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CBSE - Class 10 Mathematics Real numbers Worksheet
Show that every positive integer is of the form 6q+1, or 6q+3, or 6q+5 ,where q is some integer
7 x 144
B)54 x 244
C)12 x 7
D)70 x 35
For all a,b belong R, this imply
The smallest number by which 1/13 should be multiplied so that its decimal expansion terminates after two decimal places is
13/100
B)13/10
C)10/13
D)100/13
The smallest rational number by which should be multiplied so that it's decimal expansion terminates after one place of decimal is
3
D)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
For some integer m, every even integer is of the form
m
B)m+1
C)2m
D)2m+1
Find the greatest number which divides 243 an 2051 such that leaves reminder 3 in each case.
16
B)7
C)245
D)2053
2 rational numbers between 5 & 6 are 11/2 & 21/4 [As per METHOD 1 { ie Any rational number between two rational numbers "r" & "s" can be found using the formula [(r+s)/2] }]
TRUE
B)FALSE
π is
An integer
B)A rational number
C)An irrational number
D)None of these
Transitive property of order of real numbers is that for all a, b,c belong R.
The least number that is divisible by all the numbers from 1 to 5 (both inclusive) is
5
B)20
C)60
D)120
An army contingent of 616 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march?
6
B)8
C)12
D)4
Explain why 7×11×13+13 and 7×6×5×4×3×2×1+5 are composite numbers.
Assertion (A) : HCF of two or more numbers = Product of the smallest power of each common prime factor, involved in the numbers.
Reason (R) : The HCF of 12, 21 and 15 is 3.
Both A and R are true and R is the correct explanation of A.
B)Both A and R are true but R is not the correct explanation of A.
C)A is true but R is false.
D)A is false but R is true.
The product of LCM and HCF of two numbers m and n is
m+n
B)m-n
C)m X n
D)none of these
Show that any positive odd integer is of the form 4q+1,or 4q+3, where q is some integer.
CBSE - Class 10 Mathematics Real numbers Worksheet
Answers
Solution:
Using Method1, ie Rational Number between 2 Rational Numbers "r" & "s" can be found with formula (r+s)/2.
Step1: 1st Rational Number between 5&6 = (5+6)/2=11/2
Step2: 2nd Rational Number between 5 & 11/2 = (5+11/2)/2=(5/1+11/2)/2
=((5*2+11*1)/2)/2
=((10+11)/2)/2
=(21/2)/2
=21/4
Thus 2 Rational Numbers between 5 &6 are 11/2 & 21/4
Solution:
LCM of 2, 3, 4, 5 = 60
