At the sea level, the dry air mass percentage composition is given as nitrogen gas : 70.0, oxygen gas : 27.0, and argon gas : 3.0. If the total pressure is 1.15 atm, then calculate the ratio of the following respectively:
(i) Partial pressure of nitrogen gas to partial pressure of oxygen gas
(ii) Partial pressure of oxygen gas to partial pressure of argon gas
(Given: Molar mass of N, O, and Ar are 14, 16, and 40 g mol$^{-1}$ respectively)
If a random variable \( x \) has the probability distribution 
then \( P(3<x \leq 6) \) is equal to
An infinitely long straight wire carrying current $I$ is bent in a planar shape as shown in the diagram. The radius of the circular part is $r$. The magnetic field at the centre $O$ of the circular loop is :
