CAT 2020 Slot 1 Previous Year Questions with Detailed Solutions

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 $\log_4 5 = (\log_4 y)(\log_6 \sqrt{5})$, 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 $x = (4096)^{7+4\sqrt{3}}$, then which of the following equals 64?

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