model 2 divisibility, multiples, add and subtract based number system Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (a)

In this problem, put any even positive value for both m & n,

For example m = 4 & n = 2

∴ (m² – n²) = (4² – 2²) = 16 - 4

= 12 is always divisible by 4.

Answer: (b)

When the second divisor is a factor of the first divisor, the second remainder is obtained by dividing the first remainder by the second divisor.

Hence, on dividing 29 by 8, the remainder is 5.

Answer: (d)

As we know, xⁿ – aⁿ is exactly divisible by (x – a) if n is odd.

∴ (49)¹⁵ – (1 )¹⁵ is exactly divisible by 49 – 1 = 48, that is a multiple of 8.

Hence required answer is 8.