CBSE 12 Maths Question Paper-2025 Set-1

If the feasible region of a linear programming problem with objective function Z=ax+by, is bounded, then which of the following is correct?

The unit vector perpendicular to both the vectors î - ĵ and î + ĵ is:

If ∫ₒ¹ (eˣ / (1+x)) dx = α, then ∫ₒ¹ (eˣ / (1+x)²) dx is:

If ∫(2¹/ˣ / x²) dx = k⋅2¹/ˣ + C, then k is equal to:

If A = [-1 0 0; 0 1 0; 0 0 1], then A⁻¹ is:

What is the order and degree of the differential equation: x (d²y/dx²)³ + 2(dy/dx)² + y = 0?

If the vectors are mutually parallel, then the value of λ is: α = î - 4ĵ + 9k̂ and β = 2î - 8ĵ + λk̂

The value of ∫ (1 - 2sinx) / cos²x dx is:

If a + b + c = 0, |a| = √37, |b| = 3 and |c| = 4, then the angle between vectors b and c is:

The value of ∫₋₁¹ |x|/x dx, x≠0 is:

If a relation R on the set A = {1, 2, 3} is R = {(1, 1), (2, 2), (3, 3)}, then the relation R is:

The value of ∫₋₂² |x+1| dx is:

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

The differential equation of the family of curves y = Acos x + Bsin x is:

If f(x) = |x-1|+|x| is continuous at x=0 and x=1, then f(x) is also:

The function f(x) = sin x is:

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

If the sum of the order and degree of the differential equation d/dx (x³ d²y/dx² + y = 0) is 3, then the degree of this differential equation is:

Assertion (A): The function f: R → R defined as 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.

If a line passes through the point (2, -1, 3) and is perpendicular to the lines (x-1)/1 = (y+1)/2 = (z-2)/3 and (x-2)/1 = (y-1)/-1 = (z+1)/1, then the equation of the line is:

The value of ∫ sin²x dx is:

If a card is drawn from a well-shuffled pack of 52 cards, then the probability that the card is a red card is: