JEE Main 12 January 2019 Shift 1 Question Paper

Question 1

An ordered pair $(\alpha, \beta)$ for which the system of linear equations
$(1 + \alpha)x + \beta y + z = 2$
$\alpha x + (1 + \beta)y + z = 3$
$\alpha x + \beta y + 2z = 2$
has a unique solution, is:

Accepted Answer

(A) $(2, 4)$

Answer

(B) $(-3, 1)$

Answer

(C) $(-4, 2)$

Answer

(D) $(1, -3)$

Question 2

The product of three consecutive terms of a G.P. is 512. If 4 is added to each of the first and the second of these terms, the three terms now form an A.P. Then the sum of the original three terms of the given G.P. is:

Accepted Answer

(D) 28

Answer

(A) 36

Answer

(B) 32

Answer

(C) 24

Question 3

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

Accepted Answer

(C) $(\sim p) \wedge (\sim q)$

Answer

(A) $p \wedge q$

Answer

(B) $p \wedge (\sim q)$

Answer

(D) $p \vee (\sim q)$

Question 4

Consider three boxes, each containing 10 balls labelled 1, 2, ....., 10. Suppose one ball is randomly drawn from each of the boxes. Denote by $n_i$, the label of the ball drawn from the $i^{th}$ box, $(i = 1, 2, 3)$. Then, the number of ways in which the balls can be chosen such that $n_1 < n_2 < n_3$ is:

Accepted Answer

(A) 120

Answer

(B) 82

Answer

(C) 240

Answer

(D) 164

Question 5

A tetrahedron has vertices P(1, 2, 1), Q(2, 1, 3), R(-1, 1, 2) and O(0, 0, 0). The angle between the faces OPQ and PQR is:

Accepted Answer

(B) $\cos^{-1}\left(\dfrac{19}{35}\right)$

Answer

(A) $\cos^{-1}\left(\dfrac{17}{31}\right)$

Answer

(C) $\cos^{-1}\left(\dfrac{9}{35}\right)$

Answer

(D) $\cos^{-1}\left(\dfrac{7}{31}\right)$

Question 6

The maximum area (in sq. units) of a rectangle having its base on the x-axis and its other two vertices on the parabola, $y = 12 - x^{2}$ such that the rectangle lies inside the parabola, is:

Accepted Answer

(C) 32

Answer

(A) 36

Answer

(B) $20\sqrt{2}$

Answer

(D) $18\sqrt{3}$

Question 7

If the straight line, $2x - 3y + 17 = 0$ is perpendicular to the line passing through the points (7, 17) and $(15, \beta)$, then $\beta$ equals:

Accepted Answer

(D) 5

Answer

(A) $\dfrac{35}{3}$

Answer

(B) -5

Answer

(C) $-\dfrac{35}{3}$

Question 8

The sum of the distinct real values of $\mu$, for which the vectors, $\mu\hat{i} + \hat{j} + \hat{k}$, $\hat{i} + \mu\hat{j} + \hat{k}$, $\hat{i} + \hat{j} + \mu\hat{k}$ are co-planar, is:

Accepted Answer

(A) -1

Answer

(B) 0

Answer

(C) 1

Answer

(D) 2

Question 9

Let P(4, -4) and Q(9, 6) be two points on the parabola, $y^{2} = 4x$ and let X be any point on the arc POQ of this parabola, where O is the vertex of this parabola, such that the area of $	riangle PXQ$ is maximum. Then this maximum Area (in sq. units) is:

Accepted Answer

(B) $\dfrac{125}{4}$

Answer

(A) $\dfrac{75}{2}$

Answer

(C) $\dfrac{625}{4}$

Answer

(D) $\dfrac{125}{2}$

Question 10

Let $P = \begin{bmatrix} 1 & 0 & 0 \ 3 & 1 & 0 \ 9 & 3 & 1 \end{bmatrix}$ and $Q = [q_{ij}]$ be two $3 	imes 3$ matrices such that $Q - P^{5} = I_{3}$. Then $\dfrac{q_{21} + q_{31}}{q_{32}}$ is equal to:

