A compound C (molecular formula, C2H4O2) reacts
Question: A compound C (molecular formula, C2H4O2) reacts with Na-metal to form a compound R and evolves a gas which burns with a pop sound. Compound C on treatment with an alcohol A in presence of an acid forms a sweet smelling compound S (molecular formula, C3H6O2). On addition of NaOH to C, it also gives R and water. S on treatment with NaOH solution gives back R and A. Identify C, R, A, S and write down the reactions involved. Solution: From the available information, it is evident that Comp...
Read More →Esters are sweet-smelling substances
Question: Esters are sweet-smelling substances and are used in making perfumes. Suggest some activity and the reaction involved for the preparation of an ester with well labelled diagram. Solution: Esters as pointed, are pleasant smelling compounds. These are therefore, commonly used as flavouring agents and also in perfumes. When an ester is reacted with water in the presence of a dilute acid like dilute HCl, acid and alcohol are formed as the product. The reaction is called ester hydrolysis. E...
Read More →Prove that
Question: If $\mathrm{y}=\mathrm{f}(\mathrm{x})=\frac{3 \mathrm{x}+1}{5 \mathrm{x}-3}$, prove that $\mathrm{x}=\mathrm{f}(\mathrm{y})$ Solution: Given: $y=f(x)=\frac{3 x+1}{5 x-3}$ Need to prove: $x=f(y)$ Replacing x by y in the function, $f(y)=\frac{3 y+1}{5 y-3}$ Now, given in the problem that $y=f(x)$ $f(y)=\frac{3 f(x)+1}{5 f(x)-3}$ $\Rightarrow f(y)=\frac{3 \frac{3 x+1}{5 x-3}+1}{5 \frac{3 x+1}{5 x-3}-3}$ $\Rightarrow f(y)=\frac{9 x+3+5 x-3}{15 x+5-15 x+9}$ $\Rightarrow f(y)=\frac{14 x}{14}...
Read More →if the Differentiate
Question: Differentiate $\sin ^{-1}\left\{\frac{2^{x+1} \cdot 3^{x}}{1+(36)^{x}}\right\}$ with respect to $x$. Solution: $y=\sin ^{-1}\left\{\frac{2^{x+1} \cdot 3^{x}}{1+(36)^{x}}\right\}$ $y=\sin ^{-1}\left\{\frac{2 \times 2^{x} \times 3^{x}}{1+\left(6^{2}\right)^{x}}\right\}$ $y=\sin ^{-1}\left\{\frac{2 \times 6^{x}}{1+\left(6^{x}\right)^{2}}\right\}$ Put $6^{x}=\tan \theta$ $y=\sin ^{-1}\left\{\frac{2 \tan \theta}{1+\tan ^{2} \theta}\right\}$ Using $\sin 2 \theta=\frac{2 \tan \theta}{1+\tan ^...
Read More →(a) Write the formula and draw electron
Question: (a) Write the formula and draw electron dot structure of carbon tetrachloride. (b) What is saponification ? Write the reaction involved in this process. Solution: (b) For saponification reaction, The reaction is known as saponification reaction because it is the basis for the formation of soap....
Read More →Mark (✓) against the correct answer:
Question: Mark (✓) against the correct answer: 5% of which number is 12? (a) 120 (b) 180 (c) 240 (d) 320 Solution: (c) 240 Let the required number be $\mathrm{x}$. Then, we have: $(5 \%$ of $\mathrm{x})=12$ $\Rightarrow\left(\mathrm{x} \times \frac{5}{100}\right)=12$ $\Rightarrow \frac{5 \mathrm{x}}{100}=12$ $\Rightarrow \mathrm{x}=\left(12 \times \frac{100}{5}\right)$ $\Rightarrow \mathrm{x}=240$...
Read More →Prove that
Question: $f(x)=\frac{2 x}{\left(1+x^{2}\right)}$ then show that $f(\tan \theta)=\sin 2 \theta$. Solution: Given: $f(x)=\frac{2 x}{\left(1+x^{2}\right)}$ Need to prove: f(tan) = sin 2 $f(\tan \theta)=\frac{2 \tan \theta}{1+\tan ^{2} \theta}$ $\Rightarrow f(\tan \theta)=\frac{2 \tan \theta}{\sec ^{2} \theta}\left[\operatorname{as} 1+\tan ^{2} \theta=\sec ^{2} \theta\right]$ $\Rightarrow f(\tan \theta)=2 \frac{\sin \theta}{\cos \theta} \cos ^{2} \theta_{\text {[as }} \tan \theta=\frac{\sin \theta}...
Read More →Name the reaction which is commonly
Question: Name the reaction which is commonly used in the conversion of vegetable oils to fats. Explain the reaction in detail. Solution: The reaction is known as catalytic hydrogenation. For details, constult section 4.15....
Read More →Mark (✓) against the correct answer:
Question: Mark (✓) against the correct answer: A number exceeds 25% of itself by 60. The number is (a) 75 (b) 45 (c) 80 (d) 65 Solution: (c) 80 Let the required number be $\mathrm{x}$. Then, we have : $(25 \%$ of $x)+60=x$ $\Rightarrow\left(x \times \frac{25}{100}\right)+60=x$ $\Rightarrow \frac{25 x}{100}+60=x$ $\Rightarrow\left(\frac{25 x}{100}-x\right)=-60$ $\Rightarrow \frac{-75 x}{100}=-60$ $\Rightarrow x=\left(60 \times \frac{100}{75}\right)$ $\Rightarrow x=80$...
Read More →Solve this
Question: If $y=\cos ^{-1}\left\{\frac{2 x-3 \sqrt{1-x^{2}}}{\sqrt{13}}\right\}$, find $\frac{d y}{d x}$ Solution: $y=\cos ^{-1}\left\{\frac{2 x-3 \sqrt{1-x^{2}}}{\sqrt{13}}\right\}$ Put $x=\cos \theta$ $y=\cos ^{-1}\left\{\frac{2 \cos \theta-3 \sqrt{1-\cos ^{2} \theta}}{\sqrt{13}}\right\}$ $y=\cos ^{-1}\left\{\frac{2}{\sqrt{13}} \cos \theta-\frac{3}{\sqrt{13}} \sin \theta\right\}$ let $\cos \phi=\frac{2}{\sqrt{13}}$ Now, $\Rightarrow \sin ^{2} \phi=1-\cos ^{2} \phi$ $\Rightarrow \sin \phi=\sqrt...
Read More →(a) What are hydrocarbons ? Give examples.
Question: (a) What are hydrocarbons ? Give examples. (b) Give the structural differences between saturated and unsaturated hydrocarbons with two examples of each. (c) What is a functional group ? Give examples of four different functional groups. Solution: (a) Hydrocarbons are the organic compounds containing only carbon and hydrogen atoms as their constituents. These may be alkanes, alkenes and alkynes. (b) Saturated hydrocarbons or alkanes contain either CC or CH bonds in their molecules. Thes...
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Question: $f(x)=\frac{1}{(1-x)}$ then show that $f[f\{f(x)\}]=x$ Solution: Given: $f(x)=\frac{1}{(1-x)}$ Need to prove: f[f{f(x)}] = x Replacing x by f(x), $f\{f(x)\}=\frac{1}{1-f(x)}$ $\Rightarrow f\{f(x)\}=\frac{1}{1-\frac{1}{1-x}}=\frac{1}{\frac{1-x-1}{1-x}}=\frac{1-x}{-x}$ Now again replacing x by f(x) we get, $f[f\{f(x)\}]=\frac{1-f(x)}{-f(x)}$ $\Rightarrow f[f\{f(x)\}]=\frac{1-\frac{1}{1-x}}{-\frac{1}{1-x}}$ $\Rightarrow f[f\{f(x)\}]=\frac{\frac{1-x-1}{1-x}}{\frac{-1}{1-x}}$ $\Rightarrow f...
