Two satellites A and B of masses
Question: Two satellites $A$ and $B$ of masses $200 \mathrm{~kg}$ and $400 \mathrm{~kg}$ are revolving round the earth at height of $600 \mathrm{~km}$ and $1600 \mathrm{~km}$ respectively. If $\mathrm{T}_{\mathrm{A}}$ and $\mathrm{T}_{\mathrm{B}}$ are the time periods of $\mathrm{A}$ and $\mathrm{B}$ respectively then the value of $T_{B}-T_{A}$ : [Given : radius of earth $=6400 \mathrm{~km}$, mass of earth $\left.=6 \times 10^{24} \mathrm{~kg}\right]$$1.33 \times 10^{3} \mathrm{~s}$$3.33 \times ...
Read More →Moment of inertia
Question: Moment of inertia (M.I.) of four bodies, having same mass and radius, are reported as ; $\mathrm{I}_{1}=$ M.I. of thin circular ring about its diameter. $\mathrm{I}_{2}=$ M.I. of circular disc about an axis perpendicular to the disc and going through the centre, $\mathrm{I}_{3}=$ M.I. of solid cylinder about its axis and $\mathrm{I}_{4}=$ M.I. of solid sphere about its diameter. Then :$\mathrm{I}_{1}+\mathrm{I}_{3}\mathrm{I}_{2}+\mathrm{I}_{4}$$\mathrm{I}_{1}+\mathrm{I}_{2}=\mathrm{I}_...
Read More →A current through a wire depends
Question: A current through a wire depends on time as $\mathrm{i}=\alpha_{0} \mathrm{t}+\beta \mathrm{t}^{2}$ where $\alpha_{0}=20 \mathrm{~A} / \mathrm{s}$ and $\beta=8 \mathrm{As}^{-2}$. Find the charge crossed through a section of the wire in $15 \mathrm{~s}$.$2250 \mathrm{C}$$11250 \mathrm{C}$$2100 \mathrm{C}$$260 \mathrm{C}$Correct Option: , 2 Solution: $\mathrm{i}=20 \mathrm{t}+8 \mathrm{t}^{2}$ $\mathrm{i}=\frac{\mathrm{dq}}{\mathrm{dt}} \Rightarrow \int \mathrm{dq}=\int \mathrm{idt}$ $\R...
Read More →A student is performing the experiment of resonance column.
Question: A student is performing the experiment of resonance column. The diameter of the column tube is $6 \mathrm{~cm}$. The frequency of the tuning fork is $504 \mathrm{~Hz}$. Speed of the sound at the given temperature is $336 \mathrm{~m} / \mathrm{s}$. The zero of the meter scale coincides with the top end of the resonance column tube. The reading of the water level in the column when the first resonance occurs is:$13 \mathrm{~cm}$$16.6 \mathrm{~cm}$$18.4 \mathrm{~cm}$$14.8 \mathrm{~cm}$Cor...
Read More →The maximum and minimum distances
Question: The maximum and minimum distances of a comet from the Sun are $1.6 \times 10^{12} \mathrm{~m}$ and $8.0 \times 10^{10} \mathrm{~m}$ respectively. If the speed of the comet afthe nearest point is $6 \times 10^{4} \mathrm{~ms}^{-1}$, the speed at the farthest point is:$1.5 \times 10^{3} \mathrm{~m} / \mathrm{s}$$6.0 \times 10^{3} \mathrm{~m} / \mathrm{s}$$3.0 \times 10^{3} \mathrm{~m} / \mathrm{s}$$4.5 \times 10^{3} \mathrm{~m} / \mathrm{s}$Correct Option: , 3 Solution: By angular moment...
Read More →Two stars of masses
Question: Two stars of masses $\mathrm{m}$ and $2 \mathrm{~m}$ at a distance $\mathrm{d}$ rotate about their common centre of mass in free space. The period of revolution is :$\frac{1}{2 \pi} \sqrt{\frac{\mathrm{d}^{3}}{3 \mathrm{Gm}}}$$2 \pi \sqrt{\frac{\mathrm{d}^{3}}{3 \mathrm{Gm}}}$$\frac{1}{2 \pi} \sqrt{\frac{3 \mathrm{Gm}}{\mathrm{d}^{3}}}$$2 \pi \sqrt{\frac{3 \mathrm{Gm}}{\mathrm{d}^{3}}}$Correct Option: , 2 Solution: $\mathrm{F}=\frac{\mathrm{G}(2 \mathrm{~m}) \mathrm{m}}{\mathrm{d}^{2}}...
Read More →Given below are two statement : one is labelled as Assertion A
Question: Given below are two statement : one is labelled as Assertion $A$ and the other is labelled as Reason R. Assertion A : When a rod lying freely is heated, no thermal stress is developed in it. Reason $R$ : On heating the length of the rod increases. In the light of the above statements, choose the correct answer from the options given below:Both $A$ and $R$ are true but $R$ is NOT the correct explanation of $\mathrm{A}$$A$ is false but $R$ is true$A$ is true but $R$ is falseBoth $\mathrm...
Read More →A plane electromagnetic wave of frequency 500 MHz is travelling in vacuum along y-direction.
Question: A plane electromagnetic wave of frequency $500 \mathrm{MHz}$ is travelling in vacuum along $\mathrm{y}$-direction. At a particular point in space and time, $\overrightarrow{\mathrm{B}}=8.0 \times 10^{-8} \hat{\mathrm{z}} \mathrm{T}$. The value of electric field at this point is : $\left(\right.$ speed of light $=3 \times 10^{8} \mathrm{~ms}^{-1}$ ) $\hat{\mathrm{x}}, \hat{\mathrm{y}}, \hat{\mathrm{z}}$ are unit vectors along $\mathrm{x}, \mathrm{y}$ and $\mathrm{z}$ direction.$-24 \hat...
Read More →In a Young's double slit experiment,
Question: In a Young's double slit experiment, the width of the one of the slit is three times the other slit. The amplitude of the light coming from a slit is proportional to the slit-width. Find the ratio of the maximum to the minimum intensity in the interference pattern.$1: 4$$3: 1$$4: 1$$2: 1$Correct Option: , 3 Solution: Amplitude $\propto$ Width of slit $\Rightarrow A_{2}=3 A_{1}$ $\frac{\mathrm{I}_{\max }}{\mathrm{I}_{\min }}=\left(\frac{\sqrt{\mathrm{I}_{1}}+\sqrt{\mathrm{I}_{2}}}{\left...
Read More →The focal length f
Question: The focal length $f$ is related to the radius of curvature $r$ of the spherical convex mirror by:$f=+\frac{1}{2} r$$f=-r$$\mathrm{f}=-\frac{1}{2} \mathrm{r}$$f=r$Correct Option: 1 Solution: For convex mirror, focus is behind the mirror....
Read More →n mole a perfect gas
Question: $\mathrm{n}$ mole a perfect gas undergoes a cyclic process ABCA (see figure) consisting of the following processes. $\mathrm{A} \rightarrow \mathrm{B}:$ Isothermal expansion at temperature $T$ so that the volume is doubled from $V_{1}$ to $V_{2}=2 V_{1}$ and pressure changes from $P_{1}$ to $P_{2}$. $\mathrm{B} \rightarrow \mathrm{C}:$ Isobaric compression at pressure $\mathrm{P}_{2}$ to initial volume $V_{1}$. $\mathrm{C} \rightarrow \mathrm{A}:$ Isochoric change leading to change of ...
Read More →Potassium chlorate is prepared by electrolysis of KCl
Question: Potassium chlorate is prepared by electrolysis of KCl in basic solution as shown by following equation. $6 \mathrm{OH}^{-}+\mathrm{Cl}^{-} \rightarrow \mathrm{ClO}_{3}^{-}+3 \mathrm{H}_{2} \mathrm{O}+6 \mathrm{e}^{-}$. A current of xA has to be passed for 10h to produce 10.0g of potassium chlorate. the value of x is _______. (Nearest integer) (Molar mass of $\mathrm{KClO}_{3}=122.6 \mathrm{~g} \mathrm{~mol}^{-1}$, $\mathrm{F}=96500 \mathrm{C}$ ) Solution: Given balanced equation is $\s...
