Solve the following
Question: Solve: $\frac{3(y-5)}{4}-4 y=3-\frac{(y-3)}{2}$ Solution: $\frac{3(y-5)}{4}-4 y=3-\frac{(y-3)}{2}$ $\Rightarrow \frac{3 y-15}{4}-4 y=3-\frac{y-3}{2}$ $\Rightarrow \frac{3 y-15-16 y}{4}=3-\frac{y-3}{2} \quad($ L. C.M. of 4 and 1 is 4$)$ $\Rightarrow \frac{-13 y-15}{4}=\frac{6-y+3}{2}$ $\Rightarrow \frac{-13 y-15}{4}=\frac{9-y}{2}$ $\Rightarrow 2(-13 y-15)=4(9-y)$ $\Rightarrow-26 y-30=36-4 y$ $\Rightarrow-26 y+4 y=36+30$ $\Rightarrow-22 y=66$ $\Rightarrow 22 y=-66 \quad$ (multiplying bot...
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Question: Solve: $4-\frac{2(z-4}{3}=\frac{1}{2}(2 z+5)$ Solution: $4-\frac{2(z-4}{3}=\frac{1}{2}(2 z+5)$ $\Rightarrow \frac{12-2(z-4)}{3}=\frac{1(2 z+5)}{2} \quad$ (L. C.M. of 1 and 3 is 3$)$ $\Rightarrow \frac{12-2 z+8}{3}=\frac{2 z+5}{2}$ $\Rightarrow \frac{20-2 z}{3}=\frac{2 z+5}{2}$ $\Rightarrow 2(20-2 z)=3(2 z+5) \quad$ (by cross multiplication) $\Rightarrow 40-4 z=6 z+15$ $\Rightarrow 40-15=6 z+4 z$ $\Rightarrow 25=10 z$ $\Rightarrow 10 z=25 \quad$ (by transposition) $\Rightarrow z=\frac{2...
Read More →Why do we store silver chloride
Question: Why do we store silver chloride in a dark coloured bottle ? Solution: Silver chloride is a white solid. However, it is very senstive to sun light and decomposes in the presence of light to form silver (grey in colour) and chlorine. In order to avoid action by sun light, it is kept in a coloured bottle....
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Question: Solve: $5 x-\frac{1}{3}(x+1)=6\left(x+\frac{1}{30}\right)$ Solution: $5 x-\frac{1}{3}(x+1)=6\left(x+\frac{1}{30}\right)$ $\Rightarrow 5 x-\frac{1(x+1)}{3}=6\left(\frac{30 x+1}{30}\right) \quad($ L.C.M. of 1 and 30 is 30$)$ $\Rightarrow 5 x-\frac{(x+1)}{3}=\frac{30 x+1}{5}$ $\Rightarrow \frac{15 x-x-1}{3}=\frac{30 x+1}{5} \quad$ (L.C.M. of 1 and 3 is 3$)$ $\Rightarrow \frac{14 x-1}{3}=\frac{30 x+1}{5}$ $\Rightarrow 5(14 x-1)=3(30 x+1) \quad$ (by cross multiplication) $\Rightarrow 70 x-5...
Read More →Write a balanced chemical equation for each of
Question: Write a balanced chemical equation for each of the following reactions and also classify them. (a) Lead acetate solution is treated with dilute hydrochloric acid to form lead chloride and acetic acid solution. (b) A piece of sodium metal is added to absolute ethanol to form sodium ethoxide and hydrogen gas. (c) Iron (III) oxide on heating with carbon monoxide gas reacts to form solid iron and liberates carbon dioxide gas. (d) Hydrogen sulphide gas reacts with oxygen gas to form solid s...
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Question: Solve: $\frac{5 x-4}{6}=4 x+1-\frac{3 x+10}{2}$ Solution: $\frac{5 x-4}{6}=4 x+1-\frac{3 x+10}{2}$ $\Rightarrow \frac{5 x-4}{6}=\frac{2(4 x+1)-3 x-10}{2} \quad$ (L.C.M. of 1 and 2 is 2$)$ $\Rightarrow \frac{5 x-4}{6}=\frac{8 x+2-3 x-10}{2}$ $\Rightarrow \frac{5 x-4}{6}=\frac{8 x-3 x+2-10}{2}$ $\Rightarrow \frac{5 x-4}{6}=\frac{5 x-8}{2}$ $\Rightarrow 2(5 x-4)=6(5 x-8)$ $\Rightarrow 10 x-8=30 x-48$ $\Rightarrow 10 x-30 x=-48+8$ $\Rightarrow-20 x=-40$ $\Rightarrow x=\frac{-40}{-20}=2$ $\...
Read More →A substance ‘A’, which is an oxide of a group 2 element,
Question: A substance A, which is an oxide of a group 2 element, is used intensively in the cement industry. This element is present in bones also. On treatment with water it forms a solution which turns red litmus blue. Identify A and also write the chemical reactions involved. Solution: The available information suggests that the substance A is oxide of the element calcium (Ca) which is present in group 2 of the periodic table. Calcium is also a constituent of our bones in the form of calcium ...
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Question: If $\mathrm{y}=\frac{1}{2} \log \left(\frac{1-\cos 2 \mathrm{x}}{1+\cos 2 \mathrm{x}}\right)$, prove that $\frac{\mathrm{dy}}{\mathrm{dx}}=2 \operatorname{cosec} 2 \mathrm{x}$. Solution: Given $y=\frac{1}{2} \log \left(\frac{1-\cos 2 x}{1+\cos 2 x}\right)$ We have $1+\cos (2 \theta)=2 \cos ^{2} \theta$ and $1+\cos (2 \theta)=2 \sin ^{2} \theta$. $\Rightarrow y=\frac{1}{2} \log \left(\frac{2 \sin ^{2} x}{2 \cos ^{2} x}\right)$ $\Rightarrow y=\frac{1}{2} \log \left(\tan ^{2} x\right)$ $\...
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Question: Solve: $\frac{2 x+7}{5}-\frac{3 x+11}{2}=\frac{2 x+8}{3}-5$ Solution: $\frac{2 x+7}{5}-\frac{3 x+11}{2}=\frac{2 x+8}{3}-5$ $\Rightarrow \frac{2 x+7}{5}-\frac{3 x+11}{2}=\frac{2 x+8-15}{3} \quad($ L.C.M. of 3 and 1 is 3$)$ $\Rightarrow 30\left(\frac{2 x+7}{5}\right)-30\left(\frac{3 x+11}{2}\right)=30\left(\frac{2 x+8-15}{3}\right) \quad$ (multiplyin $g$ throughout by 30, which is the L. C.M. of 5,2 and 3$)$ $\Rightarrow 6(2 x+7)-15(3 x+11)=10(2 x+8-15)$ $\Rightarrow 12 x+42-45 x-165=20 ...
Read More →During the reaction of some metals
Question: During the reaction of some metals with dilute hydrochloric acid, following observations are made. (a) Silver metal does not show any change (b) The temperature of the reaction mixture rises when aluminium (Al) is added. (c) The reaction of sodium metal is found to be highly explosive (d) Some bubbles of a gas are seen when lead (Pb) is reacted with the acid. Explain these observations giving suitable reasons. Solution: (a) Silver (Ag) is placed below hydrogen in the activity series. I...
Read More →Which among the following are physical
Question: Which among the following are physical or chemical changes ? (a) Evaporation of petrol (b) Burning of Liquefied Petroleum Gas (LPG) (c) Heating of an iron rod to red hot. (d) Curding of milk (e) Sublimation of solid ammonium chloride Solution: (a) Physical (b) Chemical (c) Physical (d) Chemical (e) Physical....
Read More →Grapes hanging on the plants do not
Question: Grapes hanging on the plants do notferment but after being plucked from the plant, can be fermented. Under what conditions do these grapes ferment ? Is it a chemical or a physical change ? Solution: Grapes hanging on the plants are living in nature. Their immune system does not allow any fermentation. However, when these are plucked, they are no longer living. They undergo fermentation under aerobic conditions (in the absence of air or oxygen). The other factors which favour fermentati...
Read More →Why do fire flies glow at night ?
Question: Why do fire flies glow at night ? Solution: Fire flies are associated with certain protein. In the presence of a enzyme, the protein undergoes aerial oxidation. The reaction is accompanied by emission of light. As a result, fire flies glow at night....
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Question: Solve: $\frac{3 t-2}{4}-\frac{2 t+3}{3}=\frac{2}{3}-t$ Solution: $\frac{3 t-2}{4}-\frac{2 t+3}{3}=\frac{2}{3}-t$ $\Rightarrow \frac{3 t-2}{4}-\frac{2 t+3}{3}=\frac{2-3 t}{3} \quad(3$ is the L.C.M. of 1 and 3$)$ $\Rightarrow 12\left(\frac{3 t-2}{4}\right)-12\left(\frac{2 t+3}{3}\right)=12\left(\frac{2-3 t}{3}\right) \quad($ multiplying throughout by 12, which is the L. C.M. of 4,3 and 3$)$ $\Rightarrow 3(3 t-2)-4(2 t+3)=4(2-3 t)$ $\Rightarrow 9 t-6-8 t-12=8-12 t$ $\Rightarrow 9 t-8 t-6-...
Read More →Ferrous sulphate decomposes with the evolution
Question: Ferrous sulphate decomposes with the evolution of a gas having a characteristic smell of burning sulphur. Write the chemical reaction involved and identify the type of reaction. Solution: The chemical reaction is an example of thermal decomposition reaction. $2 \mathrm{FeSO}_{4}(s) \stackrel{\text { heat }}{\longrightarrow} \mathrm{Fe}_{2} \mathrm{O}_{3}(s)+\mathrm{SO}_{2}(g)+\mathrm{SO}_{3}(g)$ The gases evolved are a mixture of sulphur dioxide and sulphur trioxide. Both have the smel...
Read More →A solution of potassium chloride
Question: A solution of potassium chloride when mixed with silver nitrate solution, an insoluble substance is formed. Write the chemical reaction involved and mention the type of the chemical reaction. Solution: The chemical reaction is : It is an example of the double displacement reaction....
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Question: Solve: $\frac{x-5}{2}-\frac{x-3}{5}=\frac{1}{2}$ Solution: $\frac{x-5}{2}-\frac{x-3}{5}=\frac{1}{2}$ $\Rightarrow 10\left(\frac{x-5}{2}\right)-10\left(\frac{x-3}{5}\right)=10\left(\frac{1}{2}\right)$(multiplying throughout by 10, which is the L.C.M. of 2,2 and 5 ) $\Rightarrow 5(x-5)$ $-2(x-3)=5$ $\Rightarrow 5 x-25-2 x+6=5$ $\Rightarrow 5 x-2 x-25+6=5$ $\Rightarrow 3 x-19=5$ $\Rightarrow 3 x=5+19$ $\Rightarrow 3 x=24$ $\Rightarrow x=$$\frac{24}{3}=8$ $\therefore x=8$...
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Question: If $y=e^{x} \cos x$, prove that $\frac{d y}{d x}=\sqrt{2} e^{x} \cos \left(x+\frac{\pi}{4}\right)$ Solution: Given $y=e^{x} \cos (x)$ On differentiating y with respect to $x$, we get $\frac{d y}{d x}=\frac{d}{d x}\left(e^{x} \cos x\right)$ $\Rightarrow \frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\mathrm{d}}{\mathrm{dx}}\left(\mathrm{e}^{\mathrm{x}} \times \cos \mathrm{x}\right)$ Recall that (uv)' $=v u^{\prime}+u v^{\prime}$ (product rule) $\Rightarrow \frac{d y}{d x}=\cos x \frac{d}{d x}\le...
Read More →Write the balanced chemical equations for the following reactions
Question: Write the balanced chemical equations for the following reactions (a) Sodium carbonate on reaction with hydrochloric acid in equal molar concentrations gives sodium chloride and sodium hydrogen carbonate. (b) Sodium hydrogen carbonate on reaction with hydrochloric acid gives sodium chloride, water and liberates carbon dioxide. (c) Copper sulphate on treatment with potassium iodide precipitates cuprous iodide (Cu2I2), liberates iodine gas and also forms potassium sulphate. Identify the ...
Read More →Identify the oxidising agent (oxidant)
Question: Identify the oxidising agent (oxidant) in the following reactions (a) Pb3O4+ 8HCl - 3PbCl2+ Cl2+ 4H2O (b) 2Ca + O2- 2CaO (c) CuSO4+ Zn - Cu + ZnSO4 (d) V2O5+ 5Ca 2V + 5Ca (e) 3Fe + 4H2O Fe3O4+ 4H2 (f) ZnO + H2 Zn + H2O Solution: (a) Pb3O4 (b) O2 (c) CuSO4 (d) V2O5 (e) H2O (f) ZnO...
Read More →Solve: 3(5x − 7) − 2(9x − 11) = 4(8x − 13) − 17
Question: Solve:3(5x 7) 2(9x 11) = 4(8x 13) 17 Solution: 3(5x 7) 2(9x 11) = 4(8x 13) 17 $\Rightarrow 15 x-21-18 x+22=32 x-52-17$ $\Rightarrow 15 x-18 x-21+22=32 x-69$ $\Rightarrow-3 x+1=32 x-69$ $\Rightarrow 1+69=32 x+3 x$ $\Rightarrow 70=35 x$ $\Rightarrow 35 x=70 \quad(b y$ transposition $)$ $\Rightarrow x=\frac{70}{35}=2$ $\therefore x=2$...
Read More →Which among the following changes are exothermic
Question: Which among the following changes are exothermic or endothermic in nature ? (a) Decomposition of ferrous sulphate (b) Dilution of sulphuric acid (c) Dissolution of sodium hydroxide in water (d) Dissolution of ammonium chloride in water Solution: (a) Endothermic (b) Exothermic (c) Exothermic (d) Endothermic....
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Question: If $y=(x-1) \log (x-1)-(x+1) \log (x+1)$, prove that $\frac{d y}{d x}=\log \left(\frac{x-1}{1+x}\right)$ Solution: Given $y=(x-1) \log (x-1)-(x+1) \log (x+1)$ On differentiating $y$ with respect to $x$, we get $\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\mathrm{d}}{\mathrm{dx}}[(\mathrm{x}-1) \log (\mathrm{x}-1)-(\mathrm{x}+1) \log (\mathrm{x}+1)]$ $\Rightarrow \frac{d y}{d x}=\frac{d}{d x}[(x-1) \log (x-1)]-\frac{d}{d x}[(x+1) \log (x+1)]$ $\Rightarrow \frac{d y}{d x}=\frac{d}{d x}[(x-1) \...
Read More →Complete the missing components/variables
Question: Complete the missing components/variables given as x and y in the following reactions (a) Pb(NO3)2(aq) + 2KI(aq) PbI2(x) + 2KNO3(y) (b) Cu(s) + 2AgNO3(aq) Cu(NO3)2(aq) + x(s) (c) Zn(s) + H2SO4(aq) ZnSO4(x) + H2(g) (d) CaCO3(s) CaO(s) + CO2(g) Solution: (a) x = yellow precipitate, y = (aq) (b) x = 2Ag(s) (c) x = (aq) ; y = (g) (d) x = heat....
Read More →Solve: 15(y − 4) − 2(y − 9) + 5(y + 6) = 0
Question: Solve: 15(y 4) 2(y 9) + 5(y + 6) = 0 Solution: 15(y 4) 2(y 9) + 5(y + 6) = 0 $\Rightarrow 15 y-60-2 y+18+5 y+30=0$ $\Rightarrow 15 y-2 y+5 y-60+18+30=0$ $\Rightarrow 18 y-12=0$ $\Rightarrow 18 y=12$ $\Rightarrow y=\frac{12}{18}=\frac{2}{3}$ $\therefore y=\frac{2}{3}$...
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