AIEEE 2007 — 29 Apr Offline Set O (Previous Year Paper)

In a geometric progression consisting of positive terms, each term equals the sum of the next two terms. Then the common ratio of this progression equals

1. A.$\frac{1}{2}(1-\sqrt{5})$
2. B.$\frac{1}{2}\sqrt{5}$
3. C.$\sqrt{5}$
4. D.$\frac{1}{2}(\sqrt{5}-1)$✓

Correct answer: D

If $\sin^{-1}\left(\frac{x}{5}\right) + \csc^{-1}\left(\frac{5}{4}\right) = \frac{\pi}{2}$ then a value of x is

1. A.1
2. B.3✓
3. C.4
4. D.5

Correct answer: B

In the binomial expansion of $(a - b)^n$, $n \ge 5$, the sum of $5^{th}$ and $6^{th}$ terms is zero, then $\frac{a}{b}$ equals

1. A.$\frac{5}{n-4}$
2. B.$\frac{6}{n-5}$
3. C.$\frac{n-5}{6}$
4. D.$\frac{n-4}{5}$✓

Correct answer: D

The set S = {1, 2, 3, ..., 12} is to be partitioned into three sets A, B, C of equal size. Thus, $A\cup B\cup C = S$, $A\cap B = B\cap C = A\cap C = \phi$. The number of ways to partition S is

1. A.$\frac{12!}{3!(4!)^3}$
2. B.$\frac{12!}{3!(3!)^4}$
3. C.$\frac{12!}{(4!)^3}$✓
4. D.$\frac{12!}{(3!)^4}$

Correct answer: C

The largest interval lying in $\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$ for which the function $f(x) = 4^{-x^2} + \cos^{-1}\left(\frac{x}{2} - 1\right) + \log(\cos x)$ is defined, is

1. A.$[0, \pi]$
2. B.$\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$
3. C.$\left[-\frac{\pi}{4}, \frac{\pi}{2}\right)$
4. D.$\left[0, \frac{\pi}{2}\right)$✓

Correct answer: D

A body weighing 13 kg is suspended by two strings 5 m and 12 m long, their other ends being fastened to the extremities of a rod 13 m long. If the rod be so held that the body hangs immediately below the middle point. The tensions in the strings are

1. A.12 kg and 13 kg
2. B.5 kg and 5 kg
3. C.5 kg and 12 kg✓
4. D.5 kg and 13 kg

Correct answer: C

A pair of fair dice is thrown independently three times. The probability of getting a score of exactly 9 twice is

1. A.1/729
2. B.8/9
3. C.8/729
4. D.8/243✓

Correct answer: D

Consider a family of circles which are passing through the point (-1, 1) and are tangent to x-axis. If (h, k) are the co-ordinates of the centre of the circles, then the set of values of k is given by the interval

1. A.$0 < k < \frac{1}{2}$
2. B.$k \ge \frac{1}{2}$✓
3. C.$-\frac{1}{2} \le k \le \frac{1}{2}$
4. D.$k \le \frac{1}{2}$

Correct answer: B

Let L be the line of intersection of the planes $2x + 3y + z = 1$ and $x + 3y + 2z = 2$. If L makes an angle $\alpha$ with the positive x-axis, then $\cos\alpha$ equals

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

Correct answer: A

The differential equation of all circles passing through the origin and having their centres on the x-axis is

1. A.$x^2 = y^2 + xy\frac{dy}{dx}$
2. B.$x^2 = y^2 + 3xy\frac{dy}{dx}$
3. C.$y^2 = x^2 + 2xy\frac{dy}{dx}$✓
4. D.$y^2 = x^2 - 2xy\frac{dy}{dx}$

Correct answer: C

If p and q are positive real numbers such that $p^2 + q^2 = 1$, then the maximum value of (p + q) is

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

Correct answer: D

A tower stands at the centre of a circular park. A and B are two points on the boundary of the park such that AB (= a) subtends an angle of $60^\circ$ at the foot of the tower, and the angle of elevation of the top of the tower from A or B is $30^\circ$. The height of the tower is

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

Correct answer: C

The sum of the series ${}^{20}C_0 - {}^{20}C_1 + {}^{20}C_2 - {}^{20}C_3 + \dots + {}^{20}C_{10}$ is

1. A.$-{}^{20}C_{10}$
2. B.$\frac{1}{2}{}^{20}C_{10}$✓
3. C.0
4. D.${}^{20}C_{10}$

Correct answer: B

If $|z + 4| \le 3$, then the maximum value of $|z + 1|$ is

1. A.4
2. B.10
3. C.6✓
4. D.0

Correct answer: C

The resultant of two forces P N and 3 N is a force of 7 N. If the direction of 3 N force were reversed, the resultant would be $\sqrt{19}$ N. The value of P is

1. A.5 N✓
2. B.6 N
3. C.3 N
4. D.4 N

Correct answer: A

If $D = \begin{vmatrix} 1 & 1 & 1 \\ 1 & 1+x & 1 \\ 1 & 1 & 1+y \end{vmatrix}$ for $x \ne 0$, $y \ne 0$ then D is

1. A.divisible by neither x nor y
2. B.divisible by both x and y✓
3. C.divisible by x but not y
4. D.divisible by y but not x

Correct answer: B

For the hyperbola $\frac{x^2}{\cos^2\alpha} - \frac{y^2}{\sin^2\alpha} = 1$, which of the following remains constant when $\alpha$ varies?

1. A.eccentricity
2. B.directrix
3. C.abscissae of vertices
4. D.abscissae of foci✓

Correct answer: D

If a line makes an angle of $\frac{\pi}{4}$ with the positive directions of each of x-axis and y-axis, then the angle that the line makes with the positive direction of the z-axis is

1. A.$\frac{\pi}{6}$
2. B.$\frac{\pi}{3}$
3. C.$\frac{\pi}{4}$
4. D.$\frac{\pi}{2}$✓

Correct answer: D

A value of C for which the conclusion of Mean Value Theorem holds for the function $f(x) = \log_ex$ on the interval [1, 3] is

1. A.$2\log_3e$✓
2. B.$\frac{1}{2}\log_e3$
3. C.$\log_3e$
4. D.$\log_e3$

Correct answer: A

The function $f(x) = \tan^{-1}(\sin x + \cos x)$ is an increasing function in

1. A.$\left(\frac{\pi}{4}, \frac{\pi}{2}\right)$
2. B.$\left(-\frac{\pi}{2}, \frac{\pi}{4}\right)$✓
3. C.$\left(0, \frac{\pi}{2}\right)$
4. D.$\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$

Correct answer: B

Let $A = \begin{bmatrix} 5 & 5\alpha & \alpha \\ 0 & \alpha & 5\alpha \\ 0 & 0 & 5 \end{bmatrix}$. If $|A^2| = 25$, then $|\alpha|$ equals

1. A.$5^2$
2. B.1
3. C.1/5✓
4. D.5

Correct answer: C

The sum of the series $\frac{1}{2!} - \frac{1}{3!} + \frac{1}{4!} - \dots$ upto infinity is

1. A.$e^{-2}$
2. B.$e^{-1}$✓
3. C.$e^{-1/2}$
4. D.$e^{1/2}$

Correct answer: B

If $\hat{u}$ and $\hat{v}$ are unit vectors and $\theta$ is the acute angle between them, then $2\hat{u}\times3\hat{v}$ is a unit vector for

1. A.exactly two values of $\theta$
2. B.more than two values of $\theta$
3. C.no value of $\theta$
4. D.exactly one value of $\theta$✓

Correct answer: D

A particle just clears a wall of height b at distance a and strikes the ground at a distance c from the point of projection. The angle of projection is

