Tick (✓) the correct answer
Question: Tick (✓) the correct answer: (180% of ?) 2 = 504 (a) 400 (b) 480 (c) 600 (d) 560 Solution: (d) 560 Let the required number be $\mathrm{x}$. Then, we have : $(180 \%$ of $x) \div 2=504$ $\Rightarrow\left(x \times \frac{180}{100}\right) \div 2=504$ $\Rightarrow\left(\frac{180 x}{100}\right) \div 2=504$ $\Rightarrow\left(\frac{180 x}{100} \times \frac{1}{2}\right)=504$ $\Rightarrow \frac{9 x}{10}=504$ $\Rightarrow x=\left(504 \times \frac{10}{9}\right)$ $\Rightarrow x=560$...
Read More →Oils on treating with hydrogen in the presence
Question: Oils on treating with hydrogen in the presence of palladium or nickel catalyst form fats. This is an example of (a)Addition reaction (b)Substitution reaction (c)Displacement reaction (d)Oxidation reaction Solution: (a).Oils are unsaturated in nature. By the addition of hydrogen, they become saturated....
Read More →Tick (✓) the correct answer
Question: Tick (✓) the correct answer: ?% of 400 = 60 (a) 6 (b) 12 (c) 15 (d) 20 Solution: (c) 15 Let the required number be $x$. Then, we have: $x \%$ of $400=60$ $\Rightarrow\left(400 \times \frac{x}{100}\right)=60$ $\Rightarrow \frac{400 x}{100}=60$ $\Rightarrow 4 x=60$ $\Rightarrow x=\frac{60}{4}$ $\Rightarrow x=15$...
Read More →Differentiate the following functions with respect to x :
Question: Differentiate the following functions with respect to $x$ : $\tan ^{-1}\left\{\frac{x^{1 / 3}+a^{1 / 3}}{1-(a x)^{1 / 3}}\right\}$ Solution: $y=\tan ^{-1}\left(\frac{x^{\frac{1}{3}}+a^{\frac{1}{3}}}{1-(a x)^{\frac{1}{3}}}\right)$ Arranging the terms in equation $y=\tan ^{-1}\left(\frac{x^{\frac{1}{3}}+a^{\frac{1}{3}}}{1-x^{\frac{1}{3}} \times a^{\frac{1}{3}}}\right)$ Using, $\tan ^{-1} x+\tan ^{-1} y=\tan ^{-1}\left(\frac{x+y}{1-x y}\right)$ $y=\tan ^{-1}\left(x^{\frac{1}{3}}\right)+\t...
Read More →In the above reaction, alkaline KMnO4 acts as
Question: In the above reaction, alkaline KMnO4acts as (a)reducing agent (b)oxidising agent (c)catalyst (d)dehydrating agent. Solution: (b).Alkaline KMnO4is also known as Baeyers reagent. It acts as an oxidising agent....
Read More →Tick (✓) the correct answer
Question: Tick (✓) the correct answer: 40% of ? = 240 (a) 60 (b) 600 (c) 6000 (d) 960 Solution: (b) 600 Let the required number be $\mathrm{x}$. Then, we have : $40 \%$ of $x=240$ $\Rightarrow\left(x \times \frac{40}{100}\right)=240$ $\Rightarrow \frac{40 x}{100}=240$ $\Rightarrow x=\left(240 \times \frac{100}{40}\right)$ $\Rightarrow x=600$...
Read More →Which of the following are correct chain isomers of butane ?
Question: Which of the following are correct chain isomers of butane ? (a)(i) and (iii) (b)(ii) and (iv) (c)(i) and (ii) (d)(iii) and (iv) Solution: (c).Isomer (i) has a straight chain while (ii) is a branched chain isomer....
Read More →Buckminster fullerene is an allotropie form of
Question: Buckminster fullerene is an allotropie form of (a)nitrogen (b)sulphur (c)carbon (d)tin Solution: (c)carbon...
Read More →Tick (✓) the correct answer:
Question: Tick (✓) the correct answer: What per cent of 10 kg is 250 g? (a) 25% (b) 5% (c) 10% (d) 2.5% Solution: (d) 2.5% Required percentage $=\left(\frac{250}{(10 \times 1000)} \times 100\right) \%=2.5 \%$...
Read More →Let X = {12, 13, 14, 15, 16, 17} and f
Question: Let $X=\{12,13,14,15,16,17\}$ and $f: A \rightarrow Z: f(x)=$ highest prime factor of $x$. Find range (f) Solution: Given: f(x) = highest prime factor of x And since $x \in A, A=\{12,13,14,15,16,17\}$ Value of $x$ can only be $12,13,14,15,16,17$ Doing prime factorization of the above, we get Hence, range of f = {2, 3, 5, 7, 13, 17}...
Read More →A molecule of ammonia (NH3) has
Question: A molecule of ammonia (NH3) has (a)only single bonds (b)only double bonds (c)only triple bonds (d)two double bonds and two single bonds. Solution: (a).All bonds are single covalent in nature....
Read More →Differentiate the following functions with respect to x :
Question: Differentiate the following functions with respect to $x$ : $\tan ^{-1}\left\{\frac{\cos x+\sin x}{\cos x-\sin x}\right\},-\frac{\pi}{4}x\frac{\pi}{4}$ Solution: $y=\tan ^{-1}\left(\frac{\cos x+\sin x}{\cos x-\sin x}\right)$ Dividing numerator and denominator by $\cos x$ $y=\tan ^{-1}\left(\frac{1+\frac{\sin x}{\cos x}}{1-\frac{\sin x}{\cos x}}\right)$ $y=\tan ^{-1}\left(\frac{1+\tan x}{1-\tan x}\right)$ $y=\tan ^{-1}\left(\frac{\tan \left(\frac{\pi}{4}\right)+\tan x}{1-\tan \left(\fra...
Read More →Which of the following statements are usually correct for carbon compounds ?
Question: Which of the following statements are usually correct for carbon compounds ? These (i) are good conductors of heat and electricity (ii) are poor conductors of electricity (iii) have strong forces of attraction between their molecules (iv) do not have strong forces of attraction between their molecules (a)(i) and (iii) (b)(ii) and (iii) (c)(i) and (iv) (d)(ii) and (iv) Solution: (d).Carbon compounds are of covalent nature. That is why these are poor conductors of electricity and do not ...
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Question: Tick (✓) the correct answer: What per cent of 92 is 120? (a) 75% (b) $33 \frac{1}{3} \%$ (c) $133 \frac{1}{3} \%$ (d) none of these Solution: (c) $133 \frac{1}{3} \%$ Required percentage $=\left(\frac{120}{90} \times 100\right) \%$ $=133 \frac{1}{3} \%$...
Read More →Carbon exists in the atmosphere in the form of
Question: Carbon exists in the atmosphere in the form of (a)carbon monoxide only (b)carbon monoxide and carbon dioxide in traces (c)carbon dioxide only (d)coal gas. Solution: (b).Both CO and CO2gases are present in traces in the atmosphere....
Read More →Tick (✓) the correct answer
Question: Tick (✓) the correct answer: 5% of a number is 9. The number is (a) 45 (b) 90 (c) 135 (d) 180 Solution: (d) 180 Let $x$ be the required number. Then, we have : $5 \%$ of $x=9$ $\Rightarrow\left(x \times \frac{5}{100}\right)=9$ $\Rightarrow \frac{5 x}{100}=9$ $\Rightarrow x=\left(9 \times \frac{100}{5}\right)$ $\Rightarrow x=180$...
Read More →find the value of
Question: If $f(x)=x^{2}$, find the value of $\frac{\{(f)(1.1)-f(1)\}}{(1.1)-1}$ Solution: Given: $f(x)=x^{2}$ Firstly, we find the f(1.1) Putting the value of x = 1.1 in the given eq., we get $f(1.1)=(1.1)^{2}$ $\Rightarrow f(1.1)=1.21$ Similarly, $f(1)=(1)^{2}$ $\Rightarrow f(1)=1$ Putting the value of f(1.1) and f(1) in eq. (i), we get $\frac{\mathrm{f}(1.1)-\mathrm{f}(1)}{(1.1-1)}=\frac{1.21-1}{1.1-1}=\frac{0.21}{0.1}=2.1$ Hence, the value of $\frac{\mathrm{f}(1.1)-\mathrm{f}(1)}{(1.1-1)}=2....
Read More →Differentiate the following functions with respect to x :
Question: Differentiate the following functions with respect to $x$ : $\tan ^{-1}\left\{\frac{5 x}{1-6 x^{2}}\right\},-\frac{1}{\sqrt{6}}x\frac{1}{\sqrt{6}}$ Solution: $y=\tan ^{-1}\left(\frac{5 x}{1-6 x^{2}}\right)$ Arranging the terms in equation $y=\tan ^{-1}\left(\frac{3 x+2 x}{1-3 x \times 2 x}\right)$ Using, $\tan ^{-1} x+\tan ^{-1} y=\tan ^{-1}\left(\frac{x+y}{1-x y}\right)$ $y=\tan ^{-1}(3 x)+\tan ^{-1}(2 x)$ Differentiating w.r.t $x$ we get $\frac{d y}{d x}=\frac{d}{d x}\left(\tan ^{-1}...
Read More →Tick (✓) the correct answer:
Question: Tick (✓) the correct answer: 6 : 5 when expressed as a percentage, is (a) $83 \frac{1}{3} \%$ (b) $90 \%$ (c) $120 \%$ (d) $6.5 \%$ Solution: (c) 120% $6: 5=\frac{6}{5}$ $=\left(\frac{6}{5} \times 100\right) \%$ $=120 \%$...
Read More →Differentiate the following functions with respect to x :
Question: Differentiate the following functions with respect to $x$ : $\tan ^{-1}\left(\frac{x}{1+6 x^{2}}\right)$ Solution: $y=\tan ^{-1}\left(\frac{x}{1+6 x^{2}}\right)$ Arranging the terms in equation $y=\tan ^{-1}\left(\frac{3 x-2 x}{1+3 x \times 2 x}\right)$ Using, $\tan ^{-1} x-\tan ^{-1} y=\tan ^{-1}\left(\frac{x-y}{1+x y}\right)$ $y=\tan ^{-1}(3 x)-\tan ^{-1}(2 x)$ Differentiating w.r.t $\mathrm{x}$ we get $\frac{d y}{d x}=\frac{d}{d x}\left(\tan ^{-1}(3 x)-\tan ^{-1}(2 x)\right)$ $\frac...
Read More →Tick (✓) the correct answer
Question: Tick (✓) the correct answer: 0.8% when expressed as a decimal, is (a) 0.08 (b) 0.008 (c) 8 (d) 0.8 Solution: (b) 0.008 $0.8 \%=\frac{0.8}{100}$ =0.008...
Read More →Tick (✓) the correct answer:v
Question: Tick (✓) the correct answer: $\frac{3}{5}=?$ (a) 30% (b) 40% (c) 45% (d) 60% Solution: (d) 60% $\frac{3}{5}=\left(\frac{3}{5} \times 100\right) \%$ =60%...
Read More →Differentiate the following functions with respect to x :
Question: Differentiate the following functions with respect to $x$ : $\tan ^{-1}\left(\frac{\mathrm{x}-\mathrm{a}}{\mathrm{x}+\mathrm{a}}\right)$ Solution: $y=\tan ^{-1}\left(\frac{x-a}{x+a}\right)$ Dividing numerator and denominator by $x$ $\mathrm{y}=\tan ^{-1}\left(\frac{1-\frac{\mathrm{a}}{\mathrm{x}}}{1+1 \times \frac{\mathrm{a}}{\mathrm{x}}}\right)$ Using, $\tan ^{-1} x-\tan ^{-1} y=\tan ^{-1}\left(\frac{x-y}{1+x y}\right)$ $y=\tan ^{-1} 1-\tan ^{-1} \frac{a}{x}$ Differentiating w.r.t $x$...
Read More →the value of
Question: If $f(x)=x^{2}$, find the value of $\frac{\{(f)(5)-f(1)\}}{(5-1)} Solution: Given: $f(x)=x^{2}$ find: $\frac{f(5)-f(1)}{(5-1)} \ldots$ (i) Firstly, we find the f(5) Putting the value of x = 5 in the given eq., we get $f(5)=(5)^{2}$ $\Rightarrow f(5)=25$ Similarly, $f(1)=(1)^{2}$ $\Rightarrow f(1)=1$ Putting the value of f(5) and f(1) in eq. (i), we get $\frac{\mathrm{f}(5)-\mathrm{f}(1)}{(5-1)}=\frac{25-1}{5-1}=\frac{24}{4}=6$ Hence, the value of $\frac{\mathrm{f}(5)-\mathrm{f}(1)}{(5-...
Read More →Two ores ‘X’ and ‘Y’ were taken. On heating,
Question: Two ores X and Y were taken. On heating, ore X gives CO2whereas ore Y gives SO2. What steps will you take to convert them into respective metals ? Solution: Since the ore A of the metal gives CO2upon heating, it is some metal carbonate (MCO3). It can be converted to the metallic form as follows : Since the ore Y of the metal gives SO2upon heating, it can be some metal sulphide (MS). It can be converted to the metallic form as follows :...
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