Speed Math

If $\mathrm{a}$ and $\mathrm{b}$ are positive integers satisfying ${\mathrm{a}}^{\mathrm{b}}+{\mathrm{b}}^{\mathrm{a}}=57$, then $\mathrm{a}$ and $\mathrm{b}$ are _____

The sum of five consecutive odd numbers is $265$. What is the sum of the largest number and twice the smallest number?

What will come in place of the question mark (?) in the following questions?

$3+\frac{1}{4}+2+\frac{1}{2}-\frac{5}{6}=\frac{{(?)}^2}{10}+1+\frac{5}{12}$

If $\frac{x}{\sqrt{512}}=\frac{\sqrt{648}}{x}$, then find the value of $x?$

What is the sum of the series $\frac{1}{5\times 8}+\frac{1}{8\times 11}..............+\frac{1}{242\times 245}$?

The simplified value of  $\left(1-\frac{1}{3}\right)\left(1-\frac{1}{4}\right)\left(1-\frac{1}{5}\right).....\left(1-\frac{1}{99}\right)\left(1-\frac{1}{100}\right)$ ______.

Find the digit in the unit's place of the product $49237 \times 3995 \times 738 \times 83 \times 9$.

If $(1^2+2^2+3^2+...+{10}^2)=385$, then find the value of $(2^2+4^2+6^2+...+{20}^2)$.

What is the value of $4.1\overline{2}$?

When $x^m$ is multiplied by $x^n$, the product is $1$. Find the relation between $m$ and $n$

Refer the table below and answer the following questions related to the table
Gross exports (Value in Rs. crore)

The square root of $33-4\sqrt{35}$ is _____.

Find the value of ${sin}^{2}A+\left[\left(\frac{1}{1+{tan}^{2}A}\right)\right]$:

A tap drips at a rate of one drop/sec. $600$ drops make $100 \mathrm{ml}$. The number of litres wasted in $300$ days is -

If the numerator of a fraction is increased by $800\%$ and the denominator is increased by $300\%$, then the resultant fraction is $1\frac{2}{7}$. What was the original fraction?

If $x=\sqrt[3]{5}+2$, then the value of $x^3-6x^2+12x-13$ is-

Find the value of $3\sqrt{147}-\frac{7}{3}\sqrt{\frac{1}{3}}-\sqrt{\frac{1}{27}}$.

What value will come in place of question mark (?) in the following questions?

$\frac{7}{10}+\frac{4}{11}+\frac{8}{15}=?$

$p, q$, and $r$ are prime numbers such that $p<q<r<13$. In how many cases would $(p+q+r)$ also be a prime number?

In a class, $20$ students opted for Physics, $17$ for Maths, $5$ for both and $10$ for other subjects. how many students are there in the class?