Question 1 - Case Based Questions (MCQ) - Chapter 4 Class 12 Determinants

Last updated at April 16, 2024 by Teachoo

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 50m, then its area will remain same, but if length is decreased by 10m & breadth is decreased by 20m, then area will decrease by 5300 m
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Based on the information given above, answer the following questions:

Question 1

The equations in terms of X and Y are

(a) x – y = 50, 2x – y = 550

(b) x – y = 50, 2x + y = 550

(c) x + y = 50, 2x + y = 550

(d) x + y = 50, 2x + y = 550

Question 2

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

Question 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 50m, then its area will remain same, but if length is decreased by 10m & breadth is decreased by 20m, then area will decrease by 5300 m2 Based on the information given above, answer the following questions:
Question 1 The equations in terms of X and Y are (a) x – y = 50, 2x – y = 550 (b) x – y = 50, 2x + y = 550 (c) x + y = 50, 2x + y = 550 (d) x + y = 50, 2x + y = 550
Let Length of plot = x m
Breadth of plot = y m
Now,
Area of plot = xy m2
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
Also,
if length is decreased by 10m & breadth is decreased by 20m, then area will decrease by 5300 m2
(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 2 Which of the following matrix equation is represented by the given information (a) [■8(1&−1@2&1)] [■8(𝑥@𝑦)] = [■8(50@550)] (b) [■8(1&1@2&1)] [■8(𝑥@𝑦)] = [■8(50@550)] (c) [■8(1&1@2&−1)] [■8(𝑥@𝑦)] = [■8(50@550)] (d) [■8(1&1@2&1)] [■8(𝑥@𝑦)] = [■8(−50@−550)]
Since our equations are
x – y = 50
2x + y = 550
Matrix equation will look like
[■8(𝟏&−𝟏@𝟐&𝟏)] [■8(𝒙@𝒚)] = [■8(𝟓𝟎@𝟓𝟓𝟎)]
So, the correct answer is (a)
Question 3 The value of x (length of rectangular field) is (a) 150 m (b) 400 m (c) 200 m (d) 320 m
Since our equations are
x – y = 50 …(1)
2x + y = 550 …(1)
Adding (1) and (2)
(x – y) + (2x + y) = 50 + 550
3x = 600
x = 600/2
x = 200 m
So, the correct answer is (c)
Question 4 The value of y (breadth of rectangular field) is (a) 150m (b) 200m (c) 430m (d) 350m
Putting x = 200 in (1)
x − y = 50
200 − y = 50
200 − 50 = y
150 = y
y = 150 m
So, the correct answer is (a)
Question 5 How much is the area of rectangular field? (a) 60000 sq. m. (b) 30000 sq. m. (c) 30000 m (d) 3000 m
Area of rectangular field = Length × Breadth
= 200 × 150
= 30,000 m2
= 30,000 sq. m
So, the correct answer is (b)

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo

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