AIEEE 2012 — 29 Apr Offline Set C (Previous Year Paper)

The equation $e^{\sin x} - e^{-\sin x} - 4 = 0$ has

1. A.infinite number of real roots
2. B.no real roots✓
3. C.exactly one real root
4. D.exactly four real roots

Correct answer: B

Let $\hat{a}$ and $\hat{b}$ be two unit vectors. If the vectors $\vec{c} = \hat{a} + 2\hat{b}$ and $\vec{d} = 5\hat{a} - 4\hat{b}$ are perpendicular to each other, then the angle between $\hat{a}$ and $\hat{b}$ is

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

Correct answer: C

A spherical balloon is filled with $4500\pi$ cubic meters of helium gas. If a leak in the balloon causes the gas to escape at the rate of $72\pi$ cubic meters per minute, then the rate (in meters per minute) at which the radius of the balloon decreases 49 minutes after the leakage began is

1. A.$\frac{9}{7}$
2. B.$\frac{7}{9}$
3. C.$\frac{2}{9}$✓
4. D.$\frac{9}{2}$

Correct answer: C

Statement 1: The sum of the series $1 + (1 + 2 + 4) + (4 + 6 + 9) + (9 + 12 + 16) + \dots + (361 + 380 + 400)$ is 8000. Statement 2: $\sum_{k=1}^{n}\left(k^3 - (k-1)^3\right) = n^3$ for any natural number n.

1. A.Statement 1 is false, statement 2 is true
2. B.Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1✓
3. C.Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1
4. D.Statement 1 is true, statement 2 is false

Correct answer: B

The negation of the statement 'If I become a teacher, then I will open a school' is

1. A.I will become a teacher and I will not open a school✓
2. B.Either I will not become a teacher or I will not open a school
3. C.Neither I will become a teacher nor I will open a school
4. D.I will not become a teacher or I will open a school

Correct answer: A

If the integral $\int\frac{5\tan x}{\tan x - 2}\,dx = x + a\ln|\sin x - 2\cos x| + k$, then a is equal to

1. A.$-1$
2. B.$-2$
3. C.1
4. D.2✓

Correct answer: D

Statement 1: An equation of a common tangent to the parabola $y^2 = 16\sqrt{3}x$ and the ellipse $2x^2 + y^2 = 4$ is $y = 2x + 2\sqrt{3}$. Statement 2: If the line $y = mx + \frac{4\sqrt{3}}{m}$, $(m \ne 0)$ is a common tangent to the parabola $y^2 = 16\sqrt{3}x$ and the ellipse $2x^2 + y^2 = 4$, then m satisfies $m^4 + 2m^2 = 24$.

1. A.Statement 1 is false, statement 2 is true
2. B.Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1✓
3. C.Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1
4. D.Statement 1 is true, statement 2 is false

Correct answer: B

Let $A = \begin{pmatrix} 1 & 0 & 0 \\ 2 & 1 & 0 \\ 3 & 2 & 1 \end{pmatrix}$. If $u_1$ and $u_2$ are column matrices such that $Au_1 = \begin{pmatrix} 1 \\ 0 \\ 0 \end{pmatrix}$ and $Au_2 = \begin{pmatrix} 0 \\ 1 \\ 0 \end{pmatrix}$, then $u_1 + u_2$ is equal to

1. A.$\begin{pmatrix} -1 \\ 1 \\ 0 \end{pmatrix}$
2. B.$\begin{pmatrix} -1 \\ 1 \\ -1 \end{pmatrix}$
3. C.$\begin{pmatrix} -1 \\ -1 \\ 0 \end{pmatrix}$
4. D.$\begin{pmatrix} 1 \\ -1 \\ -1 \end{pmatrix}$✓

Correct answer: D

If n is a positive integer, then $\left(\sqrt{3}+1\right)^{2n} - \left(\sqrt{3}-1\right)^{2n}$ is

1. A.an irrational number✓
2. B.an odd positive integer
3. C.an even positive integer
4. D.a rational number other than positive integers

Correct answer: A

If 100 times the $100^{th}$ term of an AP with non zero common difference equals the 50 times its $50^{th}$ term, then the $150^{th}$ term of this AP is

1. A.$-150$
2. B.150 times its $50^{th}$ term
3. C.150
4. D.zero✓

Correct answer: D

In a $\triangle PQR$, if $3\sin P + 4\cos Q = 6$ and $4\sin Q + 3\cos P = 1$, then the angle R is equal to

