Vidaara.orgClass 11 · Mathematics
CodeVID-M11-12-CT
Limits and Derivatives — Full Chapter Test
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.
$\displaystyle\lim_{x\to2}(x+1)=$
- A.$2$
- B.$3$
- C.$1$
- D.$0$
2.
$\displaystyle\lim_{x\to0}\dfrac{\sin x}{x}=$
- A.$0$
- B.$1$
- C.$\infty$
- D.$-1$
3.
$\dfrac{d}{dx}(x^n)=$
- A.$x^{n-1}$
- B.$nx^{n-1}$
- C.$nx^n$
- D.$n$
4.
$\displaystyle\lim_{x\to a} c=$
- A.$0$
- B.$c$
- C.$a$
- D.$\infty$
5.
$\displaystyle\lim_{x\to0}\dfrac{\tan x}{x}=$
- A.$0$
- B.$1$
- C.$\infty$
- D.$2$
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
Evaluate $\displaystyle\lim_{x\to1}(2x+3)$.
7.
Evaluate $\displaystyle\lim_{x\to0}\dfrac{\sin 2x}{x}$.
8.
Differentiate $x^3$.
9.
Evaluate $\displaystyle\lim_{x\to2}(x^2-1)$.
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
Evaluate $\displaystyle\lim_{x\to2}\dfrac{x^2-4}{x-2}$.
11.
Evaluate $\displaystyle\lim_{x\to0}\dfrac{\sin 3x}{5x}$.
12.
Differentiate $x^2$ from first principles.
13.
Evaluate $\displaystyle\lim_{x\to1}\dfrac{x^3-1}{x-1}$.
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
Evaluate $\displaystyle\lim_{x\to3}\dfrac{x^2-9}{x^2-x-6}$.
15.
Evaluate $\displaystyle\lim_{x\to0}\dfrac{\tan x-\sin x}{x^3}$.
Answer Key
Section A — Multiple Choice Questions
- (B) $3$
- (B) $1$
- (B) $nx^{n-1}$
- (B) $c$
- (B) $1$
Section B — Short Answer (2 marks)
- $5$.
- $2$.
- $3x^2$.
- $3$.
Section C — Short Answer (3 marks)
- $4$.
- $\tfrac35$.
- $2x$.
- $3$.
Section D — Long Answer (5 marks)
- $\tfrac65$.
- $\tfrac12$.
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