JEE Main 10 April 2019 Shift 1 Question Paper

Question 1

If the coefficients of x$^{2}$ and x$^{3}$ are both zero, in the expansion of the expression (1 + ax + bx$^{2}$) (1 − 3x)$^{15}$ in powers of x, then the ordered pair (a, b) is equal to

Accepted Answer

(C) (28, 315)

Answer

(A) (−54, 315)

Answer

(B) (28, 861)

Answer

(D) (−21, 714)

Question 2

The sum $\frac{3 	imes 1}{1^{2}} + \frac{5 	imes (1^{3}+2^{3})}{1^{2}+2^{2}} + \frac{7 	imes (1^{3}+2^{3}+3^{3})}{1^{2}+2^{2}+3^{2}} + ........$ upto 10$^{th}$ term, is

Accepted Answer

(B) 660

Answer

(A) 620

Answer

(C) 680

Answer

(D) 600

Question 3

Which one of the following Boolean expressions is a tautology?

Accepted Answer

(D) (p ∨ q) ∨ (p∨∼q)

Answer

(A) (p ∨ q) ∧ (p∨∼q)

Answer

(B) (p ∧ q) ∨ (p∧∼q)

Answer

(C) (p ∨ q) ∧ (∼p∨∼q)

Question 4

If α and β are the roots of the quadratic equation, x$^{2}$ + x sinθ − 2sinθ = 0, θ ∈ (0, $\frac{\pi}{2}$) then $\frac{\alpha^{12}+\beta^{12}}{(\alpha^{-12}+\beta^{-12})(\alpha-\beta)^{24}}$ is equal to:

Accepted Answer

(A) $\frac{2^{12}}{(\sin	heta+8)^{12}}$

Answer

(B) $\frac{2^{12}}{(\sin	heta-4)^{12}}$

Answer

(C) $\frac{2^{12}}{(\sin	heta-8)^{6}}$

Answer

(D) $\frac{2^{6}}{(\sin	heta+8)^{12}}$

Question 5

ABC is a triangular park with AB = AC = 100 metres. A vertical tower is situated at the mid-point of BC. If the angles of elevation of the top of the tower at A and B are cot$^{-1}$(3$\sqrt{2}$) and cosec$^{-1}$(2$\sqrt{2}$) respectively, then the height of the tower (in metres) is:

Accepted Answer

(D) 20

Answer

(A) 25

Answer

(B) $10\sqrt{5}$

Answer

(C) $\frac{100}{3\sqrt{3}}$

Question 6

If a > 0 and z = $\frac{(1+i)^{2}}{a-i}$, has magnitude $\sqrt{\frac{2}{5}}$, then $\bar{z}$ is equal to:

Accepted Answer

(B) $-\frac{1}{5}-\frac{3}{5}i$

Answer

(A) $-\frac{3}{5}-\frac{1}{5}i$

Answer

(C) $-\frac{1}{5}+\frac{3}{5}i$

Answer

(D) $\frac{1}{5}-\frac{3}{5}i$

Question 7

If y = 1f(x) is the solution of the differential equation $\frac{dy}{dx}=(	an x - y)\sec^{2}x$, x ∈ ($-\frac{\pi}{2}, \frac{\pi}{2}$), such that y(0) = 0, then y($-\frac{\pi}{4}$) is equal to

Accepted Answer

(C) $e-2$

Answer

(A) $\frac{1}{2}-e$

Answer

(B) $\frac{1}{e}-2$

Answer

(D) $2+\frac{1}{e}$

Question 8

Let f: R → R be differentiable at c ∈ R and f(c) = 0. If g(x) = |f(x)|, then at x = c, g is:

Accepted Answer

(A) differentiable if f′(c) = 0

Answer

(B) differentiable if f′(c) ≠ 0

Answer

(C) not differentiable

Answer

(D) not differentiable if f′(c) = 0

Question 9

Let f(x) = x$^{2}$, x ∈ R. For any A ⊆ R, define g(A) = {x ∈ R : f(x) ∈ A}. If S = [0, 4], then which one of the following statements is not true?

Accepted Answer

(D) g(f(S)) = g(S)

Answer

(A) f(g(S)) ≠ f(S)

Answer

(B) f(g(S)) = S

Answer

(C) g(f(S)) ≠ S

Question 10

The number of 6 digit numbers hat can be formed using the digits 0, 1, 2, 5, 7 and 9 which are divisible by 11 and no digits is repeated, is

Accepted Answer

(B) 60

Answer

(A) 36

Answer

(C) 72

Answer

(D) 48

Question 11

The line x = y touches a circle at the point (1, 1). If the circle also passes through the point (1, −3), then its radius is

Accepted Answer

(D) $2\sqrt{2}$

Answer

(A) $3\sqrt{2}$

Answer

(B) 3

Answer

(C) 2

Question 12

Let f(x) = $e^{x}-x$ and g(x) = $x^{2}-x$, $\forall$ x $\in$ R. Then the set of all x $\in$ R, where the function h(x) = (fog) (x) is increasing is:

Accepted Answer

(A) $\left[0,\dfrac{1}{2}\right] \cup [1,\infty)$

Answer

(B) $\left[1,\dfrac{1}{2}\right] \cup \left[\dfrac{1}{2},\infty\right)$

Answer

(C) $\left[\dfrac{-1}{2},0\right] \cup [1,\infty)$

Answer

(D) $[0,\infty)$

Question 13

The value of $\displaystyle\int_{0}^{2\pi} [\sin 2x(1+\cos 3x)]\, dx$ where [t] denotes the greatest integer function, is:

Accepted Answer

(D) $-\pi$

Answer

(A) $\pi$

Answer

(B) $-2\pi$

Answer

(C) $2\pi$

Question 14

If the circles $x^{2}+y^{2}+5Kx+2y+K=0$ and $2(x^{2}+y^{2})+2Kx+3y-1=0$, (K$\in$R), intersect at the points P and Q, then the line 4x + 5y − K = 0 passes through P and Q for:

Accepted Answer

(B) not value of K

Answer

(A) exactly one value of K

Answer

(C) infinitely many values of K

Answer

(D) exactly two values of K

Question 15

If a$_{1}$, a$_{2}$, a$_{3}$ ........... a$_{n}$ are in A.P and a$_{1}$ + a$_{4}$ + a$_{7}$ + ............... + a$_{16}$ = 114, then a$_{1}$ + a$_{6}$ + a$_{11}$ + a$_{16}$ is equal to

Accepted Answer

(A) 76

Answer

(B) 64

Answer

(C) 98

Answer

(D) 38

Question 16

If for some x $\in$ R, the frequency distribution of the marks obtained by 20 students in a test is Then the mean of the marks is:

Accepted Answer

(A) 2.8

Answer

(B) 3.2

Answer

(C) 2.5

Answer

(D) 3.0

Question 17

If $\displaystyle\lim_{x	o 1}\dfrac{x^{4}-1}{x-1}=\lim_{x	o k}\dfrac{x^{3}-k^{3}}{x^{2}-k^{2}}$, then k is

Accepted Answer

(B) $\dfrac{8}{3}$

Answer

(A) $\dfrac{3}{8}$

Answer

(C) $\dfrac{4}{3}$

Answer

(D) $\dfrac{3}{2}$

Question 18

All the pairs (x, y) that satisfy the inequality $2^{\sqrt{\sin^{2}x-2\sin x+5}}\cdot\dfrac{1}{4^{\sin^{2}y}}\le 1$ also Satisfy the equation:

Accepted Answer

(B) $\sin x=|\sin y|$

Answer

(A) $2|\sin x|=3\sin y$

Answer

(C) $2\sin x=\sin y$

Answer

(D) $\sin x=2\sin y$

Question 19

$\displaystyle\lim_{n	o\infty}\left(\dfrac{(n+1)^{1/3}}{n^{4/3}}+\dfrac{(n+2)^{1/3}}{n^{4/3}}+....+\dfrac{(2n)^{1/3}}{n^{4/3}}ight)$ is equal to:

Accepted Answer

(A) $\dfrac{3}{4}(2)^{4/3}-\dfrac{3}{4}$

Answer

(B) $\dfrac{4}{3}(2)^{3/4}$

Answer

(C) $\dfrac{3}{4}(2)^{4/3}-\dfrac{4}{3}$

Answer

(D) $\dfrac{4}{3}(2)^{4/3}$

Question 20

If a directrix of a hyperbola centered at the origin and passing through the point $(4,-2\sqrt{3})$ is $5x=4\sqrt{5}$ and its eccentricity is e, then

Accepted Answer

(B) $4e^{4}-24e^{2}+35=0$

Answer

(A) $4e^{4}+8e^{2}-35=0$

Answer

(C) $4e^{4}-12e^{2}-27=0$

Answer

(D) $4e^{4}-24e^{2}+27=0$

Question 21

The region represented by $|x-y|\le 2$ and $|x+y|\le 2$ is bounded by a:

Accepted Answer

(D) square of side length $2\sqrt{2}$ units

Answer

(A) rhombus of area $8\sqrt{2}$ sq. units

Answer

(B) square of area 16 sq. units

Answer

(C) rhombus of side length 2 units

Question 22

Assume that each born child is equally likely to be a boy or a girl. If two families have two children each, then the conditional probability that all children are girls given that at least two are girls is:

Accepted Answer

(D) $\dfrac{1}{11}$

Answer

(A) $\dfrac{1}{10}$

Answer

(B) $\dfrac{1}{17}$

Answer

(C) $\dfrac{1}{12}$

Question 23

Let A(3, 0, −1), B(2, 10, 6) and C(1, 2, 1) be the vertices of a triangle and M be the midpoint of AC. If G divides BM in the ratio, 2 : 1, then cos($\angle$GOA) (O being he origin) is equal to:

Accepted Answer

(D) $\dfrac{1}{\sqrt{15}}$

Answer

(A) $\dfrac{1}{\sqrt{30}}$

Answer

(B) $\dfrac{1}{2\sqrt{15}}$

Answer

(C) $\dfrac{1}{6\sqrt{10}}$

Question 24

If $\displaystyle\int \dfrac{dx}{(x^{2}-2x+10)^{2}}=A\left(	an^{-1}\left(\dfrac{x-1}{3}ight)+\dfrac{f(x)}{x^{2}-2x+10}ight)+C$ where C is a constant of integration, then:

Accepted Answer

(C) $A=\dfrac{1}{54}$ and $f(x)=3(x-1)$

Answer

(A) $A=\dfrac{1}{27}$ and $f(x)=-(x-1)$

Answer

(B) $A=\dfrac{1}{54}$ and $f(x)=9(x-1)^{2}$

Answer

(D) $A=\dfrac{1}{81}$ and $f(x)=3(x-1)$

Question 25

A particle of mass m is moving along a trajectory given by
$x = x_{0} + a\cos\omega_{1}t$
$y = y_{0} + b\sin\omega_{2}t$
The torque, acing on the particle about the origin, at t = 0 is:

Accepted Answer

(A) $my_{0}a\omega_{1}^{2}\hat{k}$

Answer

(B) $m(-x_{0}b + y_{0}a)\omega_{1}^{2}\hat{k}$

Answer

(C) $-m(-x_{0}b\omega_{2}^{2} - y_{0}a\omega_{1}^{2})\hat{k}$

Answer

(D) Zero

Question 26

A stationary source emits sound waves of frequency 500 Hz. Two observers moving along a line passing through the source detect sound to be of frequencies 480 Hz and 530 Hz. Their respective speeds are, in ms$^{-1}$ (Given speed of sound = 300 m/s)

Accepted Answer

(D) 12, 18

Answer

(A) 16, 14

Answer

(B) 12, 16

Answer

(C) 8, 18

Question 27

Given below in the left column are different modes of communication using the kinds of waves given in the right column. From the options given below, find the most appropriate match between entries in the left and the right column.