Accepted Answer

(A) 10

Answer

(B) 135

Answer

(C) 15

Answer

(D) 9

Question 11

Let $y = y(x)$ be the solution of the differential equation, $x\dfrac{dy}{dx} + y = x\log_{e} x, (x > 1)$. If $2y(2) = \log_{e} 4 - 1$, then $y(e)$ is equal to:

Accepted Answer

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

Answer

(A) $-\dfrac{e}{2}$

Answer

(B) $-\dfrac{e^{2}}{2}$

Answer

(D) $\dfrac{e^{2}}{4}$

Question 12

The area (in sq. units) of the region bounded by the parabola, $y = x^{2} + 2$ and the lines, $y = x + 1$, $x = 0$ and $x = 3$, is:

Accepted Answer

(D) $\dfrac{15}{2}$

Answer

(A) $\dfrac{15}{4}$

Answer

(B) $\dfrac{21}{2}$

Answer

(C) $\dfrac{17}{4}$

Question 13

In a random experiment, a fair die is rolled until two fours are obtained in succession. The probability that the experiment will end in the fifth throw of the die is equal to:

Accepted Answer

(D) $\dfrac{175}{6^{5}}$

Answer

(A) $\dfrac{200}{6^{5}}$

Answer

(B) $\dfrac{150}{6^{5}}$

Answer

(C) $\dfrac{225}{6^{5}}$

Question 14

Let $C_1$ and $C_2$ be the centres of the circles $x^{2} + y^{2} - 2x - 2y - 2 = 0$ and $x^{2} + y^{2} - 6x - 6y + 14 = 0$ respectively. If P and Q are the points of intersection of these circles, then the area (in sq. units) of the quadrilateral $PC_1QC_2$ is:

Accepted Answer

(D) 4

Answer

(A) 8

Answer

(B) 6

Answer

(C) 9

Question 15

The maximum value of $3\cos	heta + 5\sin\left(	heta - \dfrac{\pi}{6}ight)$ for any real value of $	heta$ is:

Accepted Answer

(A) $\sqrt{19}$

Answer

(B) $\dfrac{\sqrt{79}}{2}$

Answer

(C) $\sqrt{34}$

Answer

(D) $\sqrt{31}$

Question 16

Considering only the principal values of inverse functions, the set $A=\left\{x\geq 0: 	an^{-1}(2x)+	an^{-1}(3x)=\frac{\pi}{4}ight\}$

Accepted Answer

(C) is a singleton

Answer

(A) contains two elements

Answer

(B) contains more than two elements

Answer

(D) is an empty set

Question 17

If $\lambda$ be the ratio of the roots of the quadratic equation in x, $3m^{2}x^{2}+m(m-4)x+2=0$, then the least value of m for which $\lambda+\frac{1}{\lambda}=1$, is:

Accepted Answer

(B) $4-3\sqrt{2}$

Answer

(A) $2-\sqrt{3}$

Answer

(C) $-2+\sqrt{2}$

Answer

(D) $4-2\sqrt{3}$

Question 18

If a variable line, $3x+4y-\lambda=0$ is such that the two circles $x^{2}+y^{2}-2x-2y+1=0$ and $x^{2}+y^{2}-18x-2y+78=0$ are on its opposite sides, then the set of all values of $\lambda$ is the interval:

Accepted Answer

(C) $[12, 21]$

Answer

(A) $(2, 17)$

Answer

(B) $[13, 23]$

Answer

(D) $(23, 31)$

Question 19

For x > 1, if $(2x)^{2y}=4e^{2x-2y}$, then $(1+\log_{e}2x)^{2}\frac{dy}{dx}$ is equal to:

Accepted Answer

(A) $\frac{x\log_{e}2x-\log_{e}2}{x}$

Answer

(B) $\log_{e}2x$

Answer

(C) $\frac{x\log_{e}2x+\log_{e}2}{x}$

Answer

(D) $x\log_{e}2x$

Question 20

The integral $\int \cos(\log_{e}x)dx$ is equal to: (where C is a constant of integration)

