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CBSE · Class 11 · Mathematics

Binomial Theorem

Standard difficulty · 20 questions · 40 marks

Name: Date: Score: ____ / 40

Show your working for Sections B and C. Answers are on the last page — try every question first!

Section A — Choose the correct answer8 × 1 = 8 marks
1.
How many terms are there in the expansion of (x + y)5?
  1. 7
  2. 5
  3. 10
  4. 6
2.
The coefficient of x5 in the expansion of (x + 4)8 is:
  1. 56
  2. 57,344
  3. 3,584
  4. −3,584
3.
The coefficient of the middle term of (x − 1)4 is:
  1. −6
  2. 7
  3. −4
  4. 6
4.
The sum of the coefficients in the expansion of (4x − 2)5 is:
  1. 33
  2. 32
  3. 992
  4. 7,776
5.
The number of terms in the expansion of (a + b)ⁿ is:
  1. 2n
  2. n
  3. n + 1
  4. n − 1
6.
The 4th term of (x − 3)7 is:
  1. −945x3
  2. 2,835x3
  3. 35x4
  4. −945x4
7.
Using the binomial theorem, (98)4 equals:
  1. 92,236,716
  2. 92,236,824
  3. 92,236,816
  4. 96,059,600
8.
Assertion (A): In the expansion of (1 + x)14, the coefficients of x4 and x10 are equal.
Reason (R): ⁿCᵣ = ⁿCn−ᵣ, so terms equidistant from the two ends have equal coefficients.
  1. Both A and R are true, and R is the correct explanation of A.
  2. Both A and R are true, but R is not the correct explanation of A.
  3. A is true, but R is false.
  4. A is false, but R is true.
Section B — Short answer8 × 2 = 16 marks
9.
Expand (3x + 2)4.
10.
Find the coefficient of x in (2x + 4)6.
11.
Use the binomial theorem to evaluate (103)3.
12.
Find the term independent of x in (x2 + 3/x)3.
13.
Find the middle terms of (x − 4)5.
14.
Simplify (x + 1)6 − (x − 1)6.
15.
Find the 5th term of (x − 3)5.
16.
Find 19C0 + 19C1 + … + 19C19, and 19C1 + 19C3 + 19C5 + ….
Section C — Word problems4 × 4 = 16 marks
17.
Expand (3x + 3)5 fully. What is the coefficient of x4, and what is the sum of all the coefficients?
18.
Find (√6 + √7)4 + (√6 − √7)4.
19.
Using the binomial theorem, find the remainder when 528 is divided by 6.
20.
Using the first three terms of the binomial expansion, find an approximate value of (1.01)4.
AmbifulWorksheets
Practice that never repeats
CBSE · Class 11 · Mathematics

Answer key

Binomial Theorem · AW-11M-BIN-2026-V1 · For parents — fold back or tear off before handing the sheet to your child.

QAnswerWorking
1(d) 6—
2(c) 3,584term with x5: 8C3 × (4)3
3(d) 6term 3: 4C2 × (−1)2
4(b) 32put x = 1: (2)5
5(c) n + 1—
6(d) −945x4Tᵣ+1 = ⁿCᵣ x7−ʳ aʳ with r = 3
7(c) 92,236,816(100 − 2)4
8(a) Both A and R are true, and R is the correct explanation of A.A is true: 14C4 = 1,001; 14C10 = 1,001. R is true and explains A.
981x4 + 216x3 + 216x2 + 96x + 16coefficients 4C0, 4C1, 4C2, 4C3, 4C4
1012,2886C5 × (2)1 × (4)5
111,092,727(100 + 3)3 = 3C0 × 1003 × (3)0 + 3C1 × 1002 × (3)1 + 3C2 × 1001 × (3)2 + …
1227x^(2(3 − r) − r) = x0 when r = 2
13160x3 and −640x2n = 5 is odd: terms 3 and 4
1412x5 + 40x3 + 12xterms with even powers of the second term cancel
15405xT5 = 5C4 x1 (−3)4
16524,288; 262,144put x = 1 in (1 + x)19; odd and even terms split the total equally
17243x5 + 1215x4 + 2430x3 + 2430x2 + 1215x + 243; coefficient of x4: 1,215; sum 7,776Tᵣ+1 = ⁿCᵣ (px)ⁿ−ʳ qʳ
18674the odd terms cancel: 2(a4 + 6a2b2 + b4) with a2 = 6, b2 = 7
191528 = (6 − 1)28: every term except the last has a factor 6; the last is (−1)28 = 1
201.0406(1 + 0.01)4 ≈ 1 + 4 × 0.01 + 6 × 0.0001