JEE Main 4 September 2020 Shift 2 Question Paper

Question 1

If a and b are real numbers such that $(2 + \alpha)^{4} = a + b\alpha$, where $\alpha = \frac{-1 + i\sqrt{3}}{2}$, then a + b is equal to:

Accepted Answer

(A) 9

Answer

(B) 33

Answer

(C) 57

Answer

(D) 24

Question 2

Contrapositive of the statement:
'If a function f is differentiable at a, then it is also continuous at a', is:

Accepted Answer

(A) If a function f is not continuous at a, then it is not differentiable at a.

Answer

(B) If a function f is continuous at a, then it is differentiable at a.

Answer

(C) If a function f is not continuous at a. then it is differentiable at a.

Answer

(D) If a function f is continuous at a, then it is not differentiable at a.

Question 3

If for some positive integer n, the coefficients of three consecutive terms in the binomial expansion of $(1 + x)^{N+5}$ are in the ratio 5 : 10 : 14, then the largest coefficient in the expansion is:

Accepted Answer

(D) 462

Answer

(A) 252

Answer

(B) 330

Answer

(C) 792

Question 4

The function $f(x) = \begin{cases} \frac{\pi}{4} + 	an^{-1} x, & |x| \leq 1 \ \frac{1}{2}\left(|x| - 1ight), & |x| > 1 \end{cases}$ is:

Accepted Answer

(C) continuous on R − {1} and differentiable on R − {−1, 1}.

Answer

(A) both continuous and differentiable on R − {1}.

Answer

(B) both continuous and differentiable on R − {−1}.

Answer

(D) continuous on R − {−1} and differentiable on R − {−1, 1}.

Question 5

If the system of equations
x + y + z = 2
2x + 4y − z = 6
$3x + 2y + \lambda z = \mu$
has infinitely many solutions, then:

Accepted Answer

(B) $2\lambda + \mu = 14$

Answer

(A) $\lambda + 2\mu = 14$

Answer

(C) $2\lambda - \mu = 5$

Answer

(D) $\lambda - 2\mu = -5$

Question 6

Let $\lambda 
eq 0$ be in R. If $\alpha$ and $\beta$ are the roots of the equation, $x^{2} - x + 2\lambda = 0$ and $\alpha$ and $\gamma$ are the roots of the equation, $3x^{2} - 10x + 27\lambda = 0$, then $\frac{\beta\gamma}{\lambda}$ is equal to:

Accepted Answer

(A) 18

Answer

(B) 36

Answer

(C) 9

Answer

(D) 27

Question 7

The circle passing through the intersection of the circles, $x^{2} + y^{2} - 6x = 0$ and $x^{2} + y^{2} - 4y = 0$, having its centre on the line, $2x - 3y + 12 = 0$, also passes through the point:

Accepted Answer

(B) (−3, 6)

Answer

(A) (−1, 3)

Answer

(C) (−3, 1)

Answer

(D) (1, −3)

Question 8

The integral $\int_{\pi/6}^{\pi/3} 	an^{3} x \cdot \sin^{2} 3x \left(2\sec^{2} x \cdot \sin^{2} 3x + 3	an x \cdot \sin 6xight) dx$ is

Accepted Answer

(A) $-\frac{1}{18}$

Answer

(B) $-\frac{1}{9}$

Answer

(C) $\frac{9}{2}$

Answer

(D) $\frac{7}{18}$

Question 9

The area (in sq. units) of the largest rectangle ABCD whose vertices A and B lie on the x-axis and vertices C and D lie on the parabola, $y = x^{2} - 1$ below the x-axis, is:

Accepted Answer

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

Answer

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

Answer

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

Answer

(D) $\frac{2}{3\sqrt{3}}$

Question 10

The solution of differential equation $\frac{dy}{dx} - \frac{y + 3x}{\log_{e}\left(y + 3x\right)} + 3 = 0$ is:
(where C is a constant of integration.)

Accepted Answer

(B) $x - \frac{1}{2}\left(\log_{e}\left(y + 3x\right)\right)^{2} = C$

Answer

(A) $y + 3x - \frac{1}{2}\left(\log_{e} x\right)^{2} = C$

Answer

(C) $x - 2\log_{e}\left(y + 3x\right) = C$

Answer

(D) $x - \log_{e}\left(y + 3x\right) = C$

Question 11

The minimum value of $2^{\sin x} + 2^{\cos x}$ is:

Accepted Answer

(A) $2^{1 - \frac{1}{\sqrt{2}}}$

Answer

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

Answer

(C) $2^{-1 + \sqrt{2}}$

Answer

(D) $2^{-1 + \frac{1}{\sqrt{2}}}$

Question 12

Let f : (0, ∞) → (0, ∞) be a differentiable function such that f(1) = e and $\lim_{t 	o x} \frac{t^{2}f^{2}(x) - x^{2}f^{2}(t)}{t - x} = 0$. If f(x) = 1, then x is equal to:

Accepted Answer

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

Answer

(A) e

Answer

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

Answer

(D) 2e

Question 13

The distance of the point (1, –2, 3) from the plane x − y + z = 5 measured parallel to the line $\frac{x}{2} = \frac{y}{3} = \frac{z}{-6}$ is:

Accepted Answer

(D) 1

Answer

(A) $\frac{1}{7}$

Answer

(B) 7

Answer

(C) $\frac{7}{5}$

Question 14

In a game two players A and B take turns in throwing a pair of fair dice starting with player A and total of scores on the two dice, in each throw is noted. A wins the game if he throws a total of 6 before B throws a total of 7 and B wins the game if he throws a total of 7 before A throws a total of six. The game stops as soon as either of the players wins. The probability of A winning the game is:

Accepted Answer

(C) $\frac{30}{61}$

Answer

(A) $\frac{5}{6}$

Answer

(B) $\frac{31}{61}$

Answer

(D) $\frac{5}{31}$

Question 15

The angle of elevation of a cloud C from a point P, 200 m above a still take is 30°. If the angle of depression of the image of C in the lake from the point P is 60°, then PC (in m) is equal to

Accepted Answer

(C) 400

Answer

(A) $200\sqrt{3}$

Answer

(B) 100

Answer

(D) $400\sqrt{3}$

Question 16

Let x = 4 be a directrix to an ellipse whose centre is at the origin and its eccentricity is $\frac{1}{2}$. If P(1, β), β > 0 is a point on this ellipse, then the equation of the normal to it at P is:

Accepted Answer

(A) 4x − 2y = 1

Answer

(B) 4x − 3y = 2

Answer

(C) 7x − 4y = 1

Answer

(D) 8x − 2y = 5

Question 17

Let $\bigcup_{i=1}^{50} X_{i} = \bigcup_{i=1}^{n} Y_{i} = T$, where each $X_{i}$ contains 10 elements and each Yi contains 5 elements. If each element of the set T is an element of exactly 20 of sets $X_{i}$'s and exactly 6 of sets $Y_{i}$'s then n is equal to:

Accepted Answer

(B) 30

Answer

(A) 15

Answer

(C) 45

Answer

(D) 50

Question 18

If the perpendicular bisector of the line segment joining the points P(1, 4) and Q(k, 3) has y-intercept equal to –4, then a value of k is:

Accepted Answer

(C) – 4

Answer

(A) $\sqrt{14}$

Answer

(B) $\sqrt{15}$

Answer

(D) – 2

Question 19

If $\vec{a} = 2\hat{i} + \hat{j} + 2\hat{k}$, then the value of $\left|\hat{i} 	imes \left(\vec{a} 	imes \hat{i}ight)ight|^{2} + \left|\hat{j} 	imes \left(\vec{a} 	imes \hat{j}ight)ight|^{2} + \left|\hat{k} 	imes \left(\vec{a} 	imes \hat{k}ight)ight|^{2}$ is equal to:

Accepted Answer

18

Question 20

A test consists of 6 multiple choice questions, each having 4 alternative answers of which only one is correct. The number of ways, in which a candidate answers all six questions such that exactly four of the answers are correct, is ……

Accepted Answer

135

Question 21

Let PQ be a diameter of the circle $x^{2} + y^{2} = 9$. If α and β are the lengths of the perpendiculars from P and Q on the straight line, x + y = 2 respectively, then the maximum value of αβ is……

Accepted Answer

7

Question 22

If the variance of the following frequency distribution : is 50, then x is equal to:

Accepted Answer

4

Question 23

Let {x} and [x] denote the fractional part of x and the greatest integer ≤x respectively of a real number x. if $\int_{0}^{n} \{x\}dx$, $\int_{0}^{n} [x]dx$ and $10(n^{2} - n)$, (n ∈ N, n > 1) are three consecutive terms of a G.P. then n is equal to ……

Accepted Answer

21

Question 24

A capacitor C is fully charged with voltage $V_0$. After disconnecting the voltage source, it is connected in parallel with another uncharged capacitor of capacitance. $\frac{C}{2}$. The energy loss in the process after the charge is distributed between the two capacitor is:

Accepted Answer

(A) $\frac{1}{6}CV_0^{2}$

Answer

(B) $\frac{1}{2}CV_0^{2}$

Answer

(C) $\frac{1}{4}CV_0^{2}$

Answer

(D) $\frac{1}{3}CV_0^{2}$

Question 25

In photoelectric effect experiment, the graph of stopping potential V versus reciprocal of wavelength obtained is shown in the figure. As the intensity of incident radiation is increased:

Accepted Answer

(D) Graph does not change

Answer

(A) Slope of the straight line get more steep

Answer

(B) Straight line shifts to left

Answer

(C) Straight line shifts to right

Question 26

Consider two uniform discs of the same thickness and different radii $R_1 = R$ and $R_2 = \alpha R$ made of the same material. If the ratio of their moments of inertia $I_1$ and $I_2$, respectively, about their axes is $I_1 : I_2 = 1 : 16$ then the value of α is:

Accepted Answer

(C) 2

Answer

(A) 4

Answer

(B) $\sqrt{2}$

Answer

(D) $2\sqrt{2}$

Question 27

A quantity X is given by $(IF\upsilon^{2}/WL^{4})$ in terms of moment of inertia I, force F, velocity υ, work W and Length L. The dimensional formula for x is same as that of:

Accepted Answer

(C) energy density

Answer

(A) coefficient of viscosity

Answer

(B) planck's constant

Answer

(D) force constant

Question 28

For a uniform rectangular sheet shown in the figure, the ratio of moments of inertia about the axes perpendicular to the sheet and passing through O (the centre of mass) and O′ (corner point) is:

Accepted Answer

(C) 1/4

Answer

(A) 1/2

Answer

(B) 2/3

Answer

(D) 1/8

Question 29

Identify the operation performed by the circuit given below:

Accepted Answer

(A) AND

Answer

(B) NOT

Answer

(C) NAND

Answer

(D) OR

Question 30

A particle of charge q and mass m is subjected to an electric field $E = E_0(1 - ax^{2})$ in the x-direction, where a and $E_0$ are constants. Initially the particle was at rest at $x = 0$. Other then the initial position the kinetic energy of the particle becomes zero when the distance of the particle from the origin is:

Accepted Answer

(A) $\sqrt{\frac{3}{a}}$

Answer

(B) $\sqrt{\frac{1}{a}}$

Answer

(C) a

Answer

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

Question 31

The value of current $i_1$ flowing from A to C in the circuit diagram is:

Accepted Answer

(D) 1

Answer

(A) 4

Answer

(B) 2

Answer

(C) 5

Question 32

Two identical cylindrical vessels are kept on the ground and each contain the same liquid of density d. The area of the base of both vessels is S but the height of liquid in one vessel is x1 and in the other, x2. When both cylinders are connected through a pipe of negligible volume very close to the bottom, the liquid flows from one vessel to the other until it comes to equilibrium at a new height. The change in energy of the system in the process is :

Accepted Answer

(C) $\frac{1}{4}gdS\left(x_2 - x_1\right)^{2}$

Answer

(A) $\frac{3}{4}gdS\left(x_2 - x_1\right)^{2}$

Answer

(B) $gdS\left(x_2 + x_1\right)^{2}$

Answer

(D) $gdS\left(x_2^{2} + x_1^{2}\right)$

Question 33

The driver of bus approaching a big wall notices that the frequency of his bus's horn changes from 420 Hz to 490 Hz when he hears it after it gets reflected from the wall. Find the speed of the bus if speed of the sound is 330 ms$^{-1}$ :

