If f(x) is defined on domain [0, 1], then f(2 sin x) is defined on
\(\bigcup\limits_{n∈I}\){[2nπ,2nπ+π/6]\(\bigcup\)[2nπ+\(\frac{5π}{6}\),(2n+1)π]}
\(\bigcup\limits_{n∈I}\)[2nπ,2nπ+\(\fracπ6\)]
\(\bigcup\limits_{n∈I}\)[2nπ+\(\frac{5π}{6}\),(2n+1)π]
None of these
Let $ P_n = \alpha^n + \beta^n $, $ n \in \mathbb{N} $. If $ P_{10} = 123,\ P_9 = 76,\ P_8 = 47 $ and $ P_1 = 1 $, then the quadratic equation having roots $ \alpha $ and $ \frac{1}{\beta} $ is:
Let \( T_r \) be the \( r^{\text{th}} \) term of an A.P. If for some \( m \), \( T_m = \dfrac{1}{25} \), \( T_{25} = \dfrac{1}{20} \), and \( \displaystyle\sum_{r=1}^{25} T_r = 13 \), then \( 5m \displaystyle\sum_{r=m}^{2m} T_r \) is equal to: