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

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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&−[email protected]&1)] [■8(𝑥@𝑦)] = [■8([email protected])] (b) [■8(1&[email protected]&1)] [■8(𝑥@𝑦)] = [■8([email protected])] (c) [■8(1&[email protected]&−1)] [■8(𝑥@𝑦)] = [■8([email protected])] (d) [■8(1&[email protected]&1)] [■8(𝑥@𝑦)] = [■8(−[email protected]−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)