List of top Mathematics Questions on Algebra asked in UP Board X

If the sum and difference of two numbers are 8 and 2 respectively, the numbers will be:

A fraction becomes \( \frac{1}{3} \) when 1 is added to the numerator and it becomes \( \frac{1}{4} \) when 1 is subtracted from its denominator. Find the fraction.

The sum of the digits of a two-digit number is 9. Nine times this number is twice the number obtained by reversing the order of the digits. Find the number.

The numerator of a fraction is 3 less than its denominator. If 2 is added to both the numerator and the denominator, then the sum of new fraction and the original fraction is \( \frac{29}{20} \). Find the original fraction.

Solve the following pair of equations by reducing them to a pair of linear equations: \[ \frac{10}{x + y} + \frac{2}{x - y} = 4 \] \[ \frac{15}{x + y} - \frac{5}{x - y} = 2 \]

If \( m = 5 \) and \( n = m + 7 \), then the value of \( \sqrt{m^2 + n^2} \) will be: