To determine the total number of sigma (\(\sigma\)) and pi (\(\pi\)) bonds in 2-oxohex-4-ynoic acid, analyze the structure:
\[\text{HO-CH}_2 - \text{C(=O)} - \text{CH}_2 - \text{C} \equiv \text{C} - \text{CH}_3\]
Count the sigma bonds (\(\sigma\)-bonds):
\(6 \, \sigma\)-bonds in carbon-hydrogen (C-H) bonds.
\(5 \, \sigma\)-bonds in carbon-carbon (C-C) single bonds.
\(2 \, \sigma\)-bonds in carbon-oxygen (C=O and C-O) bonds.
\(1 \, \sigma\)-bond in the hydroxyl (O-H) group.
Total \(\sigma\)-bonds: \(6 + 5 + 2 + 1 = 14\)
Count the pi bonds (\(\pi\)-bonds):
\(1 \, \pi\)-bond in the C=O bond.
\(3 \, \pi\)-bonds in the C \(\equiv\) C triple bond (\(2 \, \pi\)-bonds in the triple bond).
Total \(\pi\)-bonds: \(1 + 3 = 4\)
Therefore, the total number of bonds (sigma and pi) is:
\[14 + 4 = 18\]
Identify the correct orders against the property mentioned:
A. H$_2$O $>$ NH$_3$ $>$ CHCl$_3$ - dipole moment
B. XeF$_4$ $>$ XeO$_3$ $>$ XeF$_2$ - number of lone pairs on central atom
C. O–H $>$ C–H $>$ N–O - bond length
D. N$_2$>O$_2$>H$_2$ - bond enthalpy
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: