Science (English Medium) इयत्ता १२ - CBSE Question Bank Solutions for Mathematics

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`

Evaluate `∫_0^(3/2)|x cosπx|dx`

Evaluate `int_(-1)^2|x^3-x|dx`

Evaluate :

`∫_(-pi)^pi (cos ax−sin bx)^2 dx`

find `∫_2^4 x/(x^2 + 1)dx`

Evaluate :

`∫_0^π(4x sin x)/(1+cos^2 x) dx`

If `int_0^a1/(4+x^2)dx=pi/8` , find the value of a.

Evaluate :

`int_e^(e^2) dx/(xlogx)`

Evaluate the integral by using substitution.

`int_0^1 x/(x^2 +1)`dx

Evaluate the integral by using substitution.

`int_0^(pi/2) sqrt(sin phi) cos^5 phidphi`

Evaluate the integral by using substitution.

`int_0^1 sin^(-1) ((2x)/(1+ x^2)) dx`

Evaluate the integral by using substitution.

`int_0^2 xsqrt(x+2)`  (Put x + 2 = `t^2`)

Evaluate the integral by using substitution.

`int_0^(pi/2) (sin x)/(1+ cos^2 x) dx`