Class 11

Math

JEE Main Questions

Binomial Theorem

Find the 7th term in the expansion of $(54x +2x5 )_{8}˙$

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If the 3rd, 4th , 5th and 6th term in the expansion of $(x+α)_{n}$ be, respectively, $a,b,candd,$ prove that $c_{2}−bdb_{2}−ac =3c5a ˙$

Find n, if the ratio of the fifth term from the beginning to the fifth term from the end in the expansion of $(42 +43 1 )_{n}$ is $6 :1$

Prove that the coefficient of $x_{r}$ in the expansion of $(1−2x)_{−21}$ is $(2_{r})(r!)_{2}2r! $

Write the general term in the expansion of $(x_{2}−y)_{6}$.

Prove that $1C_{1} −2C_{2} +3C_{3} −4C_{4} ++n(−1)_{n−1} C_{n}=1+21 +31 ++n1 ˙$

If the sum of coefficient of first half terms in the expansion of $(x+y)_{n}is256$ , then find the greatest coefficient in the expansion.

Find the value of $_{4}nC_{0}+_{4n}C_{4}+_{4n}C_{8}++_{4n}C_{4n}$ .

Find (i) the last digit, (ii) the last two digits, and (iii) the last three digits of $17_{256}˙$