A cylindrical bucket 28 cm in diameter and 72 cm
Question: A cylindrical bucket 28 cm in diameter and 72 cm high is full of water. The water is emptied into a rectangular tank 66 cm long and 28 cm wide. Find the height of the water level in the tank. Solution: Let h be the height of rectangular tank = volume of cylindrical bucket $66 \times 28 \times h=\pi\left(\frac{28}{2}\right)^{2} \times 72$ $h=24 \mathrm{~cm}$ Hence, the height of rectangular tank is 24 cm....
Read More →Write the names of reagents and equations for the preparation of the following ethers by Williamson’s synthesis:
Question: Write the names of reagents and equations for the preparation of the following ethers by Williamsons synthesis: (i)1-Propoxypropane (ii)Ethoxybenzene (iii)2-Methoxy-2-methylpropane (iv)1-Methoxyethane Solution: (i) (ii) (iii) (iv)...
Read More →Two cylindrical vessels are filled with oil.
Question: Two cylindrical vessels are filled with oil. Their radii are 15 cm, 12 cm and heights 20 cm, 16 cm respectively. Find the radius of a cylindrical vessel 21 cm in height, which will just contain the oil of the two given vessels. Solution: The volume of $1^{\text {st }}$ cylindrical vessel $=\pi \times(15)^{2} \times 20$ $=225 \times 20 \times \pi$ $=4500 \pi \mathrm{cm}^{2}$ The volume of $2^{\text {nd }}$ cylindrical vessel $=\pi \times(12)^{2} \times 16$ $=144 \times 16 \times \pi$ $=...
Read More →Give IUPAC names of the following ethers:
Question: Give IUPAC names of the following ethers: (i) (ii) (iii) (iv) (v) (vi) Solution: (i)1-Ethoxy-2-methylpropane (ii)2-Chloro-1-methoxyethane (iii)4-Nitroanisole (iv)1-Methoxypropane (v)1-Ethoxy-4, 4-dimethylcyclohexane (vi)Ethoxybenzene...
Read More →Give reason for the higher boiling point of ethanol in comparison to methoxymethane.
Question: Give reason for the higher boiling point of ethanol in comparison to methoxymethane. Solution: Ethanol undergoes intermolecular H-bonding due to the presence of OH group, resulting in the association of molecules. Extra energy is required to break these hydrogen bonds. On the other hand, methoxymethane does not undergo H-bonding. Hence, the boiling point of ethanol is higher than that of methoxymethane....
Read More →Match the following columns:
Question: Match the following columns: Solution: (a) - (s)Let AEbex. Therefore, $\mathrm{EC}=5.6-x$ It is given that $\mathrm{DE} \| \mathrm{BC}$. Therefore, by B.P.T., we get: $\frac{A D}{D B}=\frac{A E}{E C}$ $\Rightarrow \frac{3}{5}=\frac{x}{5.6-x}$ $\Rightarrow 3(5.6-x)=5 x$ $\Rightarrow 16.8-3 x=5 x$ $\Rightarrow 8 x=16.8$ $\Rightarrow x=2.1 \mathrm{~cm}$ (b) - (q) $\because \triangle A B C \sim \triangle D E F$ $\therefore \frac{A B}{D E}=\frac{B C}{E F}$ $\Rightarrow \frac{3}{2}=\frac{6}{...
Read More →The inner and outer radii of a hollow cylinder are 15 cm and 20 cm,
Question: The inner and outer radii of a hollow cylinder are 15 cm and 20 cm, respectively. The cylinder is melted and recast into a solid cylinder of the same height. Find the radius of the base of new cylinder. Solution: Inner radius of hollow cylinderr1= 15 cm Outer radius of hollow cylinderr2= 20 cm The volume of hollow cylinder $=\pi\left(r_{2}^{2}-r_{1}^{2}\right) h$ Since, The hollow cylinder is melted and recast into a solid cylinder of same height. Let r be the radius of solid cylinder....
Read More →Name the reagents used in the following reactions:
Question: Name the reagents used in the following reactions: (i)Oxidation of a primary alcohol to carboxylic acid. (ii)Oxidation of a primary alcohol to aldehyde. (iii)Bromination of phenol to 2,4,6-tribromophenol. (iv)Benzyl alcohol to benzoic acid. (v)Dehydration of propan-2-ol to propene. (vi)Butan-2-one to butan-2-ol. Solution: (i) Acidified potassium permanganate (ii) Pyridinium chlorochromate (PCC) (iii) Bromine water (iv) Acidified potassium permanganate (v) 85% phosphoric acid (vi) NaBH4...
