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 $R$ be a relation defined on the set $\{1,2,3,4\times\{1,2,3,4\}$ by \[ R=\{((a,b),(c,d)) : 2a+3b=3c+4d\} \] Then the number of elements in $R$ is
Let \(M = \{1, 2, 3, ....., 16\}\), if a relation R defined on set M such that R = \((x, y) : 4y = 5x – 3, x, y (\in) M\). How many elements should be added to R to make it symmetric.
Which one of the following graphs accurately represents the plot of partial pressure of CS₂ vs its mole fraction in a mixture of acetone and CS₂ at constant temperature?

Let \( \alpha = \dfrac{-1 + i\sqrt{3}}{2} \) and \( \beta = \dfrac{-1 - i\sqrt{3}}{2} \), where \( i = \sqrt{-1} \). If
\[ (7 - 7\alpha + 9\beta)^{20} + (9 + 7\alpha - 7\beta)^{20} + (-7 + 9\alpha + 7\beta)^{20} + (14 + 7\alpha + 7\beta)^{20} = m^{10}, \] then the value of \( m \) is ___________.