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 |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.
- 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.