Algebra Questions

Which of the following quadratic equations has equal roots?

Total expenses of a hostel are partly constant and partly vary directly as the number of boarders. When the number of boarders is $120$ and $100$, the total expenses are $\text{Rs. }2000$ and $\text{Rs. }1700$ respectively. Find the total number of boarders if the total expense is $\text{Rs. }1880$.

The sum of the digits of a two-digit number is $12$. When the digits are interchanged, the resulting number is $36$ more than the original number. What is the original two-digit number?

The age of a father is twice that of his elder son. Ten years hence, the age of the father will be three times that of his younger son. If the difference between the ages of the two sons is $15\text{years}$, the current age of the father is:

How many ways can a captain and a vice-captain be selected from a team of $11$ players?

A number $X$ lies between $0$ and $1$. Which of the following is true?

Simplify the given algebraic expression:
$$\frac{437bxaz}{23ab}$$

If $4+3x\le 6+x$ and $3x+5>2+2x$, then $x$ can take which of the following values?