Read More →An aqueous solution of
Question: An aqueous solution of $\mathrm{NiCl}_{2}$ was heated with excess sodium cyanide in presence of strong oxidizing agent to form $\left[\mathrm{Ni}(\mathrm{CN})_{6}\right]^{2-}$. The total change in number of unpaired electrons on metal centre is Solution: $\left[\mathrm{Ni}(\mathrm{CN})_{6}\right]^{2-}$ $\mathrm{Ni}^{+4} \rightarrow \mathrm{d}^{6}$ strong field ligand Pairing will be there zero unpaired electron $\mathrm{NiCl}_{2} \rightarrow \mathrm{Ni}^{2+} \rightarrow \mathrm{d}^{8}$...
Read More →Diamond has a three dimensional structure of C
Question: Diamond has a three dimensional structure of C atoms formed by covalent bonds. The structure of diamond has face centred cubic lattice where 50% of the tetrahedral voids are also occupied by carbon atoms. The number of carbon atoms present per unit cell of diamond is _______. Solution: Carbon atoms occupy FCC lattice points as well as half of the tetrahedral voids therefore number of carbon atoms atoms per unit cell = 8...
Read More →Solve this
Question: $\mathrm{PCl}_{5}(\mathrm{~g}) \rightarrow \mathrm{PCl}_{3}(\mathrm{~g})+\mathrm{Cl}_{2}(\mathrm{~g})$ In the above first order reaction the concentration of $\mathrm{PCl}_{5}$ reduces from initial concentration $50 \mathrm{~mol} \mathrm{~L}^{-1}$ to $10 \mathrm{~mol} \mathrm{~L}^{-1}$ in 120 minutes at $300 \mathrm{~K}$. The rate constant for the reaction at $300 \mathrm{~K}$ is $\mathrm{x} \times 10^{-2} \mathrm{~min}^{-1}$. The value of $\mathrm{x}$ is $[$ Given $\log 5=0.6989]$ Sol...
Read More →Solve this
Question: $100 \mathrm{ml}$ of $0.0018 \%(\mathrm{w} / \mathrm{v})$ solution of $\mathrm{Cl}^{-}$ion was the minimum concentration of $\mathrm{Cl}^{-}$required to precipitate a negative sol in one $\mathrm{h}$. The coagulating value of $\mathrm{Cl}^{-}$ion is _________(Nearest integer) Solution: Official Ans. by NTA (1)...
Read More →When 0.15 g of an organic compound was analyzed using
Question: When 0.15 g of an organic compound was analyzed using Carius method for estimation of bromine, 0.2397 g of AgBr was obtained. The percentage of bromine in the organic compound is _______. (Nearest integer) [Atomic mass : Silver = 108, Bromine = 80] Solution: Moles of $\mathrm{Br}=$ Moles of $\mathrm{AgBr}$ obtained $\Rightarrow$ Mass of $\mathrm{Br}=\frac{0.2397}{188} \times 80 \mathrm{~g}$ therefore $\% \mathrm{Br}$ in the organic compound $=\frac{\mathrm{W}_{\mathrm{Br}}}{\mathrm{W}_...
Read More →4g equimolar mixture of NaOH
Question: $4 \mathrm{~g}$ equimolar mixture of $\mathrm{NaOH}$ and $\mathrm{Na}_{2} \mathrm{CO}_{3}$ contains $x g$ of $\mathrm{NaOH}$ and y $g$ of $\mathrm{Na}_{2} \mathrm{CO}_{3}$. The value of $\mathrm{x}$ is g. (Nearest integer) Solution:...
Read More →The vapour pressures of A and B
Question: The vapour pressures of $\mathrm{A}$ and $\mathrm{B}$ at $25^{\circ} \mathrm{C}$ are $90 \mathrm{~mm} \mathrm{Hg}$ and $15 \mathrm{~mm} \mathrm{Hg}$ respectively. If $\mathrm{A}$ and $\mathrm{B}$ are mixed such that the mole fraction of $\mathrm{A}$ in the mixture is $0.6$, then the mole fraction of B in the vapour phase is $x \times 10^{-1}$. The value of $x$ is (Nearest integer) Solution: Given $\mathrm{P}_{\mathrm{A}}{ }^{\circ}=90 \mathrm{~mm} \mathrm{Hg}$, at $25^{\circ} \mathrm{C...
Read More →The wavelength of electrons accelerated from rest through
Question: The wavelength of electrons accelerated from rest through a potential difference of $40 \mathrm{kV}$ is $\mathrm{x} \times 10^{-12} \mathrm{~m}$. The value of $\mathrm{x}$ is (Nearest integer) Given : Mass of electron $=9.1 \times 10^{-31} \mathrm{~kg}$ Charge on an electron $=1.6 \times 10^{-19} \mathrm{C}$ Planck's constant $=6.63 \times 10^{-34} \mathrm{JS}$ Solution: De-broglie-wave length of electron: $\lambda_{\mathrm{e}}=\frac{\mathrm{h}}{\sqrt{2 \mathrm{~m}(\mathrm{KE})}}\left\...
Read More →For a given chemical reaction
Question: For a given chemical reaction $\mathrm{A} \rightarrow \mathrm{B}$ at $300 \mathrm{~K}$ the free energy change is $-49.4 \mathrm{~kJ} \mathrm{~mol}^{-1}$ and the enthalpy of reaction is $51.4 \mathrm{~kJ} \mathrm{~mol}^{-1}$. The entropy change of the reaction is $\mathrm{J} \mathrm{K}^{-1} \mathrm{~mol}^{-1}$. Solution: $\mathrm{A} \underset{\mathrm{T} 300 \mathrm{~K}}{\longrightarrow} \mathrm{B} \quad[\Delta \mathrm{G}]_{\mathrm{P}, \mathrm{T}}=-49.4 \mathrm{~kJ} / \mathrm{mol}$ $\Del...
Read More →Solve this
Question: The correct order of their reactivity towards hydrolysis at room temperature is :$(\mathrm{A})(\mathrm{B})(\mathrm{C})(\mathrm{D})$$(\mathrm{D})(\mathrm{A})(\mathrm{B})(\mathrm{C})$$(\mathrm{D})(\mathrm{B})(\mathrm{A})(\mathrm{C})$$(\mathrm{A})(\mathrm{C})(\mathrm{B})(\mathrm{D})$Correct Option: 1, Solution:...
Read More →The angle of deviation through a prism is minimum when
Question: The angle of deviation through a prism is minimum when (A) Incident ray and emergent ray are symmetric to the prism (B) The refracted ray inside the prism becomes parallel to its base (C) Angle of incidence is equal to that of the angle of emergence (D) When angle of emergence is double the angle of incidence Choose the correct answer from the options given below :Statements (A), (B) and (C) are trueOnly statement (D) is trueOnly statements (A) and (B) are trueStatements (B) and (C) ar...
Read More →The pressure acting on a submarine is 3 × 105 Pa at a certain depth. If the depth is doubled, the percentage increase in the pressure acting on the submarine would be :
Question: The pressure acting on a submarine is $3 \times 10^{5}$ $\mathrm{Pa}$ at a certain depth. If the depth is doubled, the percentage increase in the pressure acting on the submarine would be : (Assume that atmospheric pressure is $1 \times 10^{5} \mathrm{~Pa}$ density of water is $10^{3} \mathrm{~kg} \mathrm{~m}^{-3}, \mathrm{~g}=10 \mathrm{~ms}^{-2}$ )$\frac{200}{3} \%$$\frac{200}{5} \%$$\frac{5}{200} \%$$\frac{3}{200} \%$Correct Option: 1 Solution: $\mathrm{P}_{1}=\rho \mathrm{gd}+\math...
Read More →Which one of the following gases is reported
Question: Which one of the following gases is reported to retard photosynthesis ?COCFCs$\mathrm{CO}_{2}$$\mathrm{NO}_{2}$Correct Option: , 4 Solution: According to NCERT only $\mathrm{NO}_{2}$ from the given options can retard the photosynthesis process in plants....
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