An \(\alpha\)-particle, a proton and an electron have the same kinetic energy. Which one of the following is correct in case of their De-Broglie wavelength:

In an experiment to verify Stokes law, a small spherical ball of radius \(r\) and density \(\rho\) falls under gravity through a distance \(h\) in air before entering a tank of water. If the terminal velocity of the ball inside water is same as its velocity just before entering the water surface, then the value of \(h\) is proportional to : (ignore viscosity of air)

A parallel plate air capacitor has a capacitance \(C\). When it is half filled as show in figure with a dielectric constant \(K = 5\), the percentage increase in the capacitance is _______.

Two coils of self inductance \(L _{1}\) and \(L _{2}\) are connected in series combination having mutual inductance of the coils as \(M\). The equivalent self inductance of the combination will be ...............

Given below are two statements : one is labelled as Assertion \(A\) and the other is labelled as Reason \(R\). Assertion \(A\) : When a body is projected at an angle \(45^{\circ}\), it's range is maximum. Reason \(R\) : For maximum range, the value of \(\sin 2 \theta\) should be equal to one. In the light of the above statements, choose the correct answer from the options given below :

Consider the \(LR\) circuit shown in the figure. If the switch \(S\) is closed at \(t = 0\) then the amount of charge that passes through the battery between \(t = 0\) and \(t = \frac{L}{R}\) is

Given below are two statements: Statement \(I\) : In hydrogen atom, the frequency of radiation emitted when an electron jumps from lower energy orbit \(\left( E _{1}\right)\) to higher energy orbit \(\left( E _{2}\right)\), is given as \(hf = E _{1}- E _{2}\). Statement \(II\) : The jumping of electron from higher energy orbit \(\left(E_{2}\right)\) to lower energy orbit \(\left(E_{1}\right)\) is associated with frequency of radiation given as \(f\) \(=\left( E _{2}- E _{1}\right) / h\) This condition is Bohr's frequency condition. In the light of the above statements, choose the correct answer from the options given below

An upright object is placed at a distance of \(40\, cm\) in front of a convergent lens of focal length \(20\, cm\). A convergent mirror of focal length \(10\, cm\) is placed at a distance of \(60\, cm\) on the other side of the lens. The position and size of the final image will be

Given below are two statements : Statement \((I)\) : dimensions of specific heat is \(\left[\mathrm{L}^2 \mathrm{~T}^{-2} \mathrm{~K}^{-1}\right]\) Statement \((II)\) : dimensions of gas constant is \(\left[\mathrm{ML}^2 \mathrm{~T}^{-1} \mathrm{~K}^{-1}\right]\)

A potential \(V_0\) is applied across a uniform wire of resistance \(R\). The power dissipation is \(P_1\). The wire is then cut into two equal halves and a potential of \(V _0\) is applied across the length of each half. The total power dissipation across two wires is \(P_2\). The ratio \(P_2: P_1\) is \(\sqrt{x}: 1\). The value of \(x\) is \(.............\).

The energy released when \(\dfrac{7}{17.13}\) kg of \(^{7}_{3}\text{Li}\) is converted into \(^{4}_{2}\text{He}\) by proton bombardment is \(\alpha \times 10^{32}\) eV. The value of \(\alpha\) is _______. (Nearest integer) (Mass of \(^{7}_{3}\text{Li} = 7.0183\) u, mass of \(^{4}_{2}\text{He} = 4.004\) u, mass of proton \(= 1.008\) u and \(1\) u \(= 931\) MeV/c\(^2\) and Avogadro number \(= 6.0 \times 10^{23}\))