Let m be the smallest positive integer such that the coefficient of x2 in the expansion of (1+x)2+(1+x)3+(1+x)4+……..+(1+x)49+(1+mx)50 is (3n+1).51C3 for some positive integer n. Then the value of n is
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Using binomial theorem, prove that 6n−5n
always leaves he remainder 1 when divided by 25.
Find the 13th term in the expansion of (9x−3x1)18,x=0
r=1∑np=0∑r−1′nCr⋅rCp⋅2p is equal to
If (1+px+x2)n=1+a1x+a2x2+…+a2nx2n. Which of the following is true for 1<r<2n
Using binomial theorem compute : (102)6
If nC0−nC1+nC2−nC3+…+(−1)r⋅nCr=28 , then n is equal to ……
Find an approximation of (0.99)5
using the first three terms of its expansion.
If p4+q(3)=2(p>0,q>0), then the maximum value of term independent of x in the expansion of (px121+qx−91)14 is