Identify the correct matches
Column – I | Column – II |
A. Tetany | i. Autoimmune disorder |
B. Myasthenia gravis | ii. Decreased bone mass |
C. Gout | iii. Rapid muscle spasms |
D. Osteoporosis | iv. Accumulation of uric acid in joints |
The range of the real valued function \( f(x) =\) \(\sin^{-1} \left( \frac{1 + x^2}{2x} \right)\) \(+ \cos^{-1} \left( \frac{2x}{1 + x^2} \right)\) is:
If \(3A = \begin{bmatrix} 1 & 2 & 2 \\[0.3em] 2 & 1 & -2 \\[0.3em] a & 2 & b \end{bmatrix}\) and \(AA^T = I\), then\(\frac{a}{b} + \frac{b}{a} =\):
\(\begin{vmatrix} a+b+2c & a & b \\[0.3em] c & b+c+2c & b \\[0.3em] c & a & c+a2b \end{vmatrix}\)