Quadratic Equations — Class 10 Mathematics (Standard) PYQs

The value of $p$ for which roots of the quadratic equation $x^2-px+6=0$ are rational, is

The value of $k$ for which the equation $k{x}^2-6x-4=0$ has real and equal roots, is

By selling an article for ₹$48$, a trader loses as much percent as half of the cost price of the article. Calculate the cost price and loss amount of the article.

The value of $m$ for which the quadratic equation $3x^2-7x+m=0$ has real and equal roots, is

Two water taps together can fill a tank in $8\frac{8}{9}$ hours. The tap of larger diameter takes $4$ hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.

(a) The perimeter of a right triangle is $60\text{cm}$ and its hypotenuse is $25\text{cm}$. Find the lengths of other two sides of the triangle.
OR
(b) A train travels a distance of $480\text{km}$ at a uniform speed. If the speed had been $8\text{km/h}$ less, then it would have taken $3$ hours more to cover the same distance. Find the speed of the train.

(a) A two-digit number is such that the product of its digits is $12$. When $36$ is added to this number, the digits interchange their places. Find the number.
OR
(b) A student scored a total of $32$ marks in class tests in Mathematics and Science. Had he scored $2$ marks less in Science and $4$ marks more in Mathematics, the product of his marks would have been $253$. Find his marks in the two subjects.

The quadratic equation whose roots are $7$ and $\frac{1}{7}$ is :

(a) The sum of the areas of two squares is $52{\text{cm}}^2$ and difference of their perimeters is $8\text{cm}$. Find the lengths of the sides of the two squares.
OR
(b) The time taken by a person to travel an upward distance of $150\text{km}$ was $2\frac{1}{2}$ hours more than the time taken in the downward return journey. If he returned at a speed of $10\text{km/h}$ more than the speed while going up, find the speeds in each direction.

(a) The numerator of a fraction is $3$ less than its denominator. If $2$ is added to both numerator and denominator, then the sum of the new fraction and the original fraction is $1\frac{9}{20}$. Find the original fraction.
OR
(b) A train travelling at a uniform speed for $360\text{km}$ would have taken $48$ minutes less to travel the same distance if its speed were $5\text{km/h}$ more. Find the original speed of the train.