JEE Main 6 September 2020 Shift 2 Question Paper

Question 1

The integral $\int_{1}^{2} e^{x} \cdot x^{2}(2+\log_{e} x)dx$ equals:

Accepted Answer

(C) $e(4e - 1)$

Answer

(A) $e(4e + 1)$

Answer

(B) $4e^{2} - 1$

Answer

(D) $e(2e - 1)$

Question 2

The area (in sq. units) of the region enclosed by the curves $y = x^{2} - 1$ and $y = 1 - x^{2}$ is equal to

Accepted Answer

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

Answer

(A) $\frac{4}{3}$

Answer

(C) $\frac{7}{2}$

Answer

(D) $\frac{16}{3}$

Question 3

The angle of elevation of the summit of a mountain from a point on the ground is 45°. After climbing up one km towards the summit at an inclination of 30° from the ground, the angle of elevation of the summit is found to be 60°. Then the height (in km) of the summit from the ground is:

Accepted Answer

(C) $\frac{1}{\sqrt{3}-1}$

Answer

(A) $\frac{\sqrt{3}-1}{\sqrt{3}+1}$

Answer

(B) $\frac{\sqrt{3}+1}{\sqrt{3}-1}$

Answer

(D) $\frac{1}{\sqrt{3}+1}$

Question 4

The set of all real values of $\lambda$ for which the function $f(x) = (1 - \cos^{2} x)\cdot(\lambda + \sin x)$, $x \in \left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$, has exactly one maxima and exactly one minima, is

Accepted Answer

(D) $\left(-\frac{3}{2}, \frac{3}{2}\right) - \{0\}$

Answer

(A) $\left(-\frac{1}{2}, \frac{1}{2}\right) - \{0\}$

Answer

(B) $\left(-\frac{3}{2}, \frac{3}{2}\right)$

Answer

(C) $\left(-\frac{1}{2}, \frac{1}{2}\right)$

Question 5

If $\alpha$ and $\beta$ are the roots of the equation $2x(2x + 1) = 1$, then $\beta$ is equal to:

Accepted Answer

(B) $-2\alpha(\alpha + 1)$

Answer

(A) $2\alpha(\alpha + 1)$

Answer

(C) $2\alpha(\alpha - 1)$

Answer

(D) $2\alpha^{2}$

Question 6

For all twice differentiable functions $f : R 	o R$, with $f(0) = f(1) = f'(0) = 0$,

Accepted Answer

(B) $f''(x) = 0$, for some $x \in (0,1)$

Answer

(A) $f''(x) 
eq 0$, at every point $x \in (0,1)$

Answer

(C) $f''(0) = 0$

Answer

(D) $f''(x) = 0$, at every point $x \in (0, 1)$

Question 7

If $y = \left(\frac{2}{\pi}x - 1\right)\operatorname{cosec} x$ is the solution of the differential equation, $\frac{dy}{dx} + p(x)y = \frac{2}{\pi}\operatorname{cosec}\ x, 0 < x < \frac{\pi}{2}$, then the function p(x) is equal to:

Accepted Answer

(A) $\cot x$

Answer

(B) $\operatorname{cosec} x$

Answer

(C) $\sec x$

Answer

(D) $	an x$

Question 8

Let L denote the line in the xy-plane with x and y intercepts as 3 and 1 respectively. Then the image of the point $(-1, -4)$ in this line is:

Accepted Answer

(A) $\left(\frac{11}{5}, \frac{28}{5}\right)$

Answer

(B) $\left(\frac{29}{5}, \frac{8}{5}\right)$

Answer

(C) $\left(\frac{8}{5}, \frac{29}{5}\right)$

Answer

(D) $\left(\frac{29}{5}, \frac{11}{5}\right)$

Question 9

If the tangent to the curve, $y = f(x) = x\log_{e} x$, $(x > 0)$ at a point $(c, f(c))$ is parallel to the line – segment joining the points $(1, 0)$ and $(e, e)$ then c is equal to:

Accepted Answer

(C) $e^{\left(\frac{1}{e-1}\right)}$

Answer

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

Answer

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

Answer

(D) $e^{\left(\frac{1}{1-e}\right)}$

Question 10

Let $f : R 	o R$ be a function defined by $f(x) = \max\{x, x^{2}\}$. Let S denote the set of all points in R, where f is not differentiable. Then:

Accepted Answer

(A) $\{0, 1\}$

Answer

(B) $\{0\}$

Answer

(C) $\phi$(an empty set)

Answer

(D) $\{1\}$

Question 11

Let $	heta = \frac{\pi}{5}$ and $A = \begin{bmatrix} \cos	heta & \sin	heta \ -\sin	heta & \cos	heta \end{bmatrix}$. If $B = A + A^{4}$, then det (B):

Accepted Answer

(D) lies in (1, 2).

Answer

(A) is one.

Answer

(B) lies in (2, 3).

Answer

(C) is zero.

Question 12

A plane P meets the coordinate axes at A, B and C respectively. The centroid of $	riangle ABC$ is given to be (1, 1, 2). Then the equation of the line through this centroid and perpendicular to the plane P is:

Accepted Answer

(C) $\frac{x-1}{2} = \frac{y-1}{2} = \frac{z-2}{1}$

Answer

(A) $\frac{x-1}{2} = \frac{y-1}{1} = \frac{z-2}{1}$

Answer

(B) $\frac{x-1}{1} = \frac{y-1}{1} = \frac{z-2}{2}$

Answer

(D) $\frac{x-1}{2} = \frac{y-1}{2} = \frac{z-2}{2}$

Question 13

The common difference of the A.P. $b_{1}, b_{2}, \ldots, b_{m}$ is 2 more than the common difference of A.P. $a_{1}, a_{2}, \ldots, a_{n}$. If $a_{40} = -159$, $a_{100} = -399$ and $b_{100} = a_{70}$, then $b_{1}$ is equal to:

Accepted Answer

(C) −81

Answer

(A) 81

Answer

(B) −127

Answer

(D) 127

Question 14

If the normal at an end of a latus rectum of an ellipse passes through an extremity of the minor axis, then the eccentricity e of the ellipse satisfies:

Accepted Answer

(D) $e^4 + e^2 - 1 = 0$

Answer

(A) $e^4 + 2e^2 - 1 = 0$

Answer

(B) $e^2 + e - 1 = 0$

Answer

(C) $e^2 + 2e - 1 = 0$

Question 15

For a suitably chosen real constant a, let a function, $f : R - \{-a\} 	o R$ be defined by $f(x) = \frac{a - x}{a + x}$. Further suppose that for any real number $x 
eq -a$ and $f(x) 
eq -a$, $(fof)(x) = x$. Then $f\left(-\frac{1}{2}ight)$ is equal to:

Accepted Answer

(D) $3$

Answer

(A) $\frac{1}{3}$

Answer

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

Answer

(C) $-3$

Question 16

If the constant term in the binomial expansion of $\left(\sqrt{x} - \frac{k}{x^2}\right)^{10}$ is 405, then $|k|$ equals:

Accepted Answer

(C) $3$

Answer

(A) $9$

Answer

(B) $1$

Answer

(D) $2$

Question 17

The centre of the circle passing through the point $(0, 1)$ and touching the parabola $y = x^2$ at the point $(2, 4)$ is:

Accepted Answer

(D) $\left(\frac{-16}{5}, \frac{53}{10}\right)$

Answer

(A) $\left(\frac{-53}{10}, \frac{16}{5}\right)$

Answer

(B) $\left(\frac{6}{5}, \frac{53}{10}\right)$

Answer

(C) $\left(\frac{3}{10}, \frac{16}{5}\right)$

Question 18

Let $z = x + iy$ be a non-zero complex number such that $z^2 = i|z|^2$, where $i = \sqrt{-1}$, then z lies on the:

Accepted Answer

(C) line, $y = x$

Answer

(A) line, $y = -x$

Answer

(B) imaginary axis

Answer

(D) real axis

Question 19

Consider the statement: “For an integer n, if $n^3 - 1$ is even, then n is odd.” The contrapositive statement of this statement is:

Accepted Answer

(A) For an integer n, if n is even, then $n^3 - 1$ is odd.

