## JEE Main 26 August 2021 (Shift – 2) Questions with Answer Key

1. The value of 2Sin(π/8)Sin(2π/8)Sin(3π/8)….Sin(7π/8) is.

(A) 1/2
(B) 1/4
(C) 1/8
(D) 1/16

Answer: Option (C) is the correct choice.

1. The locus of the mid-point of the chord of the hyperbola x² – y² = 4, which touches the curve y² = 8x is.

(A) x³ + 2y² – y²x = 0
(B) x³ + 2y² + y²x = 0
(C) x³ – 2y² – y²x = 0
(D) x³ + 3y² – y²x = 0

Answer: Option (A) is the correct choice.

1. If 2x²dy + (eʸ – 2x)dx = 0 and y(e) = 1, then the value of y(1) is.

(A) 0
(B) 2
(C) ln2
(D) ln3

Answer: Option (C) is the correct choice.

1. The circle C touches the straight line 2y = x at the point (2, 1) and it intersects the circle C₁: x² + y² + 2y = 5 at P and Q. If PQ is the diameter of circle C₁, then calculate the square of the diameter of the circle C.

Answer: The square of the diameter of the circle Cis 245.

1. A dice is rolled till 6 appears, then the probability P((x ≥ 5)/(x > 2)) is.

(A) 1/6
(B) 1/2
(C) 23/36
(D) 25/36

Answer: Option (D) is the correct choice.

1. The mean and variance of the 4 observations 3, 7, x, and y (where x > y) is 5 and 10 respectively. The mean of the observations 4 + x + y, 7 + x, x + y, and x – y will be.

(A) 8
(B) 10
(C) 12
(D) 14

Answer: Option (C) is the correct choice.

1. Let the plane P passes trough the point (1, 2, 3) and it contains the line of intesection of the planes x + y + 4z = 16 and -x + y + z = 6. Then which of the following points does not lie on the plane P.

(A) (-8, 8, 6)
(B) (-4, 3, 5)
(C) (8, -5, 1)
(D) (-8, 8, 5)

Answer: Option (D) is the correct choice.

1. If f(x) = ((2/x)ˣ)², then maximum value of f(x) is.

(A) e²
(B) e²ᵉ⁻¹
(C) eᵉ⁻¹
(D) e

Answer: Option (B) is the correct choice.

1. if a₁, a₂ ,….,a₁₀ are in A. P. with common difference -3 and b₁, b₂ ,….,b₁₀ are in G. P. with common ratio 2. If cₖ = aₖ + bₖ, {where k = 1, 2, 3, …., 10}, c₂ = 12 and c₃ = 13, then the value of Σ(cₖ) {where k = 1, 2, 3, …., 10} is.

Answer: The value of Σ(cₖ) is 2021.

1. If (√3 + i) = 2⁹⁹(a + ib), then a and b are the roots of the equation {where i = √-1}.

(A) x² – (√3 + 1)x + √3 = 0
(B) x² + (√3 + 1)x – √3 = 0
(C) x² – (√3 – 1)x + √3 = 0
(D) x² – (√3 – 1)x – √3 = 0

Answer: Option (D) is the correct choice.

1. If the function f(x) = 2x³ – 6x² – 18x has local maxima at x = a and the local minima at x = b. If the area of the region bounded by the function f(x), x = a, and x = b is A, then the value of 4A will be

Answer: The value of 4A will be 404.

1. Minimum value of n for which (2i)ⁿ/(1 – i)ⁿ⁻² is a positive integer {where i = √-1, and n is a Natural Number}.

Answer: The minimum value of n is 6.

1. The angle between the two diagonals PB and CQ of a cuboid is Cos⁻¹(1/5). The length and breath of the cuboid are equal in length and is eqaul to 10. The height of the cuboid is.

(A) 5√2
(B) 5√5
(C) 25
(D) 50

Answer: Option (A) is the correct choice.

14. The value of the definite integral I = $\int ^{\dfrac{\pi }{2}}_{-\dfrac{\pi }{2}}\left( \dfrac{1+\sin ^{2}x}{1+\pi ^{\sin x}}\right) dx$ is.

(A) π/4
(B) 3π/4
(C) π/2
(D) 3π/2

Answer: Option (B) is the correct choice.

15. If the matrix A = $\begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 1 \\ 1 & 0 & 0 \end{bmatrix}$, then the value of A²⁰²⁵ – A²⁰²⁰ is.

(A) A⁶ – A
(B) A⁶
(C) A⁵ – A
(D) A⁵

Answer: Option (A) is the correct choice.

16. If $\sum ^{50}_{t=1}\tan ^{-1}\left( \dfrac{1}{2t^{2}}\right) = P$, then the value of tan(P) is.

(A) 50/51
(B) 51/50
(C) 100/101
(D) 101/100

Answer: Option (A) is the correct choice.