Vidaara.orgClass 11 · Mathematics
CodeVID-M11-07-SPT-01
Special / Particular Terms — Assignment
Name: ____________________
Roll No.: __________
Date: ____________
General Instructions
- 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.
The term independent of $x$ has $x$ to the power:
- A.$1$
- B.$0$
- C.$-1$
- D.$2$
2.
To find the coefficient of $x^k$, set the exponent equal to:
- A.$0$
- B.$k$
- C.$n$
- D.$1$
3.
The constant term in $\left(x+\dfrac1x\right)^2$ is:
- A.$1$
- B.$2$
- C.$0$
- D.$3$
4.
The greatest binomial coefficient in $(1+x)^6$ is:
- A.$6$
- B.$15$
- C.$20$
- D.$1$
5.
The number of constant terms in $\left(x+\dfrac1x\right)^4$ is:
- A.$0$
- B.$1$
- C.$2$
- D.$4$
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
Find the constant term in $\left(x+\dfrac1x\right)^4$.
7.
Find the coefficient of $x^2$ in $(1+x)^5$.
8.
Find the term independent of $x$ in $\left(x^2+\dfrac1x\right)^3$.
9.
Find the coefficient of $x$ in $(1+x)^3$.
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
Find the term independent of $x$ in $\left(x+\dfrac{2}{x^2}\right)^6$.
11.
Find the coefficient of $x^4$ in $(1+x)^7$.
12.
Find the coefficient of $x^6$ in $(2+x)^8$.
13.
Find the constant term in $\left(2x-\dfrac1x\right)^6$.
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
Find the term independent of $x$ in the expansion of $\left(2x^2-\dfrac1x\right)^{12}$.
15.
Find the coefficient of $x^5$ in the expansion of $(1+x)^4(1+x)^6$.
Answer Key
Section A — Multiple Choice Questions
- (B) $0$
- (B) $k$
- (B) $2$
- (C) $20$
- (B) $1$
Section B — Short Answer (2 marks)
- $6$.
- $10$.
- $3$.
- $3$.
Section C — Short Answer (3 marks)
- $60$.
- $35$.
- $112$.
- $-160$.
Section D — Long Answer (5 marks)
- $7920$.
- $252$.
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