Class 11

Math

JEE Main Questions

Binomial Theorem

If $pandq$ are ositive, then prove that the coefficients of $x_{p}andx_{q}$ in the expansion of $(1+x)_{p+q}$ will be equal.

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if the sum of coefficients in the expansion of $(x−2y+3z)_{n}$ is 128, then find the greatest coefficients in the expansion of $(1+x)_{n}˙$

Find the condition for which the formula $(a+b)_{m}a_{m}+ma_{m−1}b+1×2m(m−1) a_{m−2}b_{2}+$ holds.

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 $6 :1.$

Find a, b and n in the expansion of $(a+b)_{n}$if the first three terms of the expansion are 729, 7290 and 30375, respectively.

Find the coefficient of $x_{5}$ in the expansioin of the product $(1+2x)_{6}(1−x)_{7}˙$

Find the $r_{th}$term from the end in the expansion of $(x+a)_{n}$.

Find the coefficient of $a_{3}b_{4}c_{5}$ in the expansion of $(bc+ca+ab)_{6}˙$

Show that no three consecutive binomial coefficients can be in (i) G.P., (ii) H.P.