Commerce (English Medium) Class 12 - CBSE Question Bank Solutions for Mathematics

Let the relation R be defined on the set A = {1, 2, 3, 4, 5} by R = {(a, b) : |a² – b²| < 8. Then R is given by ______.

Let R = {(3, 1), (1, 3), (3, 3)} be a relation defined on the set A = {1, 2, 3}. Then R is symmetric, transitive but not reflexive.

Every relation which is symmetric and transitive is also reflexive.

An integer m is said to be related to another integer n if m is a integral multiple of n. This relation in Z is reflexive, symmetric and transitive.

The relation R on the set A = {1, 2, 3} defined as R = {{1, 1), (1, 2), (2, 1), (3, 3)} is reflexive, symmetric and transitive.

If f(x) = 2x and g(x) = `x^2/2 + 1`, then which of the following can be a discontinuous function ______.

The function f(x) = `(4 - x^2)/(4x - x^3)` is ______.

The function f(x) = `"e"^|x|` is ______.

Let f(x) = |sin x|. Then ______.

If f.g is continuous at x = a, then f and g are separately continuous at x = a.

Prove that the function f(x) = tanx – 4x is strictly decreasing on `((-pi)/3, pi/3)`

Determine for which values of x, the function y = `x^4 – (4x^3)/3` is increasing and for which values, it is decreasing.

Show that f(x) = 2x + cot^–1x + `log(sqrt(1 + x^2) - x)` is increasing in R

Show that for a ≥ 1, f(x) = `sqrt(3)` sinx – cosx – 2ax + b ∈ is decreasing in R

Show that f(x) = tan^–1(sinx + cosx) is an increasing function in `(0, pi/4)`

The interval on which the function f(x) = 2x³ + 9x² + 12x – 1 is decreasing is ______.

Let the f : R → R be defined by f (x) = 2x + cosx, then f : ______.

y = x(x – 3)² decreases for the values of x given by : ______.

The function f(x) = 4 sin³x – 6 sin²x + 12 sinx + 100 is strictly ______.

Which of the following functions is decreasing on `(0, pi/2)`?