Other Physics · JEE Main previous year questions

A force on an object of mass $100\text{ g}$ is $\left(10\hat{i}+5\hat{j}\right)\text{ N}$. The position of that object at $t=2\text{ s}$ is $\left(a\hat{i}+b\hat{j}\right)\text{ m}$ after starting from rest. The value of $\frac{a}{b}$ will be $\underline{}$.

Two buses P and Q start from a point at the same time and move in a straight line and their positions are represented by $X_P(t)=\alpha t+\beta t^2$ and $X_Q(t)=ft-t^2$. At what time, both the buses have same velocity?

1. A.$\frac{\alpha -f}{1+\beta }$
2. B.$\frac{\alpha +f}{2(\beta -1)}$
3. C.$\frac{\alpha +f}{2(1+\beta )}$
4. D.$\frac{f-\alpha }{2(1+\beta )}$

A solid metallic cube having total surface area $24{\mathrm{m}}^2$ is uniformly heated. If its temperature is increased by $10^{\circ }\mathrm{C}$, calculate the increase in volume of the cube. (Given $\alpha =5.0\times 10^{-4}{}^{\circ }{\mathrm{C}}^{-1}$).

1. A.$2.4\times 10^6\mathrm{c}{\mathrm{m}}^3$
2. B.$1.2\times 10^5\mathrm{c}{\mathrm{m}}^3$
3. C.$6.0\times 10^4\mathrm{c}{\mathrm{m}}^3$
4. D.$4.8\times 10^5\mathrm{c}{\mathrm{m}}^3$

27 identical drops are charged at 22V each. They combine to form a bigger drop. The potential of the bigger drop will be _____________ V.

The distance between Sun and Earth is R. The duration of year if the distance between Sun and Earth becomes 3R will be :

1. A.$\sqrt{3}\mathrm{years}$
2. B.$3\mathrm{years}$
3. C.$9\mathrm{years}$
4. D.$3\sqrt{3}\mathrm{years}$

The soft-iron is a suitable material for making an electromagnet. This is because soft-iron has

1. A.low coercivity and high retentivity.
2. B.low coercivity and low permeability.
3. C.high permeability and low retentivity.
4. D.high permeability and high retentivity.

Two light beams of intensities in the ratio of 9 : 4 are allowed to interfere. The ratio of the intensity of maxima and minima will be :

1. A.2 : 3
2. B.16 : 81
3. C.25 : 169
4. D.25 : 1

A sample contains $10^{-2}\mathrm{kg}$ each of two substances A and B with half lives $4\mathrm{s}$ and $8\mathrm{s}$ respectively. The ratio of their atomic weights is $1:2$. The ratio of the amounts of A and B after $16\mathrm{s}$ is $\frac{x}{100}$. The value of x is ____.

The temperature of equal masses of three different liquids x, y and z are $10^{\circ }\mathrm{C}$, $20^{\circ }\mathrm{C}$ and $30^{\circ }\mathrm{C}$ respectively. The temperature of mixture when x is mixed with y is $16^{\circ }\mathrm{C}$ and that when y is mixed with z is $26^{\circ }\mathrm{C}$. The temperature of mixture when x and z are mixed will be :

1. A.$28.32^{\circ }\mathrm{C}$
2. B.$25.62^{\circ }\mathrm{C}$
3. C.$23.84^{\circ }\mathrm{C}$
4. D.$20.28^{\circ }\mathrm{C}$

1. A.${\tan }^{-1}\left(\frac{-\frac{B}{2}}{A-B\frac{\sqrt{3}}{2}}\right)$
2. B.${\tan }^{-1}\left(\frac{A}{0.7B}\right)$
3. C.${\tan }^{-1}\left(\frac{\sqrt{3}B}{2A-B}\right)$
4. D.${\tan }^{-1}\left(\frac{B\cos \theta }{A-B\sin \theta }\right)$

A bomb is dropped by fighter plane flying horizontally. To an observer sitting in the plane, the trajectory of the bomb is a :

1. A.hyperbola
2. B.parabola in the direction of motion of plane
3. C.straight line vertically down the plane
4. D.parabola in a direction opposite to the motion of plane

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

An automobile of mass 'm' accelerates starting from origin and initially at rest, while the engine supplies constant power P. The position is given as a function of time by :

1. A.${\left(\frac{9P}{8m}\right)}^{\frac{1}{2}}{t}^{\frac{3}{2}}$
2. B.${\left(\frac{8P}{9m}\right)}^{\frac{1}{2}}{t}^{\frac{2}{3}}$
3. C.${\left(\frac{9m}{8P}\right)}^{\frac{1}{2}}{t}^{\frac{3}{2}}$
4. D.${\left(\frac{8P}{9m}\right)}^{\frac{1}{2}}{t}^{\frac{3}{2}}$

