Question

For some Integer q , every odd integer is of the form a: q , b: q+1 , c: 2q , d: none of these​

Answer 1

Answer:

hope it helps u

Step-by-step explanation:

We know that, odd integers are 1,3,5….

So, it can be written in the form of 2q+1.

Where, q=integer=Z

where q=integer=Z

or q=…,-1,0,1,2,3…..

∴ 2q+1=…,-3,-1,1,3,5…

Alternative method

Let 'a' be given positive integer. On dividing 'a' by 2, let q be the quotient and r be the remainder. Then by Euclid's division algorithm, we have

a=2q+r, where 0≤r≤2

⇒ a=2q+r, where 0 or r=1

⇒ a=2q or 2q+1

When, a=2q+1 for some integer q, then clearly a is odd.

Answer 2

Answer:

here u go dude

Step-by-step explanation:

as it is a mcq question so we will solve it using the options

option a:-

           it is clearly stated in the question that q is some integer means it can be both odd and even number

option b:-

           as q can be any integer means it can be both odd and even so adding 1 will not bring any great change

option c:-

           we can see that it is clearly an even number

   lets take some examples

let q be 1, 2, 3, 4

then,

2*1= 2 (even)

2*2= 4 (even)

2*3= 6 (even)

2*4= 8 (even)

option d:-

             (only one option remaining so it is the answer)

none of these

now real answer will be

2q+1 as we saw above that 2q is always even then adding 1 will make it always odd.

Thank you for reading this answer

best of luck for your upcoming exam

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