The minimum value of `(x^4+y^4+z^2)/(x y z)` for positive real numbers `x ,y ,z` is (a)`sqrt(2)` (b)`2sqrt(2)` (c)`4sqrt(2)` (d)`8sqrt(2)`

Radius of the circle that passes through the origin and touches the parabola y^2=4a x at the point (a ,2a) is (a) 5/(sqrt(2))a (b) 2sqrt(2)a (c) sqrt(5/2)a (d) 3/(sqrt(2))a

The length of the chord of the parabola y^2=x which is bisected at the point (2, 1) is (a) 2sqrt(3) (b) 4sqrt(3) (c) 3sqrt(2) (d) 2sqrt(5)

The differential of y if y =sqrt(x^(4) + x^(2)-1)

Given that x,y,z are positive real numbers such that xyz=32 , the minimum value of sqrt((x+2y)^(2)+2z^(2)-15) is equal to

If two different tangents of y^2=4x are the normals to x^2=4b y , then (a) |b|>1/(2sqrt(2)) (b) |b| 1/(sqrt(2)) (d) |b|<1/(sqrt(2))

Find GCD of 25x^(2) y^(2)z, 45x^(2) y^(4) z^(3) b

min[(x_1-x_2)^2+(3+sqrt(1-x_1^2)-sqrt(4x_2))^2],AAx_1,x_2 in R , is (a) 4sqrt(5)+1 (b) 3-2sqrt(2) (c) sqrt(5)+1 (d) sqrt(5)-1

If P(1+t/(sqrt(2)),2+t/sqrt(2)) is any point on a line, then the range of the values of t for which the point P lies between the parallel lines x+2y=1a n d2x+4y=15. is (a) (4sqrt(2))/3lttlt5(sqrt(2)) 6 (b) 0lttlt(5sqrt(2)) (c) 4sqrt(2)lttlt0 (d) none of these

Normals at two points (x_1y_1)a n d(x_2, y_2) of the parabola y^2=4x meet again on the parabola, where x_1+x_2=4. Then |y_1+y_2| is equal to sqrt(2) (b) 2sqrt(2) (c) 4sqrt(2) (d) none of these