## JEE Main 26 August 2021 (Shift – 1) Questions with Answer Key

1. Sum of an infinite GP with first term ‘a’ and common ratio ‘r’ is 15 and the sum of the squares of the terms of the same GP is 150. The sum of an infinite GP with first term ‘a’ and the common ratio ‘r²’ is.

(A) 1/5
(B) 23/5
(C) 27/5
(D) 25/2

Answer: Option (D) is the correct choice.

1. If (1 + x)²⁰ is expanded in the form of Σ(20Cr.xʳ) (0 ≤ r ≤20), then tha value of Σ(r².20Cr), where (0 ≤ r ≤20) is.

(A) 95.2²⁰
(B) 105.2²⁰
(C) 95.2¹⁸
(D) 105.2¹⁸

Answer: Option (B) is the correct choice.

1. If the probability of independent events A and B are P(A) = p and P(B) = 2p and probability of exactly one of A and B is 5/9, then the value of p is.

(A) 2/5
(B) 1/3
(C) 1/12
(D) 7/12

Answer: Option (B) is the correct choice.

1. Let Arg((z + 1)/(z – 1)) = π/4. Then the locus of z be a circle whose radius and centre respectively are.

(A) √2, (0, -1)
(B) √2, (0, 0)
(C) √2, (0, 1)
(D) 1, (0, 1)

Answer: Option (A) is the correct choice.

1. The mean of 20 observations is 10 and standard deviation is 2.5. If one of the observations 25 is replaced by 35, then new mean and standard deviation are a and √b respectively. Then the ordered pair (a, b) is.

(A) (10.5, 23)
(B) (10.5, 25)
(C) (10.5, 26)
(D) (10.5, 36)

Answer: Option (C) is the correct choice.

1. In a city 89% people are suffered from Diabetes and 98% people are suffered from heart diseases. If x% people are suffered from Diabetes as well as heart diseases then x will not lie in the set.

(A) {81, 83, 85, 86}
(B) {82, 87, 88, 91}
(C) {87, 88, 89, 90}
(D) {88, 89, 92, 95}

Answer: Option (A) is the correct choice.

1. If ln(x + y) = 4xy, then the value of d²y/dx² at x = 0 will be.

(A) 30
(B) 35
(C) 38
(D) 40

Answer: Option (D) is the correct choice.

1. If locus of a variable point P, whose sum of squares of distances from the points (0, 0), (0, 1), (1, 0) and (1, 1) is 18, is a cicle of diameter d, then the value of d² is equal to.

Answer: The value of d² is 16.

9. If a = i + j + k, b = i – k, a x c = b, and a . c = 3, then the value of [a b c] is.

(A) -2
(B) -√2
(C) √2
(D) 2

Answer: Option (A) is the correct choice.

10. If A and B are two square matrices of order 2 x 2 such that A = $\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$; B = $\begin{bmatrix} 1 & 0 \\ i & 1 \end{bmatrix}$, where i = √-1, and AᵀB²⁰²¹A = Q, then the value of AQAᵀ is.

(A) $\begin{bmatrix} 1 & 0 \\ i & 1 \end{bmatrix}$
(B) $\begin{bmatrix} 1 & 0 \\ 2021i & 1 \end{bmatrix}$
(C) $\begin{bmatrix} 1 & 0 \\ 1 & 1 \end{bmatrix}$
(D) $\begin{bmatrix} 1 & 0 \\ 2022i & 1 \end{bmatrix}$

Answer: Option (B) is the correct choice.

11. The value of the definite integration I = $\int ^{1/2}_{-1/2}\left[ \left( \dfrac{x+1}{x-1}\right) ^{2}+\left( \dfrac{x-1}{x+1}\right) ^{2}-2\right] ^{\dfrac{1}{2}}dx$ is.

(A) 2 ln(3/2)
(B) 4 ln(3/2)
(C) 4 ln(3/4)
(D) 4 ln(4/3)

Answer: Option (D) is the correct choice.

1. If (1 + y)Tan²x + (Tanx)(dy/dx) + y = 0 and Limₓ→₀⁺(xy) = 1, then the value of y(π/4) is.

(A) -π/2
(B) -π/4
(C) 0
(D) π/4

Answer: Option (D) is the correct choice.