Question

1. For some integer m, every even integer is of the form (a) m (b) m+ 1 (c) 2m (d) 2m +1

2. For some integer q, every odd integer is of the form

(a) q (b) q+1 (c) 2q (d) 2q +1

3. n-1 is divisible by 8, if n is (b) a natural number

(a) an integer (c) an odd integer (d) an even integer

4. If the HCF of 65 and 117 is expressible in the form 65m-117, then the value of mis (a) 4 (b) 2 (c) 1 (d) 3

5. The largest number which divides 70 and 125, leaving remainders 5 and 8, respectively, is (a) 13 (b) 65 (c) 875 (d) 1750

6. If two positive integers a and b are written as axy and b= xyx, y are prime numbers, then HCF (a, b) is (a) xy (b) xy² (c) x'y'

= 7. If two positive integers p and q can be expressed as p ab and qab; a, b being prime numbers, then LCM (p, q) is (a) ab (b) a b (c) a¹b²

8. The product of a non-zero rational and an irrational number is (b) always rational (d) one

(a) always irrational (c) rational or irrational

9. The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is (a) 10 (b) 100 (c) 504 (d) 2520

14587 10. The decimal expansion of the rational number will terminate after: 1250 (b) two decimal places (d) four decimal places

(a) one decimal place (c) three decimal places

11. The decimal expansion of the rational number 33 25 will terminate after (b) two decimal places

(a) one decimal place (c) three decimal places (d) more than 3 decimal places​

Answer 1

Answer:

1.   2m

Step-by-step explanation:

An even integer is a multiple of 2.

Hence, every even integer is of the form of 2m.

2.  We know that, odd intergers are 1,3,5,...

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

where, q = integer = z

or q = ...,-1,0,1,2,3,...

∴ 2q + 1 = ...,-3,-1,1,3,5,...

Alternate method

Let 'a' be the 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 r = 0 or r = 1

⇒ a = 2q or 2q + 1

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

Step-by-step explanation:

Answer 2

Answer:

thanks for the points and the answer may u be blessed ☺