3D Geometry · NDA previous year questions

2010 11 questions

1. Q462010 · 22 Aug 2010

   The two planes $ax+by+cz+d=0$ and $ax+by+cz+d_1=0$, where $d\ne d_1$, have

   1. A.one point only in common
   2. B.three points in common
   3. C.infinite points in common
   4. D.no points in common
   Show answer

   Answer: D

2. Q482010 · 22 Aug 2010

   What is the distance of the origin from the plane $2x+6y-3z+7=0$ ?

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

   Answer: A

3. Q492010 · 22 Aug 2010

   $PQRS$ is a parallelogram, where $\overrightarrow{PQ}=3\hat{i}+2\hat{j}-m\hat{k}$, $\overrightarrow{PS}=\hat{i}+3\hat{j}+\hat{k}$ and the area of the parallelogram is $\sqrt{90}$. What is the value of $m$?

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

   Answer: A

4. Q742010 · 22 Aug 2010

   If at any instant $t$, for a sphere, $r$ denotes the radius, $S$ denotes the surface area and $V$ denotes the volume, then what is $\frac{dV}{dt}$ equal to?

   1. A.$\frac{1}{2}S\frac{dr}{dt}$
   2. B.$\frac{1}{2}r\frac{dS}{dt}$
   3. C.$r\frac{dS}{dt}$
   4. D.$\frac{1}{2}{r}^2\frac{dS}{dt}$
   Show answer

   Answer: B

5. Q752010 · 22 Aug 2010

   If $f(x)=\frac{2}{3}x+\frac{3}{2},x\in R$, then what is $f^{-1}(x)$ equal to?

   1. A.$\frac{3}{2}x+\frac{2}{3}$
   2. B.$\frac{3}{2}x-\frac{9}{4}$
   3. C.$\frac{2}{3}x-\frac{4}{9}$
   4. D.$\frac{2}{3}x-\frac{2}{3}$
   Show answer

   Answer: B

6. Q102010 · 18 Apr 2010

   The planes $px+2y+2z-3=0$ and $2x-y+z+2=0$ intersect at an angle $\pi /4$. What is the value of $p^2$?

   1. A.24
   2. B.12
   3. C.6
   4. D.3
   Show answer

   Answer: A

7. Q112010 · 18 Apr 2010

   The growth of a quantity N(t) at any instant t is given by $\frac{dN(t)}{dt}=\alpha N(t)$. Given that $N(t)=c{e}^{kt}$, c is a constant. What is the value of $\alpha$?

   1. A.c
   2. B.k
   3. C.$c+k$
   4. D.$c-k$
   Show answer

   Answer: B

8. Q422010 · 18 Apr 2010

   Under what condition do the planes $bx-ay=n$, $cy-bz=l$, $az-cx=m$ intersect in a line?

   1. A.$a+b+c=0$
   2. B.$a=b=c$
   3. C.$al+bm+cn=0$
   4. D.$l+m+n=0$
   Show answer

   Answer: C

9. Q472010 · 18 Apr 2010

   What is the equation of the plane through z-axis and parallel to the line $\frac{x-1}{\cos \theta }=\frac{y+2}{\sin \theta }=\frac{z-3}{0}$?

   1. A.$x\cot \theta +y=0$
   2. B.$x\tan \theta -y=0$
   3. C.$x+y\cot \theta =0$
   4. D.$x-y\tan \theta =0$
   Show answer

   Answer: B

10. Q482010 · 18 Apr 2010

    If the lines $3y+4x=1$, $y=x+5$ and $5y+bx=3$ are concurrent, then what is the value of $b$?

    1. A.1
    2. B.3
    3. C.6
    4. D.0
    Show answer

    Answer: C

11. Q492010 · 18 Apr 2010

    What is the least value of $f(x)=2x^3-3x^2-12x+1$ on $[-2,2.5]$?

    1. A.$-3$
    2. B.8
    3. C.$-19$
    4. D.$-16.5$
    Show answer

    Answer: C