Coordinate Geometry · NDA previous year questions

2011 30 questions

1. 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

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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
   Show answer

   Answer: B

8. 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

9. 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

10. 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

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

    Answer: A

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

    Answer: B

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

    Answer: C

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

    Answer: D

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

    Answer: A

16. 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

17. 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

18. 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
    Show answer

    Answer: D

19. 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
    Show answer

    Answer: B

20. 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.$2\sin \alpha$
    Show answer

    Answer: C

21. 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

22. 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

23. Q772011 · 17 Apr 2011

    What is the equation of the line joining the origin with the point of intersection of the lines $4x+3y=12$ and $3x+4y=12$?

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

    Answer: D

24. Q782011 · 17 Apr 2011

    If the sum of the squares of the distances of the point $(x,y)$ from the points $(a,0)$ and $(-a,0)$ is $2b^2$, then which one of the following is correct?

    1. A.$x^2+a^2=b^2+y^2$
    2. B.$x^2+a^2=2b^2-y^2$
    3. C.$x^2-a^2=b^2+y^2$
    4. D.$x^2+a^2=b^2-y^2$
    Show answer

    Answer: D

25. Q792011 · 17 Apr 2011

    If $f(x)=2^x$, then what is $f^{\prime \prime }(x)$ equal to?

    1. A.$2^x(\ln 2{)}^2$
    2. B.$x(x-1)2^{x-2}$
    3. C.$2^{x+1}(\ln 2)$
    4. D.$2^x({\log }_{10}2{)}^2$
    Show answer

    Answer: A