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Vidaara.orgClass 12 · Mathematics
CodeVID-M12-14-CT
Application of Calculus (Commerce) — Full Chapter Test
Chapter: Application of Calculus (Commerce)
Topic: Complete chapter — all topics
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • This is a full-length test covering the whole chapter — every topic is included.
  • All questions are compulsory.
  • Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
  • Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions 5 × 1 = 5 marks
1.
Profit function is:
  • A.$R(x)+C(x)$
  • B.$R(x)-C(x)$
  • C.$C(x)-R(x)$
  • D.$R(x)\cdot C(x)$
2.
Marginal revenue is:
  • A.$R(x)/x$
  • B.$\dfrac{dR}{dx}$
  • C.$\int R\,dx$
  • D.$R-C$
3.
Break-even occurs when:
  • A.$R=2C$
  • B.$P(x)=0$
  • C.$C=0$
  • D.$R=0$
4.
Profit is maximised when:
  • A.$\text{MR}=\text{MC}$
  • B.$\text{MR}=0$
  • C.$\text{MC}=0$
  • D.$R=C$
5.
If $C(x)=2x+50$ and $R(x)=7x$, the break-even output is:
  • A.$5$
  • B.$10$
  • C.$50$
  • D.$7$
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
If $C(x)=2x+50$ and the price is $\textsf{Rs }7$ per unit, write the profit function.
7.
If $C(x)=x^2+4x+10$, find the marginal cost at $x=5$.
8.
Find the break-even output for $C(x)=2x+50,\ R(x)=7x$.
9.
If $R(x)=20x-x^2$, find the marginal revenue at $x=3$.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
If $C(x)=3x+40$ and price is $\textsf{Rs }8$, find the profit function and break-even output.
11.
If $C(x)=0.005x^3-0.02x^2+30x+5000$, find the marginal cost at $x=3$.
12.
If $R(x)=50x-x^2$, find $R$ at $x=10$.
13.
If $R(x)=30x-2x^2$, find the marginal revenue and the output where $\text{MR}=0$.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
The cost is $C(x)=x^2+2x+10$ and the selling price is $\textsf{Rs }22$ per unit. Find the profit function and the output for maximum profit.
15.
The demand function is $p=50-2x$. Find the marginal revenue and the output that maximises revenue.

Answer Key

Section A — Multiple Choice Questions
  1. (B) $R(x)-C(x)$
  2. (B) $\dfrac{dR}{dx}$
  3. (B) $P(x)=0$
  4. (A) $\text{MR}=\text{MC}$
  5. (B) $10$
Section B — Short Answer (2 marks)
  1. $P(x)=5x-50$.
  2. $14$.
  3. $x=10$.
  4. $14$.
Section C — Short Answer (3 marks)
  1. $P(x)=5x-40$; break-even at $x=8$.
  2. $30.015$.
  3. $400$.
  4. $\text{MR}=30-4x$; $x=7.5$.
Section D — Long Answer (5 marks)
  1. $P(x)=-x^2+20x-10$; maximum at $x=10$ (profit $\textsf{Rs }90$).
  2. $\text{MR}=50-4x$; revenue maximum at $x=12.5$ (max revenue $\textsf{Rs }312.50$).
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