JEE Main 2025 · 2 Apr 2025 Shift 2

If the domain of the function f(x) = 1/√(10+3x−x²) + 1/√(x+|x|) is (a, b), then (1+a)²+b² is equal to:

1. A26
2. B25
3. C29
4. D30

Let A = {1, 2, 3,...., 100} and R be a relation on A such that R = {(a, b) : a = 2b + 1}. Let (a₁, a₂), (a₂, a₃), (a₃, a₄), ...., (aₖ, aₖ₊₁) be a sequence of k elements of R such that the second entry of an ordered pair is equal to the first entry of the next ordered pair. Then the largest integer k, for which such a sequence exists, is equal to:

1. A5
2. B6
3. C7
4. D8

Let A be a 3 × 3 real matrix such that A²(A − 2I) − 4(A − I)=O, where I and O are the identity and null matrices, respectively. If A⁵ = αA² + βA + γI, where α, β, and γ are real constants, then α + β + γ is equal to:

1. A4
2. B12
3. C20
4. D76

If the system of equations 2x + λy + 3z = 5, 3x + 2y − z = 7, 4x + 5y + μz = 9 has infinitely many solutions, then (λ² + μ²) is equal to:

1. A18
2. B22
3. C26
4. D30

The number of terms of an A.P. is even; the sum of all the odd terms is 24, the sum of all the even terms is 30 and the last term exceeds the first by 21/2. Then the number of terms which are integers in the A.P. is :

1. A4
2. B6
3. C8
4. D10

If ∑ᵣ₌₀¹⁰ ((10ʳ⁺¹−1)/10ʳ) · ¹¹Cᵣ₊₁ = (α¹¹ − 11¹¹)/10¹⁰, then α is equal to :

1. A11
2. B15
3. C20
4. D24

If the mean and the variance of 6, 4, a, 8, b, 12, 10, 13 are 9 and 9.25 respectively, then a + b + ab is equal to :

1. A100
2. B103
3. C105
4. D106

Let the area of the triangle formed by a straight line L : x + by + c = 0 with co-ordinate axes be 48 square units. If the perpendicular drawn from the origin to the line L makes an angle of 45° with the positive x-axis, then the value of b² + c² is :

1. A83
2. B90
3. C93
4. D97