CBSE 12 Maths Question Paper-2025 Set-2

If the binary operation '*' on the set Z of integers is defined by a * b = a + 3b², then the value of 3 * 2 is:

The value of sin⁻¹(sin(3π/5)) is:

If a matrix A is of order m x n and A² exists, then:

If A = [1 2; 3 4], then det(2A) is:

The corner points of the feasible region of a linear programming problem are (0, 0), (2, 0), (0, 3) and (2, 3). The minimum value of the objective function Z = 4x + 6y is:

If the binary operation '' on the set Z of integers is defined as ab = 2a + 3b - 1, then the value of 5*4 is:

The value of cos⁻¹(cos(7π/6)) is:

If A = [2 -3; 5 1] and B = [-1 0; 2 3], then 2A + 3B is:

If a square matrix A of order 3 has |A| = 4, then |adj A| is:

The value of ∫ log x dx is:

If the lines r⃗ = (2î - ĵ - 3k̂) + λ(2î + 5ĵ - 3k̂) and r⃗ = (-2î - 4ĵ + 7k̂) + μ(aî + 3ĵ + 5k̂) are perpendicular, then the value of a is:

The order and degree (if defined) of the differential equation y''' + 4y'' + 5(y')³ = x is:

The integrating factor of the differential equation x dy/dx + 2y = x² (x ≠ 0) is:

If P(A) = 3/10, P(B) = 1/2 and P(A∪B) = 3/5, then P(B/A) is:

A bag contains 5 red and 3 black balls. All the balls are drawn one by one without replacement. The probability of getting balls of alternate colours is:

Assertion (A): The function f(x) = |x| is not differentiable at x=0. Reason (R): A function is not differentiable at a point where the graph has a sharp corner.

Assertion (A): The position vectors of three points A, B and C are respectively î+ĵ+k̂, 2î+3ĵ+4k̂ and -î-2ĵ-3k̂. These three points are collinear. Reason (R): Three points A, B and C are collinear if vector AB = λ(vector AC) for some scalar λ.

The value of ∫₋₂² (x³+1)dx is:

The integrating factor of the differential equation x dy/dx - y = 2x² is:

A random variable X has the following probability distribution: X: 0, 1, 2, 3, 4 P(X): 0.1, 0.2, 0.1, 0.3, k. The value of k is:

The coordinates of the foot of the perpendicular drawn from the origin to the plane 2x - 3y + 4z - 6 = 0 are:

The value of ∫ sin²x dx is:

The probability of getting a red card when a card is drawn from a well-shuffled pack of 52 cards is: