There are two thin parallel charged sheets having surface charge density \( \sigma \) placed at a small distance apart. Which of the following statements are correct?
(A) If both the sheets are positively charged, then the electric field between them is \( \sigma/\epsilon_0 \)
(B) If both the sheets are negatively charged, then the electric field between them is \( \sigma/\epsilon_0 \)
(C) If the left sheet is positively charged and the right sheet is negatively charged the field between them is \( \sigma/\epsilon_0 \)
(D) If the right sheet is positively charged and the left sheet is negatively charged then the field between them is \( \sigma/\epsilon_0 \)
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In a cyclotron, if a deutron can gain a maximum energy of 40 MeV, then a proton can gain a maximum energy of _________

In amplitude modulation, modulation index '\( \mu \)' should be:

A current through a wire varies with time, as \( I = \alpha t + \beta t^2 \) where \( \alpha = 10 \, \text{A s}^{-1} \) and \( \beta = 4 \, \text{A s}^{-2} \). How much charge will cross through a section of the wire in 12 s?

An inductor coil joined to a 12 V battery draws a steady current of 12 A. This coil is connected to a capacitor and ac source of rms voltage 12 V in series. What will be the rms current, if the current in the circuit is in phase with the emf?

An electron of mass \( 9.1 \times 10^{-31} \text{ kg} \) carrying charge \( 1.6 \times 10^{-19} \text{ C} \), is moving horizontally with a speed of \( 4 \times 10^6 \text{ m/s} \) in a uniform magnetic field of magnitude \( 8 \times 10^{-4} \text{ T} \) acting vertically upward. The radius of its circular path is,

The distance estimation for which ray optics is good approximation for an aperture of 3 mm and wavelength 300 nm would be :

Match List-I with List-II

List-I (Techniques)	List-II (Related features)
(A) ELISA	(I) Production of mature insulin
(B) PCR	(II) Antigen-antibody interaction
(C) Autoradiograph	(III) Amplification of DNA
(D) Recombinant DNA technology	(IV) Photographic film

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Choose the examples of first order reactions.
(A) Artificial radioactive decay of unstable nuclei
(B) Hydrogenation of ethylene
(C) Thermal decomposition of HI on gold surface
(D) Decomposition of N2O
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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

Read the passage carefully and answer
When a metal is placed in a solution of its ions, the metal can lose electron and can go in the solution as ion or the metal ion in the solution can take electron from the electrode and get deposited as metal. Thus, the electrode acquires either positive or negative charge with respect to the solution leading to the development of a potential difference between the metal electrode and the solution. This potential difference is called the electrode potential of the metal. The electrode potential of a metal is a measure of relative tendency to undergo oxidation (loss of electron) or reduction (gain of electron). When the concentration of the ions in the solution is unity, the electrode potential is called standard electrode potential. The magni of potential depends upon the nature of electrode, concentration of ions in solution and the temperature. In a galvanic cell, the electrode at which oxidation occurs is known as anodic half-cell and the electrode at which reduction occurs is known as cathodic half cell. The emf of the cell in terms of standard reduction potential is given by \(E_{\text {cell }}^{\circ}=E_{\text {cathode }}^{\circ}-E_{\text {anode. }}^{\circ}\).The standard free energy change of the redox reaction taking place in the cell is related to \(E_{\text {cell }}^{\circ}\) by \(\Delta G^{\circ}=-n F E^{\circ}\). A redox reaction would occur spontaneously if the free energy change is negative. The equilibrium constant of the reaction is related to the standard free energy change by \(\Delta G^{\circ}=-R T \ln K\).
The half call reaction is the one that

If \(A=\left[\begin{array}{ccc}0 & l & -3 \\ -2 & 0 & 1 \\ m & -1 & 0\end{array}\right]\) is a skew symmetric matrix, then

A TV tower has a height of 20 m and the radius of earth is \(6.4 \times 10^6 m\). The range of the tower is: