SolveItClass 10 · NCERT

NCERT Solutions · Class 10 Mathematics Real Numbers

10 questions · 10 still being checked

EXERCISE 1.1 1–7 (part 1 of 2)

  1. Exercise 1

    Express each number as a product of its prime factors:
    (i)
    140\displaystyle 140
    (ii)
    156\displaystyle 156
    (iii)
    3825\displaystyle 3825
    (iv)
    5005\displaystyle 5005
    (v)
    7429\displaystyle 7429
    NCERT’s answer
    (i)
    $\displaystyle 2^{2} \times 5 \times 7$ (ii) $\displaystyle 2^{2} \times 3 \times 13$ (iv) $\displaystyle 5 \times 7 \times 11 \times 13$ (v) $\displaystyle 17$ × $\displaystyle 19$ × $\displaystyle 23$

    Working being prepared

  2. Exercise 2

    Find the LCM and HCF of the following pairs of integers and verify that LCM×HCF=\displaystyle \mathrm{LCM} \times \mathrm{HCF}= product of the two numbers.
    (i)
    26\displaystyle 26 and 91\displaystyle 91
    (ii)
    510\displaystyle 510 and 92\displaystyle 92
    (iii)
    336\displaystyle 336 and 54\displaystyle 54
    NCERT’s answer
    (i)
    $\displaystyle \mathrm{LCM}=182 ; \mathrm{HCF}=13$

    Working being prepared

  3. Exercise 3

    Find the LCM and HCF of the following integers by applying the prime factorisation method.
    (i)
    12\displaystyle 12, 15\displaystyle 15 and 21\displaystyle 21
    (ii)
    17\displaystyle 17, 23\displaystyle 23 and 29\displaystyle 29
    (iii)
    8\displaystyle 8, 9\displaystyle 9 and 25\displaystyle 25
    NCERT’s answer
    (i)
    $\displaystyle \mathrm{LCM}=420 ; \mathrm{HCF}=3$ (ii) $\displaystyle \mathrm{LCM}=11339 ; \mathrm{HCF}=1$ (iii) $\displaystyle \mathrm{LCM}=1800 ; \mathrm{HCF}=1$

    Working being prepared

  4. Exercise 4

    Given that HCF⁡(306,657)=9\displaystyle \operatorname{HCF}(306,657)=9, find LCM⁡(306,657)\displaystyle \operatorname{LCM}(306,657).
    NCERT’s answer
    $\displaystyle 22338$

    Working being prepared

  5. Exercise 5

    Check whether 6n\displaystyle 6^{n} can end with the digit 0\displaystyle 0 for any natural number n\displaystyle n.

    Solution being prepared

  6. Exercise 6

    Explain why 7×11×13+13\displaystyle 7 \times 11 \times 13+13 and 7×6×5×4×3×2×1+5\displaystyle 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1+5 are composite numbers.

    Solution being prepared

  7. Exercise 7

    There is a circular path around a sports field. Sonia takes 18\displaystyle 18 minutes to drive one round of the field, while Ravi takes 12\displaystyle 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?
    NCERT’s answer
    $\displaystyle 36$ minutes

    Working being prepared