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Question

# List I has four entries and List II has five entries. Each entry of List I is to be matched with one or more than one entries of List II. List IList II (A)The possible value(s) of a for which the largest(P)9value of sin2x−2asinx+a+3 is 7 is/are(B)The possible value(s) of a for which the smallest(Q)16value of x4−ax2+2a−1 for x∈[−1,2] is−7, is/are(C)If a relation R is defined on set of integers as(R)−3 R={(x,y):4x2+9y2≤36}, then possibleelement(s) in the domain is/are(D)If sinx+cosx=15, then |12tanx| is equal to(S)1 (T)11 Which of the following is the only CORRECT combination?

A
(A)(Q),(S)
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B
(A)(Q),(R)
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C
(B)(Q),(S)
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D
(B)(R),(T)
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Solution

## The correct option is D (B)→(R),(T)(A) Let f(x)=sin2x−2asinx+a+3 Let sinx=t, where t∈[−1,1] Given equation is t2−2at+(a+3) In t∈[−1,1] Largest value can occur at t=1 or t=−1 At t=1,−a+4=7 ⇒a=−3 At t=−1, 1+3a+3=7 ⇒a=1 (A)→(R),(S) (B) f(x)=x4−ax2+2a−1,x∈[−1,2] Let t=x2,t∈[0,4] g(t)=t2−at+(2a−1) in t∈[0,4] Smallest value can occur at g(0)=2a−1=−7 ⇒a=−3g(4)=15−2a=−7 ⇒a=11g(a2)=a24−a22+2a−1=−7⇒a2−8a−24=0⇒a=4±2√10 (B)→(R),(T)

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