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ICOME
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Unit 1

Unit-1: Arithematic

(a) Number system

(b) Exponents of real numbers, surds and rationalisation

Q1. (3 +)(3 -)is a rational number.
(a) yes (b)no (c) can't say.

Solution.
(a + b) (a - b) = a2 - b2

So, (3 +)(3 -) = 9 - 3 = 6

Thus 6 is a rational number.
Solution

Q2. Sum of two irrational number ia always an irrational number.
(a) True (b)False (c) Can't say.

Solution.
False, Sum of two irrational number can be rational or irrational number

(3 +)+(3 -) = 6(Rational number)

(3 +)+(3 +) = 6 + 2(Irrational number)
Solution

Q3. 9 + is a _____ number ..

Solution.
9 + is a irrational number.
9 is a rational number and is an irrational number and as we known that sum of rational number and an irrational number is always an irrational number.
Solution

Q4. Insert a rational number and an irrational number between 3 and 4.

Solution.
If a and b are rational numbers and ab is not a perfect square, then is an irrational numbers between a and b

Rational number between a and b is (a + b)/2

So, irrational number:

rational number : (3 + 4) /2 = 3.5 .
Solution

Q5. Can we represent an irrational number on number line.

Solution.
Yes.
Solution

Q6. Evaluate (64)-2/3 .

Solution.
= (43)-2/3 = 4-2 = 1/(42) = 1/16
Solution

Q7. Find the value of x, if 5(x - 4). 3(2x - 10) = 225 .

Solution.
5(x - 4). 3(2x - 10) = 52 x 32

x - 4 = 2 and 2x - 10 = 2

x = 6 , 2x = 12

x = 6
Solution

Q8. Simplify .

Solution.
Solution

Q9. Find x, If 24 x 42 =4x .

Solution.
24 x 24 = 22x

28 = 22x

8 = 2x

x = 4.
Solution

Q10. If (x- 1)3 = 64, find the value of x3.

Solution.
(x - 1)3 = 43

x - 1 = 4

x = 5

So, 53 = 125
Solution