ISC (Commerce) Class 12 - CISCE Important Questions

Let \[f\left(x\right) = x^3\] be a function with domain {0, 1, 2, 3}. Then domain of \[f^{-1}\] is ______.

A relation R on (1, 2, 3) is given by R = {(1, 1), (2, 2), (1, 2), (3, 3), (2, 3)}. Then the relation R is ______.

If f(x) = [4 – (x – 7)³]^1/5 is a real invertible function, then find f^–1(x).

Let A = R – {2} and B = R – {1}. If f: A `→` B is a function defined by f(x) = `(x - 1)/(x - 2)` then show that f is a one-one and an onto function.

Let L be a set of all straight lines in a plane. The relation R on L defined as 'perpendicular to' is ______.

Which one of the following graphs is a function of x?

Graph A	Graph B

Let `f : R {(-1)/3} → R - {0}` be defined as `f(x) = 5/(3x + 1)` is invertible. Find f^–1(x).

If f : R `rightarrow` R is defined by `f(x) = (2x - 7)/4`, show that f(x) is one-one and onto.

Statement 1: The intersection of two equivalence relations is always an equivalence relation.

Statement 2: The Union of two equivalence relations is always an equivalence relation.

Which one of the following is correct?

If cos^-1 x + cos ^-1 y + cos ^-1 z = π , prove that x² + y² + z² + 2xyz = 1.

If y = `(x sin^-1 x)/sqrt(1 -x^2)`, prove that: `(1 - x^2)dy/dx = x + y/x`

If `tan^-1 ((x - 1)/(x + 1)) + tan^-1 ((2x - 1)/(2x + 1)) = tan^-1 (23/36)` = then prove that 24x² – 23x – 12 = 0

The value of cosec `[sin^-1((-1)/2)] - sec[cos^-1((-1)/2)]` is equal to ______.

Solve for x: `sin^-1(x/2) + cos^-1x = π/6`

If sin^–1x + sin^–1y + sin^–1z = π, show that `x^2 - y^2 - z^2 + 2yzsqrt(1 - x^2) = 0`