Answer

(B) For an integer n, if $n^3 - 1$ is not even then n is not odd.

Answer

(C) For an integer n, if n is even, then $n^3 - 1$ is even.

Answer

(D) For an integer n, if n is odd, then $n^3 - 1$ is even.

Question 20

The probabilities of three events A, B and C are given by $P(A) = 0.6$, $P(B) = 0.4$ and $P(C) = 0.5$. If $P(A \cup B) = 0.8$, $P(A \cap C) = 0.3$, $P(A \cap B \cap C) = 0.2$, $P(B \cap C) = \beta$ and $P(A \cup B \cup C) = \alpha$, where $0.85 \leq \alpha \leq 0.95$, then $\beta$ lies in the interval:

Accepted Answer

(B) $[0.25, 0.35]$

Answer

(A) $[0.35, 0.36]$

Answer

(C) $[0.20, 0.25]$

Answer

(D) $[0.36, 0.40]$

Question 21

Suppose that a function $f : R 	o R$ satisfies $f(x + y) = f(x)f(y)$ for all $x, y \in R$ and $f(1) = 3$. If $\sum_{i=1}^{n} f(i) = 363$, then n is equal to __________.

Accepted Answer

5

Question 22

The sum of distinct values of $\lambda$ for which the system of equations
$(\lambda - 1)x + (3\lambda + 1)y + 2\lambda z = 0$
$(\lambda - 1)x + (4\lambda - 2)y + (\lambda + 3)z = 0$
$2x + (3\lambda + 1)y + 3(\lambda - 1)z = 0,$
has non-zero solutions, is __________.

Accepted Answer

3

Question 23

If $\vec{x}$ and $\vec{y}$ be two non-zero vectors such that $|\vec{x} + \vec{y}| = |\vec{x}|$ and $2\vec{x} + \lambda\vec{y}$ is perpendicular to $\vec{y}$, then the value of $\lambda$ is

Accepted Answer

1

Question 24

Consider the data on x taking the values $0, 2, 4, 8, \ldots, 2^n$ with frequencies $^{n}C_0$, $^{n}C_1$, $^{n}C_2$, $\ldots$, $^{n}C_n$ respectively. If the mean of this data is $\frac{728}{2^n}$, then n is equal to __________.

Accepted Answer

6

Question 25

The number of words (with or without meaning) that can be formed from all the letters of the word “LETTER” in which vowels never come together is __________.

Accepted Answer

120

Question 26

In the figure shown, the current in the 10 V battery is close to:

Accepted Answer

(C) 0.21 A from positive to negative terminal.

Answer

(A) 0.71 A from positive to negative terminal

Answer

(B) 0.42 A from positive to negative terminal

Answer

(D) 0.36 A from negative to positive terminal.

Question 27

A charged particle going around in a circle can be considered to be a current loop. A particle of mass m carrying charge q is moving in a plane with speed v under the influence of magnetic field $\vec{B}$. The magnetic moment of this moving particle:

Accepted Answer

(D) $-\frac{mv^{2}\vec{B}}{2B^{2}}$

Answer

(A) $\frac{mv^{2}\vec{B}}{2B^{2}}$

Answer

(B) $-\frac{mv^{2}\vec{B}}{2\pi B^{2}}$

Answer

(C) $-\frac{mv^{2}\vec{B}}{B^{2}}$

Question 28

Three rods of identical cross-section and lengths are made of three different materials of thermal conductivity $K_{1}$, $K_{2}$ and $K_{3}$, respectively. They are joined together at their ends to make a long rod (see figure). One end of the long rod is maintained at 100°C and the other at 0°C (see figure). If the joints of the rod are at 70°C and 20°C in steady state and there is no loss of energy from the surface of the rod, the correct relationship between $K_{1}$, $K_{2}$ and $K_{2}$ is:

