Linear Equation in two variables MCQS

1. A test consists of 'True' or 'False' questions. One mark awarded for every correct answer
1
while 4 mark is deducted for every wrong answer. A student knew answers to some of the
questions. Rest of the questions he attempted by guessing. He answered 120 questions
and scored 95 marks.
(i) If answer to all questions he attempted by guessing were wrong, then the number of
questions he answered correctly is
(a) 24 (b) 96 (c) 100 (d) 90
(ii) The number of questions he guessed, is
(a) 24 (b) 96 (c) 20 (d) 90
(iii) If answers to all questions he attempted by guessing were wrong and answered 80
correctly, then how many marks he got?
(a) 40 (b) 45 (c) 70 (d) 35
(iv) If answer to all questions he attempted by guessing were wrong, then the number
of questions answered correctly to score 95 marks is
(a) 100 (b) 105 (c) 90 (d) 95
2. Ravish is planning to buy a house whose layout is given below. The design and the
measurement has been made such that areas of two bedrooms and kitchen together is
95 m2.

Fig. 3.1
(i) The pair of linear equations in two variables describing this situation is
(a) 2x + y = 19, x + y = 13 (b) x + 2y = 19, x + y = 13
(c) 2x + y = 13, x + y = 13 (d) 2x + y = 13, x + y = 19
(ii) The perimeter and area of the house are respectively
(a) 54 m, 180 m2 (b) 180 m, 54 m2 (c) 27 m, 90 m2 (d) 108 m, 180 m2
(iii) The value of xy is : (a) 42 (b) 48 (c) 49 (d) 13

Page 1 of 6
www.theconceptuallearning.com Ph: 9811628163 C-2/21, sector15, Rohini
 (iv) The value of x - y is: (a) 13 (b) 1 (c) -1 (d) .42
(iv) The cost of laying tiles in the kitchen at the rate of Rs. 70 per m2 is
(a) Rs.1750 (b) Rs. 2400 (c) Rs.2450 (d) Rs.2550
3. It is common that governments revise travel fares from time to time based on various
factors such as inflation (a general increase in prices and fall in the purchasing value of
money) on different types of vehicles like auto rickshaws, taxis, radio cabs etc. The auto
charges in a city comprise of a fixed charge together with the charge for the distance
covered. Study the following situations:

Fig. 3.2

Name of the City Distance travelled (km) (Amount paid (Rs.))

City A 10 75

15 110

City B 8 91

14 145

(i) If the fixed charges of autorickshaw be Rs. x and the running charges be Rs. y km/hr,
the pair of linear equations representing the travel in city A is
(a) x + 10y = 75, x + 5y = 145 (b) x + 10y = 75, x + 15y = 110
(c) x + 8y = 91, x + 14y = 145 (d) x + 8y = 145, x + 14y = 91
(ii) If the fixed charges of autorikshaw be Rs. x and the running charges be Rs. y km/hr,
the pair of linear equations representing the travel in City B is
(a) x + 10y = 75, x + 5y = 145 (b) x + 10y = 75, x + 15y = 110
(c) x + 8y = 91, x + 14y = 145 (d) x + 8y = 145, x + 14y = 91
(iii) The amount paid by a person travelling 100 km in city A is
(a) Rs. 310 (b) Rs. 510 (c) Rs. 705 (d) Rs. 710
(iv) The amount paid by a person travelling 60 km in city B is
(a) Rs. 370 (b) Rs. 578 (c) Rs. 559 (d) Rs. 610
(v) The amount paid by a person in travelling 50 km in City A and 30 km in City B is
(a) Rs. 355 (b) Rs. 289 (c) Rs. 644 (d) Rs. 746

