Light of wavelength $\lambda$ is incident on a single slit of width $a$ and the distance between the slit and the screen is $D$. In the diffraction pattern,if the slit width is equal to the width of the central maximum,then $D$ is equal to:

If $y = \sec(\tan^{-1}x)$,then $\frac{dy}{dx}$ at $x = 1$ is equal to:

The combined equation of the lines passing through the origin and having slopes $\frac{2}{3}$ and $-\frac{2}{3}$ is

$A$ sonometer wire resonates with a given tuning fork,forming standing waves with five antinodes between the two bridges when a mass of $9 \, kg$ is suspended from the wire. When this mass is replaced by a mass $M$,the wire resonates with the same tuning fork,forming three antinodes for the same positions of the bridges. The value of $M$ is .... $kg$.

Two bulbs are connected in parallel. Bulb $A$ is brighter than bulb $B$. If their resistances are $R_A$ and $R_B$ respectively,then:

If $\alpha, \beta, \gamma, \delta$ are the smallest positive angles in ascending order of magnitude which have their sines equal to the positive quantity $k$,then the value of $4\sin \frac{\alpha}{2} + 3\sin \frac{\beta}{2} + 2\sin \frac{\gamma}{2} + \sin \frac{\delta}{2}$ is equal to