NCERT Exemplar Problems – Class 10 Mathematics
Chapter 3: Pair of Linear Equations in Two Variables
Multiple Choice Questions (Exercise 3.1) with Correct Answers
Source: NCERT Exemplar Problems Class 10 Mathematics (Official Answer Key)
1. Graphically, the pair of equations
\(6x - 3y + 10 = 0\)
\(2x - y + 9 = 0\)
represents two lines which are
(A) intersecting at exactly one point.
(B) intersecting at exactly two points.
(C) coincident.
(D) parallel.
Correct Answer: (D)
2. The pair of equations \(x + 2y + 5 = 0\) and \(-3x - 6y + 1 = 0\) have
(A) a unique solution
(B) exactly two solutions
(C) infinitely many solutions
(D) no solution
Correct Answer: (D)
3. If a pair of linear equations is consistent, then the lines will be
(A) parallel
(B) always coincident
(C) intersecting or coincident
(D) always intersecting
Correct Answer: (C)
4. The pair of equations \(y = 0\) and \(y = -7\) has
(A) one solution
(B) two solutions
(C) infinitely many solutions
(D) no solution
Correct Answer: (D)
5. The pair of equations \(x = a\) and \(y = b\) graphically represents lines which are
(A) parallel
(B) intersecting at \((b, a)\)
(C) coincident
(D) intersecting at \((a, b)\)
Correct Answer: (D)
6. For what value of \(k\), do the equations \(3x - y + 8 = 0\) and \(6x - ky = -16\) represent coincident lines?
(A) \(\dfrac{1}{2}\)
(B) \(-\dfrac{1}{2}\)
(C) \(2\)
(D) \(-2\)
Correct Answer: (C)
7. If the lines given by \(3x + 2ky = 2\) and \(2x + 5y + 1 = 0\) are parallel, then the value of \(k\) is
(A) \(-\dfrac{5}{4}\)
(B) \(\dfrac{2}{5}\)
(C) \(\dfrac{15}{4}\)
(D) \(\dfrac{3}{2}\)
Correct Answer: (C)
8. The value of \(c\) for which the pair of equations \(cx - y = 2\) and \(6x - 2y = 3\) will have infinitely many solutions is
(A) \(3\)
(B) \(-3\)
(C) \(-12\)
(D) no value
Correct Answer: (D)
9. One equation of a pair of dependent linear equations is \(-5x + 7y = 2\). The second equation can be
(A) \(10x + 14y + 4 = 0\)
(B) \(-10x - 14y + 4 = 0\)
(C) \(-10x + 14y + 4 = 0\)
(D) \(10x - 14y = -4\)
Correct Answer: (D)
10. A pair of linear equations which has a unique solution \(x = 2\), \(y = -3\) is
(A) \(x + y = -1\) \(2x - 3y = -5\)
(B) \(2x + 5y = -11\) \(4x + 10y = -22\)
(C) \(2x - y = 1\) \(3x + 2y = 0\)
(D) \(x - 4y - 14 = 0\) \(5x - y - 13 = 0\)
Correct Answer: (D)
11. If \(x = a\), \(y = b\) is the solution of the equations \(x - y = 2\) and \(x + y = 4\), then the values of \(a\) and \(b\) are, respectively
(A) 3 and 5
(B) 5 and 3
(C) 3 and 1
(D) –1 and –3
Correct Answer: (C)
12. Aruna has only Re 1 and Rs 2 coins with her. If the total number of coins that she has is 50 and the amount of money with her is Rs 75, then the number of Re 1 and Rs 2 coins are, respectively
(A) 35 and 15
(B) 35 and 20
(C) 15 and 35
(D) 25 and 25
Correct Answer: (D)
13. The father’s age is six times his son’s age. Four years hence, the age of the father will be four times his son’s age. The present ages, in years, of the son and the father are, respectively
(A) 4 and 24
(B) 5 and 30
(C) 6 and 36
(D) 3 and 24
Correct Answer: (C)
Answers taken from the official NCERT Exemplar answer key.