The figure shows a system of logic gates. From the study of the truth table,it can be found that to produce a high output $(1)$ at $R$,we must have

If $x + \sqrt{x^2 + 1} = a$,then $x =$

$A$ block placed on a rough inclined plane of inclination $\theta=30^{\circ}$ can just be pushed upwards by applying a force $F$ as shown. If the angle of inclination of the inclined plane is increased to $\theta=60^{\circ}$,the same block can just be prevented from sliding down by application of a force of the same magnitude $F$. The coefficient of friction between the block and the inclined plane is:

If $u=\sin ^{-1}\left(\frac{x^2+y^2}{x+y}\right)$ then $x \frac{\partial u}{\partial x}+y \frac{\partial u}{\partial y}$ is equal to:

Which of the following statements are correct about herbarium?

Fresnel diffraction is produced due to light rays falling on a small obstacle. The intensity of light at a point on a screen beyond an obstacle depends on