IPMAT Rohtak 2019 (QA) PYQs

A natural number $n$ lies between $100$ and $400$, and the sum of its digits is $10$. The probability that $n$ is divisible by $4$, is

The expression 2x³ + ax² + bx + 3, where a and b are constants, has a factor of x-1 and leaves a remainder of 15 when divided by x + 2. Then, (a, b) =

Given below are two statements:

Statement (I): The difference, the sum, and the product of two numbers are in the ratio 1: 5: 12. The product of the two numbers is 18.

Statement (II): The last digit in the decimal representation of 2⁹¹ is 6.

In light of the above statements, choose the most appropriate answer from the options given below.