Science (English Medium) कक्षा ११ - CBSE Question Bank Solutions

`(x^2 cos  pi/4)/sinx`

(sin x + cos x)²

(2x – 7)² (3x + 5)³ 

x² sin x + cos 2x

sin³x cos³x

If `y = sqrt(x) + 1/sqrt(x)`, then`(dy)/(dx)` at x = 1 is  ______.

if `f(x) = (x - 4)/(2sqrt(x))`, then f'(1) is ______.

If `y = (1 + 1/x^2)/(1 - 1/x^2)` then `(dy)/(dx)` is ______.

If `y = (sin x + cos x)/(sin x - cos x)`, then `(dy)/(dx)` at x = 0 is ______.

If `y = (sin(x + 9))/cosx` then `(dy)/(dx)` at x = 0 is ______.

If `f(x) = 1 + x + x^2/2 + ... + x^100/100`, then f'(1) is equal to ______.

If `f(x) = x^100 + x^99 .... +  x + 1`, then f'(1) is equal to ______.

If `f(x) = 1 - x + x^2 - x^3 + ... -x^99 + x^100`, then f'(1) is equal to ______.

If `y = 1 + x/(1!) + x^2/(2!) + x^3/(3!) + ...,` then `(dy)/(dx)` = ______.

In a certain lottery 10,000 tickets are sold and ten equal prizes are awarded. What is the probability of not getting a prize if you buy two tickets.

In a certain lottery 10,000 tickets are sold and ten equal prizes are awarded. What is the probability of not getting a prize if you buy 10 tickets.

Find the union of the following pairs of sets:

X = {1, 3, 5} Y = {1, 2, 3}

Find the union of the following pairs of sets:

A = {a, e, i, o, u}, B = {a, b, c} 

Find the union of the following pairs of sets:

A = {x : x is a natural number and multiple of 3}

B = {x : x is a natural number less than 6}

Find the union of the following pairs of sets:

A = {x : x is a natural number and 1 < x ≤ 6}

B = {x : x is a natural number and 6 < x < 10}