CAT Quadratic Equations Questions & Solutions

A sample of real CAT Quadratic Equations past-year questions, each with a worked solution and the correct answer highlighted. AthenaPrep has 48 Quadratic Equations questions in all — sign up free to practise them timed.

1. Q1.CAT 2025

   A value of $c$ for which the minimum value of $f(x)=x^{2}-4cx+8c$ is greater than the maximum value of $g(x)=-x^{2}+3cx-2c$, is

   • $2$

   • $\dfrac{1}{2}$

   • $-\dfrac{1}{2}$

   • $-2$

2. Q2.CAT 2025

   The equations $3x^{2}-5x+p=0$ and $2x^{2}-2x+q=0$ have one common root. The sum of the other roots of this equations is

   • $\frac{8}{3}-p+\frac{3}{2}q$

   • $\frac{2}{3}-p+\frac{3}{2}q$

   • $\frac{8}{3}+p+\frac{1}{3}q$

   • $\frac{2}{3}-2p+\frac{2}{3}q$

3. Q3.CAT 2024

   lf the equations $x^{2}+mx+9=0, x^{2}+nx+17=0$ and $x^{2}+(m+n)x+35=0$ have a common negative root, then the value of $(2m+3n)$ is

   Answer: 38

4. Q4.CAT 2023

   The sum of all possible values of x satisfying the equation $2^{4x^{2}}-2^{2x^{2}+x+16}+2^{2x+30}=0$, is

   • $3$

   • $\frac{3}{2}$

   • $\frac{5}{2}$

   • $\frac{1}{2}$

5. Q5.CAT 2022

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

   • 9

   • 7

   • 8

   • 13

6. Q6.CAT 2021

   If r is a constant such that $\mid x^2 - 4x - 13 \mid = r$ has exactly three distinct real roots, then the value of r is

   • 17

   • 21

   • 15

   • 18

7. Q7.CAT 2020

   How many disticnt positive integer-valued solutions exist to the equation $(x^{2}-7x+11)^{(x^{2}-13x+42)}=1$ ?

   • 8

   • 4

   • 2

   • 6

8. Q8.CAT 2019

   Let A be a real number. Then the roots of the equation $x^2 - 4x - log_{2}{A} = 0$ are real and distinct if and only if

   • $A > \frac{1}{16}$

   • $A < \frac{1}{16}$

   • $A < \frac{1}{8}$

   • $A > \frac{1}{8}$

9. Q9.CAT 2018

   If $U^{2}+(U-2V-1)^{2}$= −$4V(U+V)$ , then what is the value of $U+3V$ ?

   • $0$

   • $\dfrac{1}{2}$

   • $\dfrac{-1}{4}$

   • $\dfrac{1}{4}$

10. Q10.CAT 2007

    A quadratic function f(x) attains a maximum of 3 at x = 1. The value of the function at x = 0 is 1. What is the value of f (x) at x = 10?

    • -119

    • -159

    • -110

    • -180

    • -105

11. Q11.CAT 2002

    Davji Shop sells samosas in boxes of different sizes. The samosas are priced at Rs. 2 per samosa up to 200 samosas. For every additional 20 samosas, the price of the whole lot goes down by 10 paise per samosa. What should be the maximum size of the box that would maximise the revenue?

    • 240

    • 300

    • 400

    • None of these

12. Q12.CAT 1996

    Given the quadratic equation $x^2 - (A - 3)x - (A - 2)$, for what value of $A$ will the sum of the squares of the roots be zero?

    • -2

    • 3

    • 6

    • None of these

CAT Quadratic Equations previous year questions with solutions — AthenaPrep