Mark (✓) against the correct answer:
Question: Mark (✓) against the correct answer: What per cent of $\frac{2}{9}$ is $\frac{1}{45} ?$ (a) $2.5 \%$ (b) $5 \%$ (c) $7.5 \%$ (d) $10 \%$ Solution: (d) $10 \%$ Required percentage $=\left(\frac{1}{45} \times \frac{9}{2} \times 100\right) \%=10 \%$...
Read More →Catenation is the ability of an atom to form bonds
Question: Catenation is the ability of an atom to form bonds with other atoms of the same element. It is exhibited by both carbon and silicon. Compare the ability of catenation of the two elements. Give reasons. Solution: The tendency to show catenation is very small in case of Si as compared to C although both the elements belong to the same group (14). This is because of greater atomic size of Si atom (118 pm) than that of carbon (77 pm). As a result, the strength of SiSi bond is less as compa...
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Question: If $f(x)=x^{3}-\frac{1}{x^{3}}$ then show that $f(x)+f\left(\frac{1}{x}\right)=0$ Solution: Given: $f(x)=x^{3}-\frac{1}{x^{3}}$ Need to prove: $f(x)+f\left(\frac{1}{x}\right)=0$ Replacing $x$ by $\frac{1}{x}$ we get, $f\left(\frac{1}{x}\right)=\frac{1}{x^{3}}-\frac{1}{\frac{1}{x^{3}}}=\frac{1}{x^{3}}-x^{3}$ Now according to the problem, $f(x)+f\left(\frac{1}{x}\right)=x^{3}-\frac{1}{x^{3}}+\frac{1}{x^{3}}-x^{3}$ $\Rightarrow f(x)+f\left(\frac{1}{x}\right)=0$ [Proved]...
Read More →In electron dot structure, the valence shell electrons
Question: In electron dot structure, the valence shell electrons are represented by crosses or dots. (a) The atomic number of chlorine is 17. Write its electronic configuration (b) Draw the electron dot structure of chlorine molecule. Solution: (a) 2, 8, 7...
Read More →Carbon, Group (14) element in the Periodic Table,
Question: Carbon, Group (14) element in the Periodic Table, is known to form compounds with many elements. Write an example of a compound formed with (a) chlorine (Group 17 of Periodic Table) (b) oxygen (Group 16 of Periodic Table) Solution: (a) The compound is carbon tetrachloride (CCl4) (b) The compound is carbon dioxide (CO2)...
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Question: If $f(x)=\frac{x-1}{x+1}$ then show that (i) $f\left(\frac{1}{x}\right)=-f(x)$ (ii) $f\left(\frac{-1}{x}\right)=\frac{-1}{f(x)} f$ Solution: Given: $f(x)=\frac{x-1}{x+1}$ (i) Need to prove: $f\left(\frac{1}{x}\right)=-f(x)$ Now replacing $x$ by $\frac{1}{x}$ we get, $f\left(\frac{1}{x}\right)=\frac{\frac{1}{x}-1}{\frac{1}{x}+1}$ $\Rightarrow f\left(\frac{1}{x}\right)=\frac{1-x}{1+x}$ $\Rightarrow f\left(\frac{1}{x}\right)=\frac{-(x-1)}{(x+1)}=-f(x)$ [Proved] (ii) Need to prove: $f\left...
Read More →Ethene is formed when ethanol at 443 K
Question: Ethene is formed when ethanol at 443 K is heated with excess of concentrated sulphuric acid. What is the role of sulphuric acid in this reaction ? Write the balanced chemical equation of this reaction. Solution: Concentrated sulphuric acid acts as a dehydrating agent in the reaction. Ethene is formed as the...
Read More →A gas is evolved when ethanol reacts with sodium.
Question: A gas is evolved when ethanol reacts with sodium. Name the gas evolved and also write the balanced chemical equation for the reaction involved. Solution: The gas evolved is hydrogen. The balanced chemical equation for the reactibn is :...
Read More →Intake of small quantity of methanol
Question: Intake of small quantity of methanol can be lethal. Comment. Solution: From methanol: These days ethanoic acid is manufactured by the reaction between methanol and carbon monoxide in the presence of iodine- rhodium (I2 Rh) catalyst mixture....
