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RD Chapter 1 Real Numbers Ex VSAQS Solutions

Question - 1 : - State Euclid’s division lemma.

Answer - 1 : -

Euclid’s division lemma:
Let a and b be any two positive integers, then there exist unique integers q and r such that
a = bq + r, 0 ≤ r < b
If b\a, then r = 0, otherwise x. satisfies the stronger inequality 0 < r < b.

Question - 2 : - State Fundamental Theorem of Arithmetic.

Answer - 2 : -

Fundamental Theorem of Arithmetics :
Every composite number can be expressed (factorised) as a product of primes and this factorization is unique except for the order in which the prime factors occur.

Question - 3 : - Write 98 as product of its prime factors.

Answer - 3 : -


Question - 4 : - Write the exponent of 2 in the prime factorization of 144.

Answer - 4 : -


Question - 5 : - Write the sum of the exponents of prime factors in theprime factorization of 98

Answer - 5 : -

98 = 2 x 7 x 7 = 21 x72
Sum of exponents = 1 + 2 = 3

Question - 6 : - If the prime factorization of a natural number n is 23 x 32 x52 x 7, write the number ofconsecutive zeros in n.

Answer - 6 : -

n = 23 x 32 x 52 x7
Number of zeros will be 52 x 22 = 102 twozeros

Question - 7 : - If the product of two numbers is 1080 and their H.C.F. is 30, find their L.C.M.

Answer - 7 : -

Product of two numbers = 1080
H.C.F. = 30

Question - 8 : - Write the condition to be satisfied by q so that a rational number p/q has a terminating decimal expansion. [C.B.S.E. 2008]

Answer - 8 : -

In therational number p ,the factorization of denominator q must be in form of 2m x5n where m and n are non-negativeintegers.

Question - 9 : - Write the condition to be satisfied by q so that a rational number p/q has a non-terminating decimal expansion.

Answer - 9 : - In the rational number p/q , the factorization of denominator q, is not in the form of 2m x 5n where m and n are non-negative integers.

Question - 10 : - Complete the missing entries in the following factor tree.

Answer - 10 : -


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