Matching Explanation: -
(A) Carbon tetrachloride: Used as a fire extinguisher in the past due to its non-flammable properties. Hence, it matches with (III).
(B) Methylene chloride: Commonly used as a paint remover due to its ability to dissolve paint and coatings. Hence, it matches with (I).
(C) DDT: Known for its use as a non-biodegradable insecticide, which has been widely restricted due to environmental concerns. Hence, it matches with (IV).
(D) Freons: These are used as refrigerants and in air conditioners due to their heat absorption and transfer properties. Hence, it matches with (II).
Conclusion: The correct matching is:
• (A)-(III)
• (B)-(I)
• (C)-(IV)
• (D)-(II)
Given below are two statements:
Statement I: A homoleptic octahedral complex, formed using monodentate ligands, will not show stereoisomerism
Statement II: cis- and trans-platin are heteroleptic complexes of Pd.
In the light of the above statements, choose the correct answer from the options given below
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: