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NDA Binomial Theorem PYQs with Solutions

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

79 questionsMathematics2010–2026Answers + solutions

About Binomial Theorem PYQs

Binomial Theorem has 79 previous year questions in the Quantrex Academy NDA Mathematics bank. The 79 questions in this list come from NDA (79), spanning 2010 to 2026. Each question opens on its own page with the options, the correct answer and the worked solution where available.

NDA Binomial Theorem PYQs with Solutions

About Binomial Theorem PYQs

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Binomial Theorem questions with solutions

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 ?

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.

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 ?

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

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 ?

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) ?

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

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?

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

What is the remainder when 5^ 99 is divided by 13 ?

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

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

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) ?

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

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?

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 ?

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)) ?

What is the coefficient of x^ 10 in the expansion of (1-x^2)^ 20 (2-x^2-(1)/(x^2))^ -5 ?

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

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

Let (1+x)^n=1+T_1 x+T_2 x^2+T_3 x^3+…+T_n x^n What is 1-T_1+2 T_2-3 T_3+…+(-1)^n n T_n equal to?

Let (1+x)^n=1+T_1 x+T_2 x^2+T_3 x^3+…+T_n x^n What is T_1+2 T_2+3 T_3+…+n T_n equal to?

Let (1+x)^n=1+T_1 x+T_2 x^2+T_3 x^3+…+T_n x^n What is T_1+T_2+T_3+…+T_n equal to ?

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 ?

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

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

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

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

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

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 )?

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.

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 ?

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

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

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) ?

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

If C_0, C_1, C_2, …, C_n are the coefficients in the expansion of (1+x)^n , then what is the value of C_1+C_2+C_3+…+C_n ?

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

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

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?

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?

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 ?

If (1+2 x-x^2)^6=a_0+a_1 x+a_2 x^2+… .+a_ 12 x^ 12 , then what is a_0-a_1+a_2-a_3+a_4-… .+a_ 12 equal to?

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

If the middle term in the expansion of (x^2+(1)/(x))^ 2 x 184756 x^ 10 , then what is the value of n ?

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?

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

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

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

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

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

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) ?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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 x^ 10 is 0. Question: What is the value of the independent

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 x^ 10 is 0. Question: What is n equal to?

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 x^ 10 is 0. Question: What is the sum of the coefficients

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

What is ∑_ r=0 ^n C(n, r) equal to?

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

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

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

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

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