The remainder, if `1+2+2^2+.......+2^(1999)` is divided by 5 is.

Find the remainder when 1!+2!+3!+4!+.......+n ! is divided by 15, if ngeq5.

The remainder when 1!+2!+3!+4!+......+1000! is divided by 10 is

Assertion (A) : The remainder of x^(3)+2x^(2)-5x-3 which is divided by x-2 is 3. Reason (R) : The remainder of the polynomial f(x) when divided by x-a is f(a)

STATEMENT 1 : When a polynomial P(x)(d egr e e >2) is divided by (x-1) and (x-2) the remainders are -1 and 1 respectively. If the same polynomial is divided by (x-1)(x-2) then the remainder is (2x-3) STATEMENT 2 : If P(x) is divided by a quadratic expression, then the remainder is either 0 or a polynomial whose degree is at most 1.

Find, in each case, the remainder when : (i) x^(4)- 3x^2 + 2x + 1 is divided by x - 1. (ii) x^2 + 3x^2 - 12x + 4 is divided by x - 2. (iii) x^4+ 1 is divided by x + 1.

Find the remainder when 1!+2!+3!+4!++n ! is divided by 15, if ngeq5.

The remainder when the positive integer m is divided by n is r. What is the remainder when 2m is divided by 2n?