Question

Match List I with List II and select the correct answer using the codes given below the lists:

A. `{:(a,b,c,d),(s,r,p,q):}`
B. `{:(a,b,c,d),(s,r,p,q):}`
C. `{:(a,b,c,d),(r,s,q,p):}`
D. `{:(a,b,c,d),(r,s,p,q):}`

Answer 1

Correct Answer - B
`(cos(tan^(-1) y) + y sin (tan^(-1) y))/(cot (sin^(-1) y) + tan (sin^(-1) y))`
`= ((1)/(sqrt(1 + y^(2))) + (y^(2))/(sqrt(1 + y^(2))))/(sqrt(1 -y^(2))/(y) + (y)/(sqrt(1 -y^(2)))) = (sqrt(1 + y^(2))/(1))/((1)/(ysqrt(1 -y^(2))))`
`=y sqrt(1 -y^(4))`
`rArr(1)/(y^(2)) ((cos(tan^(-1) y) + y sin (tan^(-1) y))/(cos (sin^(-1) y) + tan (sin^(-1) y)))^(2) + y^(4)`
`= (1)/(y^(2)) (y^(2) (1 -y^(4))) + y^(4)`
`= 1-y^(4) + y^(4) = 1`
`cot(sin^(-1) sqrt(1 -x^(2)) = sin (tan^(-1) (x sqrt6)))`
`rArr cot(cot^(-1).(x)/(sqrt(1 -x^(2)))) = sin (sin^(-1).(xsqrt6)/(sqrt(1 + 6x^(2))))`
`rArr (x)/(sqrt(1 -x^(2))) = (x sqrt6)/(sqrt(6x^(2) + 1))`
`rArr 6x^(2) + 1 = 6 - 6x^(2)`
`rArr 12 x^(2) = 5`
`rArr x = sqrt((5)/(12)) = (1)/(2) sqrt((5)/(3))`
Note : Solution of the remaining parts are given in their respective chapters.