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Prove that √3 is an irrational number.
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.
Check whether 15ⁿ × 2ⁿ, n being a natural number, ends with the digit zero.
The traffic lights at three different road crossings change after every 45 seconds, 75 seconds and 60 seconds respectively. If they change together at 5.00 a.m., then at what time they will change together next ?
Show that the number 2 × 5 × 7 × 11 + 11 × 13 is a composite number.
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