AIEEE 2005 — 1 May Offline (Previous Year Paper)

A projectile can have the same range R for two angles of projection. If $t_1$ and $t_2$ be the times of flights in the two cases, then the product of the two time of flights is proportional to

1. A.$R^2$
2. B.$1/R^2$
3. C.1/R
4. D.R✓

Correct answer: D

An annular ring with inner and outer radii $R_1$ and $R_2$ is rolling without slipping with a uniform angular speed. The ratio of the forces experienced by the two particles situated on the inner and outer parts of the ring, $F_1/F_2$ is

1. A.$\frac{R_2}{R_1}$
2. B.$\left(\frac{R_1}{R_2}\right)^2$
3. C.1
4. D.$\frac{R_1}{R_2}$✓

Correct answer: D

A smooth block is released at rest on a $45^\circ$ incline and then slides a distance d. The time taken to slide is n times as much to slide on rough incline than on a smooth incline. The coefficient of friction is

1. A.$\mu_k = 1 - \frac{1}{n^2}$✓
2. B.$\mu_k = \sqrt{1 - \frac{1}{n^2}}$
3. C.$\mu_s = 1 - \frac{1}{n^2}$
4. D.$\mu_s = \sqrt{1 - \frac{1}{n^2}}$

Correct answer: A

The upper half of an inclined plane with inclination $\phi$ is perfectly smooth while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom if the coefficient of friction for the lower half is given by

1. A.$2\sin\phi$
2. B.$2\cos\phi$
3. C.$2\tan\phi$✓
4. D.$\tan\phi$

Correct answer: C

A bullet fired into a fixed target loses half of its velocity after penetrating 3 cm. How much further it will penetrate before coming to rest assuming that it faces constant resistance to motion?

1. A.3.0 cm
2. B.2.0 cm
3. C.1.5 cm
4. D.1.0 cm✓

Correct answer: D

Out of the following pair, which one does NOT have identical dimensions is

1. A.angular momentum and Planck's constant
2. B.impulse and momentum
3. C.moment of inertia and moment of a force✓
4. D.work and torque

Correct answer: C

The relation between time t and distance x is $t = ax^2 + bx$ where a and b are constants. The acceleration is

1. A.$-2abv^2$
2. B.$2bv^3$
3. C.$-2av^3$✓
4. D.$2av^2$

Correct answer: C

A particle is moving eastwards with a velocity of 5 m/s in 10 seconds the velocity changes to 5 m/s northwards. The average acceleration in this time is

1. A.$\frac{1}{\sqrt{2}}$ m/s$^2$ towards north-east
2. B.$\frac{1}{2}$ m/s$^2$ towards north.
3. C.zero
4. D.$\frac{1}{\sqrt{2}}$ m/s$^2$ towards north-west✓

Correct answer: D

A parachutist after bailing out falls 50 m without friction. When parachute opens, it decelerates at 2 m/s$^2$. He reaches the ground with a speed of 3 m/s. At what height, did he bail out?

1. A.91 m
2. B.182 m
3. C.293 m✓
4. D.111 m

Correct answer: C

A block is kept on a frictionless inclined surface with angle of inclination $\alpha$. The incline is given an acceleration a to keep the block stationary. Then a is equal to

1. A.$g/\tan\alpha$
2. B.$g\,\text{cosec}\,\alpha$
3. C.g
4. D.$g\tan\alpha$✓

Correct answer: D

A spherical ball of mass 20 kg is stationary at the top of a hill of height 100 m. It rolls down a smooth surface to the ground, then climbs up another hill of height 30 m and finally rolls down to a horizontal base at a height of 20 m above the ground. The velocity attained by the ball is

1. A.40 m/s✓
2. B.20 m/s
3. C.10 m/s
4. D.$10\sqrt{30}$ m/s

Correct answer: A

A body A of mass M while falling vertically downwards under gravity breaks into two parts; a body B of mass 1/3 M and a body C of mass 2/3 M. The centre of mass of bodies B and C taken together shifts compared to that of body A towards

1. A.depends on height of breaking
2. B.does not shift✓
3. C.body C
4. D.body B

Correct answer: B

The moment of inertia of a uniform semicircular disc of mass M and radius r about a line perpendicular to the plane of the disc through the centre is

1. A.$\frac{1}{4}Mr^2$
2. B.$\frac{2}{5}Mr^2$
3. C.$Mr^2$
4. D.$\frac{1}{2}Mr^2$✓

Correct answer: D

A particle of mass 0.3 kg is subjected to a force F = -kx with k = 15 N/m. What will be its initial acceleration if it is released from a point 20 cm away from the origin?

1. A.3 m/s$^2$
2. B.15 m/s$^2$
3. C.5 m/s$^2$
4. D.10 m/s$^2$✓

Correct answer: D

The block of mass M moving on the frictionless horizontal surface collides with a spring of spring constant K and compresses it by length L. The maximum momentum of the block after collision is

1. A.$\sqrt{MK}L$✓
2. B.$\frac{KL^2}{2M}$
3. C.zero
4. D.$\frac{ML^2}{K}$

Correct answer: A

A mass 'm' moves with a velocity v and collides inelastically with another identical mass. After collision the $1^{st}$ mass moves with velocity $v/\sqrt{3}$ in a direction perpendicular to the initial direction of motion. Find the speed of the $2^{nd}$ mass after collision

1. A.v
2. B.$\sqrt{3}v$
3. C.$2v/\sqrt{3}$✓
4. D.$v/\sqrt{3}$

Correct answer: C

A 20 cm long capillary tube is dipped in water. The water rises up to 8 cm. If the entire arrangement is put in a freely falling elevator the length of water column in the capillary tube will be

1. A.8 cm
2. B.10 cm
3. C.4 cm
4. D.20 cm✓

Correct answer: D

If S is stress and Y is Young's modulus of material of a wire, the energy stored in the wire per unit volume is

1. A.$2S^2Y$
2. B.$S^2/2Y$✓
3. C.$2Y/S^2$
4. D.$S/2Y$

Correct answer: B

Average density of the earth

1. A.does not depend on g
2. B.is a complex function of g
3. C.is directly proportional to g✓
4. D.is inversely proportional to g

Correct answer: C

A body of mass m is accelerated uniformly from rest to a speed v in a time T. The instantaneous power delivered to the body as a function time is given by

1. A.$\frac{mv^2}{T^2}\cdot t$✓
2. B.$\frac{mv^2}{T^2}\cdot t^2$
3. C.$\frac{1}{2}\frac{mv^2}{T^2}\cdot t$
4. D.$\frac{1}{2}\frac{mv^2}{T^2}\cdot t^2$

Correct answer: A

Consider a car moving on a straight road with a speed of 100 m/s. The distance at which car can be stopped is [$\mu_k = 0.5$]

1. A.800 m
2. B.1000 m✓
3. C.100 m
4. D.400 m

Correct answer: B

A 'T' shaped object with dimensions shown in the figure, is lying on a smooth floor. A force F is applied at the point P parallel to AB, such that the object has only the translational motion without rotation. Find the location of P with respect to C

1. A.$\frac{2}{3}\ell$
2. B.$\frac{3}{2}\ell$
3. C.$\frac{4}{3}\ell$✓
4. D.$\ell$

Correct answer: C

The change in the value of g at a height 'h' above the surface of the earth is the same as at a depth 'd' below the surface of earth. When both 'd' and 'h' are much smaller than the radius of earth, then which one of the following is correct?

1. A.$d = \frac{h}{2}$
2. B.$d = \frac{3h}{2}$
3. C.d = 2h✓
4. D.d = h

Correct answer: C

A particle of mass 10 g is kept on the surface of a uniform sphere of mass 100 kg and radius 10 cm. Find the work to be done against the gravitational force between them to take the particle far away from the sphere (you may take $G = 6.67\times10^{-11}$ Nm$^2$/kg$^2$)

1. A.$13.34\times10^{-10}$ J
2. B.$3.33\times10^{-10}$ J
3. C.$6.67\times10^{-9}$ J
4. D.$6.67\times10^{-10}$ J✓

Correct answer: D

A gaseous mixture consists of 16 g of helium and 16 g of oxygen. The ratio $\frac{C_p}{C_v}$ of the mixture is

1. A.1.59
2. B.1.62✓
3. C.1.4
4. D.1.54

Correct answer: B

The intensity of gamma radiation from a given source is I. On passing through 36 mm of lead, it is reduced to $\frac{I}{8}$. The thickness of lead which will reduce the intensity to $\frac{I}{2}$ will be

1. A.6 mm
2. B.9 mm
3. C.18 mm
4. D.12 mm✓

Correct answer: D

The electrical conductivity of a semiconductor increases when electromagnetic radiation of wavelength shorter than 2480 nm is incident on it. The band gap in (eV) for the semiconductor is

1. A.1.1 eV
2. B.2.5 eV
3. C.0.5 eV✓
4. D.0.7 eV

Correct answer: C

A photocell is illuminated by a small bright source placed 1 m away. When the same source of light is placed $\frac{1}{2}$ m away, the number of electrons emitted by photo cathode would

1. A.decrease by a factor of 4
2. B.increase by a factor of 4✓
3. C.decrease by a factor of 2
4. D.increase by a factor of 2

Correct answer: B

Starting with a sample of pure $^{66}$Cu, 7/8 of it decays into Zn in 15 minutes. The corresponding half-life is

1. A.10 minutes
2. B.15 minutes
3. C.5 minutes✓
4. D.$7\frac{1}{2}$ minutes

Correct answer: C

If radius of $^{27}_{13}Al$ nucleus is estimated to be 3.6 Fermi then the radius $^{125}_{52}Te$ nucleus be nearly

1. A.6 fermi✓
2. B.8 fermi
3. C.4 fermi
4. D.5 fermi

Correct answer: A

The temperature-entropy diagram of a reversible engine cycle is given in the figure. Its efficiency is

1. A.1/2
2. B.1/4
3. C.1/3✓
4. D.2/3

Correct answer: C

The figure shows a system of two concentric spheres of radii $r_1$ and $r_2$ and kept at temperatures $T_1$ and $T_2$ respectively. The radial rate of flow of heat in a substance between the two concentric sphere is proportional to

1. A.$\frac{r_2-r_1}{r_1r_2}$
2. B.$\ln\left(\frac{r_2}{r_1}\right)$
3. C.$\frac{r_1r_2}{r_2-r_1}$✓
4. D.$\ln(r_2-r_1)$

Correct answer: C

A system goes from A to B via two processes I and II as shown in the figure. If $\Delta U_1$ and $\Delta U_2$ are the changes in internal energies in the processes I and II respectively, the

1. A.$\Delta U_1 = \Delta U_2$✓
2. B.relation between $\Delta U_1$ and $\Delta U_2$ can not be determined
3. C.$\Delta U_2 > \Delta U_1$
4. D.$\Delta U_2 < \Delta U_1$

Correct answer: A

The function $\sin^2(\omega t)$ represents

1. A.a periodic, but not simple harmonic motion with a period $2\pi/\omega$
2. B.a periodic, but not simple harmonic motion with a period $\pi/\omega$
3. C.a simple harmonic motion with a period $2\pi/\omega$
4. D.a simple harmonic motion with a period $\pi/\omega$✓

Correct answer: D

A Young's double slit experiment uses a monochromatic source. The shape of the interference fringes formed on a screen is

1. A.hyperbola
2. B.circle
3. C.straight line✓
4. D.parabola

Correct answer: C

Two simple harmonic motions are represented by the equation $y_1 = 0.1\sin\left(100\pi t + \frac{\pi}{3}\right)$ and $y_2 = 0.1\cos\pi t$. The phase difference of the velocity of particle 1 w.r.t. the velocity of the particle 2 is

1. A.$-\pi/6$✓
2. B.$\pi/3$
3. C.$-\pi/3$
4. D.$\pi/6$

Correct answer: A

A fish looking up through the water sees the outside world contained in a circular horizon. If the refractive index of water is 4/3 and the fish is 12 cm below the surface, the radius of this circle in cm is

1. A.$36\sqrt{7}$
2. B.$36/\sqrt{7}$✓
3. C.$36\sqrt{5}$
4. D.$4\sqrt{5}$

Correct answer: B

Two point white dots are 1 mm apart on a black paper. They are viewed by eye of pupil diameter 3 mm. Approximately, what is the maximum distance at which these dots can be resolved by the eye? [Take wavelength of light = 500 nm]

1. A.5 m✓
2. B.1m
3. C.6 m
4. D.3m

Correct answer: A

The diagram shows the energy levels for an electron in a certain atom. Which transition shown represents the emission of a photon with the most energy ?

1. A.III✓
2. B.IV
3. C.I
4. D.II

Correct answer: A

If the kinetic energy of a free electron doubles. Its deBroglie wavelength changes by the factor

1. A.$\frac{1}{2}$
2. B.2
3. C.$\frac{1}{\sqrt{2}}$✓
4. D.$\sqrt{2}$

Correct answer: C

In a common base amplifier, the phase difference between the input signal voltage and output voltage is

1. A.$\frac{\pi}{4}$
2. B.$\pi$
3. C.0✓
4. D.$\frac{\pi}{2}$

Correct answer: C

In a full wave rectifier circuit operating from 50 Hz mains frequency, the fundamental frequency in the ripple would be

1. A.50 Hz
2. B.25 Hz
3. C.100 Hz✓
4. D.70.7 Hz

Correct answer: C

A nuclear transformation is denoted by X(n, $\alpha$) $^7_3Li$. Which of the following is the nucleus of element X ?

1. A.$^{12}C_6$
2. B.$^{10}_5B$✓
3. C.$^9_5B$
4. D.$^{11}_4Be$

Correct answer: B

A moving coil galvanometer has 150 equal divisions. Its current sensitivity is 10 divisions per milliampere and voltage sensitivity is 2 divisions per millivolt. In order that each division reads 1 volt, the resistance in ohms needed to be connected in series with the coil will be

1. A.$10^3$
2. B.$10^5$
3. C.99995
4. D.9995✓

Correct answer: D

Two voltameters one of copper and another of silver, are joined in parallel. When a total charge q flows through the voltameters, equal amount of metals are deposited. If the electrochemical equivalents of copper and silver are $z_1$ and $z_2$ respectively the charge which flows through the silver voltameter is

1. A.$\frac{q}{1+\frac{z_1}{z_2}}$
2. B.$\frac{q}{1+\frac{z_2}{z_1}}$✓
3. C.$q\frac{z_1}{z_2}$
4. D.$q\frac{z_2}{z_1}$

Correct answer: B

In the circuit, the galvanometer G shows zero deflection. If the batteries A and B have negligible internal resistance, the value of the resistor R will be

1. A.$200\,\Omega$
2. B.$100\,\Omega$✓
3. C.$500\,\Omega$
4. D.$1000\,\Omega$

Correct answer: B

Two sources of equal emf are connected to an external resistance R. The internal resistance of the two sources are $R_1$ and $R_2$ ($R_2 > R_1$). If the potential difference across the source having internal resistance $R_2$ is zero, then

1. A.$R = R_2\times(R_1+R_2)/(R_2-R_1)$
2. B.$R = R_2 - R_1$✓
3. C.$R = R_1R_2/(R_1+R_2)$
4. D.$R = R_1R_2/(R_2-R_1)$

Correct answer: B

A fully charged capacitor has a capacitance 'C' it is discharged through a small coil of resistance wire embedded in a thermally insulated block of specific heat capacity 's' and mass 'm'. If the temperature of the block is raised by '$\Delta T$'. The potential difference V across the capacitance is

1. A.$\sqrt{\frac{2mC\Delta T}{s}}$
2. B.$\frac{mC\Delta T}{s}$
3. C.$\frac{ms\Delta T}{C}$
4. D.$\sqrt{\frac{2ms\Delta T}{C}}$✓

Correct answer: D

One conducting U tube can slide inside another as shown in figure, maintaining electrical contacts between the tubes. The magnetic field B is perpendicular to the plane of the figure. if each tube moves towards the other at a constant speed V, then the emf induced in the circuit in terms of B, $\ell$ and V where $\ell$ is the width of each tube will be

1. A.$B\ell V$
2. B.$-B\ell V$
3. C.zero
4. D.$2B\ell V$✓

Correct answer: D

A heater coil is cut into two equal parts and only one part is now used in the heater. The heat generated will now be

1. A.doubled✓
2. B.four times
3. C.one fourth
4. D.halved

Correct answer: A

Two thin, long parallel wires separated by a distance 'd' carry a current of 'i' A in the same direction. They will

1. A.attract each other with a force of $\mu_0i^2/(2\pi d)$✓
2. B.repel each other with a force of $\mu_0i^2/(2\pi d)$
3. C.attract each other with a force of $\mu_0i^2/(2\pi d^2)$
4. D.repel each other with a force of $\mu_0i^2/(2\pi d^2)$

Correct answer: A

When an unpolarized light of intensity $I_0$ is incident on a polarizing sheet, the intensity of the light which does not get transmitted is

1. A.$\frac{1}{2}I_0$✓
2. B.$\frac{1}{4}I_0$
3. C.zero
4. D.$I_0$

Correct answer: A

A charged ball B hangs from a silk thread S which makes an angle $\theta$ with a large charged conducting sheet P, as show in the figure. The surface charge density $\sigma$ of the sheet is proportional to

1. A.$\cos\theta$
2. B.$\cot\theta$
3. C.$\sin\theta$
4. D.$\tan\theta$✓

Correct answer: D

Two point charges + 8q and - 2q are located at x = 0 and x = L respectively. The location of a point on the x axis at which the net electric field due to these two point charges is zero is

1. A.2L✓
2. B.L/4
3. C.8L
4. D.4L

Correct answer: A

Two thin wires rings each having a radius R are placed at a distance d apart with their axes coinciding. The charges on the two rings are +q and -q. The potential difference between the centres of the two rings is

1. A.$QR/4\pi\epsilon_0d^2$
2. B.$\frac{Q}{2\pi\epsilon_0}\left[\frac{1}{R} - \frac{1}{\sqrt{R^2+d^2}}\right]$✓
3. C.zero
4. D.$\frac{Q}{4\pi\epsilon_0}\left[\frac{1}{R} - \frac{1}{\sqrt{R^2+d^2}}\right]$

Correct answer: B

A parallel plate capacitor is made by stacking n equally spaced plates connected alternatively. If the capacitance between any two adjacent plates is C then the resultant capacitance is

1. A.(n - 1)C✓
2. B.(n + 1)C
3. C.C
4. D.nC

Correct answer: A

When two tuning forks (fork 1 and fork 2) are sounded simultaneously, 4 beats per second are heard. Now, some tape is attached on the prong of the fork 2. When the tuning forks are sounded again, 6 beats per seconds are heard. If the frequency of fork 1 is 200 Hz, then what was the original frequency of fork 2?

1. A.200 Hz
2. B.202 Hz
3. C.196 Hz✓
4. D.204 Hz

Correct answer: C

If a simple harmonic motion is represented by $\frac{d^2x}{dt^2} + \alpha x = 0$, its time period is

1. A.$\frac{2\pi}{\alpha}$
2. B.$\frac{2\pi}{\sqrt{\alpha}}$✓
3. C.$2\pi\alpha$
4. D.$2\pi\sqrt{\alpha}$

Correct answer: B

The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscillation bob gets suddenly unplugged. During observation, till water is coming out, the time period of oscillation would

1. A.first increase and then decrease to the original value.✓
2. B.first decreased then increase to the original value.
3. C.remain unchanged.
4. D.increase towards a saturation value.

Correct answer: A

An observer moves towards a stationary source of sound, with a velocity one fifth of the velocity of sound. What is the percentage increase in the apparent frequency?

1. A.zero.
2. B.0.5%
3. C.5%
4. D.20%✓

Correct answer: D

Two concentric coils each of radius equal to $2\pi$ cm are placed at right angles to each other. 3 Ampere and 4 ampere are the currents flowing in each coil respectively. The magnetic induction in Weber/m$^2$ at the centre of the coils will be ($\mu_0 = 4\pi\times10^{-7}$ Wb/A-m)

1. A.$12\times10^{-5}$
2. B.$10^{-5}$
3. C.$5\times10^{-5}$✓
4. D.$7\times10^{-5}$

Correct answer: C

A coil of inductance 300 mH and resistance $2\,\Omega$ is connected to a source of voltage 2V. The current reaches half of its steady state value in

1. A.0.05 s
2. B.0.1 s✓
3. C.0.15 s
4. D.0.3 s

Correct answer: B

The self inductance of the motor of an electric fan is 10 H. In order to impart maximum power at 50 Hz, it should be connected to a capacitance of

1. A.4$\mu$F
2. B.8$\mu$F
3. C.1$\mu$F✓
4. D.2$\mu$F

Correct answer: C

An energy source will supply a constant current into the load of its internal resistance is

1. A.equal to the resistance of the load.
2. B.very large as compared to the load resistance.✓
3. C.zero.
4. D.non-zero but less than the resistance of the load.

Correct answer: B

A circuit has a resistance of $12\,\Omega$ and an impedance of $15\,\Omega$. The power factor of the circuit will be

1. A.0.8✓
2. B.0.4
3. C.1.25
4. D.0.125

Correct answer: A

The phase difference between the alternating current and emf is $\pi/2$. Which of the following cannot be the constituent of the circuit?

1. A.C alone
2. B.R, L✓
3. C.L, C
4. D.L alone

Correct answer: B

A uniform electric field and a uniform magnetic field are acting along the same direction in a certain region. If an electron is projected along the direction of the fields with a certain velocity then

1. A.its velocity will decrease.✓
2. B.its velocity will increase.
3. C.it will turn towards right of direction of motion.
4. D.it will turn towards left of direction of motion.

Correct answer: A

A charged particle of mass m and charge q travels on a circular path of radius r that is perpendicular to a magnetic field B. The time taken by the particle to complete one revolution is

1. A.$\frac{2\pi mq}{B}$
2. B.$\frac{2\pi q^2B}{m}$
3. C.$\frac{2\pi qB}{m}$
4. D.$\frac{2\pi m}{qB}$✓

Correct answer: D

In a potentiometer experiment the balancing with a cell is at length 240 cm. On shunting the cell with a resistance of $2\,\Omega$ the balancing length becomes 120 cm. The internal resistance of the cell is

1. A.$1\,\Omega$
2. B.$0.5\,\Omega$
3. C.$4\,\Omega$
4. D.$2\,\Omega$✓

Correct answer: D

The resistance of hot tungsten filament is about 10 times the cold resistance. What will be the resistance of 100 W and 200 V lamp when not in use?

1. A.$40\,\Omega$✓
2. B.$20\,\Omega$
3. C.$400\,\Omega$
4. D.$200\,\Omega$

Correct answer: A

A magnetic needle is kept in a non-uniform magnetic field. It experiences

1. A.a torque but not a force
2. B.neither a force nor a torque
3. C.a force and a torque.✓
4. D.a force but not a torque.

Correct answer: C

Which of the following oxides is amphoteric in character?

1. A.CaO
2. B.$CO_2$
3. C.$SiO_2$
4. D.$SnO_2$✓

Correct answer: D

Which one of the following species is diamagnetic in nature?

1. A.$He_2^+$
2. B.$H_2$✓
3. C.$H_2^+$
4. D.$H_2^-$

Correct answer: B

If $\alpha$ is the degree of dissociation of $Na_2SO_4$, the vant Hoff's factor (i) used for calculating the molecular mass is

1. A.$1 + \alpha$
2. B.$1 - \alpha$
3. C.$1 + 2\alpha$✓
4. D.$1 - 2\alpha$

Correct answer: C

The oxidation state of Cr in $[Cr(NH_3)_4Cl_2]^+$ is

1. A.+3✓
2. B.+2
3. C.+1
4. D.0

Correct answer: A

Hydrogen bomb is based on the principle of

1. A.Nuclear fission
2. B.Natural radioactivity
3. C.Nuclear fusion✓
4. D.Artificial radioactivity

Correct answer: C

An ionic compound has a unit cell consisting of A ions at the corners of a cube and B ions on the centres of the faces of the cube. The empirical formula for this compound would be

1. A.AB
2. B.$A_2B$
3. C.$AB_3$✓
4. D.$A_3B$

Correct answer: C

For a spontaneous reaction the $\Delta G$, equilibrium constant (K) and $E^\circ_{cell}$ will be respectively

1. A.-ve, >1, +ve✓
2. B.+ve, >1, -ve
3. C.-ve, <1, -ve
4. D.-ve, >1, -ve

Correct answer: A

Which of the following is a polyamide?

1. A.Teflon
2. B.Nylon-66✓
3. C.Terylene
4. D.Bakelite

Correct answer: B

Which one of the following types of drugs reduces fever?

1. A.Analgesic
2. B.Antipyretic✓
3. C.Antibiotic
4. D.Tranquiliser

Correct answer: B

Due to the presence of an unpaired electron, free radicals are:

1. A.Chemically reactive✓
2. B.Chemically inactive
3. C.Anions
4. D.Cations

Correct answer: A

Lattice energy of an ionic compounds depends upon

1. A.Charge on the ion only
2. B.Size of the ion only
3. C.Packing of ions only
4. D.Charge on the ion and size of the ion✓

Correct answer: D

The highest electrical conductivity of the following aqueous solutions is of

1. A.0.1 M acetic acid
2. B.0.1 M chloroacetic acid
3. C.0.1 M fluoroacetic acid
4. D.0.1 M difluoroacetic acid✓

Correct answer: D

Aluminium oxide may be electrolysed at $1000^\circ$C to furnish aluminium metal (Atomic mass = 27 amu; 1 Faraday = 96,500 Coulombs). The cathode reaction is $Al^{3+} + 3e^- \rightarrow Al^\circ$. To prepare 5.12 kg of aluminium metal by this method would require

1. A.$5.49\times10^7$ C of electricity✓
2. B.$1.83\times10^7$ C of electricity
3. C.$5.49\times10^4$ C of electricity
4. D.$5.49\times10^1$ C of electricity

Correct answer: A

Consider an endothermic reaction, $X \rightarrow Y$ with the activation energies $E_b$ and $E_f$ for the backward and forward reactions, respectively. In general

1. A.$E_b < E_f$✓
2. B.$E_b > E_f$
3. C.$E_b = E_f$
4. D.There is no definite relation between $E_b$ and $E_f$

Correct answer: A

Consider the reaction: $N_2 + 3H_2 \rightarrow 2NH_3$ carried out at constant temperature and pressure. If $\Delta H$ and $\Delta U$ are the enthalpy and internal energy changes for the reaction, which of the following expressions is true?

1. A.$\Delta H = 0$
2. B.$\Delta H = \Delta U$
3. C.$\Delta H < \Delta U$✓
4. D.$\Delta H > \Delta U$

Correct answer: C

Which one of the following statements is NOT true about the effect of an increase in temperature on the distribution of molecular speeds in a gas?

1. A.The most probable speed increases
2. B.The fraction of the molecules with the most probable speed increases✓
3. C.The distribution becomes broader
4. D.The area under the distribution curve remains the same as under the lower temperature

Correct answer: B

The volume of a colloidal particle, $V_C$ as compared to the volume of a solute particle in a true solution $V_S$, could be

1. A.$\frac{V_C}{V_S} = 1$
2. B.$\frac{V_C}{V_S} = 10^{23}$
3. C.$\frac{V_C}{V_S} = 10^{-3}$
4. D.$\frac{V_C}{V_S} = 10^3$✓

Correct answer: D

The solubility product of a salt having general formula $MX_2$, in water is: $4\times10^{-12}$. The concentration of $M^{2+}$ ions in the aqueous solution of the salt is

1. A.$2.0\times10^{-6}$ M
2. B.$1.0\times10^{-4}$ M✓
3. C.$1.6\times10^{-4}$ M
4. D.$4.0\times10^{-10}$ M

Correct answer: B

Benzene and toluene form nearly ideal solutions. At $20^\circ$C, the vapour pressure of benzene is 75 torr and that of toluene is 22 torr. The partial vapour pressure of benzene at $20^\circ$C for a solution containing 78 g of benzene and 46 g of toluene in torr is

1. A.50✓
2. B.25
3. C.37.5
4. D.53.5

Correct answer: A

The exothermic formation of $ClF_3$ is represented by the equation: $Cl_2(g) + 3F_2(g) \rightleftharpoons 2ClF_3(g)$; $\Delta_rH = -329$ kJ. Which of the following will increase the quantity of $ClF_3$ in an equilibrium mixture of $Cl_2$, $F_2$ and $ClF_3$?

1. A.Increasing the temperature
2. B.Removing $Cl_2$
3. C.Increasing the volume of the container
4. D.Adding $F_2$✓

Correct answer: D

Two solutions of a substance (non electrolyte) are mixed in the following manner. 480 ml of 1.5 M first solution + 520 mL of 1.2 M second solution. What is the molarity of the final mixture?

1. A.1.20 M
2. B.1.50 M
3. C.1.344 M✓
4. D.2.70 M

Correct answer: C

For the reaction $2NO_2(g) \rightleftharpoons 2NO(g) + O_2(g)$, ($K_c = 1.8\times10^{-6}$ at $184^\circ$C) (R = 0.0831 kJ/(mol.K)). When $K_p$ and $K_c$ are compared at $184^\circ$C, it is found that

1. A.$K_p$ is greater than $K_c$✓
2. B.$K_p$ is less than $K_c$
3. C.$K_p = K_c$
4. D.Whether $K_p$ is greater than, less than or equal to $K_c$ depends upon the total gas pressure

Correct answer: A

Hydrogen ion concentration in mol/L in a solution of pH = 5.4 will be

1. A.$3.98\times10^8$
2. B.$3.88\times10^6$
3. C.$3.68\times10^{-6}$
4. D.$3.98\times10^{-6}$✓

Correct answer: D

A reaction involving two different reactants can never be

1. A.Unimolecular reaction✓
2. B.First order reaction
3. C.second order reaction
4. D.Bimolecular reaction

Correct answer: A

If we consider that $\frac{1}{6}$, in place of $\frac{1}{12}$, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will

1. A.Decrease twice
2. B.Increase two fold
3. C.Remain unchanged✓
4. D.Be a function of the molecular mass of the substance

Correct answer: C

In a multi - electron atom, which of the following orbitals described by the three quantum numbers will have the same energy in the absence of magnetic and electric fields? (a) n = 1, l = 0, m = 0 (b) n = 2, l = 0, m = 0 (c) n = 2, l = 1, m = 1 (d) n = 3, l = 2, m = 1 (e) n = 3, l = 2, m = 0

1. A.(a) and (b)
2. B.(b) and (c)
3. C.(c) and (d)
4. D.(d) and (e)✓

Correct answer: D

During the process of electrolytic refining of copper, some metals present as impurity settle as 'anode mud' These are

1. A.Sn and Ag
2. B.Pb and Zn
3. C.Ag and Au✓
4. D.Fe and Ni

Correct answer: C

Using the molar conductances at infinite dilution in $H_2O$ at $25^\circ$C (S cm$^2$ mol$^{-1}$): KCl 149.9, $KNO_3$ 145.0, HCl 426.2, NaOAc 91.0, NaCl 126.5, calculate $\Lambda^\infty_{HOAc}$.

1. A.517.2
2. B.552.7
3. C.390.7✓
4. D.217.5

Correct answer: C