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

Correct answer: B

An equation of a plane parallel to the plane $x - 2y + 2z - 5 = 0$ and at a unit distance from the origin is

1. A.$x - 2y + 2z - 3 = 0$✓
2. B.$x - 2y + 2z + 1 = 0$
3. C.$x - 2y + 2z - 1 = 0$
4. D.$x - 2y + 2z + 5 = 0$

Correct answer: A

If the line $2x + y = k$ passes through the point which divides the line segment joining the points (1, 1) and (2, 4) in the ratio 3 : 2, then k equals

1. A.$\frac{29}{5}$
2. B.5
3. C.6✓
4. D.$\frac{11}{5}$

Correct answer: C

Let $x_1, x_2, \dots, x_n$ be n observations, and let $\bar{x}$ be their arithmetic mean and $\sigma^2$ be their variance. Statement 1: Variance of $2x_1, 2x_2, \dots, 2x_n$ is $4\sigma^2$. Statement 2: Arithmetic mean of $2x_1, 2x_2, \dots, 2x_n$ is $4\bar{x}$.

1. A.Statement 1 is false, statement 2 is true
2. B.Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1
3. C.Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1
4. D.Statement 1 is true, statement 2 is false✓

Correct answer: D

The population p(t) at time t of a certain mouse species satisfies the differential equation $\frac{dp(t)}{dt} = 0.5\,p(t) - 450$. If $p(0) = 850$, then the time at which the population becomes zero is

1. A.$2\ln18$✓
2. B.$\ln9$
3. C.$\frac{1}{2}\ln18$
4. D.$\ln18$

Correct answer: A

Let $a, b \in \mathbb{R}$ be such that the function f given by $f(x) = \ln|x| + bx^2 + ax$, $x \ne 0$ has extreme values at $x = -1$ and $x = 2$. Statement 1: f has local maximum at $x = -1$ and at $x = 2$. Statement 2: $a = \frac{1}{2}$ and $b = \frac{-1}{4}$.

1. A.Statement 1 is false, statement 2 is true
2. B.Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1✓
3. C.Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1
4. D.Statement 1 is true, statement 2 is false

Correct answer: B

The area bounded between the parabolas $x^2 = \frac{y}{4}$ and $x^2 = 9y$, and the straight line $y = 2$ is

1. A.$20\sqrt{2}$
2. B.$\frac{10\sqrt{2}}{3}$
3. C.$\frac{20\sqrt{2}}{3}$✓
4. D.$10\sqrt{2}$

Correct answer: C

Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be selected from 10 white, 9 green and 7 black balls is

1. A.880
2. B.629
3. C.630
4. D.879✓

Correct answer: D

If $f : \mathbb{R} \to \mathbb{R}$ is a function defined by $f(x) = [x]\cos\left(\frac{2x-1}{2}\right)\pi$, where [x] denotes the greatest integer function, then f is

1. A.continuous for every real x✓
2. B.discontinuous only at $x = 0$
3. C.discontinuous only at non-zero integral values of x
4. D.continuous only at $x = 0$

Correct answer: A

If the lines $\frac{x-1}{2} = \frac{y+1}{3} = \frac{z-1}{4}$ and $\frac{x-3}{1} = \frac{y-k}{2} = \frac{z}{1}$ intersect, then k is equal to

1. A.$-1$
2. B.$\frac{2}{9}$
3. C.$\frac{9}{2}$✓
4. D.0

Correct answer: C

Three numbers are chosen at random without replacement from {1, 2, 3, ......, 8}. The probability that their minimum is 3, given that their maximum is 6, is

1. A.$\frac{3}{8}$
2. B.$\frac{1}{5}$✓
3. C.$\frac{1}{4}$
4. D.$\frac{2}{5}$

Correct answer: B

If $z \ne 1$ and $\frac{z^2}{z-1}$ is real, then the point represented by the complex number z lies

1. A.either on the real axis or on a circle passing through the origin✓
2. B.on a circle with centre at the origin
3. C.either on the real axis or on a circle not passing through the origin
4. D.on the imaginary axis

Correct answer: A

Let P and Q be $3\times3$ matrices with $P \ne Q$. If $P^3 = Q^3$ and $P^2Q = Q^2P$, then determinant of $(P^2 + Q^2)$ is equal to

