A train covers a distance of 300 km at a uniform speed. If the speed of the train is increased by 5 km/hour, it takes 2 hours less in the journey.
Question: A train covers a distance of 300 km at a uniform speed. If the speed of the train is increased by 5 km/hour, it takes 2 hours less in the journey. Find the original speed of the train. Solution: Distance covered by the train = 300 km We know that distance covered $(d)=\operatorname{speed}(s) \times \operatorname{time}(t)$ $\Rightarrow s \times t=300$ $\Rightarrow t=\frac{300}{s} \quad \ldots(\mathrm{i})$ Also, given that if the speed is increased by 5 km/h, time of travel gets reduced ...
Read More →Consider a gas of triatomic molecules.
Question: Consider a gas of triatomic molecules. The molecules are assumed to be triangular and made of massless rigid rods whose vertices are occupied by atoms. The internal energy of a mole of the gas at temperature $T$ is :(1) $\frac{5}{2} R T$(2) $\frac{3}{2} R T$(3) $\frac{9}{2} R T$(4) $3 R T$Correct Option: 4, Solution: (4) Here degree of freedom, $f=3+3=6$ for triatomic nonlinear molecule. Internal energy of a mole of the gas at temperature $T$, $U=\frac{f}{2} n R T=\frac{6}{2} R T=3 R T...
Read More →In molecule, the hybridization of carbon $1,2,3$ and 4 respectively are:
Question: In molecule, the hybridization of carbon $1,2,3$ and 4 respectively are:$\mathrm{sp}^{2}, \mathrm{sp}, \mathrm{sp}^{2}, \mathrm{sp}^{3}$$\mathrm{sp}^{2}, \mathrm{sp}^{2}, \mathrm{sp}^{2}, \mathrm{sp}^{3}$$\mathrm{sp}^{2}, \mathrm{sp}^{3}, \mathrm{sp}^{2}, \mathrm{sp}^{3}$$\mathrm{sp}^{3}, \mathrm{sp}, \mathrm{sp}^{3}, \mathrm{sp}^{3}$Correct Option: 1 Solution:...
Read More →The locus of the mid-point of the line
Question: The locus of the mid-point of the line segment joining the focus of the parabola $\mathrm{y}^{2}=4$ ax to a moving point of the parabola, is another parabola whose directrix is:(1) $x=a$(2) $x=0$(3) $x=-\frac{a}{2}$(4) $x=\frac{a}{2}$Correct Option: , 2 Solution: $\mathrm{h}=\frac{\mathrm{at}^{2}+\mathrm{a}}{2}, \mathrm{k}=\frac{2 \mathrm{at}+0}{2}$ $\Rightarrow \mathrm{t}^{2}=\frac{2 \mathrm{~h}-\mathrm{a}}{\mathrm{a}}$ and $\mathrm{t}=\frac{\mathrm{k}}{\mathrm{a}}$ $\Rightarrow \frac...
Read More →An ideal gas in a closed container is slowly heated.
Question: An ideal gas in a closed container is slowly heated. As its temperature increases, which of the following statements are true? (a) The mean free path of the molecules decreases (b) The mean collision time between the molecules decreases (c) The mean free path remains unchanged (d) The mean collision time remains unchanged(1) (b) and (c)(2) (a) and (b)(3) (c) and (d)(4) (a) and (d)Correct Option: 1 Solution: (1) As we know mean free path $\lambda=\frac{1}{\sqrt{2}\left(\frac{N}{V}\right...
Read More →Given below are two statement :
Question: Given below are two statement : Statement I : o-Nitrophenol is steam volatile due to intramolecular hydrogen bonding Statement II : 0-Nitrophenol has high melting point due to hydrogen bonding. In the light of the above statements, choose the most appropriate answer from the options given below :Both Statement I and Statement II are falseStatement I is false but Statement II is trueBoth Statement I and Statement II are trueStatement I is true but Statement II is falseCorrect Option: , ...
Read More →A train travels 180 km at a uniform speed. If the speed had been 9 km/hr more, it would have taken 1 hour less for the same journey.
Question: A train travels 180 km at a uniform speed. If the speed had been 9 km/hr more, it would have taken 1 hour less for the same journey. Find the speed of the train. Solution: Distance covered by the train = 180 km We know that distance covered $(d)=\operatorname{speed}(s) \times \operatorname{time}(t)$ $\Rightarrow s \times t=180$ $\Rightarrow s=\frac{180}{t} \quad \ldots(\mathrm{i})$ Also, given that if the speed is increased by 9km/h, time of travel gets reduced by 1 hour. $\Rightarrow(...
Read More →The correct order of acid character of the following compounds is :
Question: The correct order of acid character of the following compounds is : $\mathrm{II}\mathrm{III}\mathrm{IV}\mathrm{I}$$\mathrm{III}\mathrm{II}\mathrm{I}\mathrm{IV}$$I VI I II II$$\mathrm{I}\mathrm{II}\mathrm{III}\mathrm{IV}$Correct Option: 1 Solution:...
