Question:
The number of integral terms in the expansion$\left(\sqrt{3}+\sqrt[8]{5}\right)^{256}$
The number of integral terms in the expansion$\left(\sqrt{3}+\sqrt[8]{5}\right)^{256}$
Updated On: Jul 7, 2022
- 32
- 44
- 34
- 35
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The Correct Option is B
Solution and Explanation
$T _{ r +1}={ }^{256} C _{ r }\left(3^{1 / 2}\right)^{256-6}\left(5^{1 / 8}\right)^{ r }$
It is an integer if $\frac{256- r }{2}$ and $\frac{ r }{8}$ are positive integers.
$\therefore 256- r \geq 0$ and $r$ is a multiple of $8 \Rightarrow r$ can be $0,8,16,24, \ldots \ldots \ldots, 8 \times 32$
These are 33 .
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Concepts Used:
Integrals of Some Particular Functions
There are many important integration formulas which are applied to integrate many other standard integrals. In this article, we will take a look at the integrals of these particular functions and see how they are used in several other standard integrals.
Integrals of Some Particular Functions:
- ∫1/(x2 – a2) dx = (1/2a) log|(x – a)/(x + a)| + C
- ∫1/(a2 – x2) dx = (1/2a) log|(a + x)/(a – x)| + C
- ∫1/(x2 + a2) dx = (1/a) tan-1(x/a) + C
- ∫1/√(x2 – a2) dx = log|x + √(x2 – a2)| + C
- ∫1/√(a2 – x2) dx = sin-1(x/a) + C
- ∫1/√(x2 + a2) dx = log|x + √(x2 + a2)| + C
These are tabulated below along with the meaning of each part.
