A convex lens of focal length 30 cm is placed in contact with a concave lens of focal length 20 cm. An object is placed at 20 cm to the left of this lens system. The distance of the image from the lens in cm is ________

A satellite of mass \(\mathrm{m}\) is launched vertically upwards with an initial speed \(u\) from the surface of the earth. After it reaches height \(\mathrm{R}\) (\(R =\) radius of the earth), it ejects a rocket of mass \(\frac{\mathrm{m}}{10}\) so that subsequently the satellite moves in a circular orbit. The kinetic energy of the rocket is (\(G\) is the gravitational constant: \(\mathrm{M}\) is the mass of the earth)

Three different processes that can occur in an ideal monoatomic gas are shown in the \(P\) vs \(V\) diagram. The paths are labelled as \(A \rightarrow B, A \rightarrow C\) and \(A \rightarrow D .\) The change in internal energies during these process are taken as \(E _{ AB }, E _{ AC }\) and \(E _{ AD }\) and the work done as \(W _{ AB }\) \(W _{ AC }\) and \(W _{ AD }\) The correct relation between these parameters are

If Rydberg's constant is \(R\), the longest wavelength of radiation in Paschen series will be \(\frac{\alpha}{7 R}\), where \(\alpha=\)____________

The electric field of a plane electromagnetic wave, travelling in an unknown non-magnetic medium is given by,
\(E_y=20 \sin \left(3 \times 10^6 x-4.5 \times 10^{14} t\right) V / m\)
(where \(x, t\) and other values have S.I. units). The dielectric constant of the medium is __________ .
(speed of light in free space is \(3 \times 10^8 m / s\) )

A rectangular parallelopiped is measured as \(1\,cm \times 1\,cm \times 100\,cm\). If its specific resistance is \(3 \times 10^{-7}\,\Omega\,m\), then the resistance between its two opposite rectangular faces will be \(..........x^{-7} \Omega\).

Two long, straight wires carry equal currents in opposite directions as shown in figure. The separation between the wires is \(5.0 \mathrm{~cm}\). The magnitude of the magnetic field at a point \(P\) midway between the wires is __________\(\mu \mathrm{T}\) (Given : \(\mu_0=4 \pi \times 10^{-7} \mathrm{TmA}^{-1}\) )

A small spherical ball of radius \(0.1 \,mm\) and density \(10^{4} \,kg m ^{-3}\) falls freely under gravity through a a distance \(h\) before entering a tank of water. If after entering the water the velocity of ball does not change and it continue to fall with same constant velocity inside water, then the value of \(h\) wil be \(m\). (Given \(g =10 \,ms ^{-2}\), viscosity of water \(=1.0 \times 10^{-5} \,N - sm ^{-2}\) )

The magnitude of vectors \(\overrightarrow{ OA }, \overrightarrow{ OB }\) and \(\overrightarrow{ OC }\) in the given figure are equal. The direction of \(\overrightarrow{ OA }+\overrightarrow{ OB }-\overrightarrow{ OC }\) with \(x\)-axis will be

A particle of mass \(250\,g\) executes a simple harmonic motion under a periodic force \(F =(-25\,x) N\). The particle attains a maximum speed of \(4\,m / s\) during its oscillation. The amplitude of the motion is \(...........cm\).

The minimum frequency of photon required to break a particle of mass 15.348 amu into 4\( \alpha \) particles is __________ kHz.
[mass of He nucleus = 4.002 amu,
\(1 amu =1.66 \times 10^{-27} kg, h =6.6 \times 10^{-34} J . s\) and \(c =\) \(\left.3 \times 10^8 m / s \right]\)

A closed organ pipe has a fundamental frequency of \(1.5\, kHz\). The number of overtones that can be distinctly heard by a person with this organ pipe will be : (Assume that the highest frequency a person can hear is \(20,000\, Hz\))

Two small spheres each of mass \(10 \,mg\) are suspended from a point by threads \(0.5 \,m\) long. They are equally charged and repel each other to a distance of \(0.20 \,m\). The charge on each of the sphere is \(\frac{ a }{21} \times 10^{-8} \, C\). The value of \(a\) will be ...... . \(\left[\right.\) Given \(\left.g=10 \,ms ^{-2}\right]\)