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

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) = 3 g(2) = 9 , then f(x)-g(x) at x = 4 equals (A) 0 (B) 10 (C) 8 (D) 2

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

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

The differentiable function y= f(x) has a property that the chord joining any two points A (x _(1), f (x_(1)) and B (x_(2), f (x _(2))) always intersects y-axis at (0,2 x _(1) x _(2)). Given that f (1) =-1. then: int _(0)^(1//2) f (x) dx is equal to : (a) 1/6 (b) 1/8 (c) 1/12 (d) 1/24

If P(x ,y) is any point on the ellipse 16 x^2+25 y^2=400 and f_1=(3,0)F_2=(-3,0) , then find the value of P F_1+P F_2dot

If |f(x)-f(y)|le2|x-y|^((3)/(2)) AAx,yinR and f(0)=1 then value of int_(0)^(1)f^2(x)dx is equal to (a) 1 (b) 2 (c) sqrt2 (d) 4

If f'(x)=(1)/((1+x^(2))^(3//2)) and f(0)=0, then f(1) is equal to :

f(x)={(sqrt(1+p x)-sqrt(1-p x))/x ,-1lt=x<0(2x+1)/(x-2),0geqxgeq1 is continuous in the interval [-1,1], then p is equal to -1 (b) -1/2 (c) 1/2 (d) 1