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

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)`?

The function f(x) = tanx – x ______.

The values of a for which the function f(x) = sinx – ax + b increases on R are ______.

The function f(x) = `(2x^2 - 1)/x^4`, x > 0, decreases in the interval ______.

Let A = { 2, 3, 6 } Which of the following relations on A are reflexive?

Let R be the relation on N defined as by x + 2 y = 8 The domain of R is ____________.

Which of the following is not an equivalence relation on I, the set of integers: x, y