Estimation in mathematics means finding a value that is approximate or close to the correct value.The most common way of estimation is estimation by rounding off.For example, in a school assembly, to find the number of students present, we can calculate the number of students present in a row and ... Read More

Given :The given term is $99^3$.To do :We have to evaluate the given term.Solution :$99^3$ can be written as $(100 - 1)^3$We know that, $(a-b)^3 = a^3 - b^3 - 3ab(a-b)$So, $(100 - 1)^3 = 100^3 - 1^3 - 3(100)(1) (100-1)$                       $= 1000000 - 1 - 300(99)$                      $= 1000000 - 1 - 29700$                       $ = 999999 - 29700$                       $ = 970299$Therefore, the value of $99^3$ is 970299.

Given :The given fraction is $\frac{11}{4}$.To do :We have to convert the given fraction into a mixed fraction.Solution :To convert an improper fraction into a mixed fraction, follow these steps:1. Divide the numerator by the denominator.2. Write down the whole number answer3. Then write down any remainder above the denominator.$\frac{11}{4}$$\frac{11}{4} ... Read More

Given :The given expression is $\frac{\sqrt{5}+\sqrt{2}}{\sqrt{5}-\sqrt{2}}+\frac{\sqrt{5}-\sqrt{2}}{\sqrt{5}+\sqrt{2}}=a+b \sqrt{10}$.To do :We have to find the values of a and b.Solution :$\frac{\sqrt{5}+\sqrt{2}}{\sqrt{5}-\sqrt{2}}+\frac{\sqrt{5}-\sqrt{2}}{\sqrt{5}+\sqrt{2}} = a+b \sqrt{10}$On cross multiplying, $\Rightarrow \frac{(\sqrt{5}+\sqrt{2})^2 + (\sqrt{5}-\sqrt{2})^2}{(\sqrt{5}-\sqrt{2})(\sqrt{5}+\sqrt{2})}=a+b \sqrt{10}$We know that, $(a+b)^2 = a^2+ b^2 + 2ab$$(a-b)^2 = a^2+ b^2 - 2ab$$(a+b)(a-b) = a^2 - b^2$$\Rightarrow \frac{(\sqrt{5})^2+(\sqrt{2})^2 + 2(\sqrt{5})(\sqrt{2})  + ... Read More

In mathematics, a polynomial is an expression consisting of variables (also called indeterminate) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.If p(x) is a polynomial in x, the highest power of x in p(x) is called the degree of the polynomial ... Read More

Metals are generally solids in nature but Non-metals are generally liquids or gases in nature.Metals are generally hard solids except for sodium and potassium which are soft solids. Non-metals are generally liquid in nature except diamond and graphite which are hard solids.

Given : The difference between the simple interest the compound interest on a sum of money for 3 years at 12% per annum $=$ Rs. 216. To find : We have to find the sum. Solution : Let the sum be P.Compound interest $= P[(1+\frac{r}{100})^n - 1]$        ... Read More

Given :The difference between the Simple Interest and the Compound Interest on a sum of money for 3 years at 10% per annum$=$ Rs. 558.To find :We have to find the sum.Solution :Let the sum be P.Compound interest $=P[(1+\frac{r}{100})^n - 1]$                    ... Read More

Given :The difference between the compound interest for 1 year, compounded half-yearly and the simple interest for 1 year on a certain sum of money at 10% per annum is Rs. 360.To do :We have to find the sum.Solution :Let the sum be xRate of interest $= 10$% $= \frac{10}{100} ... Read More

Given :The money amounts to Rupees 7260 in 2 years and Rupees 7986 in 3 years and the interest is being compounded annually.To do :We have to find the rate of interest.Solution :Let the principal amount be P and the rate of interest be r.Therefore, $P(1+\frac{r}{100})^2 = 7260$...................(i)$P(1+\frac{r}{100})^3 = 7986$.................(ii)Dividing ... Read More