JEE Main 2016 — 3 Apr Offline Set F (Previous Year Paper)

A stream of electrons from a heated filament was passed between two charged plates kept at a potential difference V esu. If e and m are charge and mass of an electron, respectively, then the value of $h/\lambda$ (where $\lambda$ is wavelength associated with electron wave) is given by :

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

Correct answer: C

2-chloro-2-methylpentane on reaction with sodium methoxide in methanol yields : (a) $C_2H_5CH_2C(CH_3)_2OCH_3$ (b) $C_2H_5CH_2C(CH_3)=CH_2$ (c) $C_2H_5CH=C(CH_3)CH_3$

1. A.(a) and (c)
2. B.(c) only
3. C.(a) and (b)
4. D.All of these✓

Correct answer: D

Which of the following compounds is metallic and ferromagnetic ?

1. A.$CrO_2$✓
2. B.$VO_2$
3. C.$MnO_2$
4. D.$TiO_2$

Correct answer: A

Which of the following statements about low density polythene is FALSE ?

1. A.It is a poor conductor of electricity.
2. B.Its synthesis requires dioxygen or a peroxide initiator as a catalyst.
3. C.It is used in the manufacture of buckets, dust-bins etc.✓
4. D.Its synthesis requires high pressure.

Correct answer: C

For a linear plot of $\log(x/m)$ versus $\log p$ in a Freundlich adsorption isotherm, which of the following statements is correct ? (k and n are constants)

1. A.$1/n$ appears as the intercept.
2. B.Only $1/n$ appears as the slope✓
3. C.$\log(1/n)$ appears as the intercept.
4. D.Both k and $1/n$ appear in the slope term.

Correct answer: B

The heats of combustion of carbon and carbon monoxide are $-393.5$ and $-283.5$ kJ mol$^{-1}$, respectively. The heat of formation (in kJ) of carbon monoxide per mole is :

1. A.676.5
2. B.$-676.5$
3. C.$-110.5$✓
4. D.110.5

Correct answer: C

The hottest region of Bunsen flame shown in the figure below is :

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

Correct answer: A

Which of the following is an anionic detergent ?

1. A.Sodium lauryl sulphate✓
2. B.Cetyltrimethyl ammonium bromide
3. C.Glyceryl oleate
4. D.Sodium stearate

Correct answer: A

18 g glucose $(C_6H_{12}O_6)$ is added to 178.2 g water. The vapour pressure of water (in torr) for this aqueous solution is :

1. A.76.0
2. B.752.4✓
3. C.759.0
4. D.7.6

Correct answer: B

The distillation technique most suited for separating glycerol from spent-lye in the soap industry is :

1. A.Fractional distillation
2. B.Steam distillation
3. C.Distillation under reduced pressure✓
4. D.Simple distillation

Correct answer: C

The species in which the N atom is in a state of sp hybridization is :

1. A.$NO_2^-$
2. B.$NO_3^-$
3. C.$NO_2$
4. D.$NO_2^+$✓

Correct answer: D

Decomposition of $H_2O_2$ follows a first order reaction. In fifty minutes the concentration of $H_2O_2$ decreases from 0.5 to 0.125 M in one such decomposition. When the concentration of $H_2O_2$ reaches 0.05 M, the rate of formation of $O_2$ will be :

1. A.$6.93\times10^{-4}$ mol min$^{-1}$✓
2. B.2.66 L min$^{-1}$ at STP
3. C.$1.34\times10^{-2}$ mol min$^{-1}$
4. D.$6.93\times10^{-2}$ mol min$^{-1}$

Correct answer: A

The pair having the same magnetic moment is : [At. No.: Cr = 24, Mn = 25, Fe = 26, Co = 27]

1. A.$[Cr(H_2O)_6]^{2+}$ and $[Fe(H_2O)_6]^{2+}$✓
2. B.$[Mn(H_2O)_6]^{2+}$ and $[Cr(H_2O)_6]^{2+}$
3. C.$[CoCl_4]^{2-}$ and $[Fe(H_2O)_6]^{2+}$
4. D.$[Cr(H_2O)_6]^{2+}$ and $[CoCl_4]^{2-}$

Correct answer: A

The absolute configuration of the Fischer projection with $CO_2H$ at top, $CH_3$ at bottom, C2 bearing H (left) and OH (right), C3 bearing H (left) and Cl (right) is :

1. A.(2S, 3R)✓
2. B.(2S, 3S)
3. C.(2R, 3R)
4. D.(2R, 3S)

Correct answer: A

The equilibrium constant at 298 K for a reaction $A + B \rightleftharpoons C + D$ is 100. If the initial concentration of all the four species were 1M each, then equilibrium concentration of D (in mol L$^{-1}$) will be:

1. A.0.818
2. B.1.818✓
3. C.1.182
4. D.0.182

Correct answer: B

Which one of the following ores is best concentrated by froth floatation method?

1. A.Siderite
2. B.Galena✓
3. C.Malachite
4. D.Magnetite

Correct answer: B

The pair in which phosphorous atoms have a formal oxidation state of +3 is:

1. A.Pyrophosphorous and hypophosphoric acids
2. B.Orthophosphorous and hypophosphoric acids
3. C.Pyrophosphorous and pyrophosphoric acids
4. D.Orthophosphorous and pyrophosphorous acids✓

Correct answer: D

Which one of the following complexes shows optical isomerism? (en = ethylenediamine)

1. A.cis$[Co(en)_2Cl_2]Cl$✓
2. B.trans$[Co(en)_2Cl_2]Cl$
3. C.$[Co(NH_3)_4Cl_2]Cl$
4. D.$[Co(NH_3)_3Cl_3]$

Correct answer: A

The reaction of zinc with dilute and concentrated nitric acid, respectively, produces:

1. A.$NO_2$ and $NO$
2. B.$NO$ and $N_2O$
3. C.$NO_2$ and $N_2O$
4. D.$N_2O$ and $NO_2$✓

Correct answer: D

Which one of the following statements about water is FALSE?

1. A.Water can act both as an acid and as a base.
2. B.There is extensive intramolecular hydrogen bonding in the condensed phase.✓
3. C.Ice formed by heavy water sinks in normal water
4. D.Water is oxidized to oxygen during photosynthesis

Correct answer: B

The concentration of fluoride, lead, nitrate and iron in a water sample from an underground lake was found to be 1000 ppb, 40 ppb, 100 ppm and 0.2 ppm, respectively. This water is unsuitable for drinking due to high concentration of :

1. A.Lead
2. B.Nitrate✓
3. C.Iron
4. D.Fluoride

Correct answer: B

The main oxides formed on combustion of Li, Na and K in excess of air are, respectively:

1. A.$LiO_2$, $Na_2O_2$ and $K_2O$
2. B.$Li_2O_2$, $Na_2O_2$ and $KO_2$
3. C.$Li_2O$, $Na_2O_2$ and $KO_2$✓
4. D.$Li_2O$, $Na_2O$ and $KO_2$

Correct answer: C

Thiol group is present in :

1. A.Cystine
2. B.Cysteine✓
3. C.Methionine
4. D.Cytosine

Correct answer: B

Galvanization is applying a coating of:

1. A.Cr
2. B.Cu
3. C.Zn✓
4. D.Pb

Correct answer: C

Which of the following atoms has the highest first ionization energy?

1. A.Na
2. B.K
3. C.Sc✓
4. D.Rb

Correct answer: C

In the Hofmann bromamide degradation reaction, the number of moles of NaOH and $Br_2$ used per mole of amine produced are:

1. A.Four moles of NaOH and two moles of $Br_2$.
2. B.Two moles of NaOH and two moles of $Br_2$
3. C.Four moles of NaOH and one mole of $Br_2$✓
4. D.One mole of NaOH and one mole of $Br_2$

Correct answer: C

Two closed bulbs of equal volume (V) containing an ideal gas initially at pressure $p_i$ and temperature $T_1$ are connected through a narrow tube of negligible volume as shown in the figure below. The temperature of one of the bulbs is then raised to $T_2$. The final pressure $p_f$ is

1. A.$2p_i\left(\frac{T_1}{T_1+T_2}\right)$
2. B.$2p_i\left(\frac{T_2}{T_1+T_2}\right)$✓
3. C.$2p_i\left(\frac{T_1T_2}{T_1+T_2}\right)$
4. D.$p_i\left(\frac{T_1T_2}{T_1+T_2}\right)$

Correct answer: B

The reaction of propene with HOCl $(Cl_2 + H_2O)$ proceeds through the intermediate:

1. A.$CH_3-CH^+-CH_2-Cl$✓
2. B.$CH_3-CH(OH)-CH_2^+$
3. C.$CH_3-CHCl-CH_2^+$
4. D.$CH_3-CH^+-CH_2-OH$

Correct answer: A

The product of the reaction given below is: 4-tert-butylcyclohexene $\xrightarrow{1.\ NBS/h\nu;\ 2.\ H_2O/K_2CO_3}$ X

1. A.5-tert-butylcyclohex-2-en-1-ol✓
2. B.5-tert-butylcyclohex-2-en-1-one
3. C.5-tert-butylcyclohex-2-ene-1-carboxylic acid
4. D.4-tert-butylcyclohexene (unchanged)

Correct answer: A

Two sides of a rhombus are along the lines, $x - y + 1 = 0$ and $7x - y - 5 = 0$. If its diagonals intersect at $(-1, -2)$, then which one of the following is a vertex of this rhombus?

1. A.$(-3, -8)$
2. B.$\left(\frac{1}{3}, -\frac{8}{3}\right)$✓
3. C.$\left(-\frac{10}{3}, -\frac{7}{3}\right)$
4. D.$(-3, -9)$

Correct answer: B

If the $2^{nd}$, $5^{th}$ and $9^{th}$ terms of a non-constant A.P. are in G.P., then the common ratio of this G.P. is:

1. A.$\frac{4}{3}$✓
2. B.1
3. C.$\frac{7}{4}$
4. D.$\frac{8}{5}$

Correct answer: A

Let P be the point on the parabola, $y^2 = 8x$ which is at a minimum distance from the centre C of the circle, $x^2 + (y + 6)^2 = 1$. Then the equation of the circle, passing through C and having its centre at P is:

1. A.$x^2 + y^2 - x + 4y - 12 = 0$
2. B.$x^2 + y^2 - \frac{x}{4} + 2y - 24 = 0$
3. C.$x^2 + y^2 - 4x + 9y + 18 = 0$
4. D.$x^2 + y^2 - 4x + 8y + 12 = 0$✓

Correct answer: D

The system of linear equations $x + \lambda y - z = 0$, $\lambda x - y - z = 0$, $x + y - \lambda z = 0$ has a non-trivial solution for :

1. A.exactly one value of $\lambda$.
2. B.exactly two values of $\lambda$.
3. C.exactly three values of $\lambda$.✓
4. D.infinitely many values of $\lambda$.

Correct answer: C

If $f(x) + 2f\left(\frac{1}{x}\right) = 3x$, $x \ne 0$, and $S = \{x \in \mathbb{R} : f(x) = f(-x)\}$; then S:

1. A.contains exactly one element.
2. B.contains exactly two elements.✓
3. C.contains more than two elements.
4. D.is an empty set.

Correct answer: B

Let $p = \lim_{x\to0^+}\left(1 + \tan^2\sqrt{x}\right)^{\frac{1}{2x}}$ then $\log p$ is equal to:

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

Correct answer: B

A value of $\theta$ for which $\frac{2 + 3i\sin\theta}{1 - 2i\sin\theta}$ is purely imaginary, is:

1. A.$\frac{\pi}{6}$
2. B.$\sin^{-1}\left(\frac{\sqrt{3}}{4}\right)$
3. C.$\sin^{-1}\left(\frac{1}{\sqrt{3}}\right)$✓
4. D.$\frac{\pi}{3}$

Correct answer: C

The eccentricity of the hyperbola whose length of the latus rectum is equal to 8 and the length of its conjugate axis is equal half of the distance between its foci, is:

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

Correct answer: B

If the standard deviation of the numbers 2, 3, a and 11 is 3.5, then which of the following is true?

1. A.$3a^2 - 32a + 84 = 0$✓
2. B.$3a^2 - 34a + 91 = 0$
3. C.$3a^2 - 23a + 44 = 0$
4. D.$3a^2 - 26a + 55 = 0$

Correct answer: A

The integral $\int \frac{2x^{12} + 5x^9}{\left(x^5 + x^3 + 1\right)^3}\,dx$ is equal to: (where C is an arbitrary constant)

1. A.$\frac{x^{10}}{2\left(x^5+x^3+1\right)^2}+C$✓
2. B.$\frac{x^5}{2\left(x^5+x^3+1\right)^2}+C$
3. C.$\frac{-x^{10}}{2\left(x^5+x^3+1\right)^2}+C$
4. D.$\frac{-x^5}{\left(x^5+x^3+1\right)^2}+C$

Correct answer: A

If the line, $\frac{x-3}{2} = \frac{y+2}{-1} = \frac{z+4}{3}$ lies in the plane, $lx + my - z = 9$, then $l^2 + m^2$ is equal to:

1. A.18
2. B.5
3. C.2✓
4. D.26

Correct answer: C

If $0 \le x < 2\pi$, then the number of real values of x, which satisfy the equation $\cos x + \cos 2x + \cos 3x + \cos 4x = 0$ is:

1. A.5
2. B.7✓
3. C.9
4. D.3

Correct answer: B

The area (in sq. units) of the region $\{(x, y) : y^2 \ge 2x \text{ and } x^2 + y^2 \le 4x,\ x \ge 0,\ y \ge 0\}$ is:

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

Correct answer: A

Let $\vec{a}$, $\vec{b}$ and $\vec{c}$ be three unit vectors such that $\vec{a}\times(\vec{b}\times\vec{c}) = \frac{\sqrt{3}}{2}(\vec{b} + \vec{c})$. If $\vec{b}$ is not parallel to $\vec{c}$, then the angle between $\vec{a}$ and $\vec{b}$ is:

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

Correct answer: C

A wire of length 2 units is cut into two parts which are bent respectively to form a square of side = x units and a circle of radius = r units. If the sum of the areas of the square and the circle so formed is minimum, then:

1. A.$(4 - \pi)x = \pi r$
2. B.$x = 2r$✓
3. C.$2x = r$
4. D.$2x = (\pi + 4)r$

Correct answer: B

The distance of the point $(1, -5, 9)$ from the plane $x - y + z = 5$ measured along the line $x = y = z$ is:

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

Correct answer: A

If a curve $y = f(x)$ passes through the point $(1, -1)$ and satisfies the differential equation, $y(1 + xy)\,dx = x\,dy$, then $f\left(-\frac{1}{2}\right)$ is equal to:

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

Correct answer: C

If the number of terms in the expansion of $\left(1 - \frac{2}{x} + \frac{4}{x^2}\right)^n$, $x \ne 0$, is 28, then the sum of the coefficients of all the terms in this expansion, is:

1. A.2187
2. B.243
3. C.729✓
4. D.64

Correct answer: C

Consider $f(x) = \tan^{-1}\left(\sqrt{\frac{1+\sin x}{1-\sin x}}\right)$, $x \in \left(0, \frac{\pi}{2}\right)$. A normal to $y = f(x)$ at $x = \frac{\pi}{6}$ also passes through the point:

1. A.$\left(0, \frac{2\pi}{3}\right)$✓
2. B.$\left(\frac{\pi}{6}, 0\right)$
3. C.$\left(\frac{\pi}{4}, 0\right)$
4. D.$(0, 0)$

Correct answer: A

For $x \in \mathbb{R}$, $f(x) = |\log 2 - \sin x|$ and $g(x) = f(f(x))$, then:

1. A.$g'(0) = \cos(\log 2)$✓
2. B.$g'(0) = -\cos(\log 2)$
3. C.g is differentiable at $x = 0$ and $g'(0) = -\sin(\log 2)$
4. D.g is not differentiable at $x = 0$

Correct answer: A

Let two fair six-faced dice A and B be thrown simultaneously. If $E_1$ is the event that die A shows up four, $E_2$ is the event that die B shows up two and $E_3$ is the event that the sum of numbers on both dice is odd, then which of the following statements is NOT true?

1. A.$E_2$ and $E_3$ are independent.
2. B.$E_1$ and $E_3$ are independent.
3. C.$E_1$, $E_2$ and $E_3$ are independent.✓
4. D.$E_1$ and $E_2$ are independent.

Correct answer: C

If $A = \begin{bmatrix} 5a & -b \\ 3 & 2 \end{bmatrix}$ and $A\,\text{adj}A = AA^T$, then $5a + b$ is equal to:

1. A.5✓
2. B.4
3. C.13
4. D.$-1$

Correct answer: A

The Boolean Expression $(p\wedge\sim q)\vee q\vee(\sim p\wedge q)$ is equivalent to:

1. A.$p \wedge q$
2. B.$p \vee q$✓
3. C.$p \vee \sim q$
4. D.$\sim p \wedge q$

Correct answer: B

The sum of all real values of x satisfying the equation $\left(x^2 - 5x + 5\right)^{x^2 + 4x - 60} = 1$ is:

1. A.$-4$
2. B.6
3. C.5
4. D.3✓

Correct answer: D

The centres of those circles which touch the circle, $x^2 + y^2 - 8x - 8y - 4 = 0$, externally and also touch the x-axis, lie on:

1. A.an ellipse which is not a circle.
2. B.a hyperbola.
3. C.a parabola.✓
4. D.a circle.

Correct answer: C

If all the words (with or without meaning) having five letters, formed using the letters of the word SMALL and arranged as in a dictionary; then the position of the word SMALL is:

1. A.$59^{th}$
2. B.$52^{nd}$
3. C.$58^{th}$✓
4. D.$46^{th}$

Correct answer: C

$\lim_{n\to\infty}\left(\frac{(n+1)(n+2)\dots3n}{n^{2n}}\right)^{1/n}$ is equal to:

1. A.$\frac{27}{e^2}$✓
2. B.$\frac{9}{e^2}$
3. C.$3\log3 - 2$
4. D.$\frac{18}{e^4}$

Correct answer: A

If the sum of the first ten terms of the series $\left(1\frac{3}{5}\right)^2 + \left(2\frac{2}{5}\right)^2 + \left(3\frac{1}{5}\right)^2 + 4^2 + \left(4\frac{4}{5}\right)^2 + \dots$, is $\frac{16}{5}m$, then m is equal to:

1. A.101✓
2. B.100
3. C.99
4. D.102

Correct answer: A

If one of the diameters of the circle, given by the equation, $x^2 + y^2 - 4x + 6y - 12 = 0$, is a chord of a circle S, whose centre is at $(-3, 2)$, then the radius of S is:

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

Correct answer: A

A man is walking towards a vertical pillar in a straight path, at a uniform speed. At a certain point A on the path, he observes that the angle of elevation of the top of the pillar is $30^\circ$. After walking for 10 minutes from A in the same direction, at a point B, he observes that the angle of elevation of the top of the pillar is $60^\circ$. Then the time taken (in minutes) by him, from B to reach the pillar, is:

1. A.10
2. B.20
3. C.5✓
4. D.6

Correct answer: C

A uniform string of length 20 m is suspended from a rigid support. A short wave pulse is introduced at its lowest end. It starts moving up the string. The time taken to reach the support is : (take $g = 10$ ms$^{-2}$)

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