Accepted Answer

(C) $\frac{x}{2}\left[\cos(\log_{e}x)+\sin(\log_{e}x)\right]+C$

Answer

(A) $\frac{x}{2}\left[\sin(\log_{e}x)-\cos(\log_{e}x)\right]+C$

Answer

(B) $x\left[\cos(\log_{e}x)+\sin(\log_{e}x)\right]+C$

Answer

(D) $x\left[\cos(\log_{e}x)-\sin(\log_{e}x)\right]+C$

Question 21

Let $S_{k}=\frac{1+2+3+.....+k}{k}$. If $S_{1}^{2}+S_{2}^{2}+.....+S_{10}^{2}=\frac{5}{12}A$, then A equal to:

Accepted Answer

(C) 303

Answer

(A) 283

Answer

(B) 301

Answer

(D) 156

Question 22

The perpendicular distance from the origin to the plane containing the two lines, $\frac{x+2}{3}=\frac{y-2}{5}=\frac{z+5}{7}$ and $\frac{x-1}{1}=\frac{y-4}{4}=\frac{z+4}{7}$, is:

Accepted Answer

(B) $11/\sqrt{6}$

Answer

(A) $11\sqrt{6}$

Answer

(C) 11

Answer

(D) $6\sqrt{11}$

Question 23

If the sum of the deviations of 50 observations from 30 is 50, then the mean of these observations is:

Accepted Answer

(D) 31

Answer

(A) 30

Answer

(B) 51

Answer

(C) 50

Question 24

Let S be the set of all points in $(-\pi, \pi)$ at which the function, $f(x)=\min\{\sin x, \cos x\}$ is non-differentiable. Then S is a subset of which of the following?

Accepted Answer

(B) $\left\{-\frac{3\pi}{4},-\frac{\pi}{4},\frac{3\pi}{4},\frac{\pi}{4}\right\}$

Answer

(A) $\left\{-\frac{\pi}{4},0,\frac{\pi}{4}\right\}$

Answer

(C) $\left\{-\frac{\pi}{2},-\frac{\pi}{4},\frac{\pi}{4},\frac{\pi}{2}\right\}$

Answer

(D) $\left\{-\frac{3\pi}{4},-\frac{\pi}{2},\frac{\pi}{2},\frac{3\pi}{4}\right\}$

Question 25

Let f and g be continuous functions on $[0, a]$ such that $f(x)=f(a-x)$ and $g(x)+g(a-x)=4$, then $\int_{0}^{a}f(x)g(x)dx$ is equal to:

Accepted Answer

(C) $2\int_{0}^{a}f(x)dx$

Answer

(A) $4\int_{0}^{a}f(x)dx$

Answer

(B) $\int_{0}^{a}f(x)dx$

Answer

(D) $-3\int_{0}^{a}f(x)dx$

Question 26

$\lim_{x	o \pi/4}\frac{\cot^{3}x-	an x}{\cos\left(x+\pi/4ight)}$ is:

Accepted Answer

(D) 8

Answer

(A) 4

Answer

(B) $4\sqrt{2}$

Answer

(C) $8\sqrt{2}$

Question 27

If $\frac{z-\alpha}{z+\alpha}(\alpha \in R)$ is a purely imaginary number and $|z|=2$, then a value of $\alpha$ is:

Accepted Answer

(A) 2

Answer

(B) 1

Answer

(C) $\frac{1}{2}$

Answer

(D) $\sqrt{2}$

Question 28

Let $S=\{1, 2, 3, ....., 100\}$. The number of non-empty subsets A of S such that the product of elements in A is even is:

Accepted Answer

(B) $2^{50}(2^{50}-1)$

Answer

(A) $2^{100}-1$

Answer

(C) $2^{50}-1$

Answer

(D) $2^{50}+1$

Question 29

If the vertices of a hyperbola be at $(-2, 0)$ and $(2, 0)$ and one of its foci be at $(-3, 0)$, then which one of the following points does not lie on this hyperbola?

Accepted Answer

(D) $\left(6,5\sqrt{2}\right)$

Answer

(A) $\left(-6,2\sqrt{10}\right)$

Answer

(B) $\left(2\sqrt{6},5\right)$

Answer

(C) $\left(4,\sqrt{15}\right)$

Question 30

A travelling harmonic wave is represented by the equation $y(x, t) = 10^{-3}\sin(50t + 2x)$, where x and y are in meter and t is in seconds. Which of the following is a correct statement about the wave?

Accepted Answer

(A) The wave is propagating along the negative x-axis with speed 25 ms$^{-1}$.

Answer

(B) The wave is propagating along the positive x-axis with speed 100 ms$^{-1}$.

Answer

(C) The wave is propagating along the positive x-axis with speed 25 ms$^{-1}$.

Answer

(D) The wave is propagating along the negative x-axis with speed 100 ms$^{-1}$.

Question 31

An ideal battery of 4 V and resistance R are connected in series in the primary circuit of a potentiometer of length 1 m and resistance 5 $\Omega$. The value of R, to give a difference of 5 mV across 10 cm of potentiometer wire, is:

Accepted Answer

(C) 395 $\Omega$

Answer

(A) 490 $\Omega$

Answer

(B) 480 $\Omega$

Answer

(D) 495 $\Omega$

Question 32

In a meter bridge, the wire of length 1 m has a non-uniform cross-section such that, the variation $\frac{dR}{d\ell}$ of its resistance R with length $\ell$ is $\frac{dR}{d\ell} \propto \frac{1}{\sqrt{\ell}}$. Two equal resistances are connected as shown in the figure. The galvanometer has zero deflection when the jockey is at point P. What is the length AP?

Accepted Answer

(C) 0.25 m

Answer

(A) 0.2 m

Answer

(B) 0.3 m

Answer

(D) 0.35 m

Question 33

A passenger train of length 60 m travels at a speed of 80 km/hr. Another freight train of length 120 m travels at a speed of 30 km/hr. The ratio of times taken by the passenger train to completely cross the freight train when: (i) they are moving in the same direction, and (ii) in the opposite directions is:

Accepted Answer

(A) $\frac{11}{5}$

Answer

(B) $\frac{5}{2}$

Answer

(C) $\frac{3}{2}$

Answer

(D) $\frac{25}{11}$

Question 34

Two electric bulbs, rated at (25 W, 220 V) and (100 W, 220 V), are connected in series across a 220 V voltage source. If the 25 W and 100 W bulbs draw powers P$_{1}$ and P$_{2}$ respectively, then:

Accepted Answer

(A) P$_{1}$ = 16 W, P$_{2}$ = 4 W

Answer

(B) P$_{1}$ = 16 W, P$_{2}$ = 9 W

Answer

(C) P$_{1}$ = 9 W, P$_{2}$ = 16 W

Answer

(D) P$_{1}$ = 4 W, P$_{2}$ = 16 W

Question 35

A straight rod of length L extends from x = a to x = L + a. The gravitational force it exerts on a point mass 'm' at x = 0, if the mass per unit length of the rod is A + Bx$^{2}$, is given by:

Accepted Answer

(D) $Gm\left[A\left(\frac{1}{a} - \frac{1}{a+L}\right) + BL\right]$

Answer

(A) $Gm\left[A\left(\frac{1}{a+L} - \frac{1}{a}\right) - BL\right]$

Answer

(B) $Gm\left[A\left(\frac{1}{a} - \frac{1}{a+L}\right) - BL\right]$

Answer

(C) $Gm\left[A\left(\frac{1}{a+L} - \frac{1}{a}\right) + BL\right]$

Question 36

What is the position and nature of image formed by lens combination shown in figure? (f$_{1}$, f$_{2}$ are focal lengths)

Accepted Answer

(D) 70 cm from point B at right ; real

Answer

(A) 70 cm from point B at left; virtual

Answer

(B) 40 cm from point B at right; real

Answer

(C) $\frac{20}{3}$ cm from point B at right; real

Question 37

A point source of light, S is placed at a distance L in front of the centre of plane mirror of width d which is hanging vertically on a wall. A man walks in front of the mirror along a line parallel to the mirror, at a distance 2 L as shown below. The distance over which the man can see the image of the light source in the mirror:

