Commerce (English Medium) Class 11 - CBSE Question Bank Solutions

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)`

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 + sec 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):

`x/(sin^n x)`

If `2/11` is the probability of an event, what is the probability of the event ‘not A’.

A letter is chosen at random from the word ‘ASSASSINATION’. Find the probability that letter is

1. a vowel
2. an consonant

If E and F are events such that P(E) = `1/4`, P(F) = `1/2` and P(E and F) = `1/8`, find

1. P(E or F)
2. P(not E and not F).

A and B are events such that P(A) = 0.42, P(B) = 0.48 and P(A and B) = 0.16. Determine P(not A).

A and B are events such that P(A) = 0.42, P(B) = 0.48 and P(A and B) = 0.16. Determine P (not B)

A and B are events such that P(A) = 0.42, P(B) = 0.48 and P(A and B) = 0.16. Determine P(A or B).

In Class XI of a school 40% of the students study Mathematics and 30% study Biology. 10% of the class study both Mathematics and Biology. If a student is selected at random from the class, find the probability that he will be studying Mathematics or Biology.

In an entrance test that is graded on the basis of two examinations, the probability of a randomly chosen student passing the first examination is 0.8 and the probability of passing the second examination is 0.7. The probability of passing at least one of them is 0.95. What is the probability of passing both?