Page 2 of 6
www.theconceptuallearning.com Ph: 9811628163 C-2/21, sector15, Rohini
 1. The value of k for which the system of equations kx − y = 2 and, 6x − 2y = 3 has a unique
solution, is
a. = 3 (b) ≠ 3 (c) ≠ 0 (d) = 0
2. The value of 𝑘 for which the system of equations 2𝑥 + 3𝑦 = 5 and, 4𝑥 + 𝑘𝑦 = 10 has
infinite number of solutions, is number of solutions, is : (a) 1 (b) 3 (c) 6 (d) 0
3. The value of 𝑘 for which the system of equations 𝑥 + 2𝑦 − 3 = 0 and 5𝑥 + 𝑘𝑦 + 7 = 0 has
no solution, is
a. (a) 10 (b) 6 (c) 3 (d) 1
4. The value of 𝑘 for which the system of equations 3𝑥 + 5𝑦 = 0 and 𝑘𝑥 + 10𝑦 = 0 has a
non-zero solution, is
a. (a) 0 (b) 2 (c) 6 (d) 8
5. The value of 𝑘 for which the system of equations 耂 has no solution is
3
a. (a) 6 (b) -6 (c) (d) none of these
2
6. If a pair of linear equations in two variables is consistent, then the lines represented by
two equations are
a. (a) intersecting (b) parallel (c) always coincident (d) intersecting or coincident
7. If the system of equations 2𝑥 + 3𝑦 = 5,4𝑥 + 𝑘𝑦 = 10 has infinitely many solutions, then
𝑘=
1
a. (a) 1 (b) (c) 3 (d) 6
2
8. If the system of equations 𝑘𝑥 − 5𝑦 = 2,6𝑥 + 2𝑦 = 7 has no solution, then 𝑘 =
a. (a) -10 (b) -5 (c) -6 (d) -15
9. If 𝑥 = 𝑎, 𝑦 = 𝑏 is the solution of the systems of equations 𝑥 − 𝑦 = 2 and 𝑥 + 𝑦 = 4, then
the values of 𝑎 and 𝑏 are, respectively
a. (a) 3 and 1 (b) 3 and 5 (c) 5 and 3 (d) -1 and -3
10. 10. For what value 𝑘, do the equations 3𝑥 − 𝑦 + 8 = 0 and 6𝑥 − 𝑘𝑦 + 16 = 0 represent
coincident lines?
1 1
a. (a) 2 (b) − 2 (c) 2 (d) -2
11. The pair of linear equations 𝑦 = 0 and 𝑦 = −5 has
a. (a) one solution (b) two solutions (c) infinitely many solutions (d) no solution
12. 8 chairs and 5 tables cost Rs. 10,500, while 5 chairs and 3 tables cost Rs. 6,450. The
cost of each chair will be
a. (a) Rs. 750 (b) Rs. 600 (c) Rs. 850 (d) Rs. 900
13. If ABCD is a rectangle shown in Fig. 3.4, then
a. (a) x = 10, y = 2 (b) x = 12, y = 8 (c) x = 2, y = 10 (d) x = 20, y = 0

b.
i. Fig. 3.4
14. The pair of linear equations 3𝑥 + 5𝑦 = 3 and 6𝑥 + 𝑘𝑦 = 8 do not have a solution, if 𝑘
a. (a) = 5 (b) = 10 (c) ≠ 10 (d) ≠ 5
15. If the sum of the ages of a father and his son in years is 65 and twice the difference of
their ages in years is 50 , then the age of father is

Page 3 of 6
www.theconceptuallearning.com Ph: 9811628163 C-2/21, sector15, Rohini
 a. (a) 40 years (b) 45 years (c) 55 years (d) 65 years.
16. If the system of equations 2𝑥 + 3𝑦 = 7 and, (𝑎 + 𝑏)𝑥 + (2𝑎 − 𝑏)𝑦 = 21 has infinitely many
solutions, then
a. (a) 𝑎 = 1, 𝑏 = 5 (b) 𝑎 = 5, 𝑏 = 1 (c) 𝑎 = −1, 𝑏 = 5 (d) 𝑎 = 5, 𝑏 = −1
17. If the system of equations 3𝑥 + 𝑦 = 1 and, (2𝑘 − 1)𝑥 + (𝑘 − 1)𝑦 = 2𝑘 + 1 is inconsistent,
then 𝑘 =
a. (a) 1 (b) 0 (c) -1 (d) 2
18. If 𝑎𝑚 ≠ 𝑏𝑙, then the system of equations 𝑎𝑥 + 𝑏𝑦 = 𝑐 and, 𝑙𝑥 + 𝑚𝑦 = 𝑛
a. (a) has a unique solution (b) has no solution (c) has infinitely many solutions
(d) may or may not have a solution.
19. If the system of equations
20. 2𝑥 + 3𝑦 = 7; 2𝑎𝑥 + (𝑎 + 𝑏)𝑦 = 28 ; has infinitely many solutions, then
a. (a) 𝑎 = 2𝑏 (b) 𝑏 = 2𝑎 (c) 𝑎 + 2𝑏 = 0 (d) 2𝑎 + 𝑏 = 0
21. If 2𝑥 − 3𝑦 = 7 and (𝑎 + 𝑏)𝑥 − (𝑎 + 𝑏 − 3)𝑦 = 4𝑎 + 𝑏 represent coincident lines, then 𝑎
and 𝑏 satisfy the equation
a. (a) 𝑎 + 5𝑏 = 0 (b) 5𝑎 + 𝑏 = 0 (c) 𝑎 − 5𝑏 = 0 (d) 5𝑎 − 𝑏 = 0
𝑥 𝑦
22. The area of the triangle formed by the line + = 1 with the coordinate axes is
𝑎 𝑏
1 1
a. (a) ab (b) 2ab (c) 2 ab (d) 4 ab
23. The area of the triangle formed by the lines 𝑦 = 𝑥, 𝑥 = 6 and 𝑦 = 0 is
a. 36𝑠𝑞. units (b) 18𝑠𝑞. units (c) 9 sq. units (d) 72𝑠𝑞. units
24. The area of the triangle formed by the lines 𝑥 = 3, 𝑦 = 4 and 𝑥 = 𝑦 is
a. (a) 1/2 sq. unit (b) 1 sq. unit (c) 2 sq. unit (d) None of these
25. The sum of the digits of a two digit number is 9 . If 27 is added to it, the digits of the
number get reversed. The number is
26. (a) 25 (b) 72 (c) 63 (d) 36
27. 25. Aruna has only Rs. 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 Rs. 1 and Rs. 2
coins are, respectively
a. 35 and 15 (b) 35 and 20 (c) 15 and 35 (d) 25 and 25
28. If x = a, y = b is the solution of the pair of linear equations 37x + 43y = 123,43x + 37y =
117, then a3 + b3 is equal to
a. (a) -7 (b) 7 (c) 9 (d) -9
29. The value of k for which the lines 5x + 7y = 3 and 15x + 21y = k coincide is
a. 9 (b) 5 (c) 7 (d) 18
30. One equation of a pair of dependent linear equations is −5x + 7y = 2. The second
equation is
a. (a) 10x + 14y + 4 = 0 (b) −10x − 14y + 4 = 0 (c) −10x + 14y + 4 = 0d (d)
10x − 14y = −4
31. If 217x + 131y = 913 and 131x + 227y = 827, then x + y is equal to
a. 5 (b) 6 (c) 7 (d) 8
32. The number of solutions of 3x+y = 243 and 243x−y = 3 is
a. 0 (b) 1 (c) 2 (d) infinite
33. . The area of the triangle formed by the lines 2x + 3y = 12, x − y − 1 = 0 and x = 0 (as
shown in Fig. 3.5), is
(a) 7 sq. units (b) 7.5 sq. units (c) 6.5 sq. units (d) 6 sq. units

Page 4 of 6
www.theconceptuallearning.com Ph: 9811628163 C-2/21, sector15, Rohini
 34. 35.
37. Fig. 3.6
36. Fig. 3.5

38. Figure 3.6, is the graph representing two linear equations by lines A B and C D
respectively. The area of the triangle formed by these two lines and the line x = 0 is
(a) 3 sq. units (b) 4 sq. units (c) 6 sq. units (d) 8 sq. units

Each of the following questions contains STATEMENT-1 (Assertion) and STATEMENT-2

(Reason) and has following four choices (a), (b), (c) and (d), only one of which is the correct
answer. Mark the correct choice.
(a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-
1.
(b) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for
Statement-1.
(c) Statement-1 is true, Statement-2 is false.
(d) Statement-1 is false, Statement-2 is true.
35. Statement-1 (Assertion): The system of linear equations 3x + 5y − 4 = 0 and 15x + 25y −
25 = 0 is inconsistent.
Statement-2 (Reason): The pair of linear equations a1 x + b1 y + c1 = 0 and a2 x + b2 y + c2 = 0
a b c
represents parallel lines, if a1 = b1 ≠ c1.
2 2 2

36. Statement-1 (Assertion): The area of the rectangle formed by the lines representing x = 8, y =
6 with the coordinate axes is 24 sq. units.
Statement-2 (Reason): The system of equations x = 8, y = 6 is consistent with a unique solution.
37. Statement-1 (Assertion): If a pair of linear equations represent coincident lines, then the
equations are consistent and have a unique solution.
Statement-2 (Reason): A pair of linear equations a1 x + b1 y + c1 = 0 and a2 x + b2 y + c2 = 0
a b c
represents coincident lines iff a1 = b1 = c1 .
2 2 2

38. Statement-1 (Assertion): If the system of equations 3x + 6y = 10 and 2x − ky + 5 = 0 is

Page 5 of 6
www.theconceptuallearning.com Ph: 9811628163 C-2/21, sector15, Rohini
inconsistent, then k = −4.
Statement-2 (Reason): The system of equations a1 x + b1 y + c1 = 0 and a2 x + b2 y + c2 = 0 is
a b c
inconsistent iff a1 = b1 = c1.
2 2 2

1. (b) 2. (c) 3. (a) 4. (c)

8. (d) 9. (a) 10. (c) 11. (d)

15. (b) 16 (b) 17. (d) 18. (a)

22. (b) 23. (a) 24. (d) 25. (d)

29. (a) 30. (b) 31. (b) 32. (c)

Assertions: 35. (a) 36. (b) 37. (d) 38. (c)

Page 6 of 6
www.theconceptuallearning.com Ph: 9811628163 C-2/21, sector15, Rohini