JEE Main 27 July 2021 Shift 1 Question Paper

Question 1

Let C be the set of all complex numbers. Let
$S_1 = \left\{ z \in C \,\middle|\, \left| z - 3 - 2i \right|^2 = 8 \right\}$,
$S_2 = \left\{ z \in C \,\middle|\, \operatorname{Re}(z) \ge 5 \right\}$ and
$S_3 = \left\{ z \in C \,\middle|\, \left| z - \bar{z} \right| \ge 8 \right\}$.
Then the number of element in $S_1 \cap S_2 \cap S_3$ is equal to:

Accepted Answer

(C) 1

Answer

(A) 0

Answer

(B) 2

Answer

(D) infinite

Question 2

If $\sin	heta + \cos	heta = \frac{1}{2}$, then $16\left(\sin(2	heta) + \cos(4	heta) + \sin(6	heta)ight)$ is equal to :

Accepted Answer

(B) $-23$

Answer

(A) 27

Answer

(C) $-27$

Answer

(D) 23

Question 3

Let $\vec{a} = \hat{i} + \hat{j} + 2\hat{k}$ and $\vec{b} = -\hat{i} + 2\hat{j} + 3\hat{k}$. Then the vector product
$\left(\vec{a} + \vec{b}ight) 	imes \left(\vec{a} 	imes \left(\left(\vec{a} - \vec{b}ight) 	imes \vec{b}ight)ight) 	imes \vec{b}$ is equal to :

Accepted Answer

(D) $7\left(34\hat{i} - 5\hat{j} + 3\hat{k}\right)$

Answer

(A) $5\left(34\hat{i} - 5\hat{j} + 3\hat{k}\right)$

Answer

(B) $5\left(30\hat{i} - 5\hat{j} + 7\hat{k}\right)$

Answer

(C) $7\left(30\hat{i} - 5\hat{j} + 7\hat{k}\right)$

Question 4

Let the plane passing through the point $(-1, 0, -2)$ and perpendicular to each of the planes $2x + y - z = 2$ and $x - y - z = 3$ be $ax + by + cz + 8 = 0$. Then the value of $a + b + c$ is equal to :

Accepted Answer

(A) 4

Answer

(B) 8

Answer

(C) 5

Answer

(D) 3

Question 5

Let $f : \left(-\frac{\pi}{4}, \frac{\pi}{4}ight) 	o R$ be defined as
$f(x) = \begin{cases} \left(1 + |\sin x|ight)^{\frac{3a}{|\sin x|}} & , \ -\frac{\pi}{4} < x < 0 \ b & , \ x = 0 \ e^{\cot 4x / \cot 2x} & , \ 0 < x < \frac{\pi}{4} \end{cases}$
If f is continuous at x = 0, then the value of $6a + b^2$ is equal to :

Accepted Answer

(C) $1 + e$

Answer

(A) $1 - e$

Answer

(B) e

Answer

(D) $e - 1$

Question 6

The compound statement $\left(P \vee Q\right) \wedge \left(\sim P\right) \Rightarrow Q$ is equivalent to :

Accepted Answer

(C) $\sim\left(P \Rightarrow Q\right) \Leftrightarrow P \wedge \sim Q$

Answer

(A) $P \vee Q$

Answer

(B) $P \wedge \sim Q$

Answer

(D) $\sim\left(P \Rightarrow Q\right)$

Question 7

Let
$A = \left\{ (x, y) \in R 	imes R \,\middle|\, 2x^2 + 2y^2 - 2x - 2y = 1 ight\}$,
$B = \left\{ (x, y) \in R 	imes R \,\middle|\, 4x^2 + 4y^2 - 16y + 7 = 0 ight\}$ and
$C = \left\{ (x, y) \in R 	imes R \,\middle|\, x^2 + y^2 - 4x - 2y + 5 \le r^2 ight\}$.
Then the minimum value of $|r|$ such that $A \cup B \subseteq C$ is equal to :

Accepted Answer

(B) $\frac{3 + 2\sqrt{5}}{2}$

Answer

(A) $1 + \sqrt{5}$

Answer

(C) $\frac{3 + \sqrt{10}}{2}$

Answer

(D) $\frac{2 + \sqrt{10}}{2}$

Question 8

Let $A = \begin{bmatrix} 1 & 2 \ -1 & 4 \end{bmatrix}$. If $A^{-1} = \alpha I + \beta A$, $\alpha, \beta \in R$. I is a 2 x 2 identify matrix, then $4\left(\alpha - \betaight)$ is equal to :

Accepted Answer

(C) 4

Answer

(A) 2

Answer

(B) 5

Answer

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

Question 9

Let $y = y\left(x\right)$ be solution of the differential equation $\log_e\left(\frac{dy}{dx}\right) = 3x + 4y$, with $y\left(0\right) = 0$.
If $y\left(-\frac{2}{3}\log_e 2\right) = \alpha \log_e 2$, then the value of $\alpha$ is equal to :

Accepted Answer

(B) $-\frac{1}{4}$

Answer

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

Answer

(C) 2

Answer

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

Question 10

A ray of light through (2, 1) is reflected at a point P on the y-axis and then passes through the point (5, 3). If this reflected ray is the directrix of any ellipse with eccentricity $\frac{1}{3}$ and the distance of the nearer focus from this directrix is $\frac{8}{\sqrt{53}}$, then the equation of the other directrix can be :

Accepted Answer

(C) $2x - 7y + 29 = 0$ or $\ 2x - 7y - 7 = 0$

Answer

(A) $2x - 7y - 39 = 0$ or $\ 2x - 7y - 7 = 0$

Answer

(B) $11x + 7y + 8 = 0$ or $\ 11x + 7y - 15 = 0$

Answer

(D) $11x - 7y - 8 = 0$ or $\ 11x + 7y + 15 = 0$

Question 11

The value of $\lim_{n 	o \infty} \frac{1}{n} \sum_{j=1}^{n} \frac{(2j - 1) + 8n}{(2j - 1) + 4n}$ is equal to :

Accepted Answer

(B) $1 + 2\log_e\left(\frac{3}{2}\right)$

Answer

(A) $2 - \log_e\left(\frac{2}{3}\right)$

Answer

(C) $5 + \log_e\left(\frac{3}{2}\right)$

Answer

(D) $3 + 2\log_e\left(\frac{2}{3}\right)$

Question 12

If the area of the bounded region
$R = \left\{ (x, y) : \max\left\{0, \log_e x\right\} \le y \le 2^x, \frac{1}{2} \le x \le 2 \right\}$ is, $\ \alpha\left(\log_e 2\right)^{-1} + \beta\left(\log_e 2\right) + \gamma$, then the value of $\left(\alpha + \beta - 2\gamma\right)^2$ is equal to :

Accepted Answer

(C) 2

Answer

(A) 4

Answer

(B) 8

Answer

(D) 1

Question 13

If the coefficients of $x^7$ in $\left(x^2 + \frac{1}{bx}ight)^{11}$ and $x^{-7}$ in $\left(x - \frac{1}{bx^2}ight)^{11}$, $b 
e 0$ are equal, then the value of b is equal to :

Accepted Answer

(B) 1

Answer

(A) $-1$

Answer

(C) 2

Answer

(D) $-2$

Question 14

Two tangents are drawn from the point $P\left(-1, 1\right)$ to the circle $x^2 + y^2 - 2x - 6y + 6 = 0$. If these tangents touch the circle at points A and B, and if D is a point on the circle such that length of the segments AB and AD are equal, then the area of the triangle ABD is equal to :

Accepted Answer

(C) 4

Answer

(A) $3\left(\sqrt{2} - 1\right)$

Answer

(B) $\left(3\sqrt{2} + 2\right)$

Answer

(D) 2

Question 15

The probability that a randomly selected 2-digit number belongs to the set $\left\{ n \in N : \left(2^n - 2ight) 	ext{ is a multiple of } 3 ight\}$ is equal to :

Accepted Answer

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

Answer

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

Answer

(C) $\frac{1}{6}$

Answer

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

Question 16

Let P and Q be two distinct points on a circle which has center at C(2, 3) and which passes through origin O. If OC is perpendicular to both the line segments CP and CQ, then the set $\left\{P, Q\right\}$ is equal to :

Accepted Answer

(A) $\left\{\left(-1,5\right),\left(5,1\right)\right\}$

Answer

(B) $\left\{\left(2+2\sqrt{2},3+\sqrt{5}\right),\left(2-2\sqrt{2},3-\sqrt{5}\right)\right\}$

Answer

(C) $\left\{\left(2+2\sqrt{2},3-\sqrt{5}\right),\left(2-2\sqrt{2},3+\sqrt{5}\right)\right\}$

Answer

(D) $\left\{\left(4,0\right),\left(0,6\right)\right\}$

Question 17

The value of the definite integral $\int_{-\frac{\pi}{4}}^{\frac{\pi}{4}}\frac{dx}{\left(1+e^{x\cos x}\right)\left(\sin^4 x+\cos^4 x\right)}$ is equal to :

Accepted Answer

(B) $\frac{\pi}{2\sqrt{2}}$

Answer

(A) $-\frac{\pi}{4}$

Answer

(C) $-\frac{\pi}{2}$

Answer

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

Question 18

Let $f:R 	o R$ be a function such that $f\left(2ight)=4$ and $f'\left(2ight)=1$. Then the value of $\lim_{x 	o 2}\frac{x^2 f\left(2ight)-4f\left(xight)}{x-2}$ is equal to :

Accepted Answer

(A) 12

Answer

(B) 4

Answer

(C) 16

Answer

(D) 8

Question 19

Let $\alpha,\beta$ be two roots of the equation $x^2+\left(20\right)^{\frac{1}{4}}x+\left(5\right)^{\frac{1}{2}}=0$ Then $\alpha^8+\beta^8$ is equal to :

Accepted Answer

(A) 50

Answer

(B) 100

Answer

(C) 10

Answer

(D) 160

Question 20

If the mean and variance of the following data : $6, 10, 7, 13, a, 12, b, 12$ are $9$ and $\frac{37}{4}$ respectively, then $\left(a-b\right)^2$ is equal to :

Accepted Answer

(D) 16

Answer

(A) 32

Answer

(B) 24

Answer

(C) 12

Question 21

If $y=y\left(x\right), y \in \left[0,\frac{\pi}{2}\right]$ is the solution of the differential equation $\sec y\frac{dy}{dx}-\sin\left(x+y\right)-\sin\left(x-y\right)=0$, with $y\left(0\right)=0$, then $5y'\left(\frac{\pi}{2}\right)$ is equal to ____.

Accepted Answer

2

Question 22

For real numbers $\alpha$ and $\beta$, consider the following system of linear equations: $x+y-z=2$, $x+2y+\alpha z=1$, $2x-y+z=\beta$. If the system has infinite solutions, then $\alpha+\beta$ is equal to ____.

Accepted Answer

5

Question 23

Let a plane P pass through the point $\left(3,7,-7\right)$ and contain the line, $\frac{x-2}{-3}=\frac{y-3}{2}=\frac{z+2}{1}$. If distance of the plane P from the origin is d, then $d^2$ is equal to ____.

Accepted Answer

3

Question 24

Let $F:\left[3,5ight] 	o R$ be a twice differentiable function on $\left(3,5ight)$ such that $F\left(xight)=e^{-x}\int_3^x\left(3t^2+2t+4F'\left(tight)ight)dt$. If $F'\left(4ight)=\frac{\alpha e^{\beta}-224}{\left(e^{\beta}-4ight)^2}$, then $\alpha+\beta$ is equal to ____.

Accepted Answer

16

Question 25

Let $f\left(xight)=\begin{vmatrix}\sin^2 x & -2+\cos^2 x & \cos 2x \ 2+\sin^2 x & \cos^2 x & \cos 2x \ \sin^2 x & \cos^2 x & 1+\cos 2x\end{vmatrix}$, $x \in \left[0,\piight]$. Then the maximum value of $f\left(xight)$ is equal to ____.

Accepted Answer

6

Question 26

Let $\vec{a}=\hat{i}+\hat{j}+\hat{k}$, $\vec{b}$ and $\vec{c}=\hat{j}-\hat{k}$ be three vectors such that $\vec{a} 	imes \vec{b}=\vec{c}$ and $\vec{a} \cdot \vec{b}=1$. If the length of projection vector of the vector $\vec{b}$ on the vector $\vec{a} 	imes \vec{c}$ is $\ell$, then the value of $3\ell^2$ is equal to ____.

Accepted Answer

2

Question 27

Let $f:\left[0,3ight] 	o R$ be defined by $f\left(xight)=\min\left\{x-\left[xight],1+\left[xight]-xight\}$ Where $\left[xight]$ is the greatest integer less than or equal to x. Let P denote the set containing all $x \in \left[0,3ight]$ where f is discontinuous, and Q denote the set containing all $x \in \left(0,3ight)$ where f is not differentiable. Then the sum of number of elements in P and Q is equal to ____.

Accepted Answer

5

Question 28

Let $S=\left\{1,2,3,4,5,6,7ight\}$. Then the number of possible function $f:S 	o S$ such that $f\left(m \cdot night)=f\left(might) \cdot f\left(night)$ for every $m,n \in S$ and $m \cdot n \in S$ is equal to ____.

Accepted Answer

490

Question 29

Let the domain of the function $f\left(x\right)=\log_4\left(\log_5\left(\log_3\left(18x-x^2-77\right)\right)\right)$ be $\left(a,b\right)$. Then the value of the integral $\int_a^b\frac{\sin^3 x}{\left(\sin^3 x+\sin^3\left(a+b-x\right)\right)}dx$ is equal to ____.

Accepted Answer

1

Question 30

If $\log_3 2, \log_3\left(2^x-5\right), \log_3\left(2^x-\frac{7}{2}\right)$ are in an arithmetic progression, then the value of x is equal to ____.

Accepted Answer

3

Question 31

Two identical tennis balls each having mass 'm' and charge 'q' are suspended from a fixed point by threads of length 'ℓ'. What is the equilibrium separation when each thread makes a small angle 'θ' with the vertical ?

Accepted Answer

(B) $x = \left( \frac{q^2 \ell}{2 \pi \varepsilon_0 mg} \right)^{1/3}$

Answer

(A) $x = \left( \frac{q^2 \ell}{2 \pi \varepsilon_0 mg} \right)^{1/2}$

Answer

(C) $x = \left( \frac{q^2 \ell^2}{2 \pi \varepsilon_0 m^2 g^2} \right)^{1/3}$

Answer

(D) $x = \left( \frac{q^2 \ell^2}{2 \pi \varepsilon_0 m^2 g} \right)^{1/3}$

Question 32

The figure shows two solid discs with radius R and r respectively. If mass per unit area is same for both, what is the ratio of MI of bigger disc around axis AB (which is ⊥ to the plane of the disc and passing through its centre) to MI of smaller disc around one of its diameters lying on its plane? Given 'M' is the mass of the larger disc. (MI stands for moment of inertia)

Accepted Answer

(C) $2R^4 : r^4$

Answer

(A) $R^2 : r^2$

Answer

(B) $2r^4 : R^4$

Answer

(D) $2R^2 : r^2$

Question 33

In the given figure, a battery of emf E is connected across a conductor PQ of length 'ℓ' and different area of cross- sections by having radii $r_1$ and $r_2$ ($r_2 < r_1$). Choose the correct option as one moves from P to Q :

Accepted Answer

(C) Drift velocity of electron increases.

Answer

(A) All of these

Answer

(B) Electron current decreases.

Answer

(D) Electric field decreases.

Question 34

A capacitor of capacitance C = 1μF is suddenly connected to a battery of 100 volt through a resistance R = 100Ω. The time taken for the capacitor to be charged to get 50 V is : [Take ln 2 = 0.69 ]

Accepted Answer

(D) $0.69 	imes 10^{-4}$ s

Answer

(A) $3.33 	imes 10^{-4}$ s

Answer

(B) $1.44 	imes 10^{-4}$ s

Answer

(C) $0.30 	imes 10^{-4}$ s

Question 35

Three objects A, B and c are kept in a straight line on a frictionless horizontal surface. The masses of A, B and C are m, 2 and 2 m respectively. A moves towards B with a speed of 9m / s and makes an elastic collision with it. Thereafter B makes a completely inelastic collision with C. all motions occur along same straight line. The final speed of C is :

Accepted Answer

(D) 3 m /s

Answer

(A) 4 m /s

Answer

(B) 6 m /s

Answer

(C) 9 m /s

Question 36

In the reported figure, a capacitor is formed by placing a compound dielectric between the plates of parallel plate capacitor. The expression for the capacity of the said capacitor will be : (Given area of plate = A)

Accepted Answer

(A) $\frac{15}{34} \ \frac{K \varepsilon_0 A}{d}$

Answer

(B) $\frac{15}{6} \ \frac{K \varepsilon_0 A}{d}$

Answer

(C) $\frac{25}{6} \ \frac{K \varepsilon_0 A}{d}$

Answer

(D) $\frac{9}{6} \ \frac{K \varepsilon_0 A}{d}$

Question 37

A light cylindrical vessel is kept on a horizontal surface. Area of base is A. A hole of cross-sectional area 'a' is made just at its bottom side. The minimum coefficient of friction necessary to prevent sliding the vessel due to the impact force of the emerging liquid is (a << A):

Accepted Answer

(B) $\frac{2a}{A}$

Answer

(A) None of these

Answer

(C) $\frac{A}{2a}$

Answer

(D) $\frac{a}{A}$

Question 38

The relative permittivity of distilled water is 81. The velocity of light in it will be : (Given $\mu_r$ = 1)

Accepted Answer

(D) $3.33 	imes 10^{7}$ m /s

Answer

(A) $4.33 	imes 10^{7}$ m /s

Answer

(B) $2.33 	imes 10^{7}$ m /s

Answer

(C) $5.33 	imes 10^{7}$ m /s

Question 39

Assertion A : If A, B, D are four points on a semi- circular arc with centre at 'O' such that |$\overrightarrow{AB}$| = |$\overrightarrow{BC}$| = |$\overrightarrow{CD}$|, then $\overrightarrow{AB} + \overrightarrow{AC} + \overrightarrow{AD} = 4\overrightarrow{AO} + \overrightarrow{OB} + \overrightarrow{OC}$
Reason R : Polygon law of vector addition yields $\overrightarrow{AB} + \overrightarrow{BC} + \overrightarrow{CD} = \overrightarrow{AD} = 2\overrightarrow{AO}$
In the light of the above statements, choose the most appropriate answer from the options given below :

Accepted Answer

(C) Both A and R are correct and R is the correct explanation of A.

Answer

(A) A is not correct but R is correct.

Answer

(B) A is correct but R is not correct.

Answer

(D) Both A and R are correct but R is not the correct explanation of A.

Question 40

The number of molecules in one litre of an ideal gas at 300K and 2 atmospheric pressure with mean kinetic energy $2 	imes 10^{-9}$ J per molecule is :

Accepted Answer

(D) $1.5 	imes 10^{11}$

Answer

(A) $0.75 	imes 10^{11}$

Answer

(B) $3 	imes 10^{11}$

Answer

(C) $6 	imes 10^{11}$

Question 41

In the reported figure, there is a cyclic process ABCDA on a sample of 1mol of a diatomic gas. The temperature of the gas during the process A → B and C → D are $T_1$ and $T_2$ ($T_1 > T_2$) respectively. Choose the correct option out of the following for work done if processes BC and DA are adiabatic.

Accepted Answer

(B) $W_{AD} = W_{BC}$

Answer

(A) $W_{AB} = W_{DC}$

Answer

(C) $W_{AB} < W_{CD}$

Answer

(D) $W_{BC} + W_{DA} > 0$

Question 42

If 'f' denotes the ratio of the number of nuclei decayed ($N_d$) to the number of nuclei at t = 0 ($N_0$) then for a collection of radioactive nuclei, the rate of change of 'f' with respect to time is given as : [ λ is the radioactive decay constant ]

Accepted Answer

(A) $\lambda e^{-\lambda t}$

Answer

(B) $\lambda\left(1-e^{-\lambda t}\right)$

Answer

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

Answer

(D) $-\lambda e^{-\lambda t}$

Question 43

Assertion A : If in five complete rotations of the circular scale, the distance travelled on main scale of the screw gauge is 5 mm and there are 50 total divisions on circular scale, then least count is 0.001 cm.
Reason R : Least Count = $\frac{	ext{Pitch}}{	ext{Total divisions on circular scle}}$
In the light of the above statement, choose the most appropriate answer from the options given below :

Accepted Answer

(B) A is not correct but R is correct.

Answer

(A) A is correct but R is not correct.

Answer

(C) Both A and R are correct and R is NOT the correct explanation of A .

Answer

(D) Both A and R are correct and R is the correct explanation of A .

Question 44

Two capacitors of capacities 2C and C are joined in parallel and charge up to potential V. The battery is removed and the capacitor of capacity C is filled completely with a medium of dielectric constant K. The potential difference across the capacitors will now be :

Accepted Answer

(D) $\frac{3V}{K + 2}$

Answer

(A) $\frac{3V}{K}$

Answer

(B) $\frac{V}{K}$

Answer

(C) $\frac{V}{K + 2}$

Question 45

In Young's double slit experiment, if the source of light changes from orange to blue then:

Accepted Answer

(A) the distance between consecutive fringes will decrease.

Answer

(B) the distance between consecutive fringes will increase.

Answer

(C) the central bright fringe will become a dark fringe.

Answer

(D) the intensity of the minima will increase.

Question 46

A ball is thrown up with a certain velocity so that it reaches a height 'h'. Find the ratio of the two different times of the ball reaching $\frac{h}{3}$ in both the directions.

Accepted Answer

(B) $\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}$

Answer

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

Answer

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

Answer

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

Question 47

A particle starts executing simple harmonic motion (SHM) of amplitude 'a' and total energy E. At any instant, its kinetic energy is $\frac{3E}{4}$ then its displacement 'y' is given by :

Accepted Answer

(A) y = $\frac{a}{2}$

Answer

(B) y = $\frac{a}{\sqrt{2}}$

Answer

(C) y = $\frac{a\sqrt{3}}{2}$

Answer

(D) y = a

Question 48

A 0.07 H inductor and a 12$\Omega$ resistor are connected in series to a 220 V, 50 Hz ac source. The approximate current in the circuit and the phase angle between current and source voltage are respectively. [ Take $\pi$ as $\frac{22}{7}$ ]

Accepted Answer

(B) 8.8 A and $	an^{-1}\left(\frac{11}{6}ight)$

Answer

(A) 88 A and $	an^{-1}\left(\frac{11}{6}ight)$

Answer

(C) 0.88 A and $	an^{-1}\left(\frac{11}{6}ight)$

Answer

(D) 8.8 A and $	an^{-1}\left(\frac{6}{11}ight)$

Question 49

A body takes 4 min. to cool from 61°C to 59°C.If the temperature of the surroundings is 30°C, the time taken by the body to cool from 51°C to 49°C is :

Accepted Answer

(A) 6 min.

Answer

(B) 3 min.

Answer

(C) 4 min.

Answer

(D) 8 min.

Question 50

A transistor is connected in common emitter circuit configuration, then collector supply voltage is 10 V and the voltage drop across a resistor of 1000Ω in the collector is 0.6 V. If the current gain factor (β) is 24, then the base current is ____ μA. (Round off to the Nearest Integer)

Accepted Answer

25

Question 51

A prism of refractive index $n_1$ and another prism of refractive index $n_2$ are stuck together (as shown in the figure). $n_1$ and $n_2$ depend on λ, the wavelength of light, according to the relation
$n_1 = 1.2 + \frac{10.8 	imes 10^{-14}}{\lambda^2}$ and $n_2 = 1.45 + \frac{1.8 	imes 10^{-14}}{\lambda^2}$
The wavelength for which rays incident at any angle on the interface BC pass through without bending at that interface will be ____ nm.

Accepted Answer

600

Question 52

Consider an electrical circuit containing a two way switch 'S'. Initially S is open and then $T_1$ is connected to $T_2$. As the current in R = 6Ω attains a maximum value of steady state level, $T_1$ is disconnected from $T_2$ and immediately connected to $T_3$. Potential drop across r = 3Ω resistor immediately after $T_1$ is connected to $T_3$ is ____ V. (Round off to the Nearest Integer)

Accepted Answer

3

Question 53

A stone of mass 20g is projected from a rubber catapult of length 0.1m and area of cross section $10^{-6}$ m² stretched by an amount 0.04 m. The velocity of the projected stone is ____ m /s. (Young's modulus of rubber = 0.5×$10^{9}$ N/ m² )

Accepted Answer

20

Question 54

A particle of mass 9.1×$10^{-31}$ kg travels in a medium with a speed of $10^{6}$ m /s and a photon of a radiation of linear momentum $10^{-27}$ kg m /s travels in vacuum. The wavelength of photon is ____ times the wavelength of the particle.

