JEE Main 27 August 2021 Shift 2 Question Paper

Question 1

The angle between the straight lines, whose direction cosines are given by the equations 2l + 2m − n = 0 and mn + nl + lm = 0, is :

Accepted Answer

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

Answer

(B) $\pi - \cos^{-1}\left(\frac{4}{9}\right)$

Answer

(C) $\cos^{-1}\left(\frac{8}{9}\right)$

Answer

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

Question 2

Let $A = \begin{pmatrix} [x+1] & [x+2] & [x+3] \ [x] & [x+3] & [x+3] \ [x] & [x+2] & [x+4] \end{pmatrix}$, where [t] denotes the greatest integer less than or equal to t. If det(A) = 192, then the set of values of x is the interval:

Accepted Answer

(B) [62, 63)

Answer

(A) [68, 69)

Answer

(C) [65, 66)

Answer

(D) [60, 61)

Question 3

Let M and m respectively be the maximum and minimum values of the function $f(x) = 	an^{-1}(\sin x + \cos x)$ in $\left[0, \frac{\pi}{2}ight]$, Then the value of tan(M − m) is equal to:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 4

Each of the persons A and B independently tosses three fair coins. The probability that both of them get the same number of heads is :

Accepted Answer

(C) $\frac{5}{16}$

Answer

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

Answer

(B) $\frac{5}{8}$

Answer

(D) 1

Question 5

A differential equation representing the family of parabolas with axis parallel to y-axis and whose length of latus rectum is the distance of the point (2, −3) form the line 3x + 4y = 5, is given by :

Accepted Answer

(D) $11\frac{d^{2}y}{dx^{2}} = 10$

Answer

(A) $10\frac{d^{2}y}{dx^{2}} = 11$

Answer

(B) $11\frac{d^{2}x}{dy^{2}} = 10$

Answer

(C) $10\frac{d^{2}x}{dy^{2}} = 11$

Question 6

If two tangents drawn from a point P to the parabola $y^{2} = 16(x - 3)$ are at right angles, then the locus of point P is :

Accepted Answer

(B) x + 1 = 0

Answer

(A) x + 3 = 0

Answer

(C) x + 2 = 0

Answer

(D) x + 4 = 0

Question 7

The equation of the plane passing through the line of intersection of the planes $\vec{r}\cdot\left(\hat{i} + \hat{j} + \hat{k}\right) = 1$ and $\vec{r}\cdot\left(2\hat{i} + 3\hat{j} - \hat{k}\right) + 4 = 0$ and parallel to the x-axis is:

Accepted Answer

(A) $\vec{r}\cdot\left(\hat{j} - 3\hat{k}\right) + 6 = 0$

Answer

(B) $\vec{r}\cdot\left(\hat{i} + 3\hat{k}\right) + 6 = 0$

Answer

(C) $\vec{r}\cdot\left(\hat{i} - 3\hat{k}\right) + 6 = 0$

Answer

(D) $\vec{r}\cdot\left(\hat{j} - 3\hat{k}\right) - 6 = 0$

Question 8

If the solution curve of the differential equation $(2x - 10y^{3})\,dy + y\,dx = 0$, passes through the points (0, 1) and (2, β), then β is a root of the equation:

Accepted Answer

(D) $y^{5} - y^{2} - 1 = 0$

Answer

(A) $y^{5} - 2y - 2 = 0$

Answer

(B) $2y^{5} - 2y - 1 = 0$

Answer

(C) $2y^{5} - y^{2} - 2 = 0$

Question 9

Let A(a, 0), B(b, 2b +1) and C(0, b), b ≠ 0, |b| ≠ 1, be points such that the area of triangle ABC is 1 sq. unit, then the sum of all possible values of a is :

Accepted Answer

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

Answer

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

Answer

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

Answer

(C) $\frac{2b^{2}}{b+1}$

Question 10

Let [λ] be the greatest integer less than or equal to λ. The set of all values of λ for which the system of linear equations x + y + z = 4, 3x + 2y+ 5z = 3, 9x + 4y + (28+ [λ])z = [λ] has a solution is:

Accepted Answer

(A) ℝ

Answer

(B) $(-\infty, -9) \cup (-9, \infty)$

Answer

(C) [−9, −8)

Answer

(D) $(-\infty, -9) \cup [-8, \infty)$

Question 11

The set of all values of k > −1, for which the equation $(3x^{2} + 4x + 3)^{2} - (k+1)(3x^{2} + 4x + 3)(3x^{2} + 4x + 2) + k(3x^{2} + 4x + 2)^{2} = 0$ has real roots, is :

Accepted Answer

(A) $\left(1, \frac{5}{2}\right]$

Answer

(B) [2, 3)

Answer

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

Answer

(D) $\left(\frac{1}{2}, \frac{3}{2}\right] - \{1\}$

Question 12

A box open from top is made from a rectangular sheet of dimension a × b by cutting squares each of side x from each of the four corners and folding up the flaps. If the volume of the box is maximum, then x is equal to :

Accepted Answer

(C) $\frac{a + b - \sqrt{a^{2} + b^{2} - ab}}{6}$

Answer

(A) $\frac{a + b - \sqrt{a^{2} + b^{2} - ab}}{12}$

Answer

(B) $\frac{a + b - \sqrt{a^{2} + b^{2} + ab}}{6}$

Answer

(D) $\frac{a + b + \sqrt{a^{2} + b^{2} - ab}}{6}$

Question 13

The Boolean expression $(p \wedge q) \Rightarrow ((r \wedge q) \wedge p)$ is equivalent to :

Accepted Answer

(A) $(p \wedge q) \Rightarrow (r \wedge q)$

Answer

(B) $(q \wedge r) \Rightarrow (p \wedge q)$

Answer

(C) $(p \wedge q) \Rightarrow (r \vee q)$

Answer

(D) $(p \wedge r) \Rightarrow (p \wedge q)$

Question 14

Let ℤ be the set of all integers,
A = {(x, y) ∈ ℤ × ℤ : $(x - 2)^{2} + y^{2} \le 4$},
B = {(x, y) ∈ ℤ × ℤ : $x^{2} + y^{2} \le 4$} and
C = {(x, y) ∈ ℤ × ℤ : $(x - 2)^{2} + (y - 2)^{2} \le 4$}
If the total number of relation from A ∩ B to A ∩ C is $2^{p}$, then the value of p is :

Accepted Answer

(B) 25

Answer

(A) 16

Answer

(C) 49

Answer

(D) 9

Question 15

The area of the region bounded by the parabola $(y - 2)^{2} = (x - 1)$, the tangent to it at the point whose ordinate is 3 and the x-axis is :

Accepted Answer

(A) 9

Answer

(B) 10

Answer

(C) 4

Answer

(D) 6

Question 16

If $y(x) = \cot^{-1}\left(\frac{\sqrt{1 + \sin x} + \sqrt{1 - \sin x}}{\sqrt{1 + \sin x} - \sqrt{1 - \sin x}}\right)$, x ∈ $\left(\frac{\pi}{2}, \pi\right)$, then $\frac{dy}{dx}$ at $x = \frac{5\pi}{6}$ is:

Accepted Answer

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

Answer

(B) −1

Answer

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

Answer

(D) 0

Question 17

Two poles, AB of length a metres and CD of length a + b (b ≠ a) metres are erected at the same horizontal level with bases at B and D. If BD = x and $	an \angle ACB = \frac{1}{2}$, then:

Accepted Answer

(C) $x^{2} - 2ax + b(a + b) = 0$

Answer

(A) $x^{2} + 2(a + 2b)x - b(a + b) = 0$

Answer

(B) $x^{2} + 2(a + 2b)x + a(a + b) = 0$

Answer

(D) $x^{2} - 2ax + a(a + b) = 0$

Question 18

If 0 < x < 1 and $y = \frac{1}{2}x^{2} + \frac{2}{3}x^{3} + \frac{3}{4}x^{4} + \ldots$, then the value of $e^{1+y}$ at $x = \frac{1}{2}$ is:

Accepted Answer

(A) $\frac{1}{2}e^{2}$

Answer

(B) 2e

Answer

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

Answer

(D) $2e^{2}$

Question 19

The value of the integral $\int_{0}^{1} \frac{\sqrt{x}\,dx}{(1+x)(1+3x)(3+x)}$ is:

Accepted Answer

(A) $\frac{\pi}{8}\left(1 - \frac{\sqrt{3}}{2}\right)$

Answer

(B) $\frac{\pi}{4}\left(1 - \frac{\sqrt{3}}{6}\right)$

Answer

(C) $\frac{\pi}{8}\left(1 - \frac{\sqrt{3}}{6}\right)$

Answer

(D) $\frac{\pi}{4}\left(1 - \frac{\sqrt{3}}{2}\right)$

Question 20

If $\lim_{x 	o \infty}\left(\sqrt{x^{2} - x + 1} - axight) = b$, then the ordered pair (a, b) is:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 21

Let S be the sum of all solutions (in radians) of the equation $\sin^{4}	heta + \cos^{4}	heta - \sin	heta\,\cos	heta = 0$ in $[0,\ 4\pi]$. Then $\frac{8S}{\pi}$ is equal to _________ .

Accepted Answer

56

Question 22

Let S be the mirror image of the point Q(1, 3, 4) with respect to the plane 2x − y + z + 3 = 0 and let R (3, 5, γ) be a point of this plane. Then the square of the length of the line segment SR is ___________ .

Accepted Answer

72

Question 23

The probability distribution of random variable X is given by:
X | 1 | 2 | 3 | 4 | 5
P(X) | K | 2K | 2K | 3K | K
Let p = P(1 < X < 4 | X < 3). If 5p = λK, then λ equal to _________ .

Accepted Answer

30

Question 24

Let $z_{1}$ and $z_{2}$ be two complex numbers such that $\arg\,(z_{1} - z_{2}) = \frac{\pi}{4}$ and $z_{1}$, $z_{2}$ satisfy the equation $|z - 3| = \mathrm{Re}(z)$. Then the imaginary part of $z_{1} + z_{2}$ is equal to ___________ .

Accepted Answer

6

Question 25

Let S = {1, 2, 3, 4, 5, 6, 9}. Then the number of elements in the set T = {A ⊆ S : A ≠ φ and the sum of all the elements of A is not a multiple of 3} is ___________ .

Accepted Answer

80

Question 26

Two circles each of radius 5 units touch each other at the point (1, 2). If the equation of their common tangent is 4x + 3y = 10, and $C_{1}(\alpha,\ \beta)$ and $C_{2}\,(\gamma,\ \delta)$, $C_{1} 
eq C_{2}$ are their centres, then $|(\alpha + \beta)\,(\gamma + \delta)|$ is equal to ____________ .

Accepted Answer

40

Question 27

$3 	imes 7^{22} + 2 	imes 10^{22} - 44$ when divided by 18 leaves the remainder __________ .

Accepted Answer

15

Question 28

An online exam is attempted by 50 candidates out of which 20 are boys. The average marks obtained by boys is 12 with a variance 2. The variance of marks obtained by 30 girls is also 2. The average marks of all 50 candidates is 15. If μ is the average marks of girls and $\sigma^{2}$ is the variance of marks of 50 candidates, then $\mu + \sigma^{2}$ is equal to _________ .

Accepted Answer

25

Question 29

If $\int \frac{2e^{x} + 3e^{-x}}{4e^{x} + 7e^{-x}}\,dx = \frac{1}{14}\left(ux + v\,\log_{e}(4e^{x} + 7e^{-x})\right) + C$, where C is a constant of integration, then u + v is equal to ___________ .

Accepted Answer

7

Question 30

Curved surfaces of a plano-convex lens of refractive index $\mu_{1}$ and a plano-concave lens of refractive index $\mu_{2}$ have equal radius of curvature as shown in figure. Find the ratio of radius of curvature to the focal length of the combined lenses.

Accepted Answer

(B) $\mu_{1}-\mu_{2}$

Answer

(A) $\frac{1}{\mu_{2}-\mu_{1}}$

Answer

(C) $\frac{1}{\mu_{1}-\mu_{2}}$

Answer

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

Question 31

The boxes of masses 2 kg and 8 kg are connected by a massless string passing over smooth pulleys. Calculate the time taken by box of mass 8 kg to strike the ground starting from rest. (use g = 10 m/s$^{2}$)

Accepted Answer

(D) 0.4 s

Answer

(A) 0.34 s

Answer

(B) 0.2 s

Answer

(C) 0.25 s

Question 32

For a transistor α and β are given as $\alpha = \frac{I_{C}}{I_{E}}$ and $\beta = \frac{I_{C}}{I_{B}}$. Then the correct relation between α and β will be :

Accepted Answer

(B) $\beta = \frac{\alpha}{1-\alpha}$

Answer

(A) $\alpha = \frac{1-\beta}{\beta}$

Answer

(C) $\alpha\beta = 1$

Answer

(D) $\alpha = \frac{\beta}{1-\beta}$

Question 33

Water drops are falling from a nozzle of a shower onto the floor, from a height of 9.8 m. The drops fall at a regular interval of time. When the first drop strikes the floor, at that instant, the third drop begins to fall. Locate the position of second drop from the floor when the first drop strikes the floor.

Accepted Answer

(D) 7.35 m

Answer

(A) 4.18 m

Answer

(B) 2.94 m

Answer

(C) 2.45 m

Question 34

Two discs have moments of intertia $I_{1}$ and $I_{2}$ about their respective axes perpendicular to the plane and passing through the centre. They are rotating with angular speeds, $\omega_{1}$ and $\omega_{2}$ respectively and are brought into contact face to face with their axes of rotation coaxial. The loss in kinetic energy of the system in the process is given by :

Accepted Answer

(C) $\frac{I_{1}I_{2}}{2(I_{1}+I_{2})}\left(\omega_{1}-\omega_{2}\right)^{2}$

Answer

(A) $\frac{I_{1}I_{2}}{(I_{1}+I_{2})}\left(\omega_{1}-\omega_{2}\right)^{2}$

Answer

(B) $\frac{(I_{1}-I_{2})^{2}\,\omega_{1}\omega_{2}}{2(I_{1}+I_{2})}$

Answer

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

Question 35

Three capacitors $C_{1}$ = 2μF, $C_{2}$ = 6 μF and $C_{3}$ = 12 μF are connected as shown in figure. Find the ratio of the charges on capacitors $C_{1}$, $C_{2}$ and $C_{3}$ respectively :

Accepted Answer

(C) 1 : 2 : 2

Answer

(A) 2 : 1 : 1

Answer

(B) 2 : 3 : 3

Answer

(D) 3 : 4 : 4

Question 36

The colour coding on a carbon resistor is shown in the given figure. The resistance value of the given resistor is :

Accepted Answer

(D) (7500 ± 375) Ω

Answer

(A) (5700 ± 285) Ω

Answer

(B) (7500 ± 750) Ω

Answer

(C) (5700 ± 375) Ω

Question 37

An antenna is mounted on a 400 m tall building. What will be the wavelength of signal of signal that can be radiated effectively by the transmission tower upto a range of 44 km?

Accepted Answer

(B) 605 m

Answer

(A) 37.8 m

Answer

(C) 75.6 m

Answer

(D) 302 m

Question 38

If the rms speed of oxygen molecules at 0°C is 160 m/s, find the rms speed of hydrogen molecules at 0°C.

Accepted Answer

(A) 640 m/s

Answer

(B) 40 m/s

Answer

(C) 80 m/s

Answer

(D) 332 m/s

Question 39

A constant magnetic field of 1 T is applied in the x > 0 region. A metallic circular ring of radius 1m is moving with a constant velocity of 1 m/s along the x-axis. At t = 0s, the centre of O of the ring is at x = − 1m.  What will be the value of the induced emf in the ring at t = 1s? (Assume the velocity of the ring does not change.)

Accepted Answer

(C) 2 V

Answer

(A) 1 V

Answer

(B) 2π V

Answer

(D) 0 V

Question 40

A mass of 50 kg is placed at the centre of a uniform spherical shell of mass 100 kg and radius 50 m. If the gravitational potential at a point, 25 m from the centre is V kg/m. The value of V is :

Accepted Answer

(D) − 4 G

Answer

(A) − 60 G

Answer

(B) + 2 G

Answer

(C) − 20 G

Question 41

For full scale deflection of total 50 divisions, 50 mV voltage is required in galvanometer. The resistance of galvanometer if its current sensitivity is 2 div/mA will be :

Accepted Answer

(D) 2 Ω

Answer

(A) 1 Ω

Answer

(B) 5 Ω

Answer

(C) 4 Ω

Question 42

A monochromatic neon lamp with wavelength of 670.5 nm illuminates a photo-sensitive material which has a stopping voltage of 0.48 V. What will be the stopping voltage if the source light is changed with another source of wavelength of 474.6 nm?

Accepted Answer

(B) 1.25 V

Answer

(A) 0.96 V

Answer

(C) 0.24 V

Answer

(D) 1.5 V

Question 43

Match List-I (physical quantity) with List-II (SI unit).
Choose the most appropriate answer from the options given below :

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 44

If force (F), length (L) and time (T) are taken as the fundamental quantities. Then what will be the dimension of density :

Accepted Answer

(A) [FL$^{-4}$ T$^{2}$]

Answer

(B) [FL$^{-3}$ T$^{2}$]

Answer

(C) [FL$^{-5}$ T$^{2}$]

Answer

(D) [FL$^{-3}$ T$^{3}$]

Question 45

A coaxial cable consists of an inner wire of radius 'a' surrounded by an outer shell of inner and outer radii 'b' and 'c' respectively. The inner wire carries an electric current $i_{0}$, which is distributed uniformly across cross-sectional area. The outer shell carries an equal current in opposite direction and distributed uniformly. What will be the ratio of the magnetic field at a distance x from the axis when (i) x < a and (ii) a < x < b ?

Accepted Answer

(A) $\frac{x^{2}}{a^{2}}$

Answer

(B) $\frac{a^{2}}{x^{2}}$

Answer

(C) $\frac{x^{2}}{b^{2}-a^{2}}$

Answer

(D) $\frac{b^{2}-a^{2}}{x^{2}}$

Question 46

The height of victoria falls is 63 m. What is the difference in temperature of water at the top and at the bottom of fall ?
[Given 1 cal = 4.2 J and specific heat of water = 1 cal g$^{-1}$ °C$^{-1}$]

Accepted Answer

(A) 0.147° C

Answer

(B) 14.76° C

Answer

(C) 1.476°

Answer

(D) 0.014° C

Question 47

A player kicks a football with an initial speed of 25 ms$^{-1}$ at an angle of 45° from the ground. What are the maximum height and the time taken by the football to reach at the highest point during motion ? (Take g = 10 ms$^{-2}$)

Accepted Answer

(C) h$_{max}$ = 15.625 m, T = 1.77 s

Answer

(A) h$_{max}$ = 10 m, T = 2.5 s

Answer

(B) h$_{max}$ = 15.625 m, T = 3.54 s

Answer

(D) h$_{max}$ = 3.54 m, T = 0.125 s

Question 48

The light waves from two coherent sources have same intensity $I_{1}$ = $I_{2}$ = $I_{0}$. In interference pattern the intensity of light at minima is zero. What will be the intensity of light at maxima ?

Accepted Answer

(D) 4 $I_{0}$

Answer

(A) $I_{0}$

Answer

(B) 2 $I_{0}$

Answer

(C) 5 $I_{0}$

Question 49

Figure shows a rod AB, which is bent in a 120° circular arc of radius R. A charge (−Q) is uniformly distributed over rod AB. What is the electric field $\vec{E}$ at the centre of curvature O ?

Accepted Answer

(B) $\frac{3\sqrt{3}\,Q}{8\pi^{2}\varepsilon_{0}R^{2}}(\hat{i})$

Answer

(A) $\frac{3\sqrt{3}\,Q}{8\pi\varepsilon_{0}R^{2}}(\hat{i})$

Answer

(C) $\frac{3\sqrt{3}\,Q}{16\pi^{2}\varepsilon_{0}R^{2}}(\hat{i})$

Answer

(D) $\frac{3\sqrt{3}\,Q}{8\pi^{2}\varepsilon_{0}R^{2}}(-\hat{i})$

Question 50

A heat engine operates between a cold reservoir at temperature $T_2$ = 400 K and a hot reservoir at temperature $T_1$. It takes 300 J of heat from the hot reservoir and delivers 240 J of heat to the cold reservoir in a cycle. The minimum temperature of the hot reservoir has to be __________ K.

Accepted Answer

500

Question 51

Two simple harmonic motion, are represented by the equations $y_1 = 10 \sin\left(3\pi t + \frac{\pi}{3}\right)$
$y_2 = 5(\sin 3\pi t + \sqrt{3}\cos 3\pi t)$
Ratio of amplitude of $y_1$ to $y_2$ = x : 1. The value of x is _________ .

Accepted Answer

1

Question 52

X different wavelengths may be observed in the spectrum from a hydrogen sample if the atoms are exited to states with principal quantum number n = 6 ? The value of X is ________ .

Accepted Answer

15

Question 53

A zener diode of power rating 2W is to be used as a voltage regulator. If the zener diode has a breakdown of 10 V and it has to regulate voltage fluctuated between 6 V and 14 V, the value of $R_s$ for safe operation should be ________ Ω.

Accepted Answer

20

Question 54

Wires $W_1$ and $W_2$ are made of same material having the breaking stress of 1.25 × 10$^{9}$ N/m$^{2}$. $W_1$ and $W_2$ have cross-sectional area of 8 × 10$^{-7}$ m$^{2}$ and 4 × 10$^{-7}$ m$^{2}$, respectively. Masses of 20 kg and 10 kg hang from them as shown in the figure. The maximum mass that can be placed in the pan without breaking the wires is _____ kg.
(Use g = 10 m/s$^{2}$)

Accepted Answer

40

Question 55

A bullet of 10 g, moving with velocity v, collides head-on with the stationary bob of a pendulum and recoils with velocity 100 m/s. The length of the pendulum is 0.5 m and mass of the bob is 1 kg. The minimum value of v = _____ m/s so that the pendulum describes a circle. (Assume the string to be inextensible and g = 10 m/s$^{2}$)

Accepted Answer

400

Question 56

An ac circuit has an inductor and a resistor of resistance R in series, such that $X_L$ = 3R. Now, a capacitor is added in series such that $X_C$ = 2R. The ratio of new power factor with the old power factor of the circuit is $\sqrt{5}$ : x . The value of x is _____ .

Accepted Answer

1

Question 57

The ratio of the equivalent resistance of the network (shown in figure) between the points a and b when switch is open and switch is closed is x : 8. The value of x is ________ .

Accepted Answer

9

Question 58

A plane electromagnetic wave with frequency of 30 MHz travels in free space. At particular point in space and time, electric field is 6 V/m. The magnetic field at this point will be x × 10$^{-8}$ T. The value of x is _____ .

Accepted Answer

2

Question 59

A tuning fork is vibrating at 250 Hz. The length of the shortest closed organ pipe that will resonate with the tuning fork will be _____ cm.
(Take speed of sound in air as 340 ms$^{-1}$)

Accepted Answer

34

Question 60

Choose the correct statement from the following :

Accepted Answer

(C) Among the alkali metal halides, LiF is least soluble in water.

Answer

(A) The standard enthalpy of formation for alkali metal bromides becomes less negative on descending the group.

Answer

(B) The low solubility of CsI in water is due to its high lattice enthalpy.

Answer

(D) LiF has least negative standard enthalpy of formation among alkali metal fluorides.

Question 61

The addition of dilute NaOH to Cr$^{3+}$ salt solution will give :

Accepted Answer

(B) precipitate of Cr$_{2}$O$_{3}$(H$_{2}$O)$_{n}$

Answer

(A) a solution of [Cr(OH)$_{4}$]$^{-}$

Answer

(C) precipitate of [Cr(OH)$_{6}$]$^{3-}$

Answer

(D) precipitate of Cr(OH)$_{3}$

Question 62

Given below are two statements :
Statement I : Ethyl pent–4–yn–oate on reaction with CH$_{3}$MgBr gives a 3°–alcohol.
Statement II : In this reaction one mole of ethyl pent–4–yn–oate utilizes two moles of CH$_{3}$MgBr.
In the light of the above statements, choose the most appropriate answer from the options given below :

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 63

In stratosphere most of the ozone formation is assisted by :

Accepted Answer

(C) ultraviolet radiation.

Answer

(A) cosmic rays.

Answer

(B) γ–rays.

Answer

(D) visible radiations.

Question 64

The compound/s which will show significant intermolecular H–bonding is/are :

Accepted Answer

(A) (b) only

Answer

(B) (c) only

Answer

(C) (a) and (b) only

Answer

(D) (a), (b) and (c)

List-I	List-II
a. $R_{H}$ (Rydberg constant)	i.kg m $^{-1}$ s $^{-1}$
b.h (Planck's constant)	ii.kg m $^{2}$ s $^{-1}$
c. $\mu_{B}$ (Magnetic field energy density)	iii.m $^{-1}$
d.η (coefficient of viscocity)	iv.kg m $^{-1}$ s $^{-2}$

List-I (Name of ore/mineral)	List-II (Chemical formula)
a.Calamine	i.Zns
b.Malachite	ii.FeCO $_{3}$
c.Siderite	iii.ZnCO $_{3}$
d.Sphalerite	iv.CuCO $_{3}$ · Cu(OH) $_{2}$

JEE Main 27 August 2021 Shift 2 Question Paper with Answers

Physics — JEE Main 27 August 2021 Shift 2

Chemistry — JEE Main 27 August 2021 Shift 2

Mathematics — JEE Main 27 August 2021 Shift 2

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