Previous Year Questions
79 questions — organised by subject with solutions and explanations.
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The edge length of a face centered cubic cell of an ionic substance is . If the radius of the cation is , the radius of the anion is
Which one of the following has an optical isomer?(en = ethylenediamine)
Consider the reaction : The rate equation for this reaction is rate Which of these mechanisms is/are consistent with this rate equation?(A) (slow) (B) (fast equilibrium)
The main product of the following reaction is ?
A solution containing of (molar mass ) is passed through a cation exchanger. The chloride ions obtained in solution were treated with excess of to give of (molar mass ). The formula of the complex is
At , the solubility product of is . At which , will ions start precipitating in the form of from a solution of ions ?
Biuret test is not given by
Consider the following bromides :The correct order of reactive is
In the chemical reactions,the compounds and respectively are
For a particular reversible reaction at temperature and were found to be both +ve. If is the temperature at equilibrium, the reaction would be spontaneous when
The Gibbs energy for the decomposition of at is as follows : The potential difference needed for electrolytic reduction of at is at least
Solubility product of silver bromide is . The quantity of potassium bromide (molar mass taken as of ) to be added to 1 litre of nitrate to start the precipitation of is
Ionisation energy of is . The energy of the first stationary state 1) of is
The time for half life period of a certain reaction products is 1 hour. When the initial concentration of the reactant ' ', is , how much time does it take for its concentration to come from to if it
The correct order of values with negative sign for the four successive elements , Mn, Fe and is
The standard enthalpy of formation of is . If the enthalpy of formation of from its atoms is and that of is , the average bond enthalpy of bond in is
In aqueous solution the ionization constants for carbonic acid are and Select the correct statement for a saturated solution of the carbonic acid.
Percentages of free space in cubic close packed structure and in body centred packed structure are respectively
One mole of a symmetrical alkene on ozonolysis gives two moles of an aldehyde having a molecular mass of . The alkene is
The correct sequence which shows decreasing order of the ionic radii of the elements is
From amongst the following alcohols the one that would react fastest with conc. and anhydrous , is
The correct order of increasing basicity of the given conjugate bases is
Three reactions involving are given below :(i) (ii) (iii) In which of the above does act as an acid?
Out of the following, the alkene that exhibits optical isomerism is
If of water is introduced into a flask to , how many moles of water are in the vapour phase when equilibrium is established ?(Given: Vapour pressure of at is )
The energy required to break one mole of bonds in is . The longest wavelength of light capable of breaking a single bond is and
If sodium sulphate is considered to be completely dissociated into cations and anions in aqueous solution, the change in freezing point of water , when of sodium sulphate is dissolved in of water, is
On mixing, heptane and octane form an ideal solution. At , the vapour pressures of the two liquid components (heptane and octane) are and respectively.Vapour pressure of the solution obtained by mixin
Let be a continuous function defined by Statement - 1: , for some .Statement - , for all
There are two urns. Urn A has 3 distinct red balls and urn B has 9 distinct blue balls. From each urn two balls are taken out at random and then transferred to the other. The number of ways in which t
The equation of the tangent to the curve , that is parallel to the -axis, is
Let be a matrix with non-zero entries and let , where is identity matrix. Define sum of diagonal elements of and of matrix .Statement- Statement- 2: .
A line in three-dimensional space makes angles and with the positive -axis and the positive -axis respectively. If makes an acute angle with the positive -axis, then equals
Let be defined by If has a local minimum at , then a possible value of is
The number of complex numbers such that equals
Four numbers are chosen at random (without replacement) from the set .Statement - 1: The probability that the chosen numbers when arranged in some order will form an AP is .Statement - 2: If the four
The area bounded by the curves and between the ordinates and is
For two data sets, each of size 5 , the variances are given to be 4 and 5 and the corresponding means are given to be 2 and 4 , respectively. The variance of the combined data set is
If and are the roots of the equation , then
Solution of the differential equation is
Let be a positive increasing function with
The number of non-singular matrices, with four entries as 1 and all other entries as 0 , is
Statement-1: The point is the mirror image of the point in the plane .Statement-2: The plane bisects the line segment joining and .
Let be a function defined on such that , for all and . Then equals
Let be a differentiable function with and . Let . Then
An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have differen
Consider the system of linear equations; The system has
An initially parallel cylindrical beam travels in a medium of refractive index , where and are positive constants and is the intensity of the light beam. The intensity of the beam is decreasing with i
Let there be a spherically symmetric charge distribution with charge density varying as upto , and for , where is the distance from the erigin. The electric field at a distance from the origin is give
An initially parallel cylindrical beam travels in a medium of refractive index , where and are positive constants and is the intensity of the light beam. The intensity of the beam is decreasing with i
In the circuit shown below, the key is closed at . The current through the battery is
If the vectors and are mutually orthogonal, then
Two fixed frictionless inclined planes making an angle and with the vertical are shown in the figure. Two blocks and are placed on the two planes. What is the relative vertical acceleration of with re
The respective number of significant figures for the numbers and are
Statement −1-1−1 : When ultraviolet light is incident on a photocell, its stopping potential is V0V_0V0 and the maximum kinetic energy of the photoelectrons is KmaxK_{max}Kmax. When the ultraviolet
In a series circuit and the voltage and the frequency of the main supply is and respectively. On taking out the capacitance from the circuit the current lags behind the voltage by . On taking out the
A nucleus of mass is at rest and decays into two daughter nuclei of equal mass each. Speed of light is .The speed of daughter nuclei is
Let and . Then the vector satisfying and
A particle is moving with velocity , where is a constant. The general equation for its path is
For a particle in uniform circular motion the acceleration at a point on the circle of radius is (here is measured from the -axis)
A point moves in counter-clockwise direction on a circular path as shown in the figure. The movement of is such that it sweeps out a length , where is in metres and is in seconds. The radius of the pa
Statement - 1: Two particles moving in the same direction do not lose all their energy in a completely inelastic collision.Statement : Principle of conservation of momentum holds true for all kinds of
The equation of a wave on a string of linear mass density is given by The tension in the string is
The combination of gates shown below yields
A nucleus of mass is at rest and decays into two daughter nuclei of equal mass each. Speed of light is .The binding energy per nucleon for the parent nucleus is and that for the daughter nuclei is . T
A thin semi-circular ring of radius has a positive charges distributed uniformly over it. The net field at the center is
A ball is made of a material of density where with and representing the densities of oil and water, respectively. The oil and water are immiscible. If the above ball is in equilibrium in a mixture of
A small particle of mass is projected at an angle with the -axis with an initial velocity in the plane as shown in the figure. At a time , the angular momentum of the particle is where and are unit ve
An initially parallel cylindrical beam travels in a medium of refractive index , where and are positive constants and is the intensity of the light beam. The intensity of the beam is decreasing with i
Two long parallel wires are at a distance apart. They carry steady equal currents flowing out of the plane of the paper as shown. The variation of the magnetic field along the line is given by
A radioactive nucleus (initial mass number and atomic number emits particles and 2 positrons. The ratio of number of neutrons to that of protons in the final nucleus will be
Two conductors have the same resistance at but their temperature coefficients of resistance are and . The respective temperature coefficients of their series and parallel combinations are nearly
The potential energy function for the force between two atoms in a diatomic molecule is approximately given by , where and are constants and is the distance between the atoms. If the dissociation ener
Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of with each other. When suspended in a liquid of density , the angle remains the same. If density of
Let be the capacitance of a capacitor discharging through a resistor . Suppose is the time taken for the energy stored in the capacitor to reduce to half its initial value and is the time taken for th
A diatomic ideal gas is used in a Carnot engine as the working substance. If during the adiabatic expansion part of the cycle the volume of the gas increases from to , the efficiency of the engine is
The figure shows the position-time graph of one-dimensional motion of body of mass . The magnitude of each impulse is
If a source of power produces photons/second, the radiation belongs to a part of the spectrum called
A rectangular loop has a sliding connector of length and resistance and it is moving with a speed as shown. The set-up is placed in a uniform magnetic field going into the plane of the paper. The thre