JEE Advanced 2014 Paper 1 Question Paper

Question 1

Let $f: (0, \infty) 	o \mathbb{R}$ be given by $f(x) = \int_{1/x}^{x} e^{-\left(t+\frac{1}{t}ight)} \frac{dt}{t}$, then

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(A) $f(x)$ is monotonically increasing on $[1, \infty)$

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(C) $f(x) + f\left(\frac{1}{x}\right) = 0$, for all $x \in (0, \infty)$

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(D) $f(2^x)$ is an odd function of $x$ on $\mathbb{R}$

Answer

(B) $f(x)$ is monotonically decreasing on $(0, 1)$

Question 2

Let $a \in \mathbb{R}$ and let $f: \mathbb{R} 	o \mathbb{R}$ be given by $f(x) = x^5 - 5x + a$, then

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(B) $f(x)$ has only one real roots if $a > 4$

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(D) $f(x)$ has three real roots if $-4 < a < 4$

Answer

(A) $f(x)$ has three real roots if $a > 4$

Answer

(C) $f(x)$ has three real roots if $a < -4$

Question 3

For every pair of continuous functions $f, g: [0, 1] 	o \mathbb{R}$ such that $\max\{ f(x) : x \in [0, 1]\} = \max\{g(x) : x \in [0, 1]\}$, the correct statement(s) is(are)

Accepted Answer

(A) $(f(c))^2 + 3f(c) = (g(c))^2 + 3g(c)$ for some $c \in [0, 1]$

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(D) $(f(c))^2 = (g(c))^2$ for some $c \in [0, 1]$

Answer

(B) $(f(c))^2 + f(c) = (g(c))^2 + 3g(c)$ for some $c \in [0, 1]$

Answer

(C) $(f(c))^2 + 3f(c) = (g(c))^2 + g(c)$ for some $c \in [0, 1]$

Question 4

A circle $S$ passes through the point $(0, 1)$ and is orthogonal to the circles $(x - 1)^2 + y^2 = 16$ and $x^2 + y^2 = 1$. Then

Accepted Answer

(B) radius of $S$ is $7$

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(C) centre of $S$ is $(-7, 1)$

Answer

(A) radius of $S$ is $8$

Answer

(D) centre of $S$ is $(-8, 1)$

Question 5

Let $\vec{x}$, $\vec{y}$ and $\vec{z}$ be three vectors each of magnitude $\sqrt{2}$ and the angle between each pair of them is $\frac{\pi}{3}$. If $\vec{a}$ is a non-zero vector perpendicular to $\vec{x}$ and $\vec{y} 	imes \vec{z}$ and $\vec{b}$ is a non-zero vector perpendicular to $\vec{y}$ and $\vec{z} 	imes \vec{x}$, then

Accepted Answer

(A) $\vec{b} = (\vec{b} \cdot \vec{z})(\vec{z} - \vec{x})$

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(B) $\vec{a} = (\vec{a} \cdot \vec{y})(\vec{y} - \vec{z})$

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(C) $\vec{a} \cdot \vec{b} = -(\vec{a} \cdot \vec{y})(\vec{b} \cdot \vec{z})$

Answer

(D) $\vec{a} = (\vec{a} \cdot \vec{y})(\vec{z} - \vec{y})$

Question 6

From a point $P(\lambda, \lambda, \lambda)$, perpendiculars $PQ$ and $PR$ are drawn respectively on the lines $y = x, z = 1$ and $y = -x, z = -1$. If $P$ is such that $\angle QPR$ is a right angle, then the possible value(s) of $\lambda$ is(are)

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(C) $-1$

Answer

(A) $\sqrt{2}$

Answer

(B) $1$

Answer

(D) $-\sqrt{2}$

Question 7

Let $M$ be a $2 	imes 2$ symmetric matrix with integer entries. Then $M$ is invertible if

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(C) $M$ is a diagonal matrix with non-zero entries in the main diagonal

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(D) the product of entries in the main diagonal of $M$ is not the square of an integer

Answer

(A) the first column of $M$ is the transpose of the second row of $M$

Answer

(B) the second row of $M$ is the transpose of the first column of $M$

Question 8

Let $M$ and $N$ be two $3 	imes 3$ matrices such that $MN = NM$. Further, if $M 
eq N^2$ and $M^2 = N^4$, then

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(A) determinant of $(M^2 + MN^2)$ is $0$

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(B) there is a $3 	imes 3$ non-zero matrix $U$ such that $(M^2 + MN^2)U$ is the zero matrix

Answer

(C) determinant of $(M^2 + MN^2) \geq 1$

Answer

(D) for a $3 	imes 3$ matrix $U$, if $(M^2 + MN^2)U$ equals the zero matrix then $U$ is the zero matrix

Question 9

Let $f: [a, b] 	o [1, \infty)$ be a continuous function and let $g: \mathbb{R} 	o \mathbb{R}$ be defined as $g(x) = \begin{cases} 0 & 	ext{if } x < a, \ \int_{a}^{x} f(t) dt & 	ext{if } a \le x \le b, \ \int_{a}^{b} f(t) dt & 	ext{if } x > b \end{cases}$ Then

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(A) $g(x)$ is continuous but not differentiable at $a$

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(C) $g(x)$ is continuous but not differentiable at $b$

Answer

(B) $g(x)$ is differentiable on $\mathbb{R}$

Answer

(D) $g(x)$ is continuous and differentiable at either $a$ or $b$ but not both

Question 10

Let $f: \left(-\frac{\pi}{2}, \frac{\pi}{2}ight) 	o \mathbb{R}$ be given by $f(x) = (\log(\sec x + 	an x))^3$. Then

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(A) $f(x)$ is an odd function

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(B) $f(x)$ is a one-one function

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(C) $f(x)$ is an onto function

Answer

(D) $f(x)$ is an even function

Question 11

Let $n_1 < n_2 < n_3 < n_4 < n_5$ be positive integers such that $n_1 + n_2 + n_3 + n_4 + n_5 = 20$. Then the number of such distinct arrangements $(n_1, n_2, n_3, n_4, n_5)$ is __________

Accepted Answer

7

Question 12

Let $n \geq 2$ be an integer. Take $n$ distinct points on a circle and join each pair of points by a line segment. Colour the line segment joining every pair of adjacent points by blue and the rest by red. If the number of red and blue line segments are equal, then the value of $n$ is __________

Accepted Answer

5

Question 13

Let $f: \mathbb{R} 	o \mathbb{R}$ and $g: \mathbb{R} 	o \mathbb{R}$ be respectively given by $f(x) = |x| + 1$ and $g(x) = x^2 + 1$. Define $h: \mathbb{R} 	o \mathbb{R}$ by $h(x) = \begin{cases} \max \{f(x), g(x)\} & 	ext{if } x \le 0 \ \min \{f(x), g(x)\} & 	ext{if } x > 0 \end{cases}$. Then number of points at which $h(x)$ is not differentiable is __________

Accepted Answer

3

Question 14

Let $a, b, c$ be positive integers such that $\frac{b}{a}$ is an integer. If $a, b, c$ are in geometric progression and the arithmetic mean of $a, b, c$ is $b + 2$, then the value of $\frac{a^2 + a - 14}{a+1}$ is __________

Accepted Answer

4

Question 15

Let $\vec{a}$, $\vec{b}$, and $\vec{c}$ be three non-coplanar unit vectors such that the angle between every pair of them is $\frac{\pi}{3}$. If $\vec{a} 	imes \vec{b} + \vec{b} 	imes \vec{c} = p\vec{a} + q\vec{b} + r\vec{c}$, where $p$, $q$ and $r$ are scalars, then the value of $\frac{p^2 + 2q^2 + r^2}{q^2}$ is __________

Accepted Answer

4

Question 16

The slope of the tangent to the curve $(y - x^5)^2 = x(1 + x^2)^2$ at the point $(1, 3)$ is __________

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8

Question 17

The value of $\int_{0}^{1} 4x^3 \left\{\frac{d^2}{dx^2}(1 - x^2)^5\right\} dx$ is __________

Accepted Answer

2

Question 18

The largest value of the non-negative integer $a$ for which $\lim_{x 	o 1} \left\{\frac{-ax + \sin(x - 1) + a}{x + \sin(x - 1) - 1}ight\}^{\frac{1-x}{1-\sqrt{x}}} = \frac{1}{4}$ is __________

Accepted Answer

2

Question 19

Let $f: [0, 4\pi] 	o [0, \pi]$ be defined by $f(x) = \cos^{-1}(\cos x)$. The number of points $x \in [0, 4\pi]$ satisfying the equation $f(x) = \frac{10 - x}{10}$ is __________

Accepted Answer

3

Question 20

For a point $P$ in the plane, let $d_1(P)$ and $d_2(P)$ be the distances of the point $P$ from the lines $x - y = 0$ and $x + y = 0$ respectively. The area of the region $R$ consisting of all points $P$ lying in the first quadrant of the plane and satisfying $2 \le d_1(P) + d_2(P) \le 4$, is __________

Accepted Answer

6

Question 21

A student is performing an experiment using a resonance column and a tuning fork of frequency $244 	ext{ s}^{-1}$. He is told that the air in the tube has been replaced by another gas (assume that the column remains filled with the gas). If the minimum height at which resonance occurs is $(0.350 \pm 0.005) 	ext{ m}$, the gas in the tube is (Useful information: $\sqrt{167RT} = 640 	ext{ J}^{1/2} 	ext{mole}^{-1/2}$; $\sqrt{140RT} = 590 	ext{ J}^{1/2} 	ext{mole}^{-1/2}$. The molar masses $M$ in grams are given in the options. Take the values of $\sqrt{\frac{10}{M}}$ for each gas as given there.)

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(D) Argon $\left(M = 36, \sqrt{\frac{10}{36}} = \frac{17}{32}\right)$

Answer

(A) Neon $\left(M = 20, \sqrt{\frac{10}{20}} = \frac{7}{10}\right)$

Answer

(B) Nitrogen $\left(M = 28, \sqrt{\frac{10}{28}} = \frac{3}{5}\right)$

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(C) Oxygen $\left(M = 32, \sqrt{\frac{10}{32}} = \frac{9}{16}\right)$

Question 22

At time $t = 0$, terminal $A$ in the circuit shown in the figure is connected to $B$ by a key and an alternating current $I(t) = I_0 \cos (\omega t)$, with $I_0 = 1 	ext{ A}$ and $\omega = 500 	ext{ rad/s}$ starts flowing in it with the initial direction shown in the figure. At $t = \frac{7\pi}{6\omega}$, the key is switched from $B$ to $D$. Now onwards only $A$ and $D$ are connected. A total charge $Q$ flows from the battery to charge the capacitor fully. If $C = 20 \mu	ext{F}$, $R = 10 \Omega$ and the battery is ideal with emf of $50 	ext{ V}$, identify the correct statement(s).

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(C) Immediately after $A$ is connected to $D$, the current in $R$ is $10 	ext{ A}$.

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(D) $Q = 2 	imes 10^{-3} 	ext{ C}$.

Answer

(A) Magnitude of the maximum charge on the capacitor before $t = \frac{7\pi}{6\omega}$ is $1 	imes 10^{-3} 	ext{ C}$.

Answer

(B) The current in the left part of the circuit just before $t = \frac{7\pi}{6\omega}$ is clockwise.

Question 23

A parallel plate capacitor has a dielectric slab of dielectric constant $K$ between its plates that covers $1/3$ of the area of its plates, as shown in the figure. The total capacitance of the capacitor is $C$ while that of the portion with dielectric in between is $C_1$. When the capacitor is charged, the plate area covered by the dielectric gets charge $Q_1$ and the rest of the area gets charge $Q_2$. The electric field in the dielectric is $E_1$ and that in the other portion is $E_2$. Choose the correct option/options, ignoring edge effects.

Accepted Answer

(A) $\frac{E_1}{E_2} = 1$

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(D) $\frac{C}{C_1} = \frac{2+K}{K}$

Answer

(B) $\frac{E_1}{E_2} = \frac{1}{K}$

Answer

(C) $\frac{Q_1}{Q_2} = \frac{3}{K}$

Question 24

One end of a taut string of length $3 	ext{ m}$ along the $x$ axis is fixed at $x = 0$. The speed of the waves in the string is $100 	ext{ ms}^{-1}$. The other end of the string is vibrating in the $y$ direction so that stationary waves are set up in the string. The possible waveform(s) of these stationary waves is (are)

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(A) $y(t) = A \sin \frac{\pi x}{6} \cos \frac{50\pi t}{3}$

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(C) $y(t) = A \sin \frac{5\pi x}{6} \cos \frac{250\pi t}{3}$

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(D) $y(t) = A \sin \frac{5\pi x}{2} \cos 250\pi t$

Answer

(B) $y(t) = A \sin \frac{\pi x}{3} \cos \frac{100\pi t}{3}$

Question 25

A transparent thin film of uniform thickness and refractive index $n_1 = 1.4$ is coated on the convex spherical surface of radius $R$ at one end of a long solid glass cylinder of refractive index $n_2 = 1.5$, as shown in the figure. Rays of light parallel to the axis of the cylinder traversing through the film from air to glass get focused at distance $f_1$ from the film, while rays of light traversing from glass to air get focused at distance $f_2$ from the film. Then

Accepted Answer

(A) $|f_1| = 3R$

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(C) $|f_2| = 2R$

Answer

(B) $|f_1| = 2.8R$

Answer

(D) $|f_2| = 1.4R$

Question 26

Heater of an electric kettle is made of a wire of length $L$ and diameter $d$. It takes $4$ minutes to raise the temperature of $0.5 	ext{ kg}$ water by $40 	ext{ K}$. This heater is replaced by a new heater having two wires of the same material, each of length $L$ and diameter $2d$. The way these wires are connected is given in the options. How much time in minutes will it take to raise the temperature of the same amount of water by $40 	ext{ K}$?

Accepted Answer

(B) $2$ if wires are in series

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(D) $0.5$ if wires are in parallel

Answer

(A) $4$ if wires are in parallel

Answer

(C) $1$ if wires are in series

Question 27

Two ideal batteries of emf $V_1$ and $V_2$ and three resistances $R_1$, $R_2$ and $R_3$ are connected as shown in the figure. The current in resistance $R_2$ would be zero if

Accepted Answer

(A) $V_1 = V_2$ and $R_1 = R_2 = R_3$

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(B) $V_1 = V_2$ and $R_1 = 2R_2 = R_3$

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(D) $2V_1 = V_2$ and $2R_1 = R_2 = R_3$

Answer

(C) $V_1 = 2V_2$ and $2R_1 = 2R_2 = R_3$

Question 28

Let $E_1(r)$, $E_2(r)$ and $E_3(r)$ be the respective electric fields at a distance $r$ from a point charge $Q$, an infinitely long wire with constant linear charge density $\lambda$, and an infinite plane with uniform surface charge density $\sigma$. If $E_1(r_0) = E_2(r_0) = E_3(r_0)$ at a given distance $r_0$, then

Accepted Answer

(C) $E_1(r_0/2) = 2E_2(r_0/2)$

Answer

(A) $Q = 4\sigma\pi r_0^2$

Answer

(B) $r_0 = \frac{\lambda}{2\pi\sigma}$

Answer

(D) $E_2(r_0/2) = 4E_3(r_0/2)$

Question 29

A light source, which emits two wavelengths $\lambda_1 = 400 	ext{ nm}$ and $\lambda_2 = 600 	ext{ nm}$, is used in a Young's double slit experiment. If recorded fringe widths for $\lambda_1$ and $\lambda_2$ are $\beta_1$ and $\beta_2$ and the number of fringes for them within a distance $y$ on one side of the central maximum are $m_1$ and $m_2$, respectively, then

Accepted Answer

(A) $\beta_2 > \beta_1$

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(B) $m_1 > m_2$

Accepted Answer

(C) From the central maximum, $3^{	ext{rd}}$ maximum of $\lambda_2$ overlaps with $5^{	ext{th}}$ minimum of $\lambda_1$

Answer

(D) The angular separation of fringes for $\lambda_1$ is greater than $\lambda_2$

Question 30

In the figure, a ladder of mass $m$ is shown leaning against a wall. It is in static equilibrium making an angle $	heta$ with the horizontal floor. The coefficient of friction between the wall and the ladder is $\mu_1$ and that between the floor and the ladder is $\mu_2$. The normal reaction of the wall on the ladder is $N_1$ and that of the floor is $N_2$. If the ladder is about to slip, then

Accepted Answer

(C) $\mu_1 
eq 0 \; \mu_2 
eq 0$ and $N_2 = \frac{mg}{1+\mu_1\mu_2}$

Accepted Answer

(D) $\mu_1 = 0 \; \mu_2 
eq 0$ and $N_1 	an 	heta = \frac{mg}{2}$

Answer

(A) $\mu_1 = 0 \; \mu_2 
eq 0$ and $N_2 	an 	heta = \frac{mg}{2}$

Answer

(B) $\mu_1 
eq 0 \; \mu_2 = 0$ and $N_1 	an 	heta = \frac{mg}{2}$

Question 31

During Searle's experiment, zero of the Vernier scale lies between $3.20 	imes 10^{-2} 	ext{ m}$ and $3.25 	imes 10^{-2} 	ext{ m}$ of the main scale. The $20^{	ext{th}}$ division of the Vernier scale exactly coincides with one of the main scale divisions. When an additional load of $2 	ext{ kg}$ is applied to the wire, the zero of the Vernier scale still lies between $3.20 	imes 10^{-2} 	ext{ m}$ and $3.25 	imes 10^{-2} 	ext{ m}$ of the main scale but now the $45^{	ext{th}}$ division of Vernier scale coincides with one of the main scale divisions. The length of the thin metallic wire is $2 	ext{ m}$ and its cross-sectional area is $8 	imes 10^{-7} 	ext{ m}^2$. The least count of the Vernier scale is $1.0 	imes 10^{-5} 	ext{ m}$. The maximum percentage error in the Young's modulus of the wire is

Accepted Answer

4

Question 32

Airplanes $A$ and $B$ are flying with constant velocity in the same vertical plane at angles $30^{\circ}$ and $60^{\circ}$ with respect to the horizontal respectively as shown in the figure. The speed of $A$ is $100\sqrt{3} 	ext{ ms}^{-1}$. At time $t = 0 	ext{ s}$, an observer in $A$ finds $B$ at a distance of $500 	ext{ m}$. This observer sees $B$ moving with a constant velocity perpendicular to the line of motion of $A$. If at $t = t_0$, $A$ just escapes being hit by $B$, $t_0$ in seconds is

Accepted Answer

5

Question 33

A thermodynamic system is taken from an initial state $i$ with internal energy $U_i = 100 	ext{ J}$ to the final state $f$ along two different paths $iaf$ and $ibf$, as schematically shown in the figure. The work done by the system along the paths $af$, $ib$ and $bf$ are $W_{af} = 200 	ext{ J}$, $W_{ib} = 50 	ext{ J}$ and $W_{bf} = 100 	ext{ J}$ respectively. The heat supplied to the system along the path $iaf$, $ib$ and $bf$ are $Q_{iaf}$, $Q_{ib}$ and $Q_{bf}$ respectively. If the internal energy of the system in the state $b$ is $U_b = 200 	ext{ J}$ and $Q_{iaf} = 500 	ext{ J}$, the ratio $Q_{bf} / Q_{ib}$ is

Accepted Answer

2

Question 34

Two parallel wires in the plane of the paper are distance $X_0$ apart. A point charge is moving with speed $u$ between the wires in the same plane at a distance $X_1$ from one of the wires. When the wires carry current of magnitude $I$ in the same direction, the radius of curvature of the path of the point charge is $R_1$. In contrast, if the currents $I$ in the two wires have directions opposite to each other, the radius of curvature of the path is $R_2$. If $\frac{X_0}{X_1} = 3$, the value of $\frac{R_1}{R_2}$ is

Accepted Answer

3

Question 35

To find the distance $d$ over which a signal can be seen clearly in foggy conditions, a railways engineer uses dimensional analysis and assumes that the distance depends on the mass density $\rho$ of the fog, intensity (power/area) $S$ of the light from the signal and its frequency $f$. The engineer finds that $d$ is proportional to $S^{1/n}$. The value of $n$ is

Accepted Answer

3

Question 36

A rocket is moving in a gravity free space with a constant acceleration of $2 	ext{ ms}^{-2}$ along $+ x$ direction (see figure). The length of a chamber inside the rocket is $4 	ext{ m}$. A ball is thrown from the left end of the chamber in $+ x$ direction with a speed of $0.3 	ext{ ms}^{-1}$ relative to the rocket. At the same time, another ball is thrown in $-x$ direction with a speed of $0.2 	ext{ ms}^{-1}$ from its right end relative to the rocket. The time in seconds when the two balls hit each other is

Accepted Answer

2

Question 37

A galvanometer gives full scale deflection with $0.006 	ext{ A}$ current. By connecting it to a $4990 \Omega$ resistance, it can be converted into a voltmeter of range $0-30 	ext{ V}$. If connected to a $\frac{2n}{249} \Omega$ resistance, it becomes an ammeter of range $0-1.5 	ext{ A}$. The value of $n$ is

Accepted Answer

5

Question 38

A uniform circular disc of mass $1.5 	ext{ kg}$ and radius $0.5 	ext{ m}$ is initially at rest on a horizontal frictionless surface. Three forces of equal magnitude $F = 0.5 	ext{ N}$ are applied simultaneously along the three sides of an equilateral triangle $XYZ$ with its vertices on the perimeter of the disc (see figure). One second after applying the forces, the angular speed of the disc in $	ext{rad s}^{-1}$ is

Accepted Answer

2

Question 39

A horizontal circular platform of radius $0.5 	ext{ m}$ and mass $0.45 	ext{ kg}$ is free to rotate about its axis. Two massless spring toy-guns, each carrying a steel ball of mass $0.05 	ext{ kg}$ are attached to the platform at a distance $0.25 	ext{ m}$ from the centre on its either sides along its diameter (see figure). Each gun simultaneously fires the balls horizontally and perpendicular to the diameter in opposite directions. After leaving the platform, the balls have horizontal speed of $9 	ext{ ms}^{-1}$ with respect to the ground. The rotational speed of the platform in $	ext{rad s}^{-1}$ after the balls leave the platform is

Accepted Answer

4

Question 40

Consider an elliptically shaped rail $PQ$ in the vertical plane with $OP = 3 	ext{ m}$ and $OQ = 4 	ext{ m}$. A block of mass $1 	ext{ kg}$ is pulled along the rail from $P$ to $Q$ with a force of $18 	ext{ N}$, which is always parallel to line $PQ$ (see the figure given). Assuming no frictional losses, the kinetic energy of the block when it reaches $Q$ is $(n 	imes 10)$ Joules. The value of $n$ is (take acceleration due to gravity $= 10 	ext{ ms}^{-2}$)

Accepted Answer

5

Question 41

The correct combination of names for isomeric alcohols with molecular formula $C_4H_{10}O$ is/are

Accepted Answer

(A) tert-butanol and 2-methylpropan-2-ol

Accepted Answer

(C) n-butanol and butan-1-ol

Accepted Answer

(D) isobutyl alcohol and 2-methylpropan-1-ol

Answer

(B) tert-butanol and 1, 1-dimethylethan-1-ol

Question 42

An ideal gas in a thermally insulated vessel at internal pressure $= P_1$, volume $= V_1$ and absolute temperature $= T_1$ expands irreversibly against zero external pressure, as shown in the diagram. The final internal pressure, volume and absolute temperature of the gas are $P_2$, $V_2$ and $T_2$, respectively. For this expansion,

Accepted Answer

(A) $q = 0$

Accepted Answer

(B) $T_2 = T_1$

Accepted Answer

(C) $P_2V_2 = P_1V_1$

Answer

(D) $P_2V_2^{\gamma} = P_1V_1^{\gamma}$

Question 43

Hydrogen bonding plays a central role in the following phenomena:

Accepted Answer

(A) Ice floats in water.

Accepted Answer

(B) Higher Lewis basicity of primary amines than tertiary amines in aqueous solutions.

Accepted Answer

(D) Dimerisation of acetic acid in benzene.

Answer

(C) Formic acid is more acidic than acetic acid.

Question 44

In a galvanic cell, the salt bridge

Accepted Answer

(A) does not participate chemically in the cell reaction.

Answer

(B) stops the diffusion of ions from one electrode to another.

Answer

(C) is necessary for the occurrence of the cell reaction.

Answer

(D) ensures mixing of the two electrolytic solutions.

Question 45

For the reaction: $I^- + ClO_3^- + H_2SO_4 \longrightarrow Cl^- + HSO_4^- + I_2$ The correct statement(s) in the balanced equation is/are:

Accepted Answer

(A) Stoichiometric coefficient of $HSO_4^-$ is 6.

Accepted Answer

(B) Iodide is oxidized.

Accepted Answer

(D) $H_2O$ is one of the products.

Answer

(C) Sulphur is reduced.

Question 46

The reactivity of compound Z with different halogens under appropriate conditions is given below:

The observed pattern of electrophilic substitution can be explained by

Accepted Answer

(A) the steric effect of the halogen

Accepted Answer

(B) the steric effect of the tert-butyl group

Accepted Answer

(C) the electronic effect of the phenolic group

Answer

(D) the electronic effect of the tert-butyl group

Question 47

The correct statement(s) for orthoboric acid is/are

Accepted Answer

(B) Acidity of its aqueous solution increases upon addition of ethylene glycol.

Accepted Answer

(D) It is a weak electrolyte in water.

Answer

(A) It behaves as a weak acid in water due to self ionization.

Answer

(C) It has a three dimensional structure due to hydrogen bonding.

Question 48

Upon heating with $Cu_2S$, the reagent(s) that give copper metal is/are

Accepted Answer

(B) $CuO$

Accepted Answer

(C) $Cu_2O$

Accepted Answer

(D) $CuSO_4$

Answer

(A) $CuFeS_2$

Question 49

The pair(s) of reagents that yield paramagnetic species is/are

Accepted Answer

(A) $Na$ and excess of $NH_3$

Accepted Answer

(B) $K$ and excess of $O_2$

Accepted Answer

(C) $Cu$ and dilute $HNO_3$

Answer

(D) $O_2$ and 2-ethylanthraquinol

Question 50

In the reaction shown below, the major product(s) formed is/are

Accepted Answer

(A) (A)

Answer

(B) (B)

Answer

(C) (C)

Answer

(D) (D)

Question 51

Among $PbS$, $CuS$, $HgS$, $MnS$, $Ag_2S$, $NiS$, $CoS$, $Bi_2S_3$ and $SnS_2$, the total number of BLACK coloured sulphides is

Accepted Answer

6

Question 52

The total number(s) of stable conformers with non-zero dipole moment for the following compound is(are)

Accepted Answer

3

Question 53

Consider the following list of reagents: Acidified $K_2Cr_2O_7$, alkaline $KMnO_4$, $CuSO_4$, $H_2O_2$, $Cl_2$, $O_3$, $FeCl_3$, $HNO_3$ and $Na_2S_2O_3$. The total number of reagents that can oxidise aqueous iodide to iodine is

Accepted Answer

7

Question 54

A list of species having the formula $XZ_4$ is given below. $XeF_4$, $SF_4$, $SiF_4$, $BF_4^-$, $BrF_4^-$, $[Cu(NH_3)_4]^{2+}$, $[FeCl_4]^{2-}$, $[CoCl_4]^{2-}$ and $[PtCl_4]^{2-}$. Defining shape on the basis of the location of $X$ and $Z$ atoms, the total number of species having a square planar shape is

Accepted Answer

4

Question 55

Consider all possible isomeric ketones, including stereoisomers of MW $= 100$. All these isomers are independently reacted with $NaBH_4$ (NOTE: stereoisomers are also reacted separately). The total number of ketones that give a racemic product(s) is/are

Accepted Answer

5

Question 56

In an atom, the total number of electrons having quantum numbers $n = 4$, $|m_l| = 1$ and $m_s = -1/2$ is

Accepted Answer

6

Question 57

If the value of Avogadro number is $6.023 	imes 10^{23} 	ext{ mol}^{-1}$ and the value of Boltzmann constant is $1.380 	imes 10^{-23} 	ext{JK}^{-1}$, then the number of significant digits in the calculated value of the universal gas constant is

Accepted Answer

4

Question 58

$MX_2$ dissociates in $M^{2+}$ and $X^-$ ions in an aqueous solution, with a degree of dissociation $(\alpha)$ of $0.5$. The ratio of the observed depression of freezing point of the aqueous solution to the value of the depression of freezing point in the absence of ionic dissociation is

Accepted Answer

2

Question 59

The total number of distinct naturally occurring amino acids obtained by complete acidic hydrolysis of the peptide shown below is

Accepted Answer

1

Question 60

A compound $H_2X$ with molar weight of $80 	ext{ g}$ is dissolved in a solvent having density of $0.4 	ext{ g mL}^{-1}$. Assuming no change in volume upon dissolution, the molality of a $3.2$ molar solution is

Accepted Answer

8

JEE Advanced 2014 Paper 1 Question Paper with Answers

Physics — JEE Advanced 2014 Paper 1

Chemistry — JEE Advanced 2014 Paper 1

Mathematics — JEE Advanced 2014 Paper 1

Chapters tested in this paper

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