Karnataka 1st PUC Mathematics Binomial Theorem MCQ with Answers

GOVERNMENT OF KARNATAKA
DEPARTMENT OF SCHOOL EDUCATION (PRE-UNIVERSITY)
18TH CROSS, MALLESHWARAM, BENGALURU – 560 012
CHAPTERWISE MULTIPLE CHOICE QUESTIONS FOR COMPETATIVE EXAM
SUBJECT: MATHEMATICS – I PUC
NAME OF THE CHAPTER: BINOMIAL THEOREM

An algebraic expression consisting of two terms with + or – sign between them is called
binomial expression.
Eg. ( a+b) , (x- 2y).
Binomial theorem is the formula obtained by the binomial raised to the power n, where n
can be a positive integer, negative integer or a fraction.
BINOMIAL THEOREM FOR POSITIVE INTEGRAL INDEX
If n is a positive integer and x, a ϵ R, then
(x + a)n = 𝐧𝐂𝟎 xn + 𝐧𝐂𝟏 xn-1 a + 𝐧𝐂𝟐 xn-2 a2 + … +𝐧𝐂𝐧 an
(x - a)n = 𝐧𝐂𝟎 xn - 𝐧𝐂𝟏 xn-1 a + 𝐧𝐂𝟐 xn-2 a2 - … + (−𝟏)𝐧 𝐧𝐂𝐧 an
Here nC0 , nC1 , nC2 ,… ,nCn are known as binomial coefficients of order n.
 The coefficient of xr in ( a+x)n is nCr
 The coefficient of xr in ( a-x)n is (−1)n nCr
Properties of Binomial Theorem
i. The sum of indices of x and a in each term is n.
ii. The number of terms in (x + a)n is n+1.
iii. The coefficient of terms equidistant from the beginning and the end are equal.
iv. (x + a)n + (x - a)n = 2(nC0 xn + nC2 xn-2 a2 - … )
v. (x + a)n - (x - a)n = 2(nC1 xn-1a + nC3 xn-3 a3 + … )

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Math Talk MCQs
1. The number of non-zero terms in the expansion of (2x + y) n is (E)
A) n B) n-1 C) n+1 D) 2n
2. The sum of all the coefficients in the binomial expansion of (3x+4y) 8 is (E)
A) 256 B) 128 C) 512 D) 96
3. The 4th term in the expansion of (x - 2y) 12 is (E)
A) 1760 x3y9 B) -1760 x9y3 C) 1760 x9y3 D) -1760 x3y9
4. The total number of terms in the expansion of (x + a) 100 + (x- a) 100 after
simplification is (E)
A) 202 B) 51 C) 50 D) 52
5. If (1+ ax )n = 1+ ax + 24x2 + … then the values of a and n are (E)
A) 2, 4 B) 2, 3 C) 3, 6 D) 1, 2
6. If in the expansion of (a-2b) n, the sum of the 4th and 5th term is zero, then the
𝒂
value of 𝒃 𝒊𝒔 (A)
𝑛−4 𝑛−3 5 5
A) B) C) 𝑛−4 D) 2(𝑛−4)
5 2

7. If the coefficient of 𝟒𝐭𝐡 term in the expansion of (𝒂 + 𝒃)𝒏 is 56, then 𝒏 is (E)
A) 12 B) 10 C) 8 D) 6
8. If the coefficients of 𝒙𝟐 and 𝒙𝟑 in the expansion of (𝟑 + 𝒂𝒙)𝟗 are the
same, then the value of 𝒂 is (A)
7 9 7 9
A) − 9 B) − 7 C) 9 D) 7

9. The coefficient of 𝒙𝟓 in the expansion of (𝒙 + 𝟑)𝟔 is (E)
A) 18 B) 6 C) 12 D) 10
10. The sum of coefficients in the expansion of (𝟏 + 𝒙 + 𝒙𝟐 )𝒏 is (D)
A) 2 B) 3𝑛 C) 4𝑛 D) 2𝑛
11. By using first three terms of its expansion, the approximate value
of ( 0.99)5 is (A)
A) 0.949 B) 0.951 C) 0.954 D) 0.945
12. The sum of all the coefficients in the binomial expansion of (𝒙+1)n (E)
A) 2𝑛 B) 2𝑛−1 C) n D) 2n+1
13. The sum of all the coefficients in the binomial expansion of (𝒙-1)n (E)
A) 2𝑛 B) 2𝑛−1 C) 0 D) 2n+1
14. In the expansion of (1+x)n the sum of coefficients of odd powers of x is (E)
A) 2𝑛 B) 2𝑛−1 C) 0 D) 2n+1

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15. In the expansion of (1+x)n the sum of coefficients of even powers of x is (E)
A) 2𝑛 B) 2𝑛−1 C) 0 D) 2n+1
16. 𝑪𝟎 − 𝑪𝟏 + 𝑪𝟐 − 𝑪𝟑 + ⋯ . . +(−𝟏)𝒏 𝑪𝒏 is equal to (E)
A) 2𝑛 B) 2𝑛 − 1 C) 0 D) 2𝑛−1
17. The value of 𝒏𝑪𝟎 + 𝟐. 𝒏𝑪𝟏 + 𝟒. 𝒏𝑪𝟐 + 𝟖. 𝒏𝑪𝟑 + ⋯ . +𝟐𝒏 . 𝒏𝑪𝒏 is, (A)
A) 2𝑛 B) 3𝑛 C) 4𝑛 D) n
18. The value of 1+ 𝟑. 𝟐𝟎𝑪𝟏 + 𝟗. 𝟐𝟎𝑪𝟐 + 𝟐𝟕. 𝟐𝟎𝑪𝟑 + ⋯ . +𝟑𝟐𝟎 is (A)
A) 220 B) 320 C) 420 D) 202
19. 𝟏𝟎 𝑪𝟏 + 𝟏𝟎 𝑪𝟑 + 𝟏𝟎 𝑪𝟓 + 𝟏𝟎 𝑪𝟕 + 𝟏𝟎 𝑪𝟗 = (A)
A) 29 B) 210 C) 2 10
−1 D) 0
𝟏 𝟖
20. Coefficient of 𝒙𝟐 in the expansion of (𝒙 − ) is (D)
𝟐𝒙
1 −1
A) 7 B) 7 C) -7 D) 7

21. If 𝟐𝟏𝐬𝐭 and 𝟐𝟐𝐧𝐝 terms in the expansion of (𝟏 + 𝒙)𝟒𝟒 are equal,
then 𝒙 is equal to (A)-CET-2015
21 23 8 7
A) 22 B) 24 C) 7 D) 8

𝟏 𝟏𝟒
22. The 𝟏𝟏 𝐭𝐡 term in the expansion of (𝒙 + 𝒙) is (A)-CET-2017
√
999 1001 𝑥
A) 𝑥 B) C) 𝑖 D) 1001
𝑥

23. The total number of terms in the expansion of (𝒙 + 𝒂)𝟒𝟕 − (𝒙 − 𝒂)𝟒𝟕
after simplification is (E) - CET-2018
A) 24 B) 47 C) 48 D) 96
24. The number of terms in the expansion of (𝒙𝟐 + 𝒚𝟐 )𝟐𝟓 − (𝒙𝟐 − 𝒚𝟐 )𝟐𝟓
After simplification is (A)
A) 26 B) 0 C) 50 D) 13
25. The number of terms in the expansion of (𝒙 + 𝒚 + 𝒛)𝟏𝟎 is (D) - CET-2021
A) 110 B) 66 C) 142 D) 11
𝐂 𝐂 𝐂 𝐂
26. In the expansion of (𝟏 + 𝒙)𝒏 , 𝐂𝟏 + 𝟐 𝐂𝟐 + 𝟑 𝐂𝟑 + ⋯ … + 𝐧 𝐂 𝐧 is equal to (D) - CET2025
𝟎 𝟏 𝟐 𝐧−𝟏

n(n+1) n n+1
A) B) 2 C) D) 3𝑛(𝑛 + 1)
2 2

27. If the number of terms in the binomial expansion of (𝟐𝒙 + 𝟑)𝟑𝒏 is 22, then
the value of 𝒏 is (E) CET-2026
A) 6 B) 7 C) 9 D) 8

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𝒙𝟑 +𝟑𝒙𝟐 +𝟑𝒙+𝟏
28. The value at 𝒙 = 𝟐 for 𝒙𝟒 +𝟒𝒙𝟑 +𝟔𝒙𝟐 +𝟒𝒙+𝟏 = (A)
25 1 19
A) 3 B) 61 C) 3 D) 73

29. STATEMENT 1: (1.1)10000 is greater than 1000
STATEMENT 2: (1.1)10000 = (1+0.1)10000 (A)
A) Both STATEMENT 1 and 2 are true and STATEMENT 2 is the correct explanation
of the STATEMENT 1
(B) Both STATEMENT 1 and 2 are true and STATEMENT 2 is not the correct explanation
of the STATEMENT 1
(C) STATEMENT 1 is true and STATEMENT 2 is false.
(D) STATEMENT 1 is false and STATEMENT 1 is true
30. When divided by 25, 6𝑛−5𝑛 always leaves the remainder (E)
A) 6 B) 5 C) 1 D) 0

MATH TALK MCQS
1 2 3 4 5 6 7 8 9 10
C A B B A B C D A B
11 12 13 14 15 16 17 18 19 20
B A C B B C B C A C
21 22 23 24 25 26 27 28 29 30
D B A D B A B C B C

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