The middle term in the expression of ( x - 1 x )^ 18 is - Vidyadip

MCQ

The middle term in the expression of ${\left( {x - \frac{1}{x}} \right)^{18}}$ is

A
$^{18}{C_9}$
✓
${ - ^{18}}{C_9}$
C
$^{18}{C_0}$
D
${ - ^{18}}{C_{10}}$

✓

Answer

Correct option: B.

${ - ^{18}}{C_9}$

b
(b) If $n$ is even.

$\therefore $Middle term is $10^{th}$ term.

==> ${T_{10}} = {}^{18}{C_9}{(x)^9}.\,{\left( { - \frac{1}{x}} \right)^9} = {\rm{ }} - {}^{18}{C_9}$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "MCQ" from binomial theoram→binomial theoram — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

The line segment joining the foci of the hyperbola $x^2-y^2+1=0$ is one of the diameters of a circle. The equation of the circle is:

The value of $\sum\limits^{\text{n}}_{\text{r}=1}\Big\{\big(2\text{r}-1\big)\text{a}+\frac{1}{\text{b}^\text{r}}\Big\}$ is equal to:

If distance between the directrices be thrice the distance between the foci, then eccentricity of ellipse is

If $f(y) = 1 - (y - 1) + {(y - 1)^2} - {(y - 1)^{^3}} + ... - {(y - 1)^{17}},$ then the coefficient of $y^2$ in it is

Choose the correct answer. If $\sin\theta+\cos\theta=1,$ then the value of $\sin2\theta$ is equal to:

If $[\mathrm{x}]$ be the greatest integer less than or equal to $\mathrm{x}$, then $\sum_{\mathrm{n}=8}^{100}\left[\frac{(-1)^{n} \mathrm{n}}{2}\right]$ is equal to:

Let $A_1, A_2, \ldots \ldots, A_m$ be non-empty subsets of $\{1,2,3, \ldots, 100\}$ satisfying the following conditions:

$1.$ The numbers $\left|A_1\right|,\left|A_2\right|, \ldots,\left|A_m\right|$ are distinct.

$2.$ $A_1, A_2, \ldots, A_m$ are pairwise disjoint.(Here $|A|$ donotes the number of elements in the set $A$ )Then, the maximum possible value of $m$ is

If $n$ is a positive integer, then ${(1 + i)^n} + {(1 - i)^n}$ is equal to

Let the mean and variance of $12$ observations be $\frac{9}{2}$ and $4$ respectively. Later on, it was observed that two observations were considered as $9$ and $10$ instead of $7$ and $14$ respectively. If the correct variance is $\frac{m}{n}$, where $m$ and $n$ are co-prime, then $m + n$ is equal to

If a line with slope m makes x-intercept d. Then equation of the line is: