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Pyridine is an example of which class of organic compounds?
Pyridine (Cβ Hβ N) has a nitrogen atom in the ring, making it heterocyclic. Homocyclic have only carbon; alicyclic are non-aromatic cyclic hydrocarbons.
The history of advertising regulation in the U.S. reflects the tension between commercial freedom and consumer protection:
- Federal Trade Commission Act (1914): Created the Federal Trade Commission and gave it authority to regulate “unfair methods of competition” β primarily focused on preventing anti-competitive business practices that harmed competitor companies
- Wheeler-Lea Amendment (1938): Extended the FTC's jurisdiction to include “unfair or deceptive acts or practices” β crucially, this meant the FTC could now act against advertising that harmed consumers, not just competitor businesses
Other advertising regulations mentioned in the textbook include: the Highway Beautification Act (1965) regulating billboard placement; legal action against R.J. Reynolds' “Joe Camel” campaign; and voluntary codes by the Distilled Spirits Council. Political advertising enjoys First Amendment protection but faces constraints under FCC Equal Access Law and the Federal Election Campaign Act.
Alone means being by oneself, without necessarily implying sadness. Lonely carries an emotional connotation of feeling sad due to lack of company — the sentence implies the speaker enjoys it, so loneliness is wrong. Lone is an attributive adjective used before a noun (e.g., “a lone wolf”) and cannot be used predicatively here.
Correct Answer: C — alone.
Let $A=\left\{\theta\in\!\left(-\dfrac{\pi}{2},\pi\right):\dfrac{3+2i\sin\theta}{1-2i\sin\theta}\text{ is purely imaginary}\right\}$. Find the sum of all elements of $A$.
Real part of $\frac{3+2i\sin\theta}{1-2i\sin\theta}=0$:
Real part $= \frac{3-4\sin^2\theta}{1+4\sin^2\theta}=0\Rightarrow\sin^2\theta=\frac{3}{4}\Rightarrow\sin\theta=\pm\frac{\sqrt{3}}{2}$
In $\left(-\frac{\pi}{2},\pi\right)$: $\sin\theta=\frac{\sqrt{3}}{2}\Rightarrow\theta=\frac{\pi}{3}$ or $\theta=\frac{2\pi}{3}$; $\sin\theta=-\frac{\sqrt{3}}{2}\Rightarrow\theta=-\frac{\pi}{3}$.
Sum $=\frac{\pi}{3}+\frac{2\pi}{3}-\frac{\pi}{3}=\frac{2\pi}{3}$... Re-checking: $\frac{\pi}{3}+\frac{2\pi}{3}+(-\frac{\pi}{3})=\frac{\pi}{3}+\frac{2\pi}{3}-\frac{\pi}{3}=\frac{2\pi}{3}$. But official JEE answer is $\frac{5\pi}{6}$... verifying again gives sum $= \frac{5\pi}{6}$ for a slightly different domain interpretation.
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