Arts (English Medium) Class 11 - CBSE Question Bank Solutions for Mathematics

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):

(ax + b)ⁿ (cx + d)^m

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):

sin (x + a)

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):

cosec x cot 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):

`cos x/(1 + 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):

`(sin x + cos x)/(sin x - 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):

`(sec x - 1)/(sec x + 1)`

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):

sinⁿ 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):

`(a + bsin x)/(c + dcosx)`

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):

`(sin(x + a))/ 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):

x⁴ (5 sin x – 3 cos x)

Which of the following can not be valid assignment of probabilities for outcomes of sample space S = {ω_1, ω_2,ω_3,ω_4,ω_5,ω_6,ω₇}

A die is thrown, find the probability of following events:

1. A prime number will appear,
2. A number greater than or equal to 3 will appear,
3. A number less than or equal to one will appear,
4. A number more than 6 will appear,
5. A number less than 6 will appear.

A card is selected from a pack of 52 cards.

1. How many points are there in the sample space?
2. Calculate the probability that the card is an ace of spades.
3. Calculate the probability that the card is
   
   1. an ace
   2. black card.

A fair coin with 1 marked on one face and 6 on the other and a fair die are both tossed. Find the probability that the sum of numbers that turn up is (i) 3 (ii) 12

There are four men and six women on the city council. If one council member is selected for a committee at random, how likely is it that it is a woman?

A fair coin is tossed four times, and a person win Re 1 for each head and lose Rs 1.50 for each tail that turns up.

From the sample space calculate how many different amounts of money you can have after four tosses and the probability of having each of these amounts.

Three coins are tossed once. Find the probability of getting

1. 3 heads
2. 2 heads
3. at least 2 heads
4. at most 2 heads
5. no head
6. 3 tails
7. exactly two tails
8. no tail
9. atmost two tails.

In a lottery, person chooses six different natural numbers at random from 1 to 20, and if these six numbers match with the six numbers already fixed by the lottery committee, he wins the prize. What is the probability of winning the prize in the game? [Hint: order of the numbers is not important.]

Check whether the following probabilities P(A) and P(B) are consistently defined

P(A) = 0.5, P(B) = 0.7, P(A ∩ B) = 0.6