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Test: Determinants- Case Based Type Questions - JEE MCQ


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15 Questions MCQ Test Mathematics (Maths) Class 12 - Test: Determinants- Case Based Type Questions

Test: Determinants- Case Based Type Questions for JEE 2024 is part of Mathematics (Maths) Class 12 preparation. The Test: Determinants- Case Based Type Questions questions and answers have been prepared according to the JEE exam syllabus.The Test: Determinants- Case Based Type Questions MCQs are made for JEE 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Determinants- Case Based Type Questions below.
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Test: Determinants- Case Based Type Questions - Question 1

Read the following text and answer the following questions. On the basis of the same:

Two schools Oxford and Navdeep want to award their selected students on the values of sincerity, truthfulness and helpfulness. Oxford wants to award ₹x each, ₹y each and ₹z each for the three respective values to 3, 2 and 1 students respectively with a total award money of ₹1600. Navdeep wants to spend ₹2300 to award its 4, 1 and 3 students on the respective values (by giving the same amount to the three values as before). The total amount of the award for one prize on each is ₹900.

x + y + z = _______.

Detailed Solution for Test: Determinants- Case Based Type Questions - Question 1

From the above information, we have

3x + 2y + z = 1600 ...(i)

4x + y + 3z = 2300 ...(ii)

x + y + z = 900 ...(iii)

∴ x = 200, y = 300, z = 400

x + y + z =900 [from (iii)]

Test: Determinants- Case Based Type Questions - Question 2

Read the following text and answer the following questions on the basis of the same:
Manjit wants to donate a rectangular plot of land for a school in his village. When he was asked to give dimensions of the plot, he told that if its length is decreased by 50 m and breadth is increased by 50 m, then its area will remain same, but if length is decreased by 10 m and breadth is decreased by 20 m, then its area will decrease by 5300 m2

Which of the following matrix equation is represented by the given information

Detailed Solution for Test: Determinants- Case Based Type Questions - Question 2

Since our equations are
X - y = 50
2x + y = 550
Matrix equation will look like

So, the correct answer is a.

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Test: Determinants- Case Based Type Questions - Question 3

Read the following text and answer the following questions on the basis of the same:

The management committee of a residential colony decided to award some of its members (say x) for honesty, some (say y) for helping others and some others (say z) for supervising the workers to kept the colony neat and clean. The sum of all the awardees is 12. Three times the sum of awardees for cooperation and supervision added to two times the number of awardees for honesty is 33. The sum of the number of awardees for honesty and supervision is twice the number of awardees for helping.

x – 2y = _______.

Detailed Solution for Test: Determinants- Case Based Type Questions - Question 3

x – 2y =– z [from (iii)]

Test: Determinants- Case Based Type Questions - Question 4

Read the following text and answer the following questions on the basis of the same:

Manjit wants to donate a rectangular plot of land for a school in his village. When he was asked to give dimensions of the plot, he told that if its length is decreased by 50 m and breadth is increased by 50 m, then its area will remain same, but if length is decreased by 10 m and breadth is decreased by 20 m, then its area will decrease by 5300 m2

The value of y (breadth of rectangular field) is

Detailed Solution for Test: Determinants- Case Based Type Questions - Question 4
Putting x = 200 in (1)

x - y = 50

200 - y = 50

200 - 50 = y

150 = y

y = 150 m

Test: Determinants- Case Based Type Questions - Question 5

Read the following text and answer the following questions on the basis of the same:

The management committee of a residential colony decided to award some of its members (say x) for honesty, some (say y) for helping others and some others (say z) for supervising the workers to kept the colony neat and clean. The sum of all the awardees is 12. Three times the sum of awardees for cooperation and supervision added to two times the number of awardees for honesty is 33. The sum of the number of awardees for honesty and supervision is twice the number of awardees for helping.

The value of 2x + 3y + 5z = _______.

Detailed Solution for Test: Determinants- Case Based Type Questions - Question 5

2x + 3y + 5z = 6 + 12 + 25

= 43

Test: Determinants- Case Based Type Questions - Question 6

Read the following text and answer the following questions. On the basis of the same:

Two schools Oxford and Navdeep want to award their selected students on the values of sincerity, truthfulness and helpfulness. Oxford wants to award ₹x each, ₹y each and ₹z each for the three respective values to 3, 2 and 1 students respectively with a total award money of ₹1600. Navdeep wants to spend ₹2300 to award its 4, 1 and 3 students on the respective values (by giving the same amount to the three values as before). The total amount of the award for one prize on each is ₹900.

The value of y is _______.

Detailed Solution for Test: Determinants- Case Based Type Questions - Question 6

From the above information, we have

3x + 2y + z = 1600 ...(i)

4x + y + 3z = 2300 ...(ii)

x + y + z = 900 ...(iii)

4x + y + 3z = 2300 [from (ii)]

y = 300

Test: Determinants- Case Based Type Questions - Question 7

Read the following text and answer the following questions on the basis of the same:

Manjit wants to donate a rectangular plot of land for a school in his village. When he was asked to give dimensions of the plot, he told that if its length is decreased by 50 m and breadth is increased by 50 m, then its area will remain same, but if length is decreased by 10 m and breadth is decreased by 20 m, then its area will decrease by 5300 m2

The value of x (length of rectangular field) is

Detailed Solution for Test: Determinants- Case Based Type Questions - Question 7

x = 200

y = 150

Test: Determinants- Case Based Type Questions - Question 8

Read the following text and answer the following questions. On the basis of the same:

Two schools Oxford and Navdeep want to award their selected students on the values of sincerity, truthfulness and helpfulness. Oxford wants to award ₹x each, ₹y each and ₹z each for the three respective values to 3, 2 and 1 students respectively with a total award money of ₹1600. Navdeep wants to spend ₹2300 to award its 4, 1 and 3 students on the respective values (by giving the same amount to the three values as before). The total amount of the award for one prize on each is ₹900.

4x + y + 3z = _______.

Detailed Solution for Test: Determinants- Case Based Type Questions - Question 8

From the above information, we have

3x + 2y + z = 1600 ...(i)

4x + y + 3z = 2300 ...(ii)

x + y + z = 900 ...(iii)

From (ii)

4x + y + 3z = 2300

Test: Determinants- Case Based Type Questions - Question 9

Read the following text and answer the following questions on the basis of the same:

The management committee of a residential colony decided to award some of its members (say x) for honesty, some (say y) for helping others and some others (say z) for supervising the workers to kept the colony neat and clean. The sum of all the awardees is 12. Three times the sum of awardees for cooperation and supervision added to two times the number of awardees for honesty is 33. The sum of the number of awardees for honesty and supervision is twice the number of awardees for helping.

The value of x + 2y = _______.

Detailed Solution for Test: Determinants- Case Based Type Questions - Question 9

x + 2y = 3 + 8 = 11

Test: Determinants- Case Based Type Questions - Question 10

Read the following text and answer the following questions. On the basis of the same:

Two schools Oxford and Navdeep want to award their selected students on the values of sincerity, truthfulness and helpfulness. Oxford wants to award ₹x each, ₹y each and ₹z each for the three respective values to 3, 2 and 1 students respectively with a total award money of ₹1600. Navdeep wants to spend ₹2300 to award its 4, 1 and 3 students on the respective values (by giving the same amount to the three values as before). The total amount of the award for one prize on each is ₹900.

y – x = _______.

Detailed Solution for Test: Determinants- Case Based Type Questions - Question 10

From the above information, we have

3x + 2y + z = 1600 ...(i)

4x + y + 3z = 2300 ...(ii)

x + y + z = 900 ...(iii)

y – x = 300 – 200 = 100

Test: Determinants- Case Based Type Questions - Question 11

Read the following text and answer the following questions on the basis of the same:

Manjit wants to donate a rectangular plot of land for a school in his village. When he was asked to give dimensions of the plot, he told that if its length is decreased by 50 m and breadth is increased by 50 m, then its area will remain same, but if length is decreased by 10 m and breadth is decreased by 20 m, then its area will decrease by 5300 m2

The equations in terms of X and Y are

Detailed Solution for Test: Determinants- Case Based Type Questions - Question 11
Let length of plot = x m

Breadth of plot = y m

Now,

Area of plot = xy m*

Given that,

If its length is decreased by 50 m and breadth is increased by 50m,

Then its area will remain same.

(Length - 50) * (Breadth + 50) = Area

(x - 50) * (y + 50) = xy

x(y + 50) - 50(y + 50) = xy

xy + 50x - 50y - 2500 = xy

50x - 50y - 2500 = 0

50x - 50y = 2500

Dividing both sides by 50

x - y = 50 …(1)

Also,

If length is decreased by 10m and breadth is decreased by 20m, then

Area will decrease by 5300m*m

(Length - 10) * (Breadth - 20) = Area - 5300

(x - 10) * (y - 20) = xy - 5300

x(y - 20) - 10(y - 20) = xy - 5300

xy - 20x - 10y + 200 = xy - 5300

-20x - 10y + 200 = -5300

-20x - 10y = -5300 - 200

-20x - 10y = -5500

20x + 10y = 5500

Dividing both sides by 10

2x + y = 550

Thus, our equations are:

x - y = 50

2x + y = 550

So, the correct answer is b.

Test: Determinants- Case Based Type Questions - Question 12

Read the following text and answer the following questions on the basis of the same:

The management committee of a residential colony decided to award some of its members (say x) for honesty, some (say y) for helping others and some others (say z) for supervising the workers to kept the colony neat and clean. The sum of all the awardees is 12. Three times the sum of awardees for cooperation and supervision added to two times the number of awardees for honesty is 33. The sum of the number of awardees for honesty and supervision is twice the number of awardees for helping.

x + y + z = _______.

Detailed Solution for Test: Determinants- Case Based Type Questions - Question 12

⇒ x = 3, y = 4, z = 5

x + y + z =12 [from (i)]

Test: Determinants- Case Based Type Questions - Question 13

Read the following text and answer the following questions on the basis of the same:

Manjit wants to donate a rectangular plot of land for a school in his village. When he was asked to give dimensions of the plot, he told that if its length is decreased by 50 m and breadth is increased by 50 m, then its area will remain same, but if length is decreased by 10 m and breadth is decreased by 20 m, then its area will decrease by 5300 m2

How much is the area of rectangular field?

Detailed Solution for Test: Determinants- Case Based Type Questions - Question 13

Area of rectangular field

= xy

= 200 x 150

= 30000 sqm.

Test: Determinants- Case Based Type Questions - Question 14

Read the following text and answer the following questions. On the basis of the same:

Two schools Oxford and Navdeep want to award their selected students on the values of sincerity, truthfulness and helpfulness. Oxford wants to award ₹x each, ₹y each and ₹z each for the three respective values to 3, 2 and 1 students respectively with a total award money of ₹1600. Navdeep wants to spend ₹2300 to award its 4, 1 and 3 students on the respective values (by giving the same amount to the three values as before). The total amount of the award for one prize on each is ₹900.

The value of 2x + 3y is _______.

Detailed Solution for Test: Determinants- Case Based Type Questions - Question 14

From the above information, we have

3x + 2y + z = 1600 ...(i)

4x + y + 3z = 2300 ...(ii)

x + y + z = 900 ...(iii)

2x + 3y = 400 + 900

= 1300

Test: Determinants- Case Based Type Questions - Question 15

Read the following text and answer the following questions on the basis of the same:

The management committee of a residential colony decided to award some of its members (say x) for honesty, some (say y) for helping others and some others (say z) for supervising the workers to kept the colony neat and clean. The sum of all the awardees is 12. Three times the sum of awardees for cooperation and supervision added to two times the number of awardees for honesty is 33. The sum of the number of awardees for honesty and supervision is twice the number of awardees for helping.

The value of z is _______.

Detailed Solution for Test: Determinants- Case Based Type Questions - Question 15

z = 5

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