A square is inscribed in a circle x 2 + y 2 + 2x + 2y + 1 = 0 and its sides are parallel to coordinate axes. Which one of the following is a vertex of the square?

$(-1+\frac{1}{\sqrt{2}},-1-\frac{1}{\sqrt{2}})$

If 3x + y - 5 = 0 is the equation of a chord of the circle x^2 + y^2 - 25 = 0, then what are the coordinates of the mid-point of the chord ?

$ \left(\frac{3}{2}, \frac{1}{2}\right) $

$ \left(\frac{3}{4}, \frac{1}{4}\right)$

$ \left(\frac{3}{4},-\frac{1}{4}\right) $

$ \left(\frac{3}{2},-\frac{1}{2}\right)$

Circle — NDA Previous Year Questions

20 solved PYQs · 2021–2025 · Mathematics

Solved PYQs: 20
Years covered: 2021–2025
Avg / year: ~4
Subject: Mathematics

How many NDA questions come from Circle?

Circle has contributed 20 questions to National Defence Academy Examination papers between 2021 and 2025 — an average of about 4 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 20 questions carries a written, step-by-step solution, and each is tagged to Circle 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 Circle questions from real NDA papers

These are 5 real questions from the bank — exactly as asked, with the answer one tap away. All 20 Circle questions (with full written solutions) are available in practice.

Question 1 · NDA 2025
What is the equation of the circle whose diameter is 10 cm and the equations of two of its diameters are x+y=0 and x−y=0?
1. (A) $x^2+y^2=1$
2. (B) $x^2+y^2=25$
3. (C) $x^2+y^2=100$
4. (D) $x^2+y^2-2x-2y-23=0$
Show answerAnswer
$Answer: (B) x^2+y^2=25$
Question 2 · NDA 2025
A square is inscribed in a circle x 2 + y 2 + 2x + 2y + 1 = 0 and its sides are parallel to coordinate axes. Which one of the following is a vertex of the square?
1. (A) $(-2,2)$
2. (B) $(-2,-2)$
3. (C) $(- 1 + \frac{1}{2}, - 1 - \frac{1}{2})$
4. (D) $None of the above$
Show answerAnswer
$Answer: (C) (- 1 + \frac{1}{2}, - 1 - \frac{1}{2})$
Question 3 · NDA 2024
The equation of a circle is

(x^2 - 4x + 3) + (y^2 - 6y + 8) = 0

Which of the following statements are correct?

I. The end points of a diameter of the circle are at (1, 2) and (3, 4).

II. The end points of a diameter of the circle are at (1, 4) and (3, 2).

III. The end points of a diameter of the circle are at (2, 4) and (4, 2).

Select the answer using the code given below.
1. (A) $I and II only$
2. (B) $II and III only$
3. (C) $I and III only$
4. (D) $I, II and III$
Show answerAnswer
$Answer: (A) I and II only$
Question 4 · NDA 2023
If 3x + y - 5 = 0 is the equation of a chord of the circle x^2 + y^2 - 25 = 0, then what are the coordinates of the mid-point of the chord ?
1. (A) $(\frac{3}{4}, \frac{1}{4})$
2. (B) $(\frac{3}{2}, \frac{1}{2})$
3. (C) $(\frac{3}{4}, - \frac{1}{4})$
4. (D) $(\frac{3}{2}, - \frac{1}{2})$
Show answerAnswer
$Answer: (B) (\frac{3}{2}, \frac{1}{2})$
Question 5 · NDA 2023
Consider the following in respect of the circle 4x2 + 4y2 - 4ax - 4ay + a2 = 0:
1. The circle touches both the axes.
1. The diameter of the circle is 2a.
1. The centre of the circle lies on the line x + y = a.
How many of the statements given above are correct?
1. (A) $Only one$
2. (B) $Only two$
3. (C) $All three$
4. (D) $None$
Show answerAnswer
$Answer: (B) Only two$

Circle questions by year

Year	Questions	Share of chapter questions
2025	3
2024	6
2023	4
2022	3
2021	4

Practise these 20 questions with solutions

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FAQs

How many NDA questions have been asked from Circle?

EByAi's bank holds 20 real NDA questions from Circle, asked between 2021 and 2025 — about 4 per year on average. Every count is measured from actual papers, not estimated.

Is Circle important for NDA?

20 questions over 5 papers make Circle a steady-weightage chapter in NDA Mathematics. The year-wise table above shows exactly how often it appears.

Can I solve Circle 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.

More NDA Mathematics chapters

All NDA Mathematics chapters →NDA overview →