MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Finding Integral Part of Numbers of the Form a^b Where a Is Irrational

The value of ...

Question

The value of ${\frac{2^{4 n}}{15}}, n \in N$ is
(where {.} represents fractional part function)

A

\frac{1}{15}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

B

\frac{11}{15}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

C

\frac{4}{15}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

D

\frac{14}{15}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $\frac{1}{15}$
$2^{4 n} = 16^{n} = (1 + 15)^{n} = 1 +^{n} C_{1} \cdot 15 +^{n} C_{2} \cdot 15^{2} + \dots +^{n} C_{n} \cdot 15^{n} = 1 + 15 k, k \in N$

Now,
$\frac{2^{4 n}}{15} = k + \frac{1}{15}$

Hence, ${\frac{2^{4 n}}{15}} = \frac{1}{15}$

Suggest Corrections

thumbs-up

6

Similar questions

Q. The value of

{\frac{2^{4 n}}{15}}, n \in N

is
(where {.} represents fractional part function)

Q. The fractional part of

\frac{2^{4 n}}{15}

(n \in N)

Q. The value of

{sin \frac{25 π}{3}}

{.}

is fractional part function)

Q. Let the solution of the equation

5 {x} = 2 [x] + x

a / 4

then the value of

a

is
where {.} and [.] represents fractional part function and greatest integer function respectively.

A = [a_{i j}]

4 \times 4

a_{i j} = {\begin{matrix} 2, when i = j 0, when i \neq j \end{matrix}

,
then the value of

{\frac{det(adj(adjA))}{7}}

{.}

represents the fractional part function)

View More

Join BYJU'S Learning Program

explore_more_icon

Explore more

Finding Integral Part of Numbers of the Form a^b Where a Is Irrational

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon