Previous Year Questions
193 questions — organised by subject with solutions and explanations.
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The radius of (Atomic number of ) is . Which one of the following given values will be closest to the radius of (Atomic number of )?
When during electrolysis of a solution of coulombs of charge pass through the electroplating bath, the mass of silver deposited on the cathode will be
Complete hydrolysis of cellulose gives
How many unit cells are present in a cube shaped ideal crystal of of mass ? [Atomic masses:
For the reaction system: volume is suddenly reduce to half its value by increasing the pressure on it. If the reaction is of first order with respect to and second order with respect to NO, the rate o
The solubility in water of a sparingly soluble salt is . Its solubility product number will be
Which one of the following pairs of molecules will have permanent dipole moments for both members
For a cell reaction involving a two-electron change, the standard e.m.f. of the cell is found to be at . The equilibrium constant of the reaction at will be
of a solution of barium hydroxide on titration with a molar solution of hydrochloric acid gave a litre value of . The molarity of barium hydroxide solution was
Which one of the following nitrates will leave behind a metal on strong heating?
In respect of the equation in chemical kinetics, which one of the following statements is correct?
When is reduced with LiAlH , the compound obtained will be
In Bohr series of lines of hydrogen spectrum, the third line from the red end corresponds to which one of the following inter-orbit jumps of the electron for Bohr orbits in an atom of hydrogen
What may be expected to happen when phosphine gas is mixed with chlorine gas?
Graphite is a soft solid lubricant extremely difficult to melt. The reason for this anomalous behaviour is that graphite
What would happen when a solution of potassium chromate is treated with an excess of dilute nitric acid?
Glass is a
A red solid is insolvable in water. However it becomes soluble if some is added to water. Heating the red solid in a test tube results in liberation of some violet colored fumes and droplets of a meta
One mole of the complex compound , gives 3 moles of ions on dissolution in water. One mole of the same complex reacts with two moles of solution to yield two moles of (s). The structure of the complex
Which one of the following compounds has the smallest bond angle in its molecule?
For making good quality mirrors, plates of float glass are used. These are obtained by floating molten glass over a liquid metal which does not solidify before glass. The metal used can be
Bottles containing and l lost their original labels. They were labelled and for testing and were separately taken in test tubes and boiled with solution. The end solution in each tube was made acidic
Several blocks of magnesium are fixed to the bottom of a ship to
The rate law for a reaction between the substances and is given by Rate On doubling the concentration of and halving the concentration of , the ratio of the new rate to the earlier rate of the reactio
Ethyl isocyanide on hydrolysis in acidic medium generates
The orbital angular momentum for an electron revolving in an orbit is given by . This momentum for an s-electron will be given by
The radionucleide undergoes two successive -decays followed by one -decay. The atomic number and the mass number respectively of the resulting radionucleide are
The pair of species having identical shapes for molecules of both species is
In the coordination compound, , the oxidation state of nickel is
In the anion the two carbon-oxygen bonds are found to be of equal length. What is the reason for it?
The number of d-electrons retained in (At no of ) ion is
The correct order of increasing basic nature for the bases and is
Consider the reaction equilibrium . One the basis of Le Chatelier's principle, the condition favorable for the forward reaction is
The reaction of chloroform with alcoholic and p-toluidine forms
For the reaction equilibrium the concentrations of and at equilibrium are and respectively. The value of for the reaction is
According to the kinetic theory of gases, in an ideal gas, between two successive collisions of a gas molecule travels
The atomic numbers of vanadium (V), Chromium (Cr), manganese and iron (Fe) are respectively and 26 . Which one of these may be expected to have the highest second ionization enthalpy?
What volume of hydrogen gas at and pressure will be consumed in obtaining of elemental boron (atomic mass ) from the reduction of boron trichloride by hydrogen?
An ethar is more volatile than an alcohol having the same molecular formula. This is due to
Which one of the following statements is not true?
The reason for double helical structure of is operation of
If liquids and form an ideal solution
The atomic numbers of Vanadium (V), Chromium (cr), Manganese (Mn) and Iron (Fe), respectively, and 26. Which one of these may be expected to have the higher second ionization enthalpy?
