JEE Main 2015 — 4 Apr Offline Set B (Previous Year Paper)

Which of the following is the energy of a possible excited state of hydrogen?

1. A.$-6.8$ eV
2. B.$-3.4$ eV✓
3. C.$+6.8$ eV
4. D.$+13.6$ eV

Correct answer: B

In the following sequence of reactions: Toluene $\xrightarrow{KMnO_4}$ A $\xrightarrow{SOCl_2}$ B $\xrightarrow{H_2/Pd,\ BaSO_4}$ C, the product C is:

1. A.$C_6H_5CH_3$
2. B.$C_6H_5CH_2OH$
3. C.$C_6H_5CHO$✓
4. D.$C_6H_5COOH$

Correct answer: C

Which compound would give 5-keto-2-methyl hexanal upon ozonolysis?

1. A.1,3-dimethylcyclopentene (methyl on C1 of the double bond and on the ring carbon next to C2)✓
2. B.1,4-dimethylcyclopentene
3. C.1,5-dimethylcyclopentene (methyl on C1 and on the adjacent sp3 carbon)
4. D.1,2-dimethylcyclopentene

Correct answer: A

The ionic radii (in Å) of $N^{3-}$, $O^{2-}$ and $F^-$ are respectively:

1. A.1.36, 1.71 and 1.40
2. B.1.71, 1.40 and 1.36✓
3. C.1.71, 1.36 and 1.40
4. D.1.36, 1.40 and 1.71

Correct answer: B

The color of $KMnO_4$ is due to:

1. A.d - d transition
2. B.L $\rightarrow$ M charge transfer transition✓
3. C.$\sigma - \sigma^*$ transition
4. D.M $\rightarrow$ L charge transfer transition

Correct answer: B

Assertion : Nitrogen and Oxygen are the main components in the atmosphere but these do not react to form oxides of nitrogen. Reason : The reaction between nitrogen and oxygen requires high temperature.

1. A.Both assertion and reason are correct, but the reason is not the correct explanation for the assertion
2. B.The assertion is incorrect, but the reason is correct
3. C.Both the assertion and reason are incorrect
4. D.Both assertion and reason are correct, and the reason is the correct explanation for the assertion✓

Correct answer: D

Which of the following compounds is not an antacid?

1. A.Cimetidine
2. B.Phenelzine✓
3. C.Ranitidine
4. D.Aluminium hydroxide

Correct answer: B

In the context of the Hall-Heroult process for the extraction of Al, which of the following statements is false?

1. A.$Al_2O_3$ is mixed with $CaF_2$ which lowers the melting point of the mixture and brings conductivity
2. B.$Al^{3+}$ is reduced at the cathode to form Al
3. C.$Na_3AlF_6$ serves as the electrolyte✓
4. D.CO and $CO_2$ are produced in this process

Correct answer: C

Match the catalysts to the correct processes: Catalyst (A) $TiCl_3$ (B) $PdCl_2$ (C) $CuCl_2$ (D) $V_2O_5$; Process (i) Wacker process (ii) Ziegler - Natta polymerization (iii) Contact process (iv) Deacon's process

1. A.(A) - (ii), (B) - (i), (C) - (iv), (D) - (iii)✓
2. B.(A) - (ii), (B) - (iii), (C) - (iv), (D) - (i)
3. C.(A) - (iii), (B) - (i), (C) - (ii), (D) - (iv)
4. D.(A) - (iii), (B) - (ii), (C) - (iv), (D) - (i)

Correct answer: A

In the reaction: p-toluidine $\xrightarrow{NaNO_2/HCl,\ 0-5^\circ C}$ D $\xrightarrow{CuCN/KCN,\ \Delta}$ E + $N_2$, the product E is

1. A.4,4'-dimethylbiphenyl
2. B.p-tolunitrile (4-methylbenzonitrile)✓
3. C.Toluene
4. D.p-toluic acid (4-methylbenzoic acid)

Correct answer: B

Which polymer is used in the manufacture of paints and lacquers?

1. A.Glyptal✓
2. B.Polypropene
3. C.Poly vinyl chloride
4. D.Bakelite

Correct answer: A

The number of geometric isomers that can exist for square planar $[Pt(Cl)(py)(NH_3)(NH_2OH)]^+$ is (py = pyridine):

1. A.3✓
2. B.4
3. C.6
4. D.2

Correct answer: A

Higher order (>3) reactions are rare due to:

1. A.increase in entropy and activation energy as more molecules are involved
2. B.shifting of equilibrium towards reactants due to elastic collisions
3. C.loss of active species on collision
4. D.low probability of simultaneous collision of all the reacting species✓

Correct answer: D

Which among the following is the most reactive?

1. A.$Br_2$
2. B.$I_2$
3. C.ICl✓
4. D.$Cl_2$

Correct answer: C

Two Faraday of electricity is passed through a solution of $CuSO_4$. The mass of copper deposited at the cathode is: (at. mass of Cu = 63.5 amu)

1. A.63.5 g✓
2. B.2 g
3. C.127 g
4. D.0 g

Correct answer: A

3 g of activated charcoal was added to 50 mL of acetic acid solution (0.06N) in a flask. After an hour it was filtered and the strength of the filtrate was found to be 0.042 N. The amount of acetic acid adsorbed (per gram of charcoal) is:

1. A.36 mg
2. B.42 mg
3. C.54 mg
4. D.18 mg✓

Correct answer: D

The synthesis of alkyl fluorides is best accomplished by:

1. A.Sandmeyer's reaction
2. B.Finkelstein reaction
3. C.Swarts reaction✓
4. D.Free radical fluorination

Correct answer: C

The molecular formula of a commercial resin used for exchanging ions in water softening is $C_8H_7SO_3Na$ (Mol. Wt. 206). What would be the maximum uptake of $Ca^{2+}$ ions by the resin when expressed in mole per gram resin?

1. A.$\frac{1}{206}$
2. B.$\frac{2}{309}$
3. C.$\frac{1}{412}$✓
4. D.$\frac{1}{103}$

Correct answer: C

Which of the vitamins given below is water soluble?

1. A.Vitamin D
2. B.Vitamin E
3. C.Vitamin K
4. D.Vitamin C✓

Correct answer: D

The intermolecular interaction that is dependent on the inverse cube of distance between the molecule is:

1. A.ion-dipole interaction
2. B.London force
3. C.hydrogen bond✓
4. D.ion-ion interaction

Correct answer: C

The following reaction is performed at 298 K. $2NO(g) + O_2(g) \rightleftharpoons 2NO_2(g)$. The standard free energy of formation of NO(g) is 86.6 kJ/mol at 298 K. What is the standard free energy of formation of $NO_2$(g) at 298 K? ($K_P = 1.6\times10^{12}$)

1. A.$86600 + R(298)\ln(1.6\times10^{12})$
2. B.$86600 - \frac{\ln(1.6\times10^{12})}{R(298)}$
3. C.$0.5[2\times86,600 - R(298)\ln(1.6\times10^{12})]$✓
4. D.$R(298)\ln(1.6\times10^{12}) - 86600$

Correct answer: C

Which of the following compounds is not colored yellow?

1. A.$K_3[Co(NO_2)_6]$
2. B.$(NH_4)_3[As(Mo_3O_{10})_4]$
3. C.$BaCrO_4$
4. D.$Zn_2[Fe(CN)_6]$✓

Correct answer: D

In Carius method of estimation of halogens, 250 mg of an organic compound gave 141 mg of AgBr. The percentage of bromine in the compound is: (at. Mass Ag = 108; Br = 80)

1. A.36
2. B.48
3. C.60
4. D.24✓

Correct answer: D

Sodium metal crystallizes in a body centred cubic lattice with a unit cell edge of 4.29 Å. The radius of sodium atom is approximately:

1. A.3.22 Å
2. B.5.72 Å
3. C.0.93 Å
4. D.1.86 Å✓

Correct answer: D

Which of the following compounds will exhibit geometrical isomerism?

1. A.3-Phenyl-1-butene
2. B.2-Phenyl-1-butene
3. C.1,1-Diphenyl-1-propane
4. D.1-Phenyl-2-butene✓

Correct answer: D

The vapour pressure of acetone at $20^\circ$C is 185 torr. When 1.2 g of a non-volatile substance was dissolved in 100 g of acetone at $20^\circ$C, its vapour pressure was 183 torr. The molar mass (g mol$^{-1}$) of the substance is:

1. A.64✓
2. B.128
3. C.488
4. D.32

Correct answer: A

From the following statements regarding $H_2O_2$, choose the incorrect statement:

1. A.It decomposes on exposure to light
2. B.It has to be stored in plastic or wax lined glass bottles in dark
3. C.It has to be kept away from dust
4. D.It can act only as an oxidizing agent✓

Correct answer: D

Which one of the following alkaline earth metal sulphates has its hydration enthalpy greater than its lattice enthalpy?

