01 · CBSE BOARD EXAM 2024
CBSE 2024 Board Practice Questions
CBSE 2024 · 1 MARK
Q1. Find the discriminant of the quadratic equation 2x² - 4x + 3 = 0.
CBSE 2024 · 1 MARK
Q2. The values of k for which the quadratic equation x² + kx + 16 = 0 has equal roots are:
(A) ± 8 (B) ± 4 (C) ± 16 (D) ± 2
CBSE 2024 · 2 MARKS
Q3. Solve for x by factorisation: √2 x² + 7x + 5√2 = 0.
CBSE 2024 · 3 MARKS
Q4. Find the values of k for which the quadratic equation (k + 4)x² + (k + 1)x + 1 = 0 has equal real roots.
CBSE 2024 · 5 MARKS
Q5. A motor boat whose speed is 18 km/h in still water takes 1 hour more to go 24 km upstream than to return downstream to the same spot. Find the speed of the stream.
02 · CBSE BOARD EXAM 2023
CBSE 2023 Board Practice Questions
CBSE 2023 · 1 MARK
Q6. If the quadratic equation ax² + bx + c = 0 has real and equal roots, then c is equal to:
(A) -b / (2a) (B) b / (2a) (C) -b² / (4a) (D) b² / (4a)
CBSE 2023 · 2 MARKS
Q7. Solve for x using quadratic formula: 2x² - 5x + 3 = 0.
CBSE 2023 · 3 MARKS
Q8. If the roots of the equation (a - b)x² + (b - c)x + (c - a) = 0 are equal, prove that 2a = b + c.
CBSE 2023 · 5 MARKS
Q9. Two water taps together can fill a tank in 9⅜ hours. The tap of larger diameter takes 10 hours less than the smaller one to fill the tank separately. Find the time in which each tap can separately fill the tank.
03 · CBSE BOARD EXAM 2022
CBSE 2022 Board Practice Questions
CBSE 2022 · 1 MARK
Q10. Find the roots of the quadratic equation x² - 0.04 = 0.
CBSE 2022 · 2 MARKS
Q11. Find the nature of roots of 2x² - 6x + 3 = 0. If real roots exist, find them.
CBSE 2022 · 3 MARKS
Q12. Solve for x: [1 / (x + 4)] - [1 / (x - 7)] = 11 / 30 (x ≠ -4, 7).
04 · CBSE BOARD EXAM 2021
CBSE 2021 Board Practice Questions
CBSE 2021 · 1 MARK
Q13. Value of k for which the equation x² + 5kx + 16 = 0 has no real roots.
CBSE 2021 · 2 MARKS
Q14. Solve for x: 4x² - 4px + (p² - q²) = 0.
CBSE 2021 · 3 MARKS
Q15. A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train.
05 · CBSE BOARD EXAM 2020
CBSE 2020 Board Practice Questions
CBSE 2020 · 1 MARK
Q16. Find the value of k for which the roots of the equation 3x² - 10x + k = 0 are reciprocal of each other.
CBSE 2020 · 3 MARKS
Q17. Solve for x: [(x - 1) / (x - 2)] + [(x - 3) / (x - 4)] = 3 ⅓ (x ≠ 2, 4).
CBSE 2020 · 5 MARKS
Q18. The sum of areas of two squares is 468 m². If the difference of their perimeters is 24 m, find the sides of the two squares.
06 · SELF-PRACTICE TIPS
Tips for Solving Board PYQs
01
For equal roots questions, immediately set discriminant D = b² - 4ac = 0.
02
In speed/distance word problems, set up equation using Time = Distance / Speed.
03
Check if roots are real before applying quadratic formula: if D < 0, stop and write "No real roots".