Exemplar Math CH-1 to 5

For some integer m, every even integer is of the form

• m
• m + 1
• 2m
• 2m + 1

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

• q
• q + 1
• 2q
• 2q + 1

n² – 1 is divisible by 8, if n is

• an integer
• a natural number
• an odd integer
• an even integer

If the HCF of 65 and 117 is expressible in the form 65m – 117, then the value of m is

• 4
• 2
• 1
• 3

If the LCM of 39 and 65 can be expressed in the form 39n + 65, what is the value of n?

• 3

• 2

• 3.33

• 4

The largest number which divides 70 and 125, leaving remainders 5 and 8, respectively, is

• 13
• 65
• 875
• 1750

If two positive integers m and n are expressed as m = p²q³ and n = p³q²; where p and q are prime numbers, then HCF (m, n) is

• pq

• pq²

• p²q²

• p³q³

If two positive integers p and q can be expressed as p = ab² and q = a³b; a, b being prime numbers, then LCM (p, q) is

• ab
• a²b²
• a³b²
• a³b³

The product of a non-zero rational and an irrational number is

• always irrational
• always rational
• rational or irrational
• one

The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is

• 10
• 100
• 504
• 2520