1. A.$\tan^{-1}\frac{b}{ac}$
2. B.$45^\circ$
3. C.$\tan^{-1}\frac{bc}{a(c-a)}$✓
4. D.$\tan^{-1}\frac{bc}{a}$

Correct answer: C

The average marks of boys in a class is 52 and that of girls is 42. The average marks of boys and girls combined is 50. The percentage of boys in the class is

1. A.40
2. B.20
3. C.80✓
4. D.60

Correct answer: C

The equation of a tangent to the parabola $y^2 = 8x$ is $y = x + 2$. The point on this line from which the other tangent to the parabola is perpendicular to the given tangent is

1. A.(-1, 1)
2. B.(0, 2)
3. C.(2, 4)
4. D.(-2, 0)✓

Correct answer: D

If (2, 3, 5) is one end of a diameter of the sphere $x^2 + y^2 + z^2 - 6x - 12y - 2z + 20 = 0$, then the coordinates of the other end of the diameter are

1. A.(4, 9, -3)✓
2. B.(4, -3, 3)
3. C.(4, 3, 5)
4. D.(4, 3, -3)

Correct answer: A

Let $\vec{a} = \hat{i} + \hat{j} + \hat{k}$, $\vec{b} = \hat{i} - \hat{j} + 2\hat{k}$ and $\vec{c} = x\hat{i} + (x-2)\hat{j} - \hat{k}$. If the vector $\vec{c}$ lies in the plane of $\vec{a}$ and $\vec{b}$, then x equals

1. A.0
2. B.1
3. C.-4
4. D.-2✓

Correct answer: D

Let A(h, k), B(1, 1) and C(2, 1) be the vertices of a right angled triangle with AC as its hypotenuse. If the area of the triangle is 1, then the set of values which 'k' can take is given by

1. A.{1, 3}
2. B.{0, 2}
3. C.{-1, 3}✓
4. D.{-3, -2}

Correct answer: C

Let P = (-1, 0), Q = (0, 0) and R = $(3, 3\sqrt{3})$ be three points. The equation of the bisector of the angle PQR is

1. A.$\sqrt{3}x + y = 0$✓
2. B.$x + \frac{\sqrt{3}}{2}y = 0$
3. C.$\frac{\sqrt{3}}{2}x + y = 0$
4. D.$x + \sqrt{3}y = 0$

Correct answer: A

If one of the lines of $my^2 + (1 - m^2)xy - mx^2 = 0$ is a bisector of the angle between the lines xy = 0, then m is

1. A.-1/2
2. B.-2
3. C.1✓
4. D.2

Correct answer: C

Let $F(x) = f(x) + f\left(\frac{1}{x}\right)$, where $f(x) = \int_1^x\frac{\log t}{1+t}dt$. Then F(e) equals

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

Correct answer: A

Let $f : R \to R$ be a function defined by $f(x) = \min\{x + 1, |x| + 1\}$. Then which of the following is true?

1. A.$f(x) \ge 1$ for all $x \in R$
2. B.f(x) is not differentiable at x = 1
3. C.f(x) is differentiable everywhere✓
4. D.f(x) is not differentiable at x = 0

Correct answer: C

The function $f : R \sim \{0\} \to R$ given by $f(x) = \frac{1}{x} - \frac{2}{e^{2x}-1}$ can be made continuous at x = 0 by defining f(0) as

1. A.2
2. B.-1
3. C.0
4. D.1✓

Correct answer: D

$\int\frac{dx}{\cos x + \sqrt{3}\sin x}$ equals

1. A.$\frac{1}{2}\log\tan\left(\frac{x}{2}+\frac{\pi}{12}\right)+c$✓
2. B.$\frac{1}{2}\log\tan\left(\frac{x}{2}-\frac{\pi}{12}\right)+c$
3. C.$\log\tan\left(\frac{x}{2}+\frac{\pi}{12}\right)+c$
4. D.$\log\tan\left(\frac{x}{2}-\frac{\pi}{12}\right)+c$

Correct answer: A

The area enclosed between the curves $y^2 = x$ and $y = |x|$ is

1. A.2/3
2. B.1
3. C.1/6✓
4. D.1/3

Correct answer: C

If the difference between the roots of the equation $x^2 + ax + 1 = 0$ is less than $\sqrt{5}$, then the set of possible values of a is

1. A.(-3, 3)✓
2. B.$(-3, \infty)$
3. C.$(3, \infty)$
4. D.$(-\infty, -3)$

Correct answer: A

The displacement of an object attached to a spring and executing simple harmonic motion is given by $x = 2\times10^{-2}\cos\pi t$ metres. The time at which the maximum speed first occurs is

1. A.0.5 s✓
2. B.0.75 s
3. C.0.125 s
4. D.0.25 s

Correct answer: A

In an a.c. circuit the voltage applied is $E = E_0\sin\omega t$. The resulting current in the circuit is $I = I_0\sin\left(\omega t - \frac{\pi}{2}\right)$. The power consumption in the circuit is given by

1. A.$P = \frac{E_0I_0}{\sqrt{2}}$
2. B.P = zero✓
3. C.$P = \frac{E_0I_0}{2}$
4. D.$P = \sqrt{2}E_0I_0$

Correct answer: B

An electric charge $10^{-3}\,\mu$C is placed at the origin (0, 0) of X-Y co-ordinate system. Two points A and B are situated at $(\sqrt{2}, \sqrt{2})$ and (2, 0) respectively. The potential difference between the points A and B will be

1. A.9 volt
2. B.zero✓
3. C.2 volt
4. D.4.5 volt

Correct answer: B

A battery is used to charge a parallel plate capacitor till the potential difference between the plates becomes equal to the electromotive force of the battery. The ratio of the energy stored in the capacitor and the work done by the battery will be

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

Correct answer: D

An ideal coil of 10H is connected in series with a resistance of $5\,\Omega$ and a battery of 5V. 2 second after the connection is made the current flowing in amperes in the circuit is

1. A.(1 - e)
2. B.e
3. C.$e^{-1}$
4. D.$(1 - e^{-1})$✓

Correct answer: D

A long straight wire of radius 'a' caries a steady current i. The current is uniformly distributed across its cross section. The ratio of the magnetic field at $\frac{a}{2}$ and 2a is

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

Correct answer: C

A current I flows along the length of an infinitely long, straight, thin walled pipe. Then

1. A.the magnetic field is zero only on the axis of the pipe
2. B.the magnetic field is different at different points inside the pipe
3. C.the magnetic field at any point inside the pipe is zero✓
4. D.the magnetic field at all points inside the pipe is the same, but not zero

Correct answer: C

If $M_O$ is the mass of an oxygen isotope $_8O^{17}$, $M_p$ and $M_N$ are the masses of a proton and a neutron respectively, the nuclear binding energy of the isotope is

1. A.$(M_O - 8M_p)c^2$
2. B.$(M_O - 8M_p - 9M_N)c^2$✓
3. C.$M_Oc^2$
4. D.$(M_O - 17M_N)c^2$

Correct answer: B

In gamma ray emission from a nucleus

1. A.both the neutron number and the proton number change
2. B.there is no change in the proton number and the neutron number.✓
3. C.only the neutron number changes
4. D.only the proton number changes

Correct answer: B

If in a p-n junction diode, a square input signal of 10V is applied as shown. Then the output signal across $R_L$ will be

1. A.Waveform (1): square pulse 0 to 10 V
2. B.Waveform (2): negative pulse to -10 V
3. C.Waveform (3): negative pulse to -5 V
4. D.Waveform (4): positive pulse +5 V only✓

Correct answer: D

Photon of frequency $\nu$ has a momentum associated with it. If c is the velocity of light, the momentum is

1. A.$\nu/c$
2. B.$h\nu c$
3. C.$h\nu/c^2$
4. D.$h\nu/c$✓

Correct answer: D

The velocity of a particle is $v = v_0 + gt + ft^2$. If its position is x = 0 at t = 0, then its displacement after unit time (t = 1) is

1. A.$v_0 + 2g + 3f$
2. B.$v_0 + g/2 + f/3$✓
3. C.$v_0 + g + f$
4. D.$v_0 + g/2 + f$

Correct answer: B

For the given uniform square lamina ABCD, whose centre is O,

1. A.$\sqrt{2}I_{AC} = I_{EF}$
2. B.$I_{AD} = 3I_{EF}$
3. C.$I_{AC} = I_{EF}$✓
4. D.$I_{AC} = \sqrt{2}I_{EF}$

Correct answer: C

A point mass oscillates along the x-axis according to the law $x = x_0\cos(\omega t - \pi/4)$. If the acceleration of the particle is written as $a = A\cos(\omega t + \delta)$

1. A.$A = x_0$, $\delta = -\pi/4$
2. B.$A = x_0\omega^2$, $\delta = \pi/4$
3. C.$A = x_0\omega^2$, $\delta = -\pi/4$
4. D.$A = x_0\omega^2$, $\delta = 3\pi/4$✓

Correct answer: D

Charges are placed on the vertices of a square as shown. Let $\vec{E}$ be the electric field and V the potential at the centre. If the charges on A and B are interchanged with those on D and C respectively, then

1. A.$\vec{E}$ remains unchanged, V changes
2. B.Both $\vec{E}$ and V change
3. C.$\vec{E}$ and V remains unchanged
4. D.$\vec{E}$ changes, V remains unchanged✓

Correct answer: D

The half-life period of a radio-active element X is same as the mean life time of another radio-active element Y. Initially they have the same number of atoms. Then

1. A.X will decay faster than Y
2. B.Y will decay faster than X✓
3. C.X and Y have same decay rate initially
4. D.X and Y decay at same rate always

Correct answer: B

A Carnot engine, having an efficiency of $\eta = 1/10$ as heat engine, is used as a refrigerator. If the work done on the system is 10 J, the amount of energy absorbed from the reservoir at lower temperature is

1. A.99 J
2. B.90 J✓
3. C.1 J
4. D.100 J

Correct answer: B

Carbon, silicon and germanium have four valence electrons each. At room temperature which one of the following statements is most appropriate?

1. A.The number of free conduction electrons is significant in C but small in Si and Ge.
2. B.The number of free conduction electrons is negligible small in all the three.
3. C.The number of free electrons for conduction is significant in all the three.
4. D.The number of free electrons for conduction is significant only in Si and Ge but small in C.✓

Correct answer: D

A charged particle with charge q enters a region of constant, uniform and mutually orthogonal fields $\vec{E}$ and $\vec{B}$ with a velocity $\vec{v}$ perpendicular to both $\vec{E}$ and $\vec{B}$, and comes out without any change in magnitude or direction of $\vec{v}$. Then

1. A.$\vec{v} = \vec{E}\times\vec{B}/B^2$✓
2. B.$\vec{v} = \vec{B}\times\vec{E}/B^2$
3. C.$\vec{v} = \vec{E}\times\vec{B}/E^2$
4. D.$\vec{v} = \vec{B}\times\vec{E}/E^2$

Correct answer: A

The potential at a point x (measured in $\mu$m) due to some charges situated on the x-axis is given by $V(x) = 20/(x^2 - 4)$ Volts. The electric field E at x = 4 $\mu$m is given by

1. A.5/3 Volt/$\mu$m and in the -ve x direction
2. B.5/3 Volt/$\mu$m and in the +ve x direction
3. C.10/9 Volt/$\mu$m and in the -ve x direction
4. D.10/9 Volt/$\mu$m and in the +ve x direction✓

Correct answer: D

Which of the following transitions in hydrogen atoms emit photons of highest frequency?

1. A.n = 2 to n = 6
2. B.n = 6 to n = 2
3. C.n = 2 to n = 1✓
4. D.n = 1 to n = 2

Correct answer: C

A block of mass 'm' is connected to another block of mass 'M' by a spring (massless) of spring constant 'k'. The blocks are kept on a smooth horizontal plane. Initially the blocks are at rest and the spring is unstretched. Then a constant force 'F' starts acting on the block of mass 'M' to pull it. Find the force on the block of mass 'm'

1. A.$\frac{mF}{M}$
2. B.$\frac{(M+m)F}{m}$
3. C.$\frac{mF}{(m+M)}$✓
4. D.$\frac{MF}{(m+M)}$

Correct answer: C

Two lenses of power -15 D and +5 D are in contact with each other. The focal length of the combination is

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

Correct answer: B

One end of a thermally insulated rod is kept at a temperature $T_1$ and the other at $T_2$. The rod is composed of two sections of lengths $\ell_1$ and $\ell_2$ and thermal conductivities $k_1$ and $k_2$ respectively. The temperature at the interface of the two sections is

1. A.$(k_2\ell_2T_1 + k_1\ell_1T_2)/(k_1\ell_1 + k_2\ell_2)$
2. B.$(k_2\ell_1T_1 + k_1\ell_2T_2)/(k_2\ell_1 + k_1\ell_2)$
3. C.$(k_1\ell_2T_1 + k_2\ell_1T_2)/(k_1\ell_2 + k_2\ell_1)$✓
4. D.$(k_1\ell_1T_1 + k_2\ell_2T_2)/(k_1\ell_1 + k_2\ell_2)$

Correct answer: C

A sound absorber attenuates the sound level by 20 dB. The intensity decreases by a factor of

1. A.1000
2. B.10000
3. C.10
4. D.100✓

Correct answer: D

If $C_p$ and $C_v$ denote the specific heats of nitrogen per unit mass at constant pressure and constant volume respectively, then

1. A.$C_p - C_v = R/28$✓
2. B.$C_p - C_v = R/14$
3. C.$C_p - C_v = R$
4. D.$C_p - C_v = 28R$

Correct answer: A

A charged particle moves through a magnetic field perpendicular to its direction. Then

1. A.the momentum changes but the kinetic energy is constant✓
2. B.both momentum and kinetic energy of the particle are not constant
3. C.both, momentum and kinetic energy of the particle are constant
4. D.kinetic energy changes but the momentum is constant

Correct answer: A

Two identical conducting wires AOB and COD are placed at right angles to each other. The wire AOB carries an electric current $I_1$ and COD carries a current $I_2$. The magnetic field on a point lying at a distance 'd' from O, in a direction perpendicular to the plane of the wires AOB and COD, will be given by

1. A.$\frac{\mu_0}{2\pi}\left(\frac{I_1+I_2}{d}\right)^{1/2}$
2. B.$\frac{\mu_0}{2\pi d}(I_1^2+I_2^2)^{1/2}$✓
3. C.$\frac{\mu_0}{2\pi d}(I_1+I_2)$
4. D.$\frac{\mu_0}{2\pi d}(I_1^2+I_2^2)$

Correct answer: B

The resistance of a wire is 5 ohm at $50^\circ$C and 6 ohm at $100^\circ$C. The resistance of the wire at $0^\circ$C will be

1. A.2 ohm
2. B.1 ohm
3. C.4 ohm✓
4. D.3 ohm

Correct answer: C

A parallel plate condenser with a dielectric of dielectric constant K between the plates has a capacity C and is charged to a potential V volts. The dielectric slab is slowly removed from between the plates and then reinserted. The net work done by the system in this process is

1. A.$\frac{1}{2}(K-1)CV^2$
2. B.$CV^2(K-1)/K$
3. C.$(K-1)CV^2$
4. D.zero✓

Correct answer: D

If $g_E$ and $g_m$ are the accelerations due to gravity on the surfaces of the earth and the moon respectively and if Millikan's oil drop experiment could be performed on the two surfaces, one will find the ratio $\frac{\text{electronic charge on the moon}}{\text{electronic charge on the earth}}$ to be

