JEE Main 2019 B.E./B.Tech Question Paper with Answer Keys (April 9, 2019- Afternoon Session)

If the sum and product of the first three term in an A.P. are 33 and 1155, respectively, then a value of its 11^th term is :-

• (1) \(-25\)
• (2) \(-36\)
• (3) \(25\)
• (4) \(-35\)

If \(\cos x\,\frac{dy}{dx} - y\sin x = 6x\), \(\left(0 \lt x \lt \frac{\pi}{2}\right)\) and \(y\left(\frac{\pi}{3}\right) = 0\) then \(y\left(\frac{\pi}{6}\right)\) is equal to :-

• (1) \(-\frac{\pi^2}{2}\)
• (2) \(-\frac{\pi^2}{4\sqrt{3}}\)
• (3) \(\frac{\pi^2}{2\sqrt{3}}\)
• (4) \(-\frac{\pi^2}{2\sqrt{3}}\)

If f : R \(\to\) R is a differentiable function and f(2) = 6, then \(\displaystyle\lim_{x\to 2}\frac{\int_{6}^{f(x)} 2t\,dt}{(x-2)}\) is :-

• (1) \(2f'(2)\)
• (2) \(24f'(2)\)
• (3) \(0\)
• (4) \(12f'(2)\)

The value of \(\sin 10^\circ \sin 30^\circ \sin 50^\circ \sin 70^\circ\) is :-

• (1) \(\frac{1}{36}\)
• (2) \(\frac{1}{16}\)
• (3) \(\frac{1}{32}\)
• (4) \(\frac{1}{18}\)

The mean and the median of the following ten numbers in increasing order \(10, 22, 26, 29, 34, x 42, 67, 70,\, y\) are \(42\) and \(35\) respectively, then \(\frac{y}{x}\) is equal to :

• (1) 44745
• (2) 44808
• (3) 44744
• (4) 44776

Two newspapers A and B are published in a city. It is known that 25% of the city populations reads A and 20% reads B while 8% reads both A and B. Further, 30% of those who read A but not B look into advertisements and 40% of those who read B but not A also look into advertisements, while 50% of those who read both A and B look into advertisements. Then the percentage of the population who look into advertisement is :-

• (1) 13.5
• (2) 13
• (3) 12.8
• (4) 13.9

If \(m\) is chosen in the quadratic equation \((m^2 + 1) x^2 - 3x + (m^2 + 1)^2 = 0\) such that the sum of its roots is greatest, then the absolute difference of the cubes of its roots is :

• (1) \( 8 \sqrt{3}\)
• (2) \( 4 \sqrt{3}\)
• (3) \(10 \sqrt{5}\)
• (4) \(8 \sqrt{5}\)

If the function \(f(x) = \begin{cases} a|\pi - x| + 1, & x \le 5 \\ b|x - \pi| + 3, & x \gt 5 \end{cases}\) is continuous at x = 5, then the value of a - b is :-

• (1) \(\frac{2}{\pi - 5}\)
• (2) \(\frac{2}{5 - \pi}\)
• (3) \(\frac{-2}{\pi + 5}\)
• (4) \(\frac{2}{\pi + 5}\)

The area (in sq. units) of the region \(A = \left\{(x, y) : \frac{y^2}{2} \le x \le y + 4\right\}\) is :-

• (1) 30
• (2) 18
• (3) \(\frac{53}{3}\)
• (4) 16

\(\int e^{\sec x}\left(\sec x\tan x\, f(x) + \sec x\tan x + \sec^2 x\right)dx = e^{\sec x} f(x) + C\) then a possible choice of f(x) is :-

• (1) x sec x + tan x + 1/2
• (2) sec x + x tan x - 1/2
• (3) sec x - tan x - 1/2
• (4) sec x + tan x + 1/2

The total number of matrices \(A = \begin{pmatrix} 0 & 2y & 1 \\ 2x & y & -1 \\ 2x & -y & 1 \end{pmatrix}\) \((x, y \in R,\ x \ne y)\) for which \(A^{T}A = 3I_3\) is :-

