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Definition of Functions

10386-86103 i...

Question

( $103)^{86} - (86)^{103}$ is divisible by

A

7

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B

13

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C

17

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D

23

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Solution

The correct option is C
17

Give Expression

$= (1 + 102)^{86} - (1 + 85)^{103} = (1 +^{86} C_{1} 102 +^{86} C_{2} (102)^{2} + \dots \dots;) - (1 +^{103} C_{1} 85 +^{103} C_{2} (85)^{2} + \dots \dots)$

= 17 $\times$ an integer

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Similar questions

Q. Mark the correct answer in each of the following:
The negation of the statement "72 is divisible by 2 and 3", is
(a) 72 is not divisible by 2 or 72 is not divisible by 3.
(b) 72 is not divisible by 2 and 72 is not divisible by 3.
(c) 72 is divisible by 2 and 72 is not divisible by 3.
(d) 72 is not divisible by 2 and 72 is divisible by 3.

Q. Fill in the blanks
a)A number is divisible by

24

if it is divisible by both ____ and ____.
b)A number is divisible by ____ if it is divisible by

4

9

.

P (x)

Q (x)

be two polynomials. Suppose that

f (x) = P (x^{3}) + x Q (x^{3})

is divisible by

x^{2} + x + 1

If P(k) is the statement 2^3k - 1 is divisible by 7, then P(k + 1) is

n \in N, f (n) = 37^{n + 2} + 16^{n + 1} + 30^{n}

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