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 P(x , y) ,F_(1) (3,0) , F_(2) (-3, 0) " and " 16x^(2) + 25 y^(2) = 400 then show that PF_(1)+PF_(2)=10

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

Let f:[-1,2]->[0,oo) be a continuous function such that f(x)=f(1-x)fora l lx in [-1,2]dot Let R_1=int_(-1)^2xf(x)dx , and R_2 be the area of the region bounded by y=f(x),x=-1,x=2, and the x-axis . Then (a) R_1=2R_2 (b) R_1=3R_2 (c) 2R_1 (d) 3R_1=R_2

Let A ={:[(2,0,1),(2,1,3),(1,-1,0)] and f(x) = x^(2) -5x + 6 , find f(A).

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/y)= f(x)/f(y) , AA y, f (y)!=0 and f' (1) = 2 , find f(x) .

A rectangle A B C D , where A-=(0,0),B-=(4,0),C-=(4,2)D-=(0,2) , undergoes the following transformations successively: f_1(x ,y)to(y ,x) f_2(x , y)to(x+3y ,y) f_3(x , y)to((x-y)/2),(x+y)/2) The final figure will be (a) square (b) a rhombus (c) a rectangle (d) a parallelogram

If f(x+y)=f(x)+f(y)-x y-1AAx , y in R and f(1)=1, then the number of solution of f(n)=n , n in N , is 0 (b) 1 (c) 2 (d) more than 2

If f(x)=x/(x^2+1) and f(A)={y:-1/2 le y lt 0} , then set A is

If f(x)=int(3x^2+1)/((x^2-1)^3)dx and f(0)=0, then the value of |2/(f(2))| is___