Solve the following
Question: Find $4 \frac{1}{2} \%$ of Rs 3600 Solution: $4 \frac{1}{2} \%=\frac{9}{2 \times 100}$ $\therefore \frac{9}{200}$ of Rs $3600=\frac{9}{200} \times 3600=$ Rs 162...
Read More →A metal ‘M’, which is used in thermite process,
Question: A metal M, which is used in thermite process,when heated with oxygen gives an oxide, which is amphoteric in nature. Identify M and its oxide. Write down the reactions of oxide with HCl and NaOH. Solution: The information suggests that the metal M is aluminium (Al). The formula of its oxide is Al2O3 which is amphoteric in nature. It reacts with both acid and base....
Read More →What per cent of 150 is 96?
Question: (i) What per cent of 150 is 96? (ii) What per cent of 5 kg is 200 g? (iii) What per cent of 2 litres is 250 mL? Solution: (i) Required percentage $=\left(\frac{96}{150} \times 100\right) \%=64 \%$ (ii) Required percentage $=\left(\frac{200}{5 \times 1000} \times 100\right) \%=4 \%$ (iii) Required percentage $=\left(\frac{250}{2 \times 1000} \times 100\right) \%=12.5 \%$...
Read More →What are the constituents of solder alloy ?
Question: What are the constituents of solder alloy ? Which property of solder makes it suitable for welding electrical wires ? Solution: The constituents of solder alloy are ; lead (Pb) and tin (Sn). Being a low melting solid and also a good conductor of electricity, solder is used for welding electrical wires and cables....
Read More →Which is largest in
Question: Which is largest in $6 \frac{2}{3} \%, \frac{3}{20}$ and $0.14 ?$ Solution: We have: $6 \frac{2}{3} \%=\frac{20}{3} \%$ $=\left(\frac{20}{3} \times \frac{1}{100}\right)$ $=\frac{1}{15}$ $=0.06$ Also, $\frac{3}{20}=0.15$ The third number is $0.14$. Clearly, $0.15$ is the largest. Hence, $\frac{3}{20}$ is the largest....
Read More →The following reaction takes place
Question: The following reaction takes place when aluminium powder is heated with Mn02. $3 \mathrm{MnO}_{2}(s)+4 \mathrm{Al}(s) \longrightarrow 3 \mathrm{Mn}(s)+2 \mathrm{Al}_{2} \mathrm{O}_{3}(s)+$ Heat (a) Is aluminium getting reduced ? (b) Is Mn02 getting oxidised ? Solution: (a) Aluminium is getting oxidised to Al2O3. (b) Manganese dioxide is getting reduced to Mn....
Read More →Solve this
Question: Let $X=\{-1,0,3,7,9\}$ and $f: X \rightarrow R: f(x) x^{3}+1$. Express the function $f$ as set of ordered pairs. Solution: Given: $f: X \rightarrow R, f(x)=x^{3}+1$ Here, $X=\{-1,0,3,7,9\}$ For $x=-1$ $f(-1)=(-1)^{3}+1=-1+1=0$ For $x=0$ $f(0)=(0)^{3}+1=0+1=1$ For $x=3$ $f(3)=(3)^{3}+1=27+1=28$ For $x=7$ $f(7)=(7)^{3}+1=343+1=344$ For $x=9$ $f(9)=(9)^{3}+1=729+1=730$ $\therefore$ the ordered pairs are $(-1,0),(0,1),(3,28),(7,344),(9,730)$...
Read More →Differentiate the following functions with respect to x :
Question: Differentiate the following functions with respect to $x$ : $\tan ^{-1}\left\{\frac{4 x}{1-4 x^{2}}\right\},-\frac{1}{2}x\frac{1}{2}$ Solution: $y=\tan ^{-1}\left\{\frac{4 x}{1-4 x^{2}}\right\}$ Let $2 x=\tan \theta$ $y=\tan ^{-1}\left\{\frac{2 \tan \theta}{1-\tan ^{2} \theta}\right\}$ Using $\tan 2 \theta=\frac{2 \tan \theta}{1-\tan ^{2} \theta}$ $y=\tan ^{-1}(\tan 2 \theta)$ Considering the limits, $-\frac{1}{2}x\frac{1}{2}$ $-12 x1$ $-1\tan \theta1$ $-\frac{\pi}{4}\theta\frac{\pi}{4...
Read More →A non-metal X-exists in two different forms Y and Z.
