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Binomial Theorem — NDA Mathematics PYQs

79 previous year questions from Binomial Theorem with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

79 questionsMathematicsSolutions on every page
1

A set S contains (2n+1) elements. If the number of subsets of S which contain at most n elements is 1024 , then what is the value of n ?

NDA 2026 Solution View → 2

Passage: Let u be a positive integer and f be a real number lying between 0 and 1 . Further, ( 2 +1 )¹⁰=u+f and ( 2 -1 )¹⁰=v . Question: Consider the following statements : I. (u+v

NDA 2026 Solution View → 3

Passage: Let u be a positive integer and f be a real number lying between 0 and 1 . Further, ( 2 +1 )¹⁰=u+f and ( 2 -1 )¹⁰=v . Question: What is the value of u ?

NDA 2026 Solution View → 4

What is the greatest value of r satisfying the inequality 15 r+1 >2 ¹⁵C_r ?

NDA 2026 Solution View → 5

Passage: Let u be a positive integer and f be a real number lying between 0 and 1 . Further, ( 2 +1 )¹⁰=u+f and ( 2 -1 )¹⁰=v . Question: What is the value of uv ?

NDA 2026 Solution View → 6

Passage: Let u be a positive integer and f be a real number lying between 0 and 1 . Further, ( 2 +1 )¹⁰=u+f and ( 2 -1 )¹⁰=v . Question: What is the value of (v+f) ?

NDA 2026 Solution View → 7

Passage: Let u be a positive integer and f be a real number lying between 0 and 1 . Further, ( 2 +1 )¹⁰=u+f and ( 2 -1 )¹⁰=v . Question: What is the multiplicative inverse of ( 2 +

NDA 2026 Solution View → 8

If the sum of binomial coefficients in the expansion of (x + y)^n is 256, then the greatest binomial coefficient occurs in which one of the following terms?

NDA 2025 Solution View → 9

If k < ( 2 +1)^3 < k+2 , where k is a natural number, then what is the value of k ?

NDA 2025 Solution View → 10

What is the remainder when 5⁹⁹ is divided by 13 ?

NDA 2025 Solution View → 11

What is the number of rational terms in the expansion of (3^ 1 2 + 5^ 1 4 )¹² ?

NDA 2025 Solution View → 12

Which one of the following is the greatest coefficient in the expansion of (1 + x)¹⁰⁰ ?

NDA 2025 Solution View → 13

In the expansion of (1+x)^p(1+x)^q , if the coefficient of x^3 is 35 , then what is the value of (p+q) ?

NDA 2024 Solution View → 14

What is the remainder when 7^n-6 n is divided by 36 for n=100 ?

NDA 2024 Solution View → 15

Paragraph: Let (8+3 7 )²⁰= U + V and (8-3 7 )²⁰= W , where U is an integer and 0 Question: What is V + W equal to?

NDA 2024 Solution View → 16

Paragraph: Let (8+3 7 )²⁰= U + V and (8-3 7 )²⁰= W , where U is an integer and 0 Question: What is the value of ( U + V ) W ?

NDA 2024 Solution View → 17

In a binomial expansion of (x+y)^ 2 n+1 (x-y)^ 2 n+1 , the sum of middle terms is zero. What is the value of ( x^2 y^2 ) ?

NDA 2024 Solution View → 18

What is the coefficient of x¹⁰ in the expansion of (1-x^2 )²⁰ (2-x^2- 1 x^2 )⁻⁵ ?

NDA 2024 Solution View → 19

If the 4th term in the expansion of (m x+ 1 x )^n is 5 2 , then that is the value of m n ?

NDA 2024 Solution View → 20

A set S contains (2n +1) elements. There are 4096 subset of S which contain at most n elements. what is n equal to

NDA 2023 Solution View → 21

Let (1+x)^n=1+T₁ x+T₂ x^2+T₃ x^3+ +T_n x^n What is 1-T₁+2 T₂-3 T₃+ +(-1)^n n T_n equal to?

NDA 2023 Solution View → 22

Let (1+x)^n=1+T₁ x+T₂ x^2+T₃ x^3+ +T_n x^n What is T₁+2 T₂+3 T₃+ +n T_n equal to?

NDA 2023 Solution View → 23

Let (1+x)^n=1+T₁ x+T₂ x^2+T₃ x^3+ +T_n x^n What is T₁+T₂+T₃+ +T_n equal to ?

NDA 2023 Solution View → 24

If the sixth term in the binomial expansion of (x^ - 8 3 +x^2 ₁₀ x )^8 is 5600 , then what is the value of x ?

NDA 2023 Solution View → 25

How many terms are there in the expansion of (3 x-y)^4(x+3 y)^4 ?

NDA 2023 Solution View → 26

Consider the following statements for a fixed natural number n : 1. C (n, r) is greatest if n=2 r 2. C (n, r) is greatest if n=2 r-1 and n=2 r+1 Which of the statements given above

NDA 2023 Solution View → 27

Paragraph: Consider the binomial expansion of (p+q x)^9 : Question: What is the ratio of the coefficients of middle terms in the expansion (when expanded in ascending powers of x )

NDA 2022 Solution View → 28

How many terms are there in the expansion of (1+ 2 x )^9 (1- 2 x )^9 ?

NDA 2022 Solution View → 29

Paragraph: Consider the binomial expansion of (p+q x)^9 : Question: Under what condition the coefficients of x^2 and x^4 are equal?

NDA 2022 Solution View → 30

In the expansion of (x+ 1 x )^ 2 n , what is the (n+1) th term from the end (when arranged in descending powers of x )?

NDA 2022 Solution View → 31

Consider the following statements in respect of the expansion of (x+y)¹⁰ : 1. Among all the coefficients of the terms, the coefficient of the 6th term has the highest value 2. The

NDA 2022 Solution View → 32

Paragraph: Consider the binomial expansion of (p+q x)^9 : Question: What is the value of q if the coefficients of x^3 and x^6 are equal ?

NDA 2022 Solution View → 33

What is _ r=0 ^n 2^r C(n, r) equal to?

NDA 2022 Solution View → 34

If n 7 , then what is the probability that C(n, 7) is a multiple of 7?

NDA 2022 Solution View → 35

What is the value of C(51,21)-C(51,22)+C(51,23)-C(51,24)+C(51,25)-C(51,26)+C(51,27)-C(51,28)+C(51,29)-C(51,30) ?

NDA 2022 Solution View → 36

How many terms are there in the expansion of ( a^2 b^2 + b^2 a^2 +2 )²¹ where a 0, b 0 ?

NDA 2021 Solution View → 37

If C₀, C₁, C₂, , C_n are the coefficients in the expansion of (1+x)^n , then what is the value of C₁+C₂+C₃+ +C_n ?

NDA 2021 Solution View → 38

What is C(n, 1)+C(n, 2)+ +C(n, n) equal to?

NDA 2021 Solution View → 39

What is the coefficient of the middle term in the expansion of (1+4 x+4 x^2 )^5 ?

NDA 2021 Solution View → 40

What is the sum of the coefficients of first and last terms in the expansion of (1+x)^ 2 n , where n is a natural number?

NDA 2021 Solution View → 41

Consider the expansion of (1+x)^n . Let p, q, r and s be the coefficients of first, second, n^ th and (n+1)^ th terms respectively. What is ( p s+q r ) equal to?

NDA 2021 Solution View → 42

What is the sum of the last five coefficients in the expansion of (1+x)^9 when it is expanded in ascending powers of x ?

NDA 2020 Solution View → 43

If (1+2 x-x^2 )^6=a₀+a₁ x+a₂ x^2+ .+a₁₂ x¹² , then what is a₀-a₁+a₂-a₃+a₄- .+a₁₂ equal to?

NDA 2020 Solution View → 44

The term independent of x in the binomial expansion of ( 2 x^2 - x )¹⁰ is equal to

NDA 2020 Solution View → 45

If the middle term in the expansion of (x^2+ 1 x )^ 2 x 184756 x¹⁰ , then what is the value of n ?

NDA 2019 Solution View → 46

In the expansion of (1+a x)^ n , the first three terms are respectively 1,12 x and 64 x^2 . What is n equal to?

NDA 2019 Solution View → 47

If the constant term in the expansion of ( x - k x^2 )¹⁰ is 405 , then what can be the values of k ?

NDA 2019 Solution View → 48

How many terms are there in the expansion of (1+2 x+x^2 )^5+ (1+4 y+4 y^2 )^5 ?

NDA 2019 Solution View → 49

What is the number of terms in the expansion of [(2 x-3 y)^2 . .(2 x +3 y )^2 ]^2 ?

NDA 2019 Solution View → 50

What is the coefficient of the middle term in the binomial expansion of (2+3 x )^4 ?

