Circles · JEE Main previous year questions

2017 5 questions

1. Q32017 · 9 Apr 2017 · Shift 1

   The equation $\mathrm{Im}\left(\frac{iz-2}{z-i}\right)+1=0$, $z\in \mathbf{C}$, $z\ne i$ represents a part of a circle having radius equal to :

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

   Answer: C

2. Q152017 · 9 Apr 2017 · Shift 1

   A line drawn through the point $\mathrm{P}(4,7)$ cuts the circle $x^2+y^2=9$ at the points A and B. Then $\mathrm{PA}\cdot \mathrm{PB}$ is equal to :

   1. A.$53$
   2. B.$56$
   3. C.$74$
   4. D.$65$
   Show answer

   Answer: B

3. Q112017 · 8 Apr 2017 · Shift 1

   If a point P has co-ordinates $(0,-2)$ and Q is any point on the circle, $x^2+y^2-5x-y+5=0$, then the maximum value of $(\mathrm{PQ}{)}^2$ is :

   1. A.$\frac{25+\sqrt{6}}{2}$
   2. B.$14+5\sqrt{3}$
   3. C.$\frac{47+10\sqrt{6}}{2}$
   4. D.$8+5\sqrt{3}$
   Show answer

   Answer: B

4. Q172017 · 8 Apr 2017 · Shift 1

   If two parallel chords of a circle, having diameter 4units, lie on the opposite sides of the center and subtend angles ${\cos }^{-1}\left(\frac{1}{7}\right)$ and ${\sec }^{-1}(7)$ at the center respectivey, then the distance between these chords, is :

   1. A.$\frac{4}{\sqrt{7}}$
   2. B.$\frac{8}{\sqrt{7}}$
   3. C.$\frac{8}{7}$
   4. D.$\frac{16}{7}$
   Show answer

   Answer: B

5. Q272017 · 8 Apr 2017 · Shift 1

   If the common tangents to the parabola, $x^2=4y$ and the circle, $x^2+y^2=4$ intersect at the point P, then the distance of P from the origin, is :

   1. A.$\sqrt{2}+1$
   2. B.$2(3+2\sqrt{2})$
   3. C.$2(\sqrt{2}+1)$
   4. D.$3+2\sqrt{2}$
   Show answer

   Answer: C