List-I Alkali Metal | List-II Emission Wavelength in nm |
---|---|
(A) Li | (I) 589.2 |
(B) Na | (II) 455.5 |
(C) Rb | (III) 670.8 |
(D) Cs | (IV) 780.0 |
This is a fact-based question regarding the emission wavelengths of alkali metals. The correct matches based on known data are:
(A) Li – (III) 670.8 nm
(B) Na – (I) 589.2 nm
(C) Rb – (IV) 780.0 nm
(D) Cs – (II) 455.5 nm
Let \( S = \left\{ m \in \mathbb{Z} : A^m + A^m = 3I - A^{-6} \right\} \), where
\[ A = \begin{bmatrix} 2 & -1 \\ 1 & 0 \end{bmatrix} \]Then \( n(S) \) is equal to ______.
Let \( T_r \) be the \( r^{\text{th}} \) term of an A.P. If for some \( m \), \( T_m = \dfrac{1}{25} \), \( T_{25} = \dfrac{1}{20} \), and \( \displaystyle\sum_{r=1}^{25} T_r = 13 \), then \( 5m \displaystyle\sum_{r=m}^{2m} T_r \) is equal to: