Question 1 & 2

Question 1: Evaluate  10\times 10^{9}

FPSC AD IB 2017



Solution:

How any thing having power zero becomes 1 ?

we generally know;

\frac{x}{x}=1

Why? It is because each ‘x’ has power 1 in above fraction  i-e

\frac{x}{x}=\frac{ x^{1}}{ x^{1}}= x^{1-1}= x^{0}

Comparing both expressions for same ration we get;

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If any figure or amount  has exponent or power of zero ‘0’ then its value is equal to 1

I- e

 1000000000000^{0}=1

 1^{0}=1

 if  zero has power zero,  then result is  undefined i-e

\frac{0}{0}=undefined

Because division by zero is not allowed in maths, so,

 0^{0} =undefined

So, in the asked question 10 has power 0, so its value is equal to 1, so we solve it;

10\times10^{0}=10\times1 =10

Question 2: What is missing term in the sequence 2,6,18,_,162 ?

FPSC AD IB 2017

Solution:

If we multiply 2 with 3 it gives 6

if we multiply 6 with 3 it gives 18

and so on ……………………..

I f we divide 18 by 3 , we get 6

If we divide 6 by 3 , we get 2

i-e previous term of sequence is achieved by dividing a term ahead

so, if divide 162 by three, we get 54

so the missing term is 54

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