CBSE 12 Maths Question Paper-2022 Set-5

Find the value of k for which the function f(x) = {kx+1, if x≤5; 3x-5, if x>5} is continuous at x=5.

Find the equation of the line passing through the point (2, 3, 2) and parallel to the line (x-2)/3 = (y+1)/2 = (z-1)/5.

Find the general solution of the differential equation: (dy/dx) = e^(x-y) + x²e^(-y).

Find the area of the region bounded by the curve y² = 4x and the line x = 3.

Evaluate: ∫(from 0 to 1) tan⁻¹(x) dx.

A and B are two events such that P(A)=0.5, P(B)=0.6 and P(A∪B)=0.8. Find P(A|B).

Find the equation of the plane passing through the point (-1, 3, 2) and perpendicular to the planes x+2y+3z=5 and 3x+3y+z=0.

Find the shortest distance between the lines r = (2i - j - k) + λ(i + 2j + 3k) and r = (i + j + 2k) + μ(4i + 5j + 6k).

Find the area of the region bounded by the parabola y = x² and the line y = x.

A die is thrown 6 times. If 'getting an odd number' is a success, what is the probability of 5 successes?

Find the value of 'a' for which the vectors 2i - j + k and i + aj - 3k are coplanar with the vector 3i + 2j + k.

Evaluate: ∫(sin²x)/(1+cos x) dx.

If A = [2 -1 1; -1 2 -1; 1 -1 2], find the value of |A|.

Find the general solution of the differential equation: (dy/dx) = eˣ⁺ʸ + x²eʸ.

Find the area of the region bounded by the parabola y = 4x² and the line y = 1.

Evaluate: ∫(from 0 to 1) [x(1-x)]ⁿ dx.

A speaks truth in 75% of the cases and B in 80% of the cases. In what percentage of cases are they likely to contradict each other in stating the same fact?

Find the equation of the plane containing the line (x+1)/3 = (y-2)/2 = (z+1)/5 and the point (0, 0, 0).

Find the shortest distance between the lines r = (i + 2j + 3k) + λ(2i + 3j + 4k) and r = (2i + 4j + 5k) + μ(3i + 4j + 5k).

Find the area of the region bounded by the curves x² = y and y = |x|.

A pair of dice is thrown. Find the conditional probability that the numbers 4 or 5 appear on atleast one die, given that the sum of numbers is 6.

Evaluate: ∫(cos 2x - cos 2α)/(cos x - cos α) dx.