JEE Main 5 September 2020 Shift 2 Question Paper

Question 1

The value of $\left(\dfrac{-1+i\sqrt{3}}{1-i}\right)^{30}$ is:

Accepted Answer

(D) $-2^{15}i$

Answer

(A) $2^{15}i$

Answer

(B) $-2^{15}$

Answer

(C) $6^5$

Question 2

If the system of linear equations
$x+y+3z=0$
$x+3y+k^2z=0$
$3x+y+3z=0$
has a non-zero solution $(x,y,z)$ for some $k\in R$, then $x+\left(\dfrac{y}{z}\right)$ is equal to:

Accepted Answer

(C) $-3$

Answer

(A) $3$

Answer

(B) $9$

Answer

(D) $-9$

Question 3

$\displaystyle\lim_{x	o 0}\dfrac{x\left(e^{\left(\sqrt{1+x^2+x^4}-1ight)/x}-1ight)}{\sqrt{1+x^2+x^4}-1}$

Accepted Answer

(B) is equal to $1$

Answer

(A) does not exist

Answer

(C) is equal to $\sqrt{e}$

Answer

(D) is equal to $0$

Question 4

If for some $\alpha\in R$, the lines $L_1:\dfrac{x+1}{2}=\dfrac{y-2}{-1}=\dfrac{z-1}{1}$ and $L_2:\dfrac{x+2}{\alpha}=\dfrac{y+1}{5-\alpha}=\dfrac{z+1}{1}$ are coplanar, then the line $L_2$ passes through the point:

Accepted Answer

(A) $(2,-10,-2)$

Answer

(B) $(10,-2,-2)$

Answer

(C) $(10,2,2)$

Answer

(D) $(-2,10,2)$

Question 5

Let $y=y(x)$ be the solution of the differential equation $\cos x\dfrac{dy}{dx}+2y\sin x=\sin 2x, x\in\left(0,\dfrac{\pi}{2}\right)$. If $y(\pi/3)=0$, then $y(\pi/4)$ is equal to:

Accepted Answer

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

Answer

(A) $2+\sqrt{2}$

Answer

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

Answer

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

Question 6

If $L=\sin^2\left(\dfrac{\pi}{16}\right)-\sin^2\left(\dfrac{\pi}{8}\right)$ and $M=\cos^2\left(\dfrac{\pi}{16}\right)-\sin^2\left(\dfrac{\pi}{8}\right)$, then:

Accepted Answer

(C) $M=\dfrac{1}{2\sqrt{2}}+\dfrac{1}{2}\cos\dfrac{\pi}{8}$

Answer

(A) $M=\dfrac{1}{4\sqrt{2}}+\dfrac{1}{4}\cos\dfrac{\pi}{8}$

Answer

(B) $L=-\dfrac{1}{2\sqrt{2}}+\dfrac{1}{2}\cos\dfrac{\pi}{8}$

Answer

(D) $L=\dfrac{1}{4\sqrt{2}}-\dfrac{1}{4}\cos\dfrac{\pi}{8}$

Question 7

Which of the following point lies on the tangent to the curve $x^4e^y+2\sqrt{y+1}=3$ at the point $(1,0)$?

Accepted Answer

(B) $(-2,6)$

Answer

(A) $(2,2)$

Answer

(C) $(-2,4)$

Answer

(D) $(2,6)$

Question 8

The derivation of $	an^{-1}\left(\dfrac{\sqrt{1+x^2}-1}{x}ight)$ with respect to $	an^{-1}\left(\dfrac{2x\sqrt{1-x^2}}{1-2x^2}ight)$ at $x=\dfrac{1}{2}$ is:

Accepted Answer

(B) $\dfrac{\sqrt{3}}{10}$

Answer

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

Answer

(C) $\dfrac{\sqrt{3}}{12}$

Answer

(D) $\dfrac{2\sqrt{3}}{5}$

Question 9

If the sum of the second, third and fourth terms of a positive term G.P. is 3 and the sum of its sixth, seventh and eights terms is 243, then the sum of the first 50 terms of this G.P. is:

Accepted Answer

(A) $\dfrac{1}{26}\left(3^{50}-1\right)$

Answer

(B) $\dfrac{1}{13}\left(3^{50}-1\right)$

Answer

(C) $\dfrac{2}{13}\left(3^{50}-1\right)$

Answer

(D) $\dfrac{1}{26}\left(3^{49}-1\right)$

Question 10

If $\displaystyle\int\dfrac{\cos	heta}{5+7\sin	heta-2\cos^2	heta}\,d	heta=A\log_e\left|B(	heta)ight|+C$, where C is a constant of integration, then $\dfrac{B(	heta)}{A}$ can be:

Accepted Answer

(B) $\dfrac{5(2\sin	heta+1)}{\sin	heta+3}$

Answer

(A) $\dfrac{5(\sin	heta+3)}{2\sin	heta+1}$

Answer

(C) $\dfrac{2\sin	heta+1}{5(\sin	heta+3)}$

Answer

(D) $\dfrac{2\sin	heta+1}{\sin	heta+3}$

Question 11

If $\alpha$ and $\beta$ are the roots of the equation, $7x^2-3x-2=0$, then the value of $\dfrac{\alpha}{1-\alpha^2}+\dfrac{\beta}{1-\beta^2}$ is equal to:

Accepted Answer

(B) $\dfrac{27}{16}$

Answer

(A) $\dfrac{27}{32}$

Answer

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

Answer

(D) $\dfrac{1}{24}$

Question 12

If the length of the chord of the circle, $x^2+y^2=r^2\ (r>0)$ along the line $y-2x=3$ is r, the $r^2$ is equal to:

Accepted Answer

(B) $\dfrac{12}{5}$

Answer

(A) $12$

Answer

(C) $\dfrac{9}{5}$

Answer

(D) $\dfrac{24}{5}$

Question 13

The statement $(P 	o (q 	o p)) 	o (p 	o (p \vee q))$ is:

Accepted Answer

(A) a tautology

Answer

(B) equivalent to $(p \wedge q) \vee (\sim q)$

Answer

(C) equivalent to $(p \vee q) \wedge (\sim p)$

Answer

(D) a contradiction

Question 14

There are 3 sections in a question paper and each section contains 5 questions. A candidate has to answer a total of 5 questions, choosing at least one question from each section. Then the number of ways, in which the candidate can choose the questions, is:

Accepted Answer

(C) 2250

Answer

(A) 2255

Answer

(B) 3000

Answer

(D) 1500

Question 15

If a + x = b + y = c + z + 1, where a, b, c, x, y, x are non-zero distinct real numbers then $\begin{vmatrix} x & a+y & x+a \ y & b+y & y+b \ z & c+y & z+c \end{vmatrix}$ is equal to:

Accepted Answer

(A) y(a - b)

Answer

(B) y(b - a)

Answer

(C) 0

Answer

(D) y(a - c)

Question 16

If the sum of the first 20 terms of the series $\log_{(7^{1/2})} x + \log_{(7^{1/3})} x + \log_{(7^{1/4})} x + ...$ is 460, then x is equal to:

Accepted Answer

(A) $7^2$

Answer

(B) $7^{46/21}$

Answer

(C) $7^{1/2}$

Answer

(D) $e^2$

Question 17

If the line y = mx + c is a common tangent to the hyperbola $\dfrac{x^2}{100} - \dfrac{y^2}{64} = 1$ and the circle $x^2 + y^2 = 36$, then which one of the following is true?

Accepted Answer

(A) $4c^2 = 369$

Answer

(B) $c^2 = 369$

Answer

(C) $5m = 4$

Answer

(D) $8m + 5 = 0$

Question 18

If the mean and standard deviation of the data 3, 5, 7, a, b are 5 and 2 respectively, then a and b are the roots of the equation:

Accepted Answer

(A) $x^2 - 10x + 19 = 0$

Answer

(B) $x^2 - 20x + 18 = 0$

Answer

(C) $x^2 - 10x + 18 = 0$

Answer

(D) $2x^2 - 20x + 19 = 0$

Question 19

Let $A = (a, b, c)$ and $B = (1, 2, 3, 4)$. Then the number of elements in the set $C = \{f : A 	o B \mid 2 \in f(A) 	ext{ and } f 	ext{ is not one-one}\}$ is __________.

Accepted Answer

19.00

Question 20

The coefficient of $x^4$ in the expansion of $(1 + x + x^2 + x^3)^6$ in powers of x, is __________.

Accepted Answer

120.00

Question 21

If the lines x + y = a and x - y = b touch the curve $y = x^2 - 3x + 2$ at the points where the curve intersects the x-axis, then $\dfrac{a}{b}$ is equal to __________.

Accepted Answer

0.50

Question 22

Let the vectors $\vec{a}, \vec{b}, \vec{c}$ be such that $|\vec{a}| = 2, |\vec{b}| = 4$ and $|\vec{c}| = 4$. if the projection of $\vec{b}$ on $\vec{a}$ is equal to the projection of $\vec{c}$ on $\vec{a}$ and $\vec{b}$ is perpendicular to $\vec{c}$, then the value of $|\vec{a} + \vec{b} - \vec{c}|$ is __________.

Accepted Answer

6.00

Question 23

In a bombing attack, there is 50% chance that a bomb will hit the target. At least two independent hits are required to destroy the target completely. Then the minimum number of bombs, that must be dropped to ensure that there is at least 99% chance of completely destroying the target, is __________.

Accepted Answer

11.00

Question 24

Two coherent sources of sound, $S_1$ and $S_2$ produce source waves of the same wavelength, $\lambda = 1$ m, in phase. $S_1$ and $S_2$ are placed 1.5 m apart (see fig). A listener located at L, directly in front of $S_2$ finds that the intensity is at a minimum when he is 2 m away from $S_2$. The listener moves away from $S_1$, keeping his distance from $S_2$ fixed. The adjacent maximum of intensity is observed when the listener is at a distance d from $S_1$. Then, d is:

Accepted Answer

(B) 3 m

Answer

(A) 12 m

Answer

(C) 5 m

Answer

(D) 2 m

Question 25

Two different wires having lengths $L_1$ and $L_2$, and respective temperature coefficient of linear 4expansion $\alpha_1$ and $\alpha_2$, are joined end-to-end. Then the effective temperature coefficient of linear expansion is:

Accepted Answer

(C) $\dfrac{\alpha_1 L_1 + a_2 L_2}{L_1+L_2}$

Answer

(A) $\dfrac{\alpha_1+\alpha_2}{2}$

Answer

(B) $2\sqrt{\alpha_1\alpha_2}$

Answer

(D) $4\dfrac{\alpha_1\alpha_2}{\alpha_1+\alpha_2}\dfrac{L_1 L_2}{(L_2+L_1)^{2}}$

Question 26

In the circuit shown, charge on the 5 $\mu$F capacitor is:

Accepted Answer

(A) 16.36 $\mu$C

Answer

(B) 5.45 $\mu$C

Answer

(C) 10.90 $\mu$C

Answer

(D) 18.00 $\mu$C

Question 27

In adiabatic process, the density of a diatomic gas becomes 32 times its initial value. The final pressure of the gas is found to be n times the initial pressure. The value of n is:

Accepted Answer

(A) 128

Answer

(B) $\dfrac{1}{32}$

Answer

(C) 32

Answer

(D) 326

Question 28

An iron rod of volume $10^{-3}$ m$^3$ and relative permeability 1000 is placed as core in a solenoid with 10 turns/cm. If a current of 0.5 A is passed through the solenoid, then the magnetic moment of the rod will be:

Accepted Answer

(D) $5 	imes 10^{2}$ Am$^2$

Answer

(A) $0.5 	imes 10^{2}$ Am$^2$

Answer

(B) $50 	imes 10^{2}$ Am$^2$

Answer

(C) $500 	imes 10^{2}$ Am$^2$

Question 29

The correct match between the entries in column I and column II are:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 30

A radioactive nucleus decays by two difference processes. The half life for the first process is 10 s and that for the second is 100 s. The effective half life of the nucleus is closes to:

Accepted Answer

(B) 9 sec.

Answer

(A) 6 sec.

Answer

(C) 12 sec.

Answer

(D) 55 sec.

Question 31

Ten charges are placed on the circumference of a circle of radius R with constant angular separation between successive charges. Alternate charges 1, 3, 5, 7, 9 have charge (+ q) each, while 2, 4, 6, 8, 10 have charge (− q) each. The potential V and the electric field E at the centre of the circle are respectively: (Take V = 0 at infinity)

Accepted Answer

(C) $V = 0$ ; $E = 0$

Answer

(A) $V = \dfrac{10q}{4\pi \epsilon_0 R}$; $E = \dfrac{10q}{4\pi \epsilon_0 R^{2}}$

Answer

(B) $V = 0$; $E = \dfrac{10q}{4\pi \epsilon_0 R^{2}}$

Answer

(D) $V = \dfrac{10q}{4\pi \epsilon_0 R}$; $E = 0$

Question 32

A driver in a car, approaching a vertical wall notices that the frequency of his car horn, has changed from 440 Hz to 480 Hz, when it gets reflected from the wall. If the speed of sound in air is 345 m/s, then the speed of the car is:

Accepted Answer

(D) 54 km/hr

Answer

(A) 24 km/hr

Answer

(B) 36 km/hr

Answer

(C) 18 km/hr

Question 33

A parallel plate capacitor has plate of length '\ell', width 'w' and separation of plates is 'd'. It is connected to a battery of emf V. A dielectric slap of the same thickness 'd' and of dielectric constant k = 4 is being, inserted between the plates of the capacitor. At what length of the slab inside plates, will be energy stored in the capacitor be two times the initial energy stored?

Accepted Answer

(D) $\ell/3$

Answer

(A) $2\ell/3$

Answer

(B) $\ell/2$

Answer

(C) $\ell/4$

Question 34

A spaceship in space sweeps stationary interplanetary dust. As a result, its mass increases at a rate $\dfrac{dM(t)}{dt} = bv^{2}(t)$, where v(t) its instantaneous velocity. The instantaneous acceleration of the satellite is:

Accepted Answer

(B) $-\dfrac{bv^{3}}{M(t)}$

Answer

(A) $-\dfrac{2bv^{3}}{M(t)}$

Answer

(C) $-bv(t)$

Answer

(D) $-\dfrac{bv^{3}}{2M(t)}$

Question 35

The acceleration due to gravity on the earth's surface at the poles is g an and angular velocity of the earth about the axis passing through the pole is $\omega$. An object is weight at the equator and at a height h above the poles by using a spring balance. If the weights are found to be same, then h is : (h<<R, where R is the radius of the earth)

Accepted Answer

(A) $\dfrac{R^{2}\omega^{2}}{2g}$

Answer

(B) $\dfrac{R^{2}\omega^{2}}{g}$

Answer

(C) $\dfrac{R^{2}\omega^{2}}{8g}$

Answer

(D) $\dfrac{R^{2}\omega^{2}}{4g}$

Question 36

In an experiment to verify Stokes law, a small spherical ball of radius r and density $\rho$ falls under gravity through a distance h in air before entering a tank of water. If the terminal velocity of the ball inside water is same as its velocity just before entering the water surface, then the value of h is proportional to: (ignore viscosity of air)

Accepted Answer

(B) $r^{4}$

Answer

(A) $r^{3}$

Answer

(C) $r^{2}$

Answer

(D) $r$

Question 37

A ring is hung on a nail. It can oscillate, without slipping or sliding (i) in its plane with a time period T$_1$ and, T(ii) back and forth in a direction perpendicular to its plane, with a period T$_2$. The ratio $\dfrac{T_1}{T_2}$ will be:

