A thin prism of angle \(6^{\circ}\) and refractive index for yellow light \(\left(n_{Y}\right) 1.5\) is combined with another prism of angle \(5^{\circ}\) and \(n _{ Y }=1.55\). The combination produces no dispersion. The net average deviation ( \(\delta\) ) produced by the combination is \(\left(\frac{1}{x}\right)^{\circ}\). The value of \(x\) is.......

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

A 4.0 cm long straight wire carrying a current of 8A is placed perpendicular to an uniform magnetic field of strength 0.15 T. The magnetic force on the wire is ______ mN.

The voltage across the \(10\, \Omega\) resistor in the given circuit is \(x\) volt. The value of \('x'\) to the nearest integer is..........

Consider a water tank as shown in the figure. It's cross-sectional area is \(0.4\, m ^{2}\). The tank has an opening \(B\) near the bottom whose cross-section area is \(1\, cm ^{2}\). A load of \(24\, kg\) is applied on the water at the top when the height of the water level is \(40\, cm\) above the bottom, the velocity of water coming out the opening \(B\) is \(v\, ms ^{-1}\). The value of \(v\), to the nearest integer, is ......\(m/s\). [Take value of \(g\) to be \(10 \,ms ^{-2}\) ]

Work done by a Carnot engine operating between temperatures \(127^{\circ}\,C\) and \(27^{\circ}\,C\) is \(2\,kJ\). The amount of heat transferred to the engine by the reservoir is \(........\,kJ\)

Figure shows a network of capacitors where the numbers indicates capacitances in micro Farad. The value of capacitance \(C\) if the equivalent capacitance between point \(A\) and \(B\) is to be \(1\,\mu F\) is 

A parallel plate capacitor with plate area \('A'\) and distance of separation \('d'\) is filled with a dielectric. What is the capacity of the capacitor when permittivity of the dielectric varies as : \(\varepsilon(x)=\varepsilon_{0}+k x, \text { for }\left(0\,<\,x \leq \frac{d}{2}\right)\) \(\varepsilon(x)=\varepsilon_{0}+k(d-x)\), for \(\left(\frac{d}{2} \leq x \leq d\right)\)

Given below are two statements: Statement-\(I\): Figure shows the variation of stopping potential with frequency \((v)\) for the two photosensitive materials \(M_1\) and \(M_2\). The slope gives value of \(\frac{h}{e}\), where \(h\) is Planck's constant, \(e\) is the charge of electron. Statement-\(II\): \(M_2\) will emit photoelectrons of greater kinetic energy for the incident radiation having same frequency. In the light of the above statements, choose the most appropriate answer from the options given below.

A null point is found at \(200\,cm\) in potentiometer when cell in secondary circuit is shunted by \(5\,\Omega\). When a resistance of \(15\,\Omega\) is used for shunting null point moves to \(300\,cm\). The internal resistance of the cell is \(..............\,\Omega\).

A particle moves along the \(x\)-axis and has its displacement \(x\) varying with time \(t\) according to the equation \(\mathrm{x}=\mathrm{c}_0\left(\mathrm{t}^2-2\right)+\mathrm{c}(\mathrm{t}-2)^2\) where \(c_0\) and \(c\) are constants of appropriate dimensions. Then, which of the following statements is correct?