Coordinate Geometry · NDA previous year questions

2020 11 questions

1. Q512020 · 6 Sept 2020

   The center of the circle $(x-2a)(x-2b)+(y-2c)(y-2d)=0$ is

   1. A.$(2a,2c)$
   2. B.$(2b,2d)$
   3. C.$(a+b,c+d)$
   4. D.$(a-b,c-d)$
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   Answer: C

2. Q522020 · 6 Sept 2020

   The point $(1,-1)$ is one of the vertices of a square. If $3x+2y=5$ is the equation of one diagonal of the square, then what is the equation of the other diagonal?

   1. A.$3x-2y=5$
   2. B.$2x-3y=1$
   3. C.$2x-3y=5$
   4. D.$2x+3y=-1$
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   Answer: C

3. Q532020 · 6 Sept 2020

   Let $P(x,y)$ be any point on the ellipse $25x^2+16y^2=400$. If $Q(0,3)$ and $R(0,-3)$ are two points, then what is $(PQ+PR)$ equal to?

   1. A.12
   2. B.10
   3. C.8
   4. D.6
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   Answer: B

4. Q542020 · 6 Sept 2020

   If the circumcentre of the triangle formed by the lines $x+2=0$, $y+2=0$ and $kx+y+2=0$ is $(-1,-1)$, then what is the value of $k$?

   1. A.$-1$
   2. B.$-2$
   3. C.1
   4. D.2
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   Answer: C

5. Q552020 · 6 Sept 2020

   In the parabola $y^2=x$, what is the length of the chord passing through the vertex and inclined to the $x$-axis at an angle $\theta$ ?

   1. A.$\sin \theta \cdot {\sec }^2\theta$
   2. B.$\cos \theta \cdot {\mathrm{cosec}}^2\theta$
   3. C.$\cot \theta \cdot {\sec }^2\theta$
   4. D.$2\tan \theta \cdot {\mathrm{cosec}}^2\theta$
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   Answer: B

6. Q562020 · 6 Sept 2020

   Under which condition, are the points $(a,b)$, $(c,d)$ and $(a-c,b-d)$ collinear?

   1. A.$ab=cd$
   2. B.$ac=bd$
   3. C.$ad=bc$
   4. D.$abc=d$
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   Answer: C

7. Q572020 · 6 Sept 2020

   Let ABC be a triangle. If $D(2,5)$ and $E(5,9)$ are the mid-points of the sides AB and AC respectively, then what is the length of the side BC ?

   1. A.8
   2. B.10
   3. C.12
   4. D.14
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   Answer: B

8. Q582020 · 6 Sept 2020

   If the foot of the perpendicular drawn from the point $(0,k)$ to the line $3x-4y-5=0$ is $(3,1)$, then what is the value of $k$?

   1. A.3
   2. B.4
   3. C.5
   4. D.6
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   Answer: C

9. Q592020 · 6 Sept 2020

   What is the obtuse angle between the lines whose slopes are $2-\sqrt{3}$ and $2+\sqrt{3}$ ?

   1. A.$105^{\circ }$
   2. B.$120^{\circ }$
   3. C.$135^{\circ }$
   4. D.$150^{\circ }$
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   Answer: B

10. Q602020 · 6 Sept 2020

    If $3x-4y-5=0$ and $3x-4y+15=0$ are the equations of a pair of opposite sides of a square, then what is the area of the square?

    1. A.4 square units
    2. B.9 square units
    3. C.16 square units
    4. D.25 square units
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    Answer: C

11. Q672020 · 6 Sept 2020

    Let A be a point in space such that $|\overrightarrow{OA}|=12$, where O is the origin. If $\overrightarrow{OA}$ is inclined at angles $45^{\circ }$ and $60^{\circ }$ with $x$-axis and $y$-axis respectively, then what is $\overrightarrow{OA}$ equal to?

    1. A.$6\hat{i}+6\hat{j}\pm \sqrt{2}\hat{k}$
    2. B.$6\hat{i}+6\sqrt{2}\hat{j}\pm 6\hat{k}$
    3. C.$6\sqrt{2}\hat{i}+6\hat{j}\pm 6\hat{k}$
    4. D.$3\sqrt{2}\hat{i}+3\hat{j}\pm 6\hat{k}$
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    Answer: C