CBSE Class 9 Mathematics Linear Equations in two variables Assignment Set 01

Question. If x + 1/x  = 3, what would the value of x² + 1/x²  be?
(a) 18
(b) 9
(c) 7
(d) 6

Answer : C

Question. There are only 1-rupee and 2-rupee coins in a bag. The total value of the 1-rupee coins is the same as the total value of the 2-rupee coins. If the bag has x coins in all, what is their total value (in Rs.)?
(a) 3x
(b) 4x/3
(c) 3x/4
(d) 3x/2

Answer : B

Question. A 3 kg bag of rice lasts exactly 30 days for Mrs. and Mr. Pestonjee when both consume equal amounts. If Mr. Pestonjee cuts down his rice intake by half on his doctor's advice, how many days would a 3 kg bag last them?

(a) 35
(b) 40
(c) 42
(d) 45

Answer : B

Question. A 200 metre long train running at a speed of 10 metre/second starts passing by a 200 metre long platform at exactly 11:00:10. See the adjoining images.What would be the time when the entire train just finishes crossing the platform?

(a) 11:00:20
(b) 11:00:30
(c) 11:00:44
(d) 11:00:50

Answer : D

Question. A shopkeeper decreases the selling price of a ceiling fan by 10% at the start of winter. When winter is over, he decides to raise the price back to the original selling price. By what percent would he need to increase the lowered price in order to do this?
(a) 20%
(b) 11.11%
(c) 10%
(d) 9.99%

Answer : B

Question. Sohail's autumn break lasted x days. Of these, he was out of station for 8 days. For the remaining days, his mother promised him Rs. 10 per day to clean up the whole house. At the end of the break, she was so happy with his work, that she decided to square the amount due to him. What is the amount that Sohail got?

(a) Rs. (100x² - 8)
(b) Rs. [10+x - 8)²
(c) Rs. 10(x - 8)²
(d) Rs. 100(x - 8)²

Answer : D

Question. What value of A will be printed if  flowchart shown in the image , is executed?(A←  5 means that the value of A is set to 5)

(a) 8
(b) 12
(c) 10
(d) 17

Answer : C

Question. The graph of y = p is shown in the adjoining image. Which of the following depicts the graph of y = p - 2?

Answer : B

Question. Mrs. Nair opts for a mobile phone offer that charges a monthly fee of Rs. 250 plus a charge of Rs. 1.25 per minute for local calls.She fixes a budget of Rs. 400 per month for her mobile phone bill. At most how many minutes can she use the phone (local) each month while staying within her budget
(a) 100
(b) 110
(c) 120
(d) 150

Answer : C

Question. The graph in the adjoining image  shows the average maximum and minimum monthly temperatures in Ahmedabad in a year.In which of the following periods did the average maximum  temperature record a steady fall?

(a) July to Sep
(b) Sep to Nov
(c) Feb to Apr
(d) May to July

Answer : D

Question. The ratio of the sum of the first m even natural numbers to that of the first m odd numbers is given in the table. According to this, the ratio of the sum of the first m even numbers and that of the first m odd numbers is given by the expression

Answer : D

Question. While doing her Physics homework, Archana has to use the formula 1/R = 1/R1+ 1/R2 . How could she rewrite this formula to get the correct value of R2 when R and R1 are given?
(a) R₂ = R - R₁
(b) R₂ = 1/(R-R₁)
(c) R₂ = (R-R1-RR₁)
(d) R₂ = RR₁/(R₁-R)

Answer : D

Question. A painter is able to paint a flat in 8 days. How many days would it have taken to paint the flat if he had two more painters working with him - one working at the same speed as him, and another working at double that speed ?
(a) 11
(b) 5
(c) 4
(d) 2

Answer : D

Question. The ratio of the height of two plants X and Y is 2:1. If plant X grows at the rate of 2 metres per year, at what rate should plant Y grow so that after 4 years they are of the same height?
(a) 1.5 metres per year
(b) 2.25 metres per year
(c) 2.5 metres per year
(d) It will vary depending on the height of Y.

