CBSE 12 Maths Question Paper-2024 Set-4

If a matrix A = [[tan x, 1], [-1, tan x]] and A + A' = 2√3I, where A' is the transpose of matrix A and I is an identity matrix, then the value of x∈[0,π/2] is:

If a matrix has 36 elements, the number of possible orders it can have is:

The value of ∫[1,2] x⁻¹ dx is:

The range of the function f(x)=tan⁻¹(x) is:

If for the matrix A = [[tan x, 1], [-1, tan x]], A + A' = 2√3I, then the value of x∈[0,π/2] is:

The differential equation dy/dx=F(x,y) will not be a homogeneous differential equation, if F(x,y) is:

The value of ∫[1,2] x⁻¹ dx is:

If the sides of a square are decreasing at the rate of 1.5 cm/s, the rate of decrease of its perimeter is:

The number of arbitrary constants in the particular solution of a differential equation of order 2 is:

A random variable X has the following probability distribution: X: 1, 2, 3, 4, 5. P(X=x): 0.1, 0.2, 0.3, 0.2, 0.2. The mean of the distribution is:

In a linear programming problem, the constraints are always expressed in the form of:

The common region determined by all the constraints of a linear programming problem is called:

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

If the sum of two unit vectors is a unit vector, then the magnitude of their difference is:

The probability of getting a 'success' in a single trial is 1/2, then the probability of getting 3 successes in 5 trials is:

If the sum of all the elements of a 3x3 scalar matrix is 9, then the product of all its elements is:

A student may spend 1 hour to 6 hours in a day in upskilling self. The probability that a randomly chosen student spends at least 3 hours in a day in upskilling self is:

If A is a 3x3 matrix and |adjA| = k, then |A⁻¹| is equal to:

Assertion (A): For any symmetric matrix A, B'AB is a skew-symmetric matrix. Reason (R): A square matrix P is skew-symmetric if P' = -P. Choose the correct option:

Assertion (A): (b⃗ . c⃗) a⃗ is a scalar quantity. Reason (R): Dot product of two vectors is a scalar quantity. Choose the correct option: