Which of the following represents saponification
Question: Which of the following represents saponification Solution: (d).This is an example of saponification reaction. All other options are not correct....
Read More →If 34% of a number is 85,
Question: If 34% of a number is 85, find the number. Solution: Let the required number be $\mathrm{x}$. Then, we have : $(34 \%$ of $\mathrm{x})=85$ $\Rightarrow\left(\mathrm{x} \times \frac{34}{100}\right)=85$ $\Rightarrow \frac{34 \mathrm{x}}{100}=85$ $\Rightarrow \mathrm{x}=\left(85 \times \frac{100}{34}\right)$ $\Rightarrow \mathrm{x}=250$ Hence, the required number is $250 .$...
Read More →The first member of alkene family is
Question: The first member of alkene family is (a)ethyne (b)ethene (c)propyne (d)ethane Solution: (b)ethene...
Read More →Which of the following does not belong
Question: Which of the following does not belong to the same homologous series ? (a)CH4 (b)C2H6 (c)C3H8 (d)C3H6. Solution: (d).It is an alkene while the rest are all alkane molecules in nature....
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Question: If $y=\sin \left[2 \tan ^{-1}\left\{\sqrt{\frac{1-x}{1+x}}\right\}\right]$, find $\frac{d y}{d x}$ Solution: $y=\sin \left[2 \tan ^{-1}\left\{\sqrt{\frac{1-x}{1+x}}\right\}\right]$ Put $x=\cos 2 \theta$ $y=\sin \left[2 \tan ^{-1}\left\{\sqrt{\frac{1-\cos 2 \theta}{1+\cos 2 \theta}}\right\}\right]$ Using $2 \cos ^{2} \theta-1=\cos 2 \theta$ and $1-2 \sin ^{2} \theta=\cos 2 \theta$ $y=\sin \left[2 \tan ^{-1}\left\{\sqrt{\frac{2 \sin ^{2} \theta}{2 \cos ^{2} \theta}}\right\}\right]$ $y=\s...
Read More →f, g and h are three functions defined from R to R as following:
Question: f, g and h are three functions defined from R to R as following: (i) $f(x)=x^{2}$ (ii) $g(x)=x^{2}+1$ (iii) $h(x)=\sin x$ That, find the range of each function. Solution: (i) $f: R \rightarrow R$ such that $f(x)=x^{2}$ Since the value of x is squared, f(x) will always be equal or greater than 0. $\therefore$ the range is $[0, \infty)$ (ii) $g: R \rightarrow R$ such that $g(x)=x^{2}+1$ Since, the value of $x$ is squared and also adding with $1, g(x)$ will always be equal or greater than...
Read More →The heteroatoms present in
Question: The heteroatoms present in CH3OCH2CH2(Br) are (i) oxygen (ii) carbon (iii) hydrogen (iv) bromine (a)(i) and (ii) (b)(ii) and (iii) (c)(iii) and (iv) (d)(i) and (iv) Solution: (d). Both oxygen (O) and bromine (Br) are heteroatoms.Please remember that apart from C and H atoms, all other atoms present in an organic compound are hetero atoms....
Read More →The IUPAC name of the compound
Question: The IUPAC name of the compound CH3CH2CHO is (a)Propanal (b)Propanone (c)Ethanol (d)Ethanal Solution: (a)Propanal...
Read More →Express: (i) 24% as a fraction;
Question: Express: (i) 24% as a fraction; (ii) 105% as a decimal; (iii) 4 : 5 as a percentage; (iv) 56% as a ratio. Solution: (i) $24 \%=\frac{24}{100}$ $=\frac{6}{25}$ (ii) $105 \%=\frac{105}{100}$ = 1.05 (iii) $4: 5=\frac{4}{5}$ $=\left(\frac{4}{5} \times 100\right) \%$ $=80 \%$ $(i v) 56 \%=\frac{56}{100}$ $=\frac{14}{25}$ $=14: 25$...
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Question: If $y=\sec ^{-1}\left(\frac{x+1}{x-1}\right)+\sin ^{-1}\left(\frac{x-1}{x+1}\right), x0$. Find $\frac{d y}{d x}$ Solution: $y=\sec ^{-1}\left(\frac{x+1}{x-1}\right)+\sin ^{-1}\left(\frac{x-1}{x+1}\right)$ Using, $\sec ^{-1} x=\frac{1}{\cos ^{-1} x}$ $y=\cos ^{-1}\left(\frac{x-1}{x+1}\right)+\sin ^{-1}\left(\frac{x-1}{x+1}\right)$ Using, $\cos ^{-1} x+\sin ^{-1} x=\frac{\pi}{2}$ $y=\frac{\pi}{2}$ Now differentiating w.r.t $x$ we get $\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\mathrm{d}}{\ma...
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Question: Let $f: R \rightarrow R: f(x)=x^{2}$ and $g: C \rightarrow C: g(x)=x^{2}$, where $C$ is the set of all complex numbers. Show that f g. Solution: It is given that $f: R \rightarrow R$ and $g: C \rightarrow C$ Thus, Domain $(f)=R$ and Domain $(g)=C$ We know that, Real numbers $\neq$ Complex Number $\because$, Domain $(\mathrm{f}) \neq$ Domain $(\mathrm{g})$ $\therefore f(x)$ and $g(x)$ are not equal functions $\therefore \mathrm{f} \neq \mathrm{g}$...
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Question: If $y=\sec ^{-1}\left(\frac{x+1}{x-1}\right)+\sin ^{-1}\left(\frac{x-1}{x+1}\right), x0$. Find $\frac{d y}{d x}$ Solution: $y=\sec ^{-1}\left(\frac{x+1}{x-1}\right)+\sin ^{-1}\left(\frac{x-1}{x+1}\right)$ Using, $\sec ^{-1} x=\frac{1}{\cos ^{-1} x}$ $y=\cos ^{-1}\left(\frac{x-1}{x+1}\right)+\sin ^{-1}\left(\frac{x-1}{x+1}\right)$ Using, $\cos ^{-1} x+\sin ^{-1} x=\frac{\pi}{2}$ $y=\frac{\pi}{2}$ Now differentiating w.r.t $x$ we get $\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\mathrm{d}}{\ma...
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Question: If $y=\sec ^{-1}\left(\frac{x+1}{x-1}\right)+\sin ^{-1}\left(\frac{x-1}{x+1}\right), x0$. Find $\frac{d y}{d x}$ Solution: $y=\sec ^{-1}\left(\frac{x+1}{x-1}\right)+\sin ^{-1}\left(\frac{x-1}{x+1}\right)$ Using, $\sec ^{-1} x=\frac{1}{\cos ^{-1} x}$ $y=\cos ^{-1}\left(\frac{x-1}{x+1}\right)+\sin ^{-1}\left(\frac{x-1}{x+1}\right)$ Using, $\cos ^{-1} x+\sin ^{-1} x=\frac{\pi}{2}$ $y=\frac{\pi}{2}$ Now differentiating w.r.t $x$ we get $\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\mathrm{d}}{\ma...
Read More →Which among the following are unsaturated hydrocarbons ?
Question: Which among the following are unsaturated hydrocarbons ? (a)(i) and (iii) (b)(ii) and (iii) (c)(ii) and (iv) (d)(iii) and (iv). Solution: (c).Both (ii) and (iv) are unsaturated in nature....
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Question: Tick (✓) the correct answer What per cent of $\frac{2}{7}$ is $\frac{1}{35} ?$ (a) 2.5% (b) 10% (c) 20% (d) 25% Solution: (a)x Required percentage $=\left(\frac{1}{35} \times \frac{7}{2} \times 100\right) \%=10 \%$...
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Question: If $y=\tan ^{-1}\left(\frac{2 x}{1-x^{2}}\right)+\sec ^{-1}\left(\frac{1+x^{2}}{1-x^{2}}\right), x0$, prove that $\frac{d y}{d x}=\frac{4}{1+x^{2}}$ Solution: $y=\tan ^{-1}\left(\frac{2 x}{1-x^{2}}\right)+\sec ^{-1}\left(\frac{1+x^{2}}{1-x^{2}}\right)$ Using, $\sec ^{-1} x=\frac{1}{\cos ^{-1} x}$ $y=\tan ^{-1}\left(\frac{2 x}{1-x^{2}}\right)+\cos ^{-1}\left(\frac{1-x^{2}}{1+x^{2}}\right)$ Put $x=\tan \theta$ $y=\tan ^{-1}\left(\frac{2 \tan \theta}{1-\tan ^{2} \theta}\right)+\cos ^{-1}\...
Read More →Tick (✓) the correct answer:
Question: Tick (✓) the correct answer: x% ofyisy% of? (a)x (b) 100x (c) $\frac{x}{100}$ (d) $\frac{y}{100}$ Solution: (a)x Let the required number be $z$. Then, we have: $x \%$ of $y=y \%$ of $z$ $\Rightarrow\left(y \times \frac{x}{100}\right)=\left(z \times \frac{y}{100}\right)$ $\Rightarrow \frac{y x}{100}=\frac{z y}{100}$ $\Rightarrow z=\left(\frac{y x}{100} \times \frac{100}{y}\right)$ $\Rightarrow z=x$...
Read More →Which of the following is not a straight chain hydrocarbon ?
Question: Which of the following is not a straight chain hydrocarbon ? Solution: (d).Please note that the continuous chains of carbon atoms whether straight or bent are not branched in nature....
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Question: If $y=\cot ^{-1}\left\{\frac{\sqrt{1+\sin x}+\sqrt{1-\sin x}}{\sqrt{1+\sin x}-\sqrt{1-\sin x}}\right\}$, show that $\frac{d y}{d x}$ is independent of $x$. Solution: $y=\cot ^{-1}\left\{\frac{\sqrt{1+\sin x}+\sqrt{1-\sin x}}{\sqrt{1+\sin x}-\sqrt{1-\sin x}}\right\}$ Multiplying numerator and denominator $y=\cot ^{-1}\left\{\frac{(\sqrt{1+\sin x}+\sqrt{1-\sin x})^{2}}{(\sqrt{1+\sin x}-\sqrt{1-\sin x})(\sqrt{1+\sin x}+\sqrt{1-\sin x})}\right\}$ $y=\cot ^{-1}\left\{\frac{1+\sin x+1-\sin x...
Read More →The correct electron dot-structure of a water molecule is
Question: The correct electron dot-structure of a water molecule is Solution: (c)....
Read More →Carbon forms four covalent bonds by sharing
Question: Carbon forms four covalent bonds by sharingits four valence electrons with four univalent atoms e.g. hydrogen. After the formation of four bonds, carbon attains the electronic configuration of (a)helium (b)neon (c)argon (d)krypton Solution: (b).The compound formed is methane (CH4). In this, carbon atom has a complete octet and configuration of neon which is a noble gas element....
Read More →Tick (✓) the correct answer:
Question: Tick (✓) the correct answer: One-third of 1206 is what per cent of 134? (a) 3% (b) 30% (c) 20% (d) 300% Solution: (d) 300% Required percentage $=\left(\frac{1206}{3} \times \frac{1}{134} \times 100\right) \%=300 \%$...
Read More →Differentiate the following with respect to x :
Question: Differentiate the following with respect to $x$ : $\cot ^{-1}\left(\frac{1-x}{1+x}\right)$ Solution: $y=\cot ^{-1}\left(\frac{1-x}{1+x}\right)$ Put $x=\tan \theta$ $y=\cot ^{-1}\left(\frac{1-\tan \theta}{1+\tan \theta}\right)$ $y=\cot ^{-1}\left(\frac{\tan \left(\frac{\pi}{4}\right)-\tan \theta}{1+\tan \left(\frac{\pi}{4}\right) \tan \theta}\right)$ Using, $\tan (x-y)=\left(\frac{\tan x-\tan y}{1+\tan x \tan y}\right)$ $y=\cot ^{-1}\left(\tan \left(\frac{\pi}{4}-\theta\right)\right)$ $...
Read More →Mineral acids are stronger acids than carboxylic acids because
Question: Mineral acids are stronger acids than carboxylic acids because (i) mineral acids are completely ionised (ii) carboxylic acids are completely ionised (iii) mineral acids are partially ionised (iv) carboxylic acids are partially ionised (a)(i) and (iv) (b)(ii) and (iii) (c)(i) and (ii) (d)(iii) and (iv) Solution: (a).Mineral acids like HCl are completely ionised in solvent like water whereas carboxylic acids such as CH3COOH are only partially ionised....
Read More →Tick (✓) the correct answer :
Question: Tick (✓) the correct answer: 0.05 is what per cent of 20? (a) 25% (b) 2.5% (c) 0.25% (d) 0.025% Solution: (c) 0.25% Required percentage $=\left(\frac{0.05}{20} \times 100\right) \%=0.25 \%$...
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