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

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)/(px^2 + qx + r)`

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):

`(px^2 +qx + r)/(ax +b)`

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/x^4 = b/x^2 + 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):

`4sqrtx - 2`

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

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