Consider the diffraction pattern obtained from the sunlight incident on a pinhole of diameter \(0.1\, \mu m\). If the diameter of the pinhole is slightly increased, it will affect the diffraction pattern such that :

Read the following statements: \(A.\) When small temperature difference between a liquid and its surrounding is doubled the rate of loss of heat of the liquid becomes twice. \(B.\) Two bodies \(P\) and \(Q\) having equal surface areas are maintained at temperature \(10^{\circ}\,C\) and \(20^{\circ}\,C\). The thermal radiation emitted in a given time by \(P\) and \(Q\) are in the ratio \(1: 1.15\) \(C.\) A carnot Engine working between \(100\,K\) and \(400\,K\) has an efficiency of \(75 \%\) \(D.\) When small temperature difference between a liquid and its surrounding is quadrupled, the rate of loss of heat of the liquid becomes twice. Choose the correct answer from the options given below :

In an adiabatic process, which of the following statements is true?

As per given figure, a weightless pulley \(P\) is attached on a double inclined frictionless surface. The tension in the string (massless) will be (if \(g=\) \(10\,m / s ^2\) )

Car \(B\) overtakes another car \(A\) at a relative speed of \(40\, ms^{-1}\). How fast will the image of car \({B}\) appear to move in the mirror of focal length \(10\, cm\) fitted in car \({A}\), when the car \({B}\) is \(1.9\, m\) away from the car \({A}\) ? (In \(ms^{-1}\))

A particle executes simple harmonic motion between \(x =- A\) and \(x =+ A\). If time taken by particle to go from \(x=0\) to \(\frac{A}{2}\) is \(2 s\); then time taken by particle in going from \(x =\frac{ A }{2}\) to \(A\) is \(.........\,s\)

A metal plate of area \(1\times10^{-4}\, m^2\) is illuminated by a radiation of intensity \(16\, m\,W/m^2\). The work function of the metal is \(5\,eV\). The energy of the incident photons is \(10\, eV\) and only \(10\%\) of it produces photo electrons. The number of emitted photo electrons per second and their maximum energy, respectively, will be : \([1\, eV = 1.6\times10^{-19}\, J]\)

A light string passing over a smooth light pulley connects two blocks of masses \(m_1\) and \(m_2\) (where \(m_2>m_1\) ). If the acceleration of the system is \(\frac{\mathrm{g}}{\sqrt{2}}\), then the ratio of the masses \(\frac{\mathrm{m}_1}{\mathrm{~m}_2}\) is _______.

A tuning fork is vibrating at \(250\, {Hz}\). The length of the shortest closed organ pipe that will resonate with the tuning fork will be ..... \({cm}\) (Take speed of sound in air as \(340\, {ms}^{-1}\) )

The temperature, at which the root mean square velocity of hydrogen molecules equals their escape velocity from the earth is closest to : [Boltzmans Constant \(k_B = 1.38\times10^{-23}\, J / K\) Avogadro number \(N_A = 6.02\times10^{26}\, / kg\) Radius of Earth \(: 6.4\times10^6\, m\) Gravitation acceleration on Earth \(= 10\, ms^{-2}\)]

In a Young's double slit experiment set up, the two slits are kept 0.4 mm apart and screen is placed at 1 m from slits. If a thin transparent sheet of thickness \(20 \mu m\) is introduced in front of one of the slits then centre bring fringe shifts by 20 mm on the screen. The refractive index of transparent sheet is given by \(\frac{\alpha}{10}\), where \(\alpha\) is _________ .

Match List\(-I\) with List\(-II\) 

List\(-I\)	List\(-II\)
\((A)\) \(AC\) generator	\((I)\) Detects the presence of current in the circuit
\((B)\) Galvanometer	\((II)\) Converts mechanical energy into electrical energy
\((C)\) Transformer	\((III)\) Works on the principle of resonance in \(AC\) circuit
\((D)\) Metal detector	\((IV)\) Changes an alternating voltage for smaller or greater value

Choose the correct answer from the options given below

A double convex lens has power \(P\) and same radii of curvature \(R\) of both the surfaces. The radius of curvature of a surface of a plano-convex lens made of the same material with power \(1.5P\) is ......\(R\)