Revision Test - Mistakes

Find the value of x
3
−
x
3

1
​
when x−
x
1
​
=5.

Only two candidate were contesting against each other in an election of a village. One candidate got 43.5% votes and was defeated by 3744 votes. How many votes did the winning candidate get?

The sum of three prime numbers is 90. If one of them exceeds another by 30, then one of the numbers is:

A retailer offers the following discount schemes for buyers on an item.
i) Two successive discount of 20%.
ii) A discount of 25% followed by a discount of 15%.
iii) A discount of 40%.
Under which scheme(s) will the selling price be minimum?

If cosθ=sin(2θ)

=0, what is the value of cos
4
θ+sin
4
θ+cos
3
θ+sin
3
θ+sin
2
θ+cos
2
θ+sinθ+cosθ?