Given below are two statements:
Statement I: In a Young's double slit experiment, the angular separation of fringes will increase as the screen is moved away from the plane of the slits
Statement II : In a Young's double slit experiment, the angular separation of fringes will increase when monochromatic source is replaced by another monochromatic source of higher wavelength
In the light of the above statements, choose the correct answer from the options given below:

As shown in figure, when a spherical cavity (centred at \(\mathrm{O})\) of radius \(1\) is cut out of a uniform sphere of radius \(\mathrm{R} \text { (centred at } \mathrm{C}),\) the centre of mass of remaining (shaded) part of sphere is at \(G\), i.e, on the surface of the cavity. \(\mathrm{R}\) can be detemined by the equation

With reference to the observations in photo-electric effect, identify the correct statements from below: \(A.\) The square of maximum velocity of photoelectrons varies linearly with frequency of incident light. \(B.\) The value of saturation current increases on moving the source of light away from the metal surface. \(C.\) The maximum kinetic energy of photo-electrons decreases on decreasing the power of LED (light emitting diode) source of light. \(D.\) The immediate emission of photo-electrons out of metal surface can not be explained by particle nature of light/electromagnetic waves. \(E.\) Existence of threshold wavelength can not be explained by wave nature of light/electromagnetic waves. Choose the correct answer from the options given below:

Maatch Liat \(I\) List \(II\) Chose the correct answer from the options given below

The parameter that remains the same for molecules of all gases at a given temperature is _______.

A satellite is moving with a constant speed \(v\) in circular orbit around the earth. An object of mass \(‘m’\) is ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of ejection, the kinetic energy of the object is

In an expression a \(\times 10^{\mathrm{b}}\) _______.

Let a die be rolled \(n\) times. Let the probability of getting odd numbers seven times be equal to the probability of getting odd numbers nine times. If the probability of getting even numbers twice is \(\frac{ k }{2^{15}}\), then \(k\) is equal to:

At the centre of a half ring of radius \(R=10 \mathrm{~cm}\) and linear charge density \(4 \mathrm{n} \mathrm{C} \mathrm{m}^{-1}\), the potential is \(x \pi V\). The value of \(x\) is _______.

A particle executes simple harmonic motion. Its amplitude is \(8 \,cm\) and time period is \(6 \,s\). The time it will take to travel from its position of maximum displacement to the point corresponding to half of its amplitude, is ............. \(s\)

If the area of the region \(\left\{( x , y ):\left| x ^2-2\right| \leq y \leq x \right\}\) is \(A\), then \(6 A +16 \sqrt{2}\) is equal to \(...........\).

The given figure represents two isobaric processes for the same mass of an ideal gas, then ....

Let \(A=\left[\begin{array}{lll}1 & 0 & 0 \\ 0 & \alpha & \beta \\ 0 & \beta & \alpha\end{array}\right]\) and \(|2 A|^3=2^{21}\) where \(\alpha, \beta \in Z\), Then a value of \(\alpha \) is