Read More →In the middle of a rectangular field measuring 30 m × 20 m,
Question: In the middle of a rectangular field measuring 30 m 20 m, a well of 7 m diameter and 10 m depth is dug. The earth so removed is evenly spread over the remaining part of the field. Find the height through which the level of the field is raised. Solution: Radius of dug $=\frac{7}{2} \mathrm{~m}$ Depth of dug = 10 m The volume of dug $=\pi\left(\frac{7}{2}\right)^{2} \times 10$ The volume of dug = 385 m3 Let the height through which the level of the field is raised will bex. But, volume o...
Read More →How are the following conversions carried out?
Question: How are the following conversions carried out? (i)Propene Propan-2-ol (ii)Benzyl chloride Benzyl alcohol (iii)Ethyl magnesium chloride Propan-1-ol. (iv)Methyl magnesium bromide 2-Methylpropan-2-ol. Solution: (i)If propene is allowed to react with water in the presence of an acid as a catalyst, then propan-2-ol is obtained. (ii)If benzyl chloride is treated with NaOH (followed by acidification) then benzyl alcohol is produced. (iii)When ethyl magnesium chloride is treated with methanal,...
Read More →Write the mechanism of acid-catalysed dehydration of ethanol to yield ethene.
Question: Write the mechanism of acid-catalysed dehydration of ethanol to yield ethene. Solution: The mechanism of acid dehydration of ethanol to yield ethene involves the following three steps: Step 1: Protonation of ethanol to form ethyl oxonium ion: Step 2: Formation of carbocation (rate determining step): Step 3: Elimination of a proton to form ethene: The acid consumed in step 1 is released in Step 3. After the formation of ethene, it is removed to shift the equilibrium in a forward directi...
Read More →A well with 10 m inside diameter is dug 8.4 m deep.
Question: A well with 10 m inside diameter is dug 8.4 m deep. Earth taken out of it is spread all around it to a width of 7.5 m to form an embankment. Find the height of the embankment. Solution: Radius of well Depth of well h = 8.4 m Clearly, Volume of earth dugout $=\pi(5)^{2} \times 8.4$ $=\pi \times 25 \times 8.4$ $=\frac{22 \times 25 \times 8.4}{7} \mathrm{~m}^{3}$ Leth' be the height of embankment Clearly, Embankment forms a cylindrical shell whose inner and outer radius are 5 m and 12.5 m...
Read More →Explain the following with an example.
Question: Explain the following with an example. (i)Kolbes reaction. (ii)Reimer-Tiemann reaction. (iii)Williamson ether synthesis. (iv)Unsymmetrical ether. Solution: (i)Kolbes reaction: When phenol is treated with sodium hydroxide, sodium phenoxide is produced. This sodium phenoxide when treated with carbon dioxide, followed by acidification, undergoes electrophilic substitution to give ortho-hydroxybenzoic acid as the main product. This reaction is known as Kolbes reaction. (ii)Reimer-Tiemann r...
Read More →Which of the following is false statement?
Question: Which of the following is false statement?(a) If the areas of two similar triangles are equal, then the triangles are congruent.(b) The ratio of the areas of two similar triangles is equal to the ratio of their corresponding sides.(c) The ratio of the areas of two similar triangles is equal to the ratio of squares of their corresponding medians.(d) The ratio of the areas of two similar triangles is equal to the ratio of squares of their corresponding altitudes. Solution: (b) The ratio ...
Read More →Give equations of the following reactions:
Question: Give equations of the following reactions: (i)Oxidation of propan-1-ol with alkaline KMnO4solution. (ii)Bromine in CS2with phenol. (iii)Dilute HNO3with phenol. (iv)Treating phenol with chloroform in presence of aqueous NaOH. Solution: (i) (ii) (iii) (iv)...
Read More →Which of the following is a true statement?
Question: Which of the following is a true statement?(a) Two similar triangles are always congruent.(b) Two figures are similar if they have the same shape and size.(c) Two triangles are similar if their corresponding sides are proportional.(d) Two polygons are similar if their corresponding sides are proportional. Solution: (c) Two triangles are similar if their corresponding sides are proportional.According to the statement: $\triangle A B C \sim \triangle D E F$ if $\frac{A B}{D E}=\frac{A C}...
Read More →Explain how does the −OH group
Question: Explain how does the OH group attached to a carbon of benzene ring activate it towards electrophilic substitution? Solution: The OH group is an electron-donating group. Thus, it increases the electron density in the benzene ring as shown in the given resonance structure of phenol. As a result, the benzene ring is activated towards electrophilic substitution....
Read More →A Carnot's engine working between 400 K and 800 K has a work output of 1200 J
Question: A Carnot's engine working between $400 \mathrm{~K}$ and $800 \mathrm{~K}$ has a work output of $1200 \mathrm{~J}$ per cycle. The amount of heat energy supplied to the engine from the source in each cycle is :$3200 \mathrm{~J}$$1800 \mathrm{~J}$$1600 \mathrm{~J}$$2400 \mathrm{~J}$Correct Option: , 4 Solution: (4) $\eta=\frac{T_{2}}{T_{1}}=\frac{Q_{2}}{Q_{1}}=\frac{Q_{1}-W}{Q_{1}} \quad\left(\because W=Q_{1}-Q_{2}\right)$ $\frac{400}{800}=1-\frac{W}{Q_{1}}$ $\frac{W}{Q_{1}}=1-\frac{1}{2}...
Read More →A spherical shell of lead,
Question: A spherical shell of lead, whose external diameter is 18 cm, is melted and recast into a right circular cylinder, whose height is 8 cm and diameter 12 cm. Determine the internal diameter of the shell. Solution: External radius of spherical shell $r_{1}=\frac{18}{2}=9 \mathrm{~cm}$ Letr2be the internal radius of spherical shell. Height of right circular cylinderh= 8 cm radius of right circular cylinder $r=\frac{12}{2}=6 \mathrm{~cm}$ Clearly, volume of spherical shell = volume of right ...
Read More →Explain why is ortho nitrophenol more acidic than ortho methoxyphenol?
Question: Explain why isorthonitrophenol more acidic thanorthomethoxyphenol? Solution: The nitro-group is an electron-withdrawing group. The presence of this group in the ortho position decreases the electron density in the OH bond. As a result, it is easier to lose a proton. Also, theo-nitrophenoxide ion formed after the loss of protons is stabilized by resonance. Hence,orthonitrophenol is a stronger acid. On the other hand, methoxy group is an electron-releasing group. Thus, it increases the e...
Read More →In ∆ABC, if AB = 16 cm, BC = 12 cm and AC = 20 cm, then ∆ABC is
Question: In ∆ABC,ifAB= 16 cm,BC= 12 cm andAC= 20 cm, then ∆ABCis(a) acute-angled(b) right-angled(c) obtuse-angled Solution: (b) right-angledWe have: $A B^{2}+B C^{2}=16^{2}+12^{2}=256+144=400$ and, $A C^{2}=20^{2}=400$ $\therefore A B^{2}+B C^{2}=A C^{2}$ Hence, ∆ABC is a right-angled triangle....
Read More →Give two reactions that show the acidic nature of phenol.
Question: Give two reactions that show the acidic nature of phenol. Compare acidity of phenol with that of ethanol. Solution: The acidic nature of phenol can be represented by the following two reactions: (i)Phenol reacts with sodium to give sodium phenoxide, liberating H2. (ii)Phenol reacts with sodium hydroxide to give sodium phenoxide and water as by-products. The acidity of phenol is more than that of ethanol. This is because after losing a proton, the phenoxide ion undergoes resonance and g...
Read More →Show how will you synthesize:
Question: Show how will you synthesize: (i)1-phenylethanol from a suitable alkene. (ii)cyclohexylmethanol using an alkyl halide by an SN2 reaction. (iii)pentan-1-ol using a suitable alkyl halide? Solution: (i)By acid-catalyzed hydration of ethylbenzene (styrene), 1-phenylethanol can be synthesized. (ii)When chloromethylcyclohexane is treated with sodium hydroxide, cyclohexylmethanol is obtained. (iii)When 1-chloropentane is treated with NaOH, pentan-1-ol is produced....
Read More →Three solid spheres of radii 3,
Question: Three solid spheres of radii 3, 4 and 5 cm respectively are melted and converted into a single solid sphere. Find the radius of this sphere. Solution: Let R be the radius of single solid sphere. Therefore, Volume of single solid sphere = volume of all three spheres $\frac{4}{3} \pi R^{3}=\frac{4}{3} \pi r_{1}^{3}+\frac{4}{3} \pi r_{2}^{3}+\frac{4}{3} \pi r_{3}^{3}$ $R^{3}=\left(3^{3}+4^{3}+5^{3}\right)$ $R^{3}=27+64+125$ $R^{3}=216$ $R=\sqrt{216}$ $=6$ $R=6$ Hence, the radius of single...
Read More →You are given benzene, conc.
Question: You are given benzene, conc. H2SO4and NaOH. Write the equations for the preparation of phenol using these reagents. Solution:...
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