ISC (Commerce) कक्षा १२ - CISCE Important Questions for Applied Mathematics

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

Assertion: Let the matrices A = `((-3, 2),(-5, 4))` and B = `((4, -2),(5, -3))` be such that A¹⁰⁰B = BA¹⁰⁰

Reason: AB = BA implies AB = BA for all positive integers n.

If A and B are symmetric matrices of the same order, then AB – BA 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.

A matrix which is both symmetric and skew symmetric matrix is a ______.

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`