Differential Calculus

Ques1) Show that one of the solution of the equation -x⁴+x²-P=0 where x belongs to (0,1) and P belongs to (0,1/4) is sin (1/2 sin ^{- 1} 2 √P).

Ques2) Tangents are drawn to y = ax2+bx+c at (5,4) is parallel to x- axis. If a belongs to [2,4], then show that the max value of c is 104.

Ques3) The number of st lines parallel to 2x+6y+7 = 0 and have intercept of length 10 b/w the coordiante axis is:-
(a) 1 (b) 2 (c)4 (d) infinitely many