AIEEE 2011 — 1 May Offline Set Q (Previous Year Paper)

The transverse displacement y(x, t) of a wave on a string is given by $y(x,t) = e^{-\left(ax^2 + bt^2 + 2\sqrt{ab}\,xt\right)}$. This represents a

1. A.wave moving in $-x$ direction with speed $\sqrt{\frac{b}{a}}$✓
2. B.standing wave of frequency $\sqrt{b}$
3. C.standing wave of frequency $\frac{1}{\sqrt{b}}$
4. D.wave moving in $+x$ direction with $\sqrt{\frac{a}{b}}$

Correct answer: A

A screw gauge gives the following reading when used to measure the diameter of a wire. Main scale reading : 0 mm. Circular scale reading : 52 divisions. Given that 1 mm on main scale corresponds to 100 divisions of the circular scale. The diameter of wire from the above data is :

1. A.0.052 cm✓
2. B.0.026 cm
3. C.0.005 cm
4. D.0.52 cm

Correct answer: A

A mass m hangs with the help of a string wrapped around a pulley on a frictionless bearing. The pulley has mass m and radius R. Assuming pulley to be a perfect uniform circular disc, the acceleration of the mass m, if the string does not slip on the pulley, is

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

Correct answer: B

Work done in increasing the size of a soap bubble from a radius of 3 cm to 5 cm is nearly (Surface tension of soap solution = 0.03 Nm$^{-1}$):

1. A.$0.2\pi$ mJ
2. B.$2\pi$ mJ
3. C.$0.4\pi$ mJ✓
4. D.$4\pi$ mJ

Correct answer: C

A thin horizontal circular disc is rotating about a vertical axis passing through its centre. An insect is at rest at a point near the rim of the disc. The insect now moves along a diameter of the disc to reach its other end. During the journey of the insect, the angular speed of the disc:

1. A.continuously decreases
2. B.continuously increases
3. C.first increases and then decreases✓
4. D.remains unchanged

Correct answer: C

Two bodies of masses m and 4 m are placed at a distance r. The gravitational potential at a point on the line joining them where the gravitational field is zero is:

1. A.$-\frac{4Gm}{r}$
2. B.$-\frac{6Gm}{r}$
3. C.$-\frac{9Gm}{r}$✓
4. D.zero

Correct answer: C

Two identical charged spheres suspended from a common point by two massless strings of length l are initially a distance d $(d \ll 1)$ apart because of their mutual repulsion. The charge begins to leak from both the spheres at a constant rate. As a result the charges approach each other with a velocity v. Then as a function of distance x between them,

1. A.$v \propto x^{-1}$
2. B.$v \propto x^{1/2}$
3. C.$v \propto x$
4. D.$v \propto x^{-1/2}$✓

Correct answer: D

A boat is moving due east in a region where the earth's magnetic field is $5.0\times10^{-5}$ NA$^{-1}$m$^{-1}$ due north and horizontal. The boat carries a vertical aerial 2m long. If the speed of the boat is 1.50 ms$^{-1}$, the magnitude of the induced emf in the wire of aerial is :

1. A.0.75 mV
2. B.0.50 mV
3. C.0.15 mV✓
4. D.1 mV

Correct answer: C

An object, moving with a speed of 6.25 m/s, is decelerated at a rate given by : $\frac{dv}{dt} = -2.5\sqrt{v}$ where v is the instantaneous speed. The time taken by the object, to come to rest, would be :

1. A.2 s✓
2. B.4 s
3. C.8 s
4. D.1 s

Correct answer: A

A fully charged capacitor C with initial charge $q_0$ is connected to a coil of self inductance L at $t = 0$. The time at which the energy is stored equally between the electric and the magnetic field is :

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

Correct answer: A

Let the x - z plane be the boundary between two transparent media. Medium 1 in $z \ge 0$ has a refractive index of $\sqrt{2}$ and medium 2 with $z < 0$ has a refractive index of $\sqrt{3}$. A ray of light in medium 1 given by the vector $\vec{A} = 6\sqrt{3}\hat{i} + 8\sqrt{3}\hat{j} - 10\hat{k}$ is incident on the plane of separation. The angle of refraction in medium 2 is

1. A.$45^\circ$✓
2. B.$60^\circ$
3. C.$75^\circ$
4. D.$30^\circ$

Correct answer: A

A current I flows in an infinitely long wire with cross section in the form of a semicircular ring of radius R. The magnitude of the magnetic induction along its axis is

1. A.$\frac{\mu_0I}{2\pi^2R}$
2. B.$\frac{\mu_0I}{2\pi R}$
3. C.$\frac{\mu_0I}{4\pi^2R}$
4. D.$\frac{\mu_0I}{\pi^2R}$✓

Correct answer: D

A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heats $\gamma$. It is moving with speed v and is suddenly brought to rest. Assuming no heat is lost to the surroundings, its temperature increases by :

1. A.$\frac{(\gamma-1)}{2\gamma R}Mv^2$ K
2. B.$\frac{\gamma Mv^2}{2R}$ K
3. C.$\frac{(\gamma-1)}{2R}Mv^2$ K✓
4. D.$\frac{(\gamma-1)}{2(\gamma+1)R}Mv^2$ K

Correct answer: C

A mass M, attached to a horizontal spring, executes S.H.M. with amplitude $A_1$. When the mass M passes through its mean position then a smaller mass m is placed over it and both of them move together with amplitude $A_2$. The ratio of $\left(\frac{A_1}{A_2}\right)$ is :

1. A.$\frac{M+m}{M}$
2. B.$\left(\frac{M}{M+m}\right)^{1/2}$
3. C.$\left(\frac{M+m}{M}\right)^{1/2}$✓
4. D.$\frac{M}{M+m}$

Correct answer: C

Water is flowing continuously from a tap having an internal diameter $8\times10^{-3}$ m. The water velocity as it leaves the tap is 0.4 ms$^{-1}$. The diameter of the water stream at a distance $2\times10^{-1}$ m below the tap is close to :

1. A.$7.5\times10^{-3}$ m
2. B.$9.6\times10^{-3}$ m
3. C.$3.6\times10^{-3}$ m✓
4. D.$5.0\times10^{-3}$ m

Correct answer: C

Statement-1 : Sky wave signals are used for long distance radio communication. These signals are in general, less stable than ground wave signals. Statement-2 : The state of ionosphere varies from hour to hour, day to day and season to season.

1. A.Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation of Statement-1.✓
2. B.Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation of Statement-1.
3. C.Statement-1 is false, Statement-2 is true.
4. D.Statement-1 is true, Statement-2 is false.

Correct answer: A

Three perfect gases at absolute temperatures $T_1$, $T_2$ and $T_3$ are mixed. The masses of molecules are $m_1$, $m_2$ and $m_3$ and the number of molecules are $n_1$, $n_2$ and $n_3$ respectively. Assuming no loss of energy, the final temperature of the mixture is :

1. A.$\frac{n_1T_1 + n_2T_2 + n_3T_3}{n_1 + n_2 + n_3}$✓
2. B.$\frac{n_1T_1 + n_2T_2^2 + n_3T_3^2}{n_1T_1 + n_2T_2 + n_3T_3}$
3. C.$\frac{n_1^2T_1^2 + n_2^2T_2^2 + n_3^2T_3^2}{n_1T_1 + n_2T_2 + n_3T_3}$
4. D.$\frac{(T_1 + T_2 + T_3)}{3}$

Correct answer: A

A pulley of radius 2 m is rotated about its axis by a force $F = (20t - 5t^2)$ Newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m$^2$, the number of rotations made by the pulley before its direction of motion is reversed, is :

