## JEE Main 31 August 2021 (Shift – 1) Questions with Answer Key

1. Number of words than can be formed by the word VOWELS such that all the consonants are not together.

(A) 4. 3!
(B) 4. 4!
(C) (4!)²
(D) 6. 4!

Answer: Option (C) is the correct choice.

1. The co-efficient of the term independent of x in the expansion of (x/4 – 12/x²)¹² is.

(A) 12C₄ (3/4)⁴
(B) – 12C₄ (3/4)⁴
(C) 12C₄ (4/3)⁴
(D) – 12C₄ (4/3)⁴

Answer: Option (A) is the correct choice.

1. The mean of the first 10 terms of the sequesnce 7 x 8, 10 x 10, 13 x 12, …… is.

Answer: The required mean is 398.

1. Let the vertex and the focus of a parabola are (R, 0) and (S, 0) respectively. The length of the Latus Rectum of the parabola is.

(A) 4|S – R|
(B) 2|S – R|
(C) |S – R|
(D) |S – R|/2

Answer: Option (A) is the correct choice.

5. The angle between the vectors a and b is π/3 and a/8 is a unit vector. If |2a + 3b| = |3a + b|, then the magnitude of the vector b is.

(A) 5
(B) 6
(C) 7
(D) 8

Answer: Option (A) is the correct choice.

1. Let P(x) = x² + ax + 1 be a quadratic polynomial in x. If P(x) is increasing in the interval [1, 2], then the minimum value of a is A. If P(x) is decreasing in the interval [1, 2], then the maximum value of a is B, then the value of |A – B| is.

Answer: the value of |A – B| is 2.

1. The sum of first 10 terms of the series (3/(1² x 2²)) + (5/(2² x 3²)) + (7/(3² x 4²)) + — is.

(A) 120/121
(B) 440/441
(C) 99/100
(D) 1

Answer: Option (B) is the correct choice.

1. If the solution y(x) of the differential equation dy/dx = (2ˣ⁺ʸ – 2ˣ)/2ʸ represents a curve which passes through the point (0, 1), then the value of y(2) is.

(A) log₂(e³)
(B) log₂(e³ – 1)
(C) log₂(1 + e³)
(D) log₂(1 – e³)

Answer: Option (C) is the correct choice.

1. If the distance of the lines xCoseca + ySeca = kCot2a and xSina + yCosa = kSin2a from the origin is p and q respectively, then.

(A) 4p² – q² = k²
(B) 4p² + q² = 4k²
(C) p² + 4q² = k²
(D) 4p² + q² = k²

Answer: Option (D) is the correct choice.