Six identical cells, each of emf 3 V and internal resistance of r, are connected in series to a \( 3 \text{ } \Omega \) resistance. If the net current flowing in the circuit is 2.0 A. The internal resistance of the cell is

A vertical electric field of magnitude \( 4.9 \times 10^5 \text{ NC}^{-1} \) just prevents a water droplet of mass \( 0.1 \text{ g} \) from falling. What is the charge on the droplet? Take acceleration due to gravity \( 9.8 \text{ ms}^{-2} \).

The magnetic field of a light wave at given time parallel to y-axis and is given by \( B = B_m \sin(kz - \omega t) \). In what direction does the wave travel and parallel to which axis does the associated electric field point at that time?

The mutual inductance \( M_{12} \) of coil 1 with respect to coil 2:

Which of the following is NOT true about a shunt ?

The speed of propagation of light wave in a dispersive medium does NOT depend on the :

If a particle is dropped from a height X. The de-Broglie wavelength of the particle as a function of height is proportional to :

A proton, a deuteron and an alpha particle have the same kinetic energy and move in a uniform magnetic field perpendicular to their direction of motion. The ratio of the radii of their circular paths is :

A value of \(p\) for which the points \((1,1, p)\) and \((-3,0,1)\) are equidistant from the plane \(\vec{r} \cdot(3 \hat{i}+4 \hat{j}-12 \hat{k})+13=0\) is:

Arrange the following ions in increasing order of number of 3d-electrons
(A) Cr²⁺
(B) Cu⁺
(C) Ti³⁺
(D) Mn⁺
Choose the correct answer from the options given below :

Answer the question on the basis of passage given below :
One of the notable features of the transition element is the great variety of oxidation states it may show in its compounds. The elements which give the greatest number of oxidation states occur in or near the middle of the series. Manganese, for example exhibits all the oxidation states from +2 to +7. The lesser number of oxidation states at the extreme ends is either due to losing or sharing of few electrons (Sc, Ti) or too many d electrons of higher valence. Early in the first series scandium (II) is virtually unknown and titanium (IV) which is more stable than Ti (III) or Ti (II). On the other end, the only oxidation state of zinc is \(+ 2\).
Oxidation state of scandium is

Decomposers break down complex organic matter into -

Which of the following show Pleiotropism?