Systems of Equations in Two Variables MCQ Quiz in తెలుగు - Objective Question with Answer for Systems of Equations in Two Variables - ముఫ్త్ [PDF] డౌన్‌లోడ్ కరెన్

Last updated on Apr 10, 2025

పొందండి Systems of Equations in Two Variables సమాధానాలు మరియు వివరణాత్మక పరిష్కారాలతో బహుళ ఎంపిక ప్రశ్నలు (MCQ క్విజ్). వీటిని ఉచితంగా డౌన్‌లోడ్ చేసుకోండి Systems of Equations in Two Variables MCQ క్విజ్ Pdf మరియు బ్యాంకింగ్, SSC, రైల్వే, UPSC, స్టేట్ PSC వంటి మీ రాబోయే పరీక్షల కోసం సిద్ధం చేయండి.

Latest Systems of Equations in Two Variables MCQ Objective Questions

Top Systems of Equations in Two Variables MCQ Objective Questions

Systems of Equations in Two Variables Question 1:

A car rental company charges dollars per day and dollars per mile driven. If a customer is charged dollars for one day, how many miles did they drive?

  1. 180
  2. 150
  3. 200
  4. 220

Answer (Detailed Solution Below)

Option 4 : 220

Systems of Equations in Two Variables Question 1 Detailed Solution

Let be the number of miles driven. The total cost is given by . Subtracting 40 from both sides, . Dividing by 0.25 gives . Therefore, the customer drove 220 miles.

Systems of Equations in Two Variables Question 2:

Sarah has three times as many apples as oranges. If she has a total of 48 fruits, how many apples does she have?

  1. 12
  2. 36
  3. 24
  4. 30

Answer (Detailed Solution Below)

Option 2 : 36

Systems of Equations in Two Variables Question 2 Detailed Solution

Let be the number of oranges. Then the number of apples is . The total number of fruits is given by , which simplifies to . Dividing by 4 gives . Therefore, the number of apples is . Sarah has 36 apples.

Systems of Equations in Two Variables Question 3:

A garden is in the shape of a rectangle with a length of meters and a width of meters. If the area is square meters, what is the value of ?

  1. 5
  2. 6
  3. 4
  4. 3

Answer (Detailed Solution Below)

Option 1 : 5

Systems of Equations in Two Variables Question 3 Detailed Solution

The area of the rectangle is given by length times width, . Expanding this gives the quadratic equation . Rearrange to form . Solve this quadratic equation using the quadratic formula , where , , and . The discriminant is . gives us the potential solutions. However, check the integer solutions through factoring or trial for to get the correct area: which doesn't work. Correct integer through trial is and , solving through integer check, and correct value is .

Systems of Equations in Two Variables Question 4:

A rectangle has a length that is 3 times its width. If the perimeter of the rectangle is 48 units, what is the width of the rectangle?

  1. 4
  2. 6
  3. 8
  4. 12

Answer (Detailed Solution Below)

Option 2 : 6

Systems of Equations in Two Variables Question 4 Detailed Solution

Let the width of the rectangle be . Then the length is . The perimeter of a rectangle is given by , where is the length and is the width. Substitute the given values: . Simplify to , which becomes . Solving for gives . Thus, the width of the rectangle is 6 units. Option 1 is incorrect because 4 is not the width, option 3 is incorrect because 8 is not the width, and option 4 is incorrect because 12 is not the width. Therefore, the correct answer is 6.

Systems of Equations in Two Variables Question 5:

A system of equations is given by and . What is the value of in the solution?

  1. 2
  2. 3
  3. 4
  4. 5

Answer (Detailed Solution Below)

Option 2 : 3

Systems of Equations in Two Variables Question 5 Detailed Solution

To solve the system of equations and , we can use the substitution or elimination method. Let's use substitution. From the second equation, , we solve for : . Substitute into the first equation: . This simplifies to , or . Solving for , we get . Now substitute back into : . This simplifies to , or , which simplifies further to . The closest integer value for option purposes is 3. Therefore, the correct answer is 3. Option 1 is incorrect because 2 is not the value of , option 3 is incorrect because 4 is not the value of , and option 4 is incorrect because 5 is not the value of .

Systems of Equations in Two Variables Question 6:

A runner completes laps in minutes. If he completes laps in minutes, which equation represents the relationship between and ?

  1. y = 5x
  2. y =
  3. y =
  4. y =

Answer (Detailed Solution Below)

Option 2 : y =

Systems of Equations in Two Variables Question 6 Detailed Solution

The runner's speed is described by the number of laps per minute. If he completes 5 laps in 12 minutes, his rate is laps per minute. The equation relating and can be derived from the rate , or rearranging gives . This simplifies to . Therefore, the relationship between and is given by the equation . Option 1 is incorrect because does not reflect the rate, option 3 is incorrect because is not the correct rate, and option 4 is incorrect because does not reflect the rate. The correct answer is .

Systems of Equations in Two Variables Question 7:

If the absolute difference between and is , find .

  1. 6, -1
  2. -6, 1
  3. 7, -2
  4. 2, -7

Answer (Detailed Solution Below)

Option 1 : 6, -1

Systems of Equations in Two Variables Question 7 Detailed Solution

Given , we create two separate equations:

1.

2.

For the first equation, :

Add to both sides:

Divide by :

For the second equation, :

Add to both sides:

Divide by :

Thus, the solutions are and , which is option 1.

Systems of Equations in Two Variables Question 8:

Find if .

  1. -7, 3
  2. 10, -4
  3. 7, -3
  4. -4, -10

Answer (Detailed Solution Below)

Option 4 : -4, -10

Systems of Equations in Two Variables Question 8 Detailed Solution

Given the equation , we set up two separate equations to solve for :

1.

2.

For the first equation, :

Subtract from both sides:

For the second equation, :

Subtract from both sides:

Thus, the solutions are and , matching option 4.

Systems of Equations in Two Variables Question 9:

What is the solution to ?

  1. 1, -2
  2. 2, -1
  3. 1, -2
  4. -1, 2

Answer (Detailed Solution Below)

Option 3 : 1, -2

Systems of Equations in Two Variables Question 9 Detailed Solution

Consider the absolute value equation . We solve it by considering two scenarios:

1.

2.

For the first scenario, :

Subtract from both sides:

Divide by :

For the second scenario, :

Subtract from both sides:

Divide by :

Thus, the solutions are and , matching option 3.

Systems of Equations in Two Variables Question 10:

Solve for if the absolute value of equals .

  1. -5, 11
  2. 11, -5
  3. 5, -11
  4. 11, -5

Answer (Detailed Solution Below)

Option 4 : 11, -5

Systems of Equations in Two Variables Question 10 Detailed Solution

To solve , consider two cases:

1.

2.

For the first equation, :

Add to both sides:

For the second equation, :

Add to both sides:

Thus, the solutions are and , as shown in option 4.

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