Two springs of force constants \(300\, N/m\) (Spring \(A\)) and \(400\, N/m\) (Spring \(B\)) are joined together in series . The combination is compressed by \(8.75\, cm\). The ratio of energy stored in \(A\) and \(B\) is  \(\frac{{{E_A}}}{{{E_B}}}\).  Then \(\frac{{{E_A}}}{{{E_B}}}\) is equal to

Speed of a transverse wave on a straight wire (mass \(6.0\; \mathrm{g}\), length \(60\; \mathrm{cm}\) and area of cross-section \(1.0\; \mathrm{mm}^{2}\) ) is \(90\; \mathrm{ms}^{-1} .\) If the Young's modulus of wire is \(16 \times 10^{11}\; \mathrm{Nm}^{-2},\) the extension of wire over its natural length is

In the given circuit, the current \((I)\) through the battery will be \(..........\,A\)

The coefficient of static friction between a wooden block of mass \(0.5\, kg\) and a vertical rough wall is \(0.2\) The magnitude of horizontal force that should be applied on the block to keep it adhere to the wall will be \(N\) \(\left[ g =10\, ms ^{-2}\right]\)

Select the correct statement from the following

Two sources of light emit with a power of \(200 \mathrm{~W}\). The ratio of number of photons of visible light emitted by each source having wavelengths \(300\  \mathrm{nm}\) and \(500 \mathrm{~nm}\) respectively, will be _______.

A monochromatic light of frequency \(5 \times 10^{14} \mathrm{~Hz}\) travelling through air, is incident on a medium of refractive index ' 2 '. Wavelength of the refracted light will be :

A convex lens of focal length \(20\,cm\) is placed in front of convex mirror with principal axis coinciding each other. The distance between the lens and mirror is \(10\,cm\). A point object is placed on principal axis at a distance of \(60\,cm\) from the convex lens. The image formed by combination coincides the object itself. The focal length of the convex mirror is \(...cm\).

If the series limit frequency of the Lyman series is \(v_L\), then the series limit frequency of the \(P\)-fund series is

A polarizer - analyser set is adjusted such that the intensity of light coming out of the analyser is just \(10 \%\) of the original intensity. Assuming that the polarizer - analyser set does not absorb any light, the angle by which the analyser need to be rotated further to reduce the output intensity to be zero, is.....\(^o\)

In finding out refractive index of glass slab the following observations were made through travelling microscope \(50\) vernier scale division \(=\) \(49 \mathrm{MSD} ; 20\) divisions on main scale in each \(\mathrm{cm}\) For mark on paper \(\mathrm{MSR}=8.45 \mathrm{~cm}, \mathrm{VC}=26\) For mark on paper seen through slab \(\mathrm{MSR}=7.12 \mathrm{~cm}, \mathrm{VC}=41\) For powder particle on the top surface of the glass slab \(\mathrm{MSR}=4.05 \mathrm{~cm}, \mathrm{VC}=1\) \((\mathrm{MSR}=\) Main Scale Reading, \(\mathrm{VC}=\) Vernier Coincidence) Refractive index of the glass slab is _______.

The maximum vertical height to which a man can throw a ball is \(136\,m\). The maximum horizontal distance upto which he can throw the same ball is \(.....\,m\)

Two charged particles, having same kinetic energy, are allowed to pass through a uniform magnetic field perpendicular to the direction of motion. If the ratio of radii of their circular paths is \(6: 5\) and their respective masses ratio is \(9: 4\). Then, the ratio of their charges will be.