A particle of mass M originally at rest is subjected to a force whose direction is constant but magnitude varies with time according to the relation $$F=F_0\left[1-{\left(\frac{t-T}{T}\right)}^2\right]$$ Where ${\mathrm{F}}_0$ and T are constants. The force acts only for the time interval 2T. The velocity v of the particle after time 2T is :

1. A.$2{\mathrm{F}}_{0}T/M$
2. B.${\mathrm{F}}_{0}T/2M$
3. C.$4{\mathrm{F}}_{0}T/3M$
4. D.${\mathrm{F}}_{0}T/3M$

1. A.OR
2. B.AND
3. C.NOR
4. D.NAND

1. A.(a) $\to$ (iv), (b) $\to$ (i), (c) $\to$ (iii), (d) $\to$ (ii)
2. B.(a) $\to$ (iv), (b) $\to$ (iii), (c) $\to$ (i), (d) $\to$ (ii)
3. C.(a) $\to$ (iii), (b) $\to$ (ii), (c) $\to$ (iv), (d) $\to$ (i)
4. D.(a) $\to$ (i), (b) $\to$ (iv), (c) $\to$ (ii), (d) $\to$ (iii)

Water droplets are coming from an open tap at a particular rate. The spacing between a droplet observed at $4^{\text{th}}$ second after its fall to the next droplet is 34.3 m. At what rate the droplets are coming from the tap ? (Take g = $9.8m/{\mathrm{s}}^2$)

1. A.3 drops / 2 seconds
2. B.2 drops / second
3. C.1 drop / second
4. D.1 drop / 7 seconds

The relation between time t and distance x for a moving body is given as $t=m{x}^2+nx$, where m and n are constants. The retardation of the motion is : (When v stands for velocity)

1. A.$2m{v}^3$
2. B.$2mn{v}^3$
3. C.$2n{v}^3$
4. D.$2n^2{v}^3$

A balloon was moving upwards with a uniform velocity of 10 m/s. An object of finite mass is dropped from the balloon when it was at a height of 75 m from the ground level. The height of the balloon from the ground when object strikes the ground was around : (take the value of g as $10m/{\mathrm{s}}^2$)

1. A.300 m
2. B.200 m
3. C.125 m
4. D.250 m

Two vectors $\vec{X}$ and $\vec{Y}$ have equal magnitude. The magnitude of $(\vec{X}-\vec{Y})$ is n times the magnitude of $(\vec{X}+\vec{Y})$. The angle between $\vec{X}$ and $\vec{Y}$ is :

1. A.${\cos }^{-1}\left(\frac{-n^2-1}{n^2-1}\right)$
2. B.${\cos }^{-1}\left(\frac{n^2-1}{-n^2-1}\right)$
3. C.${\cos }^{-1}\left(\frac{n^2+1}{-n^2-1}\right)$
4. D.${\cos }^{-1}\left(\frac{n^2+1}{n^2-1}\right)$

What will be the projection of vector $\vec{A}=\hat{i}+\hat{j}+\hat{k}$ on vector $\vec{B}=\hat{i}+\hat{j}$?

1. A.$\sqrt{2}(\hat{i}+\hat{j}+\hat{k})$
2. B.$(\hat{i}+\hat{j})$
3. C.$\sqrt{2}(\hat{i}+\hat{j})$
4. D.$2(\hat{i}+\hat{j}+\hat{k})$

A body is projected vertically upwards from the surface of earth with a velocity sufficient enough to carry it to infinity. The time taken by it to reach height h is ________ s.

1. A.$\sqrt{\frac{2R_e}{g}}\left[{\left(1+\frac{h}{R_e}\right)}^{\frac{3}{2}}-1\right]$
2. B.$\frac{1}{3}\sqrt{\frac{R_e}{2g}}\left[{\left(1+\frac{h}{R_e}\right)}^{\frac{3}{2}}-1\right]$
3. C.$\sqrt{\frac{R_e}{2g}}\left[{\left(1+\frac{h}{R_e}\right)}^{\frac{3}{2}}-1\right]$
4. D.$\frac{1}{3}\sqrt{\frac{2R_e}{g}}\left[{\left(1+\frac{h}{R_e}\right)}^{\frac{3}{2}}-1\right]$

What will be the average value of energy for a monoatomic gas in thermal equilibrium at temperature T?

1. A.$\frac{3}{2}{k}_{B}T$
2. B.$k_{B}T$
3. C.$\frac{2}{3}{k}_{B}T$
4. D.$\frac{1}{2}{k}_{B}T$

Choose the correct option

1. A.True dip is always equal to apparent dip.
2. B.True dip is not mathematically related to apparent dip.
3. C.True dip is less than the apparent dip.
4. D.True dip is always greater than the apparent dip.

In 5 minutes, a body cools from $75^{\circ }\text{C}$ to $65^{\circ }\text{C}$ at room temperature of $25^{\circ }\text{C}$. The temperature of body at the end of next 5 minutes is ________ ${}^{\circ }\text{C}$.