Science (English Medium) इयत्ता १२ - CBSE Question Bank Solutions

Let A = [–1, 1]. Then, discuss whether the following functions defined on A are one-one, onto or bijective:

k(x) = x² 

Using the definition, prove that the function f: A→ B is invertible if and only if f is both one-one and onto

If the set A contains 5 elements and the set B contains 6 elements, then the number of one-one and onto mappings from A to B is ______.

Let A = {1, 2, 3, ...n} and B = {a, b}. Then the number of surjections from A into B is ______.

Let f: R → R be defined by f(x) = `1/x` ∀ x ∈ R. Then f is ______.

Which of the following functions from Z into Z are bijections?

Let f: R → R be the functions defined by f(x) = x³ + 5. Then f^–1(x) is ______.

Let f: R – `{3/5}` → R be defined by f(x) = `(3x + 2)/(5x - 3)`. Then ______.

Let f: `[2, oo)` → R be the function defined by f(x) = x² – 4x + 5, then the range of f is ______.

Let f: R → R be given by f(x) = tan x. Then f^–1(1) is ______.

If f(x) = (4 – (x – 7)³}, then f^–1(x) = ______.

Let A = {0, 1} and N be the set of natural numbers. Then the mapping f: N → A defined by f(2n – 1) = 0, f(2n) = 1, ∀ n ∈ N, is onto.

Evaluate `tan^-1(sin((-pi)/2))`.

Evaluate tan (tan^–1(– 4)).

Evaluate: `tan^-1 sqrt(3) - sec^-1(-2)`.

Evaluate: `sin^-1 [cos(sin^-1 sqrt(3)/2)]`

Evaluate `cos[sin^-1  1/4 + sec^-1  4/3]`

Prove that `2sin^-1  3/5 - tan^-1  17/31 = pi/4`

Prove that cot^–17 + cot^–18 + cot^–118 = cot^–13

Solve the equation `sin^-1 6x + sin^-1 6sqrt(3)x = - pi/2`