Arts (English Medium) कक्षा ११ - CBSE Question Bank Solutions for Mathematics

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}

Find the union of the following pairs of sets:

A = {1, 2, 3}, B = Φ

Let A = {a, b}, B = {a, b, c}. Is A ⊂ B? What is A ∪ B?

If A and B are two sets such that A ⊂ B, then what is A ∪ B?

If A = {1, 2, 3, 4}, B = {3, 4, 5, 6}, C = {5, 6, 7, 8} and D = {7, 8, 9, 10}; find

A ∪ B

Show that for any sets A and B, A = (A ∩ B) ∪ (A – B) and A ∪ (B – A) = (A ∪ B)