Accepted Answer

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

Answer

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

Answer

(C) $\dfrac{\sqrt{2}}{3}$

Answer

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

Question 38

The velocity (v) and time (t) graph of a body in a straight line motion is shown in the figure. The point S is at 4.333 seconds. The total distance covered by the body in 6 s is:

Accepted Answer

(B) $\dfrac{37}{3}$ m

Answer

(A) 11 m

Answer

(C) 12 m

Answer

(D) $\dfrac{49}{4}$ m

Question 39

A galvanometer is used in laboratory for detecting the null point in electrical experiments. If, on passing a current of 6 mA it produces a deflection of 2°, its figure of merit is close to:

Accepted Answer

(D) $3 	imes 10^{-3}$ A/div.

Answer

(A) 666° A/div.

Answer

(B) $6 	imes 10^{-3}$ A/div.

Answer

(C) 333° A/div.

Question 40

In the circuit, given in the figure currents in different branches and value of one resistor are shown. Then potential at point B with respect to the point A is:

Accepted Answer

(A) + 1 V

Answer

(B) – 1 V

Answer

(C) + 2 V

Answer

(D) – 2 V

Question 41

A thin rod of mass 0.9 kg and length 1 m is suspended, at rest, from one end so that it can freely oscillate in the vertical plane. A particle of move 0.1 kg moving in a straight line with velocity 80 m/s hits the rod at its bottom most point and sticks to it (see figure). The angular speed (in rad/s) of the rod immediately after the collision will be __________.

Accepted Answer

20.00

Question 42

The surface of a metal is illuminated alternately with photons of energies E$_1$ = 4 eV and E$_2$ = 2.5 eV respectively. The ratio of maximum speeds of the photoelectrons emitted in the two cases is 2. The work function of the metal in (eV) is __________.

Accepted Answer

2.00

Question 43

A prism of angle A = 1° has a refractive index $\mu = 1.5$. A good estimate for the minimum angle of deviation (in degrees) is close to N/10. Value of N is __________.

Accepted Answer

5.00

Question 44

A body of mass 2 kg, is driven by an engine delivering, a constant power 1 J/s. the body starts from rest and moves in a straight line. After 9 seconds, the body has moved a distance (in m) __________.

Accepted Answer

18.00

Question 45

An element crystallises in a face-centred cubic (fcc) unit cell with cell edge a. The distance between the centres of two nearest octahedral voids in the crystal lattice is:

Accepted Answer

(D) $\dfrac{a}{\sqrt{2}}$

Answer

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

Answer

(B) $\sqrt{2}a$

Answer

(C) a

Question 46

The major product of the following reaction is:

Accepted Answer

(B) (B)

Answer

(A) (A)

Answer

(C) (C)

Answer

(D) (D)

Question 47

Adsorption of a gas follows Freundlich adsorption isotherm. If x is the mass of the gas adsorbed on mass m of the adsorbent, the correct plot of $\dfrac{x}{m}$ versus p is:

Accepted Answer

(D) (D)

Answer

(A) (A)

Answer

(B) (B)

Answer

(C) (C)

Question 48

The variation of molar conductivity with concentration of an electrolyte (X) in aqueous solution is shown in the given figure.

Accepted Answer

(B) $CH_3COOH$

Answer

(A) $KNO_3$

Answer

(C) $HCl$

Answer

(D) $NaCl$

Question 49

The compound that has the largest H – M – H bond angle (M = N, O, S, C), is

Accepted Answer

(B) $CH_4$

Answer

(A) $H_2O$

Answer

(C) $H_2S$

Answer

(D) $NH_3$

Question 50

Lattice enthalpy and enthalpy of solution of NaCl are 788 kJ mol$^{-1}$ and 4 kJ mol$^{-1}$, respectively. The hydration enthalpy of NaCl is:

Accepted Answer

(B) -784 kJ mol$^{-1}$

Answer

(A) 784 kJ mol$^{-1}$

Answer

(C) 780 kJ mol$^{-1}$

Answer

(D) -780 kJ mol$^{-1}$

Question 51

The rate constant (k) of a reaction is measured at different temperatures (T), and the data are plotted in the given figure. The activation energy of the reaction in kJ mol$^{-1}$ is: (R is gas constant)

Accepted Answer

(A) 2R

Answer

(B) 2/R

Answer

(C) R

Answer

(D) 1/R

Question 52

The major product formed in the following reaction is: $CH_3CH=CHCH(CH_3)_2 \xrightarrow{HBr}$

Accepted Answer

(B) $CH_3CH_2CH_2C(Br)(CH_3)_2$

Answer

(A) $CH_3CH_2CH(Br)CH(CH_3)_2$

Answer

(C) $Br(CH_2)_3CH(CH_3)_2$

Answer

(D) $CH_3CH(Br)CH_2CH(CH_3)_2$

Question 53

Among the following compounds, geometrical isomerism is exhibited by:

Accepted Answer

(A) (A)

Answer

(B) (B)

Answer

(C) (C)

Answer

(D) (D)

Question 54

Boron and silicon of very high purity can be obtained through:

Accepted Answer

(A) zone refining

Answer

(B) electrolytic refining

Answer

(C) liquation

Answer

(D) vapour phase refining

Question 55

The following molecule acts as an:

Accepted Answer

(C) Anti-histamine

Answer

(A) Antiseptic

Answer

(B) Anti-depressant

Answer

(D) Anti-bacterial

Question 56

Which one of the following polymers is not obtained by condensation polymerisation?

Accepted Answer

(A) Buna – N

Answer

(B) Nylon 6

Answer

(C) Nylon 6, 6

Answer

(D) Bakelite

Question 57

Hydrogen peroxide, in the pure state, is:

Accepted Answer

(A) non-planar and blue in color

Answer

(B) planar and blue in color

Answer

(C) linear and blue in color

Answer

(D) linear and almost colorless

Question 58

The one that is NOT suitable for the removal of permanent hardness of water is:

Accepted Answer

(B) Clark's method

Answer

(A) Calgon's method

Answer

(C) Treatment with sodium carbonate

Answer

(D) Ion-exchange method

Question 59

Consider the complex ions,
trans $-\left[Co(en)_2Cl_2\right]^+$ (A) and
cis $-\left[Co(en)_2Cl_2\right]^+$ (B). The correct statement regarding them is:

Accepted Answer

(B) (A) cannot be optically active, but (B) can be optically active.

Answer

(A) both (A) and (B) cannot be optically active.

Answer

(C) both (A) and (B) can be optically active.

Answer

(D) (A) can be optically active, but (B) cannot be optically active.

Question 60

The number of chiral carbons present in sucrose is __________.

Accepted Answer

9.00

Question 61

Considering that $\Delta_0 > P$, the magnetic moment (in BM) of $\left[Ru(H_2O)_6\right]^{2+}$ would be __________.

Accepted Answer

0.00

Question 62

The volume, in mL, of 0.02 M K$_2$Cr$_2$O$_7$ solution required to react with 0.288 g of ferrous oxalate in acidic medium is __________.
(Molar mass of Fe = 56 mol$^{-1}$)

Accepted Answer

50.00

Question 63

For a reaction X + Y = 2Z, 1.0 mol of X, 1.5 mol of Y and 0.5 mol of Z were taken in a 1 L vessel and allowed to react. At equilibrium, the concentration of Z was 1.0 mol L$^{-1}$. The equilibrium constant of the reaction is __________ $\dfrac{x}{15}$. The value of x is __________.

Accepted Answer

16.00

Radiation	Wavelength
a.Microwave	i.100 m
b.Gamma rays	ii. $10^{-15}$ m
c.A.M. radio waves	iii. $10^{-10}$ m
d.X-rays	iv. $10^{-3}$ m

JEE Main 5 September 2020 Shift 2 Question Paper with Answers

Physics — JEE Main 5 September 2020 Shift 2

Chemistry — JEE Main 5 September 2020 Shift 2

Mathematics — JEE Main 5 September 2020 Shift 2

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