The minimum possible value of (x² − 6x + 10)/(3 − x), for x < 3, is

In a triangle ABC, AB = AC = 8 cm. A circle drawn with BC as diameter passes through A. Another circle drawn with center at A passes through B and C. Then, the area in sq. cm, of the overlapping region between the two circles is

A group of N people worked on a project. They finished 35% of the project by working 7 hours a day for 10 days. Thereafter, 10 people left the group and the remaining people finished the rest of the project in 14 days by working 10 hours a day. Then the value of N is

If (√(7/5))^(3x − y) = 875/2401 and (4a/b)^(6x − y) = (2a/b)^(y − 6x), for all non-zero real values of a and b, then the value of x + y is

Moody takes 30 seconds to finish riding an escalator if he walks on it at his normal speed in the same direction. He takes 20 seconds to finish riding the escalator if he walks at twice his normal speed in the same direction. If Moody decides to stand still on the escalator, then…

In an examination, the average marks of students in sections A and B are 32 and 60, respectively. The number of students in section A is 10 less than that in section B. If the average marks of all the students across both the sections combined is an integer, then the difference b…

Two cars travel from different locations at constant speeds. To meet each other after starting at the same time, they take 1.5 hours if they travel towards each other, but 10.5 hours if they travel in the same direction. If the speed of the slower car is 60 km/hr, then the distan…

The arithmetic mean of all the distinct numbers that can be obtained by rearranging the digits in 1421, including itself, is

Suppose k is any integer such that the equation 2x² + kx + 5 = 0 has no real roots and the equation x² + (k − 5)x + 1 = 0 has two distinct real roots for x. Then, the number of possible values of k is