cat 2020 Complete Paper Solution | Slot 1

How many 3-digit numbers are there, for which the product of their digits is more than 2 but less than 7?

If f(5 + x) = f(5 - x) for every real x and f(x) = 0 has four distinct real roots, then the sum of the roots is

Veeru invested Rs 10000 at 5% simple annual interest, and exactly after two years, Joy invested Rs 8000 at 10% simple annual interest. How many years after Veeru’s investment, will their balances, i.e., principal plus accumulated interest, be equal?

A train travelled at one-thirds of its usual speed, and hence reached the destination 30 minutes after the scheduled time. On its return journey, the train initially travelled at its usual speed for 5 minutes but then stopped for 4 minutes for an emergency. The percentage by which the train must now increase its usual speed so as to reach the destination at the scheduled time, is nearest to

If $log_{4}$ 5 = ($log_{4}$ y) ($log_{6}$ √5), then y equals

The number of real-valued solutions of the equation $2^x$ + $2^{-x}$ = 2 - $(x - 2)^2$ is

A straight road connects points A and B. Car 1 travels from A to B and Car 2 travels from B to A, both leaving at the same time. After meeting each other, they take 45 minutes and 20 minutes, respectively, to complete their journeys. If Car 1 travels at the speed of 60 km/hr, then the speed of Car 2, in km/hr, is

Let A, B and C be three positive integers such that the sum of A and the mean of B and C is 5. In addition, the sum of B and the mean of A and C is 7. Then the sum of A and B is

If x = (4096)^{7+4√3}, then which of the following equals 64?

The mean of all 4 digit even natural numbers of the form 'aabb', where a>0, is