List-I (Compound / Species) | List-II (Shape / Geometry) |
---|---|
(A) \(SF_4\) | (I) Tetrahedral |
(B) \(BrF_3\) | (II) Pyramidal |
(C) \(BrO_{3}^{-}\) | (III) See saw |
(D) \(NH^{+}_{4}\) | (IV) Bent T-shape |
(A) SF$_4$: The sulfur atom in SF$_4$ undergoes sp$^3$d hybridization, resulting in a see-saw geometry.
(B) BrF$_3$: Bromine in BrF$_3$ exhibits sp$^3$d hybridization with two lone pairs, resulting in a bent T-shape geometry.
(C) BrO$_3^-$: The bromine atom in BrO$_3^-$ is sp$^3$ hybridized, resulting in a pyramidal geometry.
(D) NH$_4^+$: The nitrogen atom in NH$_4^+$ undergoes sp$^3$ hybridization, forming a tetrahedral geometry.
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 one focus of the hyperbola $ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 $ be at $ (\sqrt{10}, 0) $, and the corresponding directrix be $ x = \frac{\sqrt{10}}{2} $. If $ e $ and $ l $ are the eccentricity and the latus rectum respectively, then $ 9(e^2 + l) $ is equal to:
Let $ P_n = \alpha^n + \beta^n $, $ n \in \mathbb{N} $. If $ P_{10} = 123,\ P_9 = 76,\ P_8 = 47 $ and $ P_1 = 1 $, then the quadratic equation having roots $ \alpha $ and $ \frac{1}{\beta} $ is: