The sum of two numbers is 15. If the sum of their reciprocals is \(\frac{3}{10}\), find the numbers.

A two digit number is such that the product of its digits is 12. When 36 is added to the number the digits interchange their places. Find the number.

Seven years ago, Varun's age was five times the square of Swati's age. Three years hence Swati's age will be two fifth of Varun's age. Find their present ages.

A chess board contains 64 equal squares and the area of each square is 6.25 cm², A border round the board is 2 cm wide.

Find two consecutive natural numbers whose product is 20.

A two digit number is such that the product of its digits is 18, when 63 is subtracted from the number, the digits interchange their places. Find the number.

If we add 1 to the numerator and subtract 1 from the denominator, a fraction reduces to 1. It becomes 1 / 2 if we only add 1 t o the denominator. What is the fraction?

Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu?

Find the LCM of the polynomial \(f(x)=18 x^{4}-36 x^{3}+18 x^{2} \text { and } g(x)=45 x^{6}-45 x^{3}\)

Find the GCD of the following polynomials using division algorithm

Find the excluded values, if any of the expression 
\(\frac{6 x^{3}+57 x^{2}+72 x}{10 x^{3}+85 x^{2}+40 x}\)

Simplify : \(\frac{x^{3}+27}{x^{2}+12 x+27} \times \frac{x^{2}+3 x}{x^{2}-4 x-21}\)

Simplify :  \(\frac{x^{2}-25}{5 x+x^{2}} \div \frac{x^{2}-10 x+25}{x^{2}+8 x+15}\)

Find the Square Root of \(x^{4}-4 x^{3}+10 x^{2}-12 x+9\) by division method

Find the square root of \(x^{4}-2 x^{3}+3 x^{2}-2 x+1\) by division method