JEE Main 5 September 2020 Shift 1 Question Paper

Question 1

If the four complex numbers, $z, \bar{z}, \bar{z} - 2	ext{Re}(\bar{z})$ and $z - 2	ext{Re}(z)$ represent the vertices of a square of side 4 units in the Argand plane, then $|z|$ is equal to:

Accepted Answer

(A) $2\sqrt{2}$

Answer

(B) 2

Answer

(C) $4\sqrt{2}$

Answer

(D) 4

Question 2

The negation of the Boolean expression $x \leftrightarrow \sim y$ is equivalent to

Accepted Answer

(D) $(x \wedge y) \vee (\sim x \wedge \sim y)$

Answer

(A) $(x \wedge \sim y) \vee (\sim x \wedge y)$

Answer

(B) $(\sim x \wedge y) \vee (\sim x \wedge \sim y)$

Answer

(C) $(x \wedge y) \wedge (\sim x \vee \sim y)$

Question 3

If $2^{10} + 2^{9}.3^{1} + 2^{8}.3^{2} + ... + 2.3^{9} + 3^{10} = S - 2^{11}$, then S is equal to

Accepted Answer

(D) $3^{11}$

Answer

(A) $\dfrac{3^{11}}{2} + 2^{10}$

Answer

(B) $3^{11} - 2^{12}$

Answer

(C) $2.3^{11}$

Question 4

Let $\lambda \in R$. The system of linear equations.
$2x_1 - 4x_2 + \lambda x_3 = 1$
$x_1 - 6x_2 + x_3 = 2$
$\lambda x_1 - 10x_2 + 4x_3 = 3$
Is inconsistent for:

Accepted Answer

(B) exactly one negative value of $\lambda$

Answer

(A) exactly one positive value of $\lambda$

Answer

(C) every value of $\lambda$

Answer

(D) exactly two values of $\lambda$

Question 5

If $\int (e^{2x} + 2e^{x} - e^{-x} - 1)e^{(e^{x}+e^{-x})}dx = g(x)e^{(e^{x}+e^{-x})}+c$ where c is a constant of integration, then g(0) is equal to:

Accepted Answer

(B) 2

Answer

(A) e

Answer

(C) $e^{2}$

Answer

(D) 1

Question 6

If $3^{2\sin 2\alpha - 1}$, 14 and $3^{4-2\sin 2\alpha}$ are the first three terms of an AP for some $\alpha$, then the sixth term of this AP is:

Accepted Answer

(C) 66

Answer

(A) 65

Answer

(B) 78

Answer

(D) 81

Question 7

A survey shows that 73% of the persons working in an office like coffee, whereas 65% like tea. If x denotes the percentage of them, who like both coffee and tea, then x cannot be:

Accepted Answer

(D) 36

Answer

(A) 63

Answer

(B) 54

Answer

(C) 38

Question 8

If the common tangent to the parabolas $y^{2} = 4x$ and $x^{2} = 4y$ also touches the circle, $x^{2} + y^{2} = c^{2}$, then c is equal to

Accepted Answer

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

Answer

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

Answer

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

Answer

(D) $\dfrac{1}{4}$

Question 9

The product of the roots of the equation $9x^{2} - 18|x| + 5 = 0$, is:

Accepted Answer

(D) $\dfrac{25}{81}$

Answer

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

Answer

(B) $\dfrac{25}{9}$

Answer

(C) $\dfrac{5}{27}$

Question 10

The value of $\displaystyle\int_{-\pi/2}^{\pi/2} \dfrac{1}{1+e^{\sin x}}dx$ is:

Accepted Answer

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

Answer

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

Answer

(C) $\pi$

Answer

(D) $\dfrac{\pi}{4}$

Question 11

If S is the sum of the first 10 terms of the series
$	an^{-1}\left(\dfrac{1}{3}ight) + 	an^{-1}\left(\dfrac{1}{7}ight) + 	an^{-1}\left(\dfrac{1}{13}ight) + 	an^{-1}\left(\dfrac{1}{21}ight) + ....$, then tan(S) is equal to:

Accepted Answer

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

Answer

(B) $\dfrac{10}{11}$

Answer

(C) $-\dfrac{6}{5}$

Answer

(D) $\dfrac{5}{11}$

Question 12

If (a, b, c) is the image of the point (1, 2, –3) in the line, $\dfrac{x+1}{2} = \dfrac{y-3}{-2} = \dfrac{z}{-1}$, then a + b+ c is equal to

Accepted Answer

(C) 2

Answer

(A) 3

Answer

(B) 1

Answer

(D) -1

Question 13

If y = y (x) is the solution of the differential equation $\dfrac{5+e^{x}}{2+y}.\dfrac{dy}{dx} + e^{x} = 0$ satisfying y(0) = 1, then a value of $y(\log_{e} 13)$ is:

Accepted Answer

(C) -1

Answer

(A) 0

Answer

(B) 1

Answer

(D) 2

Question 14

If the co-ordinates of two points A and B are $(\sqrt{7},0)$ and $(-\sqrt{7},0)$ respectively and P is any point on the conic $9x^{2}+16y^{2}=144$, then PA + PB is equal to:

Accepted Answer

(A) 8

Answer

(B) 16

Answer

(C) 9

Answer

(D) 6

Question 15

If the function $f(x)=\begin{cases} k_{1}(x-\pi)^{2}-1 & x \le \pi \ k_{2}\cos x & x > \pi \end{cases}$ is twice differentiable, then the ordered pair $(k_{1},k_{2})$ is equal to:

Accepted Answer

(D) $\left(\dfrac{1}{2},1\right)$

Answer

(A) $(1,0)$

Answer

(B) $(1,1)$

Answer

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

Question 16

The mean and variance of 7 observations are 8 and 16, respectively. If five observations are 2, 4, 10, 12, 14, then the absolute difference of the remaining two observations is:

Accepted Answer

(A) 2

Answer

(B) 4

Answer

(C) 1

Answer

(D) 3

Question 17

If the point P on the curve, $4x^{2}+5y^{2}=20$ is farthest from the point Q(0, –4) then $PQ^{2}$ is equal to:

Accepted Answer

(C) 36

Answer

(A) 21

Answer

(B) 48

Answer

(D) 29

Question 18

If the volume of a parallelepiped, whose coterminus edges are given by the vectors $\vec{a}=\hat{i}+\hat{j}+n\hat{k}, \vec{b}=2\hat{i}+4\hat{j}-n\hat{k}$ and $\vec{c}=\hat{i}+n\hat{j}+3\hat{k}$ $(n \ge 0)$, is 158 cu.units. then:

Accepted Answer

(C) $\vec{b}.\vec{c}=10$

Answer

(A) $\vec{a}.\vec{c}=14$

Answer

(B) n=7

Answer

(D) n=9

Question 19

The natural number m, for which the coefficient of x in the binomial expansion of $\left(x^{m}+\dfrac{1}{x^{2}}\right)^{22}$ is 1540, is ____

Accepted Answer

13.00

Question 20

Let $f(x)=x.\left[\dfrac{x}{2}\right]$, for $-10<x<10$, where [t] denotes the greatest integer function. Then the number of points of discontinuity of f is equal to ___

Accepted Answer

08.00

Question 21

If the line, $2x-y+3=0$ is at a distance $\dfrac{1}{\sqrt{5}}$ and $\dfrac{2}{\sqrt{5}}$ from the lines $4x-2y+\alpha=0$ and $6x-3y+\beta=0$, respectively, then the sum of all possible values of $\alpha$ and $\beta$ is ____.

Accepted Answer

30.00

Question 22

Four fair dice are thrown independently 27 times. Then the expected number of times, at least two dice show up a three or a five, a ____.

Accepted Answer

11.00

Question 23

The number of words, with or without meaning, that can be formed by taking 4 letters at a time from the letters of the word ‘SYLLABUS’ such that two letters are distinct and two letters are alike, is ____.

Accepted Answer

240.00

Question 24

A hollow spherical shell at outer radius R floats just submerged under the water surface. The inner radius of the shell is r. If the specific gravity of the shell material is $\frac{27}{8}$ w.r.t water, the value of r is.

Accepted Answer

(D) $\frac{8}{9}$R

Answer

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

Answer

(B) $\frac{4}{9}$R

Answer

(C) $\frac{1}{3}$R

Question 25

A balloon is moving up in air vertically above a point A on the ground. When it is at a height $h_1$, a girl standing at a distance d (point B) from A (see figure) sees it at the angle $45^{0}$ with respect to the vertical. When the balloon climbs up a future height $h_2$, it is seen at the angle $60^{0}$ with respect to the vertical if the girl moves further by a distance 2.464 d (point C). Then the height $h_2$ is (given tan $30^{0}$ = 0.5774):

Accepted Answer

(D) d

Answer

(A) 0.464 d

Answer

(B) 0.732 d

Answer

(C) 1.464 d

Question 26

A physical quantity z depends on four observables a, c, c and d, as z = $\dfrac{a^{2}b^{\frac{2}{3}}}{\sqrt{c}\,d^{3}}$. The percentages of error in the measurement of a, b, c and d are 2%, 1.5%, 4% and 2.5% respectively. The percentage of error in z is:

Accepted Answer

(D) 14.5%

Answer

(A) 13.5%

Answer

(B) 16.5%

Answer

(C) 12.25%

Question 27

A wheel is rotating freely with an angular speed $\omega$ on a shaft. The moment of inertia of the wheel is I and the moment of inertia of the shaft is negligible. Another wheel of moment of inertia 3I initially at rest is suddenly coupled to the same shaft. The resultant fractional loss in the kinetic energy of the system is:

Accepted Answer

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

Answer

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

Answer

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

Answer

(D) 0

Question 28

In a resonance tube experiment when the tube is filled with water up to a height of 17.0 cm from bottom, it resonates with a given tuning fork. When the water level is raised the next resonance with the same tuning fork occurs at a height of 24.5 cm. If the velocity of sound in air is 330 m/s, the tuning fork frequency is:

Accepted Answer

(B) 2200 Hz

Answer

(A) 1100 Hz

Answer

(C) 3300 Hz

Answer

(D) 550 Hz

Question 29

An electron is constrained to move along the y − axis with a speed of 0.1 c (c is the speed of light) in the presence of electromagnetic wave, whose electric field is $\vec{E} = 30\hat{j}\sin\left(1.5	imes10^{7}t - 5	imes10^{-2}xight)$ V/m. The maximum magnetic force experienced by the electron will be: (given $c = 3	imes10^{8}\,\mathrm{ms^{-1}}$ and electron charge $= 1.6	imes10^{-19}$C)

Accepted Answer

(D) $4.8	imes10^{-19}$N

Answer

(A) $3.2	imes10^{-18}$N

Answer

(B) $1.5	imes10^{-19}$N

Answer

(C) $2.4	imes10^{-18}$N

Question 30

A bullet of mass 5 g, traveling with a speed of 210 m/s, strikes a fixed wooden target. One half of its kinetic energy is converted into heat in the bullet while the other half is converted into heat in the wood. The rise of temperature of the bullet if the specific heat of its material is $0.030\,	ext{cal}/(	ext{g-}^{0}	ext{C})$ $(1	ext{cal}=4.2	imes10^{7}	ext{ ergs})$ close to:

Accepted Answer

(C) $87.5^{0}$C

Answer

(A) $83.3^{0}$C

Answer

(B) $38.4^{0}$C

Answer

(D) $119.2^{0}$C

Question 31

The value of the acceleration due to gravity is $g_1$ at a height $h=\dfrac{R}{2}$ (R= radius of the earth) from the surface of the earth. It is again equal to $g_1$ at a depth d below the surface of the earth. The ratio $\left(\dfrac{d}{R}\right)$ equals:

Accepted Answer

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

Answer

(A) $\frac{7}{9}$

Answer

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

Answer

(D) $\frac{4}{9}$

Question 32

For a concave lens of focal length f, the relation between object and image distances u and is $v$, respectively, from its pole can best be represented by (u - $v$ is the reference line):

Accepted Answer

(B) (B)

Answer

(A) (A)

Answer

(C) (C)

Answer

(D) (D)

Question 33

A galvanometer of resistance G is converted into a voltmeter of range 0 – IV by connecting a resistance $R_1$ in series with it. The additional resistance that should be connected in series with $R_1$ to increase the range of the voltmeter to 0 – 2V will be:

Accepted Answer

(A) $R_1$ + G

Answer

(B) $R_1$

Answer

(C) G

Answer

(D) $R_1$ − G

Question 34

Number of molecules in a volume of 4 cm$^3$ of a perfect monoatomic gas at some temperature T and at a pressure of 2 cm of mercury is close to? (Given, mean kinetic energy of a molecule (at T) is $4 	imes 10^{-14}$ erg, g = 980 cm / s$^2$, density of mercury = 13.6 g / cm$^3$)

Accepted Answer

(D) $4.0 	imes 10^{18}$

Answer

(A) $5.8 	imes 10^{18}$

Answer

(B) $4.0 	imes 10^{16}$

Answer

(C) $5.8 	imes 10^{16}$

Question 35

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 the z − axis and passing through the point (0, b, 0), (b >> a). The magnitude of the torque on the loop about z − axis is given by:

Accepted Answer

(D) $\dfrac{2\mu_0 I^2 a^2}{\pi b}$

Answer

(A) $\dfrac{2\mu_0 I^2 a^3}{\pi b^2}$

Answer

(B) $\dfrac{\mu_0 I^2 a^2}{2\pi b}$

Answer

(C) $\dfrac{\mu_0 I^2 a^3}{2\pi b^2}$

Question 36

Assume that the displacement (s) of air is proportional to the pressure difference $(\Lambda p)$ created by a sound wave. Displacement (s) further depends on the speed of sound (v), density of air (ρ) and the frequency (f). If $\Lambda p \sim 10	ext{Pa}$, $\upsilon \sim 300$ m/s, $ho \sim \pi 1 	ext{ lg} / 	ext{m}^3$ and f ∼ 1000 Hz, then s will be of the order of (take the multiplicative constant to be 1)

Accepted Answer

(C) $\dfrac{3}{100}$ mm

Answer

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

Answer

(B) 10 mm

Answer

(D) 1 mm

Question 37

A helicopter rises from rest on the ground vertically upwards with a constant acceleration g. A food packet is dropped from the helicopter when it is at a height h. The time taken by the packet to reach the ground is close to [g is the acceleration due to gravity]:

Accepted Answer

(C) $t = 3.4\sqrt{\left(\dfrac{h}{g}\right)}$

Answer

(A) $t = 1.8\sqrt{\dfrac{h}{g}}$

Answer

(B) $t = \sqrt{\dfrac{2h}{3g}}$

Answer

(D) $t = \dfrac{2}{3}\sqrt{\left(\dfrac{h}{g}\right)}$

Question 38

Activities of three radioactive substances A, B and C are represented by the curves A, B and C in the figure. Then their half lives $T_{1/2}(A) : T_{1/2}(B) : T_{1/2}(C)$ are in the radio:

Accepted Answer

(B) 2:1:3

Answer

(A) 3:2:1

Answer

(C) 4:3:1

Answer

(D) 2:1:1

Question 39

An electrical power line, having a total resistance of 2Ω, delivers 1 kW at 220 V. The efficiency of the transmission line is approximately:

Accepted Answer

(A) 96%

Answer

(B) 72%

Answer

(C) 91%

Answer

(D) 85%

Question 40

Two capacitors of capacitances C and 2C are charged to potential differences V and 2V, respectively. These are then connected in parallel in such a manner that the positive terminal of one is connected to the negative terminal of the other. The final energy of this configuration is:

Accepted Answer

(A) $\dfrac{3}{2}CV^2$

Answer

(B) $\dfrac{9}{2}CV^2$

Answer

(C) $\dfrac{25}{6}CV^2$

Answer

(D) zero

Question 41

A force $\vec{F} = (\hat{i} + 2\hat{j} + 3\hat{k})$ N acts at a point $(4\hat{i} + 3\hat{j} - \hat{k})$ m. Then the magnitude of torque about the point $(\hat{i} + 2\hat{j} + \hat{k})$ m will be $\sqrt{x}$ N-m. The value of x is ________.

Accepted Answer

195.00

Question 42

A particle of mass 200 MeV/c$^2$ collides with a hydrogen atom at rest. Soon after the collision the particle comes to rest, and the atom recoils and goes to its first excited state. The initial kinetic energy of the particle (in eV) is $\dfrac{N}{4}$. The value of N is: (Given the mass of the hydrogen atom to be 1 GeV / c$^2$).

Accepted Answer

51.00

Question 43

Two concentric circular coils, C$_1$ and C$_2$ are placed in the XY plane. C$_1$ has 500 turns, and a radius of 1 cm. C$_2$ has 200 turns and radius of 20 cm. C$_2$ carries a time dependent current $I(t) = (5t^2 - 2t + 3)$ A where t is in s. The emf induced in C$_1$ (in mV), at the instant t = 1 s is $\dfrac{4}{x}$. The value of x is ________.

Accepted Answer

5.00

Question 44

A compound microscope consists of an objective lens of focal length 1 cm and an eye piece of focal length 5 cm with a separation of 10 cm. The distance between an object and the objective lens, at which the strain on the eye is minimum is $\dfrac{n}{40}$ cm. The value of n is ________.

Accepted Answer

50.00

Question 45

Which of the following is not an essential amino acid?

Accepted Answer

(B) Tyrosine

Answer

(A) Valine

Answer

(C) Leucine

Answer

(D) Lysine

Question 46

A flask contains a mixture of compounds A and B. Both compounds decompose by first – order kinetics. The half lives for A and B are 300 s and 180 s, respectively. If the concentrations of A and B are equal initially, the line required for the concentration of A to be four times that of B (in s) is : (Use $\ln 2 = 0.693$)

Accepted Answer

(C) 900

Answer

(A) 120

Answer

(B) 300

Answer

(D) 180

Question 47

The equation that represents the water – gas shift reactions is:

Accepted Answer

(A) $CO(g) + H_2O(g) \xrightarrow[	ext{Catalyst}]{673\,K} CO_2(g) + H_2(g)$

Answer

(B) $C(s) + H_2O(g) \xrightarrow{1270\,K} CO(g) + H_2(g)$

Answer

(C) $2C(s) + O_2(g) + 4N_2(g) \xrightarrow{1273\,K} 2CO(g) + 4N_2(g)$

Answer

(D) $CH_4(g) + H_2O(g) \xrightarrow[	ext{Ni}]{1270\,K} CO(g) + 3H_2(g)$

Question 48

In the following reaction sequence the major products A and B are:

Accepted Answer

(B) (B)

Answer

(A) (A)

Answer

(C) (C)

Answer

(D) (D)

Question 49

If a person is suffering from the deficiency of nor – adrenaline, what kind of drug can be suggested?

Accepted Answer

(A) Antidepressant

Answer

(B) Antihistamine

Answer

(C) Analgesic

Answer

(D) Anti – inflammatory

Question 50

The potential energy curve for the $H_2$ molecule as a function of internuclear distance is :

Accepted Answer

(D) (D)

Answer

(A) (A)

Answer

(B) (B)

Answer

(C) (C)

Question 51

The most appropriate reagent for conversion of $C_2H_5CN$ into $CH_3CH_2CH_2NH_2$ is:

Accepted Answer

(C) $LiAlH_4$

Answer

(A) $CaH_2$

Answer

(B) $Na(CN)BH_3$

Answer

(D) $NaBH_4$

Question 52

Which of the following derivates of alcohol is unstable is an aqueous base?

Accepted Answer

(C) (C)

Answer

(A) (A)

Answer

(B) (B)

Answer

(D) (D)

Question 53

The condition that indicates a polluted environment is:

Accepted Answer

(C) eutrophication

Answer

(A) 0.03% of $CO_2$ in the atmosphere

Answer

(B) pH of rain water to be 5.6

Answer

(D) BOD value of 5 ppm

Question 54

The values of the crystal field stabilization energies for a high spin $d^6$ metal ion in octahedral and tetrahedral fields, respectively, are:

Accepted Answer

(C) $-0.4\Delta_o$ and $-0.6\Delta_t$

Answer

(A) $-0.4\Delta_o$ and $-0.27\Delta_t$

Answer

(B) $-1.6\Delta_o$ and $-0.4\Delta_t$

Answer

(D) $-2.4\Delta_o$ and $-0.6\Delta_t$

Question 55

The difference between the radii of 3rd and 4th orbits of $Li^{2+}$ in $\Delta R_1$.. The difference between the radii of 3rd and 4th orbits of $He^+$ is $\Delta R_2$. Ratio $\Delta R_1 : \Delta R_2$ is:

Accepted Answer

(B) 2:3

Answer

(A) 8:3

Answer

(C) 3:8

Answer

(D) 3:2

Question 56

The increasing order of the acidity of the $\alpha$-hydrogen of the following compounds is:

Accepted Answer

(C) (D) < (C) < (A) < (B)

Answer

(A) (C) < (A) < (B) < (D)

Answer

(B) (B) < (C) < (A) < (D)

Answer

(D) (A) < (C) < (D) < (B)

Question 57

The correct electronic configuration and spin – only magnetic moment (BM) of $Gd^{3+}$ (Z = 64), respectively, are:

Accepted Answer

(A) [Xe]$4f^7$ and 7.9

Answer

(B) [Xe]$4f^7$ and 8.9

Answer

(C) [Xe]$5f^7$ and 8.9

Answer

(D) [Xe]$5f^7$ and 7.9

Question 58

The total number of coordination sites in ethylenediaminetetraacetate ($EDTA^{4-}$) is ____.

Accepted Answer

6

Question 59

The minimum number of moles of $O_2$ required for complete combustion of 1 mole of propane and 2 moles of butane is ___

Accepted Answer

18

Question 60

An oxidation – reduction in which 3 electrons are transferred has a $\Delta G^0$ of 17.37 kJ $mol^{-1}$ at $25^0$ C. The value of $E^0_{cell}$ (in V is _____ × $10^{-2}$)
(1 F = 96,500 C $mol^{-1}$)

Accepted Answer

-6

Question 61

The number of chiral carbon(s) present in peptide, Ile-Arg-Pro, is ___

Accepted Answer

4

Question 62

A soft drink was bottled with a partial pressure of $CO_2$ of 3 bar over the liquid at room temperature. The partial pressure of $CO_2$ over the solution approaches a value of 30 bar when 44 g of $CO_2$ is dissolved in 1 kg of water at room temperature. The approximate pH of the soft drink is ___ x $10^{-1}$/
(First dissociation constant of $H_2CO_3$ = $4.0	imes10^{-7}$;log 2 = 0.3; density of the soft drink = 1 g $mL^{-1}$)

Accepted Answer

37

JEE Main 5 September 2020 Shift 1 Question Paper with Answers

Physics — JEE Main 5 September 2020 Shift 1

Chemistry — JEE Main 5 September 2020 Shift 1

Mathematics — JEE Main 5 September 2020 Shift 1

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