The variation of resistivity of a metallic conductor with temperature is given correctly by which of the following relations?
(Where \( \rho_T \) is the resistivity at a temperature T and \( \rho_0 \) is the resistivity at a reference temperature \( T_0 \), \( \alpha \) is the temperature coefficient of resistivity, \( T > T_0 \))

A coil \(C_1\) is connected to a galvanometer G. Second coil \(C_2\) is connected to a battery through a tapping key. The steady current in the coil \(C_2\) produces a steady magnetic field. As coil \(C_2\) is moved towards the coil \(C_1\), the galvanometer shows a deflection. To obtain a large deflection, one or more of the following steps can be taken:
(A) Use a rod made of soft iron inside the coil \(C_2\)
(B) Connect the coil \(C_2\) to a more powerful battery
(C) Move the arrangement of coil \(C_2\) rapidly towards the coil \(C_1\)
(D) hold the key pressed continuously
Choose the correct answer from the options given below:

A steady current I flow through a long straight wire of radius 'a'. The current is uniformly distributed across its cross section. The ratio of the magnetic fields due to the wire at distance a/4 and 3a respectively from the axis of the wire is

A 10 V battery of negligible internal resistance is connected with a 200 V battery and a set of parallel resistances as shown in the figure. The value of current in the circuit.

Which of the following statements best describe the temperature dependence of resistances of Cu and Si in the temperature range 27° to 127°C.

Arrange the following in the order of increasing resistivity (\( \rho \))
(A) Copper
(B) Silver
(C) Glass
(D) Carbon (graphite)
(E) Germanium
Choose the correct answer from the options given below:

A proton accelerated through a potential difference of V volts has a de-Broglie wavelength \( \lambda \) associated with it. In order to get the same wavelength with an \( \alpha \)-particle, the required accelerating potential is

If a revenue function is given by \(R(x)=2027 x-1013 x^2-675 x^3\), then the marginal revenue function \(( MR )\) is :

The standard electrode potential of copper is positive. Which of the following statements is not true?

The atomic hydrogen emits a line spectrum consisting of different series. The ratio of frequencies of the first line in Lyman and Balmer series is :

If \(y=\sin ^{-1}\left(\frac{1-x^2}{1+x^2}\right)\) then \(\frac{d y}{d x}=\)

The 'stopping potential' in photoelectric emissions

A reaction is second order with respect to a reactant. If the concentration of the reactant is increased by 1.5 times, the
rate of the reaction