Number of irrational terms in the expansion of (5^ 1 6 +2^ 1 8 )^… - Vidyadip

MCQ

Number of irrational terms in the expansion of $\Big(5^{\frac{1}{6}}+2^{\frac{1}{8}}\Big)^{100}$ is:

A
96
✓
97
C
98
D
99

✓

Answer

Correct option: B.

97

$\text{T}_{\text{r}+1}=^{100}\text{C}_\text{r}5^{\frac{(\text{r}-100)}{6}}2^{\frac{\text{r}}{8}}$
Hence we get rational terms when
r = 8k where k is an integer and $\frac{8\text{k}-100}{6}$ is an integer
r = 16, 40, 64, 88
Hence we get in total 4 rational terms.
However, total number of terms will be 101
Hence total number of irrational terms is 101 - 4
= 97 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

The line $2x + 3y = 12$ meets the $x -$ axis at $A$ and the $y -$ axis at $B$ . The line through $(5, 5)$ perpendicular to $AB$ meets the $x -$ axis, $y -$ axis $\&$ the line $AB$ at $C, D, E$ respectively. If $O$ is the origin, then the area of the $OCEB$ is :

If $\theta $ and $\phi $ are acute satisfying $\sin \theta = \frac{1}{2},$ $\cos \phi = \frac{1}{3},$ then $\theta + \phi \in $

If the line $2x + 3ay - 1 = 0$ and $3x + 4y + 1 = 0$ are mutually perpendicular, then the value of $a$ will be

The incentre of the triangle formed by $(0, 0)$, $(5,12)$, $(16, 12)$ is

The value of $\sin \frac{\pi }{{16}}\sin \frac{{3\pi }}{{16}}\sin \frac{{5\pi }}{{16}}\sin \frac{{7\pi }}{{16}}$ is

The sum of the coefficients of three consecutive terms in the binomial expansion of $(1+ x )^{ n +2}$, which are in the ratio $1: 3: 5$, is equal to

Which is the largest negative integer which satisfies $\frac{(\text{x}^2 – 1)}{(\text{x} – 2)(\text{x} – 3)}$ ?

Let $\text{A}=\{\text{x}\in\text{R}:\text{x}\neq0-4\leq\text{x}\leq4\}$ and $\text{f}:\text{A}\in\text{R}$ be defined by $\text{f(x)}=\frac{|\text{x}|}{\text{x}}$ for $\text{x}\in\text{A}$ Then A:

The figure formed by the lines $\text{ax} \pm \text{by} \pm \text{c} = 0 $ is:

A straight line passing through $P(3, 1)$ meet the coordinates axes at $A$ and $B$. It is given that distance of this straight line from the origin $'O'$ is maximum. Area of triangle $OAB$ is equal to