Assertion -A- Pn-62-63-64- leaves the remainder 59 when divided by 65- Reason- R- Pn-59mod 65

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Standard IX

Mathematics

Theorem

Assertion :A:...

Question

Assertion :(A): $P (n) = 62 \times 63 \times 64,$ leaves the remainder $59$ when divided by $65.$ Reason: (R): $P (n) = 59 (m o d 65)$

Both (A) & (R) are individually true & (R) is correct explanation of (A).

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Both (A) & (R) are individually true but (R) is not the correct (proper) explanation of (A).

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(A) is true but (R) is false.

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(A) is false but (R) is true.

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Solution

The correct option is A Both (A) & (R) are individually true & (R) is correct explanation of (A).
$62 = - 3 (M o d 65), 63 = - 2 M o d (65), 64 = - 1 (M o d 65)$

$∴ 62 \times 63 \times 64 = (- 3) (- 2) (- 1) (M o d 65) = - 6 (M o d 65) = 59 (M o d 65)$

Therefore, the remainder is $59$ .
Ans: A

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Assertion :(A): P(n)=62×63×64, leaves the remainder 59 when divided by 65. Reason: (R): P(n)=59(mod65)

The correct option is A Both (A) & (R) are individually true & (R) is correct explanation of (A).62=−3(Mod65),63=−2Mod(65),64=−1(Mod65) ∴62×63×64=(−3)(−2)(−1)(Mod65)=−6(Mod65)=59(Mod65)Therefore, the remainder is 59.Ans: A

Assertion :(A): $P (n) = 62 \times 63 \times 64,$ leaves the remainder $59$ when divided by $65.$ Reason: (R): $P (n) = 59 (m o d 65)$

The correct option is A Both (A) & (R) are individually true & (R) is correct explanation of (A).
$62 = - 3 (M o d 65), 63 = - 2 M o d (65), 64 = - 1 (M o d 65)$

$∴ 62 \times 63 \times 64 = (- 3) (- 2) (- 1) (M o d 65) = - 6 (M o d 65) = 59 (M o d 65)$

Therefore, the remainder is $59$ .
Ans: A