Skip to content

Sign in Sign up free

NDA Quadratic Equations questions with solutions

Roots, nature of roots and related equations, plus linear inequalities. 27 questions from our 2016–2025 NDA pattern papers, from the Class 11 Mathematics syllabus. Each has the answer and a full solution.

Also practise: Quadratic Equations for JEE Main · Quadratic Equations for JEE Advanced · Quadratic Equations for CAT

NDA 2025

The equation x^2+kx+9=0 has equal roots forNDA 2025 Maths · easy
If a quadratic with real coefficients has a non-real root, its conjugate is also a root. 2. If a quadratic with rational coefficients has the root…NDA 2025 Maths · medium

NDA 2024

The roots α,β of x^2-6x+4=0 are used to form the sum of reciprocals of their squares, (1)/(α^2+(1)/(β^2. Its value isNDA 2024 Maths · easy
The system of equations 2x-y=3, 4x-2y=7 hasNDA 2024 Maths · easy

NDA 2023

If the roots of the equation ax^2+bx+c=0 are in the ratio 2:3, thenNDA 2023 Maths · medium
If the roots of x^2-(k+2)x+9=0 are real and equal, the product of all possible values of k isNDA 2023 Maths · medium
The number of integers x satisfying (x-1)/(x-4)≤0 isNDA 2023 Maths · hard
If a+b+c=0, then x=1 is a root of ax^2+bx+c=0. 2. A quadratic equation with irrational coefficients cannot have a rational root.NDA 2023 Maths · medium

NDA 2022

The sum of all values of k for which x^2-2(k+1)x+(k+7)=0 has equal roots isNDA 2022 Maths · medium
The system x+2y=3, 2x+ky=6 has infinitely many solutions when k equalsNDA 2022 Maths · medium

NDA 2021

If a+b+c=0, then x=1 is a root of ax^2+bx+c=0. 2. A quadratic equation with real coefficients and negative discriminant has two conjugate complex…NDA 2021 Maths · medium
The system kx+3y=k-3, 12x+ky=k has no solution when k equalsNDA 2021 Maths · hard

NDA 2020

If the roots of the equation x^2-6x+k=0 differ by 2, then k equalsNDA 2020 Maths · medium
The equation x^2-(m-2)x+(m+1)=0 has equal roots for two values of m. Their sum isNDA 2020 Maths · medium
The equation x^2+kx+4=0 has no real roots if and only ifNDA 2020 Maths · easy
If the roots of x^2-6x+k=0 differ by 2, then k equalsNDA 2020 Maths · medium

NDA 2019

If α,β are the roots of x^2-3x+1=0, then (α^2/(β)+(β^2/(α) equalsNDA 2019 Maths · medium
The number of integer values of k for which 2x^2+kx+8>0 for every real x isNDA 2019 Maths · hard
If α,β are the roots of x^2-5x+3=0, the equation whose roots are α+1 and β+1 isNDA 2019 Maths · medium
The inequality x^2+x+1>0 holds for every real x. 2. The equation x^2+2x+3=0 has two distinct real roots.NDA 2019 Maths · easy

NDA 2018

If one root of x^2-9x+k=0 is twice the other, what is the value of k?NDA 2018 Maths · medium
If a>0 and b^2-4ac<0, then ax^2+bx+c>0 for every real x. 2. The equation x^2-x+1=0 has two distinct real roots.NDA 2018 Maths · easy
How many integers x satisfy the inequality x^2-5x-14<0?NDA 2018 Maths · medium

NDA 2017

The set of real x for which (x-2)/(x+3)>0 isNDA 2017 Maths · medium

NDA 2016

If the roots of x^2-5x+k=0 are in the ratio 2:3, then k is equal toNDA 2016 Maths · medium
One root of x^2+px+6=0 is 3. If the equation x^2+px+q=0 has equal roots, then q is equal toNDA 2016 Maths · medium
The number of real solutions of the equation x^2-3|x|+2=0 isNDA 2016 Maths · medium