Read More →How is ethene prepared from ethanol ?
Question: How is ethene prepared from ethanol ? Give the reaction involved in it. Solution: From ethanol: This method involves the slow oxidationof a dilute solution of ethanol (10-15 per cent) by oxygen present in air in the presence of an enzyme acetobactor. The acid obtained is in the form of dilute solution called vinegar. We have also studied under ethanol that it gets oxidised to ethanoic acid in the presence of dilute solution of alkaline KMnO4or acidified K2Cr2O7....
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Question: If $f(x)=x^{2}-3 x+4$ and $f(x)=f(2 x+1)$, find the values of $x$. Solution: Given: $f(x)=x^{2}-3 x+4$ (1) and f(x) = f(2x + 1) Need to Find: Value of x Replacing x by (2x + 1) in equation (1) we get, $f(2 x+1)=(2 x+1)^{2}-3(2 x+1)+4 \cdots(2)$ According to the given problem, f(x) = f(2x + 1) Comparing (1) and (2) we get, $x^{2}-3 x+4=(2 x+1)^{2}-3(2 x+1)+4$ $\Rightarrow x^{2}-3 x+4=4 x^{2}+4 x+1-6 x-3+4$ $\Rightarrow 4 x^{2}+4 x+1-6 x-3+4-x^{2}+3 x-4=0$ $\Rightarrow 3 x^{2}+x-2=0$ $\R...
Read More →Which is largest in
Question: Which is largest in $8 \frac{1}{3} \%, \frac{4}{25}$ and $0.15 ?$ Solution: We have: $8 \frac{1}{3} \%, \frac{4}{25}$ $=\left(\frac{25}{3} \times \frac{1}{100}\right)$ $=\frac{1}{12}$ $=0.083$ Also, $\frac{4}{25}=0.16$ The third number is $0.15$. Clearly, $0.16$ is the largest. i.e., $\frac{4}{25}$ is the largest....
Read More →Identify the functional groups present
Question: Identify the functional groups present in the following compounds Solution: (a) C = O (b) COOH (c) CHO (d) OH....
Read More →Why are detergents better cleansing
Question: Why are detergents better cleansing agents than soaps ? Explain. Solution: A substance capable of removing grease and dirt from any fabric or body is called detergent. The detergents are of two types Le. soapy and non- soapy detergents. The soapy detergents are soaps whereas the non-soapy detergents are synthetic detergents or simply detergents. Although both are cleansing agents, they differ in chemical composition. In the present chapter, we shall briefly discuss the composition and ...
Read More →In a class, 60% of the total number of students are boys and there are 14 girls.
Question: In a class, 60% of the total number of students are boys and there are 14 girls. How many students are there in the class? Solution: Let the total number of students be $\mathrm{x}$. Then, we have: Percentage of boys $=60 \%$ Percentage of girls $=40 \%$ $\therefore$ Number of girls $=40 \%$ of $\mathrm{x}$ $=\left(x \times \frac{40}{100}\right)$ $=\frac{40 x}{100}$ Now, $\frac{40 x}{100}=14$ $\Rightarrow x=\left(14 \times \frac{100}{40}\right)$ $\Rightarrow x=35$ $\therefore$ Total nu...
Read More →Prove that
Question: The function $F(x) \frac{9 x}{5}=+32$ is the formula to convert $\mathbf{x}^{\circ} \mathbf{C}$ to Fahrenheit units. \ Find (i) $F(0)$, (ii) $F(-10)$, (iii) The value of $x$ when $f(x)=212$. Interpret the result in each case. Solution: Given: $\mathrm{F}(\mathrm{x})=\frac{9}{5} \mathrm{x}+32$ ....(i) To find: (i) F(0) Substituting the value of x = 0 in eq. (i), we get $\mathrm{F}(\mathrm{x})=\frac{9}{5} \mathrm{x}+32$ $\Rightarrow \mathrm{F}(0)=\frac{9}{5} \times 0+32$ $\Rightarrow \ma...
Read More →A compound X is formed by the reaction of a carboxylic
Question: A compound X is formed by the reaction of a carboxylic acid C2H4O2and an alcohol in presence of a few drops of H2SO4. The alcohol on oxidation with alkaline KMnO4followed by acidification gives the same carboxylic acid as used in this reaction. Give the names and structures of (a) carboxylic acid, (b) alcohol and (c) the compound X. Also write the reaction. (CBSE Sample Paper 2017) Solution: The available information suggests that the alcohol which gives the same carboxylic acid upon o...
Read More →An alloy contains 30% copper, 42% nickel and rest zinc.
Question: An alloy contains 30% copper, 42% nickel and rest zinc. Find the mass of zinc in 1 kg of alloy. Solution: Percentage of copper $=30 \%$ Percentage of nickel $=42 \%$ Percentage of zinc $=\{100-(30+42)\} \%$ = 28% $\therefore$ Mass of zinc in $1 \mathrm{~kg}$ of the alloy $=\left(\frac{28}{100} \times 1\right) \mathrm{kg}=0.28 \mathrm{~kg}=280 \mathrm{~g}$...
Read More →If the derivative
Question: If the derivative of $\tan ^{-1}(a+b x)$ takes the value 1 at $x=0$, prove that $1+a^{2}=b$. Solution: $y=\tan ^{-1}(a+b x)$ And $y^{\prime}(0)=1$ Now $\frac{d y}{d x}=\frac{d}{d x}\left(\tan ^{-1}(a+b x)\right)$ $\frac{d y}{d x}=\frac{b}{1+(a+b x)^{2}}$ At $x=0$ $\frac{d y}{d x}=\frac{b}{1+(a+b(0))^{2}}$ $\frac{b}{1+a^{2}}=1$ $\Rightarrow b=1+a^{2}$...
Read More →Identify and name the functional
Question: Identify and name the functional groups present in the following compounds. Solution:...
Read More →Write the names of the following compounds :
Question: Write the names of the following compounds : Solution: (a) Pentanoic acid (b) But-l-yne (c) Heptanal (d) Pentan-l-ol...
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Question: If $y=\cos ^{-1}(2 x)+2 \cos ^{-1} \sqrt{1-4 x^{2}}, 0x\frac{1}{2}$, 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 $0x\frac{1}{2}$ $02 x1$ $0\cos \theta1$ $0\theta\frac{\pi}{2}$ $0-\theta-\frac{\...
Read More →The value of a machine depreciates every year by 10%.
Question: The value of a machine depreciates every year by 10%. If the present value of the machine is Rs 54000, what was its value last year? Solution: Let the value of the machine last year be Rs $\mathrm{x}$. Then. its present value $=90 \%$ of Rs $x$ $=R s\left(x \times \frac{90}{100}\right)$ $=R s \frac{90 x}{100}$ Now, $\frac{90 \mathrm{x}}{100}=54000$ $\Rightarrow \mathrm{x}=\left(54000 \times \frac{100}{90}\right)$ $\Rightarrow \mathrm{x}=\mathrm{Rs} 60000$ Hence, the value of the machin...
Read More →Draw the electron dot structure
Question: Draw the electron dot structure of ethyne and also draw its structural formula Solution:...
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Question: Let $f: R \rightarrow R: f(x)=x^{2}+1 .$ Find (i) $f^{-1}\{10\}$ (ii) $f^{-1}\{-3\}$. Solution: Given: $f(x)=x^{2}+1$ To find: (i) $f^{-1}\{10\}$ We know that, if $f: X \rightarrow Y$ such that $y \in Y$. Then $f^{-1}(y)=\{x \in X: f(x)=y\}$. In other words, $\mathrm{f}^{-1}(\mathrm{y})$ is the set of pre - images of $\mathrm{y}$ Let $f^{-1}\{10\}=x$. Then, $f(x)=10$...(i) and it is given that $f(x)=x^{2}+1 \ldots$ (ii) So, from (i) and (ii), we get $x^{2}+1=10$ $\Rightarrow x^{2}=10-1...
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