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

The probability that a student will pass the final examination in both English and Hindi is 0.5 and the probability of passing neither is 0.1. If the probability of passing the English examination is 0.75, what is the probability of passing the Hindi examination?

In a class of 60 students, 30 opted for NCC, 32 opted for NSS and 24 opted for both NCC and NSS. If one of these students is selected at random, find the probability that

1. The student opted for NCC or NSS.
2. The student has opted neither NCC nor NSS.
3. The student has opted NSS but not NCC.

A die has two faces each with number ‘1’, three faces each with number ‘2’ and one face with number ‘3’. If die is rolled once, determine

1. P(2)
2. P(1 or 3)
3. P(not 3)

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 one ticket.

Out of 100 students, two sections of 40 and 60 are formed. If you and your friend are among the 100 students, what is the probability that

1. you both enter the same sections?
2. you both enter the different sections?

Three letters are dictated to three persons and an envelope is addressed to each of them, the letters are inserted into the envelopes at random so that each envelope contains exactly one letter. Find the probability that at least one letter is in its proper envelope.

Let A = {1, 2, 3} and B = {3, 4}. Find A × B and show it graphically.

Convert the following products into factorials:

5 · 6 · 7 · 8 · 9 · 10

Convert the following products into factorials: 

3 · 6 · 9 · 12 · 15 · 18

Convert the following products into factorials: 

(n + 1) (n + 2) (n + 3) ... (2n)

Convert the following products into factorials:

1 · 3 · 5 · 7 · 9 ... (2n − 1)

Prove that: n! (n + 2) = n! + (n + 1)!

If (n + 2)! = 60 [(n − 1)!], find n. 

If (n + 1)! = 90 [(n − 1)!], find n.

If (n + 3)! = 56 [(n + 1)!], find n.

If \[\frac{(2n)!}{3! (2n - 3)!}\]  and \[\frac{n!}{2! (n - 2)!}\]  are in the ratio 44 : 3, find n.

Prove that: 

Prove that:

\[\frac{n!}{(n - r)! r!} + \frac{n!}{(n - r + 1)! (r - 1)!} = \frac{(n + 1)!}{r! (n - r + 1)!}\]

Prove that: