Punjab Board Class 12 Mathematics — Important Questions 2026

If f : R → R is defined by f(x) = x² − 3x + 2, find f(f(x)) when x = 0.

Let R be a relation on the set A = {1, 2, 3} defined as R = {(1,1),(2,2),(3,3),(1,2),(2,1),(2,3),(1,3)}. Which property does R fail to satisfy?

Let f : A → B and g : B → C be two functions. If gof is onto, which of the following must be true?

How many bijective functions can be defined from a set A = {a, b, c, d} to itself?

The range (principal value branch) of sin⁻¹(x) is:

Find the principal value of cos⁻¹(-1/2).

The value of sin⁻¹(-1/2) is:

The range of the principal value branch of tan⁻¹(x) is:

If A = [[2, 1], [1, 3]] and A² - 5A + kI = O, then the value of k is:

The number of 3×3 matrices with entries from {0, 1, 2} such that the matrix is symmetric equals:

If A = [[0, 1], [-1, 0]], then A²⁰²³ equals:

If the matrix A = [[1, 2, x], [2, 1, 0], [x, 0, 1]] is symmetric and A' = A, find x if the (1,3) entry equals the (3,1) entry. For A to also satisfy A² = 5A - 4I, what is x?