## JEE Main 31 August 2021 (Shift – 2) Questions with Answer Key

1. The distance of a point P(-2, 1, 2) from the line of intersetion of x + 3y – 2z + 1 = 0 and x – 2y + z = 0 is.

(A) √(34/35)
(B) √(35/34)
(C) 2√(34/35)
(D) 2√(35/34)

Answer: Option (C) is the correct choice.

1. The mean and variance of 7 observations are 8 and 12 respectively. If two of the observations are 8 and 6, then the variance of 5 remaining observations is.

(A) 132/25
(B) 396/25
(C) 396/50
(D) 792/25

Answer: Option (B) is the correct choice.

1. If the line (x – 2)/a = (3 – y)/5 = z/2 completely lies in the plane x + 3y – 2z + b = 0, then the value of (a + b) is.

(A) 4
(B) 6
(C) 8
(D) 10

Answer: Option (C) is the correct choice.

1. Number of 4 digits numbers which are niether divisible by 7 nor 3 are.

(A) 5142
(B) 5143
(C) 5144
(D) 5145

Answer: Option (B) is the correct choice.

5. The matrix A = $\begin{bmatrix} a & b \\ 0 & d \end{bmatrix}$ {where a, b, d ∈ {-1, 0, 1}}. If (I – A)³ = I – A³, then possible number of such matrices A are.

Answer: Possible number of such matrices A are 8.
1. If (a₁ + a₂ + … + a₁₀)/(a₁ + a₂ + … + aₚ) = 100/p², then the value of a₁₁/a₁₀ is.

(A) 19/20
(B) 19/21
(C) 20/19
(D) 21/19

Answer: Option (D) is the correct choice.

1. If S = (7/5) + (9/5²) + (13/5³) + … , then the value of 160S is.

Answer: the value of 160S is 305.

1. If a tangent to the parabola y² = 8x at (2, -4) also touches the circle x² + y² = a, then the value of a is.

Answer: the value of a is 2.

1. The negation of the logical statement (p V r) → (q V r) is.

(A) p ∧ ~q ∧ r
(B) p ∧ ~q ∧ ~r
(C) p ∧ q ∧ r
(D) ~p ∧ q ∧ r

Answer: Option (B) is the correct choice.

1. Let f: N → N for which f(m + n) = f(m) + f(n) ∀ m, n ∈ N. If f(6) = 18, then the value of f(2)f(3) is.

Answer: the value of f(2)f(3) is 54.

11. If a x [(rb) x a] + b x [(rc) x b] + c x [(ra) x c] = 0 and a, b, and c are unit vectors mutually perpendicular to each other, then r is.

(A) (abc)/2
(B) (ab + c)/2
(C) (a + b + c)/2
(D) (a + bc)/2

Answer: Option (C) is the correct choice.
1. If a straight line passes through the point (-3, -5) and intesects the ellipse (x/2)² + (y/3)² = 1 at points A and B, then the locus of the mid-point of the line joining A and B is.

(A) 4x² + 9y² + 20x + 27y = 0
(B) 9x² + 4y² + 20x + 27y = 0
(C) 4x² + 9y² + 27x + 20y = 0
(D) 9x² + 4y² + 27x + 20y = 0

Answer: Option (D) is the correct choice.

1. If the angle between the curves (x/a)² + (y/b)² = 1 and x² + y² = ab, (a > b) is θ, then the value of tanθ is.

(A) |(a – b)/√ab|
(B) |(a + b)/√ab|
(C) |(a + b)/ab|
(D) |(a – b)/ab|

Answer: Option (A) is the correct choice.