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

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:

If ⁿP₄ = 360, find the value of n.