Accepted Answer

(A) $K_{1} : K_{3} = 2 : 3$, $K_{2} : K_{3} = 2 : 5$

Answer

(B) $K_{1} < K_{2} < K_{3}$

Answer

(C) $K_{1} : K_{2} = 5 : 2$, $K_{1} : K_{3} = 3 : 5$

Answer

(D) $K_{1} > K_{2} > K_{3}$

Question 29

Two identical electric point dipoles have dipole moments $\vec{p}_{1} = p\hat{i}$ and $\vec{p}_{2} = -p\hat{i}$ and are held on the x axis at distance 'a' from each other. When released, they move along the x-axis with the direction of their dipole moments remaining unchanged. If the mass of each dipole is 'm', their speed when they are infinitely far apart is:

Accepted Answer

(B) $\frac{p}{a}\sqrt{\frac{1}{2\pi ∈_{0} ma}}$

Answer

(A) $\frac{p}{a}\sqrt{\frac{1}{\pi ∈_{0} ma}}$

Answer

(C) $\frac{p}{a}\sqrt{\frac{2}{\pi ∈_{0} ma}}$

Answer

(D) $\frac{p}{a}\sqrt{\frac{3}{2\pi ∈_{0} ma}}$

Question 30

For a plane electromagnetic wave, the magnetic field at a point x and time t is
$\vec{B}(x, t) = \left[1.2×10^{-7} \sin(0.5×10^{3}x + 1.5×10^{11}t)\hat{k}\right]$ T
The instantaneous electric field $\vec{E}$ corresponding to $\vec{B}$ is: (speed of light c = 3 × $10^{8}$ $ms^{-1}$)

Accepted Answer

(A) $\vec{E}(x, t) = \left[-36 \sin(0.5×10^{3}x + 1.5×10^{11}t)\hat{j}\right]\frac{V}{m}$

Answer

(B) $\vec{E}(x, t) = \left[36 \sin(1×10^{3}x + 0.5×10^{11}t)\hat{j}\right]\frac{V}{m}$

Answer

(C) $\vec{E}(x, t) = \left[36 \sin(0.5×10^{3}x + 1.5×10^{11}t)\hat{k}\right]\frac{V}{m}$

Answer

(D) $\vec{E}(x, t) = \left[36 \sin(1×10^{3}x + 1.5×10^{11}t)\hat{i}\right]\frac{V}{m}$

Question 31

Two planets have masses M and 16 M and their radii are a and 2a, respectively. The separation between the centres of the planets is 10a. A body of mass m is fired from the surface of the larger planet towards the smaller planet along the line joining their centres. For the body to be able to reach at the surface of smaller planet, the minimum firings speed needed is:

Accepted Answer

(D) $\frac{3}{2}\sqrt{\frac{5GM}{a}}$

Answer

(A) $2\sqrt{\frac{GM}{a}}$

Answer

(B) $4\sqrt{\frac{GM}{a}}$

Answer

(C) $\sqrt{\frac{GM^{2}}{ma}}$

Question 32

A particle moving in the xy plane experiences a velocity dependent force $\vec{F} = k\left(v_{y}\hat{i} + v_{x}\hat{j}\right)$, where $v_{x}$ and $v_{y}$ are the x and y components of its velocity $\vec{v}$. If $\vec{a}$ is the acceleration of the particle, then which of the following statements is true for the particle?

Accepted Answer

(A) quantity $\vec{v} × \vec{a}$ is constant in time

Answer

(B) $\vec{F}$ arises due to a magnetic field.

Answer

(C) kinetic energy of particle is constant in time.

Answer

(D) quantity $\vec{v} · \vec{a}$ is constant in time.

Question 33

When a car is at rest, its driver sees rain drops falling on it vertically. When driving the car with speed v, he sees that rain drops are coming at an angle 60° from the horizontal. On further increasing the speed of the car to (1 + β)v, this angle changes to 45°. The value of β is close to:

Accepted Answer

(D) 0.73

Answer

(A) 0.50

Answer

(B) 0.41

Answer

(C) 0.37

Question 34

Given the masses of various atomic particles $m_{p}$ = 1.0072 u, $m_{n}$ = 1.0087 u, $m_{e}$ = 0.000548 u, $m_{\bar{v}}$ = 0, $m_{d}$ = 2.0141 u, where p ≡ proton, n ≡ neutron, e ≡ electron, $\bar{v}$ ≡ antineutrino and d ≡ deuteron. Which of the following process is allowed by momentum and energy conservation?

Accepted Answer

(C) $n + p → d + γ$

Answer

(A) n + n → deuterium atom (electron bound to the nucleus)

Answer

(B) $p → n + e^{+} + \bar{v}$

Answer

(D) $e^{+} + e^{-} → γ$

Question 35

A circuit to verify Ohm's law uses ammeter and voltmeter in series or parallel connected correctly to the resistor. In the circuit:

Accepted Answer

(C) ammeter is always connected in series and voltmeter in parallel.

Answer

(A) ammeter is always used in parallel and voltmeter is series.

Answer

(B) both ammeter and voltmeter must be connected in parallel.

Answer

(D) both, ammeter and voltmeter must be connected in series.

Question 36

Consider the force F on a charge 'q' due to a uniformly charged spherical shell of radius R carrying charge Q distributed uniformly over it. Which one of the following statements is true for F, if 'q' is placed at distance r from the centre of the shell?

Accepted Answer

(C) $F = \frac{1}{4\pi ∈_{0}}\frac{Qq}{r^{2}}$ for $r > R$

Answer

(A) $F = \frac{1}{4\pi ∈_{0}}\frac{Qq}{R^{2}}$ for $r < R$

Answer

(B) $\frac{1}{4\pi ∈_{0}}\frac{qQ}{R^{2}} > F > 0$ for $r < R$

Answer

(D) $F = \frac{1}{4\pi ∈_{0}}\frac{Qq}{r^{2}}$ for all r

Question 37

A student measuring the diameter of a pencil of circular cross-section with the help of a vernier scale records the following four readings 5.50 mm, 5.55 mm, 5.45 mm ; 5.65 mm. The average of these four readings is 5.5375 mm and the standard deviation of the data is 0.07395 mm. The average diameter of the pencil should therefore be recorded as:

Accepted Answer

(D) (5.54 ± 0.07) mm

Answer

(A) (5.5375 ± 0.0739) mm

Answer

(B) (5.5375 ± 0.0740) mm

Answer

(C) (5.538 ± 0.074) mm

Question 38

A double convex lens has power P and same radii of curvature R of both the surfaces. The radius of curvature of a surface of a plano-convex lens made of the same material with power 1.5 P is

Accepted Answer

(D) $\frac{R}{3}$

Answer

(A) $2R$

Answer

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

Answer

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

Question 39

A square loop of side 2a and carrying current I is kept in xz plane with its centre at origin. A long wire carrying the same current I is placed parallel to z-axis and passing through point (0, b, 0), (b >> a). The magnitude of torque on the loop about z-axis will be

Accepted Answer

(B) $\frac{2\mu_{0}I^{2}a^{2}b}{\pi(a^{2}+b^{2})}$

Answer

(A) $\frac{2\mu_{0}I^{2}a^{2}}{\pi b}$

Answer

(C) $\frac{\mu_{0}I^{2}a^{2}b}{2\pi(a^{2}+b^{2})}$

Answer

(D) $\frac{\mu_{0}I^{2}a^{2}}{2\pi b}$

Question 40

A fluid is flowing through a horizontal pipe of varying cross-section, with speed v ms$^{-1}$ a ta point where the pressure is P Pascal. At another point where pressure is $\frac{P}{2}$ Pascal its speed is V ms$^{-1}$. If the density of the fluid is ρ kg m$^{-3}$ and the flow is streamline, then V is equal to:

