Let d ∊ R, and A = θ ∊ [0 , 2π] , If the minimum value of det(A) is 8,then a value of d is :

Considering only the principal valuesof inverse functions, the setA = { x ≥ 0 : (2x) + (3x) = π/4}

Let and br any two non - zero complex numbers such that = 4 If z = then :

If the system of linear equations 2x + 2y + 3z = a 3x – y + 5z = b x – 3y + 2z = c where a, b, c are non-zero real numbers, has more then one solution, then :

The area (in sq. units) bounded by theparabola y = – 1, the tangent at thepoint (2, 3) to it and the y-axis is : [9-Jan-2019 Shift 1]

Let I = dx. If I is minimum thenthe ordered pair (a, b) is :

If the tangent to the curve, at the point (1, - 5) is perpendicular to the line, , then which one of the following points lies on the curve?

The value of (where [t] denotes Greatest Integer Function)

If then is equal to

Let K be the set of all real values of x where the function f(x) = sin |x| – |x| + 2(x – π) cos |x| is not differentiable. Then the set K is equal to :-

Let A = . If = , then |p| is :

If y = y(x) is the solution of the differentialequation, x + 2y = satisfying y (1) = 1 , then y is equal to : [9-Jan-2019 Shift 1]

The mean and the median of the following ten numbers in increasing order 10,22,26,29,34,x,42,67,70,y are 42 and 35 respectively, then is equal to

If the system of linear equations , , has infinitely many solutions, then the value of is

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

The greatest value of c ∈ R for which the system of linear equations x –c y –c z = 0 cx - y + c z = 0 cx + cy – z = 0 has non – trivial solution, is:

Let f : [0,1] → R be such that f (xy) = f (x) . f (y) for allx , y , ∊ [0,1] , and f (0) ≠ 0. If y = y (x) satisfies thedifferential equation, = f (x) with y (0) = 1 , then y + y is equal to :

If = 4 (y > 0) , then dy/dx at x = e is equal to :

The number of all possible positive integral values of α for which the roots of the quadratic equation, 6x2–11x+α = 0 are rational numbers is :

Let be differentiable at and If then at is

Let Z be the set of integers. IfA = {x ∊ Z : 2 (x + 2) ( - 5x + 6)} = 1 and B = {x ∊ Z : - 3 < 2x - 1 < 9}, then the number of subsets of the set A × B, is :

Let f (x) = Let S be the set of points in the interval (–4,4)at which f is not differentiable. Then S:

If .......... then the inverse of is

The plane passing through the point (4, –1, 2)and parallel to the lines = = and = = also passes through the point :

Let S = {1,2,3, ...., 100}. The number of non-empty subsets A of S such that the product ofelements in A is even is :-

The number of integral values of m for which the quadratic expression. (1 + 2m) – 2(1 + 3m)x + 4(1 + m), x ∈ R, is always positive, is :

The integral equals :

If the standard deviation of the numbers is where , then k is equal to:

Let be the solution of the differential equation such that if ,then

Consider the quadratic equation (c–5) – 2cx + (c–4) = 0, c ≠ 5. Let S be the set of all integral values of c for which one root of the equation lies in the interval (0,2) and its other root lies in th

Let n ≥ 2 be a natural number and 0 < θ < π/2. Then ∫ dθ is equal to : (Where C is a constant of integration)

If the area enclosed between the curves y = and x = , (k > 0), is 1 square unit. Then k is:

Let be defined as where [t] denotes the greatest integer less than or equal to t. Then, f is discontinuous at:

An urn contains 5 red and 2 green balls. A ball isdrawn at random from the urn. If the drawn ballis green, then a red ball is added to the urn and ifthe drawn ball is red, then a green ball is addedto

The sum of the solutions of the equation equal to:

Two newspapers A and B are published in a city. It is known that 250% of the city population reads A and 20% reads B while 8% reads both A and B. Further, 30% of those who read A but not B look into a

Let S be the set of all points in (-π,π) at which the function, f(x) = min {sinx, cosx} is not differentiable. Then S is a subset of which of the following?

In a game, a man wins Rs. 100 if he gets 5 of 6on a throw of a fair die and loses Rs. 50 for gettingany other number on the die. If he decides to throwthe die either till he gets a five or a six or to

If and , then is equal to

If { } = K , then K is equal to :

If the sum of the deviations of 50 observations from 30 is 50, then the mean of these observation is :

The magnitude of the projection of the vector on the vector perpendicular to the plane containing the vectors and is

If ; then k is

The equation of the line passing through(–4, 3, 1), parallel to the plane x + 2y – z – 5 =0and intersecting the line = = is : [9-Jan-2019 Shift 1]

The maximum volume (in cu. m) of the right circular cone having slant height 3m is : [9-Jan-2019 Shift 1]

Let f (x) = and g (x) = |f (x)| + f (|x|) . Then, in the interval (–2, 2), g is :-

If where then is equal to:

Let , where the function f satisfies for all natural numbers x, y and . Then the natural number ‘a’ is

Let and is area of the region If for a then equals:

The number of integral values of m for which the equation has no real root is:

If one real root of the quadratic equation + kx + 256 = 0 is cube of the other root, then a value of k is

Two cards are drawn successively with replacement from a well-shuffled deck of 52 cards. Let X denote the random variable of number of aces obtained in the two drawn cards. Then P(X = 1) + P(X = 2) eq

The minimum number of times one has to toss a fair coin so that the probability of observing at least one head is at least 90% is:

If and , and then is equal to

The area of the region A = [(x , y) : 0 ≤ y ≤ x |x| + 1 and - 1 ≤ x ≤ 1] in sq. units, is :

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

If the point (2, α, β) lies on the plane which passes through the points (3, 4, 2) and (7, 0, 6) and is perpendicular to the plane 2x – 5y = 15, then 2α – 3β is equal to :-

Let f : R → R be a function such that f (x) = + xf'' (2) + f''' (3) , x ∊ R. Then f (2) equal :

For each x ∊ R, let [x] be the greatest integer lessthan or equal to x. Then is equal to

Let f : R → R be defined by f (x) = x ∊ R. Then the range of f is :

If for some x ∈ R, the frequency distribution of the marks obtained by 20 students in a test is: Marks 2 3 5 7 No. of students Then the mean of the marks is:

There are m men and two women participating in a chess tournament. Each participant plays two games with every other participant. If the number of games played by the men between themselves exceeds th

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

Consider a class of 5 girls and 7 boys. The number of different teams consisting of 2 girls and 3 boys that can be formed from this class, if there are two specific boys A and B, who refuse to be the

A 2m ladder leans against a vertical wall. If the top of the ladder begins to slide down the wall at the rate 25cm/sec., then the rate (in cm/sec.) at which the bottom of the ladder slides away from t

The value of the integral is

Let f : (–1,1) → R be a function defined by f (x) = max {- |x| , - }. If K be the set ofall points at which f is not differentiable, thenK has exactly :

Let α and β be the roots of the equation . Then for in R, is equal to:

A water tank has the shape of an inverted right circular cone, whose semi-vertical angle is . Water is poured into it at a constant rate of 5 cubic meter per minute. Then the rate (in m/min), at which

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

If ∫ dx = f (x) + C , where C is a constant of integration, then f(x) is equal to :-

The value of is equal to:

The tangent to the curve, y = passingthrough the point (1,e) also passes through thepoint :

If and are three consecutive terms of a non-constant G.P. such that the equations and have a common root, then is equal to

Let be a differentiable function Satisfying Then is equal to

If a point R(4, y, z) lies on the line segment joining the points and , then the distance of R from the origin is:

If the area (in sq.units) of the region is , then a – b is equal to

The total number matrices for which is

If then the derivative of of is

If is continuous at , then the ordered pair (p, q) is equal to:

[9-Jan-2019 Shift 1]

Let A = Then the sum of the elements in A is : [9-Jan-2019 Shift 1]

Let A={x ∊ R : x is not a positive integer} Define a function f : A → R as f (x) = then f is

The mean and the variance of five observation are 4 and 5.20, respectively. If three of the observations are 3, 4 and 4; then then absolute value of the difference of the other two observations, is :

If (α ∊ R) is a purely imaginary numberand |z| = 2, then a value of α is :

If then is equal to:

If = (a + b + c) , x ≠ 0 and a + b + c ≠ 0, then x is equal to :-

Let f : R → R be a function defined as : f (x) = Then, f is : [9-Jan-2019 Shift 1]

An ordered pair (α,β) for which the system of linear equations (1+α)x + βy+z = 2 αx+(1+β)y+z = 3 αx+βy+2z = 2 has a unique solution is

is equal to: (Where c is a constant of integration)

If A = ; then for all θ ∊ , det (A) lies in the interval :

If , where [x] denotes the greatest integer function, then:

A data consists of n observations: , ... , . If = 9n and = 5n , then the standard deviation of this data is :

If then is equal to

Let with and it satisfies for some natural number n. Then

The mean and variance of seven observations are 8 and 16, respectively. If 5 of the observations are 2,4,10,12,14, then the product of the remaining two observations is:

5 students of a class have an average height 150 cm and variance 18 . A new student, whose height is 156 cm, joined them. The variance (in ) of the height of these six students is : [9-Jan-2019 Shift

If then a possible choice of is:

The vertices B and C of a lie on line, such that BC=5 units, Then the area (in sq.units) of this triangle, given that the point A(1, -1,2)

Let α and β be two roots of the equation + 2x + 2 = 0 , then is equal to : [9-Jan-2019 Shift 1]

Let For any define If S = [0,4], then which one of the following statements is not true?

Consider three boxes, each containing 10 balls labelled 1,2,....,10. Suppose one ball is randomly drawn from each of the boxes. Denote by , the label of the ball drawn from the ith box, (i = 1, 2, 3).

If A is a symmetric matrix and B is a skew symmetric matrix such that , then AB is equal to:

If the data is such that the mean of first four of these is 11, the mean of the remaining six is 16 and the sum of squares of all of these is 2,000; then the standard deviation of this data is:

In a random experiment, a fair die is rolled untiltwo fours are obtained in succession. Theprobability that the experiment will end in thefifth throw of the die is equal to :

If = 1 - , (k > 0) , then the value of k is :

The number of 6 digits numbers that can be formed using the digits 0,1,2,5,7 and 9 which are divisible by 11 and no digit is repeated, is:

Let A,B and C be sets such that . Then which of the following statements is not true ?

If both the roots of the quadratic equation – mx + 4 = 0 are real and distinct and they lie in the interval [1,5], then m lies in the interval:

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

Consider the differential equation, . If value of y is 1 when x = 1, then the value of x for which y = 2, is:

A value of , for which , is

Let be fixed. If the integral where c is a constant of integration, then the functions A(x) and B(x) are respectively

If the tangent to the at a point on it parallel to the line then:

Let (x) = for k = 1 , 2 , 3 , ... Then for all x ∊ R, the value of (x) - (x) is equal to :

If x = (sin10) and y = (cos10), theny–x is equal to:

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

If m is the minimum value of k for which the function is increasing in the interval [0, 3] and M is the maximum value of f in [0, 3] when k = m, then the ordered pair (m, M) is equal to:

A spherical iron ball of radius 10cm is coated with a layer of ice of uniform thickness that melts a rate of 50cm3 /min When the thickness of the ice 5cm, then the rate at which the thickness (in cm/m

Let f (x) = - , x ∊ R, where a, b and d are non-zero real constants.Then :-

Let S be the set of all triangles in the xy-plane, each having one vertex at the origin and the other two vertices lie on coordinate axes with integral coordinates. If each triangle in S has area 50sq

Let P be the plane, which contains the line of intersection of the planes, and and it is perpendicular to the plane. Then the distance of the point (0,0,256) from P is equal to

Let a random variable X have a binomial distribution with mean 8 and variance If , then k is equal to:

The height of a right circular cylinder of maximum volume inscribed in a sphere of radius 3 is :

The value of the integral dx (where [x] denotes the greatest integer less than or equal to x) :

The sum of the real roots of the equation is equal to

If A = Then A is-

In a class of 60 students, 40 opted for NCC, 30opted for NSS and 20 opted for both NCC andNSS. If one of these students is selected atrandom, then the probability that the studentselected has opted ne

The derivative of with respect to where is

If the ordered pair at is equal to:

If λ be the ratio of the roots of the quadratic equation in x, + m (m - 4) x + 2 = 0, then the least value of m for which λ + = 1 , is :

Let be a twice differentiable function such that , for all If , then ϕ is:

The equation of a plane containing the line of intersection of the planes and and passing through the point is:

If , then m.n is equal to:

For (the set of natural numbers) . the integral is equal to : (where c is a constant of integration) [9-Jan-2019 Shift 1]

Let be a real number of which the system of linear equations , has infinitely many solutions .Then is a root of the quadratic equation:

If the function f given by f(x) = –3(a – 2) +3ax + 7, for some a ∊ R is increasing in (0, 1] anddecreasing in [1, 5), then a root of the equation, = 0 (x ≠ 1) is :

The solution of the differential equation with , is:

All the pairs (x,y) that satisfy the inequality also satisfy the equation:

If here C is a constant ofintegration, then

The integral xdx is equal to :

A value of such that is

If where then for all is equal to :

is equal to :

Let y = y(x) be the solution of the differential equation, such that If then the value of ‘a’ is:

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

If y(x) is the solution of the differential equation + y = , x > 0 where y (1) = , then :

A plane passing through the points and and making an angle with the plane , also passes through the point:

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

Let be a root of the quadratic equation, + x + 1 = 0. If z = 3 + , then arg z is equal to:

Let and be two complex numbers satisfying | | = 9 and | –3–4i| = 4 . Then the minimum value of | | is :

If the length of perpendicular from point (where to the line is is 3 , 2 then value of is

The vector equation of the plane through the line of intersection of the planes and which is perpendicular to the plane is :

The set of all values of λ for which the system of linear equations. x – 2y – 2z = λx x + 2y + z = λy –x – y = λz has a non-trivial solution.

If m is choosen in the quadratic equation such that the sum of its roots is greatest, then the absolute difference of the cubes of its roots is

If is a differentiable function and , then is

The equation , represents:

If f (t) dt = f (t) dt , then f' (1/2) is :

A 27 mW laser beam has a cross-sectional area of 10 . The magnitude of the maximum electric field in this electromagnetic wave is given by [Given permittivity of space SI units, Speed of light m/s]:-

A light wave is incident normally on a glass slabof refractive index 1.5. If 4% of light getsreflected and the amplitude of the electric fieldof the incident light is 30V/m, then theamplitude of the e

Two masses m and are connected at the two ends of a massless rigid rod of length . The rod is suspended by a thin wire of torsional constant k at the centre of mass of the rod-mass system(see figure).

The elastic limit of brass is .what should be the minimum diameter of a brass rod if it is to support a 400 N Load without exceeding its elastic limit?

Water from a tap emerges vertically downwards with an initial speed of .the cross-sectional area of the tap is .Assume that the pressure is constant throughout the stream of water and that the flow is

A 200Ω resistor has a certain color code. If one replaces the red color by green in the code, the new resistance will be :

A smooth wire of the length is bent into a circle and kept in a vertical plane. A bead can slide smoothly on the wire. When the circle is rotating with angular speed ω about the vertical diameter AB ,

An electron, moving along the -axis with an initial energy of , enters a region of magnetic field at S (See figure). The field extends between and . The electron is detected at the point Q on a screen

A magnet of total magnetic moment is placed in a time varying magnetic field, where Tesla and rad/s. The work done for reversing the direction of the magnetic moment at second,

A stationary source emits sound waves of frequency 500Hz. Two observers moving along a line passing through the source detect sound to be of frequencies 480 Hz ad 530Hz. Their respective speeds are,in

Four point charges –q, +q, +q and –q are placed on y-axis at y = 2d, y = -d, y = +d and y = +2d, respectively. The magnitude of the electric field E at a point on the x –axis at x = D, with D>>d, will

The specific heats, and of a gas of diatomic molecules, A, are given (in units of ) by 29 and 22, respectively. Another gas of diatomic molecules, B, has the corresponding values 30 and 21 If they are

In a Young’s double slit experiment, the ratio of the slit’s width is 4:1 The ratio of the intensity of maxima to minima, close to the central fringe on the screen, will be:

In the figure shown, after the switch 'S' is turnedfrom position 'A' to position 'B', the energydissipated in the circuit in terms of capacitance'C' and total charge 'Q' is:

The gas mixture constists of 3 moles of oxygen and 5 moles of argon at temperature T. Considering only translational and rotational modes, the total inernal energy of the system is:

A circular disc of radius b has a hole of radius a at its centre (see figure). If the mass per unit area of the disc varies as then the radius of gyration of the disc about its axis passing through th

The ratio of mass densities of nuclei of is close to:

A particle is moving along a circular path with a constant speed of 10 ms–1. What is the magnitude of the change is velocity of the particle, when it moves through an angle of 60° around the centre of

The following bodies are made to roll up (without slipping) the same inclined plane from a horizontal plane : (i) a ring of radius R, (ii) a solid cylinder of radius and (iii) a solid sphere of radius

A sample of radioactive material A, that has an activity of 10 mCi(1 Ci = 3.7 × decays/s), has twice the number of nuclei as another sample of a different radioactive maternal B which has an activity

A particle of mass ‘m’ is moving with speed ‘ ’and collides with a mass ‘2m’ moving with speed ‘ ’ in the same direction. After collision, the first mass is stopped completely while the second one spl

Two sources of sound and produce sound waves of same frequency 660 Hz. A listener is moving from source towards v with a constant speed u m/s and he hears 10 beats/s. The velocity of sound is 330 m/s.

Figure shows a DC voltage regulator circuit, with a zener diode down voltage = 6V . If the unregulated input voltage varies between 10V to 16V , then what is the maximum zener current?

In the circuit , the potential difference betweenA and B is :

As shown in the figure, two infinitely long, identical wires are bent by 90° and placed in such a way that the segments LP and QM are along the x-axis, while segments PS and QN are parallel to the y-a

A cylinder of radius R is surrounded by a cylindrical shell of inner radius R and outer radius 2R. The thermal conductivity of the material of the inner cylinder is and that of the outer cylinder is .

