2. Quadratic Equation :PYQs |CLASS10|CBSE|UP BOARD
Q.1. What will be the nature of roots of quadratic equation 2x2 - 4x + 3 = 0? [CBSE 2019 ]
3. Quadratic Equation :PYQs |CLASS10|CBSE|UP BOARD
Q.2. Find the value of k for which the quadratic equation kx (x - 2) + 6 = 0 has two equal roots. [CBSE 2019]
4. Quadratic Equation :PYQs |CLASS10|CBSE|UP BOARD
Q.3. Write the discriminant of the quadratic equation: (x + 5)2 = 2(5x - 3). [CBSE 2019]
5. Quadratic Equation :PYQs |CLASS10|CBSE|UP BOARD
Q.4. Find the value of k, for which x = 2 is a solution of the equation kx2 + 2x - 3 = 0 [CBSE 2019]
6. Quadratic Equation :PYQs |CLASS10|CBSE|UP BOARD
Q.5. Using completing the square method, show that the equation x2 - 8x + 18 = 0 has no solution . [CBSE 2019]
7. Quadratic Equation :PYQs |CLASS10|CBSE|UP BOARD
Q.6. Write all the values of p for which the quadratic equation x2 + px + 16 = 0 has
equal roots. Find the roots of the equation so obtained. [CBSE, Allahabad 2019]
8. Quadratic Equation :PYQs |CLASS10|CBSE|UP BOARD
Q.7. For what value of k, the roots of the equation x2 + 4x + k = 0 are real? [Delhi 2019]
9. Quadratic Equation :PYQs |CLASS10|CBSE|UP BOARD
Q.8. 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/h from the usual speed. Find its
usual speed. [CBSE 2018]
10. Quadratic Equation :PYQs |CLASS10|CBSE|UP BOARD
Q.9. If x = 3 is one root of the quadratic equation x2 - 2kx - 6 = 0, then find the value of k. [CBSE 2018]
11. Quadratic Equation :PYQs |CLASS10|CBSE|UP BOARD
Q.10. Divide 27 into two parts such that the sum of their reciprocals is 3/20. [CBSE 2018 (C)
12. Quadratic Equation :PYQs |CLASS10|CBSE|UP BOARD
Q.11. If the roots of the quadratic equation (a - b) x2 + (b - c) x + (c - a) = 0 are equal, prove that 2a = b + c.
[CBSE(F) 2017]
13. Quadratic Equation :PYQs |CLASS10|CBSE|UP BOARD
Q.12. Find the value of p, for which one root of the quadratic equation px2 - 14x + 8 = 0 is 6 times the other.
[CBSE (AI) 2017]
14. Quadratic Equation :PYQs |CLASS10|CBSE|UP BOARD
.13. Find the roots of the quadratic equation √2 x2 + 7x + 5 √2 = 0.
[CBSE Delhi 2017]
15. Quadratic Equation :PYQs |CLASS10|CBSE|UP BOARD
Q.14. If the roots of the equation (c2 - ab)x2 -2 (a2 - bc)x + b2 - ac = 0 in x are equal, then show
that either a = 0 or a3 + b3 + c3 = 3abc. [CBSE (AI) 2017]
16. Quadratic Equation :PYQs |CLASS10|CBSE|UP BOARD
Q.15. If the roots of the quadratic equation
(x - a) (x - b) + (x - b) (x - c) + (x - c) (x - a ) = 0
are equal, then show that a = b = c. [CBSE (F) 2017]
17. Quadratic Equation :PYQs |CLASS10|CBSE|UP BOARD
Q.16. Solve for x:
Previous Year Questions: Quadratic Equations [Delhi 2017 (C)]
18. Quadratic Equation :PYQs |CLASS10|CBSE|UP BOARD
Q.17. Find the value of k for which the equation x2 + k(2x + k - 1) = 0 has real and equal roots. [Delhi 2017]
19. Quadratic Equation :PYQs |CLASS10|CBSE|UP BOARD
Q.18. Find the value of p , for which one root of the quadratic equation px2 - 14x + 8 = 0 is 6 times the other.
[AI2017]
20. Quadratic Equation :PYQs |CLASS10|CBSE|UP BOARD
Q.19. If the equation (1 + m2)x2 + 2mcx + c2 - a2 = 0 has equal roots, then show that c2 = a2 (1 + m2)
[Delhi 2017]
21. Quadratic Equation :PYQs |CLASS10|CBSE|UP BOARD
Q.20. If ad ≠ bc, then prove that the equation (a2 + b2) x2 + 2(ac + bd)x + (c2 + d2) = 0 has no real roots.
[ CBSE 2017]
22. Quadratic Equation :PYQs |CLASS10|CBSE|UP BOARD
If x = 2/3 and x = -3 are roots of the quadratic equation ax2 + 7x + b = 0, find the values of a and b.
[CBSE Delhi 2016]
23. Quadratic Equation :PYQs |CLASS10|CBSE|UP BOARD
A two digit number is four times the sum of the digits. It is also equal to 3 times the product of digits.
Find the number. [CBSE (F) 2016]
25. Quadratic Equation :PYQs |CLASS10|CBSE|UP BOARD
Long Answer Type Questions
Q.1. The speed of a boat in still water is 15 km/h. It goes 30 km upstream
and returns back at the same point in 4 hours 30 minutes. Find the speed
of the stream.
OR
A motorboat whose speed in still water is 9 km/h, goes 15km 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]
26. Quadratic Equation :PYQs |CLASS10|CBSE|UP BOARD
Q.2. A train travels 360 km at a uniform speed. If the speed has been 5 km/h more, it would have
taken 1 hour less for the same journey. Find the speed of the train. [CBSE 2019]
27. Quadratic Equation :PYQs |CLASS10|CBSE|UP BOARD
Q.3. 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 the total journey, what is the original average speed? [CBSE 2018]
28. Quadratic Equation :PYQs |CLASS10|CBSE|UP BOARD
Q.4. A train covers a distance of 300 km at a uniform speed. If the speed of the train is
increased by 5 km/hour, it takes 2 hours less in the journey. Find the original speed of the train.
[CBSE 2018]
29. Quadratic Equation :PYQs |CLASS10|CBSE|UP BOARD
.5. A motorboat 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]
30. Quadratic Equation :PYQs |CLASS10|CBSE|UP BOARD
Q.9. Find two consecutive odd natural numbers, the sum of whose squares is 394. [Delhi 2017 (C)]
31. Quadratic Equation :PYQs |CLASS10|CBSE|UP BOARD
Q.10. The sum of the squares of two consecutive odd numbers is 394. Find the numbers. [CBSE Delhi 2017 (C)]
![Quadratic Equation :PYQs |CLASS10|CBSE|UP BOARD
Q.1. What will be the nature of roots of quadratic equation 2x2 - 4x + 3 = 0? [CBSE 2019 ]](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)