Number of Terms in Binomial Expansion

Q. $\mathrm{Number}\mathrm{of}\mathrm{terms}\mathrm{in}\mathrm{the}\mathrm{expansion}\mathrm{of}(a+b{)}^n\mathrm{is}n+1$

1. False
2. True

Q. The number of terms in the expansion of $(x^3+9x^2+27x+27{)}^{25}$ is

1. $25$
2. $26$
3. $75$
4. $76$

Q. If a relation $R$ is defined on the set of integers as follows: $(a,b)\in R\iff a^2+b^2=25$. Then domain of $R$ is

1. $\{0,3,4,5\}$
2. $\{\pm 3,\pm 4,\pm 5\}$
3. $\{0,\pm 3,\pm 4,\pm 5\}$
4. $\{3,4,5\}$

Q. The total number of terms which are dependent on the value of $x$, in the expansion of ${(x^2-2+\frac{1}{x^2})}^n,n\in N$ is equal to

1. $2n+1$
2. $2n$
3. $n$
4. $n+1$

Q. The number of distinct terms in the expansion of $(x+y^2{)}^{13}+(x^2+y{)}^{14}$ is

1. 27
2. 29
3. 28
4. 25

Q. The number of distinct terms in the expansion of $(x+y^2{)}^{13}+(x^2+y{)}^{14}$ is

1. 27
2. 29
3. 28
4. 25