JEE Main 2025 · 22 Jan 2025 Shift 2

Let A = {1, 2, 3, 4} and B = {1, 4, 9, 16}. Then the number of many-one functions f : A → B such that 1 ∈ f(A) is equal to :

1. A127
2. B139
3. C151
4. D163

For a 3 × 3 matrix M, let trace (M) denote the sum of all the diagonal elements of M. Let A be a 3 × 3 matrix such that |A| = 1/2 and trace

1. A= 3. If B = adj(adj(2A)), then the value of |B| + trace
2. Bequals :

Suppose that the number of terms in an A.P. is 2k, k∈N. If the sum of all odd terms of the A.P. is 40, the sum of all even terms is 55 and the last term of the A.P. exceeds the first term by 27, then k is equal to :

1. A4
2. B5
3. C6
4. D8

In a group of 3 girls and 4 boys, there are two boys B₁ and B₂. The number of ways, in which these girls and boys can stand in a queue such that all the girls stand together, all the boys stand together, but B₁ and B₂ are not adjacent to each other, is :

1. A72
2. B96
3. C120
4. D144

Let α, β, γ and δ be the coefficients of x⁷, x⁵, x³ and x respectively in the expansion of (x + √(x³ − 1))⁵ + (x − √(x³ − 1))⁵, x > 1. If u and v satisfy the equations αu + βv = 18, γu + δv = 20, then u + v equals :

1. A3
2. B4
3. C5
4. D8

If A and B are two events such that P(A ∩ B) = 0.1, and P(A | B) and P(B | A) are the roots of the equation 12x² − 7x + 1 = 0, then the value of P(Ā ∪ B̄)/P(Ā ∩ B̄) is :

1. A4/3
2. B5/3
3. C7/4
4. D9/4

Let E : x²/a² + y²/b² = 1, a > b and H : x²/A² − y²/B² = 1. Let the distance between the foci of E and the foci of H be 2√3. If a − A = 2, and the ratio of the eccentricities of E and H is 1/3, then the sum of the lengths of their latus rectums is equal to :

1. A7
2. B8
3. C9
4. D10

The sum of all values of θ ∈ [0, 2π] satisfying 2sin²θ = cos2θ and 2cos²θ = 3sinθ is

1. A5π/6
2. Bπ/2
3. Cπ
4. D4π