Let \(N_{\beta}\) be the number of \(\beta \) particles emitted by \(1\) gram of \(Na^{24}\) radioactive nucler (half life \(= 15\, hrs\)) in \(7.5\, hours\), \(N_{\beta}\) is close to (Avogadro number \(= 6.023\times10^{23}\,/g.\, mole\))

Three blocks \(A\), \(B\) and \(C\) are pulled on a horizontal smooth surface by a force of \(80 \mathrm{~N}\) as shown in figure. The tensions \(T_1\) and \(T_2\) in the string are respectively _______ and _______.

In hydrogen atom spectrum, (R is Rydberg's constant):
A. the maximum wavelength of the radiation of Lyman series is \(\frac{4}{3 R}\)
B. the Balmer series lies in the visible region of the spectrum
C. the minimum wavelength of the radiation of Paschen series is \(\frac{9}{R}\)
D. the minimum wavelength of Lyman series is \(\frac{5}{4 R}\)
Choose the correct answer from the options given below :

A particle of mass \(M\) originally at rest is subjected to a force whose direction is constant but magnitude varies with time according to the relation \(F=F_{0}\left(1-\left(\frac{t-T}{T}\right)^{2}\right)\) Where \(F_{0}\) and \(T\) are constants. The force acts only for the time internal \(2 T\). The velocity \(v\) of the particle after time \(2 {T}\) is -

An electron is allowed to move with constant velocity along the axis of current carrying straight solenoid. \(A.\) The electron will experience magnetic force along the axis of the solenoid. \(B.\) The electron will not experience magnetic force. \(C.\) The electron will continue to move along the axis of the solenoid. \(D.\) The electron will be accelerated along the axis of the solenoid. \(E.\) The electron will follow parabolic path-inside the solenoid. Choose the correct answer from the options given below:

Distance between object and its image \(\left( \text{magnified by } -\frac{1}{3}\right)\) is 30 cm. The focal length of the mirror used is \(\left(\frac{x}{4}\right) \mathrm{cm}\),
where magnitude of value of \(x\) is _________.

In the figure, potential difference between \(A\) and \(B\) is......\(V\)

A particle of mass \(\mathrm{m}\) and charge \(\mathrm{q}\) has an initial velocity \(\overline{\mathrm{v}}=\mathrm{v}_{0} \hat{\mathrm{j}} .\) If an electric field \(\overrightarrow{\mathrm{E}}=\mathrm{E}_{0} \hat{\mathrm{i}}\) and magnetic field \(\overrightarrow{\mathrm{B}}=\mathrm{B}_{0} \hat{\mathrm{i}}\) act on the particle, its speed will double after a time:

A transverse wave is represented by \(y=2 \sin\) \((\omega t - kx ) cm\). The value of wavelength (in \(cm\) ) for which the wave velocity becomes equal to the maximum particle velocity, will be.

A string is clamed at both the ends and it is vibrating in its \(4^{th}\) harmonic. The equation of the stationary wave is \(Y =0.3\,sin\,(0.157\,x) \,cos\,(200\pi t)\). The length of the string is ..... \(m\) (all quantities are in \(SI\) units)

Two thin convex lenses of focal length 30 cm and 10 cm are placed coaxially, 10 cm apart. The power of this combination is :