Binomial Theore...

The total number of terms in the expansion of $$(x+y)^{50}+(x-y)^{50}$$ is

$${ _{  }^{ 15 }{ C } }_{ 3 }+{ _{  }^{ 15 }{ C } }_{ 5 }+....+{ _{  }^{ 15 }{ C } }_{ 15 }$$ will be equal to

The number of terms that are integers in the binomial expansion of $$(\sqrt {7} + \sqrt [3]{5})^{35}$$ is

[AS 1] If $$A = \dfrac{1}{3} B \, and \, B = \dfrac{1}{2} C$$, then A : B : C = .. 

The expression $$^{n}\textrm{C}_{0}+4\ ^{n}\textrm{C}_{1}+4^{2}\ ^{n}\textrm{C}_{2}+..........+4^{n}\ ^{n}\textrm{C}_{n}$$, equals 

The $$3rd$$ term of $${\left( {3x - \dfrac{{{y^3}}}{6}} \right)^4}$$ is

The number of zeroes at the end of $$(101)^{11}-1$$ is

The middle terms in the expansion of $$(x^{2}-a^{2})^{5}$$ is

If sum of the coefficients in the expansion of $$(2+3cx+c^2x^2)^{12}$$ vanishes, then $$c$$ equals to

$$^{100}C_{0}-^{100}C_{2}+^{100}C_{4}+^{100}C_{8}-........+^{100}C_{100}=$$__