Coordinate Geometry · NDA previous year questions

2011 30 questions

1. Q392011 · 21 Aug 2011

   What is the area of the triangle formed by the lines joining the vertex of the parabola $x^2=12y$ to the ends of the latus rectum?

   1. A.9 square units
   2. B.12 square units
   3. C.14 square units
   4. D.18 square units
   Show answer

   Answer: D

2. Q492011 · 21 Aug 2011

   What is the focal distance of any point $P(x_1,y_1)$ on the parabola $y^2=4ax$ ?

   1. A.$x_1+y_1$
   2. B.$x_1{y}_1$
   3. C.$a{x}_1$
   4. D.$a+x_1$
   Show answer

   Answer: D

3. Q562011 · 21 Aug 2011

   If $(p,q)$ is the point on the x-axis equidistant from the points $(1,2)$ and $(2,3)$, then which one of the following is correct ?

   1. A.$p=0,q=4$
   2. B.$p=4,q=0$
   3. C.$p=3/2,q=0$
   4. D.$p=1,q=0$
   Show answer

   Answer: B

4. Q592011 · 21 Aug 2011

   If p is the length of the perpendicular drawn from the origin to the line $\frac{x}{a}+\frac{y}{b}=1$, then which one of the following is correct ?

   1. A.$\frac{1}{p^2}=\frac{1}{a^2}+\frac{1}{b^2}$
   2. B.$\frac{1}{p^2}=\frac{1}{a^2}-\frac{1}{b^2}$
   3. C.$\frac{1}{p}=\frac{1}{a}+\frac{1}{b}$
   4. D.$\frac{1}{p}=\frac{1}{a}-\frac{1}{b}$
   Show answer

   Answer: A

5. Q602011 · 21 Aug 2011

   If the sides of a triangle are in the ratio $2:\sqrt{6}:1+\sqrt{3}$, then what is the smallest angle of the triangle ?

   1. A.$75^{\circ }$
   2. B.$60^{\circ }$
   3. C.$45^{\circ }$
   4. D.$30^{\circ }$
   Show answer

   Answer: C

6. Q612011 · 21 Aug 2011

   What is the value of $\sqrt{8+2\sqrt{8+2\sqrt{8+2\sqrt{8+\dots \infty }}}}$ ?

   1. A.10
   2. B.8
   3. C.6
   4. D.4
   Show answer

   Answer: D

7. Q922011 · 21 Aug 2011

   What are the points on the curve $x^2+y^2-2x-3=0$ where the tangents are parallel to x-axis?

   1. A.$(1,2)$ and $(1,-2)$
   2. B.$(0,\sqrt{3})$ and $(0,-\sqrt{3})$
   3. C.$(3,0)$ and $(-3,0)$
   4. D.$(2,1)$ and $(2,-1)$
   Show answer

   Answer: A

8. Q932011 · 21 Aug 2011

   If $\sin 3A=1$, then how many distinct values can $\sin A$ assume?

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

   Answer: B

9. Q942011 · 21 Aug 2011

   What is the radius of the circle touching x-axis at $(3,0)$ and y-axis at $(0,3)$?

   1. A.3 units
   2. B.4 units
   3. C.5 units
   4. D.6 units
   Show answer

   Answer: A

10. Q952011 · 21 Aug 2011

    For all $n\in N$, $2^{4n}-15n-1$ is divisible by

    1. A.125
    2. B.225
    3. C.450
    4. D.None of the above
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    Answer: B

11. Q982011 · 21 Aug 2011

    What is the area of the triangle with vertices $(1,2,3)$, $(2,5,-1)$ and $(-1,1,2)$?

    1. A.$\frac{\sqrt{155}}{2}\text{ square units}$
    2. B.$\frac{\sqrt{175}}{2}\text{ square units}$
    3. C.$\frac{\sqrt{155}}{4}\text{ square units}$
    4. D.$\frac{\sqrt{175}}{4}\text{ square units}$
    Show answer

    Answer: A

12. Q992011 · 21 Aug 2011

    For what value of x does $\left(\begin{array}{ccc}1& 3& 2\end{array}\right)\left(\begin{array}{ccc}3& 0& 2\\ 2& 0& 1\end{array}\right)\left(\begin{array}{c}3\\ x\end{array}\right)=(0)$ hold?

    1. A.$-1$
    2. B.1
    3. C.$9/8$
    4. D.$-9/8$
    Show answer

    Answer: D

13. Q1052011 · 21 Aug 2011

    What is the equation of a line parallel to x-axis at a distance of 5 units below x-axis?

    1. A.$x=5$
    2. B.$x=-5$
    3. C.$y=5$
    4. D.$y=-5$
    Show answer

    Answer: D

14. Q1062011 · 21 Aug 2011
    
    1. A.810
    2. B.830
    3. C.970
    4. D.1030
    Show answer

    Answer: A

15. Q1072011 · 21 Aug 2011
    
    1. A.390
    2. B.410
    3. C.430
    4. D.470
    Show answer

    Answer: B

16. Q1082011 · 21 Aug 2011
    
    1. A.400
    2. B.460
    3. C.490
    4. D.510
    Show answer

    Answer: C

17. Q1092011 · 21 Aug 2011
    
    1. A.1000
    2. B.1020
    3. C.1040
    4. D.1050
    Show answer

    Answer: D

18. Q1102011 · 21 Aug 2011
    
    1. A.90
    2. B.100
    3. C.110
    4. D.120
    Show answer

    Answer: A

19. Q22011 · 17 Apr 2011

    Two straight lines $x-3y-2=0$ and $2x-6y-6=0$

    1. A.never intersect
    2. B.intersect at a single point
    3. C.intersect at infinite number of points
    4. D.intersect at more than one point (but finite number of points)
    Show answer

    Answer: A

20. Q32011 · 17 Apr 2011

    If $(a,0)$, $(0,b)$, $(1,1)$ are collinear, what is $(a+b-ab)$ equal to?

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

    Answer: C

21. Q42011 · 17 Apr 2011

    If $A=\left[\begin{array}{cc}3& 1\\ 0& 4\end{array}\right]$ and $B=\left[\begin{array}{cc}1& 1\\ 0& 2\end{array}\right]$, then which of the following is/are correct? 1. $AB$ is defined 2. $BA$ is defined 3. $AB=BA$ Select the correct answer using the code given below: Code:

    1. A.1 only
    2. B.2 only
    3. C.1 and 2 only
    4. D.1, 2 and 3
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    Answer: D

22. Q52011 · 17 Apr 2011

    Using the digits 1, 2, 3, 4 and 5 only once, how many numbers greater than 41000 can be formed?

    1. A.41
    2. B.48
    3. C.50
    4. D.55
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    Answer: B

23. Q62011 · 17 Apr 2011

    If an angle $\alpha$ is divided into two parts $A$ and $B$ such that $A-B=x$ and $\tan A:\tan B=2:1$, then what is $\sin x$ equal to?

    1. A.$3\sin \alpha$
    2. B.$(2\sin \alpha )/3$
    3. C.$(\sin \alpha )/3$
    4. D.$2\sin \alpha$
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    Answer: C

24. Q182011 · 17 Apr 2011

    What is the locus of the point which is at a distance 8 units to the left of $y$-axis?

    1. A.$x=8$
    2. B.$y=8$
    3. C.$x=-8$
    4. D.$y=-8$
    Show answer

    Answer: C

25. Q252011 · 17 Apr 2011

    What is the sum of the focal distances of a point of an ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$?

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

    Answer: C