Class 10 Quadratic Equations Previous Year Questions

    Q1:

    The time taken by a person to travel an upward distance of 150 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 km/h more than the speed while going up, find the speeds in each direction.

    CBSE [2025]

    Hard

    Q2:

    The sum of the areas of two squares is 52 \(cm^2\) and difference of their perimeters is 8 cm. Find the lengths of the sides of the two squares.

    CBSE [2025]

    Medium

    Q3:

    The age of a man is twice the square of the age of his son. Eight years hence, the age of the man will be 4 years more than three times the age of his son. Find their present ages.

    CBSE [2024]

    Medium

    Q4:

    Find the value of 'c' for which the quadratic equation (c + 1)x² - 6(c + 1)x + 3(c + 9) = 0, where c ≠ -1, has real and equal roots.

    CBSE [2024]

    Hard

    Q5:

    A train travels a distance of 90 km at a constant speed. Had the speed been 15 km/h more, it would have taken 30 minutes less for the journey. Find the original speed of the train.

    CBSE [2024]

    Hard

    Q6:

    The denominator of a fraction is one more than twice the numerator. If the sum of the fraction and its reciprocal is 2 16/21, find the fraction.

    CBSE [2024]

    Medium

    Q7:

    In a flight of 2800 km, an aircraft was slowed down due to bad weather. Its average speed is reduced by 100 km/h and by doing so, the time of flight is increased by 30 minutes. Find the original duration of flight.

    CBSE [2024]

    Hard

    Q8:

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    A rectangular floor area can be completely tiles with 200 square tiles. If the side length of each tile is increased by 1 unit, it would take only 128 tiles to cover the floor. (i) Assuming the original length of each side of a tile be x units, make a quadratic equation from the above information. (ii) Write the corresponding quadratic equation in standard form. (iii) (a) Find the value of x, the length of side a tile by factorisation. OR (b) Solve the quadratic equation for x, using quadratic formula.

    CBSE [2024]

    Medium

    Q9:

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    While designing the school year book, a teacher asked the student that the length and width of a particular photo is increased by x units each to double the area of the photo. The original photo is 18 cm long and 12 cm wide. Based on the above information, answer the following questions: (i) Write an algebric equation depicting the above information. (ii) Write the corresponding quadratic equation in standard form. (iii) (a) What should be the new dimensions of the enlarged photo ? OR (b) (iii) Can any rational value of x make the new area equal to 220 cm² ?

    CBSE [2023]

    Medium

    Q10:

    Find the value of ‘p’ for which the quadratic equation px(x – 2) + 6 = 0 has two equal real roots.

    CBSE [2023]

    Medium

    Q11:

    Two pipes together can fill a tank in \(\frac{15}{8}\) hours. The pipe with larger diameter takes 2 hours less than the pipe with smaller diameter to fill the tank separately. Find the time in which each pipe can fill the tank separately.

    CBSE [2023]

    Hard

    Q12:

    A train travels at a certain average speed for a distance of 54 km and then travels a distance of 63 km at an average speed of 6 km/h more than the first speed. If it takes 3 hours to complete the journey, what was its first average speed?

    CBSE [2023]

    Hard

    Q13:

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    In the picture given, one can see a rectangular in-ground swimming pool installed by a family in their backyard. There is a concrete sidewalk around the pool of width x m. The outside edges of the sidewalk measure 7 m and 12 m. The area of the pool is 36 sq.m. (a) Based on the information given above, form a quadratic equation in terms of x. (b) Find the width of the sidewalk around the pool.

    CBSE [2022]

    Hard

    Q14:

    The least positive value of k, for which the quadratic equation 2x² + kx - 4 = 0 has rational roots is

    CBSE [2023]

    Easy

    Q15:

    Had Aarush scored 8 more marks in a Mathematics test, out of 35 marks, 7 times these marks would have been 5 less than square of his actual marks. How many marks did he get in the test?

    CBSE [2022]

    Medium

    Q16:

    Find the value of 'p' for which the quadratic equation p(x - 4) (x - 2) + (x - 1)² = 0 has real and equal roots

    CBSE [2022]

    Medium

    Q17:

    The diagonal of a rectangular field is 60 metres more than the shorter side. If the longer side is 30 metres more than the shorter side, find the sides of the field.

    CBSE [2022]

    Medium

    Q18:

    For what value of m, the quadratic equation mx² - 2(m - 1)x + (m + 2) = 0 has two real and equal roots?

    CBSE [2022]

    Easy

    Q19:

    If the quadratic equation (1 + a²)x² + 2abx + (b² - c²) = 0 has equal and real roots, then prove that: b² = c²(1 + a²).

    CBSE [2022]

    Medium

    Q20:

    Solve the quadratic equation for x: x² - 2ax - (4b² - a²) = 0.

    CBSE [2022]

    Easy

    Q21:

    Solve the quadratic equation for x: x² + 2\( \sqrt{2} \)x - 6 = 0.

    CBSE [2022]

    Easy

    Q22:

    Solve the following quadratic equation for x: \( \sqrt{3} \)x² + 10x + 7\( \sqrt{3} \) = 0

    CBSE [2022]

    Easy

    Q23:

    Find the value of m for which the quadratic equation (m - 1)x² + 2(m - 1)x + 1 = 0 has two real and equal roots

    CBSE [2022]

    Easy