JEE Main Questions
Find the coefficient of x4
in the expansion of (2−x+3x2)6˙
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Show that 24n+4−5n−15,wheren∈N
is divisible by 225.
Show that no three consecutive binomial coefficients can be in (i) G.P., (ii) H.P.
Find the sum C0−C2+C4−C6+,whereCr=∧6Cr=nCr
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.
Find the cube root of 217, correct to two decimal places.
If the middle term in the binomial expansion of (x1+xsinx10)
is equal to 863,
find the value of x˙
The first three terms in the expansion of (1+ax)n(n=0)
Then find the value of aandn˙
Find the sum of the coefficients of all the integral powers of x
in the expansion of (1+2x)40˙