Arts (English Medium) Class 12 - CBSE Question Bank Solutions

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)

The value of cos²15° - cos²30° + cos²45° - cos²60° + cos²75° is ______.

The maximum value of sinx + cosx is ____________.

The minimum value of sinx - cosx is ____________.

If `"sec" theta = "x" + 1/(4 "x"), "x" in "R, x" ne 0,`then the value of  `"sec" theta + "tan" theta` is ____________.

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 ______.

The general solution of the differential equation `"dy"/"dx" = "e"^(x - y)` is ______.

The general solution of the differential equation `"dy"/"dx" + y/x` = 1 is ______.

The general solution of the differential equation x(1 + y²)dx + y(1 + x²)dy = 0 is (1 + x²)(1 + y²) = k.

The general solution of the differential equation `"dy"/"dx" + y sec x` = tan x is y(secx – tanx) = secx – tanx + x + k.