Step 1: Understanding Analytical Techniques - Various techniques are used in pharmaceutical analysis to identify and quantify impurities. The most commonly used techniques include:
- Nuclear Magnetic Resonance (NMR): Primarily used for structural elucidation of molecules.
- Mass Spectrometry (MS): Highly sensitive for identifying unknown compounds but less commonly used for routine impurity quantification.
- Infrared Spectroscopy (IR): Useful for functional group identification but not ideal for impurity quantification.
- High-Performance Liquid Chromatography (HPLC): Widely used for both qualitative and quantitative impurity profiling in drug substances.
Step 2: Evaluating the Options
- (A) NMR → Useful for structural identification but not commonly used for routine impurity quantification.
- (B) MS → Highly sensitive for detecting trace impurities but often used in conjunction with other techniques like HPLC.
- (C) IR → Identifies functional groups but is not effective for quantifying impurities.
- (D) HPLC → The best choice for identifying and quantifying impurities due to its high sensitivity and resolution.
Step 3: Selecting the Correct Answer - HPLC is the preferred method for impurity profiling in pharmaceuticals as it allows for separation, identification, and quantification of known and unknown impurities.
A closed-loop system has the characteristic equation given by: $ s^3 + k s^2 + (k+2) s + 3 = 0 $.
For the system to be stable, the value of $ k $ is:
A digital filter with impulse response $ h[n] = 2^n u[n] $ will have a transfer function with a region of convergence.