# Class 10 – Quadratic Equations – Previous Years Questions

Quadratic Equations – Previous Years Questions

1. The quadratic equation x2 – 4x + k = 0 has distinct real roots if
1. k = 4
2. k > 4
3. k = 16
4. k < 4 [CBSE 2020] [1 Mark]
2. Write the discriminant of the quadratic equation (x + 5)2 = 2(5x – 3). [CBSE 2019] [1 Mark]
3. If b = 0, c < 0 in the quadratic equation x2 + bx + c = 0, then what will be the nature of the roots? [CBSE 2017] [1 mark]
4. If x = 3 is one root of the quadratic equation x2 – 2kx – 6 = 0, then find the value of k. [CBSE 2018] [1 Mark]
5. Solve for x :
6x2 + 11x + 3 = 0 [CBSE 2020] [2 Marks]
6. Using completing the square method, show that the equation x2 – 8x + 18 = 0 has no solution. [CBSE 2019] [2 Marks]
7. In the quadratic equation kx2 – 6x – 1 = 0, determine the values of k for which the equation does not have any real root. [CBSE 2019] [2 Marks]
8. If -5 is a root of the quadratic equation 2x2 + px – 15 = 0 and the quadratic equation p(x2 + x) + k = 0 has equal roots, find the value of k. [CBSE 2016] [2 Marks]
9. If -5 is a root of the quadratic equation 2x2 + px – 15 = 0, find the value of p. [CBSE 2017] [2 Marks]
10. Solve for x :
1/(a + b + x) = 1/a + 1/b + 1/x ; a ≠ 0, b ≠ 0,
x ≠ 0 and a + b + x ≠ 0. [CBSE 2017] [3 Marks]
11. Solve for x:
1/[(x – 1)(x – 2)] + 1/[(x – 2)(x – 3)] = 2/3, x ≠ 1, 2, 3 [CBSE 2016] [3 Marks]
12. Solve for x:
1/(x + 1) + 2/(x + 2) = 4/(x + 4), x ≠ -1, –2, -4 [CBSE 2016] [[4 Marks]
13. A motorboat whose speed in still water is 9 km/h, goes 15 km downstream and comes back to the same spot, in a total time of 3 hours 45 minutes. Find the speed of the stream. [CBSE 2019] [4 Marks]
14. A motor boat, whose speed is 15 km/hr in still water, goes 30 km downstream and comes back at the same place in a total time of 4 hours and 30 minutes. Find the speed of the stream. [CBSE 2017] [4 Marks]
15. A motor boat whose speed is 24 km/h in still water takes 1 hour more to go 32 km upstream than to return downstream to the same spot. Find the speed of the stream. [CBSE 2016] [4 Marks]
16. Rs 9,000 were divided equally among a certain number of persons. Had there been 20 more persons, each would have got Rs 160 less. Find the original number of persons. [CBSE 2020] [4 Marks]
17. In a flight of 600 km, the speed of the aircraft was slowed down due to bad weather. The average speed of the trip was decreased by 200 km/hr and thus the time of flight increased by 30 minutes. Find the average speed of the aircraft originally. [CBSE 2020] [4 Marks]
18. A plane left 30 minutes late than its scheduled time and in order to reach the destination 1500 km away in time, it had to increase its speed by 100 km/hr from the usual speed. Find its usual speed. [CBSE 2018] [3 Marks]
19. A motor boat whose speed is 18 km/hr in still water takes 1 hr more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream. [CBSE 2018] [4 Marks]
20. A train travels at a certain average speed for a distance of 63 km and then travels at a distance of 72 km at an average speed of 6 km/hr more than its original speed. If it takes 3 hours to complete total journey, what is the original average speed? [CBSE 2018] [4 Maks]