91Ó°ÊÓ

\(2^{n}-1\) gives the set of all odd natural numbers for all \(\mathrm{n} \in \mathrm{N}\). Comment on the given statement. (1) True for all values of \(\mathrm{n}\) (2) False (3) True for only odd values of \(\mathrm{n}\) (4) True for only prime values of \(\mathrm{n}\)

The number of rational terms in the expansion of \(\left(x^{\frac{1}{5}}+y^{\frac{1}{10}}\right)^{45}\) is (1) 5 (2) 6 (3) 4 (4) 7

Find the coefficient of the independent term in the expansion of \(\left(\mathrm{x}^{\frac{1}{2}}+7 \mathrm{x}^{-\frac{1}{3}}\right)^{10}\). (1) \({ }^{16} \mathrm{C}_{4} 7^{4}\) (2) \({ }^{19} \mathrm{C}_{6} 7^{6}\) (3) \({ }^{10} \mathrm{C}_{6} 7^{5}\) (4) \({ }^{10} \mathrm{C}_{4} 7^{7}\)

The ratio of the coefficients of \(\mathrm{x}^{4}\) to that of the term independent of \(\mathrm{x}\) in the expansion of \(\left(x^{2}+\frac{9}{x^{2}}\right)^{15}\) is (1) \(1: 6\) (2) \(3: 8\) (3) \(1: 10\) (4) \(1: 8\)

Find the value of \((98)^{4}\) by using the binomial theorem. (1) 92236846 (2) 92236816 (3) 92236886 (4) 92236806

The sum of the first three coefficients in the expansion \(\left(x+\frac{1}{y}\right)^{n}\) is \(22 .\) Find the value of \(n\). (1) \(\underline{8}\) (2) 7 (3) 6 (4) 5