Match List I with List II and choose the correct answer

Options

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

Explanation

a. `"If "xy-log y=1" then "xy_(1)+y=y_(1)//y`
`"so "y^(2)+(xy-1)y_(1)=0`
b. `ysqrt(1-x^(2))=sin^(-1)x`
`rArr" "-(yx)/(sqrt(1-x^(2)))+y_(1)sqrt(1-x^(2))=(1)/(sqrt(1-x^(2)))`
`"so "-xy+y_(1)(1-x^(2))=1`
c. `y^(2)=2x-x^(2)rArr yy_(1)=1-x`
`rArr" "y_(1)^(2)+yy_(2)=-1`
`"so "(1-x)^(2)/(y^(2))+yy_(2)=-1`
`rArr" "y^(3)y_(2)=-[1+x^(2)-2x+y^(2)]=-1`
d. `y=e^(sqrt(x))+e^(-sqrt(x))`
`rArr" "y_(1)=(e^(sqrt(x))-e^(-sqrt(x)))/(2sqrt(x))`
`rArr" "y_(1)^(2)x=(e^(sqrt(x))-e^(-sqrt(x)))^(2)=y^(2)-4`
`rArr" "8y_(1)y_(2)x+4y_(1)^(2)=2yy_(1)`
`rArr" "4y_(2)x+2y_(1)=y`
`rArr" "xy_(2)-(1)/(2)y_(1)-(1)/(4)y=0`