In a group of $50$ people, $35$ speak Hindi, $25$ speak both Hindi and English, and all the people speak Hindi or English or both. The number of people who speak English only is

In a certain town,$25\%$ of the families own a phone and $15\%$ own a car; $65\%$ families own neither a phone nor a car and $2,000$ families own both a car and a phone. Consider the following three statements:
$(A) \, 5\%$ families own both a car and a phone
$(B) \, 35\%$ families own either a car or a phone
$(C) \, 40,000$ families live in the town
Then,

The solution set of $8x \equiv 6 \pmod{14}$,$x \in \mathbb{Z}$,is

The domain of the function $f(x) = \log (\sqrt {x - 4} + \sqrt {6 - x} )$ is

If $U = \{a, b, c, d, e, f\}$ and $A = \{a, b, c\}$,find $(U \cup A^{\prime})$.

Which of the following is the empty set?