CBSE Class 9 Maths Linear Equations in Two Variables MCQs Set 02

Question. Sum of two numbers is 64 and their difference is 22. Find the numbers.
a) 42, 22
b) 43, 21
c) 40, 24
d) 50, 28
Answer: b

Question. At the end of the year 2002, Ram was half as old as his grandpa. The sum of the years in which they were born is 3854. Age of Ram at the end of year 2003 is _______.
a) 50 years
b) 35 years
c) 51 years
d) 36 years
Answer: c

Question. If am = bl and bn ≠ cm, then the system of equations
ax + by = c
lx + my = n
a) Has a unique solution.
b) Has no solution.
c) Has infinitely many solutions.
d) May or may not have a solution.
Answer: b

Question. Value of x in pair of linear equations 36x + 24y = 702 and 24x + 36y = 558 is
a) 33/2
b) 145/7
c) 16
d) 17
Answer: a

Question. If the system of equations
2x + 3y = 7
2ax + (a + b)y = 28
has infinitely many solutions, then the values of a and b respectively are _______.
a) 2, 5
b) 5, 8
c) 4, 8
d) 3, 6
Answer: c

Question. The denominator of a rational number is greater than its numerator by 3. If 3 is subtracted from the numerator and 2 is added to the denominator, the new number becomes 1/5 . Then the original number was _______.
a) 7/11
b) 3/5
c) 5/8
d) 4/7
Answer: c

Question. In a ΔABC, ∠C = 3∠B = 2(∠A + ∠B). The three angles will be _______.
a) 20°, 40°, 120°
b) 30°, 60°, 90°
c) 45°, 45°, 90°
d) 90°, 40°, 50°
Answer: a

Question. A boat goes 32 km upstream and 36 km downstream in 7 hours. In 9 hours, it can go 40 km upstream and 48 km downstream. If x represents the speed of the boat in still water in km/hr and y represents the speed of the stream in km/hr, then_______.
a) x + y = 12, x – y = 8
b) x + y = 5, x – y = 11
c) x + y = 6, x – y = 10
d) x + y = 10, x – y = 6
Answer: a

Question. Which of the following linear equation coincide with the line 4x + 5y = 15?
a) 8x + 10y = 25
b) 2x + 3y = 7
c) 7x + 14y = 17
d) 12x + 15y = 45
Answer: d

Question. Places M and N are 90 km apart from each other on a national highway. A truck starts from M and another from N at the same time. If they go in the same direction, then they meet in 9 hours and if they go in opposite directions they meet in 9/7 hours. The speed of the trucks are _______.
a) 90 km/hr, 40 km/hr
b) 40 km/hr, 30 km/hr
c) 20 km/hr, 60 km/hr
d) 50 km/hr, 12 km/hr
Answer: b

Question. How many values of c, for which the systemof equations 6x + 3y = c – 3, 12x + cy = c has infinitely many solutions?
a) 1
b) 2
c) 3
d) Infinite
Answer: a

Question. The sum of two numbers is 8 and the sum of their reciprocals is 8/15. Find the numbers.
a) 5, 3
b) 7, 1
c) 4, 4
d) 2, 6
Answer: a

Question. The value of k, for which the system of equations kx – 3y + 6 = 0, 4x – 6y + 15 = 0 represent parallel lines, is _______.
a) 1
b) 2
c) 3
d) 4
Answer: b

Question. The solution of the system of equations 2x 5y/xy = and 4x – 5y/xy+ 3=0 (where x ≠ 0, y ≠ 0), is _______.
a) 1, 2
b) 0, 0
c) –1, 2
d) 1, –2
Answer: a

Question. The ratio of a 2-digit number to the sum of digits of that number is 4 : 1. If the digit in the unit place is 3 more than the digit in the tens place, what is the number ?
a) 63
b) 36
c) 24
d) 40
Answer: b

Question. ax + by + c = 0 does not represent an equation of line when _______.
a) a = c = 0, b ≠ 0
b) b = c = 0, a ≠ 0
c) a = b = 0
d) a = b ≠ 0
Answer: c

Question. If a pair of linear equations in two variablesis consistent, then the lines represented by two equations are
a) Always intersecting
b) Parallel
c) Always coincident
d) Intersecting or coincident
Answer: d

Question. The sum of the digits of a two-digit number is 12. The number obtained by interchanging the two digits exceeds the given number by 18. Find the number.
a) 57
b) 75
c) 85
d) 58
Answer: a

Question. On selling a tea-set at 5% loss and lemonset at 15% gain, a crockery seller gains ₹ 7. If he sells the tea-set at 5% gain and the lemon-set at 10% gain, he gains ` 13. Find the actual prices of the tea-set and the lemon-set.
a) ₹ 100, ₹ 80
b) ₹ 90, ₹ 100
c) ₹ 120, ₹ 60
d) ₹ 150, ₹ 80
Answer: a

Question. Arun and Prabhat have some books with them. Once Prabhat said to Arun that, if Arun gives 3 books to Prabhat then Arun will have only 1/2 of the books that Prabhat will have with him. Then Arun asked frankly that if Prabhat gives him only two books (to Arun), then Prabhat will have as many books as Arun will have. The total number of books that Arun and Prabhat have with them is _______.
a) 25
b) 56
c) 30
d) Can’t be determined
Answer: c

Question. Solve for x and y in the following question.

a) x = 1, y = 2
b) x = 2, y = 1
c) x = 2 y = 1/2
d) x = 1/2 y = 2
Answer: d

Question. Which of the following graphs represent the lines 2x + 4y = 8 and 3x – 4y = 12 ?

Answer: a

Question. Fill in the blanks.
(i) If pair of linear equations is consistent, then it has either P or Q solution(s).
(ii) If the pair of linear equation is inconsistent, then it has R solution(s).
(iii) If the graph of two linear equations coincide, then they have S solution(s).
    P Q R S
a) no           infinite         unique      infinite
b) unique    infinite         no             infinite
c) no           infinite         unique      unique
d) unique    no               infinite       no
Answer: b

Question. Read the statements carefully and state ‘T’ for true and ‘F’ for false.
(i) The pair of linear equations x + 2y = 5 and 7x + 3y = 13 has unique solution x = 2, y = 1.
(ii) √2x + √3y = 0, √3x − √8y = 0 has no solution.
(iii) The values of p and q for which the following system of equations 2x – y = 5, (p + q)x + (2p – q)y = 15 has infinite number of solutions, is p = 1 and q = 5.
  (i) (ii) (iii)
a) T F T
b) T T F
c) F T T
d) F F T
Answer: d

Question. Match the following.
System of equations Solutions
(P) 2x – 3y + 15 = 0               (i) x = 3, y = 5
     3x – 5 = 0
(Q) 2x – y = 1                        (ii) x = 1, y = 4
     4x + 3y = 27
(R) x + 2y – 3 = 0                 (iii) x = 5/3 y = 55/9
     3x – 2y + 7 = 0
(S) 4x + y/3 = 16/3               (iv) x =– 1,y = 2
     x/2 + 2y/4 = 5/2
a) (P) → (iii); (Q) → (iv); (R) → (i); (S) → (ii)
b) (P) → (iii); (Q) → (i); (R) → (iv); (S) → (ii)
c) (P) → (iii); (Q) → (ii); (R) → (iv); (S) → (i)
d) (P) → (ii); (Q) → (i); (R) → (iv); (S) → (iii)
Answer: b