1
In the expansion of $${\left( {\sqrt x + {1 \over {3{x^2}}}} \right)^{10}}$$, the value of constant term (independent of x) is
2
If the coefficients of xr and xr + 1 are equal in the expansion, then r is equal to
3
The average of the coefficients of the two middle terms in the expansion is
4
The sum of the coefficients of all the terms in the expansion is
5
The coefficient of x99 in the expansion of (x $$-$$ 1) (x $$-$$ 2) (x $$-$$ 3) ...... (x $$-$$ 100) is
6
What is $${}^{47}{C_4} + {}^{51}{C_3} + \sum\limits_{j = 2}^5 {{}^{52 - j}{C_3}} $$ equal to?
7
The number of terms in the expansion of (x + a)100 + (x $$-$$ a)100 after simplification is
8
In the expansion of (1 + x)50, the sum of the coefficients of odd powers of x is
9
The value of [C(7, 0) + C(7, 1)] + [C(7, 1) + C(7, 2)] + ..... + [C(7, 6) + C(7, 7)] is
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
11
What is the coefficient of the middle term in the binomial expansion of (2 + 3x)4 ?
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?
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) ?
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?
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)?
16
How many terms are there in the expansion of $${(1 + 2x + {x^2})^5} + {(1 + 4y + 4{y^2})^5}$$ ?
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?
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?
19
What is the number of terms in the expansion of $${[{(2x - 3y)^2}{(2x + 3y)^2}]^2}$$ ?
20
In the expansion of (1 + ax)n, the first three terms are respectively 1, 12x and 64x2. What is n equal to?
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)nnTn equal to ?
NDA Mathematics 3 September 2023
28
What is T1 + T2 + T3 + ... + Tn equal to ?
NDA Mathematics 3 September 2023
29
What is the mean of the numbers 1, 2, 3, ... 10 with frequencies 9C0, 9C1, 9C2 ..., 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
34
What is $\displaystyle\sum_{r=0}^n$2r C(n, r) equal to ?
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
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