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

Find the multiplicative inverse of the complex number.

–i 

Express the following expression in the form of a + ib.

`((3 + sqrt5)(3 - isqrt5))/((sqrt3 + sqrt2i)-(sqrt3 - isqrt2))`

Reduce `(1/(1-4i) - 2/(1+i))((3-4i)/(5+i))` to the standard form.

If `x – iy = sqrt((a-ib)/(c - id))` prove that `(x^2 + y^2) = (a^2 + b^2)/(c^2 + d^2)`

If α and β are different complex numbers with |β| = 1, then find `|(beta - alpha)/(1-baralphabeta)|`

If (a + ib) (c + id) (e + if) (g + ih) = A + iB, then show that (a² + b²) (c² + d²) (e² + f²) (g² + h²) = A² + B².

If `((1+i)/(1-i))^m` = 1, then find the least positive integral value of m.

Evaluate 8!

Evaluate 4! – 3!

Is 3! + 4! = 7!?

Compute `(8!)/(6! xx 2!)`

if `1/(6!) + 1/(7!) = x/(8!)`, find x

Evaluate `(n!)/((n-r)!)` when  n = 6, r = 2 

Evaluate `(n!)/((n-r)!)`, when n = 9, r = 5

How many 3-digit even numbers can be made using the digits 1, 2, 3, 4, 6, 7, if no digit is repeated?

Find the number of 4-digit numbers that can be formed using the digits 1, 2, 3, 4, 5 if no digit is repeated. How many of these will be even?

From a committee of 8 persons, in how many ways can we choose a chairman and a vice chairman assuming one person cannot hold more than one position?