Assertion (A): Every positive even integer is a multiple of 2. Reason (R): The Fundamental Theorem of Arithmetic ensures the unique prime factorization of integers greater than 1.

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Assertion-ReasonFundamental Theorem of Arithmetic

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Prove that √3 is an irrational number.

TextFundamental Theorem of ArithmeticPrime Factorisation of Natural NumbersIrrationality of Square Root of Prime NumbersProof by Contradiction Method

Fundamental Theorem of Arithmetic

Prime Factorisation of Natural Numbers

Irrationality of Square Root of Prime Numbers

Proof by Contradiction Method

State true or false for each of the following statements and justify in each case :

CASE_STUDIESFundamental Theorem of ArithmeticPrime Factorisation of Natural NumbersIrrationality of Square Root of Prime NumbersProof by Contradiction Method

Assertion (A) : Unit digit of 3ⁿ cannot be an even number for any natural number n. Reason (R) : 2 is not a prime factor of 3ⁿ for any natural number n.

Assertion-ReasonFundamental Theorem of ArithmeticPrime Factorisation of Natural Numbers

If 1080 = 2^p × 3^q × 5, then (p − q) is equal to :

MCQ (Single)Fundamental Theorem of ArithmeticPrime Factorisation of Natural Numbers

n² – 1 is divisible by 8, if n is

MCQ (Single)Fundamental Theorem of Arithmetic

Show that any number of the form 4ⁿ can never end with the digit 0.

TextFundamental Theorem of Arithmetic