If a - b = 3 and $$\begin{aligned} a^2 + b^2 = 29 \end{aligned}$$ , then find the value of ab

Answer: Option D

Explanation:

$$\begin{aligned} = 3034 -( \frac{1002}{2004} \times 100) \end{aligned}$$
$$\begin{aligned} = 3034 - 50 = 2984 \end{aligned}$$

Answer: Option C

Explanation:

Let the number of buffaloes be x and the number of ducks be y
=> 4x + 2y = 2 (x + y) + 24

=> 2x = 24 => x = 12

Answer: Option B

Explanation:

Let suppose total number of students in class are X.
Then from the question we can conclude it that,

$$\begin{aligned} X*\frac{1}{8}X = \frac{X}{2}*16 \\ => X = 64\\ \text{Total notebooks,} \\ = \frac{1}{8}X^2 \\ = \left( \frac{1}{8} * 64 * 64 \right) \\ = 512 \end{aligned}$$

Answer: Option C

Explanation:

$$\begin{aligned} \frac{\frac{7}{2}\div {\frac{5}{2}} \times {\frac{3}{2}} }{\frac{7}{2} \div { \frac{5}{2}} of \frac{3}{2} }\div 5.25 \end{aligned}$$

$$\begin{aligned} = \frac{\frac{7}{2}\times {\frac{2}{5}} \times {\frac{3}{2}} }{\frac{7}{2} \div { \frac{15}{4}}}\div 5.25 \end{aligned}$$

$$\begin{aligned} = \frac{\frac{21}{10}} {\frac{7}{2} \times { \frac{4}{15}}}\div {\frac{525}{100}} \end{aligned}$$

$$\begin{aligned} = \frac{21}{10}\times{\frac{15}{14}}\times\frac{100}{525} = \frac{6}{14} = \frac{3}{7} \end{aligned}$$

Answer: Option B

Explanation:

= (31/10) * (3/10) + (7/5) / 20
= (3.1) * (.3) + (1.4) / 20
= 0.93 + 0.07
= 1