Expression 'S1'

Q.

Which of the following point lie inside the circle $x^2+y^2-2x+3y-11=0$

1. (2, 3)

2. (1, 1)

3. (-1, 2)

4. (3, 2)

Q. Let the lines $(2–i)z=(2+i)\overline{z}$ and $(2+i)z+(i–2)\overline{z}–4i=0,$ $($here $i^2=–1$$)$ be normal to a circle $C$. If the line $iz+\overline{z}+1+i=0$ is tangent to this circle $C$, then its radius is :

1. $\frac{3}{\sqrt{2}}$
2. $3\sqrt{2}$
3. $\frac{3}{2\sqrt{2}}$
4. $\frac{1}{2\sqrt{2}}$

Q.

The point $(x_1,y_1)$ lies inside the circle $x^2+y^2+2gx+2fy+c=0$, if $x_1^2+y_1^2+2g{x}_1+2f{g}_1+c$ is less than zero

1. True

2. False

Q.

Angle between tangent $x^2+y^2=20,$ drawn to circles from the point $(6,2)$ is

1. $\frac{\pi }{2}$

2. $\pi$

3. $\frac{\pi }{4}$

4. $2\pi$

Q. Length of the tangent drawn from any point on the circle $x^2+y^2+2gx+2fy+c_1=0$ to the circle is $x^2+y^2+2gx+2fy+c=0$

1. $\sqrt{c_1-c}$
2. $\sqrt{c-c_1}$
3. $\sqrt{c_1+c}$
4. None of these

Q. If the line passing through P=(8, 3) meets the circle $S=x^2+y^2-8x-10y+26=0$ at A, B then PA.PB =

1. 5
2. 14
3. 4
4. 24

Q. Length of the tangent drawn from any point on the circle $x^2+y^2+2gx+2fy+c_1=0$ to the circle is $x^2+y^2+2gx+2fy+c=0$

1. None of these
2. $\sqrt{c-c_1}$
3. $\sqrt{c_1-c}$
4. $\sqrt{c_1+c}$

Q.

The length of a tangent extended from a point P situated outside a circle is $\sqrt{5}$ units. Another line from P intersects the circle at 2 points R and S such that PR: RS = 1: 2. What is the length of PS?

1. 

2. 

3. 

4. 

Q. If the line passing through P = (8, 3) meets the circle $S\equiv x^2+y^2-8x-10y+26=0$ at A, B then PA · PB =

1. 5
2. 14
3. 4
4. 24

Q. Length of the tangent drawn from any point on the circle $x^2+y^2+2gx+2fy+c_1=0$ to the circle is $x^2+y^2+2gx+2fy+c=0$

1. $\sqrt{c_1-c}$
2. $\sqrt{c-c_1}$
3. $\sqrt{c_1+c}$
4. None of these

Q.

The point $(x_1,y_1)$ lies inside the circle $x^2+y^2+2gx+2fy+c=0$, if $x_1^2+y_1^2+2g{x}_1+2f{g}_1+c$ is less than zero

1. True

2. False