Basics of Arithmetic

Which of the following in the largest number?

$2^{\frac{1}{2}}, 3^{\frac{1}{3}}, 6^{\frac{1}{6}}, {12}^{\frac{1}{12}}$

If $x^n+a^n$ is divisible by $x + a$Only, Then $n$is what$?$ ?

What is the value of 'P',$4^{2p}=\frac{1}{6}$?

Which of the two is greater $2^{300}$or $3^{200}$?

The expression ${\left(27+\sqrt{756}\right)}^{\frac{1}{3}}+{\left(27-\sqrt{756}\right)}^{\frac{1}{3}}$ is equal to _______?

A person travelled a distance of 50 km in 8 hours. He covered a part of the distance on foot at the rate of 4 km per hour and a part on a bicycle at the rate of 10 km per hour. How much distance did he travel on foot ?

A person has four coins each of different denominations. What is the number of different combinations of coins the person can form (using one or more coins at a time)?

A man fills a basket with eggs in such a way that the number of eggs added to the basket each day is the same as the number already present in the basket. This way, the basket gets completely filled in $24$days. After how many days the basket was one-fourth full?

Two numbers A and B are such that the sum of 3% of A and 6% of B is four-fifths of the sum of 4% of A and 6% of B. Find the ratio of A + B and A - B. 

Four friends, Priya, Kavya, Gaurvi and Shalini, have different amounts of money with them. If Priya takes ₹88 from Kavya, then she will have an amount equal to what Gaurvi has. Shalini and Kavya together have a total of $₹550$. If Gaurvi takes $₹25$, from Shalini, she will have an amount equal to what Kavya has. If the total amount with Shalini, Kavya and Gaurvi is $₹840$, how much money does Priya have?

Alekhya's was born one year after her mother's marriage.Her father is two year older than than her mother but 25 years older than Alekhya, who is 6 years older.At what age did the mothet get married?

There are $28$ persons are present at a press conference. After the conference they all shake hands with each other. If $7$ of them refuse to shake hands at all, then how many hand shakes will be there all together. 

Ankit is 30 years younger than his father. After 4 years Ankit's sister will be half the age of her father. The total of the present ages of Ankit and his sister is 67 years. What is the present age of Ankit's father?

Five sisters Meena, Reena, Teena, Beena and Neena are three in a family. Meena was born on $1989$. Teena is seven years older than Neena, while eight years younger than Meena. Beena is five years older than Neena while seven years younger than Reena. 

What is the age difference between Meena and Beena?

Solving equation ${\left(1+x\right)}^{\frac{2}{3}}+{\left(1-x\right)}^{\frac{2}{3}}=4{\left(1-x^2\right)}^{\frac{1}{3}}$ are, values of $x$

If $3^{\mathrm{x}}=115+2^{\mathrm{y}}$ and $3^{\mathrm{x}-4}+2^{\mathrm{y}-5}=7,$ find $\mathrm{x}+\mathrm{y}$

If $\left(250\sqrt{2}{\mathrm{x}}^3+24\sqrt{3}{\mathrm{y}}^3\right)÷(5\sqrt{2}\mathrm{x}+2\sqrt{3}\mathrm{y})=\left({\mathrm{Ax}}^2+{\mathrm{By}}^2-\mathrm{c}\sqrt{6}\mathrm{xy}\right),$ then the value of $\left(\frac{\mathrm{A}}{10}+\frac{{\mathrm{B}}^2}{8}+\mathrm{C}\right)$ is

In a class, every student participated in one of the three activities i.e. folk song, kathak and quiz. $22\%$ of the total students participated in folk song. $25\%$  of the remaining students participated in kathak. The remaining students participated in quiz. What percentage of students participated in quiz?

Find the value of  \( 101^2 \)  .

\( 48^2 + 32^2 + 41^2= ? + 61^2 \)