Statement I: A concave lens diverges light and does not have a centre of curvature for image formation in the context of lens theory. The centre of curvature is a concept applicable to mirrors, not lenses. Hence, Statement I is false.
Statement II: A concave lens always forms a virtual, erect, and diminished image irrespective of the position of the object. This is a fundamental property of concave lenses. Hence, Statement II is true.
Final Answer: (1) Statement I is false but Statement II is true.
A current element X is connected across an AC source of emf \(V = V_0\ sin\ 2πνt\). It is found that the voltage leads the current in phase by \(\frac{π}{ 2}\) radian. If element X was replaced by element Y, the voltage lags behind the current in phase by \(\frac{π}{ 2}\) radian.
(I) Identify elements X and Y by drawing phasor diagrams.
(II) Obtain the condition of resonance when both elements X and Y are connected in series to the source and obtain expression for resonant frequency. What is the impedance value in this case?
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: