CBSE 12 Maths Question Paper-2024 Set-5

The position vectors of points P and Q are p and q respectively. The point R divides line segment PQ in the ratio 3:1 and S is the mid-point of line segment PR. The position vector of S is:

For the matrix A = [[2,-1,1], [λ,2,0], [1,-2,3]] to be invertible, the value of λ is:

The angle which the line x/1 = y/-1 = z/0 makes with the positive direction of Y-axis is:

The Cartesian equation of the line passing through the point (1, -3, 2) and parallel to the line r=(2+λ)i + λj + (2λ-1)k is:

If A = [[x,0], [1,1]] and B = [[4,0], [-1,1]], then the value of x for which A^2=B is:

Given a curve y = 7x-x^3 and x increases at the rate of 2 units per second. The rate at which the slope of the curve is changing, when x=5 is:

Let f(x) = |[x^2, sin x], [p,-1]| where p is a constant. The value of p for which f'(0)=1 is:

If A and B are events such that P(A/B) = P(B/A) ≠ 0, then:

A function f: R→R defined as f(x) = x^2 - 4x + 5 is:

If A is a square matrix of order 3 such that |adj A| = 8, then the value of |A^T| is:

If ∫[-2, 3] x^2 dx = k∫[0, 2] x^2 dx + ∫[2, 3] x^2 dx, then the value of k is:

The value of ∫[1, e] log x dx is:

The area bounded by the curve y=√x, Y-axis and between the lines y=0 and y=3 is:

The order of the following differential equation d^3y/dx^3 + x(dy/dx)^5 = 4 log(d^4y/dx^4) is:

Derivative of e^(sin^2 x) with respect to cos x is:

If A is a square matrix of order 2 and |A|=-2, then value of |5A'| is:

The function f(x) = x/2 + 2/x has a local minima at x equal to:

The product of matrix P and Q is equal to a diagonal matrix. If the order of matrix Q is 3x2, then order of matrix P is:

If sin(xy)=1, then dy/dx is equal to:

If inverse of matrix [[1,3,3], [1,λ,3], [1,3,4]] is the matrix [[7,-3,-3], [-1,1,0], [-1,0,1]], then the value of λ is:

Find the matrix A^2, where A=[a_ij] is a 2x2 matrix whose elements are given by a_ij = maximum (i, j) - minimum (i, j):

The value of ∫[π/4, π/2] cotθ cosec^2θ dθ is:

The integral ∫ dx/√(9-4x^2) is equal to:

The area of the region bounded by the curve y^2=4x and x=1 is:

The general solution of the differential equation dy/dx = e^(x+y) is: