Quantitative Aptitude - Arithmetic Ability Questions

If x = 1 + √2 + √3 , then the value of 2x4 - 8x3 - 5x2 + 26x - 28 is

If x = a cosθ+ b sinθ and y = b cosθ- a sinθ, then x2 + y2 is equal to

A ladder 20 m long is leaning against a vertical wall. It makes an angle of 30 deg with the ground. How high on the wall does the ladder reach?

Two chords AB and CD of a circle with centre O intersect at P. If ∠APC = 40°. Then the value of ∠AOC + ∠BOD is

Simple interest on a certain sum of money for 3 years at 18% per annum is half the compound interest on Rs. 9000 for 2 years at 10% per annum. The sum placed on simple interest is:

A sum of money invested for 2 yrs and 9 months at the rate of 8% simple interest per annum became Rs.732 at the end of the period. What was the sum that was initially invested?

There are two numbers such that the first number is half of the second number. If their average is 57, then what is the first number?

In what time will Rs.4400 become Rs.4576 at 8% per annum interest compounded half-yearly?