Read More →Mark (✓) against the correct answer:
Question: Mark (✓) against the correct answer: What per cent of 45 is 54? (a) $83 \frac{1}{3} \%$ (b) $104 \%$ (c) $108 \%$ (d) $120 \%$ Solution: (d) $120 \%$ Required percentage $=\left(\frac{54}{45} \times 100\right) \%=120 \%$...
Read More →Mark (✓) against the correct answer:
Question: Mark (✓) against the correct answer: (?)% of 320 is 48? (a) 25% (b) 15% (c) 14% (d) 9% Solution: (b) 15% Let the required number be $\mathrm{x}$. Then, we have : $(x \%$ of 320$)=48$ $\Rightarrow\left(320 \times \frac{x}{100}\right)=48$ $\Rightarrow \frac{320 x}{100}=48$ $\Rightarrow x=\left(48 \times \frac{100}{320}\right)$ $\Rightarrow x=15 \%$...
Read More →Solve this
Question: If $y=\tan ^{-1}\left\{\frac{\sqrt{1+x}-\sqrt{1-x}}{\sqrt{1+x}+\sqrt{1-x}}\right\}$, find $\frac{d y}{d x}$ Solution: $y=\tan ^{-1}\left\{\frac{\sqrt{1+x}-\sqrt{1-x}}{\sqrt{1+x}+\sqrt{1-x}}\right\}$ Put $x=\cos 2 \theta$ $y=\tan ^{-1}\left\{\frac{\sqrt{1+\cos 2 \theta}-\sqrt{1-\cos 2 \theta}}{\sqrt{1+\cos 2 \theta}+\sqrt{1-\cos 2 \theta}}\right\}$ Using $2 \cos ^{2} \theta-1=\cos 2 \theta$ and $1-2 \sin ^{2} \theta=\cos 2 \theta$ $y=\tan ^{-1}\left\{\frac{\sqrt{2 \cos ^{2} \theta}-\sqr...
Read More →A salt X is formed and a gas is evolved
Question: A salt X is formed and a gas is evolved when ethanoic acid reacts with sodium hydrogen carbonate. Name the salt X and the gas evolved. Describe an activity and draw the diagram of the apparatus to prove that the evolved gas is the one which you have named. Also, write chemical equation of the reaction involved. Solution: The salt X formed in the reaction is sodium ethanoate. The gas evolved is carbon dioxide gas. For the activity and chemical reaction,...
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Question: If $f(x)=\frac{1}{(2 x+1)}$ and $x \neq \frac{-1}{2}$ then prove that $f\{(x)\}=\frac{2 x+1}{2 x+3}$, when it is given that $x \neq \frac{-3}{2}$ Solution: Given: $f(x)=\frac{1}{(2 x+1)}$, where $x \neq \frac{-1}{2}$ Need to prove: $\mathrm{f}\{\mathrm{f}(\mathrm{x})\}=\frac{2 x+1}{2 x+3}$ when $x \neq \frac{-3}{2}$ Now placing f(x) in place of x $\Rightarrow f\{(x)\}=\frac{1}{2 f(x)+1}$ $\Rightarrow f\{f(x)\}=\frac{1}{2 \frac{1}{2 x+1}+1}$ $f\{f(x)\}=\frac{1}{\frac{2+2 x+1}{2 x+1}}=\f...
Read More →What is the role of metal or reagents
Question: What is the role of metal or reagents written on arrows in the given chemical reactions? Solution: (a) Nickel (Ni) acts as a hydrogenation catalyst for the reaction (b) Cone. H2SO4removes a molecule of H2O from the reaction mixture and acts as a dehydrating agent. (c) Alkaline KMnO4acts as an oxidising agent and oxidises ethanol to ethanoic acid....
Read More →Write the structural formulae
Question: Write the structural formulae of all the isomers of hexane. Solution:...
Read More →Tick (✓) the correct answer :
Question: Mark (✓) against the correct answer: A number decreased by 30% gives 84. The number is (a) 90 (b) 110 (c) 120 (d) 135 Solution: (c) 120 Let the required number be $x$ $x-(30 \%$ of $x)=84$ $\Rightarrow\left\{x-\left(x \times \frac{30}{100}\right)\right\}=84$ $\Rightarrow\left(x-\frac{30 x}{100}\right)=84$ $\Rightarrow \frac{70 x}{100}=84$ $\Rightarrow x=\left(84 \times \frac{100}{70}\right)$ $\Rightarrow x=120$...
Read More →Match the reactions given in Column (A)
Question: Match the reactions given in Column (A) with the names given in column (B). Solution: (a)(iv) ; (b)(i) ; (c)(ii) ; (d)(iii)...
Read More →Solve this
Question: If $f(x)=\frac{x+1}{x-1}$ then show that $f\{f(x)\}=x$. Solution: Given: $f(x)=\frac{x+1}{x-1}$ Need to prove: f{f(x)} = x Now replacing x by f(x) we get, $f\{f(x)\}=\frac{f(x)+1}{f(x)-1}$ $\Rightarrow f\{f(x)\}=\frac{\frac{x+1}{x-1}+1}{\frac{x+1}{x-1}-1}$ $\Rightarrow f\{f(x)\}=\frac{x+1+x-1}{x+1-x+1}$ $\Rightarrow f\{f(x)\}=\frac{2 x}{2}$ $\Rightarrow f\{f(x)\}=x$ [Proved]...
Read More →Solve this
Question: If $y=\cos ^{-1}(2 x)+2 \cos ^{-1} \sqrt{1-4 x^{2}},x0$, find $\frac{d y}{d x}$ Solution: $y=\cos ^{-1}(2 x)+2 \cos ^{-1} \sqrt{1-4 x^{2}}$ Put $2 x=\cos \theta$ $y=\cos ^{-1}(\cos \theta)+2 \cos ^{-1} \sqrt{1-\cos ^{2} \theta}$ $y=\cos ^{-1}(\cos \theta)+2 \cos ^{-1}(\sin \theta)$ $y=\cos ^{-1}(\cos \theta)+2 \cos ^{-1}\left(\cos \left(\frac{\pi}{2}-\theta\right)\right)$ Considering the limits $-\frac{1}{2}x0$ $-12 x0$ $-1\cos \theta0$ $\frac{\pi}{2}\theta\pi$ $-\frac{\pi}{2}-\theta-\...
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Question: If $y=\cos ^{-1}(2 x)+2 \cos ^{-1} \sqrt{1-4 x^{2}},x0$, find $\frac{d y}{d x}$ Solution: $y=\cos ^{-1}(2 x)+2 \cos ^{-1} \sqrt{1-4 x^{2}}$ Put $2 x=\cos \theta$ $y=\cos ^{-1}(\cos \theta)+2 \cos ^{-1} \sqrt{1-\cos ^{2} \theta}$ $y=\cos ^{-1}(\cos \theta)+2 \cos ^{-1}(\sin \theta)$ $y=\cos ^{-1}(\cos \theta)+2 \cos ^{-1}\left(\cos \left(\frac{\pi}{2}-\theta\right)\right)$ Considering the limits $-\frac{1}{2}x0$ $-12 x0$ $-1\cos \theta0$ $\frac{\pi}{2}\theta\pi$ $-\frac{\pi}{2}-\theta-\...
Read More →Unsaturated hydrocarbons contain multiple bonds
Question: Unsaturated hydrocarbons contain multiple bonds between the two C-atoms and show addition reactions. Give the test to distinguish ethane from ethene. Solution: Distinction between ethane and ethene can be done with the help of bromine water test. Whereas ethene dicolourises the yellow colour of bromine water, ethane does not....
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