Home / Class 10 Math / Ch 3 Pair of Linear Equations in Two Variables- MCQ Online Test 3 Class 10 Maths
Chapter 3 Pair of Linear Equations in Two Variables- MCQ Online Test 3 Class 10 Maths
1.The number of solutions of two linear equations representing intersecting lines is/are
1
∞
2
0
2. The sum of the numerator and denominator of a fraction is 18. If the denominator is increased by 2, the fraction reduces to 1/3. The fraction is
5/13
-7/11
-5/13
7/11
3. Half the perimeter of a rectangular garden, whose length is 4m more than its width is 36m. The area of the garden is
320 m²
360 m²
300 m²
400 m²
4. The system of linear equations a_{1}x + b_{1}y + c_{1}= 0 and a_{2}x + b_{2}y + c_{2}= 0 has no solution if
a_{1}/a_{2} = b_{1}b_{2} = c_{1}/c_{2}
None of these
a_{1}/a_{2} = b_{1}/b_{2} ≠ c_{1}/c_{2}
a_{1}/a_{2} ≠ b_{1}/b_{2}
5. The pair of equations 5x – 15y = 8 and 3x – 9y = 24/5 has
no solution
infinitely many solutions
one solution
two solutions
6. Ritu can row downstream 20 km in 2 hours and upstream 4 km in 2 hours. The speed of the current is
4 km/hr
12 km/hr
8 km/hr
6 km/hr
7. The sum of two numbers is 8. If their sum is four times their difference, then the numbers are
7 and 1
none of these.
6 and 2
5 and 3
8. The value of ‘k’ so that the system of equations 3x – 4y – 7 = 0 and 6x – ky – 5 = 0 have a unique solution is
k≠4
k≠−8
k≠−4
k≠8
9. In ΔABC, if ∠A = x°, ∠B = 3x° and ∠C = y°. If 3y – 5x = 30, then ∠B =
90°
60°
45°
30°
10. The pair of linear equations ax + by = c and px + qy = r has a unique solution then
ap ≠ bq
aq ≠ bp
ap = bq
aq = bp
Chapter - 3 A Pair of Linear Equation in two Variables Quiz - 3 Class - 10th
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Question 1 of 10
1. Question
The number of solutions of two linear equations representing intersecting lines is/are
Correct
Explanation: The number of solutions of two linear equations representing intersecting lines is 1 because two linear equations representing intersecting lines has a unique solution.
Incorrect
Explanation: The number of solutions of two linear equations representing intersecting lines is 1 because two linear equations representing intersecting lines has a unique solution.
Question 2 of 10
2. Question
The sum of the numerator and denominator of a fraction is 18. If the denominator is increased by 2, the fraction reduces to 1/3. The fraction is
Correct
Incorrect
Question 3 of 10
3. Question
Half the perimeter of a rectangular garden, whose length is 4m more than its width is 36m. The area of the garden is
Correct
Explanation:
Let the width be x.
Then length be x+4
According to the question
l+b=36
⇒ x+(x+4)=36
⇒ 2x+4=36
⇒ 2x=36-4
⇒ 2x=32
⇒ x=16.
Hence, The length of garden will be 20 m and width will be 16 m.
Area = length × breath = 20×16 = 320 m²
Incorrect
Explanation:
Let the width be x.
Then length be x+4
According to the question
l+b=36
⇒ x+(x+4)=36
⇒ 2x+4=36
⇒ 2x=36-4
⇒ 2x=32
⇒ x=16.
Hence, The length of garden will be 20 m and width will be 16 m.
Area = length × breath = 20×16 = 320 m²
Question 4 of 10
4. Question
The system of linear equations a_{1}x + b_{1}y + c_{1}= 0 and a_{2}x + b_{2}y + c_{2}= 0 has no solution if
Correct
Explanation – The system of linear equations a_{1}x + b_{1}y + c_{1}= 0 and a_{2}x + b_{2}y + c_{2} = 0 has no solution if the equation satisfy the condition a_{1}/a_{2} = b_{1}/b_{2} ≠ c_{1}/c_{2}
Incorrect
Explanation – The system of linear equations a_{1}x + b_{1}y + c_{1}= 0 and a_{2}x + b_{2}y + c_{2} = 0 has no solution if the equation satisfy the condition a_{1}/a_{2} = b_{1}/b_{2} ≠ c_{1}/c_{2}
Question 5 of 10
5. Question
The pair of equations 5x – 15y = 8 and 3x – 9y = 24/5 has
Correct
Incorrect
Question 6 of 10
6. Question
Ritu can row downstream 20 km in 2 hours and upstream 4 km in 2 hours. The speed of the current is
Correct
Explanation
Let speed of boat = x km/h
speed of current = y km/h
∴ Downstream speed = (x+y) km/h
Upstream speed = (x−y) km/h
also,
Speed = Distance/Time
⇒ Time = Distance/Speed
According to question,
In downstream, 20/(x+y) = 2
x + y = 10 ….. (i)
In upstream, 4/(x-y) = 2
x – y = 2 ….. (ii)
Subtracting eq. (ii) from (i), we get
2y=8
⇒ y=4
Therefore, the speed of current is 4 km/h.
