Coordinate Geometry · NDA previous year questions

2017 27 questions

1. Q62017 · 10 Sept 2017

   Geometrically $\mathrm{Re}\left(z^2-i\right)=2$, where $i=\sqrt{-1}$ and $\mathrm{Re}$ is the real part, represents

   1. A.circle
   2. B.ellipse
   3. C.rectangular hyperbola
   4. D.parabola
   Show answer

   Answer: C

2. Q72017 · 10 Sept 2017

   The value of the product $6^{\frac{1}{2}}\times 6^{\frac{1}{4}}\times 6^{\frac{1}{8}}\times 6^{\frac{1}{16}}\times \dots$ up to infinite terms is

   1. A.6
   2. B.36
   3. C.216
   4. D.512
   Show answer

   Answer: A

3. Q412017 · 10 Sept 2017

   The points $(a,b),(0,0),(-a,-b)$ and $(ab,b^2)$ are

   1. A.the vertices of a parallelogram
   2. B.the vertices of a rectangle
   3. C.the vertices of a square
   4. D.collinear
   Show answer

   Answer: D

4. Q422017 · 10 Sept 2017

   The angle between the lines $x+y-3=0$ and $x-y+3=0$ is $\alpha$ and the acute angle between the lines $x-\sqrt{3}y+2\sqrt{3}=0$ and $\sqrt{3}x-y+1=0$ is $\beta$. Which one of the following is correct?

   1. A.$\alpha =\beta$
   2. B.$\alpha >\beta$
   3. C.$\alpha <\beta$
   4. D.$\alpha =2\beta$
   Show answer

   Answer: B

5. Q432017 · 10 Sept 2017

   The distance of the point $(1,3)$ from the line $2x+3y=6$, measured parallel to the line $4x+y=4$, is

   1. A.$\frac{5}{\sqrt{13}}\text{ units}$
   2. B.$\frac{3}{\sqrt{17}}\text{ unit}$
   3. C.$\sqrt{17}\text{ units}$
   4. D.$\frac{\sqrt{17}}{2}\text{ units}$
   Show answer

   Answer: D

6. Q442017 · 10 Sept 2017

   The equation of a straight line which cuts off an intercept of 5 units on negative direction of $y$-axis and makes an angle $120^{\circ }$ with positive direction of $x$-axis is

   1. A.$y+\sqrt{3}x+5=0$
   2. B.$y-\sqrt{3}x+5=0$
   3. C.$y+\sqrt{3}x-5=0$
   4. D.$y-\sqrt{3}x-5=0$
   Show answer

   Answer: A

7. Q462017 · 10 Sept 2017

   The equation of the circle which passes through the points $(1,0),(0,-6)$ and $(3,4)$ is

   1. A.$4x^2+4y^2+142x+47y+140=0$
   2. B.$4x^2+4y^2-142x-47y+138=0$
   3. C.$4x^2+4y^2-142x+47y+138=0$
   4. D.$4x^2+4y^2+150x-49y+138=0$
   Show answer

   Answer: C

8. Q482017 · 10 Sept 2017

   The position of the point $(1,2)$ relative to the ellipse $2x^2+7y^2=20$ is

   1. A.outside the ellipse
   2. B.inside the ellipse but not at the focus
   3. C.on the ellipse
   4. D.at the focus
   Show answer

   Answer: A

9. Q492017 · 10 Sept 2017

   The equation of the ellipse whose centre is at origin, major axis is along $x$-axis with eccentricity $\frac{3}{4}$ and latus rectum 4 units is

   1. A.$\frac{x^2}{1024}+\frac{7y^2}{64}=1$
   2. B.$\frac{49x^2}{1024}+\frac{7y^2}{64}=1$
   3. C.$\frac{7x^2}{1024}+\frac{49y^2}{64}=1$
   4. D.$\frac{x^2}{1024}+\frac{y^2}{64}=1$
   Show answer

   Answer: B

10. Q822017 · 10 Sept 2017

    The general solution of $\frac{dy}{dx}=\frac{ax+h}{by+k}$ represents a circle only when

    1. A.$a=b=0$
    2. B.$a=-b\ne 0$
    3. C.$a=b\ne 0,h=k$
    4. D.$a=b\ne 0$
    Show answer

    Answer: B

11. Q1132017 · 10 Sept 2017

    Consider the following statements : 1. $\frac{dy}{dx}$ at a point on the curve gives slope of the tangent at that point. 2. If $a(t)$ denotes acceleration of a particle, then $\int a(t)dt+c$ gives velocity of the particle. 3. If $s(t)$ gives displacement of a particle at time $t$, then $\frac{ds}{dt}$ gives its acceleration at that instant. Which of the above statements is/are correct?

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

    Answer: A

12. Q1142017 · 10 Sept 2017

    If $y={\sec }^{-1}\left(\frac{x+1}{x-1}\right)+{\sin }^{-1}\left(\frac{x-1}{x+1}\right)$, then $\frac{dy}{dx}$ is equal to

    1. A.0
    2. B.1
    3. C.$\frac{x-1}{x+1}$
    4. D.$\frac{x+1}{x-1}$
    Show answer

    Answer: A

13. Q1152017 · 10 Sept 2017

    If $l_1=\frac{d}{dx}\left(e^{\sin x}\right)$ $l_2={\lim }_{h\to 0}\frac{e^{\sin (x+h)}-e^{\sin x}}{h}$ $l_3=\int e^{\sin x}\cos xdx$ then which one of the following is correct?

    1. A.$l_1\ne l_2$
    2. B.$\frac{d}{dx}(l_3)=l_2$
    3. C.$\int l_{3}dx=l_2$
    4. D.$l_2=l_3$
    Show answer

    Answer: B

14. Q512017 · 23 Apr 2017

    The incentre of the triangle with vertices $A(1,\sqrt{3})$, $B(0,0)$ and $C(2,0)$ is

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

    Answer: D

15. Q522017 · 23 Apr 2017

    If the three consecutive vertices of a parallelogram are $(-2,-1)$, $(1,0)$ and $(4,3)$, then what are the coordinates of the fourth vertex?

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

    Answer: A

16. Q532017 · 23 Apr 2017

    What is the ratio in which the point $C\left(-\frac{2}{7},-\frac{20}{7}\right)$ divides the line joining the points $A(-2,-2)$ and $B(2,-4)$?

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

    Answer: B

17. Q542017 · 23 Apr 2017

    What is the equation of the straight line parallel to $2x+3y+1=0$ and passes through the point $(-1,2)$?

    1. A.$2x+3y-4=0$
    2. B.$2x+3y-5=0$
    3. C.$x+y-1=0$
    4. D.$3x-2y+7=0$
    Show answer

    Answer: A

18. Q552017 · 23 Apr 2017

    What is the acute angle between the pair of straight lines $\sqrt{2}x+\sqrt{3}y=1$ and $\sqrt{3}x+\sqrt{2}y=2$?

    1. A.${\tan }^{-1}\left(\frac{1}{2\sqrt{6}}\right)$
    2. B.${\tan }^{-1}\left(\frac{1}{\sqrt{2}}\right)$
    3. C.${\tan }^{-1}(3)$
    4. D.${\tan }^{-1}\left(\frac{1}{\sqrt{3}}\right)$
    Show answer

    Answer: A

19. Q562017 · 23 Apr 2017

    If the centroid of a triangle formed by $(7,x)$, $(y,-6)$ and $(9,10)$ is $(6,3)$, then the values of $x$ and $y$ are respectively

    1. A.5, 2
    2. B.2, 5
    3. C.1, 0
    4. D.0, 0
    Show answer

    Answer: A

20. Q572017 · 23 Apr 2017

    The two circles $x^2+y^2=r^2$ and $x^2+y^2-10x+16=0$ intersect at two distinct points. Then which one of the following is correct?

    1. A.$2<r<8$
    2. B.$r=2$ or $r=8$
    3. C.$r<2$
    4. D.$r>2$
    Show answer

    Answer: A

21. Q582017 · 23 Apr 2017

    What is the equation of the circle which passes through the points $(3,-2)$ and $(-2,0)$ and having its centre on the line $2x-y-3=0$?

    1. A.$x^2+y^2+3x+2=0$
    2. B.$x^2+y^2+3x+12y+2=0$
    3. C.$x^2+y^2+2x=0$
    4. D.$x^2+y^2=5$
    Show answer

    Answer: B

22. Q592017 · 23 Apr 2017

    What is the equation of the ellipse having foci $(\pm 2,0)$ and the eccentricity $\frac{1}{4}$?

    1. A.$\frac{x^2}{64}+\frac{y^2}{60}=1$
    2. B.$\frac{x^2}{60}+\frac{y^2}{64}=1$
    3. C.$\frac{x^2}{20}+\frac{y^2}{24}=1$
    4. D.$\frac{x^2}{24}+\frac{y^2}{20}=1$
    Show answer

    Answer: A

23. Q612017 · 23 Apr 2017

    $(0,0,0)$, $(a,0,0)$, $(0,b,0)$ and $(0,0,c)$ are four distinct points. What are the coordinates of the point which is equidistant from the four points?

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

    Answer: C

24. Q932017 · 23 Apr 2017

    Let $ABCD$ be a parallelogram whose diagonals intersect at $P$ and let $O$ be the origin. What is $\overrightarrow{OA}+\overrightarrow{OB}+\overrightarrow{OC}+\overrightarrow{OD}$ equal to?

    1. A.$2\overrightarrow{OP}$
    2. B.$4\overrightarrow{OP}$
    3. C.$6\overrightarrow{OP}$
    4. D.$8\overrightarrow{OP}$
    Show answer

    Answer: B

25. Q942017 · 23 Apr 2017

    $ABCD$ is a quadrilateral whose diagonals are $AC$ and $BD$. Which one of the following is correct?

    1. A.$\overrightarrow{BA}+\overrightarrow{CD}=\overrightarrow{AC}+\overrightarrow{DB}$
    2. B.$\overrightarrow{BA}+\overrightarrow{CD}=\overrightarrow{BD}+\overrightarrow{CA}$
    3. C.$\overrightarrow{BA}+\overrightarrow{CD}=\overrightarrow{AC}+\overrightarrow{BD}$
    4. D.$\overrightarrow{BA}+\overrightarrow{CD}=\overrightarrow{BC}+\overrightarrow{AD}$
    Show answer

    Answer: B