Answer : D

Question. The light signals at a traffic crossing (in a particular direction) were timed in such a way that the traffic had the 'STOP' signal for s seconds and the 'GO' signal for g seconds. Rajat stopped at the signal when the light had just turned RED. Due to heavy traffic at the crossing, he misses the green signal twice and starts exactly when the light turns GREEN the third time. For how many seconds was he at the crossing?
(a) 2s + g
(b) 2(s + g)
(c) 3s + 2g
(d) 3(s + g)

Answer : C

Question. Jamal's house (J) and Tarang's house (T) are 10 km apart on a straight road. One day, both of them started from their houses at the same moment and met on the road after half an hour. If Jamal walked 2 km/hr faster than Tarang, which diagram correctly shows the position of their meeting point, P?

Answer : C

Question. A cake is cut into 3 pieces whose weights are in the ratio 2:1:4.If the third piece weighs 360 g more than the second, how much did the whole cake weigh?
(a) 1.44 kg
(b) 1.26 kg
(c) 840 g
(d) 630 g

Answer : C

Question. If 1/x  = 2/y-2  then y is equal to 
(a) 2/(x + 2)
(b) 2/2(x + 2)
(c) (x + 2)/2
(d) 2x + 2

Answer : D
 

ASSERTION & REASONING QUESTIONS

DIRECTION : In the following questions, a statement of assertion (A) is followed by a
statement of reason (R) . Mark the correct choice as:
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) .
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) .
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.

Question. Assertion : A linear equation 3x + 5y = 2 has a unique solution.
Reason : A linear equation in two variables has infinitely many solutions.
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) .
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) .
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
Answer : We know that a linear equation in two variables has infinitely many solutions.
So, Reason is correct.
Hence, Assertion is not correct
Correct option is (d) Assertion (A) is false but reason (R) is true.

Question. Assertion: x = 2 is a line parallel to the y-axis.
Reason: The equation of a line parallel to the y-axis is x = a.
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) .
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) .
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
Answer : We know that equation of a line parallel to the y-axis is x = a.
So, Reason (R) is true.
Also, x = 2 is a line parallel to the y-axis.
So, Assertion (A) is true.
Thus, Reason (R) and Assertion (A) are true and Reason (R) is a correct explanation of Assertion (A) .
Correct option is (a) Both assertion (A) and reason (R) are true and reason
(R) is the correct explanation of assertion (A) .

Question. Assertion: x = 3 and y = 2 is a solution of the linear equation 2x + 3y = 12.
Reason: x = 4 and y = 2 is a solution of the linear equation x + 3y = 10.
Answer : For Assertion: The given linear equation is 2x + 3y = 12
Substituting x = 3 and y = 2, we get
LHS = 2 x 3 + 3 x 2 = 6 + 6 = 12 = RHS
So, Assertion is correct.
For Reason: The given linear equation is x + 3y = 10
Substituting x = 4 and y = 2, we get
LHS = 4 + 3 x 2 = 4 + 6 = 10 = RHS
So, Reason is also correct.
But reason (R) is not the correct explanation of assertion (A) .
Correct option is (b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A) .

Question. Assertion: x + y = 3 is the equation of a line passing through the origin.
Reason: y = 2x is the equation of a line passing through the origin.
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) .
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) .
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
Answer : For Assertion: The given linear equation is x + y = 3
Since x = 0 and y = 0 is not satisfying x + y = 3, therefore it is not passing through the origin.
So, Assertion is not correct.
Since x = 0 and y = 0 is not satisfying y = 2x, therefore it is passing through the origin.
So, Reason is correct.
Correct option is (d) Assertion (A) is false but reason (R) is true.

Question. Assertion : If x = 2, y = 1 is a solution of the equation 2x + 3y = k, then the value of k is 7.
Reason : The solution of the line will satisfy the equation of the line
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) .
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) .
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
Answer : We know that the solution of the line will satisfy the equation of the line.
So, Reason is correct.
Since x = 2, y =1 is a solution of the given linear equation, we have
2 x 2 + 3 x 1 – k = 0  ⇒ 4 + 3 – k = 0 ⇒ k =7.
So, Assertion is also correct
Correct option is (a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) ..

