Relation between Coefficient and Indices of x and y

Q.

What is a rank in solid state?

Q.

Why is crystal structure isotropic although unit cells are anisotropic?

Q. If the coefficients of $r^{\text{th}},(r+1{)}^{\text{th}}\text{and}(r+2{)}^{\text{th}}$ terms in the expansion of $(1+x{)}^{14}$ are in A.P., then value $r$ can be

1. $5$
2. $12$
3. $10$
4. $9$

Q. If the coefficients of $r^{\text{th}},(r+1{)}^{\text{th}}\text{and}(r+2{)}^{\text{th}}$ terms in the expansion of $(1+x{)}^{14}$ are in A.P., then value $r$ can be

1. $5$
2. $12$
3. $10$
4. $9$

Q. If the coefficients of second, third and fourth term in the expansion of $(1+x{)}^{2n}$ are in A.P, then $2n^2-9n+7$ is equal to

1. -1
2. \N
3. 1
4. 3/2

Q. The coefficients of three consecutive terms of $(1+x{)}^{n+5}$ are in the ratio $5:10:14$. Then $n=$ ___

Q. If the coefficients of $5^{th},6^{th}$ and $7^{th}$ terms in the expansion of $(1+x{)}^n$ be in A.P, then n =

1. 7 only
2. 14 only
3. 7 or 14
4. None of these

Q. If the coefficients of second, third and fourth term in the expansion of $(1+x{)}^{2n}$ are in A.P, then $2n^2-9n+7$ is equal to

1. -1
2. \N
3. 1
4. 3/2

Q. Let $m$ be the smallest positive integer such that the coefficient of $x^2$ in the expansion of $(1+x{)}^2+(1+x{)}^3+...+(1+x{)}^{49}+(1+mx{)}^{50}\text{is}(3n+1{)}^{51}{C}_3$ for some positive interger $n$. Then the value of $n$ is ___