Accepted Answer

(B) A - Q, B - S, C - P, D - R

Answer

(A) A - S, B - Q, C - R, D - P

Answer

(C) A - R, B - P, C - S, D - Q

Answer

(D) A - Q, B - S, C - R, D - P

Question 28

A cylinder with fixed capacity of 67.2 lit contains helium gas at STP. The amount of heat needed to raise the temperature of the gas by 20°C is: [Given that R = 8.31 J mol$^{-1}$ K$^{-1}$]

Accepted Answer

(C) 748 J

Answer

(A) 350 J

Answer

(B) 700 J

Answer

(D) 374 J

Question 29

A ball is thrown upward with an initial velocity V$_{0}$ from the surface of the earth. The motion of the ball is affected by a drag force equal to m$\gamma$v$^{2}$ (where m is mass of the ball, v is its Instantneous velocity and $\gamma$ is a constant). Time taken by the ball to rise to its zenith is:

Accepted Answer

(B) $\dfrac{1}{\sqrt{\gamma g}}	an^{-1}\left(\sqrt{\dfrac{\gamma}{g}}V_{0}ight)$

Answer

(A) $\dfrac{1}{\sqrt{\gamma g}}\ln\left(1+\sqrt{\dfrac{\gamma}{g}}V_{0}\right)$

Answer

(C) $\dfrac{1}{\sqrt{\gamma g}}\sin^{-1}\left(\sqrt{\dfrac{\gamma}{g}}V_{0}\right)$

Answer

(D) $\dfrac{1}{\sqrt{2\gamma g}}	an^{-1}\left(\sqrt{\dfrac{2\gamma}{g}}V_{0}ight)$

Question 30

A thin disc of mass M and radius R has mass per unit area $\sigma(r) = kr^{2}$ where r is the distance from its centre. Its moment of inertia about an axis going through its centre of mass and perpendicular to its plane is:

Accepted Answer

(D) $\dfrac{2MR^{2}}{3}$

Answer

(A) $\dfrac{MR^{2}}{2}$

Answer

(B) $\dfrac{MR^{2}}{3}$

Answer

(C) $\dfrac{MR^{2}}{6}$

Question 31

Two coaxial discs, having moments of inertia I$_{1}$ and $\dfrac{I_{1}}{2}$, area rotating with respectively angular velocities $\omega_{1}$ and $\dfrac{\omega_{1}}{2}$, about their common axes. They are brought in contact with each other and thereafter they rotate with a common angular velocity. If E$_{f}$ and E$_{i}$ are the final and initial total energies, then (E$_{f}$ - E$_{i}$) is:

Accepted Answer

(D) $-\dfrac{I_{1}\omega_{1}^{2}}{24}$

Answer

(A) $\dfrac{I_{1}\omega_{1}^{2}}{6}$

Answer

(B) $\dfrac{3}{8}I_{1}\omega_{1}^{2}$

Answer

(C) $-\dfrac{I_{1}\omega_{1}^{2}}{12}$

Question 32

The ratio of surface tensions of mercury and water is given to be 7.5 while the ratio of their densities is 13.6. Their contact angles, with glass, are close to 135° and 0°, respectively. It is observed that mercury gets depressed by an amount h in a capillary tube of radius r$_{1}$, while water rises by the same amount h in a capillary tube of radius r$_{2}$. The ratio, (r$_{1}$/r$_{2}$), is then close to:

Accepted Answer

(D) 2/5

Answer

(A) 3/5

Answer

(B) 4/5

Answer

(C) 2/3

Question 33

Figure shows charge (q) versus voltage (V) graph for series and parallel combination of to given capacitors. The capacitances are:

