
- **Option A:** In a purely capacitive circuit, the voltage (V) lags the current (I) by 90°. Therefore, **A-I** is correct.
- **Option B:** In a purely inductive circuit, the voltage (V) leads the current (I) by 90°. Therefore, **B-II** is correct.
- **Option C:** In an LCR series circuit at resonance, the inductive reactance (XL) equals the capacitive reactance (XC), resulting in a purely resistive behavior where the voltage and current are in phase. Therefore, **C-III** is correct.
- **Option D:** In a general LCR series circuit, the voltage and current are out of phase by an angle θ, which depends on the relative values of XL and XC. Therefore, **D-IV** is correct.
**Answer:** A-I, B-II, C-III, D-IV (Option 4)
A laser beam has intensity of $4.0\times10^{14}\ \text{W/m}^2$. The amplitude of magnetic field associated with the beam is ______ T. (Take $\varepsilon_0=8.85\times10^{-12}\ \text{C}^2/\text{N m}^2$ and $c=3\times10^8\ \text{m/s}$)
Let \( ABC \) be a triangle. Consider four points \( p_1, p_2, p_3, p_4 \) on the side \( AB \), five points \( p_5, p_6, p_7, p_8, p_9 \) on the side \( BC \), and four points \( p_{10}, p_{11}, p_{12}, p_{13} \) on the side \( AC \). None of these points is a vertex of the triangle \( ABC \). Then the total number of pentagons that can be formed by taking all the vertices from the points \( p_1, p_2, \ldots, p_{13} \) is ___________.
Consider the following two reactions A and B: 
The numerical value of [molar mass of $x$ + molar mass of $y$] is ___.
Consider an A.P. $a_1,a_2,\ldots,a_n$; $a_1>0$. If $a_2-a_1=-\dfrac{3}{4}$, $a_n=\dfrac{1}{4}a_1$, and \[ \sum_{i=1}^{n} a_i=\frac{525}{2}, \] then $\sum_{i=1}^{17} a_i$ is equal to