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Prove that √3 is an irrational number.
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State true or false for each of the following statements and justify in each case :
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.
If 1080 = 2^p × 3^q × 5, then (p − q) is equal to :
State the "Fundamental Theorem of Arithmetic" and use it to find LCM of 36 and 54.
Show that 45ⁿ can not end with the digit 0, n being a natural number. Write the prime number 'a' which on multiplying with 45ⁿ makes the product end with the digit 0.