NDA 2018 Solution View → 51

Let the coefficient of the middle term of the binomial expansion of (1+x)^ 2 n be and those of two middle terms of the binomial expansion of (1+x)^ 2 n -1 be and . Which one of the

NDA 2018 Solution View → 52

In the expansion of (1+x)⁴³ , if the coefficients of (2 r+1)^ th and ( r +2)^ th terms are equal, then what is the value of r ( r 1) ?

NDA 2018 Solution View → 53

If the coefficients of a ^ m and a ^ n in the expansion of (1+a)^ m + n are and , then which one of the following is correct?

NDA 2018 Solution View → 54

What is the number of non-zero terms in the expansion of (1+2 3 x)¹¹+(1-2 3 x)¹¹ (after simplification)?

NDA 2018 Solution View → 55

What is C(n, r)+2 C(n, r-1)+C(n, r-2) equal to?

NDA 2018 Solution View → 56

The number of terms in the expansion of (x+a)¹⁰⁰+(x-a)¹⁰⁰ after simplification is

NDA 2017 Solution View → 57

The expansion of (x-y)^n, n 5 is done in the descending powers of x . If the sum of the fifth and sixth terms is zero, then x y is equal to

NDA 2017 Solution View → 58

In the expansion of (1+x)⁵⁰ , the sum of the coefficients of odd powers of x is

NDA 2017 Solution View → 59

The value of [ C (7,0)+ C (7,1)]+[ C (7,1)+ C (7,2)]+ . .+[ C (7,6)+ C (7,7)] is

NDA 2017 Solution View → 60

In the expansion of ( x + 1 3 x ^2 )¹⁰ the value of constant term (independent of x ) is

NDA 2015 Solution View → 61

Consider the expansion of (1+x)^ 2 n+1 If the coefficients of x^r and x^ r+1 are equal in the expansion, then r is equal to

NDA 2015 Solution View → 62

Consider the expansion of (1+x)^ 2 n+1 The sum of the coefficients of all the terms in the expansion is

NDA 2015 Solution View → 63

What is ( _ r=0 ^1 n+r n ) equal to?

NDA 2015 Solution View → 64

Consider the expansion (x^2+ 1 x )¹⁵ . What is the independent term in the given expansion?

NDA 2014 Solution View → 65

Consider the expansion (x^2+ 1 x )¹⁵ . Consider the following statements: 1. The term containing x^2 does not exist in the given expansion. 2. The sum of the coefficients of all th

NDA 2014 Solution View → 66

Consider the expansion (x^2+ 1 x )¹⁵ . What is the ratio of coefficient of x¹⁵ to the term independent of x in the given expansion?

NDA 2014 Solution View → 67

Paragraph: In the expansion of (x^3- 1 x^2 )^n , where n is a positive integer, the sum of the coefficients of x^5 and x¹⁰ is 0. Question: What is the value of the independent term

NDA 2014 Solution View → 68

Paragraph: In the expansion of (x^3- 1 x^2 )^n , where n is a positive integer, the sum of the coefficients of x^5 and x¹⁰ is 0. Question: What is n equal to?

NDA 2014 Solution View → 69

Paragraph: In the expansion of (x^3- 1 x^2 )^n , where n is a positive integer, the sum of the coefficients of x^5 and x¹⁰ is 0. Question: What is the sum of the coefficients of th

NDA 2014 Solution View → 70

How many terms are there in the expansion of (1+2 x+x^2 )¹⁰ ?

NDA 2013 Solution View → 71

What is _ r=0 ^n C(n, r) equal to?

NDA 2013 Solution View → 72

In the expansion of (1+x)^n , what is the sum of even binomial coefficients?

NDA 2012 Solution View → 73

The value of the term independent of x in the expansion of (x^2- 1 x )^9 is

NDA 2012 Solution View → 74

What is the ratio of coefficient of x¹⁵ to the term independent of x in (x^2+ 2 x )¹⁵ ?

NDA 2011 Solution View → 75

What is the middle term in the expansion of (1- x 2 )^8 ?

NDA 2011 Solution View → 76

What is the number of terms in the expansion of (a+b+c)^n, n N ?

NDA 2010 Solution View → 77

What is the coefficient of x¹⁷ in the expansion of (3 x- x^3 6 )^9 ?

NDA 2010 Solution View → 78

What is the coefficient of x^4 in the expansion of ( 1-x 1+x )^2 ?

NDA 2010 Solution View → 79

What is the sum of all the coefficients in the expansion of (1+x)^n ?

NDA 2010 Solution View →
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