Other Physics · JEE Main previous year questions

A travelling wave is described by the equation $y(x,t)=[0.05\sin (8x-4t)]\mathrm{m}$ The velocity of the wave is : [all the quantities are in SI unit]

1. A.$4\mathrm{m}{\mathrm{s}}^{-1}$
2. B.$2\mathrm{m}{\mathrm{s}}^{-1}$
3. C.$8\mathrm{m}{\mathrm{s}}^{-1}$
4. D.$0.5\mathrm{m}{\mathrm{s}}^{-1}$

The maximum vertical height to which a man can throw a ball is 136 m. The maximum horizontal distance upto which he can throw the same ball is :

1. A.136 m
2. B.272 m
3. C.68 m
4. D.192 m

Given below are two statements : Statement I : An elevator can go up or down with uniform speed when its weight is balanced with the tension of its cable. Statement II : Force exerted by the floor of an elevator on the foot of a person standing on it is more than his/her weight when the elevator goes down with increasing speed. In the light of the above statements, choose the correct answer from the options given below :

1. A.Both Statement I and Statement II are false
2. B.Both Statement I and Statement II are true
3. C.Statement I is false but Statement II is true
4. D.Statement I is true but Statement II is false

Vectors $a\hat{i}+b\hat{j}+\hat{k}$ and $2\hat{i}-3\hat{j}+4\hat{k}$ are perpendicular to each other when $3a+2b=7$, the ratio of $a$ to $b$ is $\frac{x}{2}$. The value of $x$ is ____.

Given below are two statements: Statement I : Acceleration due to earth's gravity decreases as you go 'up' or 'down' from earth's surface. Statement II : Acceleration due to earth's gravity is same at a height 'h' and depth 'd' from earth's surface, if h = d. In the light of above statements, choose the most appropriate answer from the options given below

1. A.Statement I is correct but statement II is incorrect
2. B.Both Statement I and II are correct
3. C.Statement I is incorrect but statement II is correct
4. D.Both Statement I and Statement II are incorrect

If two vectors $\vec{P}=\hat{i}+2m\hat{j}+m\hat{k}$ and $\vec{Q}=4\hat{i}-2\hat{j}+m\hat{k}$ are perpendicular to each other. Then, the value of m will be :

1. A.$-1$
2. B.3
3. C.1
4. D.2

If $t=\sqrt{x}+4$, then ${\left(\frac{\mathrm{d}x}{\mathrm{d}t}\right)}_{t=4}$ is :

1. A.4
2. B.zero
3. C.8
4. D.16

Two light beams of intensities $4\mathrm{I}$ and $9\mathrm{I}$ interfere on a screen. The phase difference between these beams on the screen at point A is zero and at point B is $\pi$. The difference of resultant intensities, at the point A and B, will be ____ $\mathrm{I}$.

An $\alpha$ particle and a proton are accelerated from rest through the same potential difference. The ratio of linear momenta acquired by above two particles will be:

1. A.$\sqrt{2}:1$
2. B.$2\sqrt{2}:1$
3. C.$4\sqrt{2}:1$
4. D.$8:1$

A ball is released from a height $h$. If $t_1$ and $t_2$ be the time required to complete first half and second half of the distance respectively. Then, choose the correct relation between $t_1$ and $t_2$.

1. A.$t_1=(\sqrt{2})t_2$
2. B.$t_1=(\sqrt{2}-1)t_2$
3. C.$t_2=(\sqrt{2}+1)t_1$
4. D.$t_2=(\sqrt{2}-1)t_1$

An NCC parade is going at a uniform speed of $9km/h$ under a mango tree on which a monkey is sitting at a height of $19.6\mathrm{m}$. At any particular instant, the monkey drops a mango. A cadet will receive the mango whose distance from the tree at time of drop is: (Given $g=9.8m/{\mathrm{s}}^2$ )

1. A.$5\mathrm{m}$
2. B.$10\mathrm{m}$
3. C.$19.8\mathrm{m}$
4. D.$24.5\mathrm{m}$

If the radius of earth shrinks by $2\%$ while its mass remains same. The acceleration due to gravity on the earth's surface will approximately :

1. A.decrease by $2\%$
2. B.decrease by $4\%$
3. C.increase by $2\%$
4. D.increase by $4\%$

In the wave equation $$y=0.5\sin \frac{2\pi }{\lambda }(400t-x)\text{ m}$$ the velocity of the wave will be:

1. A.$200\text{ m/s}$
2. B.$200\sqrt{2}\text{ m/s}$
3. C.$400\text{ m/s}$
4. D.$400\sqrt{2}\text{ m/s}$

1. A.$1.0\times 10^8{\text{ ms}}^{-1}$
2. B.$0.5\times 10^8{\text{ ms}}^{-1}$
3. C.$1.5\times 10^8{\text{ ms}}^{-1}$
4. D.$3.0\times 10^8{\text{ ms}}^{-1}$

If the projection of $2\hat{i}+4\hat{j}-2\hat{k}$ on $\hat{i}+2\hat{j}+\alpha \hat{k}$ is zero. Then, the value of $\alpha$ will be _________.

At time $t=0$ a particle starts travelling from a height $7\hat{z}\text{ cm}$ in a plane keeping z coordinate constant. At any instant of time its position along the $\hat{x}$ and $\hat{y}$ directions are defined as $3t$ and $5t^3$ respectively. At $t=1\text{s}$ acceleration of the particle will be

1. A.$-30\hat{y}$
2. B.$30\hat{y}$
3. C.$3\hat{x}+15\hat{y}$
4. D.$3\hat{x}+15\hat{y}+7\hat{z}$

A vessel contains $14\text{ g}$ of nitrogen gas at a temperature of $27^{\circ }\text{C}$. The amount of heat to be transferred to the gas to double the r.m.s speed of its molecules will be : $\text{Take }\text{R}=8.32{\text{ J mol}}^{-1}{\text{ k}}^{-1}$.

1. A.$2229\text{ J}$
2. B.$5616\text{ J}$
3. C.$9360\text{ J}$
4. D.$13,104\text{ J}$

An electrical bulb rated 220 V, 100 W, is connected in series with another bulb rated 220 V, 60 W. If the voltage across combination is 220 V, the power consumed by the 100 W bulb will be about _______ W.

1. A.$18^{\circ }\text{C}$
2. B.$14^{\circ }\text{C}$
3. C.$45^{\circ }\text{C}$
4. D.$150^{\circ }\text{C}$

A magnet hung at $45^{\circ }$ with magnetic meridian makes an angle of $60^{\circ }$ with the horizontal. The actual value of the angle of dip is -

1. A.${\tan }^{-1}\left(\sqrt{\frac{3}{2}}\right)$
2. B.${\tan }^{-1}\left(\sqrt{6}\right)$
3. C.${\tan }^{-1}\left(\sqrt{\frac{2}{3}}\right)$
4. D.${\tan }^{-1}\left(\sqrt{\frac{1}{2}}\right)$

At a particular station, the TV transmission tower has a height of 100 m. To triple its coverage range, height of the tower should be increased to

1. A.200 m
2. B.300 m
3. C.600 m
4. D.900 m

The percentage decrease in the weight of a rocket, when taken to a height of $32\mathrm{km}$ above the surface of earth will be : ( Radius of earth $=6400\mathrm{km}$)

1. A.$1\%$
2. B.$3\%$
3. C.$4\%$
4. D.$0.5\%$

A monkey of mass $50\mathrm{kg}$ climbs on a rope which can withstand the tension (T) of $350\mathrm{N}$. If monkey initially climbs down with an acceleration of $4m/{\mathrm{s}}^2$ and then climbs up with an acceleration of $5m/{\mathrm{s}}^2$. Choose the correct option ($g=10m/{\mathrm{s}}^2$).

1. A.$T=700\mathrm{N}$ while climbing upward
2. B.$T=350\mathrm{N}$ while going downward
3. C.Rope will break while climbing upward
4. D.Rope will break while going downward

Two projectiles thrown at $30^{\circ }$ and $45^{\circ }$ with the horizontal respectively, reach the maximum height in same time. The ratio of their initial velocities is :

1. A.$1:\sqrt{2}$
2. B.$2:1$
3. C.$\sqrt{2}:1$
4. D.$1:2$

When a car is approaching the observer, the frequency of horn is $100\mathrm{Hz}$. After passing the observer, it is $50\mathrm{Hz}$. If the observer moves with the car, the frequency will be $\frac{x}{3}\mathrm{Hz}$ where $x=$ ____.