Class 12

Math

Algebra

Binomial Theorem

In the expansion of $(1+x)_{70}$, the sum of coefficients of odd powers of $x$ is

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If $(1+x−2x_{2})_{6}=1+a_{1}x+a_{2}x_{12}++a_{12}x_{12},$ then find the value of $a_{2}+a_{4}+a_{6}++a_{12}˙$

The smallest integer larger than $(3 +2 )_{6}$ is

Find the greatest coefficient in the expansion of $(1+2x/3)_{15}˙$ .

Consider the expansion of $(a+b+c+d)_{6}$. Then the sum of all the coefficients of the term Which contains all of $a,b,c,$ and d is

Prove that $k=0∑n (−1)_{k}.._{3n}C_{k}=(−1)_{n}.._{3n−1}C_{n}$

In $(2_{31}+3_{31}1 )_{n}$ if the ratio of 7th term from the beginning to the 7th term from the end is 1/6, then find the value of $n˙$

Find the coefficient of $x_{12}$ in expansion of $(1−x_{2}+x_{4})_{3}(1−x)_{7}$.

If $a_{1},a_{2},a_{3},a_{4}$ are the coefficient of any four consecutive term in the expansion of $(1+x)_{n}$, then prove that $a_{1}+a_{2}a_{1} +a_{3}+a_{4}a_{3} =a_{2}+a_{3}2a_{2} $.