
The correct answer is: 3

The term independent of $ x $ in the expansion of $$ \left( \frac{x + 1}{x^{3/2} + 1 - \sqrt{x}} \cdot \frac{x + 1}{x - \sqrt{x}} \right)^{10} $$ for $ x>1 $ is:

Two cells of emf 1V and 2V and internal resistance 2 \( \Omega \) and 1 \( \Omega \), respectively, are connected in series with an external resistance of 6 \( \Omega \). The total current in the circuit is \( I_1 \). Now the same two cells in parallel configuration are connected to the same external resistance. In this case, the total current drawn is \( I_2 \). The value of \( \left( \frac{I_1}{I_2} \right) \) is \( \frac{x}{3} \). The value of x is 1cm.
If $ \theta \in [-2\pi,\ 2\pi] $, then the number of solutions of $$ 2\sqrt{2} \cos^2\theta + (2 - \sqrt{6}) \cos\theta - \sqrt{3} = 0 $$ is:
Electronic configuration, also called electronic structure, the arrangement of electrons in energy levels around an atomic nucleus. According to the older shell atomic model, electrons occupy several levels from the first shell nearest the nucleus, K, through the seventh shell, Q, farthest from the nucleus. Electrons have to be filled in the s, p, d, f in accordance with the following rule.For example, the electron configuration of sodium is 1s22s22p63s1.
Maximum number of electrons that can be accommodated in a shell is based on the principal quantum number (n). It is represented by the formula 2n2, where ‘n’ is the shell number.

1. Aufbau’s principle: The filling of electrons should take place in accordance with the ascending order of energy of orbitals:
2. Pauli’s exclusion principle: No two electrons can have all the four quantum numbers to be the same or if two electrons have to be placed in an energy state they should be placed with opposite spies.
3. Hund’s rule of maximum multiplicity: In the case of filling degenerate (same energy) orbitals, all the degenerate orbitals have to be singly filled first and then only pairing has to happen.