Unit-1:Pure Arithematic
(a) Number system
(b) Squares and square roots
(c) Cubes and cubes roots
Q1.
Find two rational number between 1/5 and 1/3
Solution.
Let q1 and q2are two required rational numbers then,
q1 = 1/2(1/5 + 1/3)
= 1/2(3+5/15) = 1/2
(8/15) = 4/15
Similarly,
q2 = 1/2(4/15 + 1/3)
= 1/2 (12 + 15/45)
= 1/2 (27/45) = 1/2 (3/5) = 3/10
Hence, two rational numbers between 1/5 and 1/3 are 4/15 and 3/10.
{Formula Apply : Find rational numbers between a and b
, (a+b)/2}.
Solution
Q2.
Number 0.32323232... is
(a) Rational number (b) Irrational number (c) Whole number (d) Natural number
Solution.
This decimal numeral is rational number because it is not terminating but repeating.
Solution
Q3.
Is zero (0) a rational number ?
(a) yes (b)no (c) can't say.
Solution.
Zero is a rational number because we can write , 0/1 .
{Rational number can be expressed in the form of p/q where q is not equal to 0 .}
Solution
Q4.
If a = 4 - 
, find the value of 1/a .
Solution.
Let a = 4 -
then 1/a = 1/ 4 -
By rationalizing the denominator we get
{ In rationalization multiply both sides by conjugate}.
Solution
Q5.
Which number should be divide in 3675 to convert it into a perfect square.
(a)4 (b)5 (c)3 (d)2
Solution.
Write prime factors , we see that
3675 = 3 x 5 x 5 x 7 x 7
3 does not form a pair that is why 3675 is not a perfect square
Thus if we divide 3675 by the unpaired factor , 3 , the quotient become a perfect square.
Solution
Q6.
Is number 25453 a perfect square ?
(a) yes (b)no (c) can't say.
Solution.
End digit of this number is 3 it is not a perfect square .
{as we know that the natural number ending with digit 2,3,7 or 8
are not perfect square}
Solution
Q7.
Determine whether square of the number 369 will be even or odd ?
(a) even (b)odd (c) can't say.
Solution.
Square of this number will be odd.
{The square of an odd number is always odd.}
Solution
Q8.
Find the greatest number of 4 digits, which is a perfect square?
Solution.
Four digit greatest number = 9999
Extracting the square root of 9999, we find that (99)2is less than 9999 by 198,
Hence, the required number = 9999 - 198
= 9801
Solution
Q9.
Find the least number which must be subtracted to 4931 to make it a perfect square.
Solution.
One can observe that the given number is greater than (70)2 but less than (71)2
the number to be subtracted,
= 4931 - 4900 = 31
Solution
Q10.
The cube of the number 24 will be even or odd.
(a)even (b)odd (c) can't say
Solution.
The cube of 24 is even number
{The cube of an even number is even.}
Solution
