Vidaara.orgClass 11 · Mathematics
CodeVID-M11-07-GTM-01
General Term & Middle Term — 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 general term of $(a+b)^n$ is:
- A.$ {}^{n}C_{r}a^{r}b^{n-r}$
- B.$ {}^{n}C_{r}a^{n-r}b^{r}$
- C.$ {}^{n}C_{r}a^{n}b^{r}$
- D.$a^{n-r}b^{r}$
2.
The middle term of $(x+y)^8$ is the:
- A.4th
- B.5th
- C.6th
- D.9th
3.
For odd $n$, the number of middle terms is:
- A.$1$
- B.$2$
- C.$3$
- D.$0$
4.
In $(1+x)^n$, the coefficient of $x^r$ is:
- A.$ {}^{n}P_{r}$
- B.$ {}^{n}C_{r}$
- C.$r!$
- D.$n$
5.
The $(r+1)$th term is denoted:
- A.$T_r$
- B.$T_{r+1}$
- C.$T_{r-1}$
- D.$a_r$
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
Write the general term of $(x+2)^6$.
7.
Find the number of terms and the middle-term position in $(a+b)^{10}$.
8.
Find $T_3$ in $(1+x)^5$.
9.
Find the middle-term positions of $(x+y)^7$.
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
Find the $4$th term in the expansion of $(2x+3)^5$.
11.
Find the middle term of $\left(x+\dfrac1x\right)^8$.
12.
Find the coefficient of $x^3$ in $(1+x)^6$.
13.
Find the term independent of $x$ in $\left(x+\dfrac1x\right)^6$.
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
Find the coefficient of $x^5$ in the expansion of $(x+3)^8$.
15.
Find the two middle terms in the expansion of $\left(x+\dfrac1x\right)^7$.
Answer Key
Section A — Multiple Choice Questions
- (B) $ {}^{n}C_{r}a^{n-r}b^{r}$
- (B) 5th
- (B) $2$
- (B) $ {}^{n}C_{r}$
- (B) $T_{r+1}$
Section B — Short Answer (2 marks)
- $T_{r+1}={}^{6}C_{r}\,x^{6-r}\,2^{r}$.
- $11$ terms; middle is the $6$th term.
- $10x^2$.
- The $4$th and $5$th terms.
Section C — Short Answer (3 marks)
- $1080x^2$.
- $70$.
- $20$.
- $20$.
Section D — Long Answer (5 marks)
- $1512$.
- $35x$ and $\dfrac{35}{x}$.
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