1. A.more than 3 but less than 6✓
2. B.more than 6 but less than 9
3. C.more than 9
4. D.less than 3

Correct answer: A

A resistor R and $2\,\mu$F capacitor in series is connected through a switch to 200 V direct supply. Across the capacitor is a neon bulb that lights up at 120 V. Calculate the value of R to make the bulb light up 5 s after the switch has been closed. ($\log_{10}2.5 = 0.4$)

1. A.$1.7\times10^5\,\Omega$
2. B.$2.7\times10^6\,\Omega$✓
3. C.$3.3\times10^7\,\Omega$
4. D.$1.3\times10^4\,\Omega$

Correct answer: B

A Carnot engine operating between temperatures $T_1$ and $T_2$ has efficiency $\frac{1}{6}$. When $T_2$ is lowered by 62 K, its efficiency increases to $\frac{1}{3}$. Then $T_1$ and $T_2$ are, respectively :

1. A.372 K and 330 K
2. B.330 K and 268 K
3. C.310 K and 248 K
4. D.372 K and 310 K✓

Correct answer: D

If a wire is stretched to make it 0.1% longer, its resistance will :

1. A.increase by 0.2%✓
2. B.decrease by 0.2%
3. C.decrease by 0.05%
4. D.increases by 0.05%

Correct answer: A

A car is fitted with a convex side-view mirror of focal length 20cm. A second car 2.8 m behind the first car is overtaking the first car at relative speed of 15 m/s. The speed of the image of the second car as seen in the mirror of the first one is :

1. A.$\frac{1}{15}$ m/s✓
2. B.10 m/s
3. C.15 m/s
4. D.$\frac{1}{10}$ m/s

Correct answer: A

Energy required for the electron excitation in $Li^{++}$ from the first to the third Bohr orbit is :

1. A.36.3 eV
2. B.108.8 eV✓
3. C.122.4 eV
4. D.12.1 eV

Correct answer: B

The electrostatic potential inside a charged spherical ball is given by $\phi = a\rho^2 + b$ where $\rho$ is the distance from the centre; a, b are constants. Then the charge density inside ball is :

1. A.$-6a\epsilon_0\rho$
2. B.$-24\pi a\epsilon_0\rho$
3. C.$-6a\epsilon_0$✓
4. D.$-24\pi a\epsilon_0\rho$

Correct answer: C

A water fountain on the ground sprinkles water all around it. If the speed of water coming out of the fountain is v, the total area around the fountain that gets wet is :

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

Correct answer: A

100g of water is heated from $30^\circ$C to $50^\circ$C. Ignoring the slight expansion of the water, the change in its internal energy is (specific heat of water is 4148 J/kg/K):

1. A.8.4 kJ✓
2. B.84 kJ
3. C.2.1 kJ
4. D.4.2 kJ

Correct answer: A

The half life of a radioactive substance is 20 minutes. The approximate time interval $(t_2 - t_1)$ between the time $t_2$ when $\frac{2}{3}$ of it has decayed and time $t_1$ when $\frac{1}{3}$ of it had decayed is :

1. A.14 min
2. B.20 min✓
3. C.28 min
4. D.7 min

Correct answer: B

Statement-1 : A metallic surface is irradiated by a monochromatic light of frequency $\nu > \nu_0$ (the threshold frequency). The maximum kinetic energy and the stopping potential are $K_{max}$ and $V_0$ respectively. If the frequency incident on the surface doubled, both the $K_{max}$ and $V_0$ are also doubled. Statement-2 : The maximum kinetic energy and the stopping potential of photoelectrons emitted from a surface are linearly dependent on the frequency of incident light.

1. A.Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation of Statement-1.
2. B.Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation of Statement-1.
3. C.Statement-1 is false, Statement-2 is true.✓
4. D.Statement-1 is true, Statement-2 is false.

Correct answer: C

The lines $L_1 : y - x = 0$ and $L_2 : 2x + y = 0$ intersect the line $L_3 : y + 2 = 0$ at P and Q respectively. The bisector of the acute angle between $L_1$ and $L_2$ intersect $L_3$ at R. Statement-1 : The ratio PR : RQ equals $2\sqrt{2} : \sqrt{5}$. Statement-2 : In any triangle, bisector of an angle divides the triangle into two similar triangles.

1. A.Statement-1 is true, Statement-2 is true; Statement-2 is not a 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 true; Statement-2 is a correct explanation for Statement-1

Correct answer: B

If $A = \sin^2x + \cos^4x$, then for all real x

1. A.$\frac{13}{16} \le A \le 1$
2. B.$1 \le A \le 2$
3. C.$\frac{3}{4} \le A \le \frac{13}{16}$
4. D.$\frac{3}{4} \le A \le 1$✓

Correct answer: D

The coefficient of $x^7$ in the expansion of $\left(1 - x - x^2 + x^3\right)^6$ is

1. A.$-132$
2. B.$-144$✓
3. C.132
4. D.144

Correct answer: B

$\lim_{x\to2}\left(\frac{\sqrt{1-\cos\{2(x-2)\}}}{x-2}\right)$

1. A.equals $\sqrt{2}$
2. B.equals $-\sqrt{2}$
3. C.equals $\frac{1}{\sqrt{2}}$
4. D.does not exist✓

Correct answer: D

Statement-1 : The number of ways of distributing 10 identical balls in 4 distinct boxes such that no box is empty is ${}^9C_3$. Statement-2 : The number of ways of choosing any 3 places from 9 different places is ${}^9C_3$.

1. A.Statement-1 is true, Statement-2 is true; Statement-2 is not a 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 true; Statement-2 is a correct explanation for Statement-1✓

Correct answer: D

$\frac{d^2x}{dy^2}$ equals

1. A.$-\left(\frac{d^2y}{dx^2}\right)^{-1}\left(\frac{dy}{dx}\right)^{-3}$
2. B.$\left(\frac{d^2y}{dx^2}\right)\left(\frac{dy}{dx}\right)^{-2}$
3. C.$-\left(\frac{d^2y}{dx^2}\right)\left(\frac{dy}{dx}\right)^{-3}$✓
4. D.$\left(\frac{d^2y}{dx^2}\right)^{-1}$

Correct answer: C

If $\frac{dy}{dx} = y + 3 > 0$ and $y(0) = 2$, then $y(\ln2)$ is equal to

1. A.5
2. B.13
3. C.$-2$
4. D.7✓

Correct answer: D

Let R be the set of real numbers. Statement-1 : $A = \{(x, y) \in R\times R : y - x \text{ is an integer}\}$ is an equivalence relation on R. Statement-2 : $B = \{(x, y) \in R\times R : x = \alpha y \text{ for some rational number } \alpha\}$ is an equivalence relation on R.

1. A.Statement-1 is true, Statement-2 is true; Statement-2 is not a 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 true; Statement-2 is a correct explanation for Statement-1

Correct answer: B

The value of $\int_0^1\frac{8\log(1+x)}{1+x^2}\,dx$ is

1. A.$\frac{\pi}{8}\log2$
2. B.$\frac{\pi}{2}\log2$
3. C.$\log2$
4. D.$\pi\log2$✓

Correct answer: D

Let $\alpha, \beta$ be real and z be a complex number. If $z^2 + \alpha z + \beta = 0$ has two distinct roots on the line $\text{Re}\,z = 1$, then it is necessary that

1. A.$\beta \in (-1, 0)$
2. B.$|\beta| = 1$
3. C.$\beta \in (1, \infty)$✓
4. D.$\beta \in (0, 1)$

Correct answer: C

Consider 5 independent Bernoulli's trials each with probability of success p. If the probability of at least one failure is greater than or equal to $\frac{31}{32}$, then p lies in the interval

