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Real Numbers Te...

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  • Question 1
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    If the L.C.M. of two numbers 240 and 360 is 720, find their H.C.F.

  • Question 2
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    Which of the following are non-terminating decimal expansions?
    (i)\(\frac{35}{5^{2} \times 7 \times 2^{3}}\)
    (ii) \(\frac{7}{2^{2} \times 5^{6}}\)
    (iii) \(\frac{2}{5^{2} \times 7}\)
    (iv)\(\frac{5}{2^{2} \times 5 \times 3}\)

  • Question 3
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    If `a` is an irrational number, which of the following numbers is definitely a rational number?

  • Question 4
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    Which of the following is not a composite number?

  • Question 5
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    What is the greatest number that divides the numbers 38, 45 and 52 and leaves remainders 2, 3 and 4, respectively?

  • Question 6
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    If \(H\). \(C\). \(F\). of two numbers, \(2^{5} \times 3^{2} \times 5\) and \(2^{4} \times 3^{3} \times 5\), is of the form \(2^{a} \times 3^{b} \times 5^{c} \times 7^{d}\), then what are the values of \(a, b, c\) and \(d\), respectively?

  • Question 7
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    If \(M=77 \times 144 \times 45,\) which of the following groups gives the prime factors of \(M \)?

  • Question 8
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    When three persons step off together, their steps measure 15 cm, 25 cm and 40 cm. What is the minimum distance that each person should walk in order to cover the same distance in integral number of steps?

  • Question 9
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    Which of the following fractions will have a terminating decimal expansion?

  • Question 10
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    Three boys A, B and C started running around a circular stadium at the same time and in the same direction. 'A' completes one round of the stadium in 6 minutes, 'B' in 5 minutes and 'C' in 20 minutes (all started running from the same point). After what time will they meet again at the starting point for the first time?

  • Question 11
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    Which of the following are irrational numbers?
    (i) \(\quad(\sqrt{3}+\sqrt{2})^{2}\)
    (ii) \(\sqrt{3+5+2 \sqrt{15}}\)
    (iii) \(\quad \sqrt{(\sqrt{2})^{2}+\sqrt{14}^{2}}\)
    (iv) \(\sqrt{(\sqrt{13}+2 \sqrt{3})(\sqrt{13}-2 \sqrt{3})}\)
    (v)\( \quad(\sqrt{3}+\sqrt{50})^{2}\)
    \((\text { vi }) \quad(\sqrt{3}+\sqrt{12}) \div(\sqrt{12}+\sqrt{27})\)

  • Question 12
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    Which of the following has a non-terminating non-repeating decimal expansion?

  • Question 13
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    Which of the following statements violates the fundamental theorem of factorisation?

  • Question 14
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    Which of the following statements is true?

  • Question 15
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    Which of the following statements is true?

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