A swimmer can swim with velocity of \(12 \,km / h\) in still water. Water flowing in a river has velocity \(6\, km / h\). The direction with respect to the direction of flow of river water he should swim in order to reach the point on the other bank just opposite to his starting point is ........\(^{\circ}\). (Round off to the Nearest Integer) (find the angle in degree)

Seven identical circular planar disks, each of mass \(M\) and radius \(R\) are welded symmetrically as shown. The moment of inertia of the arrangement about the axis normal to the plane and passing through the point \(P\) is:

Four particles \(A, B, C\) and \(D\) with masses \(m_A=m, m_B=2m, m_C=3m\) and \(m_D=4m\) are at the corners of a square. They have accelerations of equal magnitude with directions as shown. The acceleration of the centre of mass of the particles is

A \(2\, W\) carbon resistor is color coded with green, black, red and brown respectively. The maximum current which can be passed through this resistor is .............. \(mA\)

Two iron solid discs of negligible thickness have radius \(R_1\) and \(R_2\) and moment of intertia \(I_1\) and \(I_2\), respectively. For \(R_2=2 R_1\), the ratio of \(I_1\) and \(I_2\) would be \(1 / x\), where \(\mathrm{x}=\) ________ -

The electric field in an electromagnetic wave is given as \(\vec{E}=20 \sin \omega\left(t-\frac{x}{c}\right) \vec{j} NC ^{-1}\) Where \(\omega\) and \(c\) are angular frequency and velocity of electromagnetic wave respectively. The energy contained in a volume of \(5 \times 10^{-4}\, m ^3\) will be \(.....\times 10^{-13}\,J\) (Given \(\varepsilon_0=8.85 \times 10^{-12}\,C ^2 / Nm ^2\) )

A point charge of \(+\,12 \,\mu C\) is at a distance \(6 \,cm\) vertically above the centre of a square of side \(12\, cm\) as shown in figure. The magnitude of the electric flux through the square will be ....... \(\times 10^{3} \,Nm ^{2} / C\)

Consider a Young’s double slit experiment as shown in figure. What should be the slit separation \(d\) in terms of wavelength \(\lambda \) such that the first minima occurs directly in front of the slit \((S_1)\)?

The tangent to the circle \(C_1 : x^2 + y^2 - 2x- 1\, = 0\) at the point \((2, 1)\) cuts off a chord of length \(4\) from a circle \(C_2\) whose centre is \((3, - 2)\). The radius of \(C_2\) is

Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason \(R\). Assertion \(A\) : If \(dQ\) and \(dW\) represent the heat supplied to the system and the work done on the system respectively. Then according to the first law of thermodynamics \(d Q=d U-d W\). Reason \(R :\) First law of thermodynamics is based on law of conservation of energy. In the light of the above statements, choose the correct answer from the option given below :

The sum of all integral values of \(\mathrm{k}(\mathrm{k} \neq 0\) ) for which the equation \(\frac{2}{x-1}-\frac{1}{x-2}=\frac{2}{k}\) in \(x\) has no real roots, is ..... .

Let \(\vec a = 2\hat i + \hat j - 2\hat k,\vec b = \hat i + \hat j\). If \(\vec c\) is a vector such that \(\vec a.\vec c = \left| {\vec c} \right|,\left| {\vec c - \vec a} \right| = 2\sqrt 2 \) and the angle between \(\vec a \times \vec b\) and \(\vec c\) is \(30^o\), then \(\left| {\left( {\vec a \times \vec b} \right) \times \vec c} \right|\) equals 

A poly-atomic molecule ( \(C_V=3 R, C_P=4 R\), where \(R\) is gas constant) goes from phase space point \(\mathrm{A}\left(\mathrm{P}_{\mathrm{A}}=10^5 \mathrm{~Pa}, \mathrm{~V}_{\mathrm{A}}=4 \times 10^{-6} \mathrm{~m}^3\right)\) to point \(\mathrm{B}\left(\mathrm{P}_{\mathrm{B}}=5 \times 10^4 \mathrm{~Pa}, \mathrm{~V}_{\mathrm{B}}=6 \times 10^{-6} \mathrm{~m}^3\right)\) to point \(\mathrm{C}\left(\mathrm{P}_{\mathrm{C}}=10^4\right.\) \(\left.\mathrm{Pa}, \mathrm{V}_{\mathrm{C}}=8 \times 10^{-6} \mathrm{~m}^3\right)\). A to B is an adiabatic path and \(B\) to \(C\) is an isothermal path. The net heat absorbed per unit mole by the system is :