If `6^83+8^83` is divided by 49, then the sum of the digits of remainder is

If R is remainder when 6^(83)+8^(83) is divided by 49, then the value of R//5 is.

If a two digits' number is divided by the sum of digits, the quotient is 6 and the residue is 3. Again, if two digits are interchanged, then the new number thus obtained, is divided by the sum of the digits, the quotient is 4 and the residue is 9. Find the number.

When (x^5 - 1) is divided by (2x + 1), then the remainder is

If x^4 + 5x^3 + 4x^2 + 8x + 24 is divided by (x + 2), then find the remainder.

A number is selected at random from the first 25 natural numbers. If it is a composite number, then it is divided by 6. But if it is not a composite number, it is divided by 2. Find the probability that there will be no remainder in the division.

Let p(x) be a quadratic polynomial with constant term 1. Suppose p(x) when divided by x-1 leaves remainder 2 and when divided by x+1 leaves remainder 4. Then the sum of the roots of p(x)=0 is

The sum of the digits of number consisting of the digits is 8. If 18 is deducted from the number. The digits of the number interchange the places. Find the number

Let P(x) be a polynomial, which when divided by x-3 and x-5 leaves remainders 10 and 6 respectively. If the polynomial is divided by (x-3)(x-5) then the remainder is-

Let P(x) be a polynomial, which when divided by x-3 and x-5 leaves remainders 10 and 6 respectively. If the polynomial is divided by (x-3) (x-5) then the remainder is

3^(2n) when divided by 8 leves the remainder-