JEE Main Questions
Using binomial theorem, prove that 6n−5n
always leaves he remainder 1 when divided by 25.
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If ∣x∣>1, then expand (1+x)−2˙
Find the remainder when 16902608+26081690
is divided by 7.
Find the coefficient of x−10 in the expansion of (xa+bx)12 .
Find the sum 1−81+81×163−8×16×241×3×5+
Find the coefficient of a4in the product (1+2a)4(2−a)5using binomial theorem.
Find the sum k=0∑10(20)Ck˙
Prove that r=0∑nnCrsinrxcos(n−r)x=2n−1sin(nx)˙
Using the principle of mathematical induction, prove that (23n−1)
is divisible by 7
for all n∈N