Inequality Maximization / Minimization — CAT Previous-Year Questions with Solutions

CAT 2022 Slot 3 · QA

Q1.

The minimum possibe value of $\frac{x^{2} - 6 x + 10}{3 - x}$ , for x < 3, is

CAT 2022 Slot 3 · QA

Q2.

If c = $\frac{16 x}{y}$ + $\frac{49 y}{x}$ for some non-zero real numbers x and y, then c cannot take the value

CAT 2018 Slot 2 · QA

Q3.

If the sum of squares of two numbers is 97, then which one of the following cannot be their product?

CAT 2017 Slot 1 · QA

Q4.

If a, b, c, and d are integers such that a + b + c + d = 30, then the minimum possible value of (a - b)² + (a - c)² + (a - d)² is

CAT 2003 Slot 1 · QA

Passage / Data

Each question is followed by two statements, A and B. Answer each question using the following instructions

Choose 1 if the question can be answered by using one of the statements alone but not by using the other statement alone.
Choose 2 if the question can be answered by using either of the statements alone.
Choose 3 if the question can be answered by using both statements together but not by either statement alone.
Choose 4 if the question cannot be answered on the basis of the two statements.

Q5.

Let a, b, c, d be four integers such that a + b + c + d = 4m + 1 where m is a positive integer. Given m, which one of the following is necessarily true?

CAT 2003 Slot 1 · QA

Passage / Data

Each question is followed by two statements, A and B. Answer each question using the following instructions

Choose 1 if the question can be answered by using one of the statements alone but not by using the other statement alone.
Choose 2 if the question can be answered by using either of the statements alone.
Choose 3 if the question can be answered by using both statements together but not by either statement alone.
Choose 4 if the question cannot be answered on the basis of the two statements.

Q6.

If x, y, z are distinct positive real numbers, then $\frac{x^{2} (y + z) + y^{2} (x + z) + z^{2} (x + y)}{x y z}$ would be

CAT 2001 · QA

Q7.

If a, b, c and d are four positive real numbers such that abcd = 1, what is the minimum value of (1 + a)(1 + b)(1 + c)(1 + d)?

CAT 2001 · QA

Passage / Data

Q8.

Let x, y be two positive numbers such that x + y = 1. Then, the minimum value of ${(x + \frac{1}{x})}^{2} + {(y + \frac{1}{y})}^{2}$ is ______.

Inequality Maximization / Minimization — CAT Previous-Year Questions

Inequality Maximization / Minimization · CAT PYQs