Quantitative Aptitude - Arithmetic Ability Questions

In the following question, select the related number from the given alternatives.
 
47 : 57 : : 93 : ?

P does half as much work as Q in 1/3 of the time. If together they take 15 days to complete a work, how many days will P take to do it alone?

Three solid spheres of radius 3 cm, 4 cm and 5 cm are melted and recasted into a solid sphere. What will be the percentage decrease in the surface area?

If the number 247_679 is completely divisible by 9, then the smallest whole number in the place of the blank digit will be

Find the number of prime factor of 1024.

Convert decimal number 101 to binary.

PQ is a diameter of a circle with centre O. RS is a chord parallel to PQ subtends an angle of 40° at the centre of the circle. If PR and QS are produced to meet at T, then what will be the measure (in degrees) of ∠PTQ?

D and E are points on the sides AB and AC respectively of ΔABC such that DE is parallel to BC and AD:DB = 4:5, CD and BE intersect each other at F. Then the ratio of the areas of ΔDEF and ΔCBF