An element forms an oxide A2O3
Question: An element forms an oxide A2O3which is acidic in nature. Identify A as a metal or non-metal. Solution: Since the oxide A2O3is acidic in nature, the element A is non-metal....
Read More →Differentiate the following functions with respect to x :
Question: Differentiate the following functions with respect to $x$ : $\tan ^{-1}\left(\frac{\sin x}{1+\cos x}\right),-\pix\pi$ Solution: $y=\tan ^{-1}\left\{\frac{\sin x}{1+\cos x}\right\}$ Function $y$ is defined for all real numbers where $\cos x \neq-1$ Using $2 \cos ^{2} \theta=1+\cos 2 \theta$ and $2 \sin \theta \cos \theta=\sin 2 \theta$ $y=\tan ^{-1}\left\{\frac{2 \sin \frac{x}{2} \cos \frac{x}{2}}{2 \cos ^{2} \frac{x}{2}}\right\}$ $y=\tan ^{-1}\left\{\tan \frac{x}{2}\right\}$ $y=\frac{x...
Read More →A metal M does not liberate hydrogen from
Question: A metal M does not liberate hydrogen from acids but reacts with oxygen to give a black coloured product. Identify M and black coloured product and also explain the reaction of M with oxygen. Solution: The avilable information suggests that the metal M is copper (Cu). It does not liberate hydrogen since it is placed below hydrogen in the reactivity series. Copper reacts with oxygen upon heating to form cupric oxide (CuO) which is black in colour....
Read More →The price of petrol goes up by 10%.
Question: The price of petrol goes up by 10%. By how much per cent must a motorist reduce the consumption of petrol so that the expenditure on it remains unchanged? Solution: Let the consumption of petrol originally be 1 unit and let its cost be Rs 100 . New cost of 1 unit of petrol $=$ Rs 110 Now, Rs 110 will yield 1 unit of petrol. i.e., Rs 100 will yield $\left(\frac{1}{110} \times 100\right)$, i.e., $\frac{10}{11}$ units of petrol. Now, reduction in consumption $=\left(1-\frac{10}{11}\right)...
Read More →Give the reaction involved during extraction of zinc from its ore by
Question: Give the reaction involved during extraction of zinc from its ore by (a) roasting of zinc ore (b) calcination of zinc ore Solution:...
Read More →Let A = {1, 2} and B = {2, 4, 6}.
Question: Let $A=\{1,2\}$ and $B=\{2,4,6\} .$ Let $f=\{(x, y): x \in A, y \in B$ and $y2 x+1\}$. Write f as a set of ordered pairs. Show that f is a relation but not a function from A to B. Solution: Given: A = {1, 2} and B = {2, 4, 6} $f=\{(x, y): x \in A, y \in B$ and $y2 x+1\}$ Putting x = 1 in y 2x + 1, we get $y2(1)+1$ $\Rightarrow y3$ and $y \in B$ this means y = 4, 6 if x = 1 because it satisfies the condition y 3 Putting x = 2 in y 2x + 1, we get $y2(2)+1$ $\Rightarrow y5$ this means y =...
Read More →Differentiate the following functions with respect to x :
Question: Differentiate the following functions with respect to $x$ : $\tan ^{-1}\left\{\frac{\sqrt{1+a^{2} x^{2}}-1}{a x}\right\}, x \neq 0$ Solution: $y=\tan ^{-1}\left\{\frac{\sqrt{1+a^{2} x^{2}}-1}{a x}\right\}$ Let $a x=\tan \theta$ Now $y=\tan ^{-1}\left\{\frac{\sqrt{1+\tan ^{2} \theta}-1}{\tan \theta}\right\}$ Using $\sec ^{2} \theta=1+\tan ^{2} \theta$ $y=\tan ^{-1}\left\{\frac{\sqrt{\sec ^{2} \theta}-1}{\tan \theta}\right\}$ $y=\tan ^{-1}\left\{\frac{\sec \theta-1}{\tan \theta}\right\}$...
Read More →A's income is 20% less than that of B.
Question: A's income is 20% less than that of B. By what per cent is B's income more than A's? Solution: Let B's income be Rs 100 Then, A's income $=$ Rs 80 Therefore, B's income is more than A's income by $=\frac{(100-80)}{80} \times 100 \%$ $=\frac{20}{80} \times 100 \%=25 \%$ = RS 125 $\therefore$ B's income is more than that of A's by $(125-100) \%$, i.e., $25 \%$....
Read More →An alkali metal A gives a compound B (molecular mass = 56) on reacting with water.
Question: An alkali metal A gives a compound B (molecular mass = 56) on reacting with water. The compound B gives a soluble compound C on treatment with aluminium oxide. Identify A, B and C and give the reaction involved. Solution: As explained under Question 42, the alkali metal A is potassium (K) and on reacting with water, it forms a compound B which is potassium hydroxide. This upon reacting with aluminium oxide (Al2O3) forms potassium metaluminate C....
Read More →An element ‘A’ reacts with water to form a compound ‘B’
Question: An element A reacts with water to form a compound B which is used in white washing. The compound B on heating forms an oxide C which on treatment with water gives back B. Identify A, B and C and give the reactions involved. Solution: Since the compound B is used for white wash, it is calcium hydroxide and the element A is calcium. Upon heating B forms calcium oxide C. It reacts with water to give calcium hydroxide B again....
Read More →Sonal attended her school on 204 days in a full year.
Question: Sonal attended her school on 204 days in a full year. If her attendance is 85%, find the number of days on which the school was opened. Solution: Let $x$ be the number of days the school was opened. Number of days Sonal attended school $=204$ days Percentage of her attendance $=85 \%$ of $\mathrm{x}$ $=\left(\mathrm{x} \times \frac{85}{100}\right)$ $=\frac{85 \mathrm{x}}{100}$ Now, $\frac{85 x}{100}=204$ $\Rightarrow x=\left(204 \times \frac{100}{85}\right)$ $\Rightarrow x=240$ $\there...
Read More →Name one metal and one non-metal
Question: Name one metal and one non-metal that exist in liquid state at room temperature. Also name two metals having melting point less than 310 K (37C). Solution: The metal mercury (Hg) and non-metal (Br2) exist in liquid state at room temperature. The two metals with melting points less than 310 K are ; cesium (Cs) with melting point 301 K and gallium (Ga) with melting point 303 K....
Read More →Differentiate the following functions with respect to x :
Question: Differentiate the following functions with respect to $x$ : $\sin ^{-1}\left\{\frac{\sqrt{1+x}+\sqrt{1-x}}{2}\right\}, 0x1$ Solution: $y=\sin ^{-1}\left\{\frac{\sqrt{1+x}+\sqrt{1-x}}{2}\right\}$ Let $x=\cos 2 \theta$ Now $y=\sin ^{-1}\left\{\frac{\sqrt{1+\cos 2 \theta}+\sqrt{1-\cos 2 \theta}}{2}\right\}$ Using $1-2 \sin ^{2} \theta=\cos 2 \theta$ and $2 \cos ^{2} \theta-1=\cos 2 \theta$ $y=\sin ^{-1}\left\{\frac{\sqrt{2 \cos ^{2} \theta}+\sqrt{2 \sin ^{2} \theta}}{2}\right\}$ Now $y=\s...
Read More →Amit was given an increment of 20% on his salary.
Question: Amit was given an increment of 20% on his salary. If his new salary is Rs 30600, what was his salary before the increment? Solution: Let $R s x$ be Amit's old salary. His salary after increment will be Rs $\left(x+\frac{20}{100} x\right)$ According to the question, we have: $\Rightarrow x+\frac{20}{100} x=30600$ $\Rightarrow \frac{100 x+20 x}{100}=30600 \quad(\mathrm{LCM}=100)$ $\Rightarrow \frac{120 x}{100}=30600$ $\Rightarrow 120 x=30600 \times 100$ $\Rightarrow x=\frac{30600 \times ...
Read More →Give two examples each of the metals
Question: Give two examples each of the metals that are good conductors and poor conductors of heat respectively. Solution: Good conductors of heat : Ag and Cu Poor conductors of heat : Pb and Hg....
Read More →A non-metal A is an important constituent
Question: A non-metal A is an important constituent of our food and forms two oxides B and C. Oxide B is toxic whereas C causes global warming (a) Identify A, B and C (b) To which Group of Periodic Table does A belong ? Solution: The non-metal A is carbon. It is an important constituent of our food in different forms. For example, glucose (C6H12O6) contains carbon. In fact, all food materials are organic compounds and these contain carbon as essential constituent. The two oxides of carbon are, c...
Read More →A football team wins 7 games, which is 35% of the total games played.
Question: A football team wins 7 games, which is 35% of the total games played. How many games were played in all? Solution: Let $x$ be the total number of games played. Percentage of games won $=35 \%$ of $x$ $=\left(x \times \frac{35}{100}\right)$ $=\frac{35 x}{100}$ Now, $\frac{35 \mathrm{x}}{100}=7$ $\Rightarrow x=\left(7 \times \frac{100}{35}\right)$ $\Rightarrow x=20$ $\therefore$ The total number games played is 20 ....
Read More →What happens when
Question: What happens when (a) ZnCO3is heated in the absence of oxygen ? (b) a mixture of Cu2O and Cu2S is heated ? Solution: (a) A mixture of ZnO(s) and CO2is formed...
Read More →Prove that
Question: Let $A=\{-1,0,1,2\}$ and $B=\{2,3,4,5\}$. Find which of the following are function from A to B. Give reason. (i) $f=\{(-1,2),(-1,3),(0,4), 1,5)\}$ (ii) $g=\{(0,2),(1,3),(2,4)\}$ (iii) $h=\{(-1,2),(0,3),(1,4),(2,5)\}$ Solution: (i) Given: $A=\{-1,0,1,2\}$ and $B=\{2,3,4,5\}$ Function: (i) all elements of the first set are associated with the elements of the second set. (ii) An element of the first set has a unique image in the second set. $f=\{(-1,2),(-1,3),(0,4),(1,5)\}$ $f=\{(-1), 2),...
Read More →Give the formulae of the stable binary
Question: Give the formulae of the stable binary compounds that would be formed by the combination of following pairs of elements. (a) Ca and N2 (b) Li and O2 (c) Ca and Cl2 (d) K and Solution: (a) Calcium nitride (Ca3N2) (b) Lithium oxide (Li2O) (c) Calcium chloride (CaCl2) (d) Potassium oxide (K2O)....
Read More →Differentiate the following functions with respect to x :
Question: Differentiate the following functions with respect to $x$ : $\tan ^{-1}\left(\frac{2 a^{x}}{1-a^{2 x}}\right), a1,-\inftyx0$ Solution: $\mathrm{y}=\tan ^{-1}\left\{\frac{2 \mathrm{a}^{\mathrm{x}}}{1-\mathrm{a}^{2 \mathrm{x}}}\right\}$ Let $\mathrm{a}^{\mathrm{x}}=\tan \theta$ $\mathrm{y}=\tan ^{-1}\left\{\frac{2 \tan \theta}{1-\tan ^{2} \theta}\right\}$ Using $\tan 2 \theta=\frac{2 \tan \theta}{1-\tan ^{2} \theta}$ $\mathrm{y}=\tan ^{-1}(\tan 2 \theta)$ Considering the limits, $-\infty...
Read More →A man saves 18% of his monthly income.
Question: A man saves 18% of his monthly income. If he saves Rs 3780 per month, what is his monthly income? Solution: Let Rs $x$ be his monthly income. His savings $=18 \%$ of Rs $\mathrm{x}$ $=\operatorname{Rs}\left(x \times \frac{18}{100}\right)$ $=\operatorname{Rs} \frac{9 x}{50}$ Now, $\frac{9 x}{50}=3780$ $\Rightarrow x=\mathrm{Rs}\left(3780 \times \frac{50}{9}\right)$ $\Rightarrow x=\mathrm{Rs} 21000$ $\therefore$ His monthly income is Rs. 21000 ....
Read More →A metal that exists as a liquid at room
Question: A metal that exists as a liquid at room temperature is obtained by heating its sulphide in the presence of air. Identify the metal and its ore and give the reaction involved. Solution: Mercury is the metal which exists as a liquid at room temper nature. It can be obtained by heating the sulphide ore in the presence of air. The process is known as roasting. The chemical reactions involved are :...
Read More →If 16% of a number is 72,
Question: If 16% of a number is 72, find the number. Solution: Let the number be $x$. $16 \%$ of $x$ is 72 . $\Rightarrow \frac{16}{100} \times x=72$ $\Rightarrow 16 x=72 \times 100$ $\Rightarrow 16 x=7200$ $\Rightarrow x=\frac{7200}{16}=450$ $\therefore$ The required number is 450 ....
Read More →Differentiate the following functions with respect to x:
Question: Differentiate the following functions with respect to $x$ : $\tan ^{-1}\left(\frac{2^{x+1}}{1-4^{x}}\right),-\inftyx0$ Solution: $y=\tan ^{-1}\left\{\frac{2^{x+1}}{1-4^{x}}\right\}$ Let $2^{x}=\tan \theta$ $y=\tan ^{-1}\left\{\frac{2 \times 2^{x}}{1-\left(2^{x}\right)^{2}}\right\}$ $y=\tan ^{-1}\left\{\frac{2 \tan \theta}{1-\tan ^{2} \theta}\right\}$ Using $\tan 2 \theta=\frac{2 \tan \theta}{1-\tan ^{2} \theta}$ $y=\tan ^{-1}(\tan 2 \theta)$ Considering the limits, $-\inftyx0$ $2^{-\in...
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