### CBSE 10 Mathematics Real Numbers Practice Paper 01

**1.**The decimal expansion of the rational number \(\frac{43}{2^4 5^3}\) will terminate after how many places of decimals?

**2.**Find the largest number that will divide 398, 436 and 542 leaving remainders 7, 11, and 15 respectively.

**3.**Find LCM of numbers whose prime factorisation are expressible as 3 × 52 and 32 × 72.

**4.**Find the largest number which divides 70 and 125 leaving remainder 5 and 8 respectively.

**5.**Explain why (17 × 5 × 11 × 3 × 2 + 2 × 11) is a composite number?

**6.**Prove that 3 + 2√3 is an irrational number.

**7.**Three bells rings at intervals of 12, 18, 21 minutes respectively. If they start ringing together, after what time will they next ring together?

**8.**Two tankers contain 850 liters and 680 liters of petrol. Find the maximum capacity of a container which can measure the petrol of each tanker in the exact number of times.

**9.**Find the HCF of 255 and 867 by Euclid’s division algorithm.

**10.**Show that any positive odd integer is of the form 4q + 1 or 4q + 3 where q is a positive integer.

**11.**Prove that √3 is an irrational number.

**12.**Prove that \(\frac{1}{\sqrt3}\) is an irrational number.

**13.**Show that any positive even integer is of the form of 6m or 6m+2 where m is some integer.

**14.**Find the largest number which divides 28 and 32 leaving remainder 8 and 12 respectively.

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