Commerce (English Medium) इयत्ता ११ - CBSE Question Bank Solutions for Mathematics

If 4-digit numbers greater than 5,000 are randomly formed from the digits 0, 1, 3, 5, and 7, what is the probability of forming a number divisible by 5 when, the repetition of digits is not allowed?

Find the derivative of `x^n  + ax^(n-1) + a^2 x^(n-2) + ...+ a^(n -1) x + a^n` for some fixed real number a.

For some constants a and b, find the derivative of (x – a) (x – b).

For some constants a and b, find the derivative of (ax² + b)².

For some constants a and b, find the derivative of `(x - a)/(x - b)`.

Find the derivative of `(x^n - a^n)/(x -a)` for some constant a.

Find the derivative of cos x from first principle.

Find the derivative of the following function.

sin x cos x 

Find the derivative of the following function:

sec x

Find the derivative of the following function:

5 sec x + 4 cos x

Find the derivative of the following function:

cosec x

Find the derivative of the following function:

3cot x + 5cosec x

Find the derivative of the following function:

5sin x – 6cos x + 7

Find the derivative of the following function:

2tan x – 7sec x

Find the derivative of the following function (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

(x² + 1) cos x

Find the derivative of the following function (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

(ax² + sin x) (p + q cos x)

Find the derivative of the following function (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

`(x + cos x)(x - tan x)`

Find the derivative of the following function (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

`(4x + 5sin x)/(3x + 7cos x)`

Find the derivative of the following function (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

`(x^2 cos (pi/4))/sin x`

Find the derivative of the following function (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers):

`x/(1 + tan x)`