Three voltmeters, all having different internal resistances are joined as shown in figure. When some potential difference is applied across \(\mathrm{A}\) and \(B\), their readings are \(V_1, V_2\) and \(V_3\). Choose the correct option.

In an experiment of determine the Young's modulus of wire of a length exactly \(1\; m\), the extension in the length of the wire is measured as \(0.4\,mm\) with an uncertainty of \(\pm 0.02\,mm\) when a load of \(1\,kg\) is applied. The diameter of the wire is measured as \(0.4\,mm\) with an uncertainty of \(\pm 0.01\,mm\). The error in the measurement of Young's modulus \((\Delta Y)\) is found to be \(x \times 10^{10}\,Nm ^{-2}\). The value of \(x\) is \(\left[\right.\) Take \(\left.g =10\,m / s ^{2}\right]\)

Two insulated circular loop \(A\) and \(B\) radius ' \(a\) ' carrying a current of ' \(\mathrm{I}\) ' in the anti clockwise direction as shown in figure. The magnitude of the magnetic induction at the centre will be _______.

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

The momentum of a body is increased by \(50 \%\). The percentage increase in the kinetic energy of the body 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 :

An organ pipe \(40\,cm\) long is open at both ends. The speed of sound in air is \(360\,ms ^{-1}\). The frequency of the second harmonic is \(...........\,Hz\).

Refer to the figure given below, current between terminals \(A\) and \(B\) is _____ A.

A quantity \(x\) is given by \(\left( IF v^{2} / WL ^{4}\right)\) in terms of moment of inertia \(I,\) force \(F\), velocity \(v\), work \(W\) and Length \(L\). The dimensional formula for \(x\) is same as that of

The mass and the diameter of a planet are three times the respective values for the Earth. The period of oscillation of a simple pendulum on the Earth is \(2\,s\). The period of oscillation of the same pendulum on the planet would be