CBSE 12 Maths Question Paper-2025 Set-4

If A = [[5, 0, 0], [0, 5, 0], [0, 0, 5]], then A³ is:

If P(A∪B)=0.9 and P(A∩B)=0.4, then P(Ā)+P(B̄) is:

The value of ∫[1 to e] (log x)³ dx is equal to:

If the curve y = ax³ + bx² + 1 is tangent to the line y = 4 at the point where x = 2, then the value of 2a + b is:

The differential equation of the family of curves y = c(x+c)² is:

The value of ∫x² tan⁻¹x dx is equal to:

The value of ∫[0 to π] |cos x - sin x| dx is :

The vector equation of the plane passing through the points (1,1,1), (-1,1,-1), and (1,3,2) is:

The equation of the tangent to the curve y² = 4ax at the point (at², 2at) is:

The area of the parallelogram whose adjacent sides are the vectors i + k and 2i + j + k is:

The solution of the differential equation (1-x²)dy + (x-x³)dx = 0 is:

The value of ∫(0 to 1) tan⁻¹x dx is:

If A = [aᵢⱼ] is a 3x3 diagonal matrix such that a₁₁=1, a₂₂=5 and a₃₃=-2, then |A| is:

If A = kB, where A and B are two square matrices of order n and k is a scalar, then:

The principal value of cot⁻¹(-1/√3) is:

If y = xⁿ, then the nth derivative of y is :

The vector of magnitude 3 along the vector joining the points (1, -2, 4) and (2, -1, 3) is:

The value of ∫₀²π sin²x cos²x dx is:

The area of the region bounded by the curves x = y² and y = x² is:

If P(A) = 0.4, P(B) = 0.8 and P(B/A) = 0.6, then P(A∪B) is equal to :

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

The angle between the lines x+1/2 = y-1/1 = z+1/-1 and x-1/2 = y+1/1 = z-1/3 is:

The vector equation of a plane which is at a distance of 3/√14 from the origin and normal to the vector 2i + 3j - k is:

The value of ∫eˣ (f(x)+f'(x))dx is:

The value of ∫(-1 to 1) |x| dx is :

The area of the region bounded by the curves y² = 2x and y = x is:

The solution of the differential equation dy/dx + y/x = 1 is:

The order and degree of the differential equation (d³y/dx³)³ + 5(d²y/dx²)⁴ + 7(dy/dx) + 2y = 0 are respectively:

The value of ∫(0 to 4) |x-2| dx is :

If a, b, c are three vectors such that a+b+c = 0 and |a| = 1, |b| = 2, |c| = 3, then the value of a·b + b·c + c·a is:

If A is a square matrix such that A² = I, then (A-I)³ + (A+I)³ is equal to:

If x=sinθ, y=cos(pθ) then (1-x²)y₂-xy₁ is equal to :

If a, b, c are non-coplanar vectors, then a·(b×c) is equal to:

If sin⁻¹(1-x) - 2 sin⁻¹x = π/2, then the value of x is:

If A = [2, -1; -1, 2] and A² - 4A + 3I = 0, then A⁻¹ is equal to:

If the equation of a line is (x-1)/1 = (y+1)/0 = (z-1)/2, then the direction cosines of the line are :