JEE Main 2024 · 8 Apr 2024 Shift 2

Let A = {2, 3, 6, 8, 9, 11} and B = {1, 4, 5, 10, 15}. Let R be a relation on A × B defined by (a, b)R(c, d) if and only if 3ad − 7bc is an even integer. Then the relation R is

1. Aan equivalence relation.
2. Breflexive but not symmetric.
3. Ctransitive but not symmetric.
4. Dreflexive and symmetric but not transitive.

Let f(x) = { −a if −a ≤ x ≤ 0; x + a if 0 < x ≤ a } where a > 0 and g(x) = (f(|x|) − |f(x)|)/2. Then the function g : [−a, a] → [−a, a] is

1. Aone-one.
2. Bonto.
3. Cboth one-one and onto.
4. Dneither one-one nor onto.

If the system of equations x + 4y − z = λ, 7x + 9y + μz = −3, 5x + y + 2z = −1 has infinitely many solutions, then (2μ + 3λ) is equal to :

1. A3
2. B−3
3. C2
4. D−2

If α ≠ a, β ≠ b, γ ≠ c and |α b c; a β c; a b γ| = 0, then a/(α −

1. a+ b/(β −
2. b+ γ/(γ −
3. cis equal to :

The number of ways five alphabets can be chosen from the alphabets of the word MATHEMATICS, where the chosen alphabets are not necessarily distinct, is equal to :

1. A175
2. B177
3. C179
4. D181

If the term independent of x in the expansion of (√a x² + 1/(2x³))¹⁰ is 105, then a² is equal to :

1. A2
2. B4
3. C6
4. D9

The sum of all possible values of θ ∈ [−π, 2π], for which (1 + i cos θ)/(1 − 2i cos θ) is purely imaginary, is equal to :

1. A2π
2. B3π
3. C4π
4. D5π

In an increasing geometric progression of positive terms, the sum of the second and sixth terms is 70/3 and the product of the third and fifth terms is 49. Then the sum of the 4th, 6th and 8th terms is equal to :

1. A78
2. B84
3. C91
4. D96