01 · CBSE BOARD EXAM 2024
CBSE 2024 Board Practice Questions
CBSE 2024 · 1 MARK
Q1. Find the value of k for which the pair of linear equations 3x + y = 1 and (2k - 1)x + (k - 1)y = 2k + 1 has no solution.
CBSE 2024 · 1 MARK
Q2. The pair of linear equations x + 2y + 5 = 0 and -3x - 6y + 1 = 0 has:
(A) a unique solution (B) exactly two solutions (C) infinitely many solutions (D) no solution
CBSE 2024 · 2 MARKS
Q3. Solve for x and y using substitution method: x + y = 14 and x - y = 4.
CBSE 2024 · 3 MARKS
Q4. Solve for x and y using elimination method: 2x + 3y = 11 and 2x - 4y = -24. Hence find m for which y = mx + 3.
CBSE 2024 · 3 MARKS
Q5. A fraction becomes 9/11, if 2 is added to both the numerator and the denominator. If 3 is added to both numerator and denominator it becomes 5/6. Find the fraction.
02 · CBSE BOARD EXAM 2023
CBSE 2023 Board Practice Questions
CBSE 2023 · 1 MARK
Q6. If the system of equations 2x + 3y = 7 and 2ax + (a + b)y = 28 has infinitely many solutions, find the values of a and b.
CBSE 2023 · 1 MARK
Q7. The line represented by x = 4 is:
(A) parallel to X-axis (B) parallel to Y-axis (C) passing through origin (D) perpendicular to Y-axis
CBSE 2023 · 2 MARKS
Q8. Solve the following pair of linear equations algebraically: 3x + 4y = 10 and 2x - 2y = 2.
CBSE 2023 · 3 MARKS
Q9. The sum of a two-digit number and the number obtained by reversing the digits is 66. If the digits of the number differ by 2, find the number. How many such numbers are there?
CBSE 2023 · 5 MARKS
Q10. 2 women and 5 men can together finish an embroidery work in 4 days, while 3 women and 6 men can finish it in 3 days. Find the time taken by 1 woman alone to finish the work, and also that taken by 1 man alone.
03 · CBSE BOARD EXAM 2022
CBSE 2022 Board Practice Questions
CBSE 2022 · 1 MARK
Q11. For what value of c, the linear equations cx - y = 2 and 6x - 2y = 3 will have no solution?
CBSE 2022 · 2 MARKS
Q12. Find whether the pair of linear equations x + 3y = 6 and 2x - 3y = 12 is consistent or inconsistent.
CBSE 2022 · 3 MARKS
Q13. Solve for x and y: 0.2x + 0.3y = 1.3 and 0.4x + 0.5y = 2.3.
04 · CBSE BOARD EXAM 2021
CBSE 2021 Board Practice Questions
CBSE 2021 · 1 MARK
Q14. If x = a, y = b is the solution of the equations x - y = 2 and x + y = 4, then find the values of a and b.
CBSE 2021 · 2 MARKS
Q15. Solve by elimination method: x/2 + 2y/3 = -1 and x - y/3 = 3.
CBSE 2021 · 3 MARKS
Q16. Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu?
05 · CBSE BOARD EXAM 2020
CBSE 2020 Board Practice Questions
CBSE 2020 · 1 MARK
Q17. If a pair of linear equations is consistent, then the lines representing them will be:
(A) parallel (B) always coincident (C) intersecting or coincident (D) always intersecting
CBSE 2020 · 3 MARKS
Q18. Solve for x and y: 99x + 101y = 499 and 101x + 99y = 501.
CBSE 2020 · 5 MARKS
Q19. The ratio of incomes of two persons is 9:7 and the ratio of their expenditures is 4:3. If each of them manages to save ₹2,000 per month, find their monthly incomes.
06 · SELF-PRACTICE TIPS
Tips for Solving Board PYQs
01
Check ratio conditions a₁/a₂ ≠ b₁/b₂ for unique solution, a₁/a₂ = b₁/b₂ = c₁/c₂ for infinite, and a₁/a₂ = b₁/b₂ ≠ c₁/c₂ for no solution.
02
For symmetric equations like 99x + 101y = 499 & 101x + 99y = 501, add and subtract the two equations first to simplify!
03
Always verify your calculated (x, y) values by substituting back into both original equations.