Determinants Test

Result

Determinants Test - 8

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0.25

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 = _______.

A
A. 800

B
B. 900

C
C. 1000

D
D. 1200

Solution

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)]
Question 2
1 / -0.25

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

A

B

C

D

Solution

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

So, the correct answer is a.
Question 3
1 / -0.25

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 = _______.

A
A. z

B
B. -z

C
C. 2z

D
D. -2z

Solution

x – 2y =– z [from (iii)]
Question 4
1 / -0.25

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

A
A. 150 m

B
B. 200 m

C
C. 430 m

D
D. 350 m

Solution

Putting x = 200 in (1)
x - y = 50
200 - y = 50
200 - 50 = y
150 = y
y = 150 m
Question 5
1 / -0.25

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 = _______.

A
A. 40

B
B. 43

C
C. 50

D
D. 53

Solution

2x + 3y + 5z = 6 + 12 + 25
= 43
Question 6
1 / -0.25

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 _______.

A
A. 200

B
B. 250

C
C. 300

D
D. 350

Solution

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
Question 7
1 / -0.25

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

A
A. 150 m

B
B. 400 m

C
C. 200 m

D
D. 320 m

Solution

x = 200
y = 150
Question 8
1 / -0.25

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 = _______.

A
A. 1600

B
B. 2300

C
C. 900

D
D. 1200

Solution

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
Question 9
1 / -0.25

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 = _______.

A
A. 9

B
B. 10

C
C. 11

D
D. 12

Solution

x + 2y = 3 + 8 = 11
Question 10
1 / -0.25

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 = _______.

A
A. 100

B
B. 200

C
C. 300

D
D. 400

Solution

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
Question 11
1 / -0.25

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

A
A. x – y = 50, 2x – y = 550

B
B. x – y = 50, 2x + y = 550

C
C. x + y = 50, 2x + y = 550

D
D. x + y = 50, 2x + y = 550

Solution

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.
Question 12
1 / -0.25

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 = _______.

A
A. 3

B
B. 5

C
C. 7

D
D. 12

Solution

⇒ x = 3, y = 4, z = 5
x + y + z =12 [from (i)]
Question 13
1 / -0.25

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?

A
A. 60000 sq.m.

B
B. 30000 sq.m.

C
C. 30000 m

D
D. 3000 m

Solution

Area of rectangular field
= xy
= 200 x 150
= 30000 sqm.
Question 14
1 / -0.25

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 _______.

A
A. 1000

B
B. 1100

C
C. 1200

D
D. 1300

Solution

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
Question 15
1 / -0.25

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 _______.

A
A. 3

B
B. 4

C
C. 5

D
D. 6

Solution

z = 5