Coordinate Geometry · NDA previous year questions

2026 8 questions

1. Q452026 · 12 Apr 2026

   Passage: Let $X(a,p),Y(b,q)$ and $Z(c,r)$ be the points such that $a,b$ and $c$ are in AP. Question: If $p,q$ and $r$ are in AP, then the points $X,Y$ and $Z$ are

   1. A.on a straight line
   2. B.on a circle
   3. C.on a parabola
   4. D.the vertices of a triangle
   Show answer

   Answer: A

2. Q462026 · 12 Apr 2026

   Passage: The equation of a straight line which passes through the origin and makes an angle $\alpha$ ($0\le \alpha \le 90^{\circ }$) with the line $L:x+\sqrt{3}y+3\sqrt{3}=0$ is $x-\sqrt{3}y=0$. Question: What is the angle made by the line $L$ with positive direction of $y$-axis ?

   1. A.$30^{\circ }$
   2. B.$45^{\circ }$
   3. C.$60^{\circ }$
   4. D.$90^{\circ }$
   Show answer

   Answer: C

3. Q472026 · 12 Apr 2026

   Passage: The equation of a straight line which passes through the origin and makes an angle $\alpha$ ($0\le \alpha \le 90^{\circ }$) with the line $L:x+\sqrt{3}y+3\sqrt{3}=0$ is $x-\sqrt{3}y=0$. Question: What is the value of $\alpha$ ?

   1. A.$30^{\circ }$
   2. B.$45^{\circ }$
   3. C.$60^{\circ }$
   4. D.$90^{\circ }$
   Show answer

   Answer: C

4. Q482026 · 12 Apr 2026

   Passage: Consider the points $A(0,2),B(2,3),C(4,5)$ and $D(0,k)$. Question: If a circle is drawn through $A,B$ and $D$, then what is the diameter of the circle ?

   1. A.$3\sqrt{10}$
   2. B.$5\sqrt{10}$
   3. C.$3\sqrt{12}$
   4. D.$5\sqrt{12}$
   Show answer

   Answer: B

5. Q492026 · 12 Apr 2026

   Passage: Consider the points $A(0,2),B(2,3),C(4,5)$ and $D(0,k)$. Question: If the points lie on a circle, then what is/are the possible value(s) of $k$ ?

   1. A.2 only
   2. B.5 only
   3. C.2, 17
   4. D.5, 17
   Show answer

   Answer: C

6. Q502026 · 12 Apr 2026

   What is the length of the chord of a unit circle which subtends at the centre of the circle an angle of $45^{\circ }$ ?

   1. A.$2\sqrt{2+\sqrt{2}}$ units
   2. B.$2\sqrt{2-\sqrt{2}}$ units
   3. C.$\sqrt{2+\sqrt{2}}$ units
   4. D.$\sqrt{2-\sqrt{2}}$ units
   Show answer

   Answer: D

7. Q942026 · 12 Apr 2026

   Passage: Let $k$ be the area between the curve $y=\sin x$ and x-axis in the interval $\left[0,\frac{\pi }{4}\right]$. Question: What is the area between the curve $y=\cos x$ and the x-axis in the interval $\left[\frac{\pi }{4},\frac{\pi }{2}\right]$ ?

   1. A.$k$
   2. B.$1-k$
   3. C.$\frac{(\pi -k)}{2}$
   4. D.$\frac{(\pi -2k)}{2}$
   Show answer

   Answer: A

8. Q952026 · 12 Apr 2026

   Passage: Let $k$ be the area between the curve $y=\sin x$ and x-axis in the interval $\left[0,\frac{\pi }{4}\right]$. Question: What is the area between the curve $y=\sin x$ and the x-axis in the interval $\left[\frac{\pi }{4},\frac{\pi }{2}\right]$ ?

   1. A.$k$
   2. B.$1-k$
   3. C.$\frac{(\pi -k)}{2}$
   4. D.$\frac{(\pi -2k)}{2}$
   Show answer

   Answer: B