| List - I | List - II | ||
| (P) | If a = 0, b = 1, c = 0 and d = 0, then | (1) | h is one-one. |
| (Q) | If a = 1, b = 0, c = 0 and d = 0, then | (2) | h is onto. |
| (R) | If a = 0, b = 0, c = 1 and d = 0, then | (3) | h is differentiable on \(\R\) |
| (S) | If a = 0, b = 0, c = 0 and d = 1, then | (4) | the range of h is [0, 1]. |
| (5) | the range of h is {0, 1}. | ||
Let \( f(x) = \sqrt{4 - x^2} \), \( g(x) = \sqrt{x^2 - 1} \). Then the domain of the function \( h(x) = f(x) + g(x) \) is equal to:
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 ___________.