The position of the image formed by the combination of lenses is _______. \(\mathrm{f}_1=10 \mathrm{~cm} \quad \mathrm{f}_2=10 \quad \mathrm{f}_3=30 \mathrm{~cm}\)

\(27\) identical drops are charged at \(22\, V\,\,each.\) They combine to form a bigger drop. The potential of the bigger drop will be............ \(V.\)

A magnet hung at \(45^{\circ}\) with magnetic meridian makes an angle of \(60^{\circ}\) with the horizontal. The actual value of the angle of dip is.

In the given figure, a mass \(M\) is attached to a horizontal spring which is fixed on one side to a rigid support. The spring constant of the spring is \(k\). The mass oscillates on a frictionless surface with time period \(T\) and amplitude \(A\). When the mass is in equilibrium position, as shown in the figure, another mass \(m\) is gently fixed upon it. The new amplitude of oscillation will be

A block of mass 1 kg , moving along x with speed \(\mathrm{v}_{\mathrm{i}}=10 \mathrm{~m} / \mathrm{s}\) enters a rough region ranging from \(\mathrm{x}=0.1 \mathrm{~m}\) to \(\mathrm{x}=1.9 \mathrm{~m}\). The retarding force acting on the block in this range is \(\mathrm{F}_{\mathrm{r}}=-\mathrm{kx} \mathrm{N}\), with \(\mathrm{k}=10 \mathrm{~N} / \mathrm{m}\). Then the final speed of the block as it crosses rough region is

A convex lens made of glass (refractive index \(=1.5\) ) has focal length 24 cm in air. When it is totally immersed in water (refractive index \(=1.33\) ), its focal length changes to ________.

In a screw gauge when the circular scale is given five complete rotations it moves linearly by \(2.5\) mm. If the circular scale has \(100\) divisions, the least count of screw gauge is _____ mm.

The equivalent capacitance of the combination shown is

Two vectors \(\overrightarrow{ A }\) and \(\overrightarrow{ B }\) have equal magnitudes. If magnitude of \(\overrightarrow{ A }+\overrightarrow{ B }\) is equal to two times the magnitude of \(\overrightarrow{ A }-\overrightarrow{ B }\), then the angle between \(\overrightarrow{ A }\) and \(\overrightarrow{ B }\) will be .......................

Two identical conducting spheres \(A\)  and \(B,\)  carry equal charge. They are separated by a distance much larger than their diameter, and the force between them is \(F\) . A third identical conducting sphere, \(C,\)  is uncharged. Sphere \(C\)  is first touched to \(A,\) then to \(B,\)  and then removed. As a result, the force between \(A\)  and \(B\)  would be equal to