Vinegar is a solution of
Question: Vinegar is a solution of (a)30% 40% acetic acid in alcohol (b)5% 8% acetic acid in alcohol (c)5% 8% acetic acid in water (d)15% 20% acetic acid in water Solution: (c)5% 8% acetic acid in water...
Read More →The correct structural formula of butanoic acid is
Question: The correct structural formula of butanoic acid is Solution: (d)....
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Question: Tick (✓) the correct answer A number decreased by $27 \frac{1}{2} \%$ gives 87 . The number is (a) 58 (b) 110 (c) 120 (d) 135 Solution: (c) 120 Let the required number be $\mathrm{x}$. Then, we have: $x-\left(27 \frac{1}{2} \%\right.$ of $\left.x\right)=87$ $\Rightarrow \mathrm{x}-\left(\frac{55}{2} \%\right.$ of $\left.\mathrm{x}\right)=87$ $\Rightarrow \mathrm{x}-\left(\mathrm{x} \times \frac{55}{2} \times \frac{1}{100}\right)=87$ $\Rightarrow \mathrm{x}-\frac{11 \mathrm{x}}{40}=87$ ...
Read More →Ethanol reacts with sodium and forms two products.
Question: Ethanol reacts with sodium and forms two products. These are : (a)sodium ethanoate and hydrogen (b)sodium ethanoate and oxygen (c)sodium ethoxide and hydrogen (d)sodium ethoxide and oxygen Solution:...
Read More →Structural formula of benzene is
Question: Structural formula of benzene is Solution: (c). The carbon atom skeleton in benzene has alternate single and double bonds...
Read More →Pentane has the molecular formula C5H12. h has
Question: Pentane has the molecular formula C5H12. h has (a)8 covalent bonds (b)10 covalent bonds (c)16 covalent bonds (d)14 covalent bonds Solution:...
Read More →In the soap micelles
Question: In the soap micelles (a)the ionic end of soap is on the surface of the cluster while the carbon chain is in the interior of the cluster. (b)ionic end of soap is in the interior of the cluster and the carbon chain is out of the cluster, (c)both ionic end and carbon chain are in the interior of the cluster (d)both ionic end and carbon chain are on the exterior of the cluster Solution: (a)the ionic end of soap is on the surface of the cluster while the carbon chain is in the interior of t...
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Question: Tick (✓) the correct answer: A number exceeds 20% of itself by 40. The number is (a) 50 (b) 60 (c) 80 (d) 320 Solution: (a) 50 Let $x$ be the required number. Then, we have: $20 \%$ of $x+40=x$ $\Rightarrow\left(x \times \frac{20}{100}\right)+40=x$ $\Rightarrow \frac{20 x}{100}+40=x$ $\Rightarrow\left(\frac{20 x}{100}-x\right)=-40$ $\Rightarrow \frac{-80 x}{100}=-40$ $\Rightarrow x=\left(40 \times \frac{100}{80}\right)$ $\Rightarrow x=50$...
Read More →Differentiate the following with respect to x :
Question: Differentiate the following with respect to $x$ : $\cos -1(\sin x)$ Solution: $y=\cos ^{-1}(\sin x)$ Function is defined for all $x$ $y=\cos ^{-1}\left(\cos \left(\frac{\pi}{2}-x\right)\right)$ $y=\frac{\pi}{2}-x$ Differentiating w.r.t $x$ we get $\frac{d y}{d x}=\frac{d}{d x}\left(\frac{\pi}{2}-x\right)$ $\frac{d y}{d x}=-1$...
Read More →Chlorine reacts with saturated hydrocarbons
Question: Chlorine reacts with saturated hydrocarbons at room temperature in the (a)absence of sunlight (b)presence of sunlight (c)presence of water (d)presence of hydrochloric acid Solution: (b).These reactions are called photochemical reactions....
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Question: Let $f: R \rightarrow R: f(x)=2^{x}$. Find (i) Range (f) (ii) $\{x: f(x)=1\}$. (iii) Find out whether $f(x+y)=f(x) . f(y)$ for all $x, y \in R$. Solution: Given that $\mathrm{f}: \mathrm{R} \rightarrow \mathrm{R}$ such that $\mathrm{f}(\mathrm{x})=2^{\mathrm{x}}$ To find: (i) Range of $x$ Here, $f(x)=2^{x}$ is a positive real number for every $x \in R$ because $2^{x}$ is positive for every $x$ ER. Moreover, for every positive real number $x, \exists \log 2^{x} \in R$ such that $f\left(...
Read More →Identify the unsaturated compounds from the following
Question: Identify the unsaturated compounds from the following (i) Propane (ii) Propene (iii) Propyne (iv) Chloropropane (a)(i) and (ii) (b)(ii) and (iv) (c)(iii) and (iv) (d)(ii) and (iii) Solution: (d).Both propene and propyne are unsaturated hydrocarbons....
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Question: Tick (✓) the correct answer: In an examination, 65% of the total examinees passed. If the number of failures is 420, the total number of examinees is (a) 500 (b) 1000 (c) 1200 (d) 1625 Solution: (c) 1200 Let $x$ be the total number of examinees. Percentage of the examinees passed $=65 \%$ Percentage of the examinees failed $=35 \%$ Number of the examinees failed $=(35 \%$ of $x)$ $=\left(x \times \frac{35}{100}\right)$ $=\frac{35 x}{100}$ Now, $\frac{35 \mathrm{x}}{100}=420$ $\Rightarr...
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Question: If $y=\sin ^{-1}\left(\frac{x}{\sqrt{1+x^{2}}}\right)+\cos ^{-1}\left(\frac{1}{\sqrt{1+x^{2}}}\right), 0x\infty$, prove that $\frac{d y}{d x}=\frac{2}{1+x^{2}}$ Solution: $y=\sin ^{-1}\left(\frac{x}{\sqrt{1+x^{2}}}\right)+\cos ^{-1}\left(\frac{1}{\sqrt{1+x^{2}}}\right)$ Put $x=\tan \theta$ $y=\sin ^{-1}\left(\frac{\tan \theta}{\sqrt{1+\tan ^{2} \theta}}\right)+\cos ^{-1}\left(\frac{1}{\sqrt{1+\tan ^{2} \theta}}\right)$ Using, $\sec ^{2} \theta=1+\tan ^{2} \theta$ $y=\sin ^{-1}\left(\fr...
Read More →Structural formula of ethyne is
Question: Structural formula of ethyne is Solution: (a)...
Read More →Tick (✓) the correct answer
Question: Tick (✓) the correct answer: A period of 4 hours 30 min is what per cent of a day? (a) $18 \frac{3}{4} \%$ (b) $20 \%$ (C) $16 \frac{2}{3} \%$ (d) $19 \%$ Solution: (a) $18 \frac{3}{4} \%$ $4 h 30 \min =(4 \times 60 \times 60)+(30 \times 60)$ = 16200 sec Now, $\left(\frac{16200}{86400} \times 100\right) \%=18 \frac{3}{4} \%$...
Read More →Which of the following is the correct
Question: Which of the following is the correct representation of electron dot structure of nitrogen ? Solution: (d).Both the N atoms have a complete octet after electron sharing....
Read More →The soap molecule has a
Question: The soap molecule has a (a)hydrophilic head and a hydrophobic tail (b)hydrophobic head and a hydrophilic tail (c)hydrophobic head and a hydrophobic tail (d)hydrophilic head and a hydrophilic tail Solution: (a).Head is a polar group and is attacked towards H2O molecules of water. Tail is a long chain of hydrocarbons and is water repellent....
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Question: If $y=\sin ^{-1}\left(\frac{2 x}{1+x^{2}}\right)+\sec ^{-1}\left(\frac{1+x^{2}}{1-x^{2}}\right), 0x1$, prove that $\frac{d y}{d x}=\frac{4}{1+x^{2}}$ Solution: $y=\sin ^{-1}\left(\frac{2 x}{1+x^{2}}\right)+\sec ^{-1}\left(\frac{1+x^{2}}{1-x^{2}}\right)$ Put $x=\tan \theta$ Using, $\sec ^{-1} x=\frac{1}{\cos ^{-1} x}$ $y=\sin ^{-1}\left(\frac{2 x}{1+x^{2}}\right)+\cos ^{-1}\left(\frac{1-x^{2}}{1+x^{2}}\right)$ $y=\sin ^{-1}\left(\frac{2 \tan \theta}{1+\tan ^{2} \theta}\right)+\cos ^{-1}...
Read More →Tick (✓) the correct answer
Question: Tick (✓) the correct answer: A number is first increased by 10% and then reduced by 10%. The number (a) does not change (b) decrease by 1 % (c) increases by 1 % (d) none of these Solution: (b) decrease by 1 % Let $x$ be the number. A $10 \%$ increase will give a new number, $\frac{110}{100} x=\frac{11}{10} x$ The number is then reduced by $10 \%$. The new number will be $\frac{90}{100}\left(\frac{11}{10} \mathrm{x}\right)=\frac{990}{1000} x=\frac{99}{100} x$ Difference $=\mathrm{x}-\fr...
Read More →In which of the following compounds,
Question: In which of the following compounds, OH is the functional group ? (a)Butanone (b)Butanol (c)Butanoic acid (d)Butanal Solution: (b).OH is the functional group in butanol which is an alcohol....
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Question: Tick (✓) the correct answer: In an examination, Nitin gets 98 marks. This amounts to 56% of the maximum marks. What are the maximum marks? (a) 75 (b) 150 (c) 175 (d) 225 Solution: (c) 175 Let the maximum marks be $\mathrm{x}$. Then, we have: $56 \%$ of $x=\left(x \times \frac{56}{100}\right)$ $=\frac{56 x}{100}$ Now, $\frac{56 x}{100}=98$ $\Rightarrow x=\left(98 \times \frac{100}{56}\right)$ $\Rightarrow x=175$...
Read More →Let R+ be the set of all positive real numbers.
Question: Let $R^{+}$be the set of all positive real numbers. Let $f: R+\rightarrow R: f(x)=\log _{e} x$. Find (i) Range (f) (ii) $\left\{x: x \in R^{+}\right.$and $\left.f(x)=-2\right\}$. (iii) Find out whether $f(x+y)=f(x) . f(y)$ for all $x, y \in R$. Solution: Given that $\mathrm{f}: \mathrm{R}+\rightarrow \mathrm{R}$ such that $\mathrm{f}(\mathrm{x})=\log _{\mathrm{e}} \mathrm{x}$ To find: (i) Range of $f$ Here, $f(x)=\log _{e} x$ We know that the range of a function is the set of images of...
Read More →Differentiate the following functions with respect to x :
Question: Differentiate the following functions with respect to $x$ : $\sin ^{-1}\left(\frac{2^{x+1}}{1+4^{x}}\right)$ Solution: $y=\sin ^{-1}\left\{\frac{2^{x+1}}{1+4^{x}}\right\}$ For function to be defined $-1 \leq \frac{2^{x+1}}{1+4^{x}} \leq 1$ Since the quantity is positive always $\Rightarrow 0 \leq \frac{2^{x+1}}{1+4^{x}} \leq 1$ $\Rightarrow 02^{x+1} \leq 1+4^{x}$ $\Rightarrow 02 \leq 2^{-x}+2^{x}$ This condition is always true, hence function is always defined. $y=\sin ^{-1}\left\{\fra...
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Question: Tick (✓) the correct answer: 20% of Rs 800 = ? (a) Rs 160 (b) Rs 16 (c) Rs 1600 (d) none of these Solution: (a) Rs 160 $20 \%$ of $R s 800=R s\left(800 \times \frac{20}{100}\right)$ =Rs 160...
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