Accepted Answer

910

Question 55

The amplitude of upper and lower side bands of A.M. wave where a carrier signal with frequency 11.21 MHz, peak voltage 15 V is amplitude modulate by a 7.7 kHz sine wave of 5 V amplitude are $\frac{a}{10}$ V and $\frac{b}{10}$ V respectively. Then the value of $\frac{a}{b}$ is ____.

Accepted Answer

1

Question 56

In a uniform magnetic field, the magnetic needle has a magnetic moment 9.85×$10^{-2}$ A / m² and moment of inertia 5×$10^{-6}$ kg m².If it performs 10 complete oscillations in 5 seconds then the magnitude of the magnetic field is ____ mT. [ Take $\pi^2$ as 9.85 ]

Accepted Answer

8

Question 57

Suppose two planets (spherical in shape) of radii R and 2R, but mass M and 9 M respectively have a centre to centre separation 8 R as shown in the figure. A satellite of mass 'm' is projected from the surface of the planet of mass 'M' directly towards the centre of the second planet. The minimum speed 'υ' required for the satellite to reach the surface of the second plant is $\sqrt{\frac{a}{7}\frac{GM}{R}}$ then the value of 'a' is ____.
[ Given : The two planets are fixed in their position ]

Accepted Answer

4

Question 58

In Bohr's atomic model, the electron is assumed to revolve in a circular orbit of radius 0.5 Å. If the speed of electron is 2.2×$10^{6}$ m /s, then the current associated with the electron will be ____ × $10^{-2}$ mA. [ Take π as $\frac{22}{7}$ ]

Accepted Answer

112

Question 59

A radioactive sample has an average life of 30ms and is decaying. A capacitor of capacitance 200 μF is first charged and later connected with resistor 'R'. If the ratio of charge on capacitor to the activity of radioactive sample is fixed with respect to time then the value of 'R' should be ____ Ω .

Accepted Answer

150

Question 60

Given below are two statements:
Statement I: Rutherford's gold foil experiment cannot explain the line spectrum of hydrogen atom.
Statement II: Bohr's model of hydrogen atom contradicts Heisenberg's uncertainty principle.
In the light of the above statements, choose the most appropriate answer from the options given below:

Accepted Answer

(C) Both Statement I and Statement II are true.

Answer

(A) Statement I is true but Statement II is false.

Answer

(B) Both Statement I and Statement II are false.

Answer

(D) Statement I is false but Statement II is true.

Question 61

For a reaction of order n, the unit of the rate constant is:

Accepted Answer

(A) $mol^{1-n} L^{n-1} s^{-1}$

Answer

(B) $mol^{1-n} L^{1-n} s^{-1}$

Answer

(C) $mol^{1-n} L^{2n} s^{-1}$

Answer

(D) $mol^{1-n} L^{1-n} s$

Question 62

Which one among the following chemical tests is used to distinguish monosaccharide from disaccharide?

Accepted Answer

(D) Barfoed test

Answer

(A) Tollen's test

Answer

(B) Seliwanoff's test

Answer

(C) Iodine test

Question 63

Staggered and eclipsed conformers of ethane are:

Accepted Answer

(D) Rotamers

Answer

(A) Mirror images

Answer

(B) Polymers

Answer

(C) Enantiomers

Question 64

The number of geometrical isomers found in the metal complexes $[PtCl_2(NH_3)_2]$, $[Ni(CO)_4]$, $[Ru(H_2O)_3Cl_3]$ and $[CoCl_2(NH_3)_4]^+$ respectively are

Accepted Answer

(B) 2,0,2,2

Answer

(A) 2,1,2,2

Answer

(C) 1,1,1,1

Answer

(D) 2,1,2,1

JEE Main 27 July 2021 Shift 1 Question Paper with Answers

Physics — JEE Main 27 July 2021 Shift 1

Chemistry — JEE Main 27 July 2021 Shift 1

Mathematics — JEE Main 27 July 2021 Shift 1

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