

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:
Since many elements were being discovered in the 19th century and the study of these elements individually was proving difficult, classification of elements was made necessary.
Classification by Johann Dobereiner - German chemist Johann Dobereiner classified certain elements on the basis of their similar properties in the groups of continuing - three elements each. These groups were called ‘triads’. In every triad, the atomic weight of the middle element was equal to the average of the atomic weights of the first and third elements.
Newlands Law of Octaves - The elements were arranged in increasing order of their atomic weights and found that every 8th element shows similarity with the 1st element.
Mendeleev’s Periodic Table - The arrangement of all 63 elements in rows or columns in order of their atomic weight was made by Mendeleev. He left some space for corresponding elements in his periodic table which were not even discovered till then. Although he predicted the properties of those elements through his periodic classification of elements.
Modern Periodic Law - The properties of the elements of the modern periodic law are periodic functions of their atomic numbers.