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Prove that 3+2√3 is irrational .
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Prove that √3 is irrational .
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There is a circular path around a sports field.Sonia takes 18 minutes to drive one round of the field, while Ravi takes 12 minutes for the same. Suppose they both start at the same point and at the same time and go in the same direction, after how many minutes will they meet again at the starting point?
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Check whether....................as shown below
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Find the LCM and HCF of the following integers by applying the prime factorization method. i) 12,15 and 21 ii) 17,23 and 29 iii) 8,9 and 25
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Find the LCM and HCF of the following pairs of integer and verify that LCM×HCF=Product of the two numbers. i) 26 and 91 ii) 510 and 92 iii) 336 and 54
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Express each number as a product of its prime factors: i)140 ii)156 iii)3825 iv)5005 v)7429
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Real Numbers
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Use Euclid’s Division lemma to show that the square of any positive integer is either of the form 3m, 3m+1 for some integer m.
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An army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march?
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Show that any positive odd integer is of the form 6q+1,6q+3 & 6q+5 where q is some integer.
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