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JEE Advanced 2020 Full Test 5 Paper 1

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This section contains SIX questions of matching type. The section contains TWO tables (each having 3 columns and 4 rows). Based on each table, there are THREE questions. Each question has FOUR options (A),(B),(C), and (D). ONLY ONE of these four options is correct.
Answer questions 44,45 and 46 by appropriately matching the information given in the three columns of the following table.

   Column -1    Column -2    Column -3
 (I)  The value of
∞
∑
n=0
2−n+(−1)n is		  (i)  The value of [
∞
∑
n=0
tan−1(‌
2
√n+2+√n+(n+2)√n+n(√n+2)
)] (where [.] denotes greatest integer function) is		  (P)  2
 (II)  Number of solutions of equation 16sin3x=14+√[3]sin‌x+7 in [0,4π] is  (ii)  If a,b,c are sides of a triangle, then ‌
2(a2+b2+c2)
ab+bc+ca
 is always less than		  (Q)  3
 (III)  Number of solutions of equation tan−1(2‌sin‌x)=cot−1(cos‌x) in [0,10π] is  (iii)  If a,b,c are distinct real numbers such that a2(b+c)=b2(a+c)=2, then the value of c2(a+b) is  (R)   4
 (IV)  If the sum of roots of the quadratic equation (−a+1)x2+(a2−a+4)x−2a+3=0 is minimum, then the value of a(a>1) is  (iv)  If P=sin‌A‌sin‌B,Q=sin‌C‌cos‌A R=sin‌A‌cos‌B S=cos‌A‌cos‌C, then the value of 5(P2+Q2+R2+S2) is  (S)   5
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Question : 46
Total: 54
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