Previous Year Questions
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Which of the following complexes will show geometrical isomerism ?[Main 16 April 2018 S1]
Given (i) ; (ii) ; . Free energy change, for the reaction will be :-
A group 13 element ‘X’ reacts with chlorine gas to produce a compound . is electron deficient and easily reacts with to form adduct;however, does not dimerize X is:[Main 16 April 2018 S1]
The major product B formed in the following reaction sequence is :[Main 16 April 2018 S1]
The major product formed in the following reaction is :[Main 8 April 2018]
For which of the following reactions ∆H is equal to ∆U?[Main 15 April 2018 S1]
The predominate form of histamine prexent in human blood is (pKa, Histidine = 6.0)[Main 8 April 2018]
Which of the following is the correct structure of Adenosine ?[Main 15 April 2018 S1]
On treatment of the following compound with a strong acid, the most susceptible site for bond cleavage is :-
Ejection of the photoelectron from metalin the photoelectric effect experiment can be stopped by applying 0.5 V when the radiation of 250 nm is used. The work function of the metal is :([Main 15 April
In which of the following reactions, an increase in the volume of the container will favour the formation of products ?[Main 15 April 2018 S1]
The correct combination is :[Main 15 April 2018 S1]
Two compounds I and II are eluted by column chromatography (adsorption of I II). Which one of the following is a correct statement ?
The incorrect geometry is represented by :[Main 16 April 2018 S1]
Which of the following salts is the most basic in aqueous solution?[Main 8 April 2018]
The major product of the following reaction is :[Main 8 April 2018]
All of the following share the same crystal structure except :-
Which of the following compounds contain(s) no covalent bond(s)? [Main 8 April 2018]
In , the nature of oxygen species and the oxidation state of oxygen atom are, respectively
An ideal gas undergoes a cyclic process as shown in Figure. Heat absorbed by the system during process CA is :[Main 15 April 2018 S1]
The most polar compound among the following is :[Main 16 April 2018 S1]
At 320 K, a gas is 20% dissociated to A(g).The standard free energy change at 320 K and 1 atm in is approximately: [Main 16 April 2018 S1]
Which of the following conversions involves change in both shape andhybridisation ?[Main 16 April 2018 S1]
Consider the following reaction statements: I) Two isomers are produced if the reactant complex ion is a cis-isomerII) Two isomers are produced if the reactant complex ion is a transisomer.III) Only o
For per gram of reactant, the maximum quantity of gas is produced in which of the following thermal decomposition reactions?(Given : Atomic wt. )
Phenol on treatment with in the presence of NaOH followed by acidification product. X on treatment with in the presence of catalytic amount of [Main 8 April 2018]
For 1 molal aqueous solution of the following compounds, which one will show the highest freezing point?[Main 8 April 2018]
If 50% of a reaction occurs in 100 second and 75% of the reaction occurs in 200 second, the order of this reaction is :[Main 16 April 2018 S1]
The trans-alkenes are formed by the reduction of alkynes with :[Main 8 April 2018]
In the molecular orbital diagram for the molecular ion, ,the number of electrons in the molecular orbital is :[Main 15 April 2018 S1]
For and ;the correct order of increasing ionic radii is :[Main 15 April 2018 S1]
Assuming ideal gas behaviour, the ratio of density of ammonia to that of hydrogen chloride at same temperature and pressure is : (Atomic wt. of Cl=35.5 u)[Main 16 April 2018 S1]
The decreasing order of bond angles in and is[Main 15 April 2018 S1]
Which of the following will most readily give the dehydrohalogenation product ?[Main 15 April 2018 S1]
According to molecular orbital theory, which of the following will not be a viable molecule?[Main 8 April 2018]
Two 5 molal solutions are prepared by dissolving a non-electrolyte non-volatile solute separately in the solvents X and Y . The molecular weights of the solvents are and , respectively where . The rel
An unknown chlorohydrocarbon has 3.55% of chlorine. If each molecule of the hydrocarbon has one chlorine atom only; chlorine atoms present in 1 g of chlorohydrocarbon are : (Atomic wt. of Cl =35.5 u;A
The major product formed in the following reaction is -
The oxidation states of Cr in , and respectively are :[Main 8 April 2018]
The number of bonds in is :-
Which of the following compounds will most readily be dehydrated to give alkene under acidic condition ?[Main 16 April 2018 S1]
When is fused with an alkali metal hydroxide in presence of oxidizing agent such as a dark green product is formed which disproportionates in acidic solution to afford a dark purple solution X is[Main
An aqueous solution contains unknown concentration .When 50 mL of a 1M solution is added, just ust begins to precipitate. The final volume is 500 mL.The solubility product of is . . What is the origin
Xenon hexafluoride on partial hydrolysis produces compounds ‘X’ and ‘Y’.Compounds ‘X’ and ‘Y’ and the oxidation state of Xe are respectively :[Main 15 April 2018 S1]
How long (approximate) should water be electrolysed by passing through 100 amperes current so that the oxygen released can completely burn 27.66g of diborane? (Atomic weight of B = 10.8 u)[Main 8 Apri
When 9.65 ampere current was passed for 1.0 hour into nitrobenzene in acidic medium, the amount of p-aminophenol produced is :[Main 16 April 2018 S1]
The mass of a non-volatile, non-electrolyte solute (molar mass needed to be dissolved in 114 g octane to reduce its vapour pressure to 75%, is :[Main 16 April 2018 S1]
Among the following, the incorrect statement is :[Main 16 April 2018 S1]
at 500 K for substance ' S ' in liquid state and gaseous state are and +103 kcal , respectively. Vapour pressure of liquid ' ' at 500 K is approximately equal to:
Which of the following statements is false ?[Main 16 April 2018 S1]
The increasing order of the acidity of the following carboxylic acids is -
Products A and B formed in the following reactions are respectively :[Main 16 April 2018 S1]
The reagent(s) required for the following conversion are :(I)(II)(III)(1) (2) (3) DIBAL-H (4) Raney [Main 15 April 2018 S1]
Following four solutions are prepared by mixing different volumes of NaOH and HCl of different concentrations, pH of which one of them will be equal to 1 ?
The total number of possible isomers for squareplanar is :-
Which of the following are Lewis acids?[Main 8 April 2018]
Which of the following lines correctly show the temperature dependence of equilibrium constant, K, for an exothermic reaction?[Main 8 April 2018]
An alkali is titrated against an acid with methyl orange an indicator, which of the following is a correct combination ?BaseAcidEnd point1.WeakStrongColourless to pink2.StrongStrongPinkish red to yell
Glucose on prolonged heating with HI gives :[Main 8 April 2018]
Identify the pair in which the geometry of the species is T-shape and square pyramidal, respectively :[Main 15 April 2018 S1]
In hydrogen azide (above) the bond ordersof bonds (I) and (II) are :(I)(II)(1) 2(2)> 2 2> 2(4)< 2< 2[Main 15 April 2018 S1]
When an electric current is passed through acidified water, 112 mL of hydrogen gas at N.T.P. was collected at the cathode in 965 seconds. The current passed, in ampere, is :[Main 15 April 2018 S1]
Lithium aluminium hybride reacts with silicon tetrachloride to form :-
In graphite and diamond, the percentage of p-characters of the hybrid orbitals in hybridisation are respectively :([Main 15 April 2018 S1]
The increasing order of diazotisation of the following compounds i s:-
Which of the following best describes the diagram below of a moleuclar orbital ?
At 518°C the rate of decomposition of a sample of gaseous acetaldehyde, initially at a pressure of 363 Torr, was 1.00 Tor when 5% had reacted and 0.5 Torr when 33% had reacted. The order of the reacti
The major product formed in the following
The main reduction product of the following compound with in methanol is :[Main 15 April 2018 S1]
A sample of is converted by heat to NaCl with a loss of 0.16 g of oxygen. The residue is dissolved in water and precipitated as AgCl. The mass of AgCl (in g) obtained will be : (Given : Molar mass of
The ratio of mass percent C and H of an organic compound is .If one of molecule of the above compound contains half as much oxygen as required to burn one molecule of compound completely to and .The e
When metal ‘M’ is treated with NaOH, a white gelatinous precipitate ‘X’ is obtained,which is soluble in excess of NaOH. Compound ‘X’ when heated strongly gives an oxide which is used in chromatography
In Wilkinson’s catalyst, the hybridization of central metal ion and its shape arerespectively :[Main 16 April 2018 S1]
Which of the following is a Lewis acid ?[Main 15 April 2018 S1]
Phenol reacts with methyl chloroformate in the presence of NaOH to form product A. A reacts with to form product B. A and B are respectively :[Main 8 April 2018]
The major product of the following reaction is :[Main 16 April 2018 S1]
The dipeptide, Gln-Gly, on treatment with followed by aqueous work work up gives :-
decomposes to and and follows first order kinetics. After 50 minutes, the pressure inside the vessel increases from to . The pressure of the gaseous mixture after 100 minute at constant temperature wi
The compound that does not produce nitrogen gas by the thermal decomposition is :[Main 8 April 2018]
The correct order of electron affinity is :-
The minimum volume of water required to dissolve 0.1 g lead(II) chloride to get a saturated solution ( of atomic mass of u) is:[Main 15 April 2018 S1]
Among the oxides of nitrogen : and ; the molecule(s) having nitrogen-nitrogen bond is/are :[Main 16 April 2018 S1]
When 2-butyne is treated with 's catalyst, compound X is produced as the major product and when treated with liq. it produces Y as the major product. Which of the following statements is correct ?
The increasing order of basicity of the following compounds is :[Main 8 April 2018]
Which type of ‘defect’ has the presence of cations in the interstitial sites?[Main 8 April 2018]
The gas phase reaction is an exothermic reaction.The decomposition of , in equilibrium mixture of and ,can be increased by:[Main 16 April 2018 S1]
Which of the following will not exist in zwitter ionic form at pH=7 ?[Main 15 April 2018 S1]
Which of the following arrangements shows the schematic alignment of magnetic moments of antiferromagnetic substance ?[Main 15 April 2018 S1]
The combustion of benzene (1) gives and .Given that heat of combustion of benzene at constant volume is at 25°C;heat of combustion (in kJ ) of benzene at constant pressure will be : [Main 8 April 2018
The increasing order of nitration of the following compounds is :[Main 15 April 2018 S1]
At a certain temperature in a 5 L vessel, 2 moles of carbon monoxide and 3 moles of chlorine were allowed to reach equilibrium according to the reaction, At equilibrium, if one mole of CO is present t
The major product of the following reaction is :[Main 16 April 2018 S1]
The correct match between items of List-I and List-II is :List - IList - II(A) Coloured impurity(P) Steam distillation(B) Mixture of o-nitrophenol and p-nitrophenol(Q) Fractional distillation(C) Crude
In , the number of bond pair( ), -bond( ) are lone pair(s) on Xe atom respectively are :-
For which of the following processes, ∆S is negative ?[Main 16 April 2018 S1]
An aqueous solution contains 0.10 M and 0.20 M HCl If the equilibrium constant for the formation of from is and that of from ions is then the concentration of ions in aqueous solution is:[Main 8 April
The incorrect statement is :[Main 16 April 2018 S1]
The IUPAC name of the following compound is :[Main 15 April 2018 S1]
Total number lone pair of electrons in ion is :[Main 8 April 2018]
The correct order of spin-only magnetic moments among the following is : (Atomic number : , )
For a first order reaction, (half life) is 10 days. The time required for conversion of A (in days) is :( )
The de-Broglie's wavelength of electron present in first Bohr orbit of ' ' atom is :-
A white sodium salt dissolves readily in water to give a solution which is neutral to litmus. When silver nitrate solution is added to the aforementioned solution, a white precipitate is obtained whic
The major product of the following reaction is :[Main 15 April 2018 S1]
The total number of optically active compounds formed in the following reaction is :-
The set of all , for which is a purely imaginary number, for all satisfying and Re , is:[Main 15 April 2018 S1]
The value of the integral is:[Main 15 April 2018 S1]
Let N denote the set of all natural numbers. Define two binary relations on N as and Then:[Main 16 April 2018 S1]
A bag contains 4 red and 6 black balls. A ball is drawn at random from the bag, its colour is observed and this ball along with two additional balls of the same colour are returned to the bag. If now
The number of four letter words that can be formed using the letters of the word BARRACK is :-
If a right circular cone, having maximum volume, is inscribed in a sphere of radius 3cm, then the curved surface area (in ) of this cone is :[Main 15 April 2018 S1]
Two different families A and B are blessed with equal number of children. There are 3 tickets to be distributed amongst the children of these families so that no child gets more than one ticket. If th
Let and Then the sum of the elements of the first column of B is:[Main 16 April 2018 S1]
Let y = y(x) b the solution of the differential equation If , then is equalton :[Main 8 April 2018]
If tanA and tanB are the roots of the quadratic equation, then the value of is:[Main 15 April 2018 S1]
The mean of a set of 30 observations is 75.If each observation is multiplied by a non-zero number λ and then each of them is decreased by 25, their mean remains the same. Then λ is equal to :[Main 15
Let and . If then the local minimum value of h(x) is:[Main 8 April 2018]
A box ‘A’ contains 2 white, 3 red and 2 black balls. Another box ‘B’ contains 4 white, 2 red and 3 black balls. If two balls are drawn at random, without replacement, from a randomly selected box and
A player X has a biased coin whose probability of showing heads is p and a player Y has a fair coin. They start playing a game with their own coins and play atlernately. The player who throws a head f
If and then is equal to:[Main 16 April 2018 S1]
An angle between the lines whose direction cosines are given by the equations, and , is :-
If the curves intersect each other at right angles, then the value of b is:[Main 8 April 2018]
If the function defined as ,is continuous at ,then the ordered pair is equal[Main 16 April 2018 S1]
If the system of linear equations has a non-zero solution (x, y, z), then is equal to[Main 8 April 2018]
The value of is:[Main 8 April 2018]
The curve satisfying the differential equation, and passing through the point is :-
An angle between the plane, and the line of intersection of the planes, and , is:[Main 15 April 2018 S1]
If then the difference between the greatest value and the least value of is :-
If (where is a constant of integration), then the ordered pair is equal to :
Suppose A is any non-singular matrix and , where and . If , then is equal to :-
If , then equals
If is the line of intersection of the planes and is the line of intersection of the planes then the distance of the origin from the plane, containing the lines and is[Main 8 April 2018]
The mean and the standard deviation(s.d.) of five observations are 9 and 0,respectively. If one of the observations ischanged such that the mean of the new set of five observations becomes 10, then th
If , (C is a constant of integration), then the ordered pair (K, A) is equal to :[Main 16 April 2018 S1]
Consider the following two binary relations on the set and . Then :[Main 15 April 2018 S1]
The number of numbers between and that can be formed with the digits (repetition of digits is not allowed) and are multiple of is :[Main 16 April 2018 S1]
The differential equation representing the family of ellipses having foci either on the x-axis or on the y-axis, centre at the origin and passing through the point (0, 3) is :[Main 16 April 2018 S1]
If the area of the region bounded by the curves, and the lines and is 1 sq.unit,then t is equal to:[Main 16 April 2018 S1]
If the angle between the lines, and is the p is equal to:[Main 16 April 2018 S1]
The least positive integer n for which is:[Main 16 April 2018 S1]
equals to:[Main 16 April 2018 S1]
The integral is equal to:(where C is a constant of integration)[Main 8 April 2018]
If the mean of the data : is 8 , then the variance of this data is :-
Two sets A and B are as under: Then;[Main 8 April 2018]
If an angle A of a ∆ABC satisfies , then the roots of the quadratic equation, are:[Main 16 April 2018 S1]
Let . Then the set S is equal to:[Main 8 April 2018]
For each , let [t] be the greatest integer less than or equal to t. Then [Main 8 April 2018]
A variable plane passes through a fixed point and meets x, y and z axes at A, B and C respectively. A plane is drawn parallel to yz-plane through A, a second plane is drawn parallel zx-plane through B
If is such that the sum of the cubes of the roots of the equation, is minimum, then the magnitude of the difference of the roots of this equation is :[Main 15 April 2018 S1]
A plane bisects the line segment joining the points and at right angles. Then this plane also passes through the point :-
If the system of linear equations : has no solution, then :-
If is a quadratic expression such that , and -1 is a root of , then the other root of is :-
Let is a differentiable function . Then S is a subset of :[Main 15 April 2018 S1]
Let and be the roots of the quadratic equation Then the area (in sq. units) bounded by the curve y = (gof)(x) and the lines and is:[Main 8 April 2018]
If and ,then the standard deviation of the 9 items is:[Main 8 April 2018]
equals :-
The number of values of k for which the system of linear equations, has no solution, is :[Main 16 April 2018 S1]
From 6 different novels and 3 different dictionaries, 4 novels and 1 dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. The number of such a
If ,then [Main 15 April 2018 S1]
If are the distinct roots, of the equation ,then is equal to:[Main 8 April 2018]
Let be a function defined as , where and . Then is :-
The sum of the intercepts on the coordinate axes of the plane passing through the point and containing the line joining the points and is:[Main 16 April 2018 S1]
Let A be a matrix such that a scalar matrix and .Then equals :[Main 15 April 2018 S1]
If ,then the ordered pair (A, B) is equal to:[Main 8 April 2018]
Let M and m be respectively the absolute maximum and the absolute minimum values of the function, in the interval , Then M−m is equal to :[Main 16 April 2018 S1]
If , then the value of at the point is:[Main 15 April 2018 S1]
The length of the projection of the line segment joining the points and on the plane , is :[Main 8 April 2018]
If then:[Main 16 April 2018 S1]
If , then is equal to:(where C is a constant of integration)[Main 15 April 2018 S1]
Let . Then S:[Main 8 April 2018]
Let be the solution of the differential equation where If then is:[Main 15 April 2018 S1]
n-digit numbers are formed using only three digits 2, 5 and 7. The smallest value of n for which 900 such distinct number scan be formed, is :[Main 15 April 2018 S1]
The value of integral is :-
Let p, q and r be real numbers , such that the roots of the equation are equal in magnitude but opposite in sign, then thesum of squares of these roots is equal to :[Main 16 April 2018 S1]
Let S be the set of all real values of k for which the system of linear equations has a unique solution. Then S is :[Main 15 April 2018 S1]
The area (in sq. units) of the region and is[Main 15 April 2018 S1]
Let Thevaue of k for which f s continuous at is :
Let be a polynomial of degree 4 having extreme values at and . If then is equal to :-
If β is one of the angles between the normals to the ellipse, at the points and ;then is equal to[Main 15 April 2018 S1]
Let A, B and C be three events, which are pair-wise independent and denotes the complement of an event E.If and , then is equal to:[Main 16 April 2018 S1]
The B-H curve for a ferromagnet is shown in the figure. The ferromagnet is placed inside a long solenoid with 1000 turns/cm.The current that should be passed in the solenoid to demagnetise the ferroma
A plano convex lens becomes an optical system of 28 cm focal length when its plane surface is silvered and illuminated from left to right as shown in Fig-A.If the same lens is instead silvered on the
