Arts (English Medium) कक्षा १२ - CBSE Question Bank Solutions for Mathematics

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 ______.

Evaluate the following:

`int x/(sqrt(x) + 1) "d"x`  (Hint: Put  `sqrt(x)` = z)

Evaluate the following:

`int sqrt(("a" + x)/("a" - x)) "d"x`

Evaluate the following:

`int x^(1/2)/(1 + x^(3/4)) "d"x`   (Hint: Put `sqrt(x)` = z⁴)

If A = `[(0,0,0),(0,0,0),(0,1,0)]` then A is ____________.

A square matrix A = [a_ij]_nxn is called a diagonal matrix if a_ij = 0 for ____________.

Find the differential equation of all non-horizontal lines in a plane.

If `[("a","b"),("c", "-a")]`is a square root of the 2 x 2 identity matrix, then a, b, c satisfy the relation ____________.

Solution of the differential equation `"dx"/x + "dy"/y` = 0 is ______.

The solution of the differential equation `x "dt"/"dx" + 2y` = x² is ______.

The number of arbitrary constants in a particular solution of the differential equation tan x dx + tan y dy = 0 is ______.