In an equilateral ∆ABC, D is the midpoint of AB and E is the midpoint of AC.
Question: In an equilateral ∆ABC,Dis the midpoint ofABandEis the midpoint ofAC. Then, ar(∆ABC) : ar(∆ADE) = ? (a) 2 : 1(b) 4 : 1(c) 1 : 2(d) 1 : 4 Solution: (b) 4:1In ∆ABC, Dis the midpoint ofABandEis the midpoint ofAC.Therefore, by midpoint theorem,DE∥BC.Also, byBasic Proportionality Theorem, $\frac{A D}{D B}=\frac{A E}{E C}$ Also, $A B=A C=B C(\because \Delta A B C$ is an equilateral triangle) So, $\frac{A D}{D B}=\frac{A E}{E C}=1$ In $\triangle A B C$ and $\triangle A D E$, we have : $\angle...
Read More →Predict the products of the following reactions:
Question: Predict the products of the following reactions: (i) (ii) (iii) (iv) Solution: (i) (ii) (iii) (iv)...
Read More →A solid is in the shape of a frustum of a cone,
Question: A solid is in the shape of a frustum of a cone, The diameters of the two circular ends are 60 cm and 36 cm and the height is 9 cm. Find the area of its whole surface and the volume. Solution: The height of the frustum of a cone ish=9cm. The radii of the upper and lower circles of the frustum of the cone arer1=30cm andr2=18cm respectively. The slant height of the frustum of the cone is $l=\sqrt{\left(r_{1}-r_{2}\right)^{2}+h^{2}}$ $=\sqrt{(30-18)^{2}+9^{2}}$ $=\sqrt{225}$ $=15 \mathrm{~...
Read More →A Carnot engine having an efficiency
Question: A Carnot engine having an efficiency of $\frac{1}{10}$ is being used as a refrigerator. If the work done on the refrigerator is $10 \mathrm{~J}$, the amount of heat absorbed from the reservoir at lower temperature is:$99 \mathrm{~J}$$100 \mathrm{~J}$$1 \mathrm{~J}$$90 \mathrm{~J}$Correct Option: , 4 Solution: (4) For carnot refrigerator Efficiency $=\frac{Q_{1}-Q_{2}}{Q_{1}}$ Where, $Q_{1}=$ heat lost from sorrounding $Q_{2}=$ heat absorbed from reservoir at low temperature. Also, $\fr...
Read More →Which of the following is an appropriate set of reactants for the preparation of
Question: Which of the following is an appropriate set of reactants for the preparation of 1-methoxy-4-nitrobenzene and why? (i) (ii) Solution: Set (ii) is an appropriate set of reactants for the preparation of 1-methoxy-4-nitrobenzene. In set (i), sodium methoxide (CH3ONa) is a strong nucleophile as well as a strong base. Hence, an elimination reaction predominates over a substitution reaction....
Read More →It is given that ∆ ABC ∼ ∆PQR and
Question: It is given that $\Delta A B C \sim \Delta P Q R$ and $\frac{B C}{Q R}=\frac{2}{3}$, then $\frac{\operatorname{ar}(\Delta P Q R)}{\operatorname{ar}(\Delta A B C)}=?$ (a) $\frac{2}{3}$ (b) $\frac{3}{2}$ (c) $\frac{4}{9}$ (d) $\frac{9}{4}$ Solution: (d) 9 : 4 It is given that $\Delta A B C \sim \Delta P Q R$ and $\frac{B C}{Q R}=\frac{2}{3}$. Therefore, $\frac{\operatorname{ar}(\triangle P Q R)}{\operatorname{ar}(\triangle A B C)}=\frac{Q R^{2}}{B C^{2}}=\left(\frac{3}{2}\right)^{2}=\fra...
Read More →A bucket made up of a metal sheet is in the form
Question: A bucket made up of a metal sheet is in the form of a frustum of a cone of height 16 cm with diameters of its lower and upper ends as 16 cm and 40 cm respectively. Find the volume of the bucket. Also, find the cost of the bucket if the cost of metal sheet used in Rs 20 per 100 cm2.(Use = 3.14) Solution: The height of the bucket ish=16cm. The radii of the upper and lower circles of the bucket arer1=20 cm andr2= 8 cm respectively. The slant height of the bucket is $l=\sqrt{\left(r_{1}-r_...
Read More →Write the reactions of Williamson synthesis of
Question: Write the reactions of Williamson synthesis of 2-ethoxy-3-methylpentane starting from ethanol and 3-methylpentan-2-ol. Solution: In Williamson synthesis, an alkyl halide reacts with an alkoxide ion. Also, it is an SN2 reaction. In the reaction, alkyl halides should be primary having the least steric hindrance. Hence, an alkyl halide is obtained from ethanol and alkoxide ion from 3-methylpentan-2-ol....
Read More →A non-isotropic solid metal cube has coefficients of linear expansion as:
Question: A non-isotropic solid metal cube has coefficients of linear expansion as: $5 \times 10^{-5} /{ }^{\circ} \mathrm{C}$ along the $x$-axis and $5 \times 10^{-6} /{ }^{\circ} \mathrm{C}$ along the $y$ and the $z$-axis. If the coefficient of volume expansion of the solid is $\mathrm{C} \times 10^{-6 /{ }^{\circ} \mathrm{C} \text { then the value }}$ of $C$ is Solution: $(60.00) \quad$ Volume, $V=I b h$ $\therefore \gamma=\frac{\Delta V}{V}=\frac{\Delta \ell}{\ell}+\frac{\Delta b}{b}+\frac{\...
Read More →Write the equations involved in the following reactions:
Question: Write the equations involved in the following reactions: (i)Reimer-Tiemann reaction (ii)Kolbes reaction Solution: Reimer-Tiemann reaction Kolbes reaction...
Read More →Corresponding sides of two similar triangles are in the ratio 4 : 9.
Question: Corresponding sides of two similar triangles are in the ratio 4 : 9. Areas of these triangles are in the ratio(a) 2 : 3(b) 4 : 9(c) 9 : 4(d) 16 : 81 Solution: If two triangles are similar, then the ratio of their areas is equal to the ratio of the squares of their corresponding sides. $\therefore \frac{\text { area of first triangle }}{\text { area of second triangle }}=\left(\frac{\text { Side of first triangle }}{\text { Side of second triangle }}\right)^{2}=\left(\frac{4}{9}\right)^...
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Question: A wire of density $9 \times 10^{-3} \mathrm{~kg} \mathrm{~cm}^{-3}$ is stretched between two clamps $1 \mathrm{~m}$ apart. The resulting strain in the wire is $4.9 \times 10^{-4}$. The lowest frequency of the transverse vibrations in the wire is (Young's modulus of wire $Y=9 \times 10^{10} \mathrm{Nm}^{-2}$ ), (to the nearest integer), Solution: $(35.00)$ Given, Denisty of wire, $\sigma=9 \times 10^{-3} \mathrm{~kg} \mathrm{~cm}^{-3}$ Young's modulus of wire, $Y=9 \times 10^{10} \mathr...
Read More →The radii of the circular ends of a solid frustum
Question: The radii of the circular ends of a solid frustum of a cone are 33 cm and 27 cm and its slant height is 10 cm. Find its total surface area. Solution: The slant height of the frustum of a cone isl=10cm. The radii of the upper and lower circles of the bucket arer1=33cm andr2=27cm respectively. The total surface area of the frustum of the cone is $S_{1}=\pi\left(r_{1}+r_{2}\right) \times l+\pi r_{1}^{2}+\pi r_{2}^{2}$ $=\pi \times(33+27) \times 10+\pi \times 33^{2}+\pi \times 27^{2}$ $=60...
Read More →In the given figure, two lines segments AC and BD intersect each other at the point P such that PA = 6 cm,
Question: In the given figure, two lines segmentsACandBDintersect each other at the pointPsuch thatPA= 6 cm,PB= 3 cm,PC= 2.5 cm,PD= 5 cm, APB= 50 and CDP= 30, then PBA= ? (a) 50(b) 30(c) 60(d) 100 Solution: (d) 100 In $\triangle A P B$ and $\triangle D P C$, we have : $\angle A P B=\angle D P C=50^{\circ}$ $\frac{A P}{B P}=\frac{6}{3}=2$ $\frac{D P}{C P}=\frac{5}{2.5}=2$ Hence, $\frac{A P}{B P}=\frac{D P}{C P}$ Applying $S A S$ theorem, we conclude that $\triangle A P B \sim \triangle D P C$. $\...
Read More →Ortho and para nitrophenols are more acidic than phenol.
Question: Orthoandparanitrophenols are more acidic than phenol. Draw the resonance structures of the corresponding phenoxide ions. Solution: Resonance structure of the phenoxide ion Resonance structures ofp-nitrophenoxide ion Resonance structures ofo-nitrophenoxide ion It can be observed that the presence of nitro groups increases the stability of phenoxide ion....
Read More →A bucket made of a aluminium sheet is of height 20 cm
Question: A bucket made of a aluminium sheet is of height 20 cm and its upper and lower ends are of radius 25 cm and 10 cm respectively. Find the cost of making the bucket if the aluminium sheet costs Rs 70 per 100 cm2. (Use = 3.14). Solution: The height of the bucket is 20cm. The radii of the upper and lower circles of the bucket arer1=25cm andr2=10cm respectively. The slant height of the bucket is $l=\sqrt{\left(r_{1}-r_{2}\right)^{2}+h^{2}}$ $=\sqrt{(25-10)^{2}+20^{2}}$ $=\sqrt{625}$ $=25 \ma...
Read More →Predict the major product of acid catalysed dehydration of
Question: Predict the major product of acid catalysed dehydration of (i)1-Methylcyclohexanol and (ii) Butan-1-ol Solution: (i) (ii)...
Read More →Solve this
Question: A proton, a deuteron and an $\alpha$ particle are moving with same momentum in a uniform magnetic field. The ratio of magnetic forces action on them is______ and their speed is_______ in the ratio.$2: 1: 1$ and $4: 2: 1$$1: 2: 4$ and $2: 1: 1$1: $2: 4$ and 1: 1:24: $2: 1$ and $2: 1: 1$Correct Option: 1 Solution: (1) As $v=\frac{p}{m} \ F=q v B$ $\therefore F=\frac{q p}{m} B$ $F_{1}=\frac{q p B}{m}, v_{1}=\frac{p}{m}$ $F_{2}=\frac{q p B}{2 m}, v_{2}=\frac{p}{2 m}$ $F_{3}=\frac{2 q p B}{...
Read More →A bucket is in the form of a frustum of a cone with
Question: A bucket is in the form of a frustum of a cone with a capacity of $12308.8 \mathrm{~cm}^{3}$ of water. The radii of the top and bottom circular ends are $20 \mathrm{~cm}$ and $12 \mathrm{~cm}$ respectively. Find the height of the bucket and the area of the metal sheet used in its making. (Use $\pi=3.14$ ). Solution: Let the depth of the bucket ishcm. The radii of the top and bottom circles of the frustum bucket arer1=20cm andr2=12cm respectively. The volume/capacity of the bucket is $V...
Read More →If in ∆ABC and ∆PQR, we have:
Question: If in $\triangle A B C$ and $\Delta P Q R$, we have: $\frac{A B}{Q R}=\frac{B C}{P R}=\frac{C A}{P Q}$, then (a) ∆PQR ∆CAB(b) ∆PQR ∆ABC(c) ∆CBA ∆PQR(d) ∆BCA ∆PQR Solution: (a) ∆PQR ∆CABIn ∆ABCand ∆PQR,we have: $\frac{A B}{Q R}=\frac{B C}{P R}=\frac{C A}{P Q}$ $\Rightarrow \triangle A B C \sim \triangle Q R P$ We can also write it as $\triangle P Q R \sim \triangle C A B$....
Read More →Give structures of the products you would expect when each of the following alcohol reacts with
Question: Give structures of the products you would expect when each of the following alcohol reacts with (a) HCl-ZnCl2(b) HBr and (c) SOCl2. (i)Butan-1-ol (ii)2-Methylbutan-2-ol Solution: (a) (i) Primary alcohols do not react appreciably with Lucas reagent (HCl-ZnCl2) at room temperature. (ii) Tertiary alcohols react immediately with Lucas reagent. (b) (i) (ii) (c) (i) (ii)...
Read More →Give structures of the products you would expect when each of the following alcohol reacts with
Question: Give structures of the products you would expect when each of the following alcohol reacts with (a) HCl-ZnCl2(b) HBr and (c) SOCl2. (i)Butan-1-ol (ii)2-Methylbutan-2-ol Solution: (a) (i) Primary alcohols do not react appreciably with Lucas reagent (HCl-ZnCl2) at room temperature. (ii) Tertiary alcohols react immediately with Lucas reagent. (b) (i) (ii) (c) (i) (ii)...
Read More →Write structures of the products of the following reactions:
Question: Write structures of the products of the following reactions: (i) (ii) (iii) Solution: (i) (ii) (iii)...
Read More →In ∆ABC and ∆DEF, it is given that ∠B = ∠E, ∠F = ∠C and AB = 3DE,
Question: In ∆ABCand ∆DEF, it is given that B= E, F= CandAB= 3DE, then the two triangles are(a) congruent but not similar(b) similar but not congruent(c) neither congruent nor similar(d) similar as well as congruent Solution: (b) similar but not congruentIn ∆ABCand ∆DEF, we have: $\angle B=\angle E$ and $\angle F=\angle C$ Applying $A A$ similarity theorem, we conclude that $\triangle A B C \sim \triangle D E F$. Also, $A B=3 D E$ $\Rightarrow A B \neq D E$ Therefore, $\triangle A B C$ and $\tri...
Read More →A metallic right circular cone 20 cm high
Question: A metallic right circular cone 20 cm high and whose vertical angle is 90 is cut into two parts at the middle point of its axis by a plane parallel to the base. If the frustum so obtained be drawn into a wire of diameter (1/16) cm, find the length of the wire. Solution: We have the following situation Let ABC be the cone. The height of the metallic cone is AO=20cm. The cone is cut into two parts at the middle point of its axis. Hence, the height of the frustum cone is AD=10cm. Since, th...
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