ISC (Commerce) Class 12 - CISCE Important Questions for Mathematics

If a relation R on the set {a, b, c} defined by R = {(b, b)}, then classify the relation.

Solve:

sin^–1 (x) + sin^–1 (1 – x) = cos^–1 x

If the function f : R → R be defined by f(x) = 2x − 3 and g : R → R by g(x) = x³ + 5, then find the value of (fog)⁻¹ (x).

Let f : W → W be defined as

`f(n)={(n-1, " if n is odd"),(n+1, "if n is even") :}`

Show that f is invertible a nd find the inverse of f. Here, W is the set of all whole
numbers.

The binary operation *: R x R → R is defined as a *b = 2a + b Find (2 * 3)*4

If the function `f(x) = sqrt(2x - 3)` is invertible then find its inverse. Hence prove that `(fof^(-1))(x) = x`

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?

Solve for x:
`tan^-1 [(x-1),(x-2)] + tan^-1 [(x+1),(x+2)] = x/4`

Evaluate: tan `[ 2 tan^-1  (1)/(2) – cot^-1 3]`

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`

Solve for x:

5tan^–1x + 3cot^–1x = 2π