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Vidaara.orgClass 11 · Mathematics
CodeVID-M11-07-CT
Binomial Theorem — Full Chapter Test
Chapter: Binomial Theorem
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.
The number of terms in $(x+y)^{10}$ is:
  • A.$10$
  • B.$11$
  • C.$9$
  • D.$20$
2.
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.$a^{n-r}b^{r}$
3.
The term independent of $x$ has $x$ to the power:
  • A.$1$
  • B.$0$
  • C.$-1$
  • D.$2$
4.
The sum of coefficients in $(1+x)^5$ is:
  • A.$10$
  • B.$32$
  • C.$25$
  • D.$16$
5.
The middle term of $(x+y)^8$ is the:
  • A.4th
  • B.5th
  • C.6th
  • D.9th
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Expand $(x+2)^3$.
7.
Write the general term of $(x+2)^6$.
8.
Find the constant term in $\left(x+\dfrac1x\right)^4$.
9.
Find the number of terms in $(1+x)^8$.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Expand $(1+x)^4$.
11.
Find the $4$th term in the expansion of $(2x+3)^5$.
12.
Find the term independent of $x$ in $\left(x+\dfrac{2}{x^2}\right)^6$.
13.
Using the binomial theorem, evaluate $(101)^3$.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
Expand $(2x-3)^4$ using the binomial theorem.
15.
Find the coefficient of $x^5$ in the expansion of $(x+3)^8$.

Answer Key

Section A — Multiple Choice Questions
  1. (B) $11$
  2. (B) $ {}^{n}C_{r}a^{n-r}b^{r}$
  3. (B) $0$
  4. (B) $32$
  5. (B) 5th
Section B — Short Answer (2 marks)
  1. $x^3+6x^2+12x+8$.
  2. $T_{r+1}={}^{6}C_{r}\,x^{6-r}\,2^{r}$.
  3. $6$.
  4. $9$.
Section C — Short Answer (3 marks)
  1. $1+4x+6x^2+4x^3+x^4$.
  2. $1080x^2$.
  3. $60$.
  4. $1030301$.
Section D — Long Answer (5 marks)
  1. $16x^4-96x^3+216x^2-216x+81$.
  2. $1512$.
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