Question: A non-metal X-exists in two different forms Y and Z. Y is the hardest natural substance, whereas Z is a good conductor of electricity. Identify X, Y and Z. Solution: Since Y is the hardest occuring non-metal, it is diamond. The non-metal X is carbon. Y is the crystalline allotropie form of carbon. The other allotropie form Z which is a good conductor of electricity is graphite....
Read More →Convert the ratio 4 : 5 to percentage.
Question: Convert the ratio 4 : 5 to percentage. Solution: $4: 5=\frac{4}{5}=\left(\frac{4}{5} \times 100\right) \%$ $=80 \%$...
Read More →Let X = {1, 2, 3, 4,}, Y = {1, 5, 9, 11, 15, 16}
Question: Let X = {1, 2, 3, 4,}, Y = {1, 5, 9, 11, 15, 16} and F = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)}. Are the following true? (i) F is a relation from X to Y (ii) F is a function from X to Y. Justify your answer in following true? Solution: X = {1, 2, 3, 4} and Y = {1, 5, 9, 11, 15, 16} and F = {(1, 5), (2, 9), (3, 1), (4, 5), (2, 11)} (i) To show: $F$ is a relation from $X$ to $Y$ First elements in $\mathrm{F}=1,2,3,4$ All the first elements are in Set $X$ So, the first element is from ...
Read More →Express each of the following as a percentage:
Question: Express each of the following as a percentage: (i) $\frac{9}{25}$ (ii) $\frac{3}{125}$ (iii) $\frac{12}{5}$ Solution: (i) $\frac{9}{25}$ $=\left(\frac{9}{25} \times 100\right) \%$ $=(9 \times 4) \%$ $=36 \%$ (ii) $\frac{3}{125}$ $=\left(\frac{3}{125} \times 100\right) \%$ $=2.4 \%$ (iii) $\frac{12}{5}$ $=\left(\frac{12}{5} \times 100\right) \%$ $=240 \%$...
Read More →When a metal ‘X’ is treated with cold water,
Question: When a metal X is treated with cold water, it gives a basic salt Y with molecular formula XOH (Molecular mass = 56) and liberates a gas Z which easily catches fire. Identify X, Y and Z and also write the reaction involved. Solution: The atomic mass of metal X = 56 Mass of OH group = 56 17 = 39u. This shows that the metal X is potassium (K) and the basic salt Y is potassium hydroxide (KOH). It is formed by reacting potassium with cold water. Hydrogen gas Z evolved in the reaction catche...
Read More →Differentiate the following functions with respect to x :
Question: Differentiate the following functions with respect to $x$ : $\cos ^{-1}\left\{\frac{x+\sqrt{1-x^{2}}}{\sqrt{2}}\right\},-1x1$ Solution: $y=\cos ^{-1}\left\{\frac{x+\sqrt{1-x^{2}}}{\sqrt{2}}\right\}$ Let $x=\sin \theta$ Now $y=\cos ^{-1}\left\{\frac{\sin \theta+\sqrt{1-\sin ^{2} \theta}}{\sqrt{2}}\right\}$ Using $\sin ^{2} \theta+\cos ^{2} \theta=1$ $y=\cos ^{-1}\left\{\frac{\sin \theta+\cos \theta}{\sqrt{2}}\right\}$ Now $y=\cos ^{-1}\left\{\sin \theta \frac{1}{\sqrt{2}}+\cos \theta \f...
Read More →Express each of the following as a decimal:
Question: Express each of the following as a decimal: (i) 6% (ii) 72% (iii) 125% Solution: (i) 6% $=\frac{6}{100}$ $=0.06$ $(i i) 72 \%$ $=\frac{72}{100}$ $=0.72$ (iii) $125 \%$ $=\frac{125}{100}$ $=1.25$...
Read More →Express each of the following as a fraction:
Question: Express each of the following as a fraction: (i) 48% (ii) 220% (iii) 2.5% Solution: (i) $48 \%$ $=\frac{48}{100}$ $=\frac{12}{25}$ (ii) $220 \%$ $=\frac{220}{100}$ $=\frac{11}{5}$ (iii) $2.5 \%$ $=\frac{2.5}{100}$ $=\frac{25}{1000}$ $=\frac{1}{40}$...
