Column-I Column-II A) \int^{1\/\sqrt3}_{-1\/\sqrt3} {\cos^{-1}(\frac{2x}{1+x^2})+Tan^{-1}(\frac{2x}{1-x^2})}/{1+e^x} dx is equal to P) \sqrt3(\pi/3-\sqrt3/4) B) If A ≡ (1/2, 0), B ≡ (3/2, 0) and C ≡ (5/2, 0), the area of theregion(in square units) of the point P satisfying maximum{PA + PB, PB + PC} Q) π/3 C) If ∫f(x) \sec^2 x dx = f (x) secx + c then f(6x) is a periodic functionwith fundamental period R) π/12 D)If the latus rectum of the hyperbola x^2 \tan^2 θ – y^2 \sec^2 θ = 1 is1/2 and 0 S) π/2\sqrt3 T) 5π/12

Correct Answer is : A - S ; B - P ; C - Q ; D - R , T

A - P , S ; B - P ; C - Q ; D - R , S , T

A - Q , S ; B - P ; C - Q ; D - R , T

A - Q , R , S ; B - P ; C - Q ; D - R , T , S

A - S ; B - P ; C - Q ; D - R , T

JEE Advanced Model Paper 20 with solutions for online practice

Question : 30 of 57

Marks: +1, -0

Column-I

Column-II

1∕√3

∫

−1∕√3

cos−1(

1+x2

)+Tan−1(

1−x2

)

1+ex

dx is equal to

P) √3(

−

√3

)

B) If A ≡ (1/2, 0), B ≡ (3/2, 0) and C ≡ (5/2, 0), the area of theregion(in square units) of the point P satisfying maximum{PA + PB, PB + PC} < 2, is

Q) π/3

C) If ∫f(x) sec2x dx = f (x) secx + c then f(6x) is a periodic functionwith fundamental period

R) π/12

D)If the latus rectum of the hyperbola x2tan2 θ – y2sec2 θ = 1 is1/2 and 0 < θ < π then θ can be

S) π/2√3

T) 5π/12

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