JEE Main Questions
Find the coefficient of a4in the product (1+2a)4(2−a)5using binomial theorem.
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Find a if the coefficients of x2and x3in the expansion of (3+ax)9are equal.
Prove that r=0∑ss=1∑nnCsnCr=3n−1.
The sum of the coefficients of the first three terms in the expansion of(x−x23)m,x=0,m being a natural number, is 559. Find the term of the expansion containing x3.
Find the sum ∑0≤i<j≤n−1∑jnCi˙
Write the general term in the expansion of (x2−yx)12,x=0
Show that 24n+4−5n−15,wheren∈N
is divisible by 225.
Find the coefficient of a5b7∈(a−2b)12