Incorrect
Explanation
Let speed of boat = x km/h
speed of current = y km/h
∴ Downstream speed = (x+y) km/h
Upstream speed = (x−y) km/h
also,
Speed = Distance/Time
⇒ Time = Distance/Speed
According to question,
In downstream, 20/(x+y) = 2
x + y = 10 ….. (i)
In upstream, 4/(x-y) = 2
x – y = 2 ….. (ii)
Subtracting eq. (ii) from (i), we get
2y=8
⇒ y=4
Therefore, the speed of current is 4 km/h.
Question 7 of 10
7. Question
The sum of two numbers is 8. If their sum is four times their difference, then the numbers are
Correct
Explanation:
x + y = 8
⇒ x = 8-y …… (1)
⇒ x + y = 4.(x – y) ….. (2)
Substitute (1) in (2)
8= 4x-4y
⇒ 2=x-y
⇒ 2=8-y-y
⇒ 2y=8-2
⇒ y=3
therefore,
x=8-3=5
Hence, the required numbers are 5 and 3.
Incorrect
Explanation:
x + y = 8
⇒ x = 8-y …… (1)
⇒ x + y = 4.(x – y) ….. (2)
Substitute (1) in (2)
8= 4x-4y
⇒ 2=x-y
⇒ 2=8-y-y
⇒ 2y=8-2
⇒ y=3
therefore,
x=8-3=5
Hence, the required numbers are 5 and 3.
Question 8 of 10
8. Question
The value of ‘k’ so that the system of equations 3x – 4y – 7 = 0 and 6x – ky – 5 = 0 have a unique solution is
Correct
Explanation
Given:
a_{1} =3, a_{2} =6, b_{1} =−4, b_{2}=−k, c_{1}=−7 and c_{2}=−5
If there is a unique solution, then
a_{1}/a_{2} ≠ b_{1}/b_{2}
⇒ 3/6 ≠ -4/-k
⇒ -3k ≠ -4×6
⇒ k ≠ 8
Incorrect
Explanation
Given:
a_{1} =3, a_{2} =6, b_{1} =−4, b_{2}=−k, c_{1}=−7 and c_{2}=−5
If there is a unique solution, then
a_{1}/a_{2} ≠ b_{1}/b_{2}
⇒ 3/6 ≠ -4/-k
⇒ -3k ≠ -4×6
⇒ k ≠ 8
Question 9 of 10
9. Question
In ΔABC, if ∠A = x°, ∠B = 3x° and ∠C = y°. If 3y – 5x = 30, then ∠B =
Correct
Explanation:
Here, A=x, B=3x, C=y.
180= 4x+y …. (i) (Sum of angles of a triangles= x+3x+y)
180-4x=y ….. (ii)
Also, 3y-5x=30 …. (iii)
Substituting the value of (ii) in (iii)
3(180-4x)-5x=30
⇒ 540-12x-5x=30
⇒ -17x= 30-540
⇒ 17x= 510
⇒ x= 30 …. (iv)
But angle B = 3x
Therefore angle B = 3×30 = 90°
Incorrect
Explanation:
Here, A=x, B=3x, C=y.
180= 4x+y …. (i) (Sum of angles of a triangles= x+3x+y)
180-4x=y ….. (ii)
Also, 3y-5x=30 …. (iii)
Substituting the value of (ii) in (iii)
3(180-4x)-5x=30
⇒ 540-12x-5x=30
⇒ -17x= 30-540
⇒ 17x= 510
⇒ x= 30 …. (iv)
But angle B = 3x
Therefore angle B = 3×30 = 90°
Question 10 of 10
10. Question
The pair of linear equations ax + by = c and px + qy = r has a unique solution then
Correct
Explanation
a_{1} = a, a_{2} = p, b_{1} = b, b_{2} = q, c_{1} = c and c_{2 }= r
Since the pair of given linear equations has a unique solution therefore,
∴ a_{1}/a_{2} ≠ b_{1}/b_{2}
⇒ a/p ≠ b/q
⇒ aq ≠ bp
Incorrect
Explanation
a_{1} = a, a_{2} = p, b_{1} = b, b_{2} = q, c_{1} = c and c_{2 }= r
Since the pair of given linear equations has a unique solution therefore,