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WB JEE 2021

MCQ (More than One Correct Answer)
English
Bengali
The remainder when $${7^{{7^{{7^{{{..}^7}}}}}}}$$ (22 time 7) is divided by 48 is
A
21
B
7
C
47
D
1

Explanation

We have

$${7^{{7^{{7^{{{..}^7}}}}}}}$$ (22 time 7)

$$ \Rightarrow {7^{{7^{{7^7}}}}}$$ is an odd number

$$\therefore$$ $${7^{(2m + 1)}} = {7^{2m}} \times 7$$

$$ = {({7^2})^m} \times 7$$

$$ = {(49)^m} \times 7$$

$$ = {(48 + 1)^m} \times 7$$

$$ = 7(1 + 48k)$$

$$ = 7 + (48 \times 7)k$$

$$\therefore$$ Remainder = 7
$${7^{{7^{{7^{{{...}^7}}}}}}}$$ (22 বার 7) -কে 48 দ্বারা ভাগ করলে ভাগশেষ হবে
A
21
B
7
C
47
D
1

Explanation

আমাদের কাছে

$${7^{{7^{{7^{{{..}^7}}}}}}}$$ (22 বার 7)

$$ \Rightarrow {7^{{7^{{7^7}}}}}$$ একটি বিজোড় সংখ্যা

$$\therefore$$ $${7^{(2m + 1)}} = {7^{2m}} \times 7$$

$$ = {({7^2})^m} \times 7$$

$$ = {(49)^m} \times 7$$

$$ = {(48 + 1)^m} \times 7$$

$$ = 7(1 + 48k)$$

$$ = 7 + (48 \times 7)k$$

$$\therefore$$ ভাগশেষ = 7

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