1. A.$BeSO_4$✓
2. B.$BaSO_4$
3. C.$SrSO_4$
4. D.$CaSO_4$

Correct answer: A

The standard Gibbs energy change at 300 K for the reaction $2A \rightleftharpoons B + C$ is 2494.2 J. At a given time, the composition of the reaction mixture is $[A] = \frac{1}{2}$, $[B] = 2$ and $[C] = \frac{1}{2}$. The reaction proceeds in the: ($R = 8.314$ J/K/mol, $e = 2.718$)

1. A.reverse direction because $Q > K_c$✓
2. B.forward direction because $Q < K_c$
3. C.reverse direction because $Q < K_c$
4. D.forward direction because $Q > K_c$

Correct answer: A

Which one has the highest boiling point?

1. A.Ne
2. B.Kr
3. C.Xe✓
4. D.He

Correct answer: C

The sum of coefficients of integral powers of x in the binomial expansion of $\left(1 - 2\sqrt{x}\right)^{50}$ is :

1. A.$\frac{1}{2}\left(3^{50}\right)$
2. B.$\frac{1}{2}\left(3^{50}-1\right)$
3. C.$\frac{1}{2}\left(2^{50}+1\right)$
4. D.$\frac{1}{2}\left(3^{50}+1\right)$✓

Correct answer: D

Let f(x) be a polynomial of degree four having extreme values at $x = 1$ and $x = 2$. If $\lim_{x\to0}\left[1 + \frac{f(x)}{x^2}\right] = 3$, then f(2) is equal to :

1. A.$-4$
2. B.0✓
3. C.4
4. D.$-8$

Correct answer: B

The mean of the data set comprising of 16 observations is 16. If one of the observation valued 16 is deleted and three new observations valued 3, 4 and 5 are added to the data, then the mean of the resultant data, is :

1. A.16.0
2. B.15.8
3. C.14.0✓
4. D.16.8

Correct answer: C

The sum of first 9 terms of the series $\frac{1^3}{1} + \frac{1^3+2^3}{1+3} + \frac{1^3+2^3+3^3}{1+3+5} + \dots$ is :

1. A.96✓
2. B.142
3. C.192
4. D.71

Correct answer: A

Let O be the vertex and Q be any point on the parabola, $x^2 = 8y$. If the point P divides the line segment OQ internally in the ratio 1 : 3, then the locus of P is :

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

Correct answer: C

Let $\alpha$ and $\beta$ be the roots of equation $x^2 - 6x - 2 = 0$. If $a_n = \alpha^n - \beta^n$, for $n \ge 1$, then the value of $\frac{a_{10} - 2a_8}{2a_9}$ is equal to :

1. A.$-6$
2. B.3✓
3. C.$-3$
4. D.6

Correct answer: B

If 12 identical balls are to be placed in 3 identical boxes, then the probability that one of the boxes contains exactly 3 balls is :

1. A.$55\left(\frac{2}{3}\right)^{10}$
2. B.$220\left(\frac{1}{3}\right)^{12}$
3. C.$22\left(\frac{1}{3}\right)^{11}$
4. D.$\frac{55}{3}\left(\frac{2}{3}\right)^{11}$✓

Correct answer: D

A complex number z is said to be unimodular if $|z| = 1$. Suppose $z_1$ and $z_2$ are complex numbers such that $\frac{z_1 - 2z_2}{2 - z_1\bar{z}_2}$ is unimodular and $z_2$ is not unimodular. Then the point $z_1$ lies on a :

1. A.straight line parallel to y-axis.
2. B.circle of radius 2.✓
3. C.circle of radius $\sqrt{2}$.
4. D.straight line parallel to x-axis.

Correct answer: B

The integral $\int \frac{dx}{x^2\left(x^4+1\right)^{3/4}}$ equals :

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

Correct answer: C

The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with vertices $(0, 0)$, $(0, 41)$ and $(41, 0)$, is :

1. A.861
2. B.820
3. C.780✓
4. D.901

Correct answer: C

The distance of the point $(1, 0, 2)$ from the point of intersection of the line $\frac{x-2}{3} = \frac{y+1}{4} = \frac{z-2}{12}$ and the plane $x - y + z = 16$, is :

1. A.8
2. B.$3\sqrt{21}$
3. C.13✓
4. D.$2\sqrt{14}$

Correct answer: C

The equation of the plane containing the line $2x - 5y + z = 3$; $x + y + 4z = 5$, and parallel to the plane, $x + 3y + 6z = 1$, is :

