Let f(x)=4x ^2-4ax+a^2-2a+2 x,aϵR If `y=f(x)` takes minimum value `3` on `x in [0,2]` and x-coordinae of vertex is greater than 2, then value of `a` is `(a)5-sqrt(10)` (b) `10-sqrt(5)` `(c)5+sqrt(10)` (d) `10+sqrt(5)`

Let f(x)=4x^2-4ax+a^2-2a+2 be a quadratic polynomial in x, a be any real number, If x- coordinate of vertex of parabola y=f(x) is less than 0 and f(x) has minimum value 3 for x in [0,2], then value of a is (a) 1+sqrt(2) (b) 1-sqrt(2) (c) 1-sqrt(3) (d) 1+sqrt(3)

If y=2x+3 is a tangent to the parabola y^(2)=24x, then is distance from the parallel normal is 5sqrt(5)(b)10sqrt(5)(c)15sqrt(5)(d) None of these

If f(x)=x^(3)-5x^(2)+5x+1 then value of f(2-sqrt(3)) is

If x=sqrt(5)+2, then x-(1)/(x) equals 2sqrt(5)(b)4 (c) 2 (d) sqrt(5)

If f(x)=sqrt(2x^(2)-6x+5)+sqrt(2x^(2)-40x+218) ,then the minimum value of f(x) is

If x-(2)/(sqrt(10)-sqrt(8)),y-(2)/(sqrt(10)+2sqrt(2)) , then (x-y)^(2) =

5sin x+4cos x=3rArr4sin x-5cos x= a) 4 b) 4sqrt(2) c) 3sqrt(2) d) sqrt(2)

The value of int_(5)^(10)(sqrt(x+sqrt(20x-100))+sqrt(x-sqrt(20x-100)))dxis (1) 10sqrt(5)(2)5sqrt(5)(3)10sqrt(2)(4)8sqrt(2)

Range of f(x)=log_(sqrt10) (sqrt5 (2 sin x+cos x)+5) is :

If x,y in R satisfy the equation x^(2)+y^(2)-4x-2y+5=0, then the value of the expression ((sqrt(x)-sqrt(y))^(2)+4sqrt(xy))/((x+sqrt(xy))) is