The number of terms whose values depends on x in the expansion of… - Vidyadip

MCQ

The number of terms whose values depends on x in the expansion of $\Big(\text{x}^{2}-2+\frac{1}{\text{x}^{2}}\Big)^{\text{n}}$ is:

A
2n + 1
✓
2n
C
n
D
None of these

✓

Answer

Correct option: B.

2n

2n

Solution:
$\Big(\text{x}^{2}-2+\frac{1}{\text{x}^{2}}\Big)^{\text{n}}$
$=\Big[\big(\text{x}-\frac{1}{\text{x}}\big)^{2}\Big]^{\text{n}}$
$=\big(\text{x}-\frac{1}{\text{x}}\big)^{{2}\text{n}}$
Hence there will be $2 \mathrm{n}+1$ terms.
The middle term i.e $\mathrm{n}+1^{\text {th }}$ term will be independent of x .
Hence total number of terms, dependent on x will be
$2 n+1-(1)$
$=2 n \text { terms. }$

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 THEOREM→BINOMIAL THEOREM — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

If $^{10}{C_r}{ = ^{10}}{C_{r + 2}}$, then $^5{C_r}$ equals

The probabilities that $A$ and $B$ will die within a year are $p$ and $q$ respectively, then the probability that only one of them will be alive at the end of the year is

Four digit numbers are formed using the digits $1 , 2 , 3, 4$ (repetition is allowed). The number of such four digit numbers divisible by $11$ is

Let $M$ be the maximum value of the product of two positive integers when their sum is $66$. Let the sample space $S=\left\{x \in Z: x(66-x) \geq \frac{5}{9} M\right\}$ and the event $A=\{ x \in S : x$ is a multiple of $3$ $\}$. Then $P ( A )$ is equal to

The ${n^{th}}$ term of series $\frac{1}{1} + \frac{{1 + 2}}{2} + \frac{{1 + 2 + 3}}{3} + .......$ will be

The equation of common tangents to the parabola ${y^2} = 8x$ and hyperbola $3{x^2} - {y^2} = 3$, is

The value of $\left(\left(\log _2 9\right)^2\right)^{\frac{1}{\log _2\left(\log _2 9\right)}} \times(\sqrt{7})^{\frac{1}{\log _4 7}}$ is. . . . . . .

If $ \text{g}(\text{x}) = 1 +\sqrt{\text{x}}$ and $ \text{fg} (\text{x}) = 3 + 2\sqrt{\text{x} +\text{ x}},$ then $\text{f}(\text{x})=$

If $\sin A = \sin B$ and $\cos A = \cos B,$ then

If a straight line through $C( - \sqrt 8 ,\sqrt 8 )$ making an angle of $135^\circ $ with the $x$ - axis cuts the circle $x = 5\cos \theta ,y = 5\sin \theta $ at points $A$ and $B$, then the length of $AB$ is