The general formula could be for open chain
Concentrated hydrochloric acid when kept in open air sometimes produces a cloud of white fumes. The explanation for it is that
The enthalpy change for a reaction does not depend upon
Which one of the following is an amphoteric oxide?
Ammonia forms the complex ion with copper ions in alkaline solutions but not in acidic solutions. What is the reason for it?
Among the following four structures to , (i) (ii) (iii) (iv) it is true that
Standard reduction electrode potentials of three metals are respectively . The reducing, powers of these metals are
In an irreversible process taking place at constant and and in which only pressure-volume work is being done, the change in Gibbs free energy and change in entropy (dS), satisfy the criteria
On mixing a certain alkane with chlorine and irradiating it with ultraviolet light, it forms only one monochloroalkane. This alkane could be
According to the Periodic Law of elements, the variation in properties of elements is related to their
In a molal aqueous solution of a weak acid the degree of ionization is . Taking for water as , the freezing point of the solution will be nearest to
Which one of the following substances has the highest proton affinity?
The reduction in atomic size with increase in atomic number is a characteristic of elements of
The correct relationship between free energy change in a reaction and the corresponding equilibrium constant
Which one of the following groupings represents a collection of isoelectronic species? (At. nos. :
A pressure cooker reduces cooking time for food because
The IUPAC name of is
During dehydration of alcohols to alkenes by heating with conc. the initiation step is
The half-life of a radioactive isotope is three hours. If the initial mass of the isotope were , the mass of it remaining undecayed after 18 hours would be
For the redox reaction taking place in a cell, is volt. for the cell will be
When rain is accompanied by a thunderstorm, the collected rain water will have a pH value
The internal energy change when a system goes from state to is . If the system goes from to by a reversible path and returns to state A by an irreversible path what would be the net change in internal
Which one of the following statements is correct?
If at the bond energies of and bonds are respectively and 435 , the value of enthalpy change for the reaction
The de Broglie wavelength of a tennis ball of mass moving with a velocity of 10 meters per second is approximately
Butene-1 may be converted to butane by reaction with
In an experiment with 15 observations on , then following results were available: One observation that was 20 was found to be wrong and was replaced by the correct value30. Then the corrected variance
The lines and are coplanar if
The function , is
Let be a polynomial function of second degree. If and are in . , then are in
If , the value of is
If the function , where , attains its maximum and minimum at and respectively such that , then equals
The mean and variance of a random variable having binomial distribution are 4 and 2 respectively, then is
If denotes the number of combination of things taken at a time, then the expression
The value of is
A student is to answer 10 out of 13 questions in an examination such that he must choose at least 4 from the first five questions. The number of choices available to him is
The number of ways in which 6 men and 5 women can dine at a round table if no two women are to sit together is given by
Let be a function satisfying with and be a function that satisfies . Then the value of the integral , is
The solution of the differential equation
If , then the value of
Domain of definition of the function , is
is
If and , then
The trigonometric equation has a solution for
If the sum of the roots of the quadratic equation is equal to the sum of the squares of their reciprocals, then and are in
If satisfies , for all and , then is
The radius of the circle in which the sphere is cut by the plane is
Let and their derivatives exist and are not equal for some . Further if then the value of is
If and are two non-zero complex numbers such that and , then is equal to
If are the cube roots of unity, then is equal to
Let and be two roots of the equation , Z being complex. Further, assume that the origin, and form an equilateral triangle. Then
Five horses are in a race. Mr. A selects two of the horses at random and bets on them. The probability that Mr. A selected the winning horse is
The value of ' ' for which one root of the quadratic equation is twice as large as the other is
The real number when added to its inverse gives the minimum value of the sum at equal to
The degree and order of the differential equation of the family of all parabolas whose axis is -axis, are respectively.
A function from the set of natural numbers to integers defined by is
If the system of linear equations has a non-zero solution, then .
The area of the region bounded by the curves and is
If then
The number of real solutions of the equation is
If and vectors and are non- coplanar, then the product equals
The median of a set of 9 distinct observations is . If each of the largest 4 observations of the set is increased by 2 , then the median of the new set
The value of the integral is
If and , then , then
Two systems of rectangular axes have the same origin. If a plane cuts then at distances and from the origin then
The shortest distance from the plane to the sphere is
If then is equal to
If then is
The two lines and will be perpendicular, if and only if
Events are mutually exclusive events such that and The set of possible values of are in the interval.
Which of the following atoms has the lowest ionization potential?
A car, moving with a speed of , can be stopped by brakes after at least . If the same car is moving at a speed of , the minimum stopping distance is
A marble block of mass lying on ice when given a velocity of is stopped by friction in . Then the coefficient of friction is
A circular disc of radius is made from an iron plate of thickness , and another disc of radius is made from an iron plate of thickness . Then the relation between the moment of inertia and is
The time period of satellite of earth is 5 hours. If the separation between the earth and the satellite is increased to 4 times the previous value, the new time period will become
The co-ordinates of a moving particle at any time ' ' are given by and . The speed to the particle at time ' ' is given by
The wavelengths involved in the spectrum of deuterium are slightly different from that of hydrogen spectrum, because
Dimensions of , where symbols have their usual meaning, are
A spring of spring constant is stretched initially by from the unstretched position. Then the work required to stretch it further by another is
If and are three non-coplanar vectors, then equals
Two coils are placed close to each other. The mutual inductance of the pair of coils depends upon
In an oscillating circuit the maximum charge on the capacitor is . The charge on the capacitor when the energy is stored equally between the electric and magnetic field is
A spring balance is attached to the ceiling of a lift. A man hangs his bag on the spring and the spring reads , when the lift is stationary. If the lift moves downward with an acceleration of , the re
The core of any transformer is laminated so as to
The escape velocity for a body projected vertically upwards from the surface of earth is 11 . If the body is projected at an angle of with the vertical, the escape velocity will be
Which of the following parameters does not characterize the thermodynamic state of matter?
The length of a wire of a potentiometer is , and the . of its standard cell is volt. It is employed to measure the . of a battery whose internal resistance in . If the balance point is obtained at fro
A tuning fork of known frequency makes 5 beats per second with the vibrating string of a piano. The beat frequency decreases to 2 beats per second when the tension in the piano string is slightly incr
If the electric flux entering and leaving an enclosed surface respectively is and , the electric charge inside the surface will be
A magnetic needle lying parallel to a magnetic field requires units of work to turn it through . The torque needed to maintain the needle in this position will be
A body executes simple harmonic motion. The potential energy , the kinetic energy and total energy are measured as a function of displacement . Which of the following statements is true?
To get three images of a single object, one should have two plane mirrors at an angle of
In the middle of the depletion layer of a reverse- biased junction, the
The difference in the variation of resistance with temperature in a metal and a semiconductor arises essentially due to the difference in the
An ammeter reads upto 1 ampere. Its internal resistance is . To increase the range to the value of the required shunt is
Which of the following radiations has the least wavelength?
The physical quantities not having same dimensions are
The image formed by an objective of a compound microscope is
Three charges and are placed as shown in the figure. The -component of the force on is proportional to
are 3 vectors, such that , , then is equal toA 1
The length of a given cylindrical wire is increased by . Due to the consequent decrease in diameter the change in the resistance of the wire will be
When the current changes from to in second, an . of is inducted in a coil. The coefficient of self-induction of the coil is
A boy playing on the roof of a high building throws a ball with a speed of at an angle of with the horizontal. How far from the throwing point will the ball be at the height of from the ground?
A particle of mass and charge moving with velocity describe a circular path of radius when subjected to a uniform transverse magnetic field of induction . The network done by the field when the partic
The magnetic lines of force inside a bar magnet
A tetrahedron has vertices at and . Then the angle between the faces and will be
When a nucleus originally at rest, decays by emitting an alpha particle having a speed , the recoil speed of the residual nucleus is
Let be the force acting on a particle having position vector , and be the torque of this force about the origin. Then
A metal wire of linear mass density of is stretched with a tension of between two rigid supports 1 metre apart. The wire passes at its middle point between the poles of a permanent magnet, and it vibr
A rocket with a lift-off mass is blasted upwards with an initial acceleration of . Then the initial thrust of the blast is
A particle of charge coulomb moving with velocity along the -axis enters a region where a magnetic field of induction is along the -axis, and an electric field of magnitude is along the negative -axis
Let and . If is a unit vector such that and , then is equal to
Three forces start acting simultaneously on a particle moving with velocity, . These forces are represented in magnitude and direction by the three sides of a triangle . The particle will now move wit
The thermo of a thermo -couple is at room temperature. A galvanometer of resistance, capable of detecting current as low as , is connected with the thermo couple. The smallest temperature difference t
"Heat cannot by itself flow from a body at lower temperature to a body at higher temperature" is a statement or consequence of
A 3 volt battery with negligible internal resistance is connected in a circuit as shown in the figure. The current , in the circuit will be
A radioactive sample at any instant has its disintegration rate 5000 disintegrations per minute. After 5 minutes, the rate is 1250 disintegrations per minute. Then, the decay constant (per minute) is
The displacement of particle varies according to the relation . The amplitude of the particle is
In the nuclear fusion reaction given that the repulsive potential energy between the two nuclei is , the temperature at which the gases must be heated to initiate the reaction is nearly[ Boltzmann's C
A carnot engine takes . of heat from a reservoir at , and gives it to a sink at . The work done by the engine is
The length of a simple pendulum executing simple harmonic motion is increased by . The percentage increase in the time period of the pendulum of increased length is
A light spring balance hangs from the hook of the other light spring balance and a block of mass hangs from the former one. Then the true statement about the scale reading is
Consider the following two statements:A. Linear momentum of a system of particles is zeroB. Kinetic energy of a system of particles is zero. then
A sheet of aluminium foil of negligible thickness is introduced between the plates of a capacitor. The capacitance of the capacitor
A nucleus with emits the following in a sequence: Then of the resulting nucleus is
The negative pole of a Daniell cell, sending a constant current through a circuit, decreases in mass by in 30 minutes. If the electrochemical equivalent of and are and respectively, the increase in th
The displacement of a wave travelling in the -direction is given by where is expressed in metres and in seconds. The speed of the wave - motion, in , is
During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio for the gas is
A block of mass is pulled along a horizontal frictionless surface by a rope of mass . If a force is applied at the free end of the rope, the force exerted by the rope on the block is
A mass is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes of time period . If the mass is increased by . the time period becomes .
According to Newton's law of cooling, the rate of cooling of a body is proportional to , where is the difference of the temperature of the body and the surrounding, and is equal to
Consider points and with positionvectors and respectively. Then is aA parallelogram but not a rhombus
A thin spherical conducting shell of radius has a charge . Another charge is placed at the center of the shell. The electrostatic potential at a point a distance from the center of the shell is
Which of the following cannot be emitted by radioactive substances during their decay?
The work done in placing a charge of coulomb on a condenser of capacity 100 micro-farad is
The vectors are the sides of triangle . The length of the median through is
Two particles and of equal masses are suspended from two massless springs of spring of spring constant and , respectively. If the maximum velocities, during oscillation, are equal, the ratio of amplit
A 220 volt, 1000 watt bulb is connected across a 110 volt mains supply. The power consumed will be
A body is moved along a straight line by a machine delivering a constant power. The distance moved by the body in time ' is proportional to
A particle performing uniform circular motion has angular frequency is doubled & its kinetic energy halved, then the new angular momentum is
Two spherical bodies of mass and and radii and respectively are released in free space with initial separation between their centers equal to . If they attract each other due to gravitational force on
A thin rectangular magnet suspended freely has a period of oscillation equal to . Now it is broken into two equal halves (each having half of the original length) and one piece is made to oscillate fr
A wire suspended vertically from one of its ends is stretched by attaching a weight of to the lower end. The weight stretches the wire by . Then the elastic energy stored in the wire is
A strip of copper and another of germanium are cooled from room temperature to . The resistance of
A horizontal force of is necessary to just hold a block stationary against a wall. The coefficient of friction between the block and the wall is . The weight of the block is
Two identical photo-cathodes receive light of frequencies and . If the velocities of the photo electrons (of mass ) coming out are respectively and , then
To demonstrate the phenomenon of interference, we require two sources which emit radiation
If the binding energy of the electron in a hydrogen atom is , the energy required to remove the electron from the first excited state of is
The earth radiates in the infra-red region of the spectrum. The spectrum is correctly given by