Other Physics · JEE Main previous year questions

The relation between time '$t$' and distance '$x$' is $t=\alpha x^2+\beta x$, where $\alpha$ and $\beta$ are constants. The relation between acceleration $(a)$ and velocity $(v)$ is :

1. A.$a=-5\alpha v^5$
2. B.$a=-3\alpha v^2$
3. C.$a=-2\alpha v^3$
4. D.$a=-4\alpha v^4$

The parameter that remains the same for molecules of all gases at a given temperature is :

1. A.kinetic energy
2. B.mass
3. C.momentum
4. D.speed

If the wavelength of the first member of Lyman series of hydrogen is $\lambda$. The wavelength of the second member will be

1. A.$\frac{27}{5}\lambda$
2. B.$\frac{5}{27}\lambda$
3. C.$\frac{27}{32}\lambda$
4. D.$\frac{32}{27}\lambda$

If two vectors $\vec{A}$ and $\vec{B}$ having equal magnitude $R$ are inclined at angle $\theta$, then

1. A.$|\vec{A}+\vec{B}|=2R\cos \left(\frac{\theta }{2}\right)$
2. B.$|\vec{A}-\vec{B}|=2R\cos \left(\frac{\theta }{2}\right)$
3. C.$|\vec{A}-\vec{B}|=\sqrt{2}R\sin \left(\frac{\theta }{2}\right)$
4. D.$|\vec{A}+\vec{B}|=2R\sin \left(\frac{\theta }{2}\right)$

By what percentage will the illumination of the lamp decrease if the current drops by 20%?

1. A.26%
2. B.36%
3. C.46%
4. D.56%

A body of mass $2\mathrm{kg}$ begins to move under the action of a time dependent force given by $\vec{F}=\left(6t\hat{i}+6t^2\hat{j}\right)N$. The power developed by the force at the time $t$ is given by:

1. A.$\left(3t^3+6t^5\right)W$
2. B.$\left(9t^5+6t^3\right)W$
3. C.$\left(6t^4+9t^5\right)W$
4. D.$\left(9t^3+6t^5\right)W$

At which temperature is the r.m.s. velocity of a hydrogen molecule equal to that of an oxygen molecule at $47^{\circ }\text{C}$ ?

1. A.$20\text{ K}$
2. B.$80\text{ K}$
3. C.$4\text{ K}$
4. D.$-73\text{ K}$

At what distance above and below the surface of the earth a body will have same weight. (take radius of earth as $R$.)

1. A.$\frac{\sqrt{3}R-R}{2}$
2. B.$\frac{R}{2}$
3. C.$\frac{\sqrt{5}R-R}{2}$
4. D.$\sqrt{5}R-R$

A ball rolls off the top of a stairway with horizontal velocity $u$. The steps are $0.1\text{ m}$ high and $0.1\text{ m}$ wide. The minimum velocity $u$ with which that ball just hits the step 5 of the stairway will be $\sqrt{x}{\text{ ms}}^{-1}$ where $x=$ _______ [use $g=10{\text{ m/s}}^2$ ].

The temperature of a gas having $2.0\times 10^{25}$ molecules per cubic meter at $1.38\text{ atm}$ (Given, $k=1.38\times 10^{-23}{\text{JK}}^{-1}$) is :

1. A.$500\text{ K}$
2. B.$300\text{ K}$
3. C.$200\text{ K}$
4. D.$100\text{ K}$

A particle is moving in a straight line. The variation of position '$x$' as a function of time '$t$' is given as $x=(t^3-6t^2+20t+15)m$. The velocity of the body when its acceleration becomes zero is :

1. A.$6\text{ m/s}$
2. B.$10\text{ m/s}$
3. C.$8\text{ m/s}$
4. D.$4\text{ m/s}$

Two metallic wires $P$ and $Q$ have same volume and are made up of same material. If their area of cross sections are in the ratio $4:1$ and force $F_1$ is applied to $P$, an extension of $\Delta l$ is produced. The force which is required to produce same extension in $Q$ is ${\mathrm{F}}_2$. The value of $\frac{F_1}{F_2}$ is _________.

Position of an ant (S in metres) moving in Y-Z plane is given by $S=2t^2\hat{j}+5\hat{k}$ (where $t$ is in second). The magnitude and direction of velocity of the ant at $t=1\text{ s}$ will be :

1. A.$16\text{ m/s}$ in $y$-direction
2. B.$4\text{ m/s}$ in $x$-direction
3. C.$9\text{ m/s}$ in $z$-direction
4. D.$4\text{ m/s}$ in $y$-direction

The acceleration due to gravity on the surface of earth is $g$. If the diameter of earth reduces to half of its original value and mass remains constant, then acceleration due to gravity on the surface of earth would be :

1. A.$g/4$
2. B.$2g$
3. C.$g/2$
4. D.$4g$

Identify the physical quantity that cannot be measured using spherometer :

1. A.Radius of curvature of concave surface
2. B.Specific rotation of liquids
3. C.Thickness of thin plates
4. D.Radius of curvature of convex surface

The radius of third stationary orbit of electron for Bohr's atom is R. The radius of fourth stationary orbit will be:

1. A.$\frac{4}{3}R$
2. B.$\frac{16}{9}R$
3. C.$\frac{3}{4}R$
4. D.$\frac{9}{16}R$

A body of mass $1000\text{ kg}$ is moving horizontally with a velocity $6\text{ m/s}$. If $200\text{ kg}$ extra mass is added, the final velocity (in $\text{m/s}$) is:

1. A.$6$
2. B.$2$
3. C.$3$
4. D.$5$

A particle starts from origin at $t=0$ with a velocity $5\hat{i}\text{ m/s}$ and moves in $x-y$ plane under action of a force which produces a constant acceleration of $(3\hat{i}+2\hat{j}){\text{m/s}}^2$. If the $x$-coordinate of the particle at that instant is $84\text{ m}$, then the speed of the particle at this time is $\sqrt{\alpha }\text{ m/s}$. The value of $\alpha$ is ________.

A ball suspended by a thread swings in a vertical plane so that its magnitude of acceleration in the extreme position and lowest position are equal. The angle $(\theta )$ of thread deflection in the extreme position will be :

1. A.${\tan }^{-1}\left(\frac{1}{2}\right)$
2. B.$2{\tan }^{-1}\left(\frac{1}{2}\right)$
3. C.$2{\tan }^{-1}\left(\frac{1}{\sqrt{5}}\right)$
4. D.${\tan }^{-1}(\sqrt{2})$

The atomic mass of ${}_6{\text{C}}^{12}$ is $12.000000\text{ u}$ and that of ${}_6{\text{C}}^{13}$ is $13.003354\text{ u}$. The required energy to remove a neutron from ${}_6{\text{C}}^{13}$, if mass of neutron is $1.008665\text{ u}$, will be :

1. A.$62.5\text{ MeV}$
2. B.$6.25\text{ MeV}$
3. C.$4.95\text{ MeV}$
4. D.$49.5\text{ MeV}$

A bullet is fired into a fixed target loses one third of its velocity after travelling $4\text{ cm}$. It penetrates further $\text{D}\times 10^{-3}\text{ m}$ before coming to rest. The value of D is :

1. A.$23$
2. B.$32$
3. C.$42$
4. D.$52$

A body falling under gravity covers two points $A$ and $B$ separated by $80\text{ m}$ in $2\text{ s}$. The distance of upper point A from the starting point is _______ $\text{m}$ (use $\text{g}=10{\text{ ms}}^{-2}$).

Which of the following Maxwell's equation is valid for time varying conditions but not valid for static conditions :

1. A.$\oint \vec{E}\cdot \overrightarrow{dl}=0$
2. B.$\oint \vec{B}\cdot \overrightarrow{dl}={\mu }_{0}I$
3. C.$\oint \vec{E}\cdot \overrightarrow{dl}=-\frac{\partial {\varphi }_B}{\partial t}$
4. D.$\oint \vec{D}\cdot \overrightarrow{dA}=Q$

The ratio of powers of two motors is $\frac{3\sqrt{x}}{\sqrt{x}+1}$, that are capable of raising $300\text{ kg}$ water in 5 minutes and $50\text{ kg}$ water in 2 minutes respectively from a well of $100\text{ m}$ deep. The value of $x$ will be

1. A.$16$
2. B.$4$
3. C.$2$
4. D.$2.4$

Match List - I with List - II | List - I (Layer of atmosphere) | List - II (Approximate height over earth's surface) | | :--- | :--- | | (A) ${\mathrm{F}}_1$ - Layer | (I) $10\text{ km}$ | | (B) $\mathrm{D}$ - Layer | (II) $170\text{ - }190\text{ km}$ | | (C) Troposphere | (III) $100\text{ km}$ | | (D) $\mathrm{E}$ - Layer | (IV) $65\text{ - }75\text{ km}$ | Choose the correct answer from the options given below:

1. A.A - II, B - IV, C - III, D - I
2. B.A - II, B - I, C - IV, D - III
3. C.A - II, B - IV, C - I, D - III
4. D.A - III, B - IV, C - I, D - II