If the straighat lines `x=1+s,y=-3-lamdas,z=1+lamdas and x=t/2,y=1+t,z=2-t` with parameters s and t respectively, are coplanar, then `lamda` equals (A) `-1/2` (B) `-1` (C) `-2` (D) `0`

Options

A. 0
B. `-1`
C. `-(1)/(2)`
D. `-2`

Answer

C

Explanation

`f(f(x))`
`(x+x^(2)+x^(4)+x^(8)+........)^(1)rarr "Co-efficient of" x^(10)=0`
`+`
`(x+x^(2)+x^(4)+x^(8)+........)^(2)rarr "Co-efficient of" x^(10)=2 (x^(2).x^(8),x^(8).x^(2))`
`+`
`(x+x^(2)+x^(4)+x^(8)+........)^(4)rarr "Co-efficient of" x^(10)(2+2+2+4=10):(4!)/(3!)=4(x^(2).x^(2).x^(2).x^(4),x.x.x^(4).x^(4))`
`+ " "(1+1+4+4=10):(4!)/(2!2!)=6`
`(x+x^(2)+x^(4)+x^(8)+........)^(8)rarr "Co-efficient of" x^(10)(1+1+1+1+1+1+2+2):(8!)/(2!6!)=28`
+
`{:( : ),( : ):}}"Co-efficient of" x^(10)=0`
`therefore "Co-efficient of" x^(10)=2+4+6+28=40`