CBSE 12 Maths Question Paper-2025 Set-5

If tan⁻¹(x²-y²)=a, where 'a' is a constant, then dy/dx is:

If A = [[0, 0, -5], [0, 3, 0], [4, 0, 0]] is a matrix, then A is a:

The value of ∫ sin²x dx is:

Let a and b be two vectors such that |a| = |b| = √2 and a·b = -1. The angle between vectors (a+b) and (a-b) is:

The order and degree of the differential equation (d²y/dx²)³ + (dy/dx)⁴ + sin(dy/dx) + 1 = 0 are respectively:

The value of ∫(0 to 1) 1/(1+x²) dx is:

The value of the principal branch of tan⁻¹(√3) - sec⁻¹(-2) is:

If a, b, c are three vectors such that |a|=2, |b|=3, |c|=4 and a+b+c=0, then the value of a·b + b·c + c·a is:

If y = xˣ, then the value of dy/dx at x=1 is:

The vector projection of the vector a = 3i - j - 2k on the vector b = i + 2j - 3k is:

If the vertices of a triangle are A(1, 2, 3), B(-1, 0, 0) and C(0, 1, 2), then the area of the triangle ABC is:

The value of ∫(-π/2 to π/2) sin³x dx is:

The points (3, -2, 4), (1, 1, 1), and (-1, 4, -2) are:

The equation of the line passing through the point (-1, 2, 3) and parallel to the line x/2 = y/3 = z/6 is:

The order and degree of the differential equation d²y/dx² = sin⁻¹(dy/dx) are respectively:

If A is a 2x2 matrix and |A|=4, then |2A| is equal to:

The value of ∫₀² dx/(x+4 - x²) is:

The value of ∫ sin(x+a) / sin(x) dx is:

If a and b are two unit vectors such that a+b is a unit vector, then the angle between a and b is:

The sum of two symmetric matrices of the same order is always:

If y = A e⁵ˣ + B e⁻⁵ˣ, then d²y/dx² is equal to :

The differential equation of the family of parabolas y = A x² is:

The value of ∫₁³ (3-x)² dx is:

The value of ∫ sin(log x) dx is:

The area of the region bounded by the circle x²+y²=4 and the line x+y=2 is:

The value of ∫(0 to 1) 1/√(1-x²) dx is:

If the sum of two unit vectors a and b is a unit vector, then the magnitude of their difference is:

If a line makes angles 90°, 135°, 45° with the positive directions of x, y, z axes respectively, then the direction cosines of the line are:

If the direction cosines of a line are k, k, k, then the value of k is:

The vector equation of the line passing through the points (3, 4, 1) and (5, 1, 6) is:

The value of ∫₀²π sin²x dx is:

The area of the region bounded by the curves y = x² and y = x is:

The solution of the differential equation x dy/dx = y is:

If P(A) = 0.6, P(B) = 0.5, P(A∪B) = 0.8, then P(A∩B) is:

A bag contains 5 red and 3 black balls. If a ball is drawn at random, the probability of drawing a red ball is:

If a line makes angles 90°, 60°, 30° with the positive directions of x, y, z axes respectively, then the value of cos²90° + cos²60° + cos²30° is: