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Find the remainder when 7103 is divided by 25.
Find the coefficient of a3b4c
in the expansion of (1+a−b+c)9˙
Prove that 10[(10+1)100−(10−1)100] is an even integer .
Prove that nC02nCn−nC12n−2Cn+nC22n−4Cn≡2n˙
divides the number 101100−1
then, find the greatest value of m˙
If the 3rd, 4th , 5th and 6th term in the expansion of (x+α)n
be, respectively, a,b,candd,
prove that c2−bdb2−ac=3c5a˙
Find the cube root of 217, correct to two decimal places.
Let n be an odd natural number greater than 1. Then , find the number of zeros at the end of the sum 99n+1.