If $\sqrt{\frac{y}{x}}+\sqrt{\frac{x}{y}}=2$,then $\frac{d y}{d x}$ is equal to

$A$ particle moves with simple harmonic motion in a straight line. In the first $\tau \, s$,after starting from rest,it travels a distance $a$,and in the next $\tau \, s$,it travels $2a$ in the same direction. Then:

The set of solutions satisfying both $x^2+5x+6 \geq 0$ and $x^2+3x-4 < 0$ is

The period of revolution of planet $A$ around the sun is $8$ times that of planet $B$. The distance of planet $A$ from the sun is how many times greater than that of planet $B$ from the sun?

The length of the subtangent at any point $(x_1, y_1)$ on the curve $y=5^x$ is

If the angle between the lines joining the origin to the points of intersection of $x+2y+\lambda=0$ and $2x^2-2xy+3y^2+2x-y-1=0$ is $\frac{\pi}{2}$,then a value of $\lambda$ is