1. A.$\left(\frac{3}{4}, \frac{11}{12}\right]$
2. B.$\left[0, \frac{1}{2}\right]$✓
3. C.$\left(\frac{11}{12}, 1\right]$
4. D.$\left(\frac{1}{2}, \frac{3}{4}\right]$

Correct answer: B

A man saves Rs. 200 in each of the first three months of his service. In each of the subsequent months his saving increases by Rs. 40 more than the saving of immediately previous month. His total saving from the start of service will be Rs. 11040 after

1. A.19 months
2. B.20 months
3. C.21 months✓
4. D.18 months

Correct answer: C

The domain of the function $f(x) = \frac{1}{\sqrt{|x| - x}}$ is

1. A.$(0, \infty)$
2. B.$(-\infty, 0)$✓
3. C.$(-\infty, \infty) - \{0\}$
4. D.$(-\infty, \infty)$

Correct answer: B

If the angle between the line $x = \frac{y-1}{2} = \frac{z-3}{\lambda}$ and the plane $x + 2y + 3z = 4$ is $\cos^{-1}\left(\sqrt{\frac{5}{14}}\right)$, then $\lambda$ equals

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

Correct answer: D

If $\vec{a} = \frac{1}{\sqrt{10}}\left(3\hat{i} + \hat{k}\right)$ and $\vec{b} = \frac{1}{7}\left(2\hat{i} + 3\hat{j} - 6\hat{k}\right)$, then the value of $(2\vec{a} - \vec{b})\cdot\left[(\vec{a}\times\vec{b})\times(\vec{a} + 2\vec{b})\right]$ is

1. A.$-3$
2. B.5
3. C.3
4. D.$-5$✓

Correct answer: D

Equation of the ellipse whose axes are the axes of coordinates and which passes through the point $(-3, 1)$ and has eccentricity $\sqrt{\frac{2}{5}}$ is

1. A.$5x^2 + 3y^2 - 48 = 0$
2. B.$3x^2 + 5y^2 - 15 = 0$
3. C.$5x^2 + 3y^2 - 32 = 0$
4. D.$3x^2 + 5y^2 - 32 = 0$✓

Correct answer: D

Let I be the purchase value of an equipment and V(t) be the value after it has been used for t years. The value V(t) depreciates at a rate given by differential equation $\frac{dV(t)}{dt} = -k(T - t)$, where $k > 0$ is a constant and T is the total life in years of the equipment. Then the scrap value V(T) of the equipment is

1. A.$I - \frac{kT^2}{2}$✓
2. B.$I - \frac{k(T-t)^2}{2}$
3. C.$e^{-kT}$
4. D.$T^2 - \frac{I}{k}$

Correct answer: A

The vector $\vec{a}$ and $\vec{b}$ are not perpendicular and $\vec{c}$ and $\vec{d}$ are two vectors satisfying: $\vec{b}\times\vec{c} = \vec{b}\times\vec{d}$ and $\vec{a}\cdot\vec{d} = 0$. Then the vector $\vec{d}$ is equal to

1. A.$\vec{c} + \left(\frac{\vec{a}\cdot\vec{c}}{\vec{a}\cdot\vec{b}}\right)\vec{b}$
2. B.$\vec{b} + \left(\frac{\vec{b}\cdot\vec{c}}{\vec{a}\cdot\vec{b}}\right)\vec{c}$
3. C.$\vec{c} - \left(\frac{\vec{a}\cdot\vec{c}}{\vec{a}\cdot\vec{b}}\right)\vec{b}$✓
4. D.$\vec{b} - \left(\frac{\vec{b}\cdot\vec{c}}{\vec{a}\cdot\vec{b}}\right)\vec{c}$

Correct answer: C

The two circles $x^2 + y^2 = ax$ and $x^2 + y^2 = c^2$ $(c > 0)$ touch each other if

1. A.$|a| = c$✓
2. B.$a = 2c$
3. C.$|a| = 2c$
4. D.$2|a| = c$

Correct answer: A

If C and D are two events such that $C \subset D$ and $P(D) \ne 0$, then the correct statement among the following is

