JEE Main 2013 — 7 Apr Offline Set Q (Previous Year Paper)

An unknown alcohol is treated with the 'Lucas reagent' to determine whether the alcohol is primary, secondary or tertiary. Which alcohol reacts fastest and by what mechanism:

1. A.tertiary alcohol by $S_N1$✓
2. B.secondary alcohol by $S_N2$
3. C.tertiary alcohol by $S_N2$
4. D.secondary alcohol by $S_N1$

Correct answer: A

The first ionization potential of Na is 5.1 eV. The value of electron gain enthalpy of $Na^+$ will be:

1. A.$-5.1$ eV✓
2. B.$-10.2$ eV
3. C.$+2.55$ eV
4. D.$-2.55$ eV

Correct answer: A

Stability of the species $Li_2$, $Li_2^-$ and $Li_2^+$ increases in the order of:

1. A.$Li_2^- < Li_2^+ < Li_2$✓
2. B.$Li_2 < Li_2^- < Li_2^+$
3. C.$Li_2^- < Li_2 < Li_2^+$
4. D.$Li_2 < Li_2^+ < Li_2^-$

Correct answer: A

The molarity of a solution obtained by mixing 750 mL of 0.5 (M) HCl with 250 mL of 2(M) HCl will be:

1. A.1.00 M
2. B.1.75 M
3. C.0.975 M
4. D.0.875 M✓

Correct answer: D

Four successive members of the first row transition elements are listed below with atomic numbers. Which one of them is expected to have the highest $E^\circ_{M^{3+}/M^{2+}}$ value?

1. A.Mn (Z = 25)
2. B.Fe (Z = 26)
3. C.Co (Z = 27)✓
4. D.Cr (Z = 24)

Correct answer: C

A solution of $(-)$-1-chloro-1-phenylethane in toluene racemises slowly in the presence of a small amount of $SbCl_5$, due to the formation of :

1. A.carbene
2. B.carbocation✓
3. C.free radical
4. D.carbanion

Correct answer: B

The coagulating power of electrolytes having ions $Na^+$, $Al^{3+}$ and $Ba^{2+}$ for arsenic sulphide sol increases in the order:

1. A.$Na^+ < Ba^{2+} < Al^{3+}$✓
2. B.$Ba^{2+} < Na^+ < Al^{3+}$
3. C.$Al^{3+} < Na^+ < Ba^{2+}$
4. D.$Al^{3+} < Ba^{2+} < Na^+$

Correct answer: A

How many litres of water must be added to 1 litre of an aqueous solution of HCl with a pH of 1 to create an aqueous solution with pH of 2?

1. A.0.9 L
2. B.2.0 L
3. C.9.0 L✓
4. D.0.1 L

Correct answer: C

Experimentally it was found that a metal oxide has formula $M_{0.98}O$. Metal M, is present as $M^{2+}$ and $M^{3+}$ in its oxide. Fraction of the metal which exists as $M^{3+}$ would be:

1. A.4.08%✓
2. B.6.05%
3. C.5.08%
4. D.7.01%

Correct answer: A

A compound with molecular mass 180 is acylated with $CH_3COCl$ to get a compound with molecular mass 390. The number of amino groups present per molecule of the former compound is:

1. A.5✓
2. B.4
3. C.6
4. D.2

Correct answer: A

Given $E^\circ_{Cr^{3+}/Cr} = -0.74$ V; $E^\circ_{MnO_4^-/Mn^{2+}} = 1.51$ V; $E^\circ_{Cr_2O_7^{2-}/Cr^{3+}} = 1.33$ V; $E^\circ_{Cl/Cl^-} = 1.36$ V. Based on the data given above, strongest oxidising agent will be:

1. A.$Cr^{3+}$
2. B.$Mn^{2+}$
3. C.$MnO_4^-$✓
4. D.$Cl^-$

Correct answer: C

Arrange the following compounds in order of decreasing acidity: (I) p-chlorophenol, (II) p-cresol (p-methylphenol), (III) p-nitrophenol, (IV) p-methoxyphenol

1. A.I > II > III > IV
2. B.III > I > II > IV✓
3. C.IV > III > I > II
4. D.II > IV > I > III

Correct answer: B

The rate of a reaction doubles when its temperature changes from 300K to 310K. Activation energy of such a reaction will be: ($R = 8.314$ JK$^{-1}$ mol$^{-1}$ and log 2 = 0.301)

1. A.48.6 kJ mol$^{-1}$
2. B.58.5 kJ mol$^{-1}$
3. C.60.5 kJ mol$^{-1}$
4. D.53.6 kJ mol$^{-1}$✓

Correct answer: D

Synthesis of each molecule of glucose in photosynthesis involves:

1. A.10 molecules of ATP
2. B.8 molecules of ATP
3. C.6 molecules of ATP
4. D.18 molecules of ATP✓

Correct answer: D

Which of the following complex species is not expected to exhibit optical isomerism?

1. A.$[Co(en)_2Cl_2]^+$
2. B.$[Co(NH_3)_3Cl_3]$✓
3. C.$[Co(en)(NH_3)_2Cl_2]^+$
4. D.$[Co(en)_3]^{3+}$

Correct answer: B

A piston filled with 0.04 mol of an ideal gas expands reversibly from 50.0 mL to 375 mL at a constant temperature of $37.0^\circ$C. As it does so, it absorbs 208J of heat. The values of q and w for the process will be: ($R = 8.314$ J/mol K) ($\ln7.5 = 2.01$)

1. A.$q = -208$ J, $w = -208$ J
2. B.$q = -208$ J, $w = +208$ J
3. C.$q = +208$ J, $w = +208$ J
4. D.$q = +208$ J, $w = -208$ J✓

Correct answer: D

A gaseous hydrocarbon gives upon combustion 0.72 g of water and 3.08 g of $CO_2$. The empirical formula of the hydrocarbon is:

1. A.$C_3H_4$
2. B.$C_6H_5$
3. C.$C_7H_8$✓
4. D.$C_2H_4$

Correct answer: C

The order of stability of the following carbocations: (I) $CH_2=CH-CH_2^+$ (allyl), (II) $CH_3CH_2CH_2^+$ (n-propyl), (III) $C_6H_5CH_2^+$ (benzyl) is:

1. A.II > III > I
2. B.I > II > III
3. C.III > I > II✓
4. D.III > II > I

Correct answer: C

Which of the following represents the correct order of increasing first ionization enthalpy for Ca, Ba, S, Se and Ar?

1. A.S < Se < Ca < Ba < Ar
2. B.Ba < Ca < Se < S < Ar✓
3. C.Ca < Ba < S < Se < Ar
4. D.Ca < S < Ba < Se < Ar

Correct answer: B

For gaseous state, if most probable speed is denoted by $C^*$, average speed by $\bar{C}$ and mean square speed by C, then for a large number of molecules the ratios of these speeds are:

1. A.$C^* : \bar{C} : C = 1.128 : 1.225 : 1$
2. B.$C^* : \bar{C} : C = 1 : 1.128 : 1.225$✓
3. C.$C^* : \bar{C} : C = 1 : 1.125 : 1.128$
4. D.$C^* : \bar{C} : C = 1.225 : 1.128 : 1$

Correct answer: B

The gas leaked from a storage tank of the Union Carbide plant in Bhopal gas tragedy was:

1. A.Methylamine
2. B.Ammonia
3. C.Phosgene
4. D.Methylisocyanate✓

Correct answer: D

Consider the following reaction: $xMnO_4^- + yC_2O_4^{2-} + zH^+ \rightarrow xMn^{2+} + 2yCO_2 + \frac{z}{2}H_2O$. The values of x, y and z in the reaction are, respectively:

1. A.2, 5 and 8
2. B.2, 5 and 16✓
3. C.5, 2 and 8
4. D.5, 2 and 16

Correct answer: B

Which of the following exists as covalent crystals in the solid state?

1. A.Silicon✓
2. B.Sulphur
3. C.Phosphorous
4. D.Iodine

Correct answer: A

Compound (A), $C_8H_9Br$, gives a white precipitate when warmed with alcoholic $AgNO_3$. Oxidation of (A) gives an acid (B), $C_8H_6O_4$. (B) easily forms anhydride on heating. Identify the compound (A).

1. A.1-bromo-2-ethylbenzene
2. B.4-methylbenzyl bromide
3. C.2-methylbenzyl bromide✓
4. D.3-methylbenzyl bromide

Correct answer: C

Energy of an electron is given by $E = -2.178\times10^{-18}$ J $\left(\frac{Z^2}{n^2}\right)$. Wavelength of light required to excite an electron in an hydrogen atom from level n = 1 to n = 2 will be ($h = 6.62\times10^{-34}$ Js and $c = 3.0\times10^8$ ms$^{-1}$)

1. A.$2.816\times10^{-7}$ m
2. B.$6.500\times10^{-7}$ m
3. C.$8.500\times10^{-7}$ m
4. D.$1.214\times10^{-7}$ m✓

Correct answer: D

An organic compound A upon reacting with $NH_3$ gives B. On heating B gives C. C in presence of KOH reacts with $Br_2$ to give $CH_3CH_2NH_2$. A is

1. A.$CH_3CH_2CH_2COOH$
2. B.$CH_3CH(CH_3)COOH$
3. C.$CH_3CH_2COOH$✓
4. D.$CH_3COOH$

Correct answer: C

In which of the following pairs of molecules/ions, both the species are not likely to exist?

1. A.$H_2^-$, $He_2^{2-}$
2. B.$H_2^{2+}$, $He_2$✓
3. C.$H_2^-$, $He_2^{2+}$
4. D.$H_2^+$, $He_2^{2-}$

Correct answer: B

The circle passing through $(1, -2)$ and touching the axis of x at $(3, 0)$ also passes through the point

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

Correct answer: B

ABCD is a trapezium such that AB and CD are parallel and $BC \perp CD$. If $\angle ADB = \theta$, BC = p and CD = q, then AB is equal to

1. A.$\frac{p^2+q^2\cos\theta}{p\cos\theta+q\sin\theta}$
2. B.$\frac{p^2+q^2}{p^2\cos\theta+q^2\sin\theta}$
3. C.$\frac{(p^2+q^2)\sin\theta}{(p\cos\theta+q\sin\theta)^2}$
4. D.$\frac{(p^2+q^2)\sin\theta}{p\cos\theta+q\sin\theta}$✓

Correct answer: D

Given : A circle, $2x^2 + 2y^2 = 5$ and a parabola, $y^2 = 4\sqrt{5}x$. Statement-I : An equation of a common tangent to these curves is $y = x + \sqrt{5}$. Statement-II : If the line, $y = mx + \frac{\sqrt{5}}{m}$ $(m \ne 0)$ is their common tangent, then m satisfies $m^4 - 3m^2 + 2 = 0$.

1. A.Statement-I is True; Statement-II is true; Statement-II is not a correct explanation for Statement-I✓
2. B.Statement-I is True; Statement-II is False.
3. C.Statement-I is False; Statement-II is True
4. D.Statement-I is True; Statement-II is True; Statement-II is a correct explanation for Statement-I

Correct answer: A

A ray of light along $x + \sqrt{3}y = \sqrt{3}$ gets reflected upon reaching x-axis, the equation of the reflected rays is

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

Correct answer: A

All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of 10 to each of the students. Which of the following statistical measures will not change even after the grace marks were given ?

1. A.median
2. B.mode
3. C.variance✓
4. D.mean

Correct answer: C

If x, y, z are in A.P. and $\tan^{-1}x$, $\tan^{-1}y$ and $\tan^{-1}z$ are also in A.P., then

1. A.$2x = 3y = 6z$
2. B.$6x = 3y = 2z$
3. C.$6x = 4y = 3z$
4. D.$x = y = z$✓

Correct answer: D

If $\int f(x)\,dx = \Psi(x)$, then $\int x^5 f(x^3)\,dx$ is equal to

1. A.$\frac{1}{3}x^3\Psi(x^3) - 3\int x^3\Psi(x^3)\,dx + C$
2. B.$\frac{1}{3}x^3\Psi(x^3) - \int x^2\Psi(x^3)\,dx + C$✓
3. C.$\frac{1}{3}\left[x^3\Psi(x^3) - \int x^3\Psi(x^3)\,dx\right] + C$
4. D.$\frac{1}{3}\left[x^3\Psi(x^3) - \int x^2\Psi(x^3)\,dx\right] + C$

Correct answer: B

The equation of the circle passing through the foci of the ellipse $\frac{x^2}{16} + \frac{y^2}{9} = 1$, and having centre at $(0, 3)$ is

1. A.$x^2 + y^2 - 6y + 7 = 0$
2. B.$x^2 + y^2 - 6y - 5 = 0$
3. C.$x^2 + y^2 - 6y + 5 = 0$
4. D.$x^2 + y^2 - 6y - 7 = 0$✓

Correct answer: D

The x-coordinate of the incentre of the triangle that has the coordinates of mid points of its sides as $(0, 1)$, $(1, 1)$ and $(1, 0)$ is

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

Correct answer: A

The intercepts on x-axis made by tangents to the curve, $y = \int_0^x |t|\,dt$, $x \in \mathbb{R}$, which are parallel to the line $y = 2x$, are equal to

1. A.$\pm2$
2. B.$\pm3$
3. C.$\pm4$
4. D.$\pm1$✓

Correct answer: D

The sum of first 20 terms of the sequence 0.7, 0.77, 0.777, ....., is

1. A.$\frac{7}{9}(99 - 10^{-20})$
2. B.$\frac{7}{81}(179 + 10^{-20})$✓
3. C.$\frac{7}{9}(99 + 10^{-20})$
4. D.$\frac{7}{81}(179 - 10^{-20})$

Correct answer: B

Consider : Statement-I : $(p\wedge\sim q)\wedge(\sim p\wedge q)$ is a fallacy. Statement-II : $(p \to q) \leftrightarrow (\sim q \to \sim p)$ is a tautology.

1. A.Statement-I is True; Statement-II is true; Statement-II is not a correct explanation for Statement-I✓
2. B.Statement-I is True; Statement-II is False.
3. C.Statement-I is False; Statement-II is True
4. D.Statement-I is True; Statement-II is True; Statement-II is a correct explanation for Statement-I

Correct answer: A

The area (in square units) bounded by the curves $y = \sqrt{x}$, $2y - x + 3 = 0$, x-axis, and lying in the first quadrant is

1. A.36
2. B.18
3. C.$\frac{27}{4}$
4. D.9✓

Correct answer: D

The expression $\frac{\tan A}{1-\cot A} + \frac{\cot A}{1-\tan A}$ can be written as

1. A.secA cosecA + 1✓
2. B.tanA + cotA
3. C.secA + cosecA
4. D.sinA cosA + 1

Correct answer: A

The real number k for which the equation, $2x^3 + 3x + k = 0$ has two distinct real roots in [0, 1]

1. A.lies between 2 and 3
2. B.lies between $-1$ and 0
3. C.does not exist✓
4. D.lies between 1 and 2

Correct answer: C

$\lim_{x\to0}\frac{(1-\cos2x)(3+\cos x)}{x\tan4x}$ is equal to

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

Correct answer: C

Let $T_n$ be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. If $T_{n+1} - T_n = 10$, then the value of n is

1. A.5✓
2. B.10
3. C.8
4. D.7

Correct answer: A

At present, a firm is manufacturing 2000 items. It is estimated that the rate of change of production P w.r.t. additional number of workers x is given by $\frac{dP}{dx} = 100 - 12\sqrt{x}$. If the firm employs 25 more workers, then the new level of production of items is

1. A.3000
2. B.3500✓
3. C.4500
4. D.2500

Correct answer: B

Statement-I : The value of the integral $\int_{\pi/6}^{\pi/3}\frac{dx}{1+\sqrt{\tan x}}$ is equal to $\frac{\pi}{6}$. Statement-II : $\int_a^b f(x)\,dx = \int_a^b f(a+b-x)\,dx$.

1. A.Statement-I is True; Statement-II is true; Statement-II is not a correct explanation for Statement-I
2. B.Statement-I is True; Statement-II is False.
3. C.Statement-I is False; Statement-II is True✓
4. D.Statement-I is True; Statement-II is True; Statement-II is a correct explanation for Statement-I

Correct answer: C

If $P = \begin{bmatrix} 1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4 \end{bmatrix}$ is the adjoint of a $3\times3$ matrix A and $|A| = 4$, then $\alpha$ is equal to

1. A.11✓
2. B.5
3. C.0
4. D.4

Correct answer: A

The number of values of k, for which the system of equations $(k + 1)x + 8y = 4k$, $kx + (k + 3)y = 3k - 1$ has no solution, is

1. A.1✓
2. B.2
3. C.3
4. D.infinite

Correct answer: A

If $y = \sec(\tan^{-1}x)$, then $\frac{dy}{dx}$ at $x = 1$ is equal to

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

Correct answer: D

If the lines $\frac{x-2}{1} = \frac{y-3}{1} = \frac{z-4}{-k}$ and $\frac{x-1}{k} = \frac{y-4}{2} = \frac{z-5}{1}$ are coplanar, then k can have

1. A.exactly one value
2. B.exactly two values✓
3. C.exactly three values
4. D.any value

Correct answer: B

Let A and B be two sets containing 2 elements and 4 elements respectively. The number of subsets of $A \times B$ having 3 or more elements is

1. A.220
2. B.219✓
3. C.211
4. D.256

Correct answer: B

If the vectors $\vec{AB} = 3\hat{i} + 4\hat{k}$ and $\vec{AC} = 5\hat{i} - 2\hat{j} + 4\hat{k}$ are the sides of a triangle ABC, then the length of the median through A is

1. A.$\sqrt{72}$
2. B.$\sqrt{33}$✓
3. C.$\sqrt{45}$
4. D.$\sqrt{18}$

Correct answer: B

A multiple choice examination has 5 questions. Each question has three alternative answers of which exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is

1. A.$\frac{13}{3^5}$
2. B.$\frac{11}{3^5}$✓
3. C.$\frac{10}{3^5}$
4. D.$\frac{17}{3^5}$

Correct answer: B

If z is a complex number of unit modulus and argument $\theta$, then $\arg\left(\frac{1+z}{1+\bar{z}}\right)$ equals

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

Correct answer: B

If the equations $x^2 + 2x + 3 = 0$ and $ax^2 + bx + c = 0$, $a, b, c \in \mathbb{R}$, have a common root, then $a : b : c$ is

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

Correct answer: D

Distance between two parallel planes $2x + y + 2z = 8$ and $4x + 2y + 4z + 5 = 0$ is

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

Correct answer: B

The term independent of x in expansion of $\left(\frac{x+1}{x^{2/3} - x^{1/3} + 1} - \frac{x-1}{x - x^{1/2}}\right)^{10}$ is

1. A.120
2. B.210✓
3. C.310
4. D.4

Correct answer: B

In an LCR circuit as shown below both switches are open initially. Now switch $S_1$ is closed, $S_2$ kept open. (q is charge on the capacitor and $\tau = RC$ is capacitive time constant). Which of the following statement is correct?

1. A.At $t = \tau$, $q = CV/2$
2. B.At $t = 2\tau$, $q = CV(1 - e^{-2})$✓
3. C.At $t = \frac{\tau}{2}$, $q = CV(1 - e^{-1})$
4. D.Work done by the battery is half of the energy dissipated in the resistor.

Correct answer: B

The supply voltage to a room is 120 V. The resistance of the lead wires is $6\,\Omega$. A 60 W bulb is already switched on. What is the decrease of voltage across the bulb, when a 240 W heater is switched on in parallel to the bulb?

1. A.2.9 Volt
2. B.13.3 Volt
3. C.10.04 Volt✓
4. D.zero volt

Correct answer: C

A uniform cylinder of length L and mass M having cross-sectional area A is suspended, with its length vertical, from a fixed point by a massless spring, such that it is half submerged in a liquid of density $\sigma$ at equilibrium position. The extension $x_0$ of the spring when it is in equilibrium is: (Here k is spring constant)

1. A.$\frac{Mg}{k}\left(1-\frac{LA\sigma}{M}\right)$
2. B.$\frac{Mg}{k}\left(1-\frac{LA\sigma}{2M}\right)$✓
3. C.$\frac{Mg}{k}\left(1+\frac{LA\sigma}{M}\right)$
4. D.$\frac{Mg}{k}$

Correct answer: B

Two charges, each equal to q, are kept at $x = -a$ and $x = a$ on the x-axis. A particle of mass m and charge $q_0 = \frac{q}{2}$ is placed at the origin. If charge $q_0$ is given a small displacement $(y \ll a)$ along the y-axis, the net force acting on the particle is proportional to:

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

Correct answer: D

A beam of unpolarised light of intensity $I_0$ is passed through a polaroid A and then through another polaroid B which is oriented so that its principal plane makes an angle of $45^\circ$ relative to that of A. The intensity of the emergent light is:

1. A.$I_0/2$
2. B.$I_0/4$✓
3. C.$I_0/8$
4. D.$I_0$

Correct answer: B

The anode voltage of a photocell is kept fixed. The wavelength $\lambda$ of the light falling on the cathode is gradually changed. The plate current I of the photocell varies as follows:

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

Correct answer: C

Two coherent point sources $S_1$ and $S_2$ are separated by a small distance 'd' as shown. The fringes obtained on the screen will be:

1. A.straight lines
2. B.semi-circles
3. C.concentric circles✓
4. D.points

Correct answer: C

A metallic rod of length $\ell$ is tied to a string of length $2\ell$ and made to rotate with angular speed $\omega$ on a horizontal table with one end of the string fixed. If there is a vertical magnetic field B in the region, the e.m.f. induced across the ends of the rod is:

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