Chapter 3: Pair of Linear Equations in Two Variables
Unique Previous Year Questions extracted from the CBSE Class 10 Standard Mathematics 2025 question paper sets, with repeated questions grouped together and original set/question references retained.
I
Multiple Choice Questions
1. Solution of a Pair of Linear Equations
1 Mark
If \(x=1\) and \(y=2\) is a solution of the pair of linear equations \(2x-3y+a=0\) and \(2x+3y-b=0\), then:
Series 30/1/1 (Q2) & 30/1/3 (Q12)2. Line Represented by an Equation
1 Mark
The line represented by the equation \(x-y=0\) is:
Series 30/2/1 (Q14), 30/2/2 (Q4) & 30/2/3 (Q10)3. Infinitely Many Solutions
1 Mark
The value of \(k\) for which the system of linear equations \(6x+y=3k\) and \(36x+6y=3\) have infinitely many solutions is:
Series 30/3/1 (Q3) & 30/3/3 (Q13)4. Inconsistent Pair
1 Mark
A system of two linear equations in two variables is inconsistent, if the lines in the graph are:
Series 30/3/2 (Q7)5. Nature of Solution
1 Mark
The system of equations \(2x+1=0\) and \(3y-5=0\) has:
Series 30/6/1 (Q17)6. No Common Solution
1 Mark
The system of equations \(x+5=0\) and \(2x-1=0\), has:
Series 30/6/2 (Q1)7. Assertion–Reason
1 Mark
Assertion (A): The pair of linear equations \(px+3y+59=0\) and \(2x+6y+118=0\) will have infinitely many solutions if \(p=1\).
Reason (R): If the pair of linear equations \(px+3y+19=0\) and \(2x+6y+157=0\) has a unique solution, then \(p
e1\).
II
Very Short Answer Type Questions
8. Algebraic Solution
2 Marks
Solve the following system of equations algebraically:
\[30x+44y=10\qquad 40x+55y=13\]
Series 30/4/1 (Q21)III
Short Answer Type Questions
9. Graphical Solution and y-intercepts
3 Marks
Solve the following system of equations graphically:
\[2x-y-2=0\qquad -4x+y+4=0\]
Also, find the absolute difference between the ordinates of the points where the given lines cut the y-axis.
Series 30/5/1 (Q28)10. Graphical Solution and y-axis Intercepts
3 Marks
Solve the following system of equations graphically:
\[2x+3y=6\qquad x+y-1=0\]
Find the coordinates of the points where the lines cut the y-axis and determine the sum of these coordinates.
Series 30/5/3 (Q31)11. Consistency and Graphical Solution
3 Marks
Check whether the following system of equations is consistent or not. If consistent, solve it graphically:
\[x+3y=6\qquad 3y-2x=-12\]
Series 30/6/1 (Q28)12. Consistency and Graphical Solution
3 Marks
Check whether the following system of equations is consistent or not. If consistent, solve graphically:
\[x-2y+4=0\qquad 2x-y-4=0\]
Series 30/6/2 (Q30)13. Consistency of a Pair
3 Marks
Check whether the given system of equations is consistent or not. If consistent, solve it graphically:
\[x-2y=0\qquad 2x+y=0\]
Series 30/6/3 (Q26)IV
Long Answer Type Questions
14. Investment and Interest
5 Marks
Vijay invested some amounts in two schemes A and B, which offer interest at the rate of 8% per annum and 9% per annum, respectively. He received ₹ 1,860 as annual interest. However, had he interchanged the amounts of investments in the two schemes, he would have received ₹ 20 more as annual interest. How much amount did he invest in each scheme?
Series 30/1/1 (Q32)15. Lending at Different Rates
5 Marks
A man lent a part of his money at 10% p.a. and the rest at 15% p.a. His income at the end of the year is ₹ 1,900. If he had interchanged the rate of interest on the two sums, he would have earned ₹ 200 more. Find the amount lent in both cases.
Series 30/3/2 (Q34)16. Students in Rows
5 Marks
The students of a class are made to stand equally in rows. If 3 students are extra in each row, there would be 1 row less. If 3 students are less in a row, there would be 2 more rows. Find the number of students in the class.
Series 30/3/3 (Q33)V
Case Study Based Question
17. Chairs and Tables for a Cultural Event
4 Marks
A school plans to rent chairs and tables for a cultural event. Rent for each chair is ₹ 50 and for each table is ₹ 200. Total items (chairs \(x\) and tables \(y\)) are 300, and the total spend is ₹ 30,000.
(i) Write down the pair of linear equations representing the given information. (1 mark)
(ii) (a) Find the number of chairs and number of tables rented by the school. (2 marks)
OR
(b) If the school wants to spend a maximum of ₹ 27,000 on 300 items, find the number of chairs and tables it can rent. (2 marks)
(iii) What is the maximum number of tables that can be rented for ₹ 30,000 if no chairs are rented? (1 mark)