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

Evaluate the definite integral:

`int_0^1 (xe^x + sin  (pix)/4)`

`int_1^(sqrt3)dx/(1+x^2) ` equals:

`int_0^(2/3) dx/(4+9x^2)` equals:

Evaluate : \[\int\frac{x \cos^{- 1} x}{\sqrt{1 - x^2}}dx\] .

`sin xy + x/y` = x² – y

sec(x + y) = xy

tan^–1(x² + y²) = a

(x² + y²)² = xy

If ax² + 2hxy + by² + 2gx + 2fy + c = 0, then show that `"dy"/"dx" * "dx"/"dy"` = 1 

If x sin (a + y) + sin a cos (a + y) = 0, prove that `"dy"/"dx" = (sin^2("a" + y))/sin"a"`

If y = tan^–1x, find `("d"^2y)/("dx"^2)` in terms of y alone.

The derivative of cos^–1(2x² – 1) w.r.t. cos^–1x is ______.

If y = 5 cos x – 3 sin x, then `("d"^2"y")/("dx"^2)` is equal to:

Derivative of cot x° with respect to x is ____________.

If y = `sqrt(ax + b)`, prove that `y((d^2y)/dx^2) + (dy/dx)^2` = 0.

If x = A cos 4t + B sin 4t, then `(d^2x)/(dt^2)` is equal to ______.

If y = tan x + sec x then prove that `(d^2y)/(dx^2) = cosx/(1 - sinx)^2`.

If x = a cos t and y = b sin t, then find `(d^2y)/(dx^2)`.

Read the following passage and answer the questions given below:

1. Find the rate of growth of the plant with respect to the number of days exposed to the sunlight.
2. Does the rate of growth of the plant increase or decrease in the first three days? What will be the height of the plant after 2 days?

Evaluate : `int_0^4(|x|+|x-2|+|x-4|)dx`