CBSE 12 Maths Question Paper-2025 Set-3

Domain of sin⁻¹(2x²-3) is:

The matrix [0 1 -2; -1 0 -7; 2 7 0] is a:

If f(x)={3x-2, 0

If y=log₂ₓ(√2x), then dy/dx is equal to :

If f:N→W is defined as f(n)={n-2, if n is even; 0, if n is odd} then f is:

The coordinates of the foot of the perpendicular drawn from the point A(-2,3,5) on the y-axis is :

If A and B are invertible matrices of order 3x3 such that det (A)=4 and det [(AB)⁻¹]=1/20 then det (B) is equal to :

For real x, let f(x)=x³+5x+1. Then :

The values of λ so that f(x)=sin x-cos x-λx+C decreases for all real values of x are:

The principal branch of cos⁻¹x is:

If A and B are square matrices of same order such that AB=A and BA=B, then A²+B² is equal to:

If f(x)={1-sin³x / 3cos²x, for x≠π/2; k, for x=π/2} is continuous at x=π/2 then the value of k is :

If the direction cosines of a line are λ, λ, λ, then λ is equal to:

If | -1 2 4; 1 x 1; 0 3 3x | = -57, then the product of possible values of x is:

The principal value of sin⁻¹(sin(-10π/3)) is:

If y=sin⁻¹x, then (1-x²)d²y/dx² is equal to:

If P is a point on the line segment joining (3, 6, -1) and (6, 2, -2) and y-coordinate of P is 4, then its z-coordinate is :

If M and N are square matrices of order 3 such that det (M)=m and MN=mI, then det (N) 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 vector equation of the plane passing through the points (1,1,1), (-1,1,-1), and (1,3,2) 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 solution of the differential equation (1-x²)dy + (x-x³)dx = 0 is:

The value of ∫eˣ (f(x)+f'(x))dx 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 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 value of ∫(0 to 1) tan⁻¹x dx is:

The value of ∫(-1 to 1) |x| dx is :