List of top Mathematics Questions on Quadratic Equations asked in CBSE Class X

A person on tour has ₹ 5,400 for his expenses. If he extends his tour by 5 days, he has to cut down his daily expenses by ₹ 180. Find the original duration of the tour and daily expense.

The sum of squares of two positive numbers is 100. If one number exceeds the other by 2, find the numbers.

In a class test, the sum of Anamika's marks obtained in Maths and Science is 30. Had she got 2 marks more in Maths and 3 marks less in Science, the product of the marks would have been 210. Find the marks she got in the two subjects.

In a flight of 600 km, an aircraft slowed down its speed due to bad weather. Its average speed for the trip reduced by 200 km/h from its usual speed and time of flight increased by 30 minutes. Find the scheduled duration of the flight.

Two pipes are used to fill a swimming pool. If the pipe of the larger diameter is used for 4 hours and the pipe of the smaller diameter for 9 hours, only half of the pool can be filled. Find how long it would take for each pipe to fill the pool, separately, if the pipe of smaller diameter takes 10 hours more than the pipe of larger diameter to fill the pool.

The length of hypotenuse (in cm) of a right-angled triangle is 6 cm more than twice the length of its shortest side. If the length of its third side is 6 cm less than thrice the length of its shortest side, find the dimensions of the triangle.

If roots of the quadratic equation \(x^2 - k\sqrt{3}x + 2 = 0\) are real and equal, then value of \(k\) is

Verify that roots of the quadratic equation \((p - q)x^2 + (q - r)x + (r - p) = 0\) are equal when \(q + r = 2p\).

The total cost of certain piece of cloth was ₹ 2,100. During special sale time, the shopkeeper offered \(2 \text{ m}\) extra cloth for free thus reducing the price of cloth per metre by ₹ 120. What was the original per metre price of cloth and its length?

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

The value of \(p\) for which roots of the quadratic equation \(x^{2} - px + 6 = 0\) are rational, 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 person on a tour has Rs 4,200 for expenses. If he extends his tour for 3 days, he has to cut down his daily expenses by Rs 70. Find the original duration of the tour.

The area of a right-angled triangle is \( 600 \text{ cm}^2 \). If the base of the triangle exceeds the altitude by 10 cm, find all the three dimensions of the triangle.

A faster train takes one hour less than a slower train for a journey of 200 km. If the speed of the slower train is 10 km/hr less than that of the faster train, find the speeds of the two trains.

The sum of areas of two squares is 640 m\(^2\). If the difference in perimeters is 64 m, find the sides.

A faster train takes one hour less than a slower train for a journey of 200 km. If the speed of the slower train is 10 km/hr less than that of the faster train, find the speeds of the two trains.

The sum of the areas of two squares is 640 $m^2$. If the difference in their perimeters is 64 m, find the sides of the two squares.

Which of the equations among the following is/are quadratic equation(s)? \(q_1 : x^2 + x = (x+1)^2\), \(q_2 : x-1 = x^2 - 1\), \(q_3 : x = x^2\), \(q_4 : \sqrt{x} = x^2 \sqrt{x+1}\)

The discriminant of the quadratic equation \(ax^2 + x + a = 0\) is :

Find the nature of roots of the equation \(3x^2 - 4\sqrt{3}x + 4 = 0\).

The sum of a number and its reciprocal is \(\frac{13}{6}\). Find the number.