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)

Three particles of masses \(50\, g\), \(100\, g\) and \(150\, g\) are placed at the vertices of an equilateral triangle of side \(1\, m\) (as shown in the figure). The \((x, y)\) coordinates of the centre of mass will be

A piece of wood of mass \(0.03\, kg\) is dropped from the top of a \(100\, m\) height building. At the same time, a bullet of mass \(0.02\, kg\) is fired vertically upward, with a velocity \(100\, ms^{- 1}\), from the ground. The bullet gets embedded in the wood. Then the maximum height to which the combined system reaches above the top of the building before falling below is ........ \(m\). \((g = 10\, ms^{-2})\)

Two identical cylindrical vessels are kept on the ground and each contain the same liquid of density \(d.\) The area of the base of both vessels is \(S\) but the height of liquid in one vessel is \(x_{1}\) and in the other, \(x_{2}\). When both cylinders are connected through a pipe of negligible volume very close to the bottom, the liquid flows from one vessel to the other until it comes to equilibrium at a new height. The change in energy of the system in the process is

Match List-I with List-II.

	List-I		List-II
A.	Coefficient of viscosity	I.	\(\left[ ML ^{-1} T^{-2}\right]\)
B.	Surface tension	II.	\(\left[ ML ^2 T^{-2}\right]\)
C.	Pressure	III.	\(\left[ ML ^0 T^{-2}\right]\)
D.	Surface energy	IV.	\(\left[ ML ^{-1} T^{-1}\right]\)

Choose the correct answer from the options given below :

A particle of charge \(q\) and mass \(m\) is moving with a velocity \(-v \hat{ i }(v \neq 0)\) towards a large screen placed in the \(Y - Z\) plane at a distance \(d.\) If there is a magnetic field \(\overrightarrow{ B }= B _{0} \hat{ k },\) the minimum value of \(v\) for which the particle will not hit the screen is

Critical angle of incidence for a pair of optical media is \(45^{\circ}\). The refractive indices of first and second media are in the ratio _______.

Water fall from a \(40\,m\) high dam at the rate of \(9 \times 10^{4}\,kg\) per \(hour\). Fifty percentage of gravitational potential energy can be converted into electrical energy. Using this hydroelectric energy number of \(100\,W\) lamps, that can be lit, is (Take \(\left.g=10\,ms ^{-2}\right)\)

A circular loop of radius \(r\) is carrying current I A. The ratio of magnetic field at the centre of circular loop and at a distance \(r\) from the center of the loop on its axis is:

While measuring diameter of wire using screw gauge the following readings were noted. Main scale reading is \(1 \mathrm{~mm}\) and circular scale reading is equal to \(42\) divisions. Pitch of screw gauge is \(1 \mathrm{~mm}\) and it has \(100\) divisions on circular scale. The diameter of the wire is \(\frac{x}{50} \mathrm{~mm}\). The value of \(x\) is _______.