Accepted Answer

(A) 40 µF and 10 µF

Answer

(B) 50 µF and 30 µF

Answer

(C) 60 µF and 40 µF

Answer

(D) 20 µF and 30 µF

Question 34

A proton, an electron, and a Helium nucleus, have the same energy. They are in circular orbitals in a plane due to magnetic field perpendicular to the plane. Let r$_{p}$, r$_{e}$ and r$_{He}$ be their respective radii, then,

Accepted Answer

(D) r$_{e}$ < r$_{p}$ = r$_{He}$

Answer

(A) r$_{e}$ > r$_{p}$ = r$_{He}$

Answer

(B) r$_{e}$ > r$_{p}$ > r$_{He}$

Answer

(C) r$_{e}$ < r$_{p}$ < r$_{He}$

Question 35

The value of acceleration due to gravity at Earth's surface is 9.8 ms$^{-2}$. The altitude above its surface at which the acceleration due to gravity decreases to 4.9 ms$^{-2}$, is close to: (Radius of earth = 6.4 $	imes$ 10$^{6}$ m)

Accepted Answer

(C) 2.6 $	imes$ 10$^{6}$ m

Answer

(A) 6.4 $	imes$ 10$^{6}$ m

Answer

(B) 9.0 $	imes$ 10$^{6}$ m

Answer

(D) 1.6 $	imes$ 10$^{6}$ m

Question 36

In the given circuit, an ideal voltmeter connected across the 10 Ω resistance reads 2 V. The internal resistance r, of each cell is:

Accepted Answer

(B) 0.5 Ω

Answer

(A) 1 Ω

Answer

(C) 1.5 Ω

Answer

(D) 0 Ω

Question 37

The electric field of a plane electromagnetic wave is given by
$\vec{E} = E_{0}\hat{i}\cos(kz)\cos(\omega t)$
The corresponding magnetic field $\vec{B}$ is then given by:

Accepted Answer

(D) $\vec{B} = \dfrac{E_{0}}{C}\hat{j}\sin(kz)\sin(\omega t)$

Answer

(A) $\vec{B} = \dfrac{E_{0}}{C}\hat{j}\sin(kz)\cos(\omega t)$

Answer

(B) $\vec{B} = \dfrac{E_{0}}{C}\hat{k}\sin(kz)\cos(\omega t)$

Answer

(C) $\vec{B} = \dfrac{E_{0}}{C}\hat{j}\cos(kz)\sin(\omega t)$

Question 38

An npn transistor operates as a common emitter amplifier, with a power gain of 60 dB. The input circuit resistance Is 100 $\Omega$ and the output load resistance is 10 k$\Omega$. the common emitter current gain $\beta$ is:

Accepted Answer

(B) $10^{2}$

Answer

(A) $6 	imes 10^{2}$

Answer

(C) 60

Answer

(D) $10^{4}$

Question 39

In a meter bridge experiment, the circuit diagram and the corresponding observation table are shown in figure.
Which of the readings is inconsistent?

Accepted Answer

(A) 4

Answer

(B) 3

Answer

(C) 2

Answer

(D) 1

Question 40

A transformer consisting of 300 turns in the primary and 150 turns in the secondary gives output power of 2.2 kW. If the current in the secondary coils is 10 A, then the input voltage and current in the primary coil are:

Accepted Answer

(A) 440 V and 5 A

Answer

(B) 440 and 20 A

Answer

(C) 220 V and 20 A

Answer

(D) 220 V and 10 A

Question 41

A uniformly charged ring of radius 3a and total charge q is placed in xy-plane centered at origin. A point charge q is moving towards the ring along the z-axis and has speed v at
z = 4a. The minimum value of v such that it crosses the origin is:

Accepted Answer

(D) $\sqrt{\dfrac{2}{m}\left(\dfrac{2}{15}\dfrac{q^{2}}{4\pi \epsilon_{0} a}\right)^{1/2}}$

