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NCERT Class 10 Maths Chapter 3 Online Test – Pair of Linear Equations in Two Variables (50 MCQs) | Board Exam 2026

📅 Friday, 30 January 2026 📖 पढ़ रहे हैं...
NCERT Class 10 Maths Chapter 3 Online Test – Pair of Linear Equations in Two Variables (50 MCQs)
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NCERT Class 10 Mathematics – Chapter 3: Pair of Linear Equations in Two Variables

Board Exam 2026 focused online test strictly based on NCERT textbook.

  • A pair of linear equations represents two straight lines.
  • Graphical method studies point of intersection.
  • Algebraic methods include substitution and elimination.
  • Three cases: intersecting, parallel, coincident lines.
  • Consistency depends on coefficients’ ratios.

Q1. A pair of linear equations in two variables represents:

Two straight lines
One curve
One line
A circle
Each linear equation represents a straight line.

Q2. The solution of a pair of linear equations is the:

Slope of lines
Distance between lines
Point of intersection
Area enclosed
Solution corresponds to intersection point.

Q3. If two lines intersect at one point, the system is:

Inconsistent
Consistent and independent
Consistent and dependent
Impossible
One unique solution.

Q4. If two lines are parallel, the system has:

One solution
Infinite solutions
Dependent solution
No solution
Parallel lines never intersect.

Q5. If two lines coincide, the system has:

No solution
One solution
Infinite solutions
Exactly two solutions
Coincident lines overlap completely.

Q6. The graphical method of solving equations means:

Drawing graphs of both equations
Eliminating variables
Substituting values
Factorising
Graphs are drawn to find intersection.

Q7. The substitution method involves:

Eliminating both variables
Expressing one variable in terms of the other
Multiplying equations
Graphing
One variable is substituted.

Q8. The elimination method aims to:

Plot graphs
Substitute variables
Eliminate one variable
Find slope
One variable is eliminated.

Q9. For consistency, if a1/a2 ≠ b1/b2, lines:

Are parallel
Coincide
Are inconsistent
Intersect
Different ratios imply intersection.

Q10. For no solution, the condition is:

a1/a2 = b1/b2 ≠ c1/c2
a1/a2 ≠ b1/b2
a1/a2 = b1/b2 = c1/c2
None
Parallel distinct lines.

Q11. For infinitely many solutions:

a1/a2 ≠ b1/b2
a1/a2 = b1/b2 ≠ c1/c2
a1/a2 = b1/b2 = c1/c2
None
Coincident lines.

Q12. The solution of equations is represented by:

Midpoint
Ordered pair (x, y)
Slope
Intercept
Solution is an ordered pair.

Q13. Which method is suitable when coefficients are easily adjustable?

Graphical
Substitution
Trial
Elimination
Elimination simplifies coefficients.

Q14. If two lines intersect at exactly one point, they are:

Consistent and independent
Consistent and dependent
Inconsistent
Parallel
Unique solution.

Q15. Which of the following is NOT a method of solving?

Graphical
Substitution
Factorisation
Elimination
Factorisation is not used here.

Q16. Two coincident lines imply:

No solution
Infinite solutions
One solution
Exactly two solutions
All points are solutions.

Q17. The graphical solution is not accurate because:

Lines are thick
Axes are inaccurate
Scale varies
Reading intersection is approximate
Graph reading is approximate.

Q18. If slopes are equal and intercepts differ, lines are:

Parallel
Intersecting
Coincident
Perpendicular
Same slope, different intercepts.

Q19. Which case gives a unique solution?

Parallel lines
Coincident lines
Intersecting lines
Horizontal lines
Intersecting once.

Q20. Algebraic methods give:

Approximate solutions
Exact solutions
Graphical outputs
Estimates
Algebraic methods are exact.

Q21. The standard form of linear equation is:

ax + by + c = 0
y = mx + c
x = a
y = b
NCERT standard form.

Q22. The solution set of inconsistent equations is:

One point
Two points
Infinite points
Empty set
No solution.

Q23. If two equations have same coefficients and constants, they are:

Parallel
Coincident
Intersecting
Perpendicular
Identical equations.

Q24. In elimination, equations are:

Subtracted randomly
Always added
Added or subtracted suitably
Multiplied only
Choose to eliminate a variable.

Q25. Which method uses graphs?

Graphical
Substitution
Elimination
Algebraic
Graphical method.

Q26. If lines intersect on the graph, solution is:

Approximate only
None
Infinite
Unique
Single intersection.

Q27. Substitution is preferred when:

Coefficients are equal
One variable has coefficient 1
Both variables equal
Graphs are easy
Simpler substitution.

Q28. Which indicates dependent equations?

Different slopes
Parallel lines
Same line
Perpendicular lines
Coincident lines.

Q29. The graphical solution gives:

Approximate value
Exact algebraic value
No value
Symbolic value
Graph reading is approximate.

Q30. If a1/a2 = b1/b2 = c1/c2, then lines:

Intersect
Are parallel
Are inconsistent
Coincide
Same line.

Q31. The point satisfying both equations is called:

Intercept
Solution
Slope
Origin
Common solution.

Q32. Which method avoids graph drawing?

Graphical
Plotting
Algebraic
Scaling
Algebraic methods.

Q33. Two equations with one solution are:

Consistent independent
Consistent dependent
Inconsistent
Parallel
Unique solution.

Q34. Which is an algebraic method?

Graphical
Plotting
Reading graph
Elimination
Elimination is algebraic.

Q35. If slopes are unequal, lines:

Coincide
Intersect
Are parallel
Overlap
Different slopes intersect.

Q36. The system with no solution is:

Consistent
Dependent
Inconsistent
Independent
No solution.

Q37. The graphical method is useful to:

Visualize solutions
Compute exact values
Eliminate variables
Factorise
Visual understanding.

Q38. Two parallel lines imply equations are:

Dependent
Independent
Consistent
Inconsistent
No solution.

Q39. Which method is exact?

Graphical
Algebraic
Approximate
Visual
Algebraic gives exact.

Q40. The point common to both graphs represents:

Intercept
Slope
Solution
Axis
Common solution.

Q41. Which condition ensures exactly one solution?

a1/a2 ≠ b1/b2
a1/a2 = b1/b2 ≠ c1/c2
a1/a2 = b1/b2 = c1/c2
None
Intersecting lines.

Q42. Which case is dependent?

Intersecting
Parallel
Independent
Coincident
Same line.

Q43. In elimination, coefficients are made:

Zero directly
Equal or opposite
Random
One
To eliminate a variable.

Q44. Which representation uses coordinates?

Algebraic
Symbolic
Graphical
Numeric
Graph uses coordinates.

Q45. The pair of equations with one solution is:

Consistent independent
Consistent dependent
Inconsistent
Parallel
Unique solution.

Q46. Which method is least accurate?

Elimination
Substitution
Algebraic
Graphical
Graphical is approximate.

Q47. If equations are inconsistent, they represent:

Same line
Parallel lines
Intersecting lines
One point
No intersection.

Q48. Which case gives infinitely many solutions?

Parallel
Intersecting
Coincident
Perpendicular
Same line.

Q49. The graphical method requires:

Drawing both lines
Eliminating variables
Factoring
Substituting
Graphs are drawn.

Q50. The main aim of this chapter is to:

Study curves
Solve linear equations simultaneously
Find areas
Plot points
NCERT objective.
Q1 Pair of linear equations represent two straight lines. Q2 Solution as point of intersection. Q3 Intersecting lines give consistent independent system. Q4 Parallel lines give no solution. Q5 Coincident lines give infinite solutions. Q6 Graphical method meaning. Q7 Substitution method. Q8 Elimination method. Q9 Condition for intersection. Q10 Condition for no solution. Q11 Condition for infinite solutions. Q12 Solution as ordered pair. Q13 Suitable method. Q14 One solution case. Q15 Not a method. Q16 Coincident lines meaning. Q17 Graphical inaccuracy. Q18 Equal slopes case. Q19 Unique solution case. Q20 Exactness of algebraic methods. Q21 Standard form. Q22 Inconsistent solution set. Q23 Coincident equations. Q24 Elimination operation. Q25 Graphical method. Q26 Unique intersection. Q27 When substitution preferred. Q28 Dependent equations. Q29 Approximate nature of graph. Q30 Coincident condition. Q31 Definition of solution. Q32 Algebraic method. Q33 One solution system. Q34 Algebraic example. Q35 Unequal slopes. Q36 Inconsistent system. Q37 Use of graph. Q38 Parallel implication. Q39 Exact method. Q40 Common point meaning. Q41 Condition for unique solution. Q42 Dependent case. Q43 Elimination requirement. Q44 Coordinate representation. Q45 Consistent independent. Q46 Least accurate method. Q47 Parallel meaning. Q48 Coincident meaning. Q49 Graphical requirement. Q50 Objective of chapter.
Disclaimer: We are not affiliated with NCERT. Although every care has been taken in creating this test, in case of any confusion, students should consider the NCERT textbooks and the opinion of their subject teacher as final.

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