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Appendix 2: Mathematical Modelling

CBSE · Class 12 · Mathematics

Practice quiz for Appendix 2: Mathematical Modelling — CBSE Class 12 Mathematics. MCQs and questions with answers to test your preparation.

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Quick Quiz: Appendix 2: Mathematical Modelling

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1

A tank contains 1000 litres of brine with 250 g of salt per litre. Brine containing 200 g of salt per litre flows in at 25 litres per minute, and the mixture flows out at the same rate. What is the amount of salt in the tank at time t minutes?

2

A manufacturer has the profit model P = (s - b)x - a. If fixed cost a = ₹12000, selling price s = ₹18 per unit, variable cost b = ₹10 per unit, and 3000 units are produced and sold, what is the profit?

3

For the profit model P = (s - b)x - a, suppose dP/dx = 12 and b = ₹9 per unit. What is the selling price s?

4

A tower has eye height h = 1.5 m, horizontal distance l = 40 m, and angle of elevation α = 45°. What is the height H of the tower?

64 Questions·
multiple choicemultiple correct

Sample Questions

1multiple choice
3 marks

For the inaccessible-foot tower model, the observer’s eye height is h = 1.8 m and the angle of depression β = 30°. What is the horizontal distance l?

Show answer

1.8√3 m

1) Use l = h cotβ. 2) For β = 30°, cot30° = √3. 3) So l = 1.8 × √3. 4) Therefore l = 1.8√3 m.

2multiple choice
3 marks

For the medicine production LPP, the feasible region has vertices O(0,0), P(20000,0), Q(20000,6000), R(10500,34500), S(5000,40000), and T(0,40000). What is the maximum value of Z = 8x + 7y?

Show answer

₹325500

1) Evaluate Z at each vertex. 2) At R(10500,34500), Z = 8(10500) + 7(34500). 3) 8(10500) = 84000 and 7(34500) = 241500. 4) Sum = 325500. 5) This is the maximum value.

3multiple choice
3 marks

A company has cost model C = a + bx with a = ₹5000 and b = ₹12 per unit, and income model I = sx with s = ₹20 per unit. What is the profit when x = 2500 units are sold?

Show answer

₹15000

1) Use P = (s - b)x - a. 2) Here s - b = 20 - 12 = 8. 3) Multiply: 8 × 2500 = 20000. 4) Subtract fixed cost: 20000 - 5000 = 15000. 5) Profit = ₹15000.

4multiple choice
3 marks

In the brine model, y(t) = 200 + 50e^{-t/40}. What is the salt amount after 40 minutes?

Show answer

200 + 50/e kg

1) Substitute t = 40 into y(t) = 200 + 50e^{-t/40}. 2) Then exponent becomes -40/40 = -1. 3) So y(40) = 200 + 50e^{-1}. 4) This is 200 + 50/e kg.

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What are the important topics in Appendix 2: Mathematical Modelling for CBSE Class 12 Mathematics?
Appendix 2: Mathematical Modelling covers several key topics that are frequently asked in CBSE Class 12 board exams. Focus on the core concepts listed on this page and practise related questions to build confidence.
How to score full marks in Appendix 2: Mathematical Modelling — CBSE Class 12 Mathematics?
Understand the core concepts first, then work through the 64 practice questions available for this chapter. Revise formulas and definitions regularly, and use flashcards for quick recall before the exam.

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