The minimum vertical distance between the graphs of `y=2+sinx` and `y=cosx` is (a)`2` (b)` 1` (c) `sqrt(2)` (d) `2-sqrt(2)`

Find the maximum vertical distance between the graphs y=2+3sinx and y=4cos x-3 .

The shortest distance between the line x=y and the curve y^(2)=x-2 is (a) 2 (b) (7)/(8) (c) (7)/(4sqrt(2)) (d) (11)/(4sqrt(2))

The shortest distance between the parabolas 2y^2=2x-1 and 2x^2=2y-1 is 2sqrt(2) (b) 1/2sqrt(2) (c) 4 (d) sqrt((36)/5)

Draw the graph of y= sqrt (x^(2)-1)

Draw the graph of y=sqrt(1+x^(2))-x

Equation of a line which is tangent to both the curve y=x^2+1\ a n d\ y=x^2 is y=sqrt(2)x+1/2 (b) y=sqrt(2)x-1/2 y=-sqrt(2)x+1/2 (d) y=-sqrt(2)x-1/2

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)

Draw the graph of y= (x^(2))/(sqrt(x+1))

Two parallel lines lying in the same quadrant make intercepts a and b on x and y axes, respectively, between them. The distance between the lines is (a) (ab)/sqrt(a^2+b^2) (b) sqrt(a^2+b^2) (c) 1/sqrt(a^2+b^2) (d) 1/a^2+1/b^2

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)