Coordinate Geometry · NDA previous year questions

2025 29 questions

1. Q552025 · 14 Sept 2025

   For the following two (02) items: Let A(1, - 1, 0) B(- 2, 1, 8) and C(- 1, 2, 7) are three consecutive vertices of a parallelogram ABCD. What is the fourth vertex D?

   1. A.(0,-2,1)
   2. B.(2,0,-1)
   3. C.(1, 0, 1)
   4. D.(1,2,0)
   Show answer

   Answer: B

2. Q562025 · 14 Sept 2025
   
   1. A.26/77
   2. B.27/77
   3. C.82/237
   4. D.83 / (237)
   Show answer

   Answer: B

3. Q572025 · 14 Sept 2025

   For different values of m, the equation 4y=mx-m+ 2 represents

   1. A.parallel lines
   2. B.concurrent lines
   3. C.lines at a fixed distance from the origin of coordinates
   4. D.the same line
   Show answer

   Answer: B

4. Q582025 · 14 Sept 2025

   The equation of the locus of a point equidistant from the points (a, b) and (c, d) is (a - c)  x + (b - d)  y + k = 0 What is the value of k?

   1. A.$a^2-c^2+b^2-d^2$
   2. B.$c^2+d^2-a^2-b^2$
   3. C.$(a^2-c^2+b^2-d^2)/2$
   4. D.$(c^2+d^2-a^2-b^2)/2$
   Show answer

   Answer: D

5. Q592025 · 14 Sept 2025

   Consider the following statements in respect of the equation $x^2+3y=0$ I. The equation represents the equation to parabola that opens upwards. II. The axis of the parabola is x = 0 III. The equation of the latus rectum is 4y - 3 = 0 How many of the statements given above are correct?

   1. A.None
   2. B.One
   3. C.Two
   4. D.All three
   Show answer

   Answer: B

6. Q602025 · 14 Sept 2025

   What is the sum of the intercepts of the line $\frac{x}{a^2}+\frac{y}{b^2}=\frac{2}{a^2+b^2}$ on the coordinate axes?

   1. A.2
   2. B.1
   3. C.1/2
   4. D.$a^2+b^2$
   Show answer

   Answer: A

7. Q612025 · 14 Sept 2025

   Which one of the following is the perpendicular form of the straight line $\sqrt{3}x+2y=7$ ?

   1. A.$y=-\frac{\sqrt{3}}{2}x+\frac{7}{2}$
   2. B.$\frac{x}{(\frac{7}{\sqrt{3}})}+\frac{y}{(\frac{7}{2})}=1$
   3. C.$\frac{\sqrt{3}}{\sqrt{7}}x+\frac{2}{\sqrt{7}}y=\sqrt{7}$
   4. D.$\frac{\sqrt{3}}{\sqrt{7}}x+\frac{2}{\sqrt{7}}y=7$
   Show answer

   Answer: C

8. Q622025 · 14 Sept 2025

   If the vertices Band D of a square ABCD are (2, 3) and (4, 1) respectively, then what is the area of the square?

   1. A.2 square units
   2. B.3 square units
   3. C.4 square units
   4. D.8 square units
   Show answer

   Answer: C

9. Q642025 · 14 Sept 2025

   The circle $x^2+y^2-2kx-2ky+k^2=0$ touches the x-axis at P and y-axis at Q. What is PQ equal to?

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

   Answer: A

10. Q652025 · 14 Sept 2025

    What is the distance between the foci of the hyperbola $x^2-4y^2=1$

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

    Answer: B

11. Q662025 · 14 Sept 2025

    Let $\vec{p}=\vec{a}-\vec{b},\vec{q}=\vec{a}+\vec{b}$. If $|\vec{a}|=|\vec{b}|=2$ and $\vec{a}\cdot \vec{b}=2$, then what is the value of $|\vec{p}\times \vec{q}|$?

    1. A.$\sqrt{3}$
    2. B.$\sqrt{6}$
    3. C.$2\sqrt{3}$
    4. D.$4\sqrt{3}$
    Show answer

    Answer: D

12. Q392025 · 13 Apr 2025
    Passage

    Consider the following for the two (02) items that follow: The top (M) of a tower is observed from three points P, Q and R lying in a horizontal straight line which passes directly along the foot (N) of the tower. The angles of elevations of M from P, Q and R are 30°, 45° and 60° respectively. Let PQ = a and QR = b

    What is PN equal to?

    1. A.$\left(\frac{3-\sqrt{3}}{2}\right)a$
    2. B.$\left(\frac{3+\sqrt{3}}{2}\right)a$
    3. C.$\left(\frac{3-\sqrt{3}}{4}\right)a$
    4. D.$\left(\frac{3+\sqrt{3}}{4}\right)a$
    Show answer

    Answer: B

13. Q402025 · 13 Apr 2025
    Passage

    Consider the following for the two (02) items that follow: The top (M) of a tower is observed from three points P, Q and R lying in a horizontal straight line which passes directly along the foot (N) of the tower. The angles of elevations of M from P, Q and R are 30°, 45° and 60° respectively. Let PQ = a and QR = b

    What is MN equal to?

    1. A.$\left(\frac{3+\sqrt{3}}{2}\right)b$
    2. B.$\left(\frac{3-\sqrt{3}}{2}\right)b$
    3. C.$\left(\frac{3-\sqrt{3}}{4}\right)b$
    4. D.$\left(\frac{3+\sqrt{3}}{4}\right)b$
    Show answer

    Answer: A

14. Q482025 · 13 Apr 2025

    A man at M, standing $100\mathrm{m}$ away from the base (P) of a chimney of height $50\mathrm{m}$, observes the angle of elevation of the highest point (Q) of the smoke to be $45^{\circ }$. The highest point of the chimney is at R. Further P, R and Q are in a straight line and the straight line is perpendicular to PM. What is the angle RMQ equal to?

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

    Answer: B

15. Q492025 · 13 Apr 2025

    If k is a root of $x^2-4x+1=0$, then what is ${\tan }^{-1}k+{\tan }^{-1}\frac{1}{k}$ equal to?

    1. A.-$\pi /2$
    2. B.0
    3. C.$\pi /4$
    4. D.$\pi /2$
    Show answer

    Answer: D

16. Q502025 · 13 Apr 2025

    If ${\tan }^{-1}k+{\tan }^{-1}\frac{1}{2}=\frac{\pi }{4}$, then what is the value of k?

    1. A.1
    2. B.1/2
    3. C.1/3
    4. D.1/4
    Show answer

    Answer: C

17. Q512025 · 13 Apr 2025

    Under what condition will the lines $m^{2}x+ny-1=0$ and $n^{2}x-my+2=0$ be perpendicular?

    1. A.mn-1=0
    2. B.mn + 1 = 0
    3. C.m + n = 0
    4. D.m - n = 0
    Show answer

    Answer: A

18. Q522025 · 13 Apr 2025

    If p and q are real numbers between 0 and 1 such that the points (p,1), (1,q) and (0,0) form an equilateral triangle, then what is (p+q) equal to?

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

    Answer: D

19. Q532025 · 13 Apr 2025

    The vertices of a triangle are A(1, 1),B(0, 0) and C(2, 0). The angular bisectors of the triangle meet at P. What are the coordinates of P?

    1. A.$(1,\sqrt{2}-1)$
    2. B.$(1,\sqrt{3}-1)$
    3. C.(1, 1/2)
    4. D.$(1/2,\sqrt{2}-1)$
    Show answer

    Answer: A

20. Q542025 · 13 Apr 2025

    Let A(3, -1) and B(1, 1) be the end points of line segment AB. Let P be the middle point of the line segment AB. Let Q be the point situated at a distance $\sqrt{2}$ units from P on the perpendicular bisector line of AB. What are the possible coordinates of Q?

    1. A.(2,1)
    2. B.(3,1)
    3. C.(2,2)
    4. D.(1,3)
    Show answer

    Answer: B

21. Q552025 · 13 Apr 2025

    ABC is an equilateral triangle and AD is the altitude on BC. If the coordinates of A are (1,2) and that of D are (−2,6), then what is the equation of BC?

    1. A.3x+4y−18=0
    2. B.4x+3y−1=0
    3. C.4x−3y+26=0
    4. D.3x−4y+30=0
    Show answer

    Answer: D

22. Q562025 · 13 Apr 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 answer

    Answer: B

23. Q572025 · 13 Apr 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.$(-1+\frac{1}{\sqrt{2}},-1-\frac{1}{\sqrt{2}})$
    4. D.None of the above
    Show answer

    Answer: C

24. Q582025 · 13 Apr 2025

    A tangent to the parabola $y^2=4x$ is inclined at an angle $45^{\circ }$ deg with the positive direction of x-axis. What is the point of contact of the tangent and the parabola?

    1. A.(1, 1)
    2. B.$(2,2\sqrt{2})$
    3. C.$(\frac{1}{2},\frac{1}{\sqrt{2}})$
    4. D.(1,2)
    Show answer

    Answer: D

25. Q592025 · 13 Apr 2025

    . What is the distance between the two foci of the hyperbola $25x^2-75y^2=225$ ?

    1. A.$2\sqrt{3}\mathrm{units}$
    2. B.$4\sqrt{3}\mathrm{units}$
    3. C.$\sqrt{6}\mathrm{units}$
    4. D.$2\sqrt{6}\mathrm{units}$
    Show answer

    Answer: B