Accepted Answer

(A) 90 kmh$^{-1}$

Answer

(B) 80 kmh$^{-1}$

Answer

(C) 61 kmh$^{-1}$

Answer

(D) 71 kmh$^{-1}$

Question 34

A series L-R circuit is connected to a battery of emf V. If the circuit is switched on at t = 0, then the time at which the energy stored in the inductor reaches (1/n) times of its maximum value, is :

Accepted Answer

(D) $\frac{L}{R}\ln\left(\frac{\sqrt{n}}{\sqrt{n}-1}\right)$

Answer

(A) $\frac{L}{R}\ln\left(\frac{\sqrt{n}}{\sqrt{n}+1}\right)$

Answer

(B) $\frac{L}{R}\ln\left(\frac{\sqrt{n}+1}{\sqrt{n}-1}\right)$

Answer

(C) $\frac{L}{R}\ln\left(\frac{\sqrt{n}-1}{\sqrt{n}}\right)$

Question 35

The electric field of a plane electromagnetic wave is given by $\vec{E} = E_{0}\left(\hat{x}+\hat{y}\right)\sin\left(kz-\omega t\right)$ Its magnetic field will be given by:

Accepted Answer

(C) $\frac{E_{0}}{c}\left(-\hat{x}+\hat{y}\right)\sin\left(kz-\omega t\right)$

Answer

(A) $\frac{E_{0}}{c}\left(\hat{x}-\hat{y}\right)\sin\left(kz-\omega t\right)$

Answer

(B) $\frac{E_{0}}{c}\left(\hat{x}-\hat{y}\right)\cos\left(kz-\omega t\right)$

Answer

(D) $\frac{E_{0}}{c}\left(\hat{x}+\hat{y}\right)\sin\left(kz-\omega t\right)$

Question 36

A person pushes a box on a rough horizontal platform surface. He applies a force of 200 N over a distance of 15m. Thereafter, he gets progressively tired and his applied force reduces linearly with distance to 100 N. The total distance through which the box has been moved is 30 m. What is the work done by the person during the total movement of the box?

Accepted Answer

(A) 5250 J

Answer

(B) 5690 J

Answer

(C) 3280 J

Answer

(D) 2780 J

Question 37

A paramagnetic sample shows a net magnetisation of 6A/m when it is placed in an external magnetic field of 0.4 T at a temperature of 4K. When the sample is placed in an external magnetic field of 0.3T at a temperature of 24K, then the magnetisation will be :

Accepted Answer

(B) 0.75 A/m

Answer

(A) 1 A/m

Answer

(C) 2.25 A/m

Answer

(D) 4 A/m

Question 38

A body is moving in a low circular orbit about a planet of mass M and radius R. The radius of the orbit can be taken to be R itself. Then the ratio of the speed of this body in the orbit to the escape velocity from the planet is :

Accepted Answer

(D) $\frac{1}{\sqrt{2}}$

Answer

(A) 2

Answer

(B) 1

Answer

(C) $\sqrt{2}$

Question 39

A small ball of mass m is thrown upward with velocity u from the ground. The ball experiences a resistive force mkv$^{2}$ where v is it speed. The maximum height attained by the ball is:

Accepted Answer

(D) $\frac{1}{2k}\ln\left(1+\frac{ku^{2}}{g}\right)$

Answer

(A) $\frac{1}{k}\ln\left(1+\frac{ku^{2}}{2g}\right)$

Answer

(B) $\frac{1}{2k}	an^{-1}\frac{ku^{2}}{g}$

Answer

(C) $\frac{1}{k}	an^{-1}\frac{ku^{2}}{2g}$

Question 40

Match the thermodynamics processes taking place in a system with the correct conditions. In the table: ΔQ is the heat supplied, ΔW is the work done and ΔU is change in internal energy of the system. Match the following:

Accepted Answer

(A) (I)→(B); (II)→(D); (III)→(A); (IV)→(C)

Answer

(B) (I)→(A); (II)→(A); (III)→(B); (IV)→(C)

Answer

(C) (I)→(A); (II)→(B); (III)→(D); (IV)→(D)

Answer

(D) (I)→(B); (II)→(A); (III)→(D); (IV)→(C)

Question 41

A cube of metal is subjected to a hydrostatic pressure 4GPa. The percentage change in the length of the side of the cube is close to: (Given bulk modulus of metal, B = $8 	imes 10^{10}$ Pa)

Accepted Answer

(C) 1.67

Answer

(A) 0.6

Answer

(B) 5

Answer

(D) 20

Question 42

The speed verses time graph for a particle is shown in the figure. The distance travelled (in m) by the particle during the time interval t = 0 to t = 5 s will be …..

Accepted Answer

20.00

Question 43

The distance between an object and a screen is 100 cm. A lens can produce real image of the object on the screen for two different positions between the screen and the object. The distance between these two positions is 40 cm. If the power of the lens is close to $\left(\frac{N}{100}\right)$ D where N is an integer, the value of N is ……….

Accepted Answer

476

Question 44

The change in the magnitude of the volume of an ideal gas when a small additional pressure ΔP is applied at a constant temperature, is the same as the change when the temperature is reduced by a small quantity ΔT at constant pressure. The initial temperature and pressure of the gas were 300 K and 2 atm. respectively. If |ΔT| = C|ΔP| then value of C in (K/atm) is ….

Accepted Answer

150

Question 45

Four resistance 40 Ω, 60 Ω, 90 Ω, and 110 Ω make the arms of a quadrilateral ABCD. Across AC is a battery of emf 40V and internal resistance negligible. The potential difference across BD in V is ……

Accepted Answer

2.00

Question 46

The Crystal Field Stabilization Energy (CFSE) of $[CoF_3(H_2O)_3]$ $(\Delta_0 < P)$ is :

Accepted Answer

(D) $-\ 0.4\ \Delta_0$

Answer

(A) $-\ 0.8\ \Delta_0$

Answer

(B) $-\ 0.4\ \Delta_0 + P$

Answer

(C) $-\ 0.8\ \Delta_0 + 2P$

Question 47

The processes of calcination and roasting in metallurgical industries, respectively, can lead to:

Accepted Answer

(C) Global warming and acid rain

Answer

(A) Photochemical smog and global warming

Answer

(B) Global warming and photochemical smog

Answer

(D) Photochemical smog and ozone layer depletion

Question 48

250 mL of a waste solution obtained from the workshop of a goldsmith contains 0.1 M $AgNO_3$ and 0.1 M $AuCl$. The solution was electrolyzed at 2 V by passing a current of 1 A for 15 minutes. The metal/metals electrodeposited will be :
$\left(E^{o}_{Ag^{+}/Ag} = 0.8\ V, E^{o}_{Au^{+}/Au} = 1.69\ V\right)$

Accepted Answer

(C) only gold

Answer

(A) silver and gold in equal mass proportion

Answer

(B) only silver

Answer

(D) silver and gold in proportion to their atomic weights

Question 49

Among the following compounds, which one has the shortest $C - Cl$ bond?

Accepted Answer

(B) (B)

Answer

(A) (A)

Answer

(C) (C)

Answer

(D) (D)

Question 50

The process that is NOT endothermic in nature is:

Accepted Answer

(A) $H_{(g)} + e^- \rightarrow H^-_{(g)}$

Answer

(B) $O^-_{(g)} + e^- \rightarrow O^{2-}_{(g)}$

Answer

(C) $Na_{(g)} \rightarrow Na^+_{(g)} + e^-$

Answer

(D) $Ar_{(g)} + e^- \rightarrow Ar^-_{(g)}$

Question 51

If the equilibrium constant for $A \rightleftharpoons B + C$ is $K^{(1)}_{(eq)}$ and that of $B + C \rightleftharpoons P$ is $K^{(2)}_{(eq)}$, the equilibrium constant for $A \rightleftharpoons P$ is:

Accepted Answer

(A) $K^{(1)}_{(eq)}K^{(2)}_{(eq)}$

Answer

(B) $K^{(1)}_{(eq)} / K^{(1)}_{(eq)}$

Answer

(C) $K^{(1)}_{(eq)} + K^{(2)}_{(eq)}$

Answer

(D) $K^{(2)}_{(eq)} - K^{(1)}_{(eq)}$

Question 52

Which of the following compounds will form the precipitate with aq. $AgNO_3$ solution most readily ?

Accepted Answer

(C) (C)

Answer

(A) (A)

Answer

(B) (B)

Answer

(D) (D)

Question 53

In the following reaction sequence, [C] is:

Accepted Answer

(C) (C)

Answer

(A) (A)

Answer

(B) (B)

Answer

(D) (D)

Question 54

The major product [R] in the following sequence of reactions is:

Accepted Answer

(D) (D)

Answer

(A) (A)

Answer

(B) (B)

Answer

(C) (C)

Question 55

The major product [C] in the following reaction sequence will be:

Accepted Answer

(A) (A)

Answer

(B) (B)

Answer

(C) (C)

Answer

(D) (D)

Question 56

A sample of red ink (a colloidal suspension) is prepared by mixing eosine dye, egg white, HCHO and water. The component which ensures stability of the ink sample is :

Accepted Answer

(A) Egg white

Answer

(B) HCHO

Answer

(C) Water

Answer

(D) Eosin dye

Question 57

The one that can exhibit highest paramagnetic behaviour among the following is:
gly = glycinato ; bpy = 2, 2'-bipyridine

Accepted Answer

(B) $[Co(OX)_2(OH)_2]^-$ $(\Delta_0 > P)$

Answer

(A) $[Fe(en)(bpy)(NH_3)_2]^{2+}$

Answer

(C) $[Pd(gly)_2]$

Answer

(D) $[Ti(NH_3)_6]^{3+}$

Question 58

The major product [B] in the following reactions is:

Accepted Answer

(B) (B)

Answer

(A) (A)

Answer

(C) (C)

Answer

(D) (D)

Question 59

The mechanism of action of "Terfenadine" (Seldane) is :

Accepted Answer

(A) Inhibits the action of histamine receptor

Answer

(B) Inhibits the secretion of histamine

Answer

(C) Helps in the secretion of histamine

Answer

(D) Activates the histamine receptor

Question 60

An alkaline earth metal 'M' readily forms water soluble sulphate and water insoluble hydroxide. Its oxide MO is very stable to heat and does not have rock-salt structure. M is:

Accepted Answer

(B) Be

Answer

(A) Sr

Answer

(C) Mg

Answer

(D) Ca

Question 61

The incorrect statement(s) among (a) - (c) is (are):
(a) W(VI) is more stable than Cr(VI).
(b) in the presence of HCl, permanganate titrations provide satisfactory results.
(c) some lanthanoid oxides can be used as phosphors.

Accepted Answer

(C) (b) only

Answer

(A) (b) and (c) only

Answer

(B) (a) only

Answer

(D) (a) and (b) only

Question 62

The molecule in which hybrid MOs involve only one d-orbital of the central atom is :

Accepted Answer

(C) [Ni(CN)$_4$]$^{2-}$

Answer

(A) XeF$_4$

Answer

(B) [CrF$_6$]$^{3-}$

Answer

(D) BrF$_5$

Question 63

The reaction in which hybridization of the underlined atom is affected is:

Accepted Answer

(A) $\underline{Xe}F_4 + SbF_5 \rightarrow$

Answer

(B) $H_2\underline{S}O_4 + NaCl \xrightarrow{420\ K}$

Answer

(C) $H_3\underline{P}O_2 \xrightarrow{	ext{Disproportionation}}$

Answer

(D) $\underline{N}H_3 \xrightarrow{H^+}$

Question 64

Five moles of an ideal gas at 1 bar and 298 K is expanded into vacuum to double the volume. The work done is :

Accepted Answer

(C) zero

Answer

(A) $C_V(T_2 - T_1)$

Answer

(B) $-RT \ln V_2/V_1$

Answer

(D) $-RT\, V_2/V_1$

Process	Condition
I.Aidabatic	A.ΔW = 0
II.Isothermal	B.ΔQ = 0
III.Isochoric	C.ΔU ≠ 0, ΔW ≠ 0, ΔQ ≠ 0
IV.Isobaric	D.ΔU = 0

JEE Main 4 September 2020 Shift 2 Question Paper with Answers

Physics — JEE Main 4 September 2020 Shift 2

Chemistry — JEE Main 4 September 2020 Shift 2

Mathematics — JEE Main 4 September 2020 Shift 2

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