Answer

(A) $\sqrt{\dfrac{2}{m}\left(\dfrac{1}{5}\dfrac{q^{2}}{4\pi \epsilon_{0} a}\right)^{1/2}}$

Answer

(B) $\sqrt{\dfrac{2}{m}\left(\dfrac{1}{15}\dfrac{q^{2}}{4\pi \epsilon_{0} a}\right)^{1/2}}$

Answer

(C) $\sqrt{\dfrac{2}{m}\left(\dfrac{4}{15}\dfrac{q^{2}}{4\pi \epsilon_{0} a}\right)^{1/2}}$

Question 42

A current of 5 A passes through a copper conductor (resistivity = $1.7 	imes 10^{-8}$ $\Omega$m) of radius of cross-section 5 mm. Find the mobility of the charges if their drift velocity is $1.1 	imes 10^{-3}$ m/s.

Accepted Answer

(B) 1.0 m$^{2}$/Vs

Answer

(A) 1.8 m$^{2}$/Vs

Answer

(C) 1.3 m$^{2}$/Vs

Answer

(D) 1.5 m$^{2}$/Vs

Question 43

n-moles of an ideal gas with constant volume heat capacity $C_{V}$ undergo an isobaric expansion by certain volume. The ratio of the work done in the process, to the heat supplied is

Accepted Answer

(B) $\dfrac{nR}{C_{V} + nR}$

Answer

(A) $\dfrac{nR}{C_{V} - nR}$

Answer

(C) $\dfrac{4nR}{C_{V} + nR}$

Answer

(D) $\dfrac{4nR}{C_{V} - nR}$

Question 44

A message signal of frequency 100 MHz and peak voltage 100 V is used to execute amplitude modulation on a carrier wave of frequency 300 GHz and peak voltage 400 V. The modulation index and difference between the two side band frequencies are:

Accepted Answer

(D) 0.25 ; $2 	imes 10^{8}$ Hz

Answer

(A) 4 ; $2 	imes 10^{8}$ Hz

Answer

(B) 4 ; $1 	imes 10^{8}$ Hz

Answer

(C) 0.25 ; $1 	imes 10^{8}$ Hz

Question 45

A ray of light AO in vacuum is incident on a glass slab at angle 60° and refracted at angle 30° along OB as shown in the figure. The optical path length of light ray from A to B is :

Accepted Answer

(D) $2a + 2b$

Answer

(A) $2a + \dfrac{2b}{\sqrt{3}}$

Answer

(B) $2a + \dfrac{2b}{3}$

Answer

(C) $\dfrac{2\sqrt{3}}{a} + 2b$

Question 46

The displacement of a damped harmonic oscillator is given by
$x(t) = e^{-0.1t}\cos(10\pi t + \varphi)$. Here t is in seconds.
The time taken for its amplitude of vibration to drop to half of its initial value is close to:

Accepted Answer

(D) 7 s

Answer

(A) 13 s

Answer

(B) 27 S

Answer

(C) 4 s

Question 47

Two radioactive materials A and B have decay constants $10\lambda$ and $\lambda$, respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of a to that of B will be 1/e after a time:

Accepted Answer

(C) $\dfrac{1}{9\lambda}$

Answer

(A) $\dfrac{1}{11\lambda}$

Answer

(B) $\dfrac{1}{10\lambda}$

Answer

(D) $\dfrac{11}{10\lambda}$

Question 48

One plano-convex and one plano-concave lens of same radius of curvature 'R' but of different materials are joined side by side as shown in the figure. If the refractive index of the material of 1 is $\mu_{1}$ and that of 2 is $\mu_{2}$, then the focal length of the combination is

Accepted Answer

(C) $\dfrac{R}{\mu_{1} - \mu_{2}}$

Answer

(A) $\dfrac{R}{2(\mu_{1} - \mu_{2})}$

Answer

(B) $\dfrac{2R}{\mu_{1} - \mu_{2}}$

Answer

(D) $\dfrac{R}{2 - (\mu_{1} - \mu_{2})}$

Question 49

The species that can have a trans-isomer is:
(en = ethane-1,2-diamine, ox = oxalate)

