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CBSE Class 10 Mathematics Worksheet
UNIT I: Number systems - Real numbers
The smallest number by which √27 should be multiplied so as to get a rational number is
3
B)√27
C)√3
D)3√3
Prove that 7/20 is terminating decimal.
For some integer m, every odd integer is of the form
m
B)m+1
C)2m
D)2m+1
The sum or difference of a rational and an irrational number is
always irrational
B)always rational
C)rational or irrational
D)none of these
is an irrational number
If n is any natural number, then always ends with
1
B)3
C)5
D)7
The decimal expansion of the rational number will terminate after
one decimal place
B)two decimal places
C)three decimal places
D)more than three decimal places
If 'm' is a positive prime number then √m
Rational number
B)Irrational number
C)Integer
D)None of these
The sum of a rational and irrational number is
rational
B)irrational
C)both of above
D)none of above
If x and y are prime numbers, then HCF of and is
xy
Prove that is an irrational number.
If two positive integers a and b are written as a = p3q2 and b = pq3; p, q are prime numbers, then HCF (a, b) is:
pq
B)pq2
C)p3q3
D)p2q2
π is
An integer
B)A rational number
C)An irrational number
D)None of these
The exponent of 2 in the prime factorisation of 144, is?
4
B)5
C)6
D)3
For all a,b belong R, this imply
CBSE Class 10 Mathematics Worksheet
UNIT I: Number systems - Real numbers
Answers
20 = 4 X 5 = 22 X 5, the prime factor of 20 are both 2s & 5s. Hence 7/20 is terminating decimal
Solution:
In the given pair, 40000 > 200 thus let 40000 = a and 200 = b
Now by applying the Euclid’s division algorithm, we get
40000=200*199+0 (where q= 199,r=0)
Since, in the above equation we get, r = 0, therefore, 200 is the HCF of the given pair 200 and 40000.
Let's assume that is a rational number Therefore, we can f ind two integers and b, such that = a/b where,b is not equal to zero.Now, . Now,.Since a and b are integers, (6b + a) and (10b) are also integers. Thus 6b+a/10b is rational hence, should also be rational. This contradicts the f act that is irrational.Theref ore, our assumption is f alse and hence, is irrational.