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

Let A = {1, 2, 3, 4}, B = {1, 5, 9, 11, 15, 16} and f = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}. Is the following true?

f is a function from A to B

Justify your answer in case.

The following example is the null set example or not?

Set of odd natural numbers divisible by 2

Find the values of other five trigonometric functions if `cos x = -1/2`, x lies in third quadrant.

Find the values of other five trigonometric functions if `sin x = 3/5` x lies in second quadrant.

Find the values of other five trigonometric function if `cot x = 3/4`, x lies in quadrant.

Find the values of other five trigonometric function if `sec x = 13/5`, x  lies in fourth quadrant.

Find the values of other five trigonometric functions if ` tan x = - 5/12`, x lies in second quadrant.

Find the value of the trigonometric function tan `(19pi)/3`.

Find the value of the trigonometric function sin `(-11pi)/3`.

Find the value of the trigonometric function cot `(-(  15pi)/4)`.

Prove that: `2  cos  pi/13 cos  (9pi)/13 + cos  (3pi)/13 + cos  (5pi)/13 = 0`

Prove that: (sin 3x + sin x) sin x + (cos 3x – cos x) cos x = 0

Prove the following by using the principle of mathematical induction for all n ∈ N: 

`1 + 3 + 3^2 + ... + 3^(n – 1) =((3^n -1))/2`

Prove the following by using the principle of mathematical induction for all n ∈ N: 

`1^3 +  2^3 + 3^3 + ... + n^3 = ((n(n+1))/2)^2`

Prove the following by using the principle of mathematical induction for all n ∈ N: 1.2.3 + 2.3.4 + … + n(n + 1) (n + 2)  = `(n(n+1)(n+2)(n+3))/(4(n+3))`

Prove the following by using the principle of mathematical induction for all n ∈ N: 

1.2 + 2.3 + 3.4+ ... + n(n+1) = `[(n(n+1)(n+2))/3]`