Both the nucleus and the atom of some element are in their respective first excited states. They get de-excited by emitting photons of wavelengths respectively. The ratio is closest to :[Main 16 April
Take the mean distance of the moon and the sun from the earth to be km and respectively. Their masses are and kg respectively. The radius of the earth is 6400 km. Let be the difference in the forces e
A thin , free to rotate in the vertical plane about the fixed end N , is held horizontal. When the end is released the speed of this end, when the rod makes an angle a with the horizontal, will be pro
A charge q is spread uniformly over an insulated loop of radius r. If it is rotated with an angular velocity ω with respect to normal axis then the magnetic moment of the loop is :[Main 16 April 2018
All the graphs below are intended to represent the same motion. One of them does it incorrectly. Pick it up[Main 8 April 2018]
A parallel plate capacitor of capacitance 90 pF is connected to a battery of emf 20V. If a dielectric material of dielectric constant is inserted between the plates, the magnitude of the included char
A thin uniform bar of length and mass 8 m lies on a smooth horizontal table. Two point masses m and 2 m are moving in the same horizontal plane from opposite sides of the bar with speeds 2 v and respe
A given object takes n times more time to slide down a 45° rough inclined plane as it takes to slide down a perfectly smooth 45° incline. The coefficient of kinetic friction between the object and the
Unpolarized light of intensity passes through an ideal polarizer A. Another identical polarizer B is placed behind A. The intensity of light beyond B is found to be . Now another identical polarizer C
A copper rod of cross-sectional area A carries a uniform current I through it. At temperature T, if the volume charge density of the rod is , how long will the charges take to travel a distance d ?
The velocity-time graphs of a car and a scooter are shown in the figure. (i) The difference between the distance travelled by the car and the scooter in 15 s and (ii)the time at which the car will cat
In a common emitter configuration with suitable bias, it is given that is the load resistance and is small signal dynamicresistance (input side). Then, voltage gain, current gain and power gain are gi
What an air bubble of radius rises from the bottom to the surface of a lake, its radius becomes . Taking the atmospheric pressure to be equal to 10 m height of water column, the depth of the lake woul
If the position vectors of the vertices and of a are respectively and , then the position vector of the point, where the bisector of meets is :
In a screw gauge, 5 complete rotations of the screw cause it to move a linear distance of . There are 100 circular scale divisions. The thickness of a wire measured by this screw gauge gives a reading
Two moles of an ideal monoatomic gas occupies a volume V at 27°C . The gas expands adiabatically to a volume 2V. Calculate (a) the final temperature of the gas and (b)change in its internal energy.[Ma
Two electrons are moving with non-relativistic speeds perpendicular to each other. If corresponding de Broglie wavelengths are and , their de Broglie wavelength in the frame of referenceattached to th
The relative error in the determination of the surface area of a sphere isα. Then the relative error in the determination of its volume is :[Main 15 April 2018 S1]
A constant voltage is applied between two ends of a metallic wire. If the length is halved and the radius of the wire is doubled, the rate of heat developed in the wire will be :
The de-Broglie wavelength ( ) associated with the electron orbiting in the second excited state of hydrogen atom is related to that in the ground state ( ) by:[Main 16 April 2018 S1]
The characteristic distance at which quantum gravitational effects are significant, the Planck length, can be determined from a suitable combination of the fundamental physical constants and c . Which
In an a.c. circuit, the instantaneous e.m.f. and current are given by In one cycle of a.c., the average power consumed by the circuit and the wattless currentare, respectively :[Main 8 April 2018]
A particle is oscillating on the X-axis with an amplitude 2 cm about the point ,with a frequency . A concave mirror of focal length 5 cm is placed at the origin (see figure).Identify the correct state
The reading of the ammeter for a silicon diode in the given circuit is:[Main 8 April 2018]
A capacitor is charged up to a voltage by connecting it to battery B through switch ( 1). Now is disconnected from battery and connected to a circuit consisting of two uncharged capacitors and through
In the given circuit all resistances are of value R ohm each. The equivalent resistance between A and B is :[Main 15 April 2018 S1]
A proton of mass collides elastically with a particle of unknown mass at rest. After the collision, the proton and the unknown particle are seen moving at an angle of with respect to each other. The m
A thin uniform tube is bent into a circle of radius r in the vertical plane. Equal volumes of two immiscible liquids, whose densities are and fill half the circle. The angle θ between the radius vecto
At the centre of a fixed large circular coil of radius R, a much smaller circular coil of radius is placed. The two coils are concentric and are in the same plane. The larger coil carries a current I.
A Helmholtz coil has a pair of loops, each with N turns and radius R. They are placed coaxially at distance R and the same current I flows through the loops in the same direction. The magnitude of mag
A particle executes simple harmonic motion and is located at x=a, b and c at times and respectively. The frequency of the oscillation is :[Main 16 April 2018 S1]
An ideal capacitor of capacitance 0.2µFis charged to a potential difference of 10 V. The charging battery is then disconnected. The capacitor is then connected to an ideal inductor of self inductance
The equivalent capacitance between A and B in the circuit given below, is[Main 15 April 2018 S1]
A electron from various excited states of hydrogen atom emit radiation to come to the ground state. Let be the de Broglie wavelength of the electron in the nth state and the ground state respectively.
From a uniform circular disc of radius R and mass , a small disc of radius is removed as shown in the figure. The moment of inertia of the remaining disc about an axis perpendicular to the plane of th
Muon ( ) is a negatively charged ( ) particle with a mass , where is the mass of the electron and e is the electronic charge. If is bound to a proton to form a hydrogen like atom, identify the correct
Two cornot engines A and B are operated in series. Engine A receives heat from a reservoir at 600 K and rejects heat to a reservoir at temperature . Engine receives heat rejected by engine and in turn
If and are unit vectors such that ,then is equal to:[Main 15 April 2018 S1]
A particle is moving with a uniform speed in a circular orbit of radius R in a central force inversely proportional to the power of R. If the period of rotation of the particles is T, then :[Main 8 Ap
The end correction of a resonance column is 1 cm. If the shortest length resonating with the tuning fork is 10 cm, the next resonating length should be :[Main 16 April 2018 S1]
A tuning fork vibrates with frequency 256 Hz and gives one beat per second with the third normal mode of vibration of an open pipe. What is the length of the pipe ? (Speed of sound in air is )[Main 15
A thin circular disk is in the xy plane as shown in the figure. The ratio of its moment of inertia about z and z' axes will be :[Main 16 April 2018 S1]
Suppose that the angular velocity of rotation of earth is increased. Then, as a consequence :[Main 16 April 2018 S1]
A body of mass m is moving in a circular orbit of radius R about a planet of mass M. At some instant, it splits into two equal masses. The first mass moves in a circular orbit of radius , and the othe
A body of mass 2 kg slides down with an acceleration of on a rough inclined plane having a slope of . The external force required to take the same body up the plane with the same acceleration will be
In the following circuit, the switch S is closed at . The charge on the capacitor as a function of time will be given by [Main 16 April 2018 S1]
Truth table for the following digital circuit will be :
An oscillator of mass M is at rest in its equilibrium position in a potential A particle of mass m comes from right with speed u and collides completely inelastically with M and sticks to it. This pro
A solid ball of radius has a charge density given by for . The electric field outside the ball is :
A galvanometer with its coil resistance 25 Ω requires a current of 1 mA for its full deflection. In order to construct an ammeter to read up to a current of 2 A, the approximate value of the shunt res
Three concentric metal shells A,B and C of respective radii a,b and c have surface charge densities and respectively. The potential of shell B is :[Main 8 April 2018]
One mole of an ideal monoatomic gas is taken along the path ABCA as shown in the PV diagram. The maximum temperature attained by the gas along the path BC is given by :[Main 16 April 2018 S1]
In a meter bridge, as shown in the figure, it is given that resistance and that the balance is obtained at a distance 39.5 cm from end A (by Jockey J). After interchanging the resistances X and Y, a n
A power transmission line feeds input power at 2300 V to a step down transformer with its primary windings having 4000 turns, giving the output power at 230 V. If the current in the primary of the tra
An EM wave from air enters a medium. The electric fields are in air and in medium, where the wave number k and frequency v refer to their values in air. The medium is non – magnetic. If and refer to r
The percentage errors in quantities P, Q,R and S are 0.5%, 1%, 3% and 1.5% respectively in the measurement of a physical quantity The maximum percentage error in the value of A will be :[Main 16 April
The mass of a hydrogen molecule is kg.If hydrogen molecules strike, per second, a fixed wall of area at an angle of 45° to the normal, and rebound elastically with a speed of m/s, then the pressure on
An unstable heavy nucleus at rest breaks into two nuclei which move away with velocities in the ratio of . The ratio of the radii of the nuclei (assumed to be spherical) is :
A ray of light is incident at an angle of 60° on one face of a prism of angle 30°. The emergent ray of light makes an angle of 30° with incident ray. The angle made by the emergent ray with second fac
A man in a car at location Q on a straight highway is moving with speed v. He decides to reach a point in qa field at a distance from the highway (point m ) as shown in the figure. Speed of the car in
A small soap bubble of radius 4 cm is trapped inside another bubble of radius6 cm without any contact. Let be the pressure inside the inner bubble and the pressure outside the outer bubble. Radius of
A body takes 10 minutes to cool from to . The temperature of surroundings is constant at . Then, the temperature of the body after next 10 minutes will be approximately :
An electron, a proton and an alpha particle having the same kinetic energy are moving in circular orbits of radii respectively in a uniform magnetic field B. The relation between is[Main 8 April 2018]
A coil of cross-sectional area A having n turns is placed in a uniform magnetic field B. When it is rotated with an angularvelocityω, the maximum e.m.f. induced in the coil will be :[Main 16 April 201
As shown in the figure, forces of each are applied in opposite directions, on the upper and lower faces of a cube of side 10 cm , shifting the upper face parallel to itself by 0.5 cm . If the side of
In the given circuit, the current through zener diode is :[Main 16 April 2018 S1]
If the de Broglie wavelengths associated with a proton and an -particle are equal, then the ratio of velocities of the proton and the -particle will be :
A current of 1 A is flowing on the sides of an equilateral triangle of side . The magnetic field at the centre of the triangle will be:
An automobile, travelling at , can be stopped at a distance of by applying brakes. If the same automobile is travelling at , the minimum stopping distance, in metres, is (assume no skidding)[Main 15 A
One mole of an ideal monoatomic gas is compressed isothermally in a rigid vessel to double its pressure at room temperature,27°C. The work done on the gas will be :[Main 15 April 2018 S1]
Let and, . The magnitude of a coplanar vector such that [Main 16 April 2018 S1]
A convergent doubled to separated lenses, corrected for spherical aberration, has resultant focal length of 10 cm . The separation between the two lenses is 2 cm . The focal lengths of the component l
A uniform rod AB is suspended from a point X, at a variable distance x from A,as shown. To make the rod horizontal, a mass m is suspended from its end A. Aset of (m,x) values is recorded. The appropri
A disc rotates about its axis of symmetry in a horizontal plane at a steady rate of 3.5 revolutions per second. A coin placed at a distance of 1.25 cm from the axis of rotation remains at rest on the
A solid sphere of radius r made of a soft material of bulk modulus K is surrounded by a liquid in a cylindrical container. A massless piston of area of floats on the surface of the liquid, covering en
In a potentiometer experiment, it is found that no current passes through the galvanometer when the terminals of the cell are connected across 52cm of the potentiometer wire. If the cell is shunted by
A heating element has a resistance of 100 Ω at room temperature. When it is connected to a supply of 220V, a steady current of 2 A passes in it and temperature is 500°C more than room temperature.What
Two simple harmonic motions, as shown below, are at right angles. They are combined to form lissajous figures. Identify the correct match below :ParametersCurve(1) Line(2) Parabola(3) Circle(4) Ellips
A charge Q is placed at a distance a/2 above the centre of the square surface of edge a as shown in the figureThe electric flux through the square surface is :[Main 15 April 2018 S1]
The value closest to the thermal velocity of a Helium atom at room temperature ( 300 K ) in is :
For an RLC circuit driven with voltage of amplitude and frequency the current exhibits resonance. The quality factor, Q is given by :[Main 8 April 2018]
A plane polarized light is incident on a polariser with its pass axis making angle with x -axis, as shown in the figure. At four different values of and , the observed intensities are same. What is th
The density of a material in the shape of a cube is determined by measuring three sides ofthe cube and its mass. If the relative errors in measuring the mass and length arerespectively 1.5% and 1%, th
Two identical conducting spheres A and B, carry equal charge. They are separated by a distance much larger than their diameters, and the force between them is F. A third identical conducting sphere, C
A Carnot’s engine works as a refrigerator between 250 K and 300 K. It receives 500 cal heat from the reservoir at the lower temperature. The amount of work done in each cycle to operate the refrigerat
Let and a vector be such that and .Then equals:[Main 16 April 2018 S1]
Unpolarized light of intensity I is incident on a system of two polarizers, A followed by B. The intensity of emergent light is I/2. If a third polarizer C is placed between A and B, the intensity of
A granite rod of 60 cm length is clamped at its middle point and is set into longitudinal vibrations. The density of granite is and its Young’s modulus is Pa.What will be the fundamental frequency of
Light of wavelength 550 nm falls normally on a slit of width cm The angular position of the second minima from the central maximum will be (in radians) :[Main 15 April 2018 S1]
On interchanging the resistances, the balance point of a meter bridge shifts to the left by 10cm. The resistance of their series combination is 1kΩ. How much was the resistance on the left slot before
At some instant, a radioactive sample having an activity has twice the number of nuclei as another sample which has an activity of . The half lives of and are:[Main 16 April 2018 S1]
A plane electromagnetic wave of wavelength has an intensity . It is propagating along the positive Y-direction. The allowed expressions for the electric and magnetic fields are given by :[Main 16 Apri
A solution containing active cobalt having activity of and decay constant is injected in an animal’s body.If of blood is drawn from the animal’s body after 10 hrs of injection, the activity found was
Two sitar strings, A and B, playing the note‘Dha’ are slightly out of tune and produce beats of frequency 5 Hz. The tension of the string B is slightly increased and the beat frequency is found to dec
A silver atom in a solid oscillates in simple harmonic motion in some direction with a frequency of What is the force constant of the bonds connecting one atom with the order ? (Mole wt. of silver = 1
A copper rod of mass slides under gravity on two smooth parallel rails, with separation and set at an angle of with the horizontal. At the bottom, rails are joined by a resistance . There is a uniform
Let be a vector coplanar with the vector and .If is perpendicular to and ,then is equal to:[Main 8 April 2018]
The dipole moment of a circular loop carrying a current I, is m and the magnetic field at the centre of the loop is When the dipole moment is doubled by keeping the current constant, the magnetic fiel
It is found that if a neutron suffers an elastic collinear collision with deuterium at rest, fractional loss of its energy is ; while for its similar collision with carbon nucleus at rest, fractional
Two particles of the same mass m are moving in circular orbits because of force,given by The first particle is at a distance , and the second, at . The best estimate for the ratio of kinetic energies
In a collinear collision, a particle with an initial speed strikes a stationary particle of the same mass. If the final total kinetic energy is 50% greater than the original kinetic energy, the magnit
Seven identical circular planar disks, each of mass M and radius R are welded symmetrically as shown. The moment of inertia of the arrangement about the axis normal to the plane and passing through th
A plane polarized monochromatic EM wave is traveling in vacuum along direction such that at it is found that the electric field is zero at a spatial point . The next zero that occurs in its neighbourh
A parallel plate capacitor with area and separation between the plates 1.5 cm , is connected across a battery of emf V . If the force of attraction between the plates is , the value of V is approximat
Two masses and , connected by an inextensible string over a frictionless pulley, are moving as shown in the figure. The coefficient of friction of horizontal surface is 0.15. The minimum weight m that
A force of 40 N acts on a point B at the end of an L-shaped object, as shown in the figure. The angle θ that will produce maximum moment of the force about point A is given by :[Main 15 April 2018 S1]
If the series limit frequency of the Lyman series is , then the series limit frequency of the Pfund series is:[Main 8 April 2018]
A body of mass M and charge q is connected to a spring of spring constant k. It is oscillating along x-direction about its equilibrium position, taken to be at , with an amplitude A. An electric field
In a circuit for finding the resistance of agalvanometer by half deflection method,a 6 V battery and a high resistance of 11 kΩ are used. The figure of merit of the galvanometer is 60µA/division. In t
The relative uncertainty in the period of a satellite orbiting around the earth is . If the relative uncertainty in the radius of the orbit is negligible, the relative uncertainty in the mass of the e
A body of mass m starts moving from rest along x-axis so that its velocity varies as where a is a constant and s is the distance covered by the body. The total work done by all the forces acting on th
A particle is moving in a circular path of radius a under the action of an attractive potential . Its total energy is :[Main 8 April 2018]
5 beats/second are heard when a turning fork is sounded with a sonometer wire under tension, when the length of the sonometer wire is either 0.95 m or 1 m . The frequency of the fork will be
The angular width of the central maximum in a single slit diffraction pattern is 60°. The width of the slit is 1µm. The slit is illuminated by monochromatic plane waves. If another slit of same width
Two batteries with e.m.f. 12V and 13V are connected in parallel across a load resistor of 10Ω . The internal resistances of the two batteries are 1Ω and 2Ω respectively. The voltage across the load li
The energy required to remove the electron from a singly ionized Helium atom is 2.2 times the energy required to remove an electron from Helium atom. The total energy required to ionize the Helium ato
Two moles of helium are mixed with n moles of hydrogen. If for the mixture, then the value of n is :[Main 16 April 2018 S1]