JEE Main Questions
Find the value of p=1∑n(m=p∑nnCmmCp)˙
And hence, find the value of (lim)n∞3n1p=1∑n(m=p∑nnCmmCp)˙
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then find the coefficient of xn
in the expansion of (1+2x+3x2+4x3+)1/2˙
Find the coefficient of x5 in (x+3)8
Find the coefficient of a4in the product (1+2a)4(2−a)5using binomial theorem.
Find the sum ∑0≤i<j≤n∑ nCinCj
If the middle term in the expansion of (x2+1/x)n
then find the value of n˙
then find the possible value of n˙
In the coefficients of rth, (r+1)th,and(r+2)th
terms in the binomial expansion of (1+y)m
are in A.P., then prove that m2−m(4r+1)+4r2−2=0.
The coefficients of three consecutive terms in the expansion of (1+a)nare in the ratio 1: 7 : 42. Find n.