Match Column I with Column II: Column I Column II (A) \sum^{\infty}_{t=1} \tan^{-1}(1/{2i^2}) = t , then tan t is (P) 2/3 (B) Sides a, b, c of a ΔABC are in A.P. and cos \theta_1 = a/{b+c} , \cos\theta_2 = b/{a+c} , \cos\theta_3 = c/{a+b} , then \tan^2(\theta_1/2)+\tan^2(\theta_3/2) is (Q) 1 (C) A line is perpendicular to x + 2y + 2z = 0 and passes through (0, 1, 0). The perpendicular distance of this line from the origin is (R) \sqrt5/3 (D) If sinAsinBsinC + cosAcosB = 1, then the value of sinC is (S) 1 [JEE Adv 2006 P1]

Correct Answer is : (A)→(Q); (B)→(P); (C)→(R)

(A)→(R); (B)→(P); (C)→(Q)

(A)→(Q); (B)→(P); (C)→(R)

(A)→(P); (B)→(Q); (C)→(R)

(A)→(Q); (B)→(P); (C)→(P)

IIT JEE Advanced 2006 Paper 1

Section: Mathematics

Question : 120 of 120

Marks: +1, -0

Match Column I with Column II:

Column I

Column II

(A)

∞

t=1

tan−1(

2i2

) = t , then tan t is

(P)

(B) Sides a, b, c of a ΔABC are in A.P. and cos θ1 =

b+c

, cosθ2 =

a+c

, cosθ3 =

a+b

, then tan2(

θ1

)+tan2(

θ3

) is

(Q) 1

(C) A line is perpendicular to x + 2y + 2z = 0 and passes through (0, 1, 0). The perpendicular distance of this line from the origin is

(R)

√5

(D) If sinAsinBsinC + cosAcosB = 1, then the value of sinC is

(S) 1

[JEE Adv 2006 P1]

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