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

If 1 is subtracted from the numerator of a fraction, then it becomes \( \frac{1}{3} \), and if 8 is added to its denominator, then it becomes \( \frac{1}{4} \). Find that fraction.
Find the values of \( x \) and \( y \) from the following equations: \[ \frac{30}{x - y} + \frac{44}{x + y} = 10 \quad \text{and} \quad \frac{40}{x - y} + \frac{55}{x + y} = 13 \]
The ratio of income of two persons is 9 : 7 and the ratio of their expenditure is 4 : 3. If each of them saves ₹ 2,000 per month, then find their monthly income.
The solution of the equation \( \frac{3}{x} - 2x = \frac{2}{x} \) will be:
Solve the following pair of equations by converting these into linear pair of equations: \[ \frac{1}{2x} - \frac{1}{3y} = 2, \quad \frac{1}{3x} + \frac{1}{2y} = \frac{13}{16}. \]
Sum of areas of two squares is 117 m\(^2\). If the difference between their perimeters is 12 m, then find the sides of both the squares.
Solution of equations \( 3x + 2y = 6 \) and \( y = 0 \) will be:
Show through graphical method that the linear equation system \( 3x - y = 2 \) and \( 9x - 3y = 6 \) have infinite number of solutions.
The sum of the digits of a two-digit number is 9. If the digits of the number are interchanged, then the new number will exceed the original number by 27. Find the number.
For what value of ‘m’, pair of equations \( x - 2y = 3 \) and \( 3x + my = 1 \) will have a unique solution?
The solution of \( 2x + 3y = 18 \); \( x - 2y = 2 \) will be:
For which value of \( k \), there will be an infinite number of solutions for the pair of linear equations \( x + ky = 1 \) and \( kx + y = k^2 \)?
If \( \frac{1}{x^2 - 2} = \frac{1}{7} \), then the value of \( x \) will be:
Solve the following pair of equations: \[ \frac{5}{x - 1} + \frac{1}{y - 2} = \frac{7}{4}, \] \[ \frac{6}{x - 1} - \frac{2}{y - 2} = \frac{1}{2}. \]
In a journey of 300 km, if a person travels 60 km by train and the rest of the distance by bus, then it takes 4 hours in all. If he travels 100 km by train and the rest of the distance by bus, then it takes 10 minutes more. Find the speed of the train and the bus respectively.
The product of the age of Punita 2 years ago and her age after 4 years from now is 1 year more than twice her present age. Find her present age.
Solve the following equation: \[ \frac{1}{x} - \frac{1}{x-2} = 3, \quad x \neq 0, 2. \]
Find two positive even consecutive numbers, the sum of whose squares is 340.
The discriminant of the quadratic equation \( x - \frac{1}{x} = 1 \) will be:
The area of a rectangular field is 30 m². If its length is 1 m greater than its breadth, then the quadratic equation to find them will be:
The mean of \( x \) and \( \frac{1}{x} \) is \( M \). Find the mean of \( x^3 \) and \( \frac{1}{x^3} \).
The sum of two numbers is 24 and one of them is twice the other. The numbers respectively will be:
Solve the following equation: \[ 2\left( \frac{2x - 1}{x + 3} \right) - 3\left( \frac{x + 3}{2x - 1} \right) = 5, \quad x \neq 3, \frac{1}{2}. \]
The sum of a two-digit number and the number obtained by reversing the order of its digits is 66. If the difference of the two digits is 2, find the number.
The sum of the square of two consecutive positive even numbers (integers) is 340. Find the numbers.