Match the following: List I List II A Let P ( x ) be a cubic polynomial with zeroes α, β, γ, if ( P ((1/2))+ P (-(1/2))/ P (0))=100 text then √(1/α β)+(1/β γ)+(1/γ α)= 1 14 B The root of the equation x2+2(a-3) x+9=0 lie between -6 and 1 and 2, h1, 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 a3 h18 is equal to 2 6 C If the sum of all possible values of x ∈(0,2 π) satisfying the equation 2 cos x operatornamecosec x-4 cos x- operatornamecosec x=-2 is equal to k π / 2(k ∈ N), then the value of k is 3 2 D If P ( t 2, 2 t ), t ∈[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

Question

Match the following: List I List II A Let P ( x ) be a cubic polynomial with zeroes α, β, &gamma;, if ( P ((1/2))+ P (-(1/2))/ P (0))=100 text then √(1/α β)+(1/β &gamma;)+(1/&gamma; α)= 1 14 B The root of the equation x2+2(a-3) x+9=0 lie between -6 and 1 and 2, h1, 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 a3 h18 is equal to 2 6 C If the sum of all possible values of x ∈(0,2 π) satisfying the equation 2 cos x operatornamecosec x-4 cos x- operatornamecosec x=-2 is equal to k π / 2(k ∈ N), then the value of k is 3 2 D If P ( t 2, 2 t ), t ∈[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 (A) P= 1 ,Q= 3 ,R= 2 ,S= 4 (B) P=2 ,Q= 4 ,R=3 ,S=1 (C) P=3 ,Q= 1 ,R=4 ,S=2 (D) P=4 ,Q= 2,R= 1,S= 3

Tardigrade Admin · Accepted Answer

Correct answer is (a) P= 1 ,Q= 3 ,R= 2 ,S= 4

List I		List II
A	Let $P (x)$ be a cubic polynomial with zeroes $α, β, γ$ , if $\frac{P ( \frac{1}{2} ) + P ( - \frac{1}{2} )}{P ( 0 )} = 100 then \frac{1}{α β} + \frac{1}{β γ} + \frac{1}{γ α} =$	1	14
B	The root of the equation $x^{2} + 2 (a - 3) x + 9 = 0$ lie between -6 and 1 and $2, h_{1}$ , $h_{2}, \dots .. h_{20}, [a]$ are in H.P. and $2, a_{1}, a_{2}, \dots . a_{20}$ , [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 $x \in (0, 2 π)$ satisfying the equation 2 $cos x cosec x - 4 cos x - cosec x = - 2$ is equal to $kπ /2 (k \in N)$ , then the value of $k$ is	3	2
D	If $P (t^{2}, 2 t), t \in [0, 2]$ 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