Normal

Q. The area of triangle formed by the tangent, normal drawn at $(1,\sqrt{3})$ to the circle $x^2+y^2=4$ and positive x-axis, is

1. $2\sqrt{3}$
2. $\sqrt{3}$
3. $4\sqrt{3}$
4. None of these

Q.

Find the equation of normal to the circle $x^2+y^2-5x+2y-48=0$ which is parallel to the line 14x - 5y - 30 = 0

1. 14x - 5y + 20 = 0

2. 14x - 5y = 40

3. 14x - 5y = 20

4. 14x - 5y + 40 = 0

Q. From which point tangent is possible to $C_1$ but not $C_2$.

1. $P_2$
2. $P_4$
3. $P_5$
4. None of these

Q. Assertion :Circles $x^2+y^2=4$ & $x^2+y^2-8x+7=0$ intersect each other in two distinct points. Reason: Circles with centres $c_1$ & $c_2$ and radius $r_1$ & $r_2$ intersect at two distinct points if $|r_1-r_2|<c_1{c}_2<r_1+r_2$

1. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
2. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
3. Assertion is correct but Reason is incorrect
4. Both Assertion and Reason are incorrect

Q. Locus of mid points of chords of the parabola $y^2=4ax$ parallel to the line $lx+my+n=0$ is

1. $21y+am=0$
2. $ly+3am=0$
3. $ly+2am=0$
4. $ly+4am=0$

Q. If a line makes $\alpha ,\beta ,\gamma ,\delta$ angles with 4 diagonals of a cube , then ${\cos }^2\alpha +{\cos }^2\beta +{\cos }^2\gamma +{\cos }^2\delta =?$

1. $1$
2. $\frac{2}{3}$
3. $\frac{4}{3}$
4. $\frac{5}{3}$