If `P=(x , y),F_1=(3,0),F_2=(-3,0),` and `16 x^2+25 y^2=400` , then `P F_1+P F_2` equal 8 (b) 6 (c) 10 (d) 12

If f(x),g(x) be twice differentiable function on [0,2] satisfying f''(x)=g''(x) , f'(1)=4 and g'(1)=6,f(2)=3,g(2)=9,then f(x)-g(x) at x=4 equals to:- (a) -16 (b) -10 (c) -8

If P={:[(-1,0),(2,-1)]:}andf(x)=x^(2)-2x+2 , then find f(P).

if f(x)=3|x|+|x-2| then f'(1) is equal to a)2 b)1 c)3 d)0

If f(x),g(x) be twice differentiable functions on [0,2] satisfying f''(x)=g''(x)f'(1)=2g'(1)=4 and f(2)=3g(2)=9 then f(x)-g(x) at x=4 equals (A) 0 (B) 10 (C) 8 (D) 2

P(x,y) is any point on ellipse 16x^(2)+25y^(2) =400 . If F_(1)-=(3,0) and F_(2) -=(-3,0) , then prove that PF_(1)+PF_(2) is constant and find its value .

If |f(x)-f(y)|<=2|x-y|^((3)/(2))AA x,y in R and f(0)=1 then value of int_(0)^(1)f^(2)(x)dx is equal to (a) 1 (b) 2 (c) sqrt(2)(d)4

If 8f(x)+6f((1)/(x))=x+5 and y=x^(2)(f(x), then (dy)/(dx) at x=-1 is equal to 0( b) (1)/(14)(c)-(1)/(4)(d) None of these

If f(x) = | x | + [ x ] , then f( -3/2 ) + f( 3/2 ) is equal to : ( a ) 1 ( b ) -1/2 ( c ) 2 ( d ) 1/2

[ If f(x)=|x|+|x-1|, then int_(0)^(2)f(x)dx equals- [ (A) 3, (B) 2, (C) 0, (D) -1]]