Q.
Match the following:
List I
List II
A
Let $P ( x )$ be a cubic polynomial with zeroes $\alpha, \beta, \gamma$, if $\frac{ P \left(\frac{1}{2}\right)+ P \left(-\frac{1}{2}\right)}{ P (0)}=100 \text { then } \sqrt{\frac{1}{\alpha \beta}+\frac{1}{\beta \gamma}+\frac{1}{\gamma \alpha}}=$
1
14
B
The root of the equation $x^2+2(a-3) x+9=0$ lie between -6 and 1 and $2, h_1$, $h _2, \ldots . . h _{20},[ a ]$ are in H.P. and $2, a _1, a _2, \ldots . a _{20}$, [a] are in A.P. where [a] denotes the integral part of $a$, then $a_3 h_{18}$ is equal to
2
6
C
If the sum of all possible values of $x \in(0,2 \pi)$ satisfying the equation 2 $\cos x \operatorname{cosec} x-4 \cos x-\operatorname{cosec} x=-2$ is equal to $k \pi / 2(k \in N)$, then the value of $k$ is
3
2
D
If $P \left( t ^2, 2 t \right), t \in[0,2]$ is an arbitrary point on parabola $y ^2=4 x$. $Q$ is foot of perpendicular from focus $S$ on the tangent at $P$, then maximum area of triangle
4
5
| List I | List II | ||
|---|---|---|---|
| A | Let $P ( x )$ be a cubic polynomial with zeroes $\alpha, \beta, \gamma$, if $\frac{ P \left(\frac{1}{2}\right)+ P \left(-\frac{1}{2}\right)}{ P (0)}=100 \text { then } \sqrt{\frac{1}{\alpha \beta}+\frac{1}{\beta \gamma}+\frac{1}{\gamma \alpha}}=$ | 1 | 14 |
| B | The root of the equation $x^2+2(a-3) x+9=0$ lie between -6 and 1 and $2, h_1$, $h _2, \ldots . . h _{20},[ a ]$ are in H.P. and $2, a _1, a _2, \ldots . a _{20}$, [a] are in A.P. where [a] denotes the integral part of $a$, then $a_3 h_{18}$ is equal to | 2 | 6 |
| C | If the sum of all possible values of $x \in(0,2 \pi)$ satisfying the equation 2 $\cos x \operatorname{cosec} x-4 \cos x-\operatorname{cosec} x=-2$ is equal to $k \pi / 2(k \in N)$, then the value of $k$ is | 3 | 2 |
| D | If $P \left( t ^2, 2 t \right), t \in[0,2]$ is an arbitrary point on parabola $y ^2=4 x$. $Q$ is foot of perpendicular from focus $S$ on the tangent at $P$, then maximum area of triangle | 4 | 5 |
Conic Sections
Solution: