Question:
Among the statements:
Among the statements:
Updated On: Mar 29, 2026
only (S1) is correct
both (S1) and (S2) are correct
only (S2) is correct
both (S1) and (S2) are incorrect
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The Correct Option is B
Approach Solution - 1
The correct option is (B): Only statement-1 is true
∵ (2002)2023 = 8 m
∵ (2002)2023 is divisible by 8 and (1919)2002 is not divisible by 8
∴ (2002)2023 - (1919)2002 is not divisible by 8.
Also, 13.(13)n - 12n - 13
= 13(1+12)n - 12n - 13
= 13 [1+12n + nC2 122 + --] - 12n - 13
= 144n + 144nC2 + --
= 144 [n + nC2 + --]
= 144K
∴, the option (B) is the correct option.
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Approach Solution -2
For (S1), we can apply modulo operations to prove that \(2023^{2022} - 1999^{2022}\) is divisible by 8.
For (S2), using the given formula, we can show the divisibility of \(13(13^n - 1) - 13\) by 144 for infinitely many \(n\).
Thus, both statements are true.
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