Accepted Answer

(D) $\sqrt{\frac{P}{ρ}+v^{2}}$

Answer

(A) $\sqrt{\frac{P}{ρ}+v}$

Answer

(B) $\sqrt{\frac{2P}{ρ}+v^{2}}$

Answer

(C) $\sqrt{\frac{P}{2ρ}+v^{2}}$

Question 41

When a particle of mass m is attached to a vertical spring of spring constant k and released, its motion is described by $y(t) = y_{0}\sin^{2}\omega t$, where 'y' is measured from the lower end of unstretched spring. Then ω is:

Accepted Answer

(C) $\sqrt{\frac{g}{2y_{0}}}$

Answer

(A) $\frac{1}{2}\sqrt{\frac{g}{y_{0}}}$

Answer

(B) $\sqrt{\frac{g}{y_{0}}}$

Answer

(D) $\sqrt{\frac{2g}{y_{0}}}$

Question 42

Assuming the nitrogen molecule is moving with r.m.s. velocity at 400 K, the de-Broglie wavelength of nitrogen molecule is close to:
(Given: nitrogen molecule weight: $4.64 × 10^{-26}$ kg, Boltzman constant: $1.38 × 10^{-23}$ J/K, Planck constant: $6.63 × 10^{-34}$ Js)

Accepted Answer

(A) 0.24 Å

Answer

(B) 0.20 Å

Answer

(C) 0.34 Å

Answer

(D) 0.44 Å

Question 43

The liner mass density of a thin rod AB of length L varies from A to B as $\lambda(x) = \lambda_{0}\left(1+\frac{x}{L}\right)$, where x is the distance from A. If M is the mass of the rod hen its moment of inertia about an axis passing through A and perpendicular to the rod is:

Accepted Answer

(B) $\frac{7}{18}ML^{2}$

Answer

(A) $\frac{5}{12}ML^{2}$

Answer

(C) $\frac{2}{5}ML^{2}$

Answer

(D) $\frac{3}{7}ML^{2}$

Question 44

The out put characteristics of a transistor is shown in the figure. When $V_{CE}$ is 10 V and $I_{C}$ = 4.0 mA, then value of $\beta_{ac}$ is ______.

Accepted Answer

150

Question 45

The centre of mass of a solid hemisphere of radius 8 cm is x cm from the centre of the flat surface. Then value of x is ______.

Accepted Answer

3.00

Question 46

A Young's double-slit experiment is performed using monochromatic light of wavelength λ. The intensity of light at a point on the screen, where the path difference is λ, is K units. The intensity of the light at a point where the path difference is $\frac{\lambda}{6}$ is given by $\frac{nK}{12}$, where 'n' is an integer. The value of 'n' is ______.

Accepted Answer

9.00

Question 47

In a series LR circuit, power of 400 W is dissipated from a source of 250 V, 50 Hz. The power factor of the circuit is 0.8. In order to bring the power factor to unity, a capacitor of value C is added in series to the L and R. Taking the value of C as $\left(\frac{n}{3\pi}\right)$ μF, then value of 'n' is ______.

Accepted Answer

400.00

Question 48

For a reaction,
4M(s) + nO$_2$(g) → 2M$_2$O$_n$(s),
the free energy change is plotted as a function of temperature. The temperature below which the oxide is stable could be inferred from the plot as the point at which

Accepted Answer

(B) the free energy change shows a change from negative to positive value.

Answer

(A) the slope changes from negative to positive.

Answer

(C) the slope changes from positive to negative.

Answer

(D) the slope changes from positive to zero.

Question 49

The average molar mass of chlorine is 35.5 g mol$^{-1}$. The ratio of $^{35}$Cl to $^{37}$Cl in naturally occurring chlorine is close to:

Accepted Answer

(B) 3 : 1

Answer

(A) 4 : 1

Answer

(C) 2 : 1

Answer

(D) 1 : 1

Question 50

The value of K$_C$ is 64 at 800 K for the reaction
N$_2$(g) + 3H$_2$(g) ⇌ 2NH$_3$(g)
The value of K$_C$ for the following reaction is:
NH$_3$(g) ⇌ $\frac{1}{2}$N$_2$(g) + $\frac{3}{2}$H$_2$(g)

Accepted Answer

(D) $\frac{1}{8}$

Answer

(A) $\frac{1}{64}$

Answer

(B) 8

Answer

(C) $\frac{1}{4}$

Question 51

Dihydrogen of high purity (>99.95%) is obtained through:

Accepted Answer

(D) the electrolysis of warm Ba(OH)$_2$ solution using Ni electrodes.

Answer

(A) the reaction of Zn with dilute HCl.

Answer

(B) the electrolysis of acidified water using Pt electrodes

Answer

(C) the electrolysis of brine solution.

Question 52

The reaction of NO with N$_2$O$_4$ at 250 K gives:

Accepted Answer

(C) N$_2$O$_3$

Answer

(A) N$_2$O

Answer

(B) NO$_2$

Answer

(D) N$_2$O$_5$

Question 53

The correct match between Item-I (starting material) and Item-II (reagent) for the preparation of benzaldehyde is:

Accepted Answer

(C) (I) − (R), (II) − (P) and (III) − (Q)

Answer

(A) (I) − (Q), (II) − (R) and (III) − (P)

Answer

(B) (I) − (P), (II) − (Q) and (III) − (R)

Answer

(D) (I) − (R), (II) − (Q) and (III) − (P)

Question 54

A crystal is made up of metal ions 'M$_1$' and 'M$_2$' and oxide ions. Oxide ions form a ccp lattice structure. The cation 'M$_1$' occupies 50% of octahedral voids and the cation 'M$_2$' occupies 12.5% of tetrahedral voids of oxide lattice. The oxidation numbers of 'M$_1$' and 'M$_2$' are respectively:

Accepted Answer

(A) +2, +4

Answer

(B) +1, +3

Answer

(C) +3, +1

Answer

(D) +4, +2

Question 55

The element that can be refined by distillation is:

Accepted Answer

(B) zinc

Answer

(A) nickel

Answer

(C) tin

Answer

(D) gallium

Question 56

For a d$^4$ metal ion in an octahedral field, the correct electronic configuration is:

Accepted Answer

(A) $t_{2g}^{3}e_{g}^{1}$ when Δ$_o$ < P

Answer

(B) $t_{2g}^{3}e_{g}^{1}$ when Δ$_o$ > P

Answer

(C) $t_{2g}^{4}e_{g}^{0}$ when Δ$_o$ < P

Answer

(D) $t_{g}^{2}e_{2g}^{2}$ when Δ$_o$ < P

Question 57

Match the following:

Accepted Answer

(C) (i)-(d), (ii)-(c), (iii)-(e), (iv)-(a)

Answer

(A) (i)-(d), (ii)-(c), (iii)-(b), (iv)-(e)

Answer

(B) (i)-(b), (ii)-(d), (iii)-(e), (iv)-(a)

Answer

(D) (i)-(b), (ii)-(a), (iii)-(c), (iv)-(d)

Question 58

Match the following compounds (Column-I) with their uses (Column-II):

Accepted Answer

(B) (i)-(B), (ii)-(D), (iii)-(A), (iv)-(A)

Answer

(A) (i)-(D), (ii)-(A), (iii)-(C), (iv)-(B)

Answer

(C) (i)-(B), (ii)-(C), (iii)-(D), (iv)-(A)

Answer

(D) (i)-(C), (ii)-(D), (iii)-(B), (iv)-(A)

Question 59

The IUPAC name of the following compound is
[structure shown]

Accepted Answer

(C) 5-amino-4hydroxymethyl-2-nitrobenzaldehyde

Answer

(A) 2-nitrogen-4-hydroxymethyl-5-amine benzaldehyde.

