$$\begin{aligned} (3\frac{1}{4}\div \{1\frac{1}{4} - \frac{1}{2}(2\frac{1}{2} - \overline {\frac{1}{4} - \frac{1}{6}} ) \} ) \end{aligned}$$

Answer: Option A

Explanation:

By taking LCM we get
= $$\begin{aligned} \frac{28+14+7+4+2+1}{28} = \frac{56}{28} = 2\end{aligned}$$

Answer: Option D

Explanation:

Let the boys are X, then girls are 7X, total = X+7X = 8X

So it should be multiple of 8, 30 is not a multiple of 8.

Answer: Option D

Explanation:

b-[b-(a+b)-{b-(b-a+b)}+2a]
=b-[b-a-b-{b-(2b-a)}+2a]
=b-[-a-{b-2b+a}+2a]
=b-[-a-{-b+a}+2a]
=b-[-a+b-a+2a]
=b-[-2a+b+2a]
=b-b
=0

Answer: Option C

Explanation:

= 2(3)-3(5)+(3*5) + 2(5)-3(3)+(5*3)
= 6-15+15+10-9+15 = 31-9 = 22

Answer: Option C

Explanation:

Remember the formula, if not then cram it :)
$$\begin{aligned} 2ab = (a^2 + b^2)- (a-b)^2 \end{aligned}$$
=> 2ab = 29 - 9 = 20
=> ab = 10