**Question 1.**

**1.**

In a group of 1000 students 750 like Mathematics and 400 like Science. Find how many like Mathematics only? How many like Science only ? How many like both Mathematics and Science?

**Question 2.**

**2.**

If $A_r=\{rn\,:\;n\in N\}$ then find $A_3 \cap A_5$.

**Question 3.**

**3.**

A school awarded 58 medals in three sports, namely 38 in football, 15 in basketball and 20 in hockey. If 3 students get medals in all three sports, how many received medals in exactly two sports?

**Question 4.**

**4.**

In a group, 50 speak Hindi, 20 speak English and 10 speak both Hindi and English. How many speak at least one of these two languages?

**Question 5.**

**5.**

If $A=\{x : Sin(x) \gt \cfrac{-1}{2}\, and\, \cfrac{-\pi}{2} \leq \cfrac{\pi}{2}\}$ and

$B=\{x:\, Cos(x)\gt \cfrac{1}{2}\, and \, 0\leq x \leq \pi\}$. Find $A\cap B$ and $A\cup B$.

**Question 6.**

**6.**

In a certain city, two of the newspapers P and Q are published only. 30% of city population reads P , 25% reads newspaper Q and 3% of city population read both newspaper. If 40% of those who read newspaper P only go through the advertisements where as 30% of those who read Q only go through the advertisements and 45% of those who read both newspaper go through advertisements. Find what % of population of city go through the advertisements?