Read More →If the three normals drawn to the parabola,
Question: If the three normals drawn to the parabola, $y^{2}=2 x$ pass through the point $(a, 0) a \neq 0$, then ' $a$ ' must be greater than :(1) $\frac{1}{2}$(2) $-\frac{1}{2}$(3) $-1$(4) 1Correct Option: , 4 Solution: For standard parabola For more than 3 normals (on axis) $x\frac{L}{2}$ (where $L$ is length of L.R.) For $y^{2}=2 x$ L.R. $=2$ for $(a, 0)$ $a\frac{\text { L.R. }}{2} \Rightarrow a1$...
Read More →A gas mixture consists of 3 moles of oxygen and 5 moles of argon at temperature T.
Question: A gas mixture consists of 3 moles of oxygen and 5 moles of argon at temperature $T$. Assuming the gases to be ideal and the oxygen bond to be rigid, the total internal energy (in units of RT) of the mixture is:(1) 15(2) 13(3) 20(4) 11Correct Option: 1 Solution: (1) Total energy of the gas mixture, $E_{\text {mix }}=\frac{f_{1} n_{1} R T_{1}}{2}+\frac{f_{2} n_{2} R T_{2}}{2}$ $=3 \times \frac{5}{2} R T+\frac{5}{2} \times 3 R T=15 R T$...
Read More →Which one of the following compounds is non-aromatic ?
Question: Which one of the following compounds is non-aromatic ?Correct Option: , 2 Solution: Hence It is non-aromatic....
Read More →The volume V of a given mass of monatomic gas changes
Question: The volume $\mathrm{V}$ of a given mass of monatomic gas changes with temperature $\mathrm{T}$ according to the relation $\mathrm{V}=\mathrm{KT}^{\frac{2}{3}}$. The work done when temperature changes by $90 \mathrm{~K}$ will be $\mathrm{xR}$. The value of $\mathrm{X}$ is_______ [ $R$ =universal gas constant] Solution: (60) Given: $V=k T^{2 / 3}$ $V^{3 / 2}=(k)^{3 / 2} T$ $\mathrm{TV}^{-3 / 2}=$ const. $\ldots(1)$ and $\mathrm{TV}^{\gamma-1}=$ const $\ldots(2)$ From (1)\(2) $-\frac{3}{2...
Read More →A train travels at a certain average speed for a distance of 54 km and then travels a distance of 63 km at an average of 6 km/hr more than the first speed.
Question: A train travels at a certain average speed for a distance of 54 km and then travels a distance of 63 km at an average of 6 km/hr more than the first speed. If it takes 3 hours to complete the total journey, what is its first speed? Solution: Let the first speed of the train bexkm/h. $\therefore$ Time taken to cover $54 \mathrm{~km}=\frac{54}{x} \mathrm{~h}$ $\left(\right.$ Time $\left.=\frac{\text { Distance }}{\text { Speed }}\right)$ New speed of the train =(x+ 6) km/h $\therefore$ T...
Read More →Given below are two statements :
Question: Given below are two statements : Statement $\mathbf{I}: \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}$ and $\mathrm{AgCN}$ both can generate nucleophile. Statement II : KCN and AgCN both will generate nitrile nucleophile with all reaction conditions.Statement I is true but statement II is falseBoth statement I and statement II are trueStatement I is false but statement II is trueBoth statement I and statement II are falseCorrect Option: Solution: Statement I is true but statement II is fal...
Read More →Given below are two statements :
Question: Given below are two statements : Statement $\mathbf{I}: \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}$ and $\mathrm{AgCN}$ both can generate nucleophile. generate nucleophile. Statement II : KCN and AgCN both will generate nitrile nucleophile with all reaction conditions.Statement I is true but statement II is falseBoth statement I and statement II are trueStatement I is false but statement II is trueBoth statement I and statement II are falseCorrect Option: Solution: Statement I is true b...
Read More →The internal energy (U), pressure (P) and volume (V)
Question: The internal energy $(U)$, pressure $(P)$ and volume $(V)$ of an ideal gas are related as $U=3 P V+4$. The gas is :(1) polyatomic only(2) monoatomic only(3) either monoatomic or diatomic(4) diatomic only.Correct Option: 1, Solution: (1) $U=3 P V+4$ $\frac{\mathrm{f}}{2} \mathrm{PV}=3 \mathrm{PV}+4 \quad \therefore \mathrm{u}=\frac{\mathrm{f}}{2} \mathrm{nRT}$ $f=6+\frac{8}{P V} \therefore \mathrm{PV}=\mathrm{nRT}$ $\mathrm{f}6 \therefore$ Polyatomic gas....
Read More →The internal energy (U), pressure $P) and volume (V)
Question: The internal energy $(U)$, pressure $(P)$ and volume $(V)$ of an ideal gas are related as $U=3 P V+4$. The gas is :(1) polyatomic only(2) monoatomic only(3) either monoatomic or diatomic(4) diatomic only.Correct Option: 1 Solution: (1) $U=3 P V+4$ $\frac{\mathrm{f}}{2} \mathrm{PV}=3 \mathrm{PV}+4 \quad \therefore \mathrm{u}=\frac{\mathrm{f}}{2} \mathrm{nRT}$ $f=6+\frac{8}{P V} \therefore \mathrm{PV}=\mathrm{nRT}$ $\mathrm{f}6 \therefore$ Polyatomic gas....
Read More →Given below are two statements :
Question: Given below are two statements : Statement $\mathbf{I}: \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}$ and $\mathrm{AgCN}$ both can generate nucleophile. Statement II : KCN and AgCN both will generate nitrile nucleophile with all reaction conditions.Statement I is true but statement II is falseBoth statement I and statement II are trueStatement I is false but statement II is trueBoth statement I and statement II are falseCorrect Option: Solution: Statement I is true but statement II is fal...
Read More →Compound with molecular formula
Question: Compound with molecular formula $\mathrm{C}_{3} \mathrm{H}_{6} \mathrm{O}$ can show :Positional isomerismBoth positional isomerism and metamerismMetamerismFunctional group isomerismCorrect Option: , 4 Solution: They are functional group isomerism....
Read More →A container is divided into two chambers by a partition.
Question: A container is divided into two chambers by a partition. The volume of first chamber is $4.5$ litre and second chamber is $5.5$ litre. The first chamber contain $3.0$ moles of gas at pressure $2.0 \mathrm{~atm}$ and second chamber contain $4.0$ moles of gas at pressure $3.0 \mathrm{~atm}$. After the partition is removed and the mixture attains equilibrium, then, the common equilibrium pressure existing in the mixture is $\mathrm{x} \times 10^{-1}$ atm. Value of $\mathrm{x}$ is Solution...
Read More →Match List-I with List-II :
Question: Match List-I with List-II : List-I (Chemicals) (a) Alcoholic potassium hydroxide (b) $\mathrm{Pd} / \mathrm{BaSO}_{4}$ (c) $\mathrm{BHC}$ (Benzene hexachloride) (d) Polyacctylenc List-II (Use / Preparation / Constituent)Electrodes in batteriesObtained by addition reactionUsed for $\beta$ - elimination reactionLindlar's catalystCorrect Option: , 2 Solution: (a) Alcoholic potassium hydroxide $\rightarrow$ used for $\beta$-elimination (b) $\mathrm{Pd} / \mathrm{BaSO}_{4} \rightarrow$ Lind...
Read More →Given below are two statements:
Question: Given below are two statements: Statement I: In a diatomic molecule, the rotational energy at a given temperature obeys Maxwell's distribution. Statement II: in a diatomic molecule, the rotational energy at a given temperature equals the translational kinetic energy for each molecule. In the light of the above statements, choose the correct answer from the options given below:(1) Both statement I and statement II are false.(2) Both statement I and statement II are true,(3) Statement I ...
Read More →Choose the correct statement regarding the formation of carbocations
Question: Choose the correct statement regarding the formation of carbocations A and $\mathrm{B}$ given :- Carbocation B is more stable and formed relatively at faster rateCarbocation A is more stable and formed relatively at slow rateCarbocation B is more stable and formed relatively at slow rateCarbocation $\mathrm{A}$ is more stable and formed relatively at faster rateCorrect Option: 1 Solution: This is more stable due to secondary cation formation and formed with faster rate due to low activ...
Read More →Prove the following
Question: Let $a-2 b+c=1$ If $f(x)=\left|\begin{array}{lll}x+a x+2 x+1 \\ x+b x+3 x+2 \\ x+c x+4 x+3\end{array}\right|$, then : (1) $f(-50)=501$(2) $f(-50)=-1$(3) $f(50)=-501$(4) $f(50)=1$Correct Option: , 4 Solution: If $f(x)=\left|\begin{array}{lll}x+a x+2 x+1 \\ x+b x+3 x+2 \\ x+c x+4 x+3\end{array}\right|$ $R_{1}=R_{1}+R_{3}-2 R_{2}$ $\Rightarrow \quad f(x)=\left|\begin{array}{ccc}1 0 0 \\ x+b x+3 x+2 \\ x+c x+4 x+3\end{array}\right|$ $\Rightarrow f(x)=1 \Rightarrow f(50)=1$...
Read More →A monoatomic gas of mass 4.0u
Question: A monoatomic gas of mass $4.0 u$ is kept in an insulated container. Container is moving with velocity $30 \mathrm{~m} / \mathrm{s}$. If container is suddenly stopped then change in temperature of the gas ( $\mathrm{R}=$ gas constant) is $\frac{x}{3 R}$. Value of $x$ is Solution: $(3600)$ $\Delta \mathrm{K}_{\mathrm{E}}=\Delta \mathrm{U}$ $\Delta \mathrm{U}=\mathrm{nC}_{\mathrm{V}} \Delta \mathrm{T}$ $\frac{1}{2} \mathrm{mv}^{2}=\frac{3}{2} \mathrm{n} \mathrm{R} \Delta \mathrm{T}$ $\fra...
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