Question. Assertion : There are infinite number of lines which passes through (3, 2) .
Reason : A linear equation in two variables has infinitely many solutions.
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) .
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) .
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
Answer : We know that a linear equation in two variables has infinitely many solutions. So, Reason is correct.
Through a point infinite lines can be drawn.
Through (3, 2) infinite number of lines can be drawn.
Hence, Assertion is also correct.
But reason (R) is not the correct explanation of assertion (A) .
Correct option is (b) Both assertion (A) and reason (R) are true and reason
(R) is not the correct explanation of assertion (A) .

Question. Assertion: y = 3x represents a line passing through the origin.
Reason: Any line parallel to the x-axis is y = a.
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) .
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) .
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
Answer : Since x = 0 and y = 0 is not satisfying y = 3x, therefore it is passing through the origin.
So, Assertion (A) is true.
Also, we know that equation of a line parallel to the x-axis is y = a.
So, Reason (R) is also true.
But Reason is not the correct explanation of Assertion.
Correct option is (b) Both assertion (A) and reason (R) are true and reason
(R) is not the correct explanation of assertion (A) .

Question. Assertion : If x = 2k – 1 and y = k is a solution of the equation 3x – 5y – 7 = 0, then the value of k is 10
Reason : A linear equation in two variables has infinitely many solutions.
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) .
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) .
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
Answer : We know that a linear equation in two variables has infinitely many solutions. So, Reason is correct.
Since x = 2k - 1 and y = k is solution of the given linear equation, we have
3 x (2k – 1) – 5k – 7 = 0 ⇒ 6k – 3 – 5k – 7 = 0 ⇒ k – 10 = 0 ⇒ k = 10.
So, Assertion is also correct
But reason (R) is not the correct explanation of assertion (A) .
Correct option is (b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A) .

Question. Assertion: x = 3 and y = 2 is a solution of the linear equation 2x + 3y = 12.
Reason: x = 4 and y = 2 is a solution of the linear equation x + 3y = 10.
Answer : For Assertion: The given linear equation is 2x + 3y = 12
Substituting x = 3 and y = 2, we get
LHS = 2 x 3 + 3 x 2 = 6 + 6 = 12 = RHS
So, Assertion is correct.
For Reason: The given linear equation is x + 3y = 10
Substituting x = 4 and y = 2, we get
LHS = 4 + 3 x 2 = 4 + 6 = 10 = RHS
So, Reason is also correct.
But reason (R) is not the correct explanation of assertion (A) .
Correct option is (b) Both assertion (A) and reason (R) are true and reason (R) is not the correct explanation of assertion (A) .

Question. Assertion : The point (2, 2) is the solution of x + y = 4.
Reason : Every point which satisfy the linear equation is a solution of the equation.
Answer : We know every point which satisfy the linear equation is a solution of the equation.
So, Reason (R) is true.
Substituting x = 2 and y = 2, we get
LHS = 2 + 2 = 4 = RHS
Since (3, 0) satisfies the equation 4x + 3y = 12, therefore the point (2, 2) is the solution of x + y = 4
So, Assertion (A) is also true.
Here, Reason is the correct explanation of Assertion.
Correct option is (a) Both assertion (A) and reason (R) are true and reason
(R) is the correct explanation of assertion (A) .

Question. Assertion : The graph of the linear equation 2x – y = 1 passes through the point (2, 3) .
Reason : Every point lying on graph is not a solution of 2x – y = 1.
(a) Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A) .
(b) Both assertion (A) and reason (R) are true but reason (R) is not the correct explanation of assertion (A) .
(c) Assertion (A) is true but reason (R) is false.
(d) Assertion (A) is false but reason (R) is true.
Answer : For Assertion: The given linear equation is 2x – y = 1
Substituting x = 2 and y = 3, we get
LHS = 2 x 2 – 3 = 4 – 3 = 1 = RHS
Since (3, 0) satisfies the equation 4x + 3y = 12, therefore graph of the
linear equation 2x – y = 1 passes through the point (2, 3) .
So, Assertion is correct.
But Reason is not correct as every point lying on graph is a solution of
2x – y = 1.
Correct option is (c) Assertion (A) is true but reason (R) is false.

Please click the link below to download CBSE Class 9 Mathematics Linear Equations in two variables Assignment Set A