If N = (11^(p+7))(7^(q−2))(5^(r+1))(3^s) is a perfect cube, where p, q, r and s are positive integers, then the smallest value of p + q + r + s is:

An institute has 5 departments and each department has 50 students. If students are picked up randomly from all 5 departments to form a committee, what should be the minimum number of students in the committee so that at least one department should have representation of minimum…

AB, CD and EF are three parallel lines, in that order. Let d1 and d2 be the distances from CD to AB and EF respectively. d1 and d2 are integers, where d1: d2 = 2: 1. P is a point on AB, Q and S are points on CD and R is a point on EF. If the area of the quadrilateral PQRS is 30 s…

A dice is rolled twice. What is the probability that the number in the second roll will be higher than that in the first?

ABCD is a rectangle. P, Q and R are the midpoint of BC, CD and DA. The point S lies on the line QR in such a way that SR: QS = 1: 3. The ratio of the area of triangle APS to area of rectangle ABCD is

The Volume of a pyramid with a square base is 200 cubic cm. The height of the pyramid is 13 cm. What will be the length of the slant edges (i.e. the distance between the apex and any other vertex), rounded to the nearest integer?

From the passage: In an innings of a T20 cricket match (a team can bowl for 20 overs) 6...

Read the two statements below: S1: The worst bowler did not bowl the minimum number of overs. S2: The best bowler is a specialist bowler. Which of the above statements or their combinations can help arrive at the minimum number of overs bowled by a non-specialist bowler?

If 5° ≤ x° ≤ 15°, then the value of sin 30° + cos x° − sin x° will be:

In a class of 60, along with English as a common subject, students can opt to major in Mathematics, Physics, Biology or a combination of any two. 6 students major in both Mathematics and Physics, 15 major in both Physics and Biology, but no one majors in both Mathematics and Biol…