Fractional part 278-31 is

The correct option is C 8/312^78= 2^3.2^75=8 (2^5 )^15=8(1+31)^15=8{^15C_0 + ^15C_1 31 +⋯⋯+ ^15C_15(31)^15} 2^78=8+an integer multiple of 31 2^78/31=8/31+ an i ...

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Byju's Answer

Standard XII

Mathematics

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

Fractional pa...

Question

Fractional part $\frac{2^{78}}{31}$ is

\frac{2}{31}

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\frac{4}{31}

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\frac{8}{31}

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\frac{10}{31}

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Solution

The correct option is C $\frac{8}{31}$
$2^{78} = 2^{3} {.2}^{75} = 8 (2^{5})^{15} = 8 (1 + 31)^{15} = 8 {^{15} C_{0} +^{15} C_{1} 31 + \dots \dots +^{15} C_{15} (31)^{15}}$
$2^{78} = 8 + a n i n t e g e r m u l t i p l e o f 31$
$\frac{2^{78}}{31} = \frac{8}{31} + a n i n t e g e r$

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Similar questions

Fractional part of $\frac{2^{78}}{31}$ is

Q. Fractional part

\frac{2^{78}}{31}

Q. Let

R = {(5 \sqrt{5} + 11)}^{31} = 1 + f

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is equal to

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\frac{- 12}{5} + \frac{43}{10}

(ii)

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\frac{- 31}{6} + \frac{- 27}{8}

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Fractional part 27831 is

The correct option is C 831278=23.275=8(25)15=8(1+31)15=8{15C0+15C131+⋯⋯+15C15(31)15} 278=8+an integer multiple of 31 27831=831+ an integer

Fractional part $\frac{2^{78}}{31}$ is

The correct option is C $\frac{8}{31}$
$2^{78} = 2^{3} {.2}^{75} = 8 (2^{5})^{15} = 8 (1 + 31)^{15} = 8 {^{15} C_{0} +^{15} C_{1} 31 + \dots \dots +^{15} C_{15} (31)^{15}}$
$2^{78} = 8 + a n i n t e g e r m u l t i p l e o f 31$
$\frac{2^{78}}{31} = \frac{8}{31} + a n i n t e g e r$