Quantitative Aptitude - Arithmetic Ability Questions

If x = 313- 3-13, then 3x2 + 9xis equal to

What is the value of sin (B – C) cos (A – D) + sin (A – B) cos (C – D) + sin (C – A) cos (B – D)?

What should be added to 5(2x-y) to obtain 4(2x - 3y) + 5(x + 4y)?

If 3x+22x+1 = a2x+1+bx+2 be an identity, then the value of b

The average marks obtained by a group of 16 students was 20. One student left the group as a result of which the average of the remaining students rose to 21. But another student joined, as a result of which the average marks of the group dropped a bit and became 20.5. What was the average marks obtained by the student who left and the one who joined?

Divide 32 into two parts such that the sum of the square of the parts is 674. What is the value of the parts?

The length of diagonal BD of a parallelogram ABCD is 36 cm. P and Q are the centroids of triangle ABC and triangle ADC respectively. What is the length (in cm) of PQ?

By increasing the price of entry ticket to a fair in the ratio 7:17, the number of visitors to the fair has decreased in the ratio 9:5. In what ratio has the total collection increased or decreased?