Answer

(B) 3-amino-4-hydroxymethyl 1-5-nitrobvenzaldehyde

Answer

(D) 4-amino-2formyl-5hydroxymethyl nitrobenzene

Question 60

Which of the following compounds can e prepared in good yield by Gabriel phthalimide synthesis?

Accepted Answer

(A) (A)

Answer

(B) CH$_3$–CH$_2$–NHCH$_3$

Answer

(C) (C)

Answer

(D) (D)

Question 61

A set of solutions is prepared using 180 g of water as a solvent and 10 g of different non-volatile solutes A, B and C. The relative lowering of vapour pressure in the presence of these solutes are in the order [Given, molar mass of A = 100 g mol$^{-1}$ ; B = 200 g mol$^{-1}$ ; C = 10,000 g mol$^{-1}$]

Accepted Answer

(C) A > B > C

Answer

(A) B > C > A

Answer

(B) C > B > A

Answer

(D) A > C > B

Question 62

For the given cell;
Cu(s) | Cu$^{2+}$ (C$_1$M) || Cu$^{2+}$ (C$_2$M) | Cu(s)
Change in Gibbs energy (ΔG) is negative, if

Accepted Answer

(D) C$_2$ = $\sqrt{2}$C$_1$

Answer

(A) C$_1$ = C$_2$

Answer

(B) $\frac{C_2 = C_1}{\sqrt{2}}$

Answer

(C) C$_1$ = 2C$_2$

Question 63

Reaction of an inorganic sulphite X with dilute H$_2$SO$_4$ generates compound Y. Reaction of Y with NaOH gives X. Further, the reaction of X. Further, the reaction of X with Y and water affords compound Z. Y and Z respectively, are:

Accepted Answer

(C) SO$_2$ and NaHSO$_3$

Answer

(A) SO$_2$ and Na$_2$SO$_3$

Answer

(B) SO$_3$ and NaHSO$_3$

Answer

(D) S and Na$_2$SO$_3$

Question 64

The increasing order of the boiling points of the major products A, B and C of the following reactions will be:

Accepted Answer

(A) B < C < A

Answer

(B) C < A < B

Answer

(C) A < B < C

Answer

(D) A < C < B

Item-I	Item-II
I.Benzene	P.HCl and SnCl $_2$ , H $_3$ O $^+$
II.Benzonitrile	Q.H $_2$ , Pd-BaSO $_4$ , S and quinoline
III.Benzoyl Chloride	R.CO, HCl and AlCl $_3$

Test / Method	Reagent
i.Lucas Test	a.C $_6$ H $_5$ SO $_2$ Cl / aq. KOH
ii.Dumas method	b.HNO $_3$ / AgNO $_3$
iii.Kjeldahl's method	c.CuO / CO $_2$
iv.Hinsberg Test	d.Conc. HCl and ZnCl $_2$
	e.H $_2$ SO $_4$

Column-I	Column-II
i.Ca(OH) $_2$	A.casts of statues
ii.NaCl	B.white wash
iii.CaSO $_4$ · $\frac{1}{2}$ H $_2$ O	C.antacid
iv.CaCO $_3$	D.Washing soda preparation

Item-I	Item-II
a.Natural rubber	I.1, 3-butadiene + styrene
b.Neoprene	II.1, 3-butadiene + acrylonitrile
c.Buna-N	III.Chloroprene
d.Buna-S	IV.Isoprene

JEE Main 6 September 2020 Shift 2 Question Paper with Answers

Physics — JEE Main 6 September 2020 Shift 2

Chemistry — JEE Main 6 September 2020 Shift 2

Mathematics — JEE Main 6 September 2020 Shift 2

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