ISC (Science) ISC Class 12 - CISCE Question Bank Solutions for Mathematics

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]`

Solve for x:

5tan^–1x + 3cot^–1x = 2π

Find the value of `tan^-1(x/y) + tan^-1((y - x)/(y + x))`

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

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 ______.

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

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

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`

Solve:

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

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 ______.

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.

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

Graph A	Graph B