Accepted Answer

(B) [Pt(en)$_2$Cl$_2$]$^{2+}$

Answer

(A) [Pt(en)Cl$_2$]

Answer

(C) [Cr(en)$_2$(ox)]$^{+}$

Answer

(D) [Zn(en)Cl$_2$]

Question 50

The major product of the following reaction is

CH$_3$CH(OH)CH$_2$CH$_2$NH$_2$ $\xrightarrow{	ext{ethyl formate (1 equiv.), triethylamine}}$

Accepted Answer

(D) CH$_3$CH(OH)CH$_2$CH$_2$NHCHO

Answer

(A) CH$_3$CH(OH)CH=CH$_2$

Answer

(B) HCO-O-CH(CH$_3$)CH$_2$CH$_2$NH$_2$

Answer

(C) CH$_3$CH=CH-CH$_2$NH$_2$

Question 51

The synonym for water gas when used in the production of methanol is

Accepted Answer

(A) syn gas

Answer

(B) natural gas

Answer

(C) fuel gas

Answer

(D) laughing gas

Question 52

The regions of the atmosphere, where clouds form and where we live, respectively, are:

Accepted Answer

(B) Troposphere and Troposphere

Answer

(A) Troposphere and Stratosphere

Answer

(C) Stratosphere and Stratosphere

Answer

(D) Stratosphere and Troposphere

Question 53

Consider the hydrated ions of Ti$^{2+}$, V$^{2+}$, Ti$^{3+}$ and Sc$^{3+}$. The correct order of their spin-only magnetic moments is:

Accepted Answer

(B) Sc$^{3+}$ < Ti$^{3+}$ < Ti$^{2}$ < V$^{2+}$

Answer

(A) Ti$^{3+}$ < T$^{2+}$ < Sc$^{3+}$ < V$^{2+}$

Answer

(C) V$^{2+}$ < Ti$^{2+}$ < Ti$^{3+}$ < Sc$^{3+}$

Answer

(D) Sc$^{3+}$ < Ti$^{3+}$ < V$^{2+}$ < Ti$^{2+}$

Question 54

Amylopectin is composed of

Accepted Answer

(C) $\alpha$-D-glucose, C$_1$-C$_4$ and C$_1$-C$_6$ linkages

Answer

(A) $\alpha$-D-glucose, C$_1$-C$_4$ and C$_2$-C$_6$ linkages

Answer

(B) $\beta$-D-glucose, C$_1$-C$_4$ and C$_2$-C$_6$ linkages

Answer

(D) $\beta$-D-glucose, C$_1$-C$_4$ and C$_1$-C$_6$ linkages

Question 55

A gas undergoes physical adsorption on a surface and follows the given Freundlich adsorption isotherm equation

$\frac{x}{m} = kp^{0.5}$

Adsorption of the gas increases with:

Accepted Answer

(A) Increase in p and decrease in T

Answer

(B) Increase in p and increase in T

Answer

(C) Decrease in p and increase in T

Answer

(D) Decrease in p and decrease in T

Question 56

A bacterial infection in an internal would grows as N'(t) = N$_0$ exp(t), where the time t is in hours. A dose of antibiotic, taken orally, needs 1 hour to reach the wound. Once it reaches there, the bacterial population goes down as $\frac{dN}{dt} = -5N^2$. What will be the plot of $\frac{N_0}{N}$ vs, t after 1 hour?

Accepted Answer

(D) (D)

Answer

(A) (A)

Answer

(B) (B)

Answer

(C) (C)

Question 57

The graph between $|\psi|^{2}$ and r(radial distance) is shown below. This represents:

Accepted Answer

(C) 2s orbital

Answer

(A) 1s orbital

Answer

(B) 3s orbital

Answer

(D) 2p orbital

Question 58

Consider the following table:

a and b are van der Waals constants. The correct statement about the gases is:

Accepted Answer

(D) Gas C will occupy more volume than gas A; gas B will be more compressible than gas D.

Answer

(A) Gas C will occupy more volume than gas A ; gas B will be lesser compressible than gas D

Answer

(B) Gas C will occupy lesser volume than gas A ; gas B will be more compressible than gas D.

Answer

(C) Gas C will occupy lesser volume than gas A ; gas B will be lesser compressible than gas D

Question 59

The principle of column chromatography is

Accepted Answer

(B) Differential adsorption of the substances on the solid phase.

Answer

(A) Differential absorption of the substances on the solid phase.

Answer

(C) Gravitational force.

Answer

(D) Capillary action.

Question 60

At 300 K and 1 atmospheric pressure, 10 mL of a hydrocarbon required 55 mL of O$_2$ for complete combustion, and 40 mL of CO$_2$ is formed. The formula of the hydrocarbon is:

Accepted Answer

(B) C$_4$H$_6$

Answer

(A) C$_4$H$_{10}$

Answer

(C) C$_4$H$_7$Cl

Answer

(D) C$_4$H$_8$

Question 61

Three complexes,
[CoCl(NH$_3$)$_5$]$^{2+}$ (I), [co(NH$_3$)$_5$H$_2$O]$^{3+}$ (II) and [Co(NH$_3$)$_6$]$^{3+}$ (III)
Absorb light in the visible region. The correct order of the wavelength of light absorbed by them is

Accepted Answer

(C) (I) > (II) > (III)

Answer

(A) (II) > (I) > (III)

Answer

(B) (III) > (II) > (I)

Answer

(D) (III) > (I) > (II)

Question 62

Major products of the following reaction are:

+ HCHO $\xrightarrow{	ext{(i) 50\% NaOH, (ii) H}_3	ext{O}^{+}}$

Accepted Answer

(B) (B)

Answer

(A) CH$_3$OH and HCO$_2$H

Answer

(C) (C)

Answer

(D) (D)

Question 63

The major product of the following reaction is:

$\xrightarrow[\Delta]{	ext{HI (excess)}}$

Accepted Answer

(C) (C)

Answer

(A) (A)

Answer

(B) (B)

Answer

(D) (D)

Question 64

Match the refining methods (Column I) with metals (Column II).

Accepted Answer

(D) (I) \u2013 (c); (II) \u2013 (d); (III) \u2013 (b); (IV) \u2013 (a)

Answer

(A) (I) \u2013 (b); (II) \u2013 (c); (III) \u2013 (d); (IV) \u2013 (a)

Answer

(B) (I) \u2013 (b); (II) \u2013 (d); (III) \u2013 (a); (IV) \u2013 (c)

Answer

(C) (I) \u2013 (c); (II) \u2013 (a); (III) \u2013 (b); (IV) \u2013 (d)

Modes of Communication	Kinds of Waves
A.Optical Fibre Communication	P.Ultrasound
B.Radar	Q.Infrared Light
C.Sonar	R.Microwaves
D.Mobile Phones	S.Radio Waves

Gas	a / (k Pa dm $^6$ mol $^{-1}$ )	b / (dm $^3$ mol $^{-1}$ )
A	642.32	0.05196
B	155.21	0.04136
C	431.91	0.05196
D	155.21	0.4382

Column I (Refining methods)	Column II (Metals)
I.Liquation	a.Zr
II.zone Refining	b.Ni
III.Mond process	C.Sn
IV.Van Arkel Method	d.Ga

JEE Main 10 April 2019 Shift 1 Question Paper with Answers

Physics — JEE Main 10 April 2019 Shift 1

Chemistry — JEE Main 10 April 2019 Shift 1

Mathematics — JEE Main 10 April 2019 Shift 1

Chapters tested in this paper

Attempt this paper under exam timing.

Sl. No.	R ( $\Omega$ )	l (cm)
1.	1000	60
2.	100	13
3.	10	1.5
4.	1	1.0