Middle Terms

Q. If $n$ is even and the middle term in the expansion of ${(x^2+\frac{1}{x})}^n$ is $924x^6$, then $n$ is equal to

1. $10$
2. $12$
3. $14$
4. $6$

Q. The coefficient of the term independent of $a$ in the expansion of ${(1+\sqrt{a}+\frac{1}{\sqrt{a}-1})}^{-30}$ is

1. ${}^{30}{C}_{20}$
2. $0$
3. ${}^{30}{C}_{10}$
4. None of these

Q. If the middle term in the expansion of ${(\frac{p}{2}+2)}^8$ is $1120$, then the value of $p$ is

1. $\pm 2$
2. $\pm 4$
3. $\pm 1$
4. $\pm 6$

Q. If the middle term in the expansion of ${(\frac{x}{2}+2)}^8$is $1120$; then $x\in R$ is equal to

1. $-2$
2. $3$
3. $-3$
4. $2$

Q. In the expansion of ${(7^{\frac{1}{3}}+{11}^{\frac{1}{9}})}^{6561}$

1. There are exactly $730$ rational terms
2. There are exactly $5831$ irrational terms
3. The term which involves greatest binomial coefficients is irrational
4. The term which involves greatest binomial coefficients is rational

Q.

If the coefficient of the middle term in the expansion of $(1+x{)}^{2n+2}$ is p and the coefficients of middle terms in the expansion of $(1+x{)}^{2n+1}$ are q and r, then

1. p + q = r

2. p + r = q

3. p = q + r

4. p + q + r = 0

Q. If the coefficient of the middle term in the expansion of $(1+x{)}^{2n+2}$ is $\alpha$ and the coefficients of middle terms in the expansion of $(1+x{)}^{2n+1}$ are $\beta$ and $\gamma$, then relation between $\alpha ,\beta$ and $\gamma$ is-

1. $\alpha +\beta +\gamma =0$
2. $\alpha =\beta +\gamma$
3. $\beta =\alpha +\gamma$
4. $\gamma =\beta +\alpha$