If the roots of the equation are equal, then which one of the following is correct?

$\frac{1}{a}+\frac{1}{c}=\frac{2}{b}$

$\frac{1}{a}+\frac{1}{c}=\frac{1}{2b}$

Which one of the following is a root of the equation?

$\rm \frac{b^2(c^2-a^2)}{2a^2(c^2-b^2)}$

$\rm \frac{b^2(c^2-a^2)}{a^2(c^2-b^2)}$

$\rm \frac{b^2(c^2-a^2)}{a^2(b^2-c^2)}$

$\rm \frac{b^2(c^2-a^2)}{2a^2(b^2-c^2)}$

If f(x) = 9x - 8√x such that g(x) = f(x) - 1, then which one of the following is correct?

g(x) = 0 has only one real root which is an integer

g(x) = 0 has two real roots which are integers

g(x) = 0 has only one real root which is not an integer

Quadratic Equations And Inequalities — NDA Previous Year Questions

39 solved PYQs · 2021–2025 · Mathematics

Solved PYQs: 39
Years covered: 2021–2025
Avg / year: ~8
Subject: Mathematics

How many NDA questions come from Quadratic Equations And Inequalities?

Quadratic Equations And Inequalities has contributed 39 questions to National Defence Academy Examination papers between 2021 and 2025 — an average of about 8 questions a year. That count is measured from EByAi’s bank of 15,695 NDA questions, not estimated from a syllabus. Every one of the 39 questions carries a written, step-by-step solution, and each is tagged to Quadratic Equations And Inequalities within Mathematics, so you can drill this chapter across every year at once instead of hunting through paper PDFs. Practising a chapter’s full PYQ history is the fastest way to learn the patterns examiners reuse.

Sample Quadratic Equations And Inequalities questions from real NDA papers

These are 5 real questions from the bank — exactly as asked, with the answer one tap away. All 39 Quadratic Equations And Inequalities questions (with full written solutions) are available in practice.

Question 1 · NDA 2025
If the roots of the equation are equal, then a, b, c are in
1. (A) $AP$
2. (B) $GP$
3. (C) $HP$
4. (D) $None of the above$
Show answerAnswer
$Answer: (C) HP$
Question 2 · NDA 2025
If the roots of the equation are equal, then which one of the following is correct?
1. (A) $a c = b^{2}$
2. (B) $a + c = 2b$
3. (C) $\frac{1}{a} + \frac{1}{c} = \frac{1}{2 b}$
4. (D) $\frac{1}{a} + \frac{1}{c} = \frac{2}{b}$
Show answerAnswer
$Answer: (D) \frac{1}{a} + \frac{1}{c} = \frac{2}{b}$
Question 3 · NDA 2024
Which one of the following is a root of the equation?
1. (A) $\frac{b ^{2} ( c ^{2} - a ^{2} )}{a ^{2} ( c ^{2} - b ^{2} )}$
2. (B) $\frac{b ^{2} ( c ^{2} - a ^{2} )}{a ^{2} ( b ^{2} - c ^{2} )}$
3. (C) $\frac{b ^{2} ( c ^{2} - a ^{2} )}{2 a ^{2} ( c ^{2} - b ^{2} )}$
4. (D) $\frac{b ^{2} ( c ^{2} - a ^{2} )}{2 a ^{2} ( b ^{2} - c ^{2} )}$
Show answerAnswer
$Answer: (C) \frac{b ^{2} ( c ^{2} - a ^{2} )}{2 a ^{2} ( c ^{2} - b ^{2} )}$
Question 4 · NDA 2024
What is the number of real roots of the equation (x - 1)^2 + (x - 3)^2 + (x - 5)^2 = 0?
1. (A) $None$
2. (B) $Only one$
3. (C) $Only two$
4. (D) $Three$
Show answerAnswer
$Answer: (A) None$
Question 5 · NDA 2024
If f(x) = 9x - 8√x such that g(x) = f(x) - 1, then which one of the following is correct?
1. (A) $g(x) = 0 has no real roots$
2. (B) $g(x) = 0 has only one real root which is an integer$
3. (C) $g(x) = 0 has two real roots which are integers$
4. (D) $g(x) = 0 has only one real root which is not an integer$
Show answerAnswer
$Answer: (B) g(x) = 0 has only one real root which is an integer$

Quadratic Equations And Inequalities questions by year

Year	Questions	Share of chapter questions
2025	8
2024	10
2023	7
2022	6
2021	8

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FAQs

How many NDA questions have been asked from Quadratic Equations And Inequalities?

EByAi's bank holds 39 real NDA questions from Quadratic Equations And Inequalities, asked between 2021 and 2025 — about 8 per year on average. Every count is measured from actual papers, not estimated.

Is Quadratic Equations And Inequalities important for NDA?

39 questions over 5 papers make Quadratic Equations And Inequalities a steady-weightage chapter in NDA Mathematics. The year-wise table above shows exactly how often it appears.

Can I solve Quadratic Equations And Inequalities PYQs online for free?

Yes. EByAi lets you solve NDA past-year questions in the browser with written solutions — free daily practice, no card needed.

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