Solve this following
Question: A charged particle (mass $m$ and charge $q$ ) moves along $X$ axis with velocity $V_{0}$. When it passes through the origin it enters a region having uniform electric field $\overrightarrow{\mathrm{E}}=-E \hat{\mathrm{j}}$ which extends upto $x=d$. Equation of path of electron in the region $xd$ is : $\mathrm{y}=\frac{\mathrm{qEd}}{\mathrm{mV}_{0}^{2}}\left(\frac{\mathrm{d}}{2}-\mathrm{x}\right)$$\mathrm{y}=\frac{\mathrm{qEd}}{\mathrm{mV}_{0}^{2}}(\mathrm{x}-\mathrm{d})$$\mathrm{y}=\fr...
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Question: If speed $\mathrm{V}$, area $\mathrm{A}$ and force $\mathrm{F}$ are chosen as fundamental units, then the dimension of Young's modulus will be : $\mathrm{FA}^{-1} \mathrm{~V}^{0}$$\mathrm{FA}^{2} \mathrm{~V}^{-1}$$\mathrm{FA}^{2} \mathrm{~V}^{-3}$$\mathrm{FA}^{2} \mathrm{~V}^{-2}$Correct Option: 1 Solution: $\mathrm{Y}=\mathrm{Fx} \mathrm{A}^{\mathrm{y}} \mathrm{V} \mathrm{z}$ $\mathrm{M}^{1} \mathrm{~L}^{-1} \mathrm{~T}^{-2}=\left[\mathrm{MLT}^{-2}\right]^{x}\left[\mathrm{~L}^{2}\righ...
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Question: A gas mixture consists of 3 moles of oxygen and 5 moles of argon at temperature $\mathrm{T}$. Assuming the gases to be ideal and the oxygen bond to be rigid, the total internal energy (in units of RT) of the mixture is : 11152013Correct Option: , 2 Solution: $\mathrm{u}=\frac{\mathrm{f}_{1} \mathrm{n}_{1} \mathrm{RT}}{2}+\frac{\mathrm{f}_{2} \mathrm{n}_{2} \mathrm{RT}}{2}$ $\mathrm{u}=\frac{5}{2} \times 3 \mathrm{RT}+\frac{3 \times 5 \mathrm{RT}}{2}=15 \mathrm{RT}$...
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Question: A uniform cylinder of mass $M$ and radius $R$ is to be pulled over a step of height a $(aR)$ by applying a force $\mathrm{F}$ at its centre ' $\mathrm{O}$ ' perpendicular to the plane through the axes of the cylinder on the edge of the step (see figure). The minimum value of $\mathrm{F}$ required is : $\mathrm{Mg} \sqrt{1-\frac{\mathrm{a}^{2}}{\mathrm{R}^{2}}}$$\operatorname{Mg} \sqrt{\left(\frac{R}{R-a}\right)^{2}-1}$$\mathrm{Mg} \frac{\mathrm{a}}{\mathrm{R}}$$\operatorname{Mg} \sqrt{...
Read More →The atomic number of Unnilunium is
Question: The atomic number of Unnilunium is_________. Solution: Unnilunium $\Rightarrow 101$...
Read More →The rate of a reaction decreased by
Question: The rate of a reaction decreased by $3.555$ times when the temperature was changed from $40^{\circ} \mathrm{C}$ to $30^{\circ} \mathrm{C}$. The activation energy (in $\mathrm{kJ} \mathrm{mol}^{-1}$ ) of the reaction is______. Take; $\mathrm{R}=8.314 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$ In $3.555=1.268$ $\mathrm{E}_{\mathrm{a}}=99.98 \frac{\mathrm{kJ}}{\mathrm{mole}}$ Solution: $\ell\left(\frac{\mathrm{K}_{\mathrm{T}_{2}}}{\mathrm{~K}_{\mathrm{T}_{1}}}\right)=\frac{\mathrm{E...
Read More →A cylindrical vessel containing a liquid is rotated about its axis
Question: A cylindrical vessel containing a liquid is rotated about its axis so that the liquid rises at its sides as shown in the figure. The radius of vessel is $5 \mathrm{~cm}$ and the angular speed of rotation is $\omega \mathrm{rad} \mathrm{s}^{-1}$. The difference in the height, $\mathrm{h}($ in $\mathrm{cm})$ of liquid at the centre of vessel and at the side will be: $\frac{25 \omega^{2}}{2 g}$$\frac{2 \omega^{2}}{5 g}$$\frac{5 \omega^{2}}{2 g}$$\frac{2 \omega^{2}}{25 \mathrm{~g}}$Correct...
Read More →If the solubility product of
Question: If the solubility product of $\mathrm{AB}_{2}$ is $3.20 \times 10^{-11} \mathrm{M}^{3}$, then the solubility of $\mathrm{AB}_{2}$ in pure water is________$---^{\times} 10^{-4} \mathrm{~mol} \mathrm{~L}^{-1}$. [Assuming that neither kind of ion reacts with water] Solution: $\mathrm{AB}_{2}(\mathrm{~s}) \rightleftharpoons \mathrm{A}_{\text {(aq.) }}^{+2}+2 \mathrm{~B}_{\text {(aq.) }}^{-}: \mathrm{K}_{\text {sp }}$ $\mathrm{K}_{\mathrm{SP}}=\mathrm{S}^{1} \times(2 \mathrm{~s})^{2}=4 \mat...
Read More →A solution of phenol in chloroform when treated with aqueous
Question: A solution of phenol in chloroform when treated with aqueous $\mathrm{NaOH}$ gives compound $\mathrm{P}$ as a major product. The mass percentage of carbon in $\mathrm{P}$ is________. (to the nearest integer) (Atomic mass : $\mathrm{C}=12 ; \mathrm{H}=1 ; \mathrm{O}=16$ ) Solution: Molecular weight of $\mathrm{C}_{7} \mathrm{H}_{6} \mathrm{O}_{2}=122$ $\% \mathrm{C}=\frac{12 \times 7 \times 100}{122}=68.85 \approx 69$...
Read More →For Freundlich adsorption isotherm,
Question: For Freundlich adsorption isotherm, a plot of $\log (\mathrm{x} / \mathrm{m})$ ( $\mathrm{y}$-axis) and $\log \mathrm{p}$ ( $\mathrm{x}$-axis) gives a straight line. The intercept and slope for the line is $0.4771$ and 2, respectively. The mass of gas, adsorbed per gram of adsorbent if the initial pressure is $0.04 \mathrm{~atm}$, is__________$\times 10^{-4 \mathrm{~g}}$ $(\log 3=0.4771)$ Solution: $\frac{\mathrm{X}}{\mathrm{m}}=\mathrm{KP}^{1 / \mathrm{n}}$ $\log \left(\frac{x}{m}\rig...
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Question: In a reactor, $2 \mathrm{~kg}$ of ${ }_{92} \mathrm{U}^{235}$ fuel is fully used up in 30 days. The energy released per fission is $200 \mathrm{MeV}$. Given that the Avogadro number, $\mathrm{N}=6.023 \times 10^{26}$ per kilo mole and $1 \mathrm{eV}=1.6 \times 10^{-19} \mathrm{~J}$. The power output of the reactor is close to : $125 \mathrm{MW}$$60 \mathrm{MW}$$35 \mathrm{MW}$$54 \mathrm{MW}$Correct Option: , 2 Solution: Number of uranium atoms in $2 \mathrm{~kg}$ $=\frac{2 \times 6.02...
Read More →The increasing order of the boiling points of the major products A,
Question: The increasing order of the boiling points of the major products A, B and C of the following reactions will be : $\mathrm{C}\mathrm{A}\mathrm{B}$$\mathrm{B}\mathrm{C}\mathrm{A}$$\mathrm{A}\mathrm{B}\mathrm{C}$$\mathrm{A}\mathrm{C}\mathrm{B}$Correct Option: , 2 Solution:...
Read More →A plane electromagnetic wave, has frequency of
Question: A plane electromagnetic wave, has frequency of $2.0 \times 10^{10} \mathrm{~Hz}$ and its energy density is $1.02 \times 10^{-8} \mathrm{~J} / \mathrm{m}^{3}$ in vacuum. The amplitude of the magnetic field of the wave is close to $\left(\frac{1}{4 \pi \varepsilon_{0}}=9 \times 10^{9} \frac{\mathrm{Nm}^{2}}{\mathrm{C}^{2}}\right.$ and $\quad$ speed $\quad$ of $\quad$ light $\left.=3 \times 10^{8} \mathrm{~ms}^{-1}\right):$ $180 \mathrm{nT}$$160 \mathrm{nT}$$150 \mathrm{nT}$$190 \mathrm{n...
Read More →Match the following compounds (Column-I) with their uses (Column-II) :
Question: Match the following compounds (Column-I) with their uses (Column-II) : (I)-(D), (II)-(A), (III)-(C), (IV)-(B)(I)-(B), (II)-(C), (III)-(D), (IV)-(A)(I)-(C), (II)-(D), (III)-(B), (IV)-(A)(I)-(B), (II)-(D), (III)-(A), (IV)-(C)Correct Option: 4, Solution: (I) $\mathrm{Ca}(\mathrm{OH})_{2}$ is used in white wash (II) $\mathrm{NaCl}$ is used in preparation of washing soda $2 \mathrm{NH}_{3}+\mathrm{H}_{2} \mathrm{O}+\mathrm{CO}_{2} \longrightarrow\left(\mathrm{NH}_{4}\right)_{2} \mathrm{CO}_...
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Question: A bead of mass $m$ stays at point $P(a, b)$ on a wire bent in the shape of a parabola $\mathrm{y}=4 \mathrm{Cx}^{2}$ and rotating with angular speed $\omega$ (see figure). The value of $\omega$ is (neglect friction): $\sqrt{\frac{2 \mathrm{gC}}{\mathrm{ab}}}$$2 \sqrt{2 \mathrm{gC}}$$\sqrt{\frac{2 g}{\mathrm{C}}}$$2 \sqrt{\mathrm{gC}}$Correct Option: , 2 Solution: $x \omega^{2}=g \cdot \frac{d y}{d x}$ $x \omega^{2}=g .(8 c x)$ $\omega^{2}=8 \mathrm{gc}$ $\omega=2 \sqrt{2 \mathrm{gc}}$...
Read More →For a reaction,
Question: For a reaction, $4 \mathrm{M}(\mathrm{s})+\mathrm{nO}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{M}_{2} \mathrm{O}_{\mathrm{n}}(\mathrm{s})$ the free energy change is plotted as a function of temperature. The temperature below which the oxide is stable could be inferred from the plot as the point at which :the slope changes from positive to zerothe free energy change shows a change from negative to positive valuethe slope changes from negative to positivethe slope changes from positive to ...
Read More →A set of solutions is prepared using 180g of water as a solvent 10g of
Question: A set of solutions is prepared using $180 \mathrm{~g}$ of water as a solvent and $10 \mathrm{~g}$ of different non-volatile solutes A, B and C. The relative lowering of vapour pressure in the presence of these solutes are in the order [Given, molar mass of $\mathrm{A}=100 \mathrm{~g} \mathrm{~mol}^{-1} ; \mathrm{B}=200 \mathrm{~g} \mathrm{~mol}^{-1}$; $\mathrm{C}=10,000 \mathrm{~g} \mathrm{~mol}^{-1}$ ]$\mathrm{A}\mathrm{B}\mathrm{C}$$ACB$$\mathrm{C}\mathrm{B}\mathrm{A}$$\mathrm{B}\mat...
Read More →Which one of the following statements not true ?
Question: Which one of the following statements not true ?Lactose contains $\alpha-\mathrm{glycosidic}$ linkage between $C_{1}$ of galactose and $C_{4}$ of glucose.Lactose $\left(\mathrm{C}_{11} \mathrm{H}_{22} \mathrm{O}_{11}\right)$ is a disaccharide and it contains 8 hydroxyl groups.On acid hydrolysis, lactose gives one molecule of $\mathrm{D}(+)$-glucose and one molecule of $\mathrm{D}(+)$-galactose.Lactose is a reducing sugar and it gives Fehling's test.Correct Option: 1 Solution:...
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Question: + Shown in the figure is rigid and uniform one meter long rod $\mathrm{AB}$ held in horizontal position by two strings tied to its ends and attached to the ceiling. The rod is of mass ' $m$ ' and has another weight of mass $2 \mathrm{~m}$ hung at a distance of $75 \mathrm{~cm}$ from A. The tension in the string at $\mathrm{A}$ is : $2 \mathrm{mg}$$0.5 \mathrm{mg}$$0.75 \mathrm{mg}$$1 \mathrm{mg}$Correct Option: , 4 Solution: $\tau_{\mathrm{B}}=0$ (torque about point $\mathrm{B}$ is zer...
Read More →The average molar mass of chlorine is 35.5g
Question: The average molar mass of chlorine is $35.5 \mathrm{~g}$ $\mathrm{mol}^{-1}$. The ratio of ${ }^{35} \mathrm{Cl}$ to ${ }^{37} \mathrm{Cl}$ in naturally occurring chlorine is close to :$4: 1$$1: 1$$2: 1$$3: 1$Correct Option: , 4 Solution:...
Read More →Interference fringes are observed on a screen by illuminating two thin slits
Question: Interference fringes are observed on a screen by illuminating two thin slits $1 \mathrm{~mm}$ apart with a light source $(\lambda=632.8 \mathrm{~nm})$. The distance between the screen and the slits is $100 \mathrm{~cm}$. If a bright fringe is observed on a screen at a distance of $1.27 \mathrm{~mm}$ from the central bright fringe, then the path difference between the waves, which are reaching this point from the slits is close to : $1.27 \mu \mathrm{m}$$2 \mathrm{~nm}$$2.87 \mathrm{~nm...
Read More →The correct match between Item-I (starting material)
Question: The correct match between Item-I (starting material) and Item-II (reagent) for the preparation of benzaldehyde is : (I)-(Q), (II)-(R) and (III)-(P)(I)-(R), (II)-(Q) and (III)-(P)(I)-(R), (II)-(P) and (III)-(Q)(I)-(P), (II)-(Q) and (III)-(R)Correct Option: , 3 Solution:...
Read More →The mass density of a spherical galaxy varies
Question: The mass density of a spherical galaxy varies as $\frac{\mathrm{K}}{\mathrm{r}}$ over a large distance ' $\mathrm{r}$ ' from its centre. In that region, a small star is in a circular orbit of radius $R$. Then the period of revolution, $T$ depends on $R$ as :$\mathrm{T} \propto \mathrm{R}$$\mathrm{T}^{2} \propto \frac{1}{\mathrm{R}^{3}}$$\mathrm{T}^{2} \propto \mathrm{R}$$\mathrm{T}^{2} \propto \mathrm{R}^{3}$Correct Option: , 3 Solution: $\mathrm{dm}=\rho \mathrm{dv}$ $\mathrm{dm}=\lef...
Read More →Which of the following compounds can be prepared in good yield
Question: Which of the following compounds can be prepared in good yield by Gabriel phthalimide synthesis?$\mathrm{CH}_{3}-\mathrm{CH}_{2}-\mathrm{NHCH}_{3}$Correct Option: 1 Solution: Gabriel phthalimide synthesis is used for preparation of $1^{\circ}$ Aliphatic amine...
Read More →The least count of the main scale of a vernier callipers
Question: The least count of the main scale of a vernier callipers is $1 \mathrm{~mm}$. Its vernier scale is divided into 10 divisions and coincide with 9 divisions of the main scale. When jaws are touching each other, the $7^{\text {th }}$ division of vernier scale coincides with a division of main scale and the zero of vernier scale is lying right side of the zero of main scale. When this vernier is used to measure length of a cylinder the zero of the vernier scale between $3.1 \mathrm{~cm}$ a...
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