Binomial Theorem - Algebra - Mathematics Previous Year Questions

The number of terms in the expansion of \(\left(x^2+y^2\right)^{25}-\left(x^2-y^2\right)^{25}\) after simplification is

The number of terms in the expansion of \((x+y+z)^{10}\) is

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

The value of ${ }^{49} C_3+{ }^{48} C_3+{ }^{47} C_3+{ }^{46} C_3+{ }^{45} C_3+{ }^{45} C_4$ is

In the expansion of $(1+x)^n$ $\frac{C_1}{C_0}+2 \frac{C_2}{C_1}+3 \frac{C_3}{2}+\ldots+n \frac{C_n}{C_{n-1}}$ is equal to

If the number of terms in the binomial expansion of $(2 \mathrm{x}+3)^{3 \mathrm{n}}$ is 22 , then the value of n is