1. A.$-2$
2. B.1
3. C.0✓
4. D.$-1$

Correct answer: C

The length of the diameter of the circle which touches the x-axis at the point (1, 0) and passes through the point (2, 3) is

1. A.$\frac{10}{3}$✓
2. B.$\frac{3}{5}$
3. C.$\frac{6}{5}$
4. D.$\frac{5}{3}$

Correct answer: A

Let X = {1, 2, 3, 4, 5}. The number of different ordered pairs (Y, Z) that can be formed such that $Y \subseteq X$, $Z \subseteq X$ and $Y \cap Z$ is empty, is

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

Correct answer: B

An ellipse is drawn by taking a diameter of the circle $(x - 1)^2 + y^2 = 1$ as its semiminor axis and a diameter of the circle $x^2 + (y - 2)^2 = 4$ as its semi-major axis. If the centre of the ellipse is the origin and its axes are the coordinate axes, then the equation of the ellipse is

1. A.$4x^2 + y^2 = 4$
2. B.$x^2 + 4y^2 = 8$
3. C.$4x^2 + y^2 = 8$
4. D.$x^2 + 4y^2 = 16$✓

Correct answer: D

Consider the function $f(x) = |x - 2| + |x - 5|$, $x \in \mathbb{R}$. Statement 1: $f'(4) = 0$. Statement 2: f is continuous in [2, 5], differentiable in (2, 5) and $f(2) = f(5)$.

1. A.Statement 1 is false, statement 2 is true
2. B.Statement 1 is true, statement 2 is true; statement 2 is a correct explanation for statement 1✓
3. C.Statement 1 is true, statement 2 is true; statement 2 is not a correct explanation for statement 1
4. D.Statement 1 is true, statement 2 is false

Correct answer: B

A line is drawn through the point (1, 2) to meet the coordinate axes at P and Q such that it forms a triangle OPQ, where O is the origin. If the area of the triangle OPQ is least, then the slope of the line PQ is

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

Correct answer: C

Let ABCD be a parallelogram such that $\vec{AB} = \vec{q}$, $\vec{AD} = \vec{p}$ and $\angle BAD$ be an acute angle. If $\vec{r}$ is the vector that coincides with the altitude directed from the vertex B to the side AD, then $\vec{r}$ is given by

1. A.$\vec{r} = 3\vec{q} - \frac{3(\vec{p}\cdot\vec{q})}{(\vec{p}\cdot\vec{p})}\vec{p}$
2. B.$\vec{r} = -\vec{q} + \left(\frac{\vec{p}\cdot\vec{q}}{\vec{p}\cdot\vec{p}}\right)\vec{p}$✓
3. C.$\vec{r} = \vec{q} - \left(\frac{\vec{p}\cdot\vec{q}}{\vec{p}\cdot\vec{p}}\right)\vec{p}$
4. D.$\vec{r} = -3\vec{q} + \frac{3(\vec{p}\cdot\vec{q})}{(\vec{p}\cdot\vec{p})}\vec{p}$

Correct answer: B

A wooden wheel of radius R is made of two semicircular parts (see figure). The two parts are held together by a ring made of a metal strip of cross sectional area S and length L. L is slightly less than $2\pi R$. To fit the ring on the wheel, it is heated so that its temperature rises by $\Delta T$ and it just steps over the wheel. As it cools down to surrounding temperature, it presses the semicircular parts together. If the coefficient of linear expansion of the metal is $\alpha$, and its Youngs' modulus is Y, the force that one part of the wheel applies on the other part is :

1. A.$2\pi SY\alpha\Delta T$
2. B.$SY\alpha\Delta T$
3. C.$\pi SY\alpha\Delta T$
4. D.$2SY\alpha\Delta T$✓

Correct answer: D

The figure shows an experimental plot for discharging of a capacitor in an R-C circuit. The time constant $\tau$ of this circuit lies between:

1. A.150 sec and 200 sec
2. B.0 and 50 sec
3. C.50 sec and 100 sec
4. D.100 sec and 150 sec✓

Correct answer: D

In a uniformly charged sphere of total charge Q and radius R, the electric field E is plotted as a function of distance from the centre. The graph which would correspond to the above will be

1. A.Graph (1)
2. B.Graph (2)
3. C.Graph (3)✓
4. D.Graph (4)

Correct answer: C

If a simple pendulum has significant amplitude (up to a factor of 1/e of original) only in the period between $t = 0$ s to $t = \tau$ s, then $\tau$ may be called the average life of the pendulum. When the spherical bob of the pendulum suffers a retardation (due to viscous drag) proportional to its velocity, with 'b' as the constant of proportionality, the average life time of the pendulum is (assuming damping is small) in seconds:

1. A.$\frac{0.693}{b}$
2. B.b
3. C.$\frac{1}{b}$
4. D.$\frac{2}{b}$✓

Correct answer: D

Hydrogen atom is excited from ground state to another state with principal quantum number equal to 4. Then the number of spectral lines in the emission spectra will be

1. A.2
2. B.3
3. C.5
4. D.6✓

Correct answer: D

A coil is suspended in a uniform magnetic field, with the plane of the coil parallel to the magnetic lines of force. When a current is passed through the coil it starts oscillating; it is very difficult to stop. But if an aluminium plate is placed near to the coil, it stops. This is due to :

1. A.development of air current when the plate is placed.
2. B.induction of electrical charge on the plate
3. C.shielding of magnetic lines of force as aluminium is a paramagnetic material.
4. D.electromagnetic induction in the aluminium plate giving rise to electromagnetic damping.✓

Correct answer: D

The mass of a spaceship is 1000 kg. It is to be launched from the earth's surface out into free space. The value of 'g' and 'R' (radius of earth) are 10 m/s$^2$ and 6400 km respectively. The required energy for this work will be ;

1. A.$6.4\times10^{11}$ Joules
2. B.$6.4\times10^8$ Joules
3. C.$6.4\times10^9$ Joules
4. D.$6.4\times10^{10}$ Joules✓

Correct answer: D

Helium gas goes through a cycle ABCDA (consisting of two isochoric and two isobaric lines) as shown in figure. Efficiency of this cycle is nearly: (Assume the gas to be close to ideal gas)

1. A.15.4%✓
2. B.9.1%
3. C.10.5%
4. D.12.5%

Correct answer: A

In Young's double slit experiment, one of the slit is wider than other, so that the amplitude of the light from one slit is double of that from other slit. If $I_m$ be the maximum intensity, the resultant intensity I when they interfere at phase difference $\phi$ is given by

1. A.$\frac{I_m}{9}(4 + 5\cos\phi)$
2. B.$\frac{I_m}{3}\left(1 + 2\cos^2\frac{\phi}{2}\right)$
3. C.$\frac{I_m}{5}\left(1 + 4\cos^2\frac{\phi}{2}\right)$
4. D.$\frac{I_m}{9}\left(1 + 8\cos^2\frac{\phi}{2}\right)$✓

Correct answer: D

A liquid in a beaker has temperature $\theta(t)$ at time t and $\theta_0$ is temperature of surroundings, then according to Newton's law of cooling the correct graph between $\log_e(\theta - \theta_0)$ and t is

1. A.Graph (1)✓
2. B.Graph (2)
3. C.Graph (3)
4. D.Graph (4)

Correct answer: A

A particle of mass m is at rest at the origin at time $t = 0$. It is subjected to a force $F(t) = F_0e^{-bt}$ in the x direction. Its speed v(t) is depicted by which of the following curves?

1. A.Graph (1)
2. B.Graph (2)
3. C.Graph (3)✓
4. D.Graph (4)

Correct answer: C

Two electric bulbs marked 25W - 220V and 100W - 220V are connected in series to a 440V supply. Which of the bulbs will fuse?

1. A.both
2. B.100 W
3. C.25 W✓
4. D.neither

Correct answer: C

Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied across it. If the percentage errors in the measurement of the current and the voltage difference are 3% each, then error in the value of resistance of the wire is

1. A.6%✓
2. B.zero
3. C.1%
4. D.3%

Correct answer: A

A boy can throw a stone up to a maximum height of 10 m. The maximum horizontal distance that the boy can throw the same stone up to will be

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

Correct answer: D

Statement 1: Davisson - Germer experiment established the wave nature of electrons. Statement 2: If electrons have wave nature, they can interfere and show diffraction.

1. A.Statement 1 is false, Statement 2 is true
2. B.Statement 1 is true, Statement 2 is false
3. C.Statement 1 is true, Statement 2 is the correct explanation for statement 1✓
4. D.Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation for statement 1.

