Quantitative Aptitude - Arithmetic Ability Questions

If 2 cos θ = 2 – sin θ, then what is the value of cos θ?

If x – (1/x) = 3, then what is the value of (2x4 + 3x3 + 13x2 – 3x + 2) / (3x4 + 3)?

If a - b = -1 and ab = 6, then what is the value of a3- b3?

The least number which when divides 37044, gives the result a perfect cube, is:

The ratio of the curved surface area and total surface area of a right circular cylinder is 2 : 5. If the total surface area is 3080 cm2, then what is the volume (in cm3) of the cylinder?

A helicopter, at an altitude of 1500 m, finds that two ships are sailing towards it, in the same direction. The angles of depression of the ships as observed from the helicopter are 60° and 30°respectively. Distance between the two ships, in metres is

The ratio of money with Ram and Gopal is 7:17 and with Gopal and Krishan is 7:17. If Ram has 490, Krishan has

If (X/4) = (Y/5) = (Z/9), then what is X : Y : Z?