1. A.$x + 3y + 6z = -7$
2. B.$x + 3y + 6z = 7$✓
3. C.$2x + 6y + 12z = -13$
4. D.$2x + 6y + 12z = 13$

Correct answer: B

The area (in sq. units) of the region described by $\{(x, y) : y^2 \le 2x \text{ and } y \ge 4x - 1\}$ is :

1. A.$\frac{5}{64}$
2. B.$\frac{15}{64}$
3. C.$\frac{9}{32}$✓
4. D.$\frac{7}{32}$

Correct answer: C

If m is the A.M. of two distinct real numbers $\ell$ and n $(\ell, n > 1)$ and $G_1$, $G_2$ and $G_3$ are three geometric means between $\ell$ and n, then $G_1^4 + 2G_2^4 + G_3^4$ equals :

1. A.$4\ell m^2n$✓
2. B.$4\ell mn^2$
3. C.$4\ell^2m^2n^2$
4. D.$4\ell^2mn$

Correct answer: A

Locus of the image of the point $(2, 3)$ in the line $(2x - 3y + 4) + k(x - 2y + 3) = 0$, $k \in \mathbb{R}$, is a :

1. A.straight line parallel to y-axis.
2. B.circle of radius $\sqrt{2}$.✓
3. C.circle of radius $\sqrt{3}$.
4. D.straight line parallel to x-axis.

Correct answer: B

The area (in sq. units) of the quadrilateral formed by the tangents at the end points of the latera recta to the ellipse $\frac{x^2}{9} + \frac{y^2}{5} = 1$, is :

1. A.18
2. B.$\frac{27}{2}$
3. C.27✓
4. D.$\frac{27}{4}$

Correct answer: C

The number of integers greater than 6,000 that can be formed, using the digits 3, 5, 6, 7 and 8, without repetition, is :

1. A.192✓
2. B.120
3. C.72
4. D.216

Correct answer: A

Let A and B be two sets containing four and two elements respectively. Then the number of subsets of the set $A \times B$, each having at least three elements is :

1. A.256
2. B.275
3. C.510
4. D.219✓

Correct answer: D

Let $\tan^{-1}y = \tan^{-1}x + \tan^{-1}\left(\frac{2x}{1-x^2}\right)$, where $|x| < \frac{1}{\sqrt{3}}$. Then a value of y is :

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

Correct answer: D

The integral $\int_2^4 \frac{\log x^2}{\log x^2 + \log(36 - 12x + x^2)}\,dx$ is equal to :

1. A.4
2. B.1✓
3. C.6
4. D.2

Correct answer: B

The negation of $\sim s \vee (\sim r \wedge s)$ is equivalent to :

1. A.$s \wedge (r \wedge \sim s)$
2. B.$s \vee (r \vee \sim s)$
3. C.$s \wedge r$✓
4. D.$s \wedge \sim r$

Correct answer: C

If the angles of elevation of the top of a tower from three collinear points A, B and C, on a line leading to the foot of the tower, are $30^\circ$, $45^\circ$ and $60^\circ$ respectively, then the ratio, AB : BC, is :

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

Correct answer: D

$\lim_{x\to0}\frac{(1 - \cos 2x)(3 + \cos x)}{x\tan 4x}$ is equal to :

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

Correct answer: B

Let $\vec{a}$, $\vec{b}$ and $\vec{c}$ be three non-zero vectors such that no two of them are collinear and $(\vec{a}\times\vec{b})\times\vec{c} = \frac{1}{3}|\vec{b}||\vec{c}|\vec{a}$. If $\theta$ is the angle between vectors $\vec{b}$ and $\vec{c}$, then a value of $\sin\theta$ is :

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

Correct answer: D

If $A = \begin{bmatrix} 1 & 2 & 2 \\ 2 & 1 & -2 \\ a & 2 & b \end{bmatrix}$ is a matrix satisfying the equation $AA^T = 9I$, where I is $3\times3$ identity matrix, then ordered pair $(a, b)$ is equal to :

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

Correct answer: C

If the function $g(x) = \begin{cases} k\sqrt{x+1}, & 0 \le x \le 3 \\ mx + 2, & 3 < x \le 5 \end{cases}$ is differentiable, then the value of $k + m$ is :

1. A.$\frac{16}{5}$
2. B.$\frac{10}{3}$
3. C.4
4. D.2✓

Correct answer: D

The set of all values of $\lambda$ for which the system of linear equations $2x_1 - 2x_2 + x_3 = \lambda x_1$, $2x_1 - 3x_2 + 2x_3 = \lambda x_2$, $-x_1 + 2x_2 = \lambda x_3$ has a non-trivial solution,

1. A.is a singleton.
2. B.contains two elements.✓
3. C.contains more than two elements.
4. D.is an empty set.

Correct answer: B

The normal to the curve, $x^2 + 2xy - 3y^2 = 0$, at $(1, 1)$ :

1. A.meets the curve again in the second quadrant.
2. B.meets the curve again in the third quadrant.
3. C.meets the curve again in the fourth quadrant.✓
4. D.does not meet the curve again.

Correct answer: C

The number of common tangents to the circles $x^2 + y^2 - 4x - 6y - 12 = 0$ and $x^2 + y^2 + 6x + 18y + 26 = 0$, is :

1. A.2
2. B.3✓
3. C.4
4. D.1

Correct answer: B

Let y(x) be the solution of the differential equation $(x\log x)\frac{dy}{dx} + y = 2x\log x$, $(x \ge 1)$. Then y(e) is equal to :

1. A.0
2. B.2✓
3. C.2e
4. D.e

Correct answer: B

As an electron makes a transition from an excited state to the ground state of a hydrogen - like atom/ion:

1. A.kinetic energy, potential energy and total energy decrease
2. B.kinetic energy decreases, potential energy increases but total energy remains same
3. C.kinetic energy and total energy decrease but potential energy increases
4. D.its kinetic energy increases but potential energy and total energy decrease✓

Correct answer: D

The period of oscillation of a simple pendulum is $T = 2\pi\sqrt{\frac{L}{g}}$. Measured value of L is 20.0 cm known to 1 mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using wrist watch of 1 s resolution. The accuracy in the determination of g is:

1. A.3%✓
2. B.1%
3. C.5%
4. D.2%

Correct answer: A

A long cylindrical shell carries positive surface charge $\sigma$ in the upper half and negative surface charge $-\sigma$ in the lower half. The electric field lines around the cylinder will look like figure given in: (figures are schematic and not drawn to scale)

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

Correct answer: D

A signal of 5 kHz frequency is amplitude modulated on a carrier wave of frequency 2 MHz. The frequencies of the resultant signal is/are:

1. A.2005 kHz, and 1995 kHz
2. B.2005 kHz, 2000 kHz and 1995 kHz✓
3. C.2000 kHz and 1995 kHz
4. D.2 MHz only

Correct answer: B

Consider a spherical shell of radius R at temperature T. The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume $u = \frac{U}{V} \propto T^4$ and pressure $p = \frac{1}{3}\left(\frac{U}{V}\right)$. If the shell now undergoes an adiabatic expansion the relation between T and R is:

1. A.$T \propto e^{-3R}$
2. B.$T \propto \frac{1}{R}$✓
3. C.$T \propto \frac{1}{R^3}$
4. D.$T \propto e^{-R}$

Correct answer: B

An inductor $(L = 0.03$ H$)$ and a resistor $(R = 0.15$ k$\Omega)$ are connected in series to a battery of 15V EMF in a circuit shown. The key $K_1$ has been kept closed for a long time. Then at $t = 0$, $K_1$ is opened and key $K_2$ is closed simultaneously. At $t = 1$ ms, the current in the circuit will be: $(e^5 \cong 150)$

1. A.67 mA
2. B.6.7 mA
3. C.0.67 mA✓
4. D.100 mA

Correct answer: C

A pendulum made of a uniform wire of cross sectional area A has time period T. When an additional mass M is added to its bob, the time period changes to $T_M$. If the Young's modulus of the material of the wire is Y then $\frac{1}{Y}$ is equal to: (g = gravitational acceleration)

1. A.$\left[\left(\frac{T_M}{T}\right)^2 - 1\right]\frac{Mg}{A}$
2. B.$\left[1 - \left(\frac{T_M}{T}\right)^2\right]\frac{A}{Mg}$
3. C.$\left[1 - \left(\frac{T}{T_M}\right)^2\right]\frac{A}{Mg}$
4. D.$\left[\left(\frac{T_M}{T}\right)^2 - 1\right]\frac{A}{Mg}$✓

Correct answer: D

A red LED emits light at 0.1 watt uniformly around it. The amplitude of the electric field of the light at a distance of 1 m from the diode is:

1. A.2.45 V/m✓
2. B.5.48 V/m
3. C.7.75 V/m
4. D.1.73 V/m

Correct answer: A

Two coaxial solenoids of different radii carry current I in the same direction. Let $\vec{F}_1$ be the magnetic force on the inner solenoid due to the outer one and $\vec{F}_2$ be the magnetic force on the outer solenoid due to the inner one. Then: