Question

The remainder left out when 82n – (62)2n+1 is divided by 9 is

Solution

Correct option is

2

    

         

The last term in each bracket being

        

All other terms will have 9 and 63 = 9.7 as factors.

∴       E is of the form 9k + 2

Hence, when given expression is divided by 9 the remainder is 2.

SIMILAR QUESTIONS

Q1

If the sum of the coefficients in the expansion of (1 – 3x + 10x2)n is A and it the sum of the coefficients in the expansion of (1 + x2)is 

B, then

Q2

The coefficient t24 in (1 + t2)12 (1 + t12) (1 + t24) is

Q3

For natural number mn if (1 – y)m (1 + y)n = 1 + ay + ay2 +….. and a1 = a2 = 10, them (mn) is

Q4

If x is + ive, the first – ive term in the expansion of (1 + x)27/5 is:

Q5

Coefficients of x11 in the expansion of (2x2 + x – 3)6 is

Q6

Coefficients of x10 in the expansion of (1 + x2 – x3)8 is

Q7

The expression [x + (x3 - 1)1/2]5 + [x – (x3 – 1)1/2]5 is a polynomial of degree

Q8

The degree of the polynomial

              is equal to

Q9

 where {x} = Fractional part of x then the value of sec –1 (8θ) is

Q10