On dividing a number by $38$, we get $90$ as quotient and $19$ as remainder. What is the number?

$\frac{901}{29} \times \frac{91}{301} \div \frac{51}{599} = ?$

$\frac{(0.188+0.077)^{2}+(0.188-0.077)^{2}}{0.188 \times 0.188+0.077 \times 0.077} = ?$

The sum of the squares of two consecutive even numbers is $6500.$ Which is the smaller number?

For what value of $M$,is $34M$ divisible by $12$?

The numerator and denominator of a fraction are in the ratio of $2:3$. If $6$ is subtracted from the numerator,the result is a fraction that has a value $\frac{2}{3}$ of the original fraction. The numerator of the original fraction is