Quantitative Ability Quiz 29

If f(x) = x³ – 4x + p, f(0) and f(1) are of opposite signs, then which of the following is necessarily true?

If a man cycles at 10 km/hr, then the arrives at a certain place at 1 p.m. If the cycles at 15 km/hr, he will arrive at the same place at 11 a.m. At what speed must he cycle to get there at noon?

In the adjoining figure, chord ED is parallel to the diameter AC of the circle. If angle CBE = 65 °, then what is the value of angle DEC?

What is the greatest possible speed a train can run 65 km and 95km in exact number of minutes?

A student is asked to form numbers between 3000 and 9000 with digits 2, 3, 5, 7 and 9. If no digit is to be repeated, in how many ways can the student do so?

11 balls are distributed among 4 boxes. The probability that the 1^st box contains 4 balls is:

Consider the set S = {1, 2, 3, . . ., 1000}. How many arithmetic progressions can be formed from the elements of S that start with 1 and end with 1000 and have at least 3 elements?

If a, b, c are the sides of a triangle, and a² + b² + c² = bc + ca + ab, then the triangle is:

P, Q, S and R are points on the circumference of a circle of radius r, such that PQR is an equilateral triangle and PS is a diameter of the circle. What is the perimeter of the quadrilateral PQSR?

A and B starts together from the same point on a circular track and walk in the same direction till they both again arrive together at the starting point. A completes one complete round in 224 s and B in 364 s. How many times will A have passed B?