1. A.$P(C|D) \ge P(C)$✓
2. B.$P(C|D) < P(C)$
3. C.$P(C|D) = \frac{P(D)}{P(C)}$
4. D.$P(C|D) = P(C)$

Correct answer: A

The number of values of k for which the linear equations $4x + ky + 2z = 0$; $kx + 4y + z = 0$; $2x + 2y + z = 0$ possess a non-zero solution is

1. A.2✓
2. B.1
3. C.zero
4. D.3

Correct answer: A

Consider the following statements P : Suman is brilliant, Q : Suman is rich, R : Suman is honest. The negation of the statement 'Suman is brilliant and dishonest if and only if Suman is rich' can be expressed as

1. A.$\sim(Q \leftrightarrow (P\wedge\sim R))$✓
2. B.$\sim Q \leftrightarrow \sim P \wedge R$
3. C.$\sim(P\wedge\sim R) \leftrightarrow Q$
4. D.$\sim P \wedge (Q \leftrightarrow \sim R)$

Correct answer: A

The shortest distance between line $y - x = 1$ and curve $x = y^2$ is

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

Correct answer: A

If the mean deviation about the median of the numbers a, 2a, ..., 50a is 50, then |a| equals

1. A.3
2. B.4✓
3. C.5
4. D.2

Correct answer: B

Statement-1 : The point A(1, 0, 7) is the mirror image of the point B(1, 6, 3) in the line $\frac{x}{1} = \frac{y-1}{2} = \frac{z-2}{3}$. Statement-2 : The line $\frac{x}{1} = \frac{y-1}{2} = \frac{z-2}{3}$ bisects the line segment joining A(1, 0, 7) and B(1, 6, 3).

1. A.Statement-1 is true, Statement-2 is true; Statement-2 is not a 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 true; Statement-2 is a correct explanation for Statement-1

Correct answer: A

Let A and B be two symmetric matrices of order 3. Statement-1 : A(BA) and (AB)A are symmetric matrices. Statement-2 : AB is symmetric matrix if matrix multiplication of A and B is commutative.

1. A.Statement-1 is true, Statement-2 is true; Statement-2 is not a 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 true; Statement-2 is a correct explanation for Statement-1

Correct answer: A

If $\omega(\ne1)$ is a cube root of unity, and $(1 + \omega)^7 = A + B\omega$. Then (A, B) equals

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

Correct answer: A

The value of p and q for which the function $f(x) = \begin{cases} \frac{\sin(p+1)x + \sin x}{x}, & x < 0 \\ q, & x = 0 \\ \frac{\sqrt{x+x^2} - \sqrt{x}}{x^{3/2}}, & x > 0 \end{cases}$ is continuous for all x in R, is

1. A.$p = \frac{5}{2}, q = \frac{1}{2}$
2. B.$p = -\frac{3}{2}, q = \frac{1}{2}$✓
3. C.$p = \frac{1}{2}, q = \frac{3}{2}$
4. D.$p = \frac{1}{2}, q = -\frac{3}{2}$

Correct answer: B

The area of the region enclosed by the curves $y = x$, $x = e$, $y = \frac{1}{x}$ and the positive x-axis is

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

Correct answer: B

For $x \in \left(0, \frac{5\pi}{2}\right)$, define $f(x) = \int_0^x\sqrt{t}\sin t\,dt$. Then f has

1. A.local minimum at $\pi$ and $2\pi$
2. B.local minimum at $\pi$ and local maximum at $2\pi$
3. C.local maximum at $\pi$ and local minimum at $2\pi$✓
4. D.local maximum at $\pi$ and $2\pi$

Correct answer: C

Among the following the maximum covalent character is shown by the compound :

1. A.$SnCl_2$
2. B.$AlCl_3$✓
3. C.$MgCl_2$
4. D.$FeCl_2$