• (1) 3
• (2) 4
• (3) 2
• (4) 6

A rectangle is inscribed in a circle with a diameter lying along the line 3y = x + 7. If the two adjacent vertices of the rectangle are (-8, 5) and (6, 5), then the area of the rectangle (in sq. units) is :

• (1) 72
• (2) 84
• (3) 56
• (4) 98

The domain of the definition of the function \(f(x) = \frac{1}{4 - x^2} + \log_{10}(x^3 - x)\) is

• (1) \((-1, 0) \cup (1, 2) \cup (2, \infty)\)
• (2) \((-2, -1) \cup (-1, 0) \cup (2, \infty)\)
• (3) \((1, 2) \cup (2, \infty)\)
• (4) \((-1, 0) \cup (1, 2) \cup (3, \infty)\)

If \(f(x) = [x] - \left[\frac{x}{4}\right],\ x \in \mathbb{R}\), where [x] denotes the greatest integer function, then

• (1) Both \(\lim_{x\to4^-} f(x)\) and \(\lim_{x\to4^+} f(x)\) exist but are not equal
• (2) f is continuous at x = 4
• (3) \(\lim_{x\to4^+} f(x)\) exists but \(\lim_{x\to4^-} f(x)\) does not exist
• (4) \(\lim_{x\to4^-} f(x)\) exists but \(\lim_{x\to4^+} f(x)\) does not exist

If a unit vector \(\vec{a}\) makes angles \(\pi/3\) with \(\hat{i} , \pi /4\) with \(\hat{j}\) and \(\theta \in (0 , \pi)\) with \(\hat{k}\), then a value of \(\theta\) is : -

• (1) \(\frac{5 \pi}{12}\)
• (2) \(\frac{5 \pi}{6}\)
• (3) \(\frac{2 \pi}{3}\)
• (4) \(\frac{\pi}{4}\)

The vertices B and C of a triangle ABC lie on the line \( \frac{x}{1} = \frac{1-y}{2} = \frac{z-2}{3} \). The coordinates of A and B are (1, 6, 3) and (4, 9, 6) respectively and C is at a distance of 10 units from B. The area (in sq. units) of \( \triangle ABC \) is:

• (1) \( 10\sqrt{13} \)
• (2) \( 15\sqrt{13} \)
• (3) \( 5\sqrt{13} \)
• (4) \( 20\sqrt{13} \)

If the two lines x + (a - 1) y = 1 and 2x + a²y = 1 \((a \in R - \{0, 1\})\) are perpendicular, then the distance of their point of intersection from the origin is :

• (1) \(\frac{2}{\sqrt{5}}\)
• (2) \(\frac{\sqrt{2}}{5}\)
• (3) \(\frac{2}{5}\)
• (4) \(\sqrt{\frac{2}{5}}\)

Let z \(\in\) C be such that |z| \(\lt\) 1. If \(\omega = \frac{5 + 3z}{5(1 - z)}\), then :

• (1) \(4\,\mathrm{Im}(\omega) \gt 5\)
• (2) \(5\,\mathrm{Im}(\omega) \lt 1\)
• (3) \(5\,\mathrm{Re}(\omega) \gt 4\)
• (4) \(5\,\mathrm{Re}(\omega) \gt 1\)

A water tank has the shape of a right circular cone with axis vertical and vertex downwards. Its semi-vertical angle is tan^-1(3/4). Water is poured in it at a constant rate of 6 cubic meter per hour. The rate (in square meter per hour), at which the wet curved surface area of the tank is increasing, when the depth of water in the tank is 4 meters, is

If the system of equations 2x + 3y - z = 0, x + ky - 2z = 0 and 2x - y + z = 0 has a non-trival solution (x, y, z), then \(\frac{x}{y} + \frac{y}{z} + \frac{z}{x} + k\) is equal to :-

• (1) -4
• (2) \(\frac{3}{4}\)
• (3) \(\frac{1}{2}\)
• (4) \(-\frac{1}{4}\)

The value of the integral \(\int_0^1 x\cot^{-1}(1-x^2+x^4)\,dx\) is :-

• (1) \(\frac{\pi}{2}-\frac{1}{2}\log_e 2\)
• (2) \(\frac{\pi}{4}-\log_e 2\)
• (3) \(\frac{\pi}{4}-\frac{1}{2}\log_e 2\)
• (4) \(\frac{\pi}{2}-\log_e 2\)

If the tangent to the parabola \(y^2=x\) at a point \((\alpha,\beta)\), \((\beta\gt 0)\) is also a tangent to the ellipse, \(x^2+2y^2=1\), then \(\alpha\) is equal to :

• (1) \(\sqrt{2}+1\)
• (2) \(\sqrt{2}-1\)
• (3) \(2\sqrt{2}+1\)
• (4) \(2\sqrt{2}-1\)

The sum of the series \(1+2\times 3+3\times 5+4\times 7+\ldots\) upto 11th term is :-

• (1) 945
• (2) 916
• (3) 915
• (4) 946

If \(p \rightarrow (p \wedge \sim q)\) is false, then the truth values of p and q are respectively :

• (1) T, T
• (2) T, F
• (3) F, T
• (4) F, F

Some identical balls are arranged in rows to form an equilateral triangle. The first row consists of one ball, the second row consists of two balls and so on. If \(99\) more identical balls are addded to the total number of balls used in forming the equilaterial triangle, then all these balls can be arranged in a square whose each side contains exactly \(2\) balls less than the number of balls each side of the triangle contains. Then the number of balls used to form the equilateral triangle is :

• (1) 190
• (2) 262
• (3) 225
• (4) 157

The area (in s units) of the smaller of the two circles that touch the parabola, \(y^2 = 4x\) at the point \((1, 2)\) and the x-axis is :

• (1) \(4 \pi ( 2 - \sqrt{2})\)
• (2) \(8\pi ( 3 - 2 \sqrt{2})\)
• (3) \(4 \pi ( 3 + \sqrt{2})\)
• (4) \(8 \pi ( 2 - \sqrt{2})\)

If some three consecutive in the binomial expansion of \((x + 1)^n\) is powers of \(x\) are in the ratio \(2 : 15 : 70\), then the average of these three coefficient is :-

• (1) 964
• (2) 625
• (3) 227
• (4) 232

The common tangent to the circles \(x^2+y^2=4\) and \(x^2+y^2+6x+8y-24=0\) also passes through the point :

• (1) \((6,-2)\)
• (2) \((4,-2)\)
• (3) \((-4,6)\)
• (4) \((-6,4)\)

Two poles standing on a horizontal ground are of heights \(5\) m and \(10\) m respectively. The line joining their tops makes an angle of \(15^\circ\) with ground. Then the distance (in m) between the poles, is :-

• (1) \(5(2+\sqrt{3})\)
• (2) \(\frac{5}{2}(2+\sqrt{3})\)
• (3) \(10(\sqrt{3}-1)\)
• (4) \(5(\sqrt{3}+1)\)

Let P be the plane, which contains the line of intersection of the planes, \(x+y+z-6=0\) and \(2x+3y+z+5=0\) and it is perpendicular to the xy-plane. Then the distance of the point \((0,0,256)\) from P is equal to :

• (1) \(205\sqrt{5}\)
• (2) \(63\sqrt{5}\)
• (3) \(\frac{11}{\sqrt{5}}\)
• (4) \(\frac{17}{\sqrt{5}}\)

Two parallel plate capacitors of capacity \(C\) and \(3 C\) are connected in parallel combination and charged to a potential difference \(18\, V\) The battery is then disconnected and the space between the plates of the capacitor of capacity \(C\) is completely filled with a material of dielectric constant \(9\) The final potential difference across the combination of capacitors will be______ \(V\)

Two materials having coefficients of thermal conductivity '3K' and 'K' and thickness 'd' and '3d', respectively, are joined to form a slab as shown in the figure. The temperatures of the outer surfaces are \('\theta_2'\) and \(' \theta_1'\) respectively, \((\theta_2 > \theta_1)\). The temperature at the interface is :-

• (1) \(\frac{\theta_{2} + \theta_{1}}{2} \)
• (2) \( \frac{\theta_{1}}{10} + \frac{9\theta_{2}}{10}\)
• (3) \( \frac{\theta_{1}}{3} + \frac{2\theta_{2}}{3}\)
• (4) \( \frac{\theta_{1}}{6} + \frac{5\theta_{2}}{6}\)

In a conductor, if the number of conduction electrons per unit volume is \(8.5\times10^{28}\ \mathrm{m^{-3}}\) and mean free time is \(25\ \mathrm{fs}\) (femto second), it's approximate resistivity is :- \((m_e=9.1\times10^{-31}\ \mathrm{kg})\)

• (1) \(10^{-8}\ \Omega\mathrm{m}\)
• (2) \(10^{-7}\ \Omega\mathrm{m}\)
• (3) \(10^{-5}\ \Omega\mathrm{m}\)
• (4) \(10^{-6}\ \Omega\mathrm{m}\)

A particle of mass 'm' is moving with speed '2v' and collides with a mass '2m' moving with speed 'v' in the same direction. After collision, the first mass is stopped completely while the second one splits into two particles each of mass 'm', which move at angle \(45^\circ\) with respect to the origianl direction. The speed of each of the moving particle will be :-

• (1) \(2\sqrt{2}\,v\)
• (2) \(v/(2\sqrt{2})\)
• (3) \(v/\sqrt{2}\)
• (4) \(\sqrt{2}\,v\)

A thin smooth rod of length L and mass M is rotating freely with angular speed \(\omega_0\) about an axis perpendicular to the rod and passing through its center. Two beads of mass m and negligible size are at the center of the rod initially. The beads are free to slide along the rod. The angular speed of the system , when the beads reach the opposite ends of the rod, will be :-

• (1) \(\frac{M\omega_0}{M+3m}\)
• (2) \(\frac{M\omega_0}{M+m}\)
• (3) \(\frac{M\omega_0}{M+6m}\)
• (4) \(\frac{M\omega_0}{M+2m}\)

The logic gate equivalent to the given circuit diagram is :

• (1) OR
• (2) NAND
• (3) NOR
• (4) AND

A wire of uniform resistance \(\lambda\) \(\Omega\)/m is bent into a circle of radius r and another piece of wire with length 2r is connected between points A and B (ACB) as shown in figure. The equivalent resistance between points A and B is_______ \(\Omega\).

• (1) 3\(\pi\)\(\lambda\) r / 8
• (2) 2\(\pi\)\(\lambda\) r
• (3) (\(\pi\) + 1)2r \(\lambda\)
• (4) 6\(\pi\)\(\lambda\) r / (3\(\pi\) + 16)

Two coils 'P' and 'Q' are separated by some distance. When a current of 3 A flows through coil 'P', a magnetic flux of \(10^{-3}\) Wb passes through 'Q'. No current is passed through 'Q'. When no current passes through 'P' and a current of 2 A passes through 'Q', the flux through 'P' is :-

• (1) \(3.67\times10^{-4}\) Wb
• (2) \(3.67\times10^{-3}\) Wb
• (3) \(6.67\times10^{-4}\) Wb
• (4) \(6.67\times10^{-3}\) Wb

A wooden block floating in a bucket of water has \(\frac{4}{5}\) of its volume submerged. When certain amount of an oil is poured into the bucket, it is found that the block is just under the oil surface with half of its volume under water and half in oil. The density of oil relative to that of water is :

• (1) 0.5
• (2) 0.7
• (3) 0.6
• (4) 0.8

Moment of inertia of a body about a given axis is \(1.5\ \mathrm{kg\,m^2}\). Initially the body is at rest. In order to produce a rotational kinetic energy of \(1200\) J, the angular accleration of \(20\ \mathrm{rad/s^2}\) must be applied about the axis for a duration of :-

• (1) 2.5 s
• (2) 3 s
• (3) 5 s
• (4) 2 s

A test particle is moving in a circular orbit in the gravitational field produced by a mass density \(\rho(r) = \frac{K}{r^2}\). Identify the correct relation between the radius \(R\) of the particle's orbit and it's period \(T\) :

• (1) \(T/R^2\) is a constant
• (2) \(TR\) is a constant
• (3) \(T^2/R^3\) is a constant
• (4) \(T/R\) is a constant

A very long solenoid of radius R is carrying current \(I(t)=kte^{-a t}\ (k\gt 0)\), as a function of time \((t\ge0)\). counter clockwise current is taken to be positive. A circular conducting coil of radius 2R is placed in the equatorial plane of the solenoid and concentric with the solenoid. The current induced in the outer coil is correctly depicted, as a function of time, by :-

• (1)
• (2)
• (3)
• (4)

The position vector of a particle changes with time according to the relation \(\vec r(t)=15t^2\hat i+(4-20t^2)\hat j\). What is the magnitude of the acceleration at \(t=1\) ?

• (1) 50
• (2) 25
• (3) 40
• (4) 100

A massless spring \((k=800\ \mathrm{N/m})\), attached with a mass \((500\ \mathrm{g})\) is completely immersed in \(1\) kg of water. The spring is stretched by \(2\) cm and released so that it starts vibrating. What would be the order of magnitude of the change in the temperature of water when the vibrations stop completely ? (Assume that the water container and spring receive negligible heat and specific heat of mass \(=400\ \mathrm{J/kg\,K}\), specific heat of water \(=4184\ \mathrm{J/kg\,K}\))

• (1) \(10^{-3}\ \mathrm{K}\)
• (2) \(10^{-1}\ \mathrm{K}\)
• (3) \(10^{-5}\ \mathrm{K}\)
• (4) \(10^{-4}\ \mathrm{K}\)

A wedge of mass \(M=4m\) lies on a frictionless plane. A particle of mass m approaches the wedge with speed v. There is no friction between the particle and the plane or between the particle and the wedge. The maximum height climbed by the particle on the wedge is given by :-

• (1) \(\frac{v^2}{g}\)
• (2) \(\frac{2v^2}{7g}\)
• (3) \(\frac{v^2}{2g}\)
• (4) \(\frac{2v^2}{5g}\)

Diameter of the objective lens of a telescope is \(250\, cm\). For light of wavelength \(600\,nm\). coming from a distant object, the limit of resolution of the telescope is close to :

• (1) \(1.5 \times 10^{-7} \; rad\)
• (2) \(2.0 \times 10^{-7} \; rad\)
• (3) \(3.0 \times 10^{-7} \; rad\)
• (4) \(4.5 \times 10^{-7} \; rad\)

The energy of \(He^+\) ion in its first excited state is, (The ground state energy for the Hydrogen atom is – 13.6 eV) :

• (1) -13.6 eV
• (2) -3.4 eV
• (3) -54.4 eV
• (4) -27.2 eV

A moving coil galvanometer has a coil with 175 turns and area 1 cm². It uses a torsion band of torsion constant \(10^{-6}\) N-m/rad. The coil is placed in a maganetic field B parallel to its plane. The coil deflects by \(1^\circ\) for a current of 1 mA. The value of B (in Tesla) is approximately :-

• (1) \(10^{-4}\)
• (2) \(10^{-2}\)
• (3) \(10^{-1}\)
• (4) \(10^{-3}\)

The specific heats, \(C_P\) and \(C_V\) of a gas of diatomic molecules, A, are given (in units of \(\mathrm{J\ mol^{-1}\ K^{-1}}\)) by 29 and 22, respectively. Another gas of diatomic molecules, B, has the corresponding values 30 and 21. If they are treated as ideal gases, then :-

• (1) A is rigid but B has a vibrational mode
• (2) A has a vibrational mode but B has none
• (3) A has one vibrational mode and B has two
• (4) Both A and B have a vibrational mode each

A thin convex lens L (refractive index = 1.5) is placed on a plane mirror M. When a pin is placed at A, such that OA = 18 cm, its real inverted image is formed at A itself, as shown in figure. When a liquid of refractive index \(\mu_1\) is put between the lens and the mirror, The pin has to be moved to A', such that OA' = 27 cm, to get its inverted real image at A' itself. The value of \(\mu_1\) will be :-

• (1) \(\sqrt{3}\)
• (2) \(3/2\)
• (3) \(\sqrt{2}\)
• (4) \(4/3\)

50 W/m² energy density of sunlight is normally incident on the surface of a solar panel. Some part of incident energy (25%) is reflected from the surface and the rest is absorbed. The force exerted on 1 m² surface area will be close to (c = \(3\times10^{8}\) m/s) :-

• (1) \(20\times10^{-8}\) N
• (2) \(35\times10^{-8}\) N
• (3) \(10\times10^{-8}\) N
• (4) \(15\times10^{-8}\) N

The area of a square is 5.29 cm². The area of 7 such squares taking into account the significant figures is :-

• (1) 37.0 cm²
• (2) 37 cm²
• (3) 37.030 cm²
• (4) 37.03 cm²

A particle 'P' is formed due to a completely inelastic collision of particles 'x' and 'y' having de-Broglie wavelengths '\(\lambda_x\)' and '\(\lambda_y\)' respectively. If x and y were moving in opposite directions, then the de-Broglie wavelength of 'P' is :-

• (1) \(\lambda_x-\lambda_y\)
• (2) \(\dfrac{\lambda_x\lambda_y}{|\lambda_x-\lambda_y|}\)
• (3) \(\lambda_x+\lambda_y\)
• (4) \(\dfrac{\lambda_x\lambda_y}{\lambda_x+\lambda_y}\)

A convex lens of focal length 20 cm produces images of the same magnification 2 when an object is kept at two distances \(x_1\) and \(x_2\) (\(x_1 \gt x_2\)) from the lens. The ratio of \(x_1\) and \(x_2\) is :-

• (1) 3 : 1
• (2) 2 : 1
• (3) 5 : 3
• (4) 4 : 3

The position of a particle as a function of time t, is given by
\(x(t)=at+bt^2-ct^3\)
where a, b and c are constants. When the particle attains zero acceleration, then its velocity will be :

• (1) \(a+\dfrac{b^2}{c}\)
• (2) \(a+\dfrac{b^2}{4c}\)
• (3) \(a+\dfrac{b^2}{3c}\)
• (4) \(a+\dfrac{b^2}{2c}\)

The resistance of a galvanometer is 50 ohm and the maximum current which can be passed through it is 0.002 A. What resistance must be connected to it in order to convert it into an ammeter of range 0 - 0.5 A ?

• (1) 0.02 ohm
• (2) 0.2 ohm
• (3) 0.002 ohm
• (4) 0.5 ohm

A string 2.0 m long and fixed at its ends is driven by a 240 Hz vibrator. The string vibrates in its third harmonic mode. The speed of the wave and its fundamental frequency is :-

• (1) 180m/s, 80 Hz
• (2) 180m/s, 120 Hz
• (3) 320m/s, 120 Hz
• (4) 320m/s, 80 Hz

Two point charges A and B of magnitude +8 × 10^–6 C and –8 × 10^–6 C respectively are placed at a distance d apart. The electric field at the middle point O between the charges is 6.4 × 10⁴ NC^–1. The distance ‘d’ between the point charges A and B is:

• (1) 2.0 m
• (2) 3.0 m
• (3) 1.0 m
• (4) 4.0 m

The physical sizes of the transmitter and receiver antenna in a communication system are :-

• (1) proportional to carrier frequency
• (2) inversely proportional to carrier frequency
• (3) inversely proportional to modulation frequency
• (4) independent of both carrier and modulation frequency

Two cars A and B are moving away from each other in opposite directions. Both the cars are moving with a speed of 20 ms^-1 with respect to the ground. If an observer in car A detects a frequency 2000 Hz of the sound coming from car B, what is the natural frequency of the sound source in car B ?
(speed of sound in air = 340 ms^-1) :-

• (1) 2300 Hz
• (2) 2060 Hz
• (3) 2250 Hz
• (4) 2150 Hz

The correct statements among I to III are : (I) Valence bond theory cannot explain the color exhibited by transition metal complexes. (II) Valence bond theory can predict quantitatively the magnetic properties of transtition metal complexes. (III) Valence bond theory cannot distinguish ligands as weak and strong field ones.

• (1) (I) and (II) only
• (2) (I), (II) and (III)
• (3) (I) and (III) only
• (4) (II) and (III) only

A solution of \({Ni(NO3)2}\) is electrolysed between platinum electrodes using \(0.1\) Faraday electricity. How many mole of \(Ni\) will be deposited at the cathode?

• (1) 0.2
• (2) 0.05
• (3) 0.1
• (4) 0.15

The peptide that gives positive ceric ammonium nitrate and carbylamine tests is :

• (1) Lys-Asp
• (2) Ser-Lys
• (3) Gln-Asp
• (4) Asp-Gln

The correct statements among I to III regarding group 13 element oxides are,
(I) Boron trioxide is acidic.
(II) Oxides of aluminium and gallium are amphoteric.
(III) Oxides of indium and thallium are basic.

• (1) (II) and (III) only
• (2) (I), (II) and (III)
• (3) (I) and (III) only
• (4) (I) and (II) only

Increasing order of reactivity of the following compounds for \(\mathrm{S_N1}\) substitution is:
(A) \((\mathrm{CH_3})_2\mathrm{CH{-}CH_2{-}Cl}\); (B) \(\mathrm{CH_3CH_2Cl}\); (C) 4-methoxybenzyl chloride (\(p\)-\(\mathrm{H_3CO{-}C_6H_4{-}CH_2Cl}\)); (D) benzyl chloride.

• (1) (A) < (B) < (D) < (C)
• (2) (B) < (C) < (D) < (A)
• (3) (B) < (A) < (D) < (C)
• (4) (B) < (C) < (A) < (D)

Which of the following potential energy (PE) diagrams represents the \(\mathrm{S_N1}\) reaction?

• (1)
• (2)
• (3)
• (4)

Consider the given plot of enthalpy of the following reaction between A and B.
\(\mathrm{A + B \rightarrow C + D}\)
Identify the incorrect statement.

• (1) Formation of A and B from C has highest enthalpy of activation.
• (2) D is kinetically stable product.
• (3) C is the thermodynamically stable product
• (4) Activation enthalpy to form C is 5 kJ mol\(^{-1}\) less than that to form D.

Among the following species, the diamagnetic molecule is

• (1) \({O_2}\)
• (2) \(NO\)
• (3) \({B_2}\)
• (4) \(CO\)

The magnetic moment of a transition metal compound has been calculated to be 3.87 B.M. The metal ion is

• (1) \(T_1^{2+}\)
• (2) \(Mn ^{2+}\)
• (3) \(V ^{2+}\)
• (4) \(Cr ^{2+}\)

In the following reaction
\(\text{Carbonyl compound} + \mathrm{MeOH} \;\overset{\mathrm{HCl}}{\rightleftharpoons}\; \text{acetal}\)
Rate of the reaction is the highest for :

• (1) Propanal as substrate and methanol in stoichiometric amount.
• (2) Acetone as substrate and methanol in stoichiometric amount
• (3) Propanal as substrate and methanol in excess
• (4) Acetone as substrate and methanol in excess

The maximum number of possible oxidation states of actinoides are shown by :

• (1) nobelium (No) and lawrencium (Lr)
• (2) actinium (Ac) and thorium (Th)
• (3) neptunium (Np) and plutonium (Pu)
• (4) berkelium (Bk) and californium (Cf)

Which one of the following about an electron occupying the 1 s orbital in a hydrogen atom is incorrect ? (Bohr's radius is represented by \(\mathrm{a}_{0}\) )

• (1) The probability density of finding the electron is maximum at the nucleus
• (2) The electron can be found at a distance \(2 \mathrm{a}_{0}\) from the nucleus
• (3) The 1s orbital is spherically symmetrical
• (4) The total energy of the electron is maximum when it is at a distance \(\mathrm{a}_{0}\) from the nucleus

HF has highest boiling point among hydrogen halides, because it has :

• (1) lowest dissociation enthalpy
• (2) strongest hydrogen bonding
• (3) lowest ionic character
• (4) strongest van der Waals' interactions

In an acid-base titration, 0.1 M HCl solution was added to the NaOH solution of unknown strength. Which of the following correctly shows the change of pH of the titraction mixture in this experiment?

• (1) (C)
• (2) (A)
• (3) (B)
• (4) (D)

What would be the molality of \(20\%\) (mass / mass) aqueous solution of \(KI\)? (molar mass of \(KI = 166\, g\, mol^{-1}\))

• (1) 1.08
• (2) 1.48
• (3) 1.51
• (4) 1.35

p-Hydroxybenzophenone upon reaction with bromine in carbon tetrachloride gives:

• (1)
• (2)
• (3)
• (4)

Hinsberg's reagent is :

• (1) \({C6H5SO2Cl}\)
• (2) \({C6H5COCl}\)
• (3) \({SOCl2}\)
• (4) \({(COCl)2}\)

The major products A and B for the following reactions are, respectively:

• (1)
• (2)
• (3)
• (4)

During compression of a spring the work done is \(10\,kJ\) and \(2\,kJ\) escaped to the surroundings as heat. The change in internal energy, \(\Delta\, U(in\,kJ)\) is:

• (1) 8
• (2) 12
• (3) -12
• (4) -8

Molal depression constant for a solvent is \(4.0\, kg\, mol^{-1}\). The depression in the freezing point of the solvent for \(0.03\, mol\, kg^{-1}\) solution of \( {K2SO4}\) is : (Assume complete dissociation of the electrolyte)

• (1) 0.12 K
• (2) 0.36 K
• (3) 0.18 K
• (4) 0.24 K

The major product of the following reaction is:

• (1)
• (2)
• (3)
• (4)

10 mL of 1 mM surfactant solution forms a monolayer covering 0.24 cm\(^2\) on a polar substrate. If the polar head is approximated as cube, what is its edge length?

• (1) 1.0 pm
• (2) 2.0 nm
• (3) 0.1 nm
• (4) 2.0 pm

At a given temperature T, gases Ne, Ar, Xe and Kr are found to deviate from ideal gas behaviour. Their equation of state is given as
\(p = \dfrac{RT}{V - b}\)
at T.
Here, b is the van der Waals constant. Which gas will exhibit steepest increase in the plot of Z (compression factor) vs p?

• (1) Xe
• (2) Ne
• (3) Ar
• (4) Kr

Assertion: For the extraction of iron, haematite ore is used.
Reason: Haematite is a carbonate ore of iron.

• (1) Both the assertion and reason are correct and the reason is the correct explanation for the assertion.
• (2) Only the reason is correct.
• (3) Both the assertion and reason are correct, but the reason is not the correct explanation for the assertion.
• (4) Only the assertion is correct.

Which of the following compounds is a constituent of the polymer

?

• (1) N-Methyl urea
• (2) Ammonia
• (3) Formaldehyde
• (4) Methylamine

The layer of atmosphere between 10 km to 50 km above the sea level is called as :

• (1) mesosphere
• (2) thermosphere
• (3) troposphere
• (4) stratosphere

The amorphous form of silica is :

• (1) quartz
• (2) kieselguhr
• (3) cristobalite
• (4) tridymite

Noradrenaline is a /an

• (1) Neurotransmitter
• (2) Antidepressant
• (3) Antihistamine
• (4) Antacid

The one that is not a carbonate ore is :

• (1) siderite
• (2) bauxite
• (3) malachite
• (4) calamine

The structures of beryllium chloride in the solid state and vapour, phase, respectively,are :

• (1) chain and dimeric
• (2) chain and chain
• (3) dimeric and dimeric
• (4) dimeric and chain