Correct answer: C

A thin liquid film formed between a U-shaped wire and a light slider supports a weight of $1.5\times10^{-2}$ N (see figure). The length of the slider is 30 cm and its weight negligible. The surface tension of the liquid film is

1. A.0.0125 Nm$^{-1}$
2. B.0.1 Nm$^{-1}$
3. C.0.05 Nm$^{-1}$
4. D.0.025 Nm$^{-1}$✓

Correct answer: D

A charge Q is uniformly distributed over the surface of non conducting disc of radius R. The disc rotates about an axis perpendicular to its plane and passing through its centre with an angular velocity $\omega$. As a result of this rotation a magnetic field of induction B is obtained at the centre of the disc. If we keep both the amount of charge placed on the disc and its angular velocity to be constant and vary the radius of the disc then the variation of the magnetic induction at the centre of the disc will be represented by the figure

1. A.Graph (1)✓
2. B.Graph (2)
3. C.Graph (3)
4. D.Graph (4)

Correct answer: A

Truth table for system of four NAND gates as shown in figure is

1. A.A,B,Y: 00-0, 01-1, 10-1, 11-0✓
2. B.A,B,Y: 00-0, 01-0, 10-1, 11-1
3. C.A,B,Y: 00-1, 01-1, 10-0, 11-0
4. D.A,B,Y: 00-1, 01-0, 10-0, 11-1

Correct answer: A

A radar has a power of 1 Kw and is operating at a frequency of 10 GHz. It is located on a mountain top of height 500 m. The maximum distance upto which it can detect object located on the surface of the earth (Radius of earth = $6.4\times10^6$ m) is

1. A.80 km✓
2. B.16 km
3. C.40 km
4. D.64 km

Correct answer: A

A Carnot engine, whose efficiency is 40%, takes in heat from a source maintained at a temperature of 500 K. It is desired to have an engine of efficiency 60%. Then, the intake temperature for the same exhaust (sink) temperature must be

1. A.efficiency of Carnot engine cannot be made larger than 50%
2. B.1200 K
3. C.750 K✓
4. D.600 K

Correct answer: C

If two springs $S_1$ and $S_2$ of force constants $k_1$ and $k_2$, respectively, are stretched by the same force, it is found that more work is done on spring $S_1$ than on spring $S_2$. Statement 1: If stretched by the same amount, work done on $S_1$, will be more than that on $S_2$. Statement 2: $k_1 < k_2$

1. A.Statement 1 is false, Statement 2 is true✓
2. B.Statement 1 is true, Statement 2 is false
3. C.Statement 1 is true, Statement 2 is the correct explanation for statement 1
4. D.Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation for statement 1.

Correct answer: A

Two cars of masses $m_1$ and $m_2$ are moving in circles of radii $r_1$ and $r_2$, respectively. Their speeds are such that they make complete circles in the same time t. The ratio of their centripetal acceleration is

1. A.$m_1r_1 : m_2r_2$
2. B.$m_1 : m_2$
3. C.$r_1 : r_2$✓
4. D.1 : 1

Correct answer: C

A cylindrical tube, open at both ends, has a fundamental frequency, f, in air. The tube is dipped vertically in water so that half of it is in water. The fundamental frequency of the air-column is now

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

Correct answer: A

An object 2.4 m in front of a lens forms a sharp image on a film 12 cm behind the lens. A glass plate 1cm thick, of refractive index 1.50 is interposed between lens and film with its plane faces parallel to film. At what distance (from lens) should object be shifted to be in sharp focus on film?

1. A.7.2 m
2. B.2.4 m
3. C.3.2 m
4. D.5.6 m✓

Correct answer: D

A diatomic molecule is made of two masses $m_1$ and $m_2$ which are separated by a distance r. If we calculate its rotational energy by applying Bohr's rule of angular momentum quantization, its energy will be given by (n is an integer)

1. A.$\frac{(m_1+m_2)^2n^2h^2}{2m_1^2m_2^2r^2}$
2. B.$\frac{n^2h^2}{2(m_1+m_2)r^2}$
3. C.$\frac{2n^2h^2}{(m_1+m_2)r^2}$
4. D.$\frac{(m_1+m_2)n^2h^2}{2m_1m_2r^2}$✓

Correct answer: D

A spectrometer gives the following reading when used to measure the angle of a prism. Main scale reading: 58.5 degree. Vernier scale reading: 09 divisions. Given that 1 division on main scale corresponds to 0.5 degree. Total divisions on the vernier scale is 30 and match with 29 divisions of the main scale. The angle of the prism from the above data

1. A.$58.59^\circ$
2. B.$58.77^\circ$
3. C.$58.65^\circ$✓
4. D.$59^\circ$

Correct answer: C

An insulating solid sphere of radius R has a uniformly positive charge density $\rho$. As a result of this uniform charge distribution there is a finite value of electric potential at the centre of the sphere, at the surface of the sphere and also at a point out side the sphere. The electric potential at infinity is zero. Statement 1: When a charge q is taken from the centre to the surface of the sphere, its potential energy changes by $\frac{q\rho}{3\epsilon_0}$. Statement 2: The electric field at a distance r (r < R) from the centre of the sphere is $\frac{\rho r}{3\epsilon_0}$.

1. A.Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation for statement 1.
2. B.Statement 1 is true, Statement 2 is false
3. C.Statement 1 is false, Statement 2 is true✓
4. D.Statement 1 is true, Statement 2 is the correct explanation for statement 1

Correct answer: C

Proton, Deuteron and alpha particle of the same kinetic energy are moving in circular trajectories in a constant magnetic field. The radii of proton, deuteron and alpha particle are respectively $r_p$, $r_d$ and $r_\alpha$. Which one of the following relations is correct?

1. A.$r_\alpha = r_p = r_d$
2. B.$r_\alpha = r_p < r_d$✓
3. C.$r_\alpha > r_d > r_p$
4. D.$r_\alpha = r_d > r_p$

Correct answer: B

Which among the following will be named as dibromidobis(ethylene diamine)chromium(III) bromide ?

1. A.$[Cr(en)_3]Br_3$
2. B.$[Cr(en)_2Br_2]Br$✓
3. C.$[Cr(en)Br_4]^-$
4. D.$[Cr(en)Br_2]Br$

Correct answer: B

Which method of purification is represented by the following equation : $Ti(s) + 2I_2(g) \xrightarrow{523K} TiI_4(g) \xrightarrow{1700K} Ti(s) + 2I_2(g)$

1. A.zone refining
2. B.cupellation
3. C.Poling
4. D.Van Arkel✓

Correct answer: D

Lithium forms body centred cubic structure. The length of the side of its unit cell is 351 pm. Atomic radius of the lithium will be :

1. A.75 pm
2. B.300 pm
3. C.240 pm
4. D.152 pm✓

Correct answer: D

The molecule having smallest bond angle is :

1. A.$NCl_3$
2. B.$AsCl_3$
3. C.$SbCl_3$✓
4. D.$PCl_3$

Correct answer: C

Which of the following compounds can be detected by Molisch's test ?

1. A.Nitro compounds
2. B.Sugars✓
3. C.Amines
4. D.Primary alcohols

Correct answer: B

The incorrect expression among the following is :

1. A.$\frac{\Delta G_{system}}{\Delta S_{total}} = -T$
2. B.In isothermal process $w_{reversible} = -nRT\ln\frac{V_f}{V_i}$
3. C.$\ln K = \frac{\Delta H^\circ - T\Delta S^\circ}{RT}$✓
4. D.$K = e^{-\Delta G^\circ/RT}$

Correct answer: C

The density of a solution prepared by dissolving 120 g of urea (mol. Mass = 60 u) in 1000g of water is 1.15 g/mL. The molarity of this solution is :

1. A.0.50 M
2. B.1.78 M
3. C.1.02 M
4. D.2.05 M✓

Correct answer: D

The species which can best serve as an initiator for the cationic polymerization is :

1. A.$LiAlH_4$
2. B.$HNO_3$
3. C.$AlCl_3$✓
4. D.BuLi

Correct answer: C

Which of the following on thermal decomposition yields a basic as well as an acidic oxide ?

1. A.$NaNO_3$
2. B.$KClO_3$
3. C.$CaCO_3$✓
4. D.$NH_4NO_3$

Correct answer: C

The standard reduction potentials for $Zn^{2+}/Zn$, $Ni^{2+}/Ni$, and $Fe^{2+}/Fe$ are $-0.76$, $-0.23$ and $-0.44$ V respectively. The reaction $X + Y^{2+} \rightarrow X^{2+} + Y$ will be spontaneous when :