CBSE 12 Maths Question Paper-2024 Set-3

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 restrictions imposed on decision variables involved in an objective function of a linear programming problem are called:

A function f : R+ -> R (where R+ is the set of all non-negative real numbers) defined by f(x) = 4x + 3 is:

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

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

The value of the determinant of a diagonal matrix A of order 3, whose diagonal elements are 2, 3, 4 is:

If A and B are two skew symmetric matrices, then (AB+BA) is:

If y = xⁿ then x(dy/dx) is:

The anti-derivative of f(x) = tan x is:

The area of the region bounded by y = sin x, x-axis, x=0, and x=π is:

The differential equation representing the growth of bacteria is given as: dP/dt = kP, where P is the number of bacteria at time t, and k is a constant. This is a differential equation of:

If a⃗ and b⃗ are two vectors, then |a⃗ x b⃗|² = |a⃗|²|b⃗|² - (a⃗.b⃗)² is known as:

The value of ∫[1,2] x⁻¹ dx 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:

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

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:

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

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

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

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

A bag contains 5 red and 3 black balls. If 2 balls are drawn at random without replacement, the probability that both balls are red is:

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

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

The feasible region of a linear programming problem is shown in the figure. Let Z = ax + by be the objective function. Maximum value of Z will be at:

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: