Binomial Theorem · Mathematics · NDA

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MCQ (Single Correct Answer)

1
In the expansion of $${\left( {\sqrt x + {1 \over {3{x^2}}}} \right)^{10}}$$, the value of constant term (independent of x) is
NDA 2015 Paper 2
2
If the coefficients of xr and xr + 1 are equal in the expansion, then r is equal to
NDA 2015 Paper 2
3
The average of the coefficients of the two middle terms in the expansion is
NDA 2015 Paper 2
4
The sum of the coefficients of all the terms in the expansion is
NDA 2015 Paper 2
5
The coefficient of x99 in the expansion of (x $$-$$ 1) (x $$-$$ 2) (x $$-$$ 3) ...... (x $$-$$ 100) is
NDA 2015 Paper 2
6
What is $${}^{47}{C_4} + {}^{51}{C_3} + \sum\limits_{j = 2}^5 {{}^{52 - j}{C_3}} $$ equal to?
NDA 2016 Paper 2
7
The number of terms in the expansion of (x + a)100 + (x $$-$$ a)100 after simplification is
NDA 2017 Paper 2
8
In the expansion of (1 + x)50, the sum of the coefficients of odd powers of x is
NDA 2017 Paper 2
9
The value of [C(7, 0) + C(7, 1)] + [C(7, 1) + C(7, 2)] + ..... + [C(7, 6) + C(7, 7)] is
NDA 2017 Paper 1
10
The expansions of (x $$-$$ y)n, n $$\ge$$ 5 is done in the descending powers of x. If the sum of the fifth and sixth terms is zero, then $${x \over y}$$ is equal to
NDA 2017 Paper 1
11
What is the coefficient of the middle term in the binomial expansion of (2 + 3x)4 ?
NDA 2018 Paper 2
12
Let the coefficient of the middle term of the binomial expansion of (1 + x)2n be $$\alpha$$ and those of two middle terms of the binomial expansion of (1 + x)2n $$-$$ 1 be $$\beta$$ and $$\gamma$$. Which one of the following relations is correct?
NDA 2018 Paper 2
13
In the expansion of (1 + x)43, if the coefficients of (2r + 1)th and (r + 2)th terms are equal, then what is the values of r(r $$\ne$$ 1) ?
NDA 2018 Paper 1
14
If the coefficients of am and an in the expansion of (1 + a)m + n are $$\alpha$$ and $$\beta$$, then which one of the following is correct?
NDA 2018 Paper 1
15
What is the number of non-zero terms in the expansion of $${(1 + 2\sqrt 3 x)^{11}} + {(1 - 2\sqrt 3 x)^{11}}$$ (after simplification)?
NDA 2018 Paper 1
16
How many terms are there in the expansion of $${(1 + 2x + {x^2})^5} + {(1 + 4y + 4{y^2})^5}$$ ?
NDA 2019 Paper 2
17
If the middle term in the expansion of $${\left( {{x^2} + {1 \over x}} \right)^{2n}}$$ is $$184756{x^{10}}$$, then what is the value of n?
NDA 2019 Paper 2
18
If the constant term in the expansion of $${\left( {\sqrt x - {k \over {{x^2}}}} \right)^{10}}$$ is 405, then what can be the values of k?
NDA 2019 Paper 2
19
What is the number of terms in the expansion of $${[{(2x - 3y)^2}{(2x + 3y)^2}]^2}$$ ?
NDA 2019 Paper 1
20
In the expansion of (1 + ax)n, the first three terms are respectively 1, 12x and 64x2. What is n equal to?
NDA 2019 Paper 1
21

What is the coefficient of $x^{10}$ in the expansion of $(1-x^2)^{20}\left(2-x^2-\frac{1}{x^2}\right)^{-5}$?

NDA Mathematics 21 April 2024
22

If the 4th term in the expansion of $\left(mx + \frac{1}{x}\right)^n$ is $\frac{5}{2}$, then what is the value of $mn$?

NDA Mathematics 21 April 2024
23
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 $\left(\frac{x^2}{y^2}\right)$ ?
NDA Mathematics 21 April 2024
24
What is the number of real roots of the equation?
NDA Mathematics 3 September 2023
25
What is the sum of all the roots of the equation?
NDA Mathematics 3 September 2023
26
What is T1 + 2T2 + 3T3 + ... + nTn equal to ?
NDA Mathematics 3 September 2023
27
What is 1 - T1 + 2T2 - 3T3 + ... + (-1)nnTequal to ? 
NDA Mathematics 3 September 2023
28
What is T1 + T+ T3 + ... + Tn equal to ?
NDA Mathematics 3 September 2023
29
What is the mean of the numbers 1, 2, 3, ... 10 with frequencies 9C09C19C2 ..., 9C9, respectively?
NDA Mathematics 3 September 2023
30
In a Binomial distribution B(n, p), n = 6 and 9P(X = 4) = P(X = 2). What is p equal to ?
NDA Mathematics 3 September 2023
31
If the sixth term in the binomial expansion of $\left(x^{-\frac{8}{3}}+x^2 \log _{10} x\right)^8$ is 5600, then what is the value of x ? 
NDA Mathematics 16 April 2023
32
How many terms are there in the expansion of (3x - y)4(x + 3y)4 ?  
NDA Mathematics 16 April 2023
33

Consider the following statements for a fixed natural number n:

1. C(n, r) is greatest if n = 2r

2. C(n, r) is greatest if n = 2r - 1 and n = 2r + 1 

Which of the statements given above is/are correct ?

NDA Mathematics 16 April 2023
34
What is $\displaystyle\sum_{r=0}^n$2C(n, r) equal to ?
NDA Mathematics 4 September 2022
35

What is the value of q if the coefficients of x3 and x6 are equal ?

NDA Mathematics 4 September 2022
36

What is the ratio of the coefficients of middle terms in the expansion (when expanded in ascending powers of x)?

NDA Mathematics 4 September 2022
37

Under what condition the coefficients of x2 and x4 are equal ?

NDA Mathematics 4 September 2022
38
How many terms are there in the expansion of $\left(1 + \frac{2}{x}\right)^9\left(1-\frac{2}{x}\right)^9 ? $
NDA Mathematics 10 April 2022
39

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 coefficient of the 3rd term is equal to coefficient of the 9th term

Which of the above statements is /are correct ?

NDA Mathematics 10 April 2022
40

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 Mathematics 10 April 2022
41
In the expansion of $\left(x + \frac{1}{x}\right)^{2n} $, what is the (n + 1)th term from the end (when arranged in descending powers of x) ?
NDA Mathematics 10 April 2022
42
What is the sum of the coefficients of first and last terms in the expansion of (1 + x)2n, where n is a natural number?
NDA Mathematics 18 April 2021
43
What is the coefficient of the middle term in the expansion of (1 + 4x + 4x2)5?
NDA Mathematics 18 April 2021
44
If C0, C1, C2, _ _ _ _ _, Cn are the coefficients in the expansion of (1 + x)n, then what is the value of C1 + C2 + C3 + _ _ _ _ _ + Cn?
NDA Mathematics 18 April 2021
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