Assuming human pupil to have a radius of \(0.25\ cm\) and a comfortable viewing distance of \(25\ cm\), the minimum separation between two objects that human eye can resolve at \(500\ nm\) wavelength is.....\(\mu m\)

A submarine \((A)\) travelling at \(18\, km/hr\) is being chased along the line of its velocity by another submarine \((B)\) travelling at \(27\, km/hr\). \(B\) sends a sonar signal of \(500\, Hz\) to detect \(A\) and receives a reflected sound of frequency \(v\). The value of \(v\) is close to ... \(Hz\) (Speed of sound in water \(= 1500\, ms^{-1}\))

A body of mass ' \({m}\) ' dropped from a height ' \({h}\) ' reaches the ground with a speed of \(0.8 \sqrt{{gh}}\). The value of workdone by the air-friction is \(.....\,{mgh}\)

A ball projected from ground at an angle of \(45^o\) just clears a wall in front. If point of projection is \(4\,m\) from the foot of wall and ball strikes the ground at a distance of \(6\,m\) on the other side of the wall, the height of the walI is  ........ \( m\)

Moment of inertia of a rod of mass ' M ' and length 'L' about an axis passing through its center and normal to its length is ' \(\alpha\) '. Now the rod is cut into two equal parts and these parts are joined symmetrically to form a cross shape. Moment of inertia of cross about an axis passing through its center and normal to plane containing cross is :

In a Young's double slit experiment, the slits are separated by \(0.3\, {mm}\) and the screen is \(1.5\, {m}\) away from the plane of slits. Distance between fourth bright fringes on both sides of central bright is \(2.4\, {cm}\). The frequency of light used is \(..........\,\times 10^{14} {Hz}\)

Given below are two statements: one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\) Assertion \(A:\) When you squeeze one end of a tube to get toothpaste out from the other end, Pascal's principle is observed. Reason \(R:\) A change in the pressure applied to an enclosed incompressible fluid is transmitted undiminished to every portion of the fluid and to the walls of its container. In the light of the above statements, choose the most appropriate answer from the options given below

A parallel plate capacitor is made of two plates of length \(l\), width \(w\) and separated by distance \(d\). A dielectric slab ( dielectric constant \(K\)) that fits exactly between the plates is held near the edge of the plates. It is pulled into the capacitor by a force \(F = -\frac{{\partial U}}{{\partial x}}\) where \(U\) is the energy of the capacitor when dielectric is inside the capacitor up to distance \(x\) (See figure). If the charge on the capacitor is \(Q\) then the force on the dielectric when it is near the edge is

\(ABC\) is a plane lamina of the shape of an equilateral triagnle. \(D,\) \(E\) are mid points of \(AB\), \(AC\) and \(G\) is the centroid of the lamina. Moment of inertia of the lamina about an axis passing through \(G\) and perpendicular to the plane \(ABC\) is \(I _{0} .\) If part \(ADE\) is removed, the moment of inertia of the remaining part about the same axis is \(\frac{ NI _{0}}{16}\) where \(N\) is an integer. Value of \(N\) is

A tuning fork resonates with a sonometer wire of length \(1 \mathrm{~m}\) stretched with a tension of \(6 \mathrm{~N}\). When the tension in the wire is changed to \(54 \mathrm{~N}\), the same tuning fork produces \(12\) beats per second with it. The frequency of the tuning fork is _______ \(\mathrm{Hz}\).