1. A.1✓
2. B.0
3. C.$g_E/g_m$
4. D.$g_m/g_E$

Correct answer: A

A circular disc of radius R is removed from a bigger circular disc of radius 2R such that the circumferences of the discs coincide. The centre of mass of the new disc is $\alpha/R$ from the centre of the bigger disc. The value of $\alpha$ is

1. A.1/3✓
2. B.1/2
3. C.1/6
4. D.1/4

Correct answer: A

A round uniform body of radius R, mass M and moment of inertia 'I', rolls down (without slipping) an inclined plane making an angle $\theta$ with the horizontal. Then its acceleration is

1. A.$\frac{g\sin\theta}{1+I/MR^2}$✓
2. B.$\frac{g\sin\theta}{1+MR^2/I}$
3. C.$\frac{g\sin\theta}{1-I/MR^2}$
4. D.$\frac{g\sin\theta}{1-MR^2/I}$

Correct answer: A

Angular momentum of the particle rotating with a central force is constant due to

1. A.Constant Force
2. B.Constant linear momentum.
3. C.Zero Torque✓
4. D.Constant Torque

Correct answer: C

A 2 kg block slides on a horizontal floor with a speed of 4 m/s. It strikes a uncompressed spring, and compresses it till the block is motionless. The kinetic friction force is 15 N and spring constant is 10,000 N/m. The spring compresses by

1. A.5.5 cm✓
2. B.2.5 cm
3. C.11.0 cm
4. D.8.5 cm

Correct answer: A

A particle is projected at $60^\circ$ to the horizontal with a kinetic energy K. The kinetic energy at the highest point is

1. A.K
2. B.Zero
3. C.K/2
4. D.K/4✓

Correct answer: D

In a Young's double slit experiment the intensity at a point where the path difference is $\frac{\lambda}{6}$ ($\lambda$ being the wavelength of the light used) is I. If $I_0$ denotes the maximum intensity, $\frac{I}{I_0}$ is equal to

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

Correct answer: D

Two springs, of force constants $k_1$ and $k_2$, are connected to a mass m as shown. The frequency of oscillation of the mass is f. If both $k_1$ and $k_2$ are made four times their original values, the frequency of oscillation becomes

1. A.f/2
2. B.f/4
3. C.4f
4. D.2f✓

Correct answer: D

When a system is taken from state i to state f along the path iaf, it is found that Q = 50 cal and W = 20 cal. Along the path ibf Q = 36 cal. W along the path ibf is

1. A.6 cal✓
2. B.16 cal
3. C.66 cal
4. D.14 cal

Correct answer: A

A particle of mass m executes simple harmonic motion with amplitude 'a' and frequency '$\nu$'. The average kinetic energy during its motion from the position of equilibrium to the end is

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

Correct answer: A

The energies of activation for forward and reverse reactions for $A_2 + B_2 \rightleftharpoons 2AB$ are 180 kJ mol$^{-1}$ and 200 kJ mol$^{-1}$ respectively. The presence of catalyst lowers the activation energy of both (forward and reverse) reactions by 100 kJ mol$^{-1}$. The enthalpy change of the reaction $(A_2 + B_2 \rightarrow 2AB)$ in the presence of catalyst will be (in kJ mol$^{-1}$)

1. A.300
2. B.120
3. C.280
4. D.20✓

Correct answer: D

The cell, $Zn|Zn^{2+}(1M)||Cu^{2+}(1M)|Cu$ ($E^\circ_{cell} = 1.10$ V), was allowed to be completely discharged at 298 K. The relative concentration of $Zn^{2+}$ to $Cu^{2+}$ $\left(\frac{[Zn^{2+}]}{[Cu^{2+}]}\right)$ is

1. A.antilog (24.08)
2. B.37.3
3. C.$10^{37.3}$✓
4. D.$9.65\times10^4$