Accepted Answer

(C) 3d

Answer

(A) d

Answer

(B) 2d

Answer

(D) $\frac{d}{2}$

Question 38

A light wave is incident normally on a glass slab of refractive index 1.5. If 4% of light gets reflected and the amplitude of the electric field of the incident light is 30 V/m, then the amplitude of the electric field for the wave propagating in the glass medium will be:

Accepted Answer

(C) 24 V/m

Answer

(A) 30 V/m

Answer

(B) 10 V/m

Answer

(D) 6 V/m

Question 39

For the given cyclic process CAB as shown for a gas, the work done is:

Accepted Answer

(B) 10 J

Answer

(A) 30 J

Answer

(C) 1 J

Answer

(D) 5 J

Question 40

Determine the electric dipole moment of the system of three charges, placed on the vertices of an equilateral triangle, as shown in the figure:

Accepted Answer

(D) $-\sqrt{3}\, q\ell \hat{j}$

Answer

(A) $\sqrt{3}\, q\ell \frac{\hat{j} - \hat{i}}{\sqrt{2}}$

Answer

(B) $(q\ell)\frac{\hat{i} + \hat{j}}{\sqrt{2}}$

Answer

(C) $2q\ell \hat{j}$

Question 41

The position vector of the centre of mass $\vec{r}$ cm of an asymmetric uniform bar of negligible area of cross-section as shown in figure is:

Accepted Answer

(A) $\vec{r}$ cm $= \frac{13}{8}L\hat{x} + \frac{5}{8}L\hat{y}$

Answer

(B) $\vec{r}$ cm $= \frac{5}{8}L\hat{x} + \frac{13}{8}L\hat{y}$

Answer

(C) $\vec{r}$ cm $= \frac{3}{8}L\hat{x} + \frac{11}{8}L\hat{y}$

Answer

(D) $\vec{r}$ cm $= \frac{11}{8}L\hat{x} + \frac{3}{8}L\hat{y}$

Question 42

A person standing on an open ground hears the sound of a jet aeroplane, coming from north at an angle 60° with ground level. But he finds the aeroplane right vertically above his position. If $\upsilon$ is the speed of sound, speed of the plane is:

Accepted Answer

(D) $\frac{\upsilon}{2}$

Answer

(A) $\frac{\sqrt{3}}{2}\upsilon$

Answer

(B) $\frac{2\upsilon}{\sqrt{3}}$

Answer

(C) $\upsilon$

Question 43

Two light identical springs of spring constant k are attached horizontally at the two ends of a uniform horizontal rod AB of length l and mass m. the rod is pivoted at its centre 'O' and can rotate freely in horizontal plane. The other ends of the two springs are fixed to rigid supports as shown in figure. The rod is gently pushed through a small angle and released. The frequency of resulting oscillation is:

Accepted Answer

(C) $\frac{1}{2\pi}\sqrt{\frac{6k}{m}}$

Answer

(A) $\frac{1}{2\pi}\sqrt{\frac{3k}{m}}$

Answer

(B) $\frac{1}{2\pi}\sqrt{\frac{2k}{m}}$

Answer

(D) $\frac{1}{2\pi}\sqrt{\frac{k}{m}}$

Question 44

A simple pendulum, made of a string of length l and a bob of mass m, is released from a small angle $	heta_0$. It strikes a block of mass M, kept on a horizontal surface at its lowest point of oscillations, elastically. It bounces back and goes up to an angle $	heta_1$. Then M is given by:

Accepted Answer

(C) $m\left(\dfrac{	heta_0+	heta_1}{	heta_0-	heta_1}ight)$

Answer

(A) $\dfrac{m}{2}\left(\dfrac{	heta_0+	heta_1}{	heta_0-	heta_1}ight)$

Answer

(B) $m\left(\dfrac{	heta_0-	heta_1}{	heta_0+	heta_1}ight)$

Answer

(D) $\dfrac{m}{2}\left(\dfrac{	heta_0-	heta_1}{	heta_0+	heta_1}ight)$

Question 45

A 100 V carrier wave is made to vary between 160 V and 40 V by a modulating signal. What is the modulation index?

Accepted Answer

(C) 0.6

Answer

(A) 0.3

Answer

(B) 0.5

Answer

(D) 0.4

Question 46

A cylinder of radius R is surrounded by a cylindrical shell of inner radius R and outer radius 2R. The thermal conductivity of the material of the inner cylinder is $K_1$ and that of the outer cylinder is $K_2$. Assuming no loss of heat, the effective thermal conductivity of the system for heat flowing along the length of the cylinder is:

Accepted Answer

(D) $\dfrac{K_1+3K_2}{4}$

Answer

(A) $\dfrac{K_1+K_2}{2}$

Answer

(B) $K_1+K_2$

Answer

(C) $\dfrac{2K_1+3K_2}{5}$

Question 47

The least count of the main scale of a screw gauge is 1 mm. The minimum number of divisions on its circular scale required to measure 5 $\mu$m diameter of a wire is:

Accepted Answer

(B) 200

Answer

(A) 50

Answer

(C) 100

Answer

(D) 500

Question 48

The output of the given logic circuit is:

Accepted Answer

(C) $A\bar{B}$

Answer

(A) $A\bar{B}+\bar{A}B$

Answer

(B) $AB+\overline{AB}$

Answer

(D) $\bar{A}B$

Question 49

As shown in the figure, two infinitely long, identical wires are bent by 90° and placed in such a way that the segments LP and QM are along the x-axis, while segments PS and QN are parallel to the y-axis. If OP = OQ = 4 cm, and the magnitude of the magnetic field at O is $10^{-4}$ T, and the two wires carry equal current (see figure), the magnitude of the current in each wire and the direction of the magnetic field at O will be ($\mu_0=4\pi	imes10^{-7}$ NA$^{-2}$):

Accepted Answer

(C) 20 A, perpendicular into the page

Answer

(A) 20 A, perpendicular out of the page

Answer

(B) 40 A, perpendicular out of the page

Answer

(D) 40 A, perpendicular into the page

Question 50

A particle of mass m moves in a circular orbit in a central potential field $U(r)=\dfrac{1}{2}kr^2$. If Bohr's quantization conditions are applied, radii of possible orbits and energy levels vary with quantum number n as:

Accepted Answer

(A) $r_n \propto \sqrt{n}$, $E_n \propto n$

Answer

(B) $r_n \propto \sqrt{n}$, $E_n \propto \dfrac{1}{n}$

Answer

(C) $r_n \propto n$, $E_n \propto n$

Answer

(D) $r_n \propto n^2$, $E_n \propto \dfrac{1}{n^2}$

Question 51

A proton and an $\alpha$-particle (with their masses in the ratio of 1:4 and charges in the ratio of 1:2 are accelerated from rest through a potential difference V. If a uniform magnetic field (B) is set up perpendicular to their velocities, the ratio of the radii $r_p : r_\alpha$ of the circular paths described by them will be:

Accepted Answer

(A) $1:\sqrt{2}$

Answer

(B) $1:2$

Answer

(C) $1:3$

Answer

(D) $1:\sqrt{3}$

Question 52

Let the moment of inertia of a hollow cylinder of length 30 cm (inner radius 10 cm and outer radius 20 cm), about its axis be I. The radius of a thin cylinder of the same mass such that its moment of inertia about its axis is also I, is:

Accepted Answer

(B) 16 cm

Answer

(A) 12 cm

Answer

(C) 14 cm

Answer

(D) 18 cm

Question 53

In the figure shown, a circuit contains two identical resistors with resistance R = 5 $\Omega$ and an inductance with L = 2 mH. An ideal battery of 15 V is connected in the circuit. What will be the current through the battery long after the switch is closed?

Accepted Answer

(D) 6 A

Answer

(A) 5.5 A

Answer

(B) 7.5 A

Answer

(C) 3 A

Question 54

In the figure shown, after the switch 'S' is turned from position 'A' to position 'B', the energy dissipated in the circuit in terms of capacitance 'C' and total charge 'Q' is:

Accepted Answer

(B) $\dfrac{3}{8}\dfrac{Q^2}{C}$

Answer

(A) $\dfrac{1}{8}\dfrac{Q^2}{C}$

Answer

(C) $\dfrac{5}{8}\dfrac{Q^2}{C}$

Answer

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

Question 55

A satellite of mass M is in a circular orbit of radius R about the centre of the earth. A meteorite of the same mass, falling towards the earth collides with the satellite completely inelastically. The speeds of the satellite and the meteorite are the same, just before the collision. The subsequent motion of the combined body will be:

Accepted Answer

(B) in an elliptical orbit

Answer

(A) such that it escapes to infinity

Answer

(C) in the same circular orbit of radius R

Answer

(D) in a circular orbit of a different radius

Question 56

The galvanometer deflection, when key $K_1$ is closed but $K_2$ is open, equals $	heta_0$ (see figure). On closing $K_2$ also and adjusting $R_2$ to 5 $\Omega$, the deflection in galvanometer becomes $\dfrac{	heta_0}{5}$. The resistance of the galvanometer is, then, given by [Neglect the internal resistance of battery]:

Accepted Answer

(B) 22 $\Omega$

Answer

(A) 5 $\Omega$

Answer

(C) 25 $\Omega$

Answer

(D) 12 $\Omega$

Question 57

A particle A of mass 'm' and charge 'q' is accelerated by a potential difference of 50 V. Another particle B of mass '4 m' and charge 'q' is accelerated by a potential difference of 2500 V. The ratio of de-Broglie wavelength $\dfrac{\lambda_A}{\lambda_B}$ is close to:

Accepted Answer

(C) 14.14

Answer

(A) 10.00

Answer

(B) 0.07

Answer

(D) 4.47

Question 58

There is a uniform spherically symmetric surface charge density at a distance $R_0$ from the origin. The charge distribution is initially at rest and starts expanding because of mutual repulsion. The figure that represents best the speed V(R(t)) of the distribution as a function of its instantaneous radius R(t) is:

Accepted Answer

(C) (C)

Answer

(A) (A)

Answer

(B) (B)

Answer

(D) (D)

Question 59

In the Hall-heroult process, aluminium is formed at the cathode. The cathode is made out of

Accepted Answer

(B) Carbon

Answer

(A) Pure Aluminium

Answer

(C) Copper

Answer

(D) Platinum

Question 60

The correct order for acid strength of compounds: $CH \equiv CH$, $CH_3-C\equiv CH$, $CH_2=CH_2$ is as follows:

Accepted Answer

(D) $HC\equiv CH > CH_3-C\equiv CH > CH_2=CH_2$

Answer

(A) $CH \equiv CH > CH_2=CH_2 > CH_3-C\equiv CH$

Answer

(B) $CH_3-C\equiv CH > CH\equiv CH > CH_2=CH_2$

Answer

(C) $CH_3-C\equiv CH > CH_2=CH_2 > HC\equiv CH$

Question 61

In a chemical reaction $A + 2B \underset{}{\overset{K}{\rightleftharpoons}} 2C + D$, the initial concentration of B was 1.5 times of A but the equilibrium concentrations of A and B were found to be equal. The equilibrium, constant(K) for the aforesaid chemical reaction is

Accepted Answer

(A) 4

Answer

(B) 16

Answer

(C) 1/4

Answer

(D) 1

Question 62

$Mn_2(CO)_{10}$ is an organometalic compound due to the presence of

Accepted Answer

(A) Mn - C bond

Answer

(B) Mn - Mn bond

Answer

(C) Mn - O bond

Answer

(D) C - O bond

Question 63

The major product of the following reaction is:

Accepted Answer

(C) (C)

Answer

(A) (A)

Answer

(B) (B)

Answer

(D) (D)

Question 64

A metal on combustion in excess air forms X, X upon hydrolysis with water yields $H_2O_2$ and $O_2$ along with another product. The metal is:

Accepted Answer

(B) Rb

Answer

(A) Na

Answer

(C) Mg

Answer

(D) Li

Aldehyde	Alcohol
HCHO	$^tBuOH$
$CH_3CHO$	MeOH

JEE Main 12 January 2019 Shift 1 Question Paper with Answers

Physics — JEE Main 12 January 2019 Shift 1

Chemistry — JEE Main 12 January 2019 Shift 1

Mathematics — JEE Main 12 January 2019 Shift 1

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