Read More →Compound A’ and aluminium are used to join railway tracks,
Question: Compound A and aluminium are used to join railway tracks, (a) Identify the compound A (b) Name the reaction (c) Write down its reaction with aluminium. Solution: Railway trakcs as we all know, are made up of iron. This means that the compound A is an oxide of iron (Fe2CO3). It is reduced by aluminium by thermit reaction with aluminium. $\mathrm{Fe}_{2} \mathrm{O}_{3}(s)+2 \mathrm{Al}(s) \longrightarrow \mathrm{Al}_{2} \mathrm{O}_{3}(s)+2 \mathrm{Fe}(s)+$ heat. The reaction is highly ex...
Read More →Generally, when metals are treated with mineral acids,
Question: Generally, when metals are treated with mineral acids, hydrogen gas is liberated but when metals (except Mn and Mg), are treated with HNCfy, hydrogen is not liberated, why ? Solution: HNO3acts as a powerful oxidising agent along with acting as acid. In this case, hydrogen gas which is intially involved is oxidised to water....
Read More →What is the fundamental difference between a relation and function?
Question: What is the fundamental difference between a relation and function? Is every relation a function? Solution: Fundamental difference between Relation and Function: Every function is a relation, but every relation need not be a function. A relation f from A to B is called a function if (i) Dom(f) = A (ii) no two different ordered pairs in f have the same first component. For. e.g Let A = {a, b, c, d} and B = {1, 2, 3, 4, 5} Some relations f, g and h are defined as follows f = {(a, 1), (b,...
Read More →Differentiate the following functions with respect to x :
Question: Differentiate the following functions with respect to $x$ : $\sin ^{-1}\left\{\frac{x+\sqrt{1-x^{2}}}{\sqrt{2}}\right\},-1x1$ Solution: $y=\sin ^{-1}\left\{\frac{x+\sqrt{1-x^{2}}}{\sqrt{2}}\right\}$ Let $x=\sin \theta$ Now $y=\sin ^{-1}\left\{\frac{\sin \theta+\sqrt{1-\sin ^{2} \theta}}{\sqrt{2}}\right\}$ Using $\sin ^{2} \theta+\cos ^{2} \theta=1$ $y=\sin ^{-1}\left\{\frac{\sin \theta+\cos \theta}{\sqrt{2}}\right\}$ Now $y=\sin ^{-1}\left\{\sin \theta \frac{1}{\sqrt{2}}+\cos \theta \f...
Read More →Why should the metal sulphides
Question: Why should the metal sulphides and carbonates be converted to metal oxides in the process of extraction of metal from them ? Solution: It is quite easy to obtain a metal from metal oxide by carrying its reduction with a suitable reducing agent. However, metal sulphides and carbonates are converted to the oxide form and then reduced....
Read More →During extraction of metals,
Question: During extraction of metals, electrolytic refining is used to obtain pure metals, (a) Which material will be used as anode and cathode for refining of copper metal by this process (b) Suggest a suitable electrolyte also, (c) In this electrolytic cell, where do we get pure copper after passing electric current ? Solution: In the electrolytic refining of impure copper metal : (a) A rod of impure copper is used as anode while that of pure copper as cathode. (b) The electrolyte is a water ...
Read More →Write 'T' for true and 'F' for false for each of the following:
Question: Write 'T' for true and 'F' for false for each of the following: (i) (5 3x2) is a binomial. (ii) 8 is a monomial. (iii) (5a 9b) (6a+ 2b) = (a 7b). (iv) When $x=2$ and $y=1$, the value of $\frac{-8}{7} x^{3} y^{4}$ is $\frac{-64}{7}$. (v) $\frac{x}{4}+\frac{x}{6}-\frac{x}{2}=\frac{3}{4} \Rightarrow x=-9$. (vi) $2 x-5=0 \Rightarrow x=\frac{2}{5}$. Solution: (i) TBinomial expression is an expression that shows the sum or the difference of two unlike terms. The above expression has two unli...
Read More →Iqbal treated a lustrous, divalent element M with sodium hydroxide.
Question: Iqbal treated a lustrous, divalent element M with sodium hydroxide. He observed the formation of bubbles in reaction mixture. He made the same observations when this element was treated with hydrochloric acid. Suggest how can he identify the produced gas. Write chemical equations for both the reactions. Solution: The divalent element M is a metal. It reacts with both sodium hydroxide (alkali) and dilute hydrochloric acid to evolve hydrogen gas $\mathrm{M}(s)+2 \mathrm{NaOH}(a q) \longr...
Read More →Which one of the following figures
Question: Which one of the following figures correctly describes the process of electrolytic refining ? Solution: (c).Cu2+ ions are released from anode by the oxidation of copper (Cu). These migrate towards cathode and are reduced to copper (Cu)....
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