The ratio of the weight of a body on the Earth’s surface to that on the surface of a planet is 9 : 4 , the mass of the planet is th of that of the Earth. If ‘R’ is the radius of the Earth, what is the

Two electric bulbs, rated at (25 W, 220 V) and (100 W, 220 V), are connected in series across a 220 V voltage source. If the 25 W and 100 W bulbs draw powers and respectively, then:

The logic gate equivalent to the given logic

A mixture of 2 moles of helium gas (atomic mass= 4 u), and 1 mole of argon gas (atomic mass= 40 u) is kept at 300 K in a container. The ratio of their rms speeds , is close to [9-Jan-2019 Shift 1]

A potentiometer wire AB having length L and resistance 12 r is joined to a cell D of emf ε and internal resistance r. A cell C having emf ε/2 and internal resistance 3r is connected. The length AJ at

A current loop, having two circular arcs joinedby two radial lines is shown in the figure. Itcarries a current of 10 A. The magnetic field atpoint O will be close to : [9-Jan-2019 Shift 1]

When the switch S, in the circuit shown, isclosed, then the value of current i will be : [9-Jan-2019 Shift 1]

Determine the electric dipole moment of thesystem of three charges, placed on the verticesof an equilateral triangle, as shown in thefigure:

A concave mirror has radius of curvature of 40 cm. It is at the bottom of a glass that has water filled up to 5 cm (see figure). It a small particle is floating on the surface of water, its image as s

The electron in a hydrogen atom first jumps from the third excited state to the first excited state. The ratio of the respective wavelengths, of the photons emitted in

The transfer characteristic curve of a transistor, having input and output resistance and respectively, is shown in the figure. The Voltage and Power gain, are respectively.

A wire of resistance R is bent to form a square ABCD as shown in the figure. The effective resistance between E and C is: (E is mid-point of arm CD)

Two identical spherical balls of mass M and radius R each are stuck on two ends of a rod of length 2R and mass M (see figure). The moment of inertia of the system about the axis passing perpendicularl

Water flows into a large tank with flat bottom at the rate of . Water is also leaking out of a hole of area 1 at its bottom. If the height of the water in the tank remains steady, then this height is:

The value of numerical aperture of the objective lens of a microscope is 1.25. If light of wavelength 5000 is used, the minimum separation between two points, to be seen as distinct, will be.

Figure shows charge ( ) versus voltage ( ) graph for series and parallel combination of two given capacitors . The capacitances are :

The stream of a river is flowing with a speed of 2 km/h. A swimmer can swim at a speed of 4 km/h. What should be the direction of the swimmer with respect to the flow of the river to cross the river s

To mop-clean a floor, a cleaning machinepresses a circular mop of radius R verticallydown with a total force F and rotates it with aconstant angular speed about its axis. If theforce F is distributed

Let the moment of inertia of a hollow cylinder of length 30 cm (inner radius 10 cm and outer radius 20 cm), about its axis be I. The radius of a thin cylinder of the same mass such that its moment of

Two wires A&B are carrying currents and as shown in the figure . the separation between them is . A third wire C carrying a current is to be kept parallel to them at a distance from such that the net

Find the magnetic field at point P due to a straight line segment AB of length 6 cm carring a current of 5 A.(See figure)

In a photoelectric experiment, the wavelength of the light incident on a metal is changed from 300 nm to 400 nm. The decrease in the stopping potential is close to :

Ship A is sailing towards north-east with velocity km/hr where points east and north. Ship B is at a distance of 80 km east and 150 km north of Ship A and is sailing towards west at 10 km/hr. A will b

The self induced emf of a coil is 25 volts. When the current in it is changed at uniform rate from 10 A to 25 A in 1s, the change in the energy of the inductance is :

Two radioactive substances A and B have decay constants respectively. At t=0, a sample has the same number of the two nuclei. The time taken for the ratio of the number of nuclei to become will be:

A parallel plate capacitor is of area 6 and a separation 3 mm. The gap is filled with three dielectric materials of equal thickness (see figure) with dielectric constants , = 10, = 12 and = 14. The di

The force of interaction between two atoms is given by F = αβ exp ; where x is the distance, k is the Boltzmann constant and T is temperature and α and β are two constants. The dimension of β is :[11

The graph shows how the magnification produced by a thin lens varies with image distance .what is the focal length of the lens used?]

A particle moves in one dimension from rest under the influence of a force that varies with the distance travelled by the particle as shown in the figure. The kinetic energy of the particle after it h

A thin strip 10 cm long is on a U shaped wire of negligible resistance and it is connected to a spring of spring constant 0.5 Nm (see figure). The assembly is kept in a uniform magnetic field of 0.1 T

A string of length 1 m and mass 5 g is fixed at both ends. The tension in the string is 8.0 N. The siring is set into vibration using an external vibrator of frequency 100 Hz. The separation between s

Two particles are projected from the same point with the same speed u such that they have the same range R, but different maximum heights, and which of the following is correct?[12 Apr 2019 Shift 2]

If the angular momentum of a planet of massm, moving around the Sun in a circular orbitis L, about the center of the Sun, its arealvelocity is : [9-Jan-2019 Shift 1]

Two equal resistance when connected in series to a battery, consume electric power of 60 W. If these resistances are now connected in parallel combination to the same battery, the electric power consu

Condiser the nuclear fission → Given that the binding energy/nucleon of , and are, respectively, 8.03 MeV, 7.07 MeV and 7.86 MeV, identify the correct statement :

A small speaker delivers 2 W of audio output. At what distance from the speaker will one detect 120dB in intensity sound? [Given reference intensity of sound as ]

In a meter bridge, the wire of length 1 m has a non-uniform cross-section such that, the variation of its resistance R with length l is α . Two equal resistances are connected as shown in the figure.

A proton and an a-particle (with their masses in the ratio of 1 : 4 and charges in the ratio of 1 : 2) are accelerated from rest through a potential difference V. If a uniform magnetic field (B) is se

Seven capacitors, each of capacitance 2 µF, areto be connected in a configuration to obtain aneffective capacitance of µF. Which ofthe combinations, shown in figures below, willachieve the desired val

A plane electromagnetic wave travels in free space along the x-direction. The electric field component of the wave at a particular point of space and time is along y-direction. Its corresponding magne

A particle of mass 20 g is released with an initial velocity 5 m/s along the curve from the point A,as shown in the figure. The point A is at height h from point B. The particle slides along the frict

Two stars of masses 3 × kg each, and at distance 2 × m rotate in a plane about their common centre of mass O. A meteorite passes through O moving perpendicular to the star's rotation plane. In order t

A string 2.0 m long and fixed at its ends is driven by a 240 Hz vibrator. The string vibrates in its third harmonic mode. The speed of the wave and its fundamental frequency is :

Two moles of helium gas is mixed with three moles of hydrogen molecules (taken to be rigid). What is the molar specific heat of mixture at constant volume? (R = 8.3 J/mol K)

A rod of length 50cm is pivoted at one end. It is raised such that if makes an angle of 30° from the horizontal as shown and released from rest. Its angular speed when it passes through the horizontal

A person standing on an open ground hears thesound of a jet aeroplane, coming from north atan angle 60° with ground level. But he findsthe aeroplane right vertically above his position.If υ is the spe

Two materials having coefficients of thermal conductivity ‘3K’ and ‘K’ and thickness ‘d’ and ‘3d’, respectively, are joined to forma slab as shown in the figure. The temperatures of the outer surfaces

Consider a Young's double slit experiment as shown in figure. What should be the slit separation in terms of wavelength such that the first minima occurs directly in front of the slit ( )?

A satellite of mass M is in a circular orbit ofradius R about the centre of the earth. Ameteorite of the same mass, falling towards theearth, collides with the satellite completelyinelastically. The s

A galvanometer of resistance 100 has 50 divisions on its scale and has sensitivity of 20 / division. It is to be converted to a voltmeter with three ranges, of 0-2V, 0- 10 V and 0-20V. The appropriate

A plano-convex lens (focal length , refractive index , radius of curvature R) fits exactly into a plano-concave lens (focal length , refractive index , radius of curvature R). Their plane surfaces are

A particle starts from the origin at time t = 0 andmoves along the positive x-axis. The graph ofvelocity with respect to time is shown in figure. Whatis the position of the particle at time t = 5s ? [

A particle undergoing simple harmonic motionhas time dependent displacement given by x (t) = A sin . The ratio of kinetic to potential energy of this particle at t = 210 s will be :

Charges –q and +q located at A and B, respectively, constitute an electric dipole. Distance AB = 2a, O is the mid point of the dipole and OP is perpendicular to AB. A charge Q is placed at P where OP

A very long solenoid of radius is carrying current , as a function of time ( ). Counter clockwise current is taken to be positive. A circular conducting coil of radius is placed in the equatorial plan

Two identical beakers A and B contain equal volumes of two different liquids at 60°C each and left to cool down. Liquid in A has density of and specific heat of while liquid in B has density of and sp

In a Frank-Hertz experiment, an electron of energy5.6 eV passes through mercury vapour andemerges with an energy 0.7 eV. The minimumwavelength of photons emitted by mercury atomsis close to :-

A block of mass m, lying on a smoothhorizontal surface, is attached to a spring (ofnegligible mass) of spring constant k. The otherend of the spring is fixed, as shown in thefigure. The block is inita

An ideal gas occupies a volume of 2m3 at a pressure of 3 × 106 Pa. The energy of the gas is:

A metal plate of area 1 × is illuminated by a radiation of intensity .The work function of the metal is 5eV. The energy of the incident photons is 10 eV and only 10% of it produces photo electrons. Th

The mass and the diameter of a planet are threetimes the respective values for the Earth. Theperiod of oscillation of a simple pendulum onthe Earth is 2s. The period of oscillation of thesame pendulum

A resonance tube is old and has jagged end. It is still used in the laboratory to determine velocity of sound in air. A tuning fork of frequency 512 Hz produces first resonance when the tube is filled

A rigid square loop of side ‘a’ and carrying current is lying on a horizontal surface near a long current carrying wire in the same plane as shown in figure. The net force on the loop due to the wire

The reverse breakdown voltage of a Zener diode is 5.6 V in the given circuit. The current through the Zener is:

Three Carnot engines operate in series between a heat source at a temperature and a heat sink at temperature (see figure). There are two other reservoirs at temperature , and , as shown, with > > > .

The magnetic field associated with a light wave is given, at the origin, by . If this light falls on a silver plate having a work function of 4.7 eV, what will be the maximum kinetic energy of the pho

A coil of self inductance 10mH and resistance is connected through a switch to a battery of internal resistance .After the switch is closed, the time taken for the current to attain 80% of the saturat

There is a uniform spherically symmetricsurface charge density at a distance R0 from theorigin. The charge distribution is initially at restand starts expanding because of mutualrepulsion. The figure

For the circuit shown below, the current throughthe Zener diode is :

An alpha-particle of mass m suffers 1-dimensional elastic coolision with a nucleus at rest of unknown mass. It is scattered directly backwards losing, 64% of its initial kinetic energy. The mass of th

Using a nuclear counter the count rate of emitted particles from a radioactive source is measured. At t = 0 it was 1600 counts per second and t = 8 seconds it was 100 counts per second. The count rate

A wooden block floating in a bucket of water has of its volume submerged. When certain amount of an oil is poured into the bucket, it is found that the block is just under the oil surface with half of

Four particles A, B, C and D with masses are at the corners of a square. They have accelerations of equal magnitude with directions as shown. The acceleration of the centre of mass of the particles is

In a Young's double slit experiment, the slits are placed 0.320 mm apart. Light of wavelength λ = 500 nm is incident on the slits. The total number of bright fringes that are observed in the angular r

When heat Q is supplied to a diatomic gas of rigid molecules, at constant volume its temperature increases by .The heat required to produce the same change in temperature, at a constant pressure is:

A thin smooth rod of length L and mass M is rotating freely with angular speed about an axis perpendicular to the rod and passing through its centre. Two beads of mass m and negligible size are at the

Let = , = and be a vector such that = and = 4 , then is equal to : [9-Jan-2019 Shift 1]

A solid conducting sphere, having a charge Q, is surrounded by an uncharged conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the oute

A uniform rod of length l is being rotated in a horizontal plane with a constant angular speed about an axis passing through one of its ends. If the tension generated in the rod due to rotation is T(x

A plane is inclined at an angle with respect to the horizontal. A particle is projected with a speed u=2m/s from the base of the plane, making an angle with respect to the plane as shown in the figure

The diameter and height of a cylinder are measured by a meter scale to be 12.6 ± 0.1 cm and 34.2 ± 0.1 cm, respectively. What will be the value of its volume in appropriate significant figures ?[10 Ja

The least count of the main scale of a screw gauge is 1 mm. The minimum number of divisions on its circular scale required to measure 5µm diameter of wire is :[12 Jan 2019 Shift 1]

Half lives of two radio active nuclei A and B are 10 minutes and 20 minutes, respectively. If , initially a sample has equal number of nuclei, then after 60 minutes, the ratio of decayed, the ratio of

A force acts on a 2 kg object so that its position is given as a function of time as x = + 5. What is the work done by this force in first 5 seconds ?

A concave mirror for face viewing has focal length of 0.4 m. The distance at which you hold the mirror from your face in order to see your image upright with a magnification of 5 is:

The bob of a simple pendulum has mass 2 g and a charge of . It is at rest in a uniform horizontal electric field of intensity 2000 V/ m. At equilibrium, the angle that the pendulum makes with the vert

A galvanometer, whose resistance is 50 ohm, has 25 divisions in it. When a current of 4 × A passes through it, its needle (pointer) deflects by one division. To use this galvanometer as a voltmeter of

A person of mass M is, sitting on a swing of length L and swinging with an angular amplitude .If the person stands up when the swing passes through its lowest point, the work done by him, assuming tha

The electric field in a region is given by , where E is in and x is in metres. The values of constants are SI unit and SI unit. If the potential at is and that at is , then is:

A 15 g mass of nitrogen gas is enclosed in a vessel at a temperature 27°C. Amount of heat transferred to the gas, so that rms velocity of molecules is doubled, is about : [Take R = 8.3 J/ K mole]

In a double slit experiment, when a thin film of thickness t having refractive index is introduced in front of one of the slits, the maximum at the centre of the fringe pattern shifts by one fringe wi

A soap bubble, blown by a mechanical pump at themough of a tube, increases in volume, with time,at a constant rate. The graph that correctly depictsthe time dependence of pressure inside the bubbleis

Water from a pipe is coming at a rate of 100 liters per minute. If the radius of the pipe is 5 cm, the Reynolds number for the flow is of the order of : (density of water =1000 kg/ , coefficient of vi

Four identical particles of mass M are located at the corners of a square of side ‘a’. What should be their speed if each of them revolves under the influence of others’ gravitational field in a circu

In a car race on straight road, car A takes a time t less than car B at the finish and passes finishing point with a speed 'v' more than that of car B. Both the cars start from rest and travel with co

An object is at a distacen of 20 m from a convex lens of focal length 0.3 m. The lens forms an image of the object. If the object moves away from the lens at a speed of 5 m/s, the speed and direction

Space between two concentric conducting spheres of radii a and b (b>a) is filled with a medium of resistivity .The resistance between the two spheres will be:

Voltage rating of a parallel plate capacitor is 500 V. Its dielectric can withstand a maximum electric field of V/ m. The plate area is . What is the dielectric constant if the capacitance is 15 pF ?

A 2mW laser operates at a wavelength of 500nm.The number of photons that will be emitted per second is:{Given plank’s constant ,speed of light }

The Wheatstone bridge shown in Fig. here, gets balanced when the carbon resistor used as has the colour code ( Orange, Red, Brown). The resistors and are 80 Ω and 40 Ω respectively. Assuming that the

At a given instant, say t = 0, two radio active substances A and B have equal activities. The ratio of their activities after time t itself decays with time t as . [f the half-life of A is , the half-

Two very long, straight, and insulated wires are kept at 90° angle from each other in xy–plane as shown in the figure. These wires carry currents of equal magnitude I, whose directions are shown in th

a moving Coil galvanometer allows a full scale current A.A series resistance of 2 MΩ is required to convert the above galvanometer into a voltmeter of range 0-5V. Therefore the value of shunt resistan

A closed organ pipe has a fundamental frequency of 1.5 kHz. The number of overtones that can be distinctly heard by a person with this organ pipe will be : (Assume that the highest frequency a person

Diameter of the objective lens of a telescope is 250 cm. For light of wavelength 600 nm. Coming from a distant object, the limit of resolution of the telescope is close to:

Charge is distributed within a sphere of radius Rwith a volume charge density ρ (r) = , where A and a are constants. If Q is the total chargeof this charge distribution, the radius R is :

A solid sphere, of radius R acquires a terminal velocity when falling (due t gravity) through a viscous fluid having a coefficient of viscosity . The sphere is broken into 27 identical solid spheres.

A ball is thrown upward with an initial velocity from the surface of the earth. the motion of the ball is affected by a drag force equal to ( where m is mass of the ball V is its instaneous velocity a

In the given circuit the current through ZenerDiode is close to :

A particle of mass m moves in a circular orbitin a central potential field U(r) = . If Bohr'squantization conditions are applied, radii ofpossible orbitals and energy levels vary withquantum number n

A body is projected at t = 0 with a velocity 10 at an angle of 60° with the horizontal. The radius of curvature of its trajectory at t = 1s is R. Neglecting air resistance and taking acceleration due

A thin ring of 10 cm radius carries a uniformly distributed charge. The ring rotates at a constant angular speed of 40 about its axis, perpendicular to its plane. If the magnetic field at its centre i

A simple harmonic motion is represented by: y = 5(sin3πt+ cos3πt) cm The amplitude and time period of the motion are:

A point source of light, is placed at adistance in front of the centre of plane mirrorof width which is hanging vertically on a wall.A man walks in front of the mirror along a lineparallel to the mirr

A current of 5A passes through a copper conductor (resistivity= Ωm) radius of cross section 5mm.Find the mobility of the charges if their drift velocity

The time dependence of the position of a particle of mass m=2 is given by . Its angular momentum, with respect to the origin, at time t=2 is:

Radiation coming from transitions n =2 to n=1 of hydrogen atoms fall on He ions in n=1 and n=2 states. The possible transition of helium ions as they absorb energy from the radiation is:

The magnitude of the magnetic field at the centre of an equilateral triangular loop of side 1 m which is carrying a current of 10A is: (take )

A long cylindrical vessel is half filled with a liquid. When the vessel is rotated about its own vertical axis, the liquid rises up near the wall. If the radius of vessel is 5 cm and its rotational sp

A particle executes simple harmonic motion withan amplitude of 5 cm. When the particle is at 4 cmfrom the mean position, the magnitude of itsvelocity in SI units is equal to that of its acceleration.T

A He ion is in its first excited state. Its ionization energy is:

A thermometer graduated according to a linear scale reads a value x0 when in contact with boiling water, and when in contact with ice. What is the temperature of an object in 0 °C, if this thermometer

In the circuit shown, find C if the effectivecapacitance of the whole circuit is to be 0.5 µF.All values in the circuit are in µF.

Let = , = and = be three vectors such that theprojection vector of on is . If is perpendicular to , then is equal to :

A rod of mass 'M' and length '2L' is suspended at its middle by a wire. It exhibits torsional oscillations; If two masses each of 'm' are attached at distance 'L/2' from its centre on both sides, it r

An equilateral triangle ABC is cut from a thin solid sheet of wood. (see figure) D, E and F are the mid-points of its sides as shown and G is the centre of the triangle. The moment of inertia of the t

Let a total charges 2 Q be distributed in a sphere of radius R, with the charge density given by , where r is the distance from the centre. Two charges A and B, of each are placed on diametrically opp

An electric field of 1000 V/m is applied to an electric dipole at angle of 45°. The value of electric dipole moment is C.m. What is the potential energy of the electric dipole ?

The magnitude of torque on a particle of mass1kg is 2.5 Nm about the origin. If the force actingon it is 1 N, and the distance of the particle fromthe origin is 5m, the angle between the force andthe

In the given circuit the internal resistance of the18 V cell is negligible. If = 400 Ω, = 100 Ωand = 500 Ω and the reading of an ideal voltmeteracross is 5V, then the value will be :

A tuning fork of frequency 480 Hz is used in an experiment for measuring speed of sound in air by resonance tube method. Resonance is observed to occur at two successive length of the air column, and

Two cars A and B are moving away from each other in opposite directions. Both the cars are moving with a speed of with respect to the ground. If an observer in car A detects a frequency 2000 Hz of the

Young’s moduli of two wires A and B are in the ratio 7:4. Wire A is 2m long and has radius R. Wire B is 1.5 m long and has radius 2 mm. If the two wires stretch by the same length for a given load, th

A solid sphere and solid cylinder of identical radii approach an incline with the same linear velocity (see figure). Both roll without slipping all throughout. The two climb maximum heights and on the

Let and be the vertices of a triangle and M is the midpoint of AC. If G divides BM in the ratio, 2 : 1, then (O being origin) is equal to :

Formation of real image using a biconvex lens isshown below : If the whole set up is immersed in water withoutdisturbing the object and the screen position, whatwill one observe on the screen ?

The figure shows a square loop L of side 5 cm which is connected to a network of resistances. The whole setup is moving towards right with a constant speed of 1cm . At some instant, a part of L is in

When M1 gram of ice at (specific heat = 0.5 cal is added to is added to of water at 50°C, finally no ice is left and the water is at 0°C. The value of latent heat of ice, in is:

An ideal battery of 4 V and resistance R are connected in series in the primary circuit of a potentiometer of length 1 m and resistance 5Ω. The value of R, to give a potential difference of 5 mV acros

Three particles of masses and are placed at the vertices of an equilateral triangle of side 1m (as shown in the figure). The co-ordinates of the centre of mass will be:

In the circuit shown, a four–wire potentiometer is made of a 400 cm long wire, which extends between A and B. The resistance per unit length of the potentiometer wire is r= 0.01 Ω/cm If an ideal voltm

Two particles move at right angle to each other. Their de Broglie wavelengths are and respectively. The particles suffer perfectly inelastic collision. The de Broglie wavelength , of the final particl

A simple pendulum, made of a string of length l and a bob of mass m, is released from a small angle . It strikes a block of mass M, kept on a horizontal surface at its lowest point of oscillations, el

Half mole of an ideal monoatomic gas is heated at constant pressure of 1atm from 20 °C to 90°C. Work done by gas is close to : ( Gas constant R = 8.31 J /mol.K)

In a double-slit experiment, green light (5303 Å) falls on a double slit having a separation of 19.44 m and a width of 4.05 µm. The number of bright fringes between the first and the second diffracti

The energy associated with electric field is ( )and with magnetic field is ( ) for anelectromagnetic wave in free space. Then :

A rigid massless rod of length 3l has twomasses attached at each end as shown in thefigure. The rod is pivoted at point P on thehorizontal axis (see figure). When released frominitial horizontal posit

The stopping potential (in volt) as a function of frequency (v) for a sodium emitter, is shown in the figure. The work function of sodium, from the data plotted in the figure, will be. (Given. Planck’

A parallel plate capacitor has 1µF capacitance. One of its two plates is given +2µC charge and the other plate, +4µC charge. The potential difference developed across the capacitor is:

The electric field of a plane polarizedelectromagnetic wave in free space at timet = 0 is given by an expression (x , y) = cos [(6x + 8z)] The magnetic field (x , z , t) is given by : (cis the velocit

A circular coil having N turns and radius r carries a current I. It is held in the XZ plane in a magnetic field . The torque on the coil due to the magnetic field is:

In an interference experiment the ratio of amplitudes of coherent waves is . The ratio of maximum and minimum intensities of fringes will be:

At some location on earth the horizontal component of earth's magnetic field is 18 × T. At this location, magnetic needle of length 0.12 m and pole strength 1.8 Am is suspended from its mid-point usin

Equation of travelling wave on a stretched string of linear density 5 g/m is y = 0.03 sin(450 t – 9x) where distance and time are measured is SI units. The tension in the string is :

In the above circuit, C = µF , = 20 Ω, L = H and = 10 Ω. Current in L - path is and in C - path it is . The voltage of A.Csource is given by V = 200 sin (100t) volts. The phase difference between and

A homogeneous solid cylindrical roller of radius R and mass M is pulled on a cricket pitch by a horizontal force. Assuming rolling with out slipping, angular acceleration of the cylinder is:

The displacement of a damped harmonic oscillator is given by . Here t it is in seconds.The time taken for its amplitude of vibration to drop to half of its initial value is close to:

One mole of an ideal gas passes through a process where pressure and volume obey the relation / .here and are constants, calculate the change in the temperature of the gas if its volume changes from t

A transformer consisting of 300 turns in the primary and 150 turns in the secondary gives output power of 2.2kw. if the current in the secondary coil is 10A, then the input voltage and current in the

Taking the wavelength of first Balmer line in hydrogen spectrum (n = 3 to n = 2) as 660 nm, the wavelength of the 2nd Balmer line (n = 4 to n = 2) will be:

The sum of the distinct real values of m, for which the vectors, , , are co-planer, is :

A square loop is carrying a steady current I and the magnitude of its magnetic dipole moment is m. If this square loop is changed to a circular loop and it carries the same current, the magnitude of t

One kg of water at , is heated in an electric kettle whose heating element has a mean (temperature averaged) resistance of . The rms voltage in the mains is . Ignoring heat loss from the kettle, time

In SI units, the dimensions of is[8 Apr 2019 Shift 1]

A simple pendulum of length is placed between the plates of a parallel plate capacitor having electric field , as shown in figure. Its bob has mass and change , The time period of the pendulum is give

A nucleus A, with a finite de–broglie wavelength , undergoes spontaneous fission into two nuclei B and C of equal mass. B flies in the same direction as that of A, while C flies in the opposite direct

A mass of 10 kg is suspended vertically by a rope from the roof. When a horizontal force is applied on the rope at some point, the rope deviated at an angle of 45° at the roof point. If the suspended

Let = (λ - 2) and = (4λ - 2) be two given vectors where vectors and are non-collinear. The value of λ for which vectors and are collinear, is :

In figure, the optical fiber is l=2 m long and has a diameter of . If a ray of light is incident on one end of the fiber at angle , the number of reflections it makes before emerging from the other en

Let and be three unit vectors, out of which vectors and are non-parallel. If α and β are the angles which vector makes with vectors and respectively and = , then |α- β| is equal to :

In an electron microscope, the resolution that can be achieved is of the order of the wavelength of electrons used. To resolve a width of 7.5 × 10−1210^{-12}10−12 m, the minimum electron energy requir

The trajectory of a projectile near the surface of the earth is given as . If it were launched at an angle with speed then

50 W/m2^{2}2 energy density of sunlight is normally incident on the surface of a solar panel. Some part of incident energy(25%) is reflected from the surface and the rest is absorbed. The force exerte

An upright object is placed at a distance of 40 cm in front of a convergent lens of focal length 20 cm. A convergent mirror of focal length 10 cm is placed at a distance of 60 cm on the other side of

Determine the charge on the capacitor in the following circuit:

A rectangular solid box of length 0.3 m is held horizontally, with one of its sides on the edge of a platform of height 5 m. When released, it slips off the table in a very short time s, remaining ess

Two radioactive materials A and B have decay constants10λ and λ , respectively . If initially they have the same number of nuclei, then the ratio of the number of nuclei, then the ratio of the number

Two vectors and have equal magnitudes.The magnitude of 'n' times themagnitude of . The angle between and is :

A system of three charges are placed as shown in the figure: If , the potential energy of the system is best given by:

A test particle is moving in a circular orbit in the gravitational field produced by a mass density . Identify the correct relation between the radius R of the particle’s orbit and its period T:

Calculate the limit of resolution of a telescope objective having a diameter of 200cm, if it has to detect Light of wavelmgth 500 nm coming from a star.

In a process, temperature and volume of one mole of an ideal monoatomic gas are varied according to the relation VT = K, where K is a constant. In this process the temperature of the gas is incresed b

Two guns A and B can fire bullets at speeds 1 km/s and 2 km/s respectively. From a point on a horizontal ground, they are fired in all possible directions. The ratio of maximum areas covered by the bu

For a given gas at 1 atm pressure, rms speed of the molecules is 200 m/s at 127ºC. At 2 atm pressure and at 227ºC, the rms speed of the molecules will be:

Let and be the position vectors of the points A, B and Cwith respect to the origin O. If the distance of Cfrom the bisector of the acute angle between OAand OB is , then the sum of all possible values

A thin disc of mass M and radius R has mass per unit area where r is the distance from its center . Its moment of inertia about an axis going through its centre of mass and perpendicular to its plane

The pitch and the number of divisions, on the circular scale, for a given screw gauge are 0.5 mm and 100 respectively. When the screw gauge is fully tightened without any object, the zero of its circu

If the deBronglie wavelength of an electron is equal to 10−310^{-3}10−3 times the wavelength of a photon of frequency 6 × 101410^{14}1014 Hz, then the speed of electron is equal to : (Speed of light =

A power transmission line feeds input power at 2300 V to a step down transformer with its primary windings having 4000 turns. The output power is delivered at 230 V bv the transformer. If the current

A uniform rectangular thin sheet ABCD of mass M has length a and breadth b, as shown in the figure. If the shaded portion HBGO is cut–off, the coordinates of the centre of mass of the remaining portio

A paramagnetic material has atoms/ . Its magnetic susceptibility at temperature 350 K is 2.8 × . Its susceptibility at 300 K is :

A current of 2 mA was passed through an unknown resistor which dissipated a power of 4.4 W. Dissipated power when an ideal power supply of 11V is connected across it is :

Two plane mirrors arc inclined to each other such that a ray of light incident on the first mirror (M1M_1M1​) and parallel to the second mirror (M2M_2M2​) is finally reflected from the second mirror (

In the figure shown, a circuit contains two identical resistors with resistance R = 5Ω and an inductance with L = 2mH. An ideal battery of 15 V is connected in the circuit. What will be the current th

A particle starts from origin O from rest and moves with a uniform acceleration along the positive x– axis. Identify all figures that correctly represent the motion qualitatively. (a = acceleration, v