A cell of emf 10 V and the internal resistance 1 \( \Omega \) is being charged by an external supply of 100 V. An external resistance of 8 \( \Omega \) is connected to the charging circuit. The current in the circuit is

The given graph shows the variation of terminal potential difference V, across the combination of three identical cells in series to an external resistor versus the current i in the circuit. The internal resistance of each cell is :

Electrical potential V and electric flux \( \phi \) are :

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

Which of the following statements are true?
(A) The potential energy for a system of two negative point charges is negative
(B) Electrostatic force is a conservative force
(C) Negative potential energy between two charges implies that the force between them is repulsive
(D) Electrostatic potential energy is a scalar quantity
Choose the correct answer from the options given below:

A point charge – 5 µC is at a distance 5 cm directly above the centre of a square of side 10 cm.
The magnitude of electric flux through this square is:

The half life of a radioactive substance is 10 days. How many days will it take to disintegrate 3/4 of its initial value ?

The typical test cross is performed between -

The programming problem
Max Z = 2x + 3y subject to the conditions \(0 \leq x \leq 3,0 \leq y \leq 4\) is:

An electron (mass \(9 \times 10^{-31} \text{ kg}\) and charge \(1.6 \times 10^{-19} \text{ C}\)) moving with a speed of \(5.0 \times 10^7 \text{ m/s}\) enters a region of uniform magnetic field of strength 0.04 T which is perpendicular to its velocity. The radius of the circular path it follows is:

Read the passage carefully and answer the questions
Nearly all the transition elements display typical metallic properties such as high tensile strength, ductility, malleability, high thermal and electrical conductivity and metallic lustre. The transition metals (with the exception of Zn, Cd and Hg) are very hard and have low volatility. Their melting and boiling points are high. They have high enthalpies of atomization. lons of the same charge in a given series show progressive decrease in radius with increasing atomic number. However, the variation within a series is quite small. The filling of 4f before 5d orbital results in a regular decrease in atomic radii called Lanthanoid contraction which essentially compensates for the expected increase in atomic size with increasing atomic number The net result of the lanthanoid contraction is that the second and the third d series exhibit similar radii (e.g., Zr 160 pm, Hf 159 pm) and have very similar physical and chemical properties. There is an increase in ionisation enthalpy along each series of the transition elements from left to right. The first ionisation enthalpy, in general, increases, but the magnitude of the increase in the second and third ionisation enthalpies for the successive elements, is much higher along a series. One of the notable features of a transition elements is the great variety of oxidation states these may show in their compounds.
In the first transition series of elements (Sc to Zn), which element show least enthalpy of atomization?

If \(2 f(x)+f\left(\frac{1}{x}\right)=x^2+1\), then \(\int f(x) d x\) is : (Here \(C\) is an arbitrary constant)

If \(A=\left[\begin{array}{ll}5 & 6 \\ 3 & 2\end{array}\right]\), then which of the following is correct?
(A) \(|A|\) is positive
(B) \(|a d j A|=-8\)
(C) Cofactor of 3 is 6
(D) \(|2 A|=-32\)
Choose the correct answer from the options given below :