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

Last updated at July 29, 2021 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)

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.