Vidaara.orgClass 11 · Mathematics
CodeVID-M11-07-BIN-01
Binomial Theorem & Pascal’s Triangle — 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 number of terms in $(x+y)^{10}$ is:
- A.$10$
- B.$11$
- C.$9$
- D.$20$
2.
The sum of coefficients in $(1+x)^5$ is:
- A.$10$
- B.$32$
- C.$25$
- D.$16$
3.
$(a+b)^3=$
- A.$a^3+b^3$
- B.$a^3+3a^2b+3ab^2+b^3$
- C.$a^3-b^3$
- D.$3a+3b$
4.
The middle term of $(a+b)^6$ is the:
- A.3rd term
- B.4th term
- C.5th term
- D.6th term
5.
$ {}^{n}C_{0}+{}^{n}C_{1}+\dots+{}^{n}C_{n}=$
- A.$n$
- B.$2^n$
- C.$n!$
- D.$n^2$
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
Expand $(x+2)^3$.
7.
Find the number of terms in $(1+x)^8$.
8.
Find the sum of the coefficients in $(2+x)^4$.
9.
Write the coefficients in the expansion of $(a+b)^4$.
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
Expand $(1+x)^4$.
11.
Using the binomial theorem, evaluate $(101)^3$.
12.
Find $n$ if the sum of the coefficients in $(1+x)^n$ is $64$.
13.
Expand $(x-2y)^3$.
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
Expand $(2x-3)^4$ using the binomial theorem.
15.
Find the value of $(\sqrt2+1)^4+(\sqrt2-1)^4$.
Answer Key
Section A — Multiple Choice Questions
- (B) $11$
- (B) $32$
- (B) $a^3+3a^2b+3ab^2+b^3$
- (B) 4th term
- (B) $2^n$
Section B — Short Answer (2 marks)
- $x^3+6x^2+12x+8$.
- $9$.
- $81$.
- $1,4,6,4,1$.
Section C — Short Answer (3 marks)
- $1+4x+6x^2+4x^3+x^4$.
- $1030301$.
- $n=6$.
- $x^3-6x^2y+12xy^2-8y^3$.
Section D — Long Answer (5 marks)
- $16x^4-96x^3+216x^2-216x+81$.
- $34$.
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