Assertion -A- Pn-7n-3n is divisible by 4- Reason- R- If a- b- then expansion an-bn is divisible by a -b if n is odd or even-

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Standard XII

Mathematics

Binomial Theorem for Any Index

Assertion :A:...

Question

Assertion :(A): $P (n) = 7^{n} - 3^{n}$ is divisible by $4$ . Reason: (R): If $a \neq b,$ then expansion $a^{n} - b^{n}$ is divisible by $a - b$ if $n$ is odd or even.

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).
$P (n) = 7^{n} - 3^{n}, n$ is either even or odd $(a = 7, b = 3)$ divisible by $a - b = 7 - 3 = 4$
Hence Assertion (A) followed by Reason (R).
Ans: A

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Assertion :(A): P(n)=7n−3n is divisible by 4. Reason: (R): If a≠b, then expansion an−bn is divisible by a−b if n is odd or even.

The correct option is A Both (A) & (R) are individually true & (R) is correct explanation of (A).P(n)=7n−3n,n is either even or odd (a=7,b=3) divisible by a−b=7−3=4 Hence Assertion (A) followed by Reason (R).Ans: A

Assertion :(A): $P (n) = 7^{n} - 3^{n}$ is divisible by $4$ . Reason: (R): If $a \neq b,$ then expansion $a^{n} - b^{n}$ is divisible by $a - b$ if $n$ is odd or even.

The correct option is A Both (A) & (R) are individually true & (R) is correct explanation of (A).
$P (n) = 7^{n} - 3^{n}, n$ is either even or odd $(a = 7, b = 3)$ divisible by $a - b = 7 - 3 = 4$
Hence Assertion (A) followed by Reason (R).
Ans: A