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

- 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.

- 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.

- 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.

- 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.- 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.

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

Answer: the value of 160S is 305.

- 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.

- 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.

- 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(B) (

(C) (

(D) (

- 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.

- 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.