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

- 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.

- 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.

- 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.

- 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 |2

**a**+ 3

**b**| = |3

**a**+

**b**|, then the magnitude of the vector

**b**is. (A) 5

(B) 6

(C) 7

(D) 8 Answer: Option (A) is the correct choice.

- 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.

- 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.

- 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.

- 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.