A balloon filled with an air sample occupies \( 3 \, \text{L} \) volume at \( 35^\circ \text{C} \). On lowering the temperature to \( T \), the volume decreases to \( 2.5 \, \text{L} \). The temperature \( T \) is: [Assume \( P \)-constant]
The largest $ n \in \mathbb{N} $ such that $ 3^n $ divides 50! is:
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: