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Write down the decimal expansions of the following rational numbers by writing their denominators in the form 2m × 5n, where, m, n are non-negative integers.\[\frac{13}{125}\]
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Write down the decimal expansions of the following rational numbers by writing their denominators in the form 2m × 5n, where, m, n are non-negative integers.\[\frac{129}{2^2 \times 5^7}\]
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State Fundamental Theorem of Arithmetic.
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Write the exponent of 2 in the price factorization of 144.
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Write the sum of the exponents of prime factors in the prime factorization of 98.
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If the prime factorization of a natural number n is 23 ✕ 32 ✕ 52 ✕ 7, write the number of consecutive zeros in n.
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If the product of two numbers is 1080 and their HCF is 30, find their LCM.
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Express the number as a product of its prime factor:
156
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Express the number as a product of its prime factor:
3825
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Express the number as a product of its prime factor:
5005
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Express the number as a product of its prime factor:
7429
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Find the LCM and HCF of the following pair of integers and verify that LCM × HCF = product of the two numbers.
510 and 92
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Find the LCM and HCF of the following pair of integers and verify that LCM × HCF = product of the two numbers.
336 and 54
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Find the LCM and HCF of the following integers by applying the prime factorisation method.
17, 23 and 29
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Find the LCM and HCF of the following integers by applying the prime factorisation method.
8, 9 and 25
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The perimeter of a triangle with vertices (0, 4), (0, 0) and (3, 0) is ______.
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If the point P(2, 1) lies on the line segment joining points A(4, 2) and B(8, 4), then ______.
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Find the value of k such that the polynomial x2-(k +6)x+ 2(2k - 1) has some of its zeros equal to half of their product.
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Find the value of k such that the polynomial x2 − (k + 6)x + 2(2k −1) has sum of its zeros equal to half of their product.
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If the sum of first n terms of an AP is n2, then find its 10th term.
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