Other Physics · JEE Main previous year questions

If $\vec{P}\times \vec{Q}=\vec{Q}\times \vec{P}$, the angle between $\vec{P}$ and $\vec{Q}$ is $\theta (0^{\circ }<\theta <360^{\circ })$. The value of '$\theta$' will be ______ ${}^{\circ }$.

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

A particle moving in the xy plane experiences a velocity dependent force $$\vec{F}=k\left(v_y\hat{i}+v_x\hat{j}\right),$$ where $v_x$ and $v_y$ are the x and y components of its velocity $\vec{v}$. If $\vec{a}$ is the acceleration of the particle, then which of the following statements is true for the particle?

1. A.kinetic energy of particle is constant in time
2. B.quantity $\vec{v}\times \vec{a}$ is constant in time
3. C.quantity $\vec{v}\cdot \vec{a}$ is constant in time
4. D.$\vec{F}$ arises due to a magnetic field

Hydrogen ion and singly ionized helium atom are accelerated, from rest, through the same potential difference. The ratio of final speeds of hydrogen and helium ions is close to :

1. A.2 : 1
2. B.1 : 2
3. C.5 : 7
4. D.10 : 7

A metallic sphere cools from $50^{\circ }\mathrm{C}$ to $40^{\circ }\mathrm{C}$ in 300 s. If atmospheric temperature around is $20^{\circ }\mathrm{C}$, then the sphere's temperature after the next 5 minutes will be close to :

1. A.$35^{\circ }\mathrm{C}$
2. B.$31^{\circ }\mathrm{C}$
3. C.$33^{\circ }\mathrm{C}$
4. D.$28^{\circ }\mathrm{C}$

The mass density of a spherical galaxy varies as $\frac{K}{r}$ over a large distance ‘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 :

1. A.${\mathrm{T}}^2\propto \mathrm{R}$
2. B.${\mathrm{T}}^2\propto {\mathrm{R}}^3$
3. C.$\mathrm{T}\propto \mathrm{R}$
4. D.${\mathrm{T}}^2\propto \frac{1}{{\mathrm{R}}^3}$

An amplitude modulated wave is represented by the expression $v_m=5(1+0.6\cos 6280t)\sin (211\times 10^{4}t)\mathrm{volts}$ The minimum and maximum amplitudes of the amplitude modulated wave are, respectively

1. A.$\frac{3}{2}\mathrm{V},5\mathrm{V}$
2. B.$\frac{5}{2}\mathrm{V},8\mathrm{V}$
3. C.$5\mathrm{V},8\mathrm{V}$
4. D.$3\mathrm{V},5\mathrm{V}$

When the temperature of a metal wire is increased from $0^{\circ }\mathrm{C}$ to $10^{\circ }\mathrm{C}$, its length increases by $0.02\%$. The percentage change in its mass density will be closest to :

1. A.0.008
2. B.0.06
3. C.0.8
4. D.2.3

1. A.0.6 A
2. B.0.3 A
3. C.0 A
4. D.0.2 A

Two gases-argon (atomic radius 0.07 nm, atomic weight 40) and xenon (atomic radius 0.1 nm, atomic weight 140) have the same number density and are at the same temperature. The ratio of their respective mean free times is closest to :

1. A.2.3
2. B.1.83
3. C.4.67
4. D.3.67

A particle starts from the origin at t = 0 with an initial velocity of $3.0\hat{i}\text{ m/s}$ and moves in the x-y plane with a constant acceleration $\left(6\hat{i}+4\hat{j}\right){\text{ m/s}}^2$. The x-coordinate of the particle at the instant when its y-coordinate is 32 m is D meters. The value of D is :-

1. A.40
2. B.32
3. C.50
4. D.60

Two steel wires having same length are suspended from a ceiling under the same load. If the ratio of their energy stored per unit volume is $1:4$, the ratio of their diameters is:

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

For the four sets of three measured physical quantities as given below. Which of the following options is correct ? (i) ${\mathrm{A}}_1=24.36,{\mathrm{B}}_1=0.0724,{\mathrm{C}}_1=256.2$ (ii) ${\mathrm{A}}_2=24.44,{\mathrm{B}}_2=16.082,{\mathrm{C}}_2=240.2$ (iii) ${\mathrm{A}}_3=25.2,{\mathrm{B}}_3=19.2812,{\mathrm{C}}_3=236.183$ (iv) ${\mathrm{A}}_4=25,{\mathrm{B}}_4=236.191,{\mathrm{C}}_4=19.5$

1. A.${\mathrm{A}}_1+{\mathrm{B}}_1+{\mathrm{C}}_1={\mathrm{A}}_2+{\mathrm{B}}_2+{\mathrm{C}}_2={\mathrm{A}}_3+{\mathrm{B}}_3+{\mathrm{C}}_3={\mathrm{A}}_4+{\mathrm{B}}_4+{\mathrm{C}}_4$
2. B.${\mathrm{A}}_4+{\mathrm{B}}_4+{\mathrm{C}}_4<{\mathrm{A}}_1+{\mathrm{B}}_1+{\mathrm{C}}_1<{\mathrm{A}}_3+{\mathrm{B}}_3+{\mathrm{C}}_3<{\mathrm{A}}_2+{\mathrm{B}}_2+{\mathrm{C}}_2$
3. C.${\mathrm{A}}_4+{\mathrm{B}}_4+{\mathrm{C}}_4<{\mathrm{A}}_1+{\mathrm{B}}_1+{\mathrm{C}}_1={\mathrm{A}}_2+{\mathrm{B}}_2+{\mathrm{C}}_2={\mathrm{A}}_3+{\mathrm{B}}_3+{\mathrm{C}}_3$
4. D.${\mathrm{A}}_4+{\mathrm{B}}_4+{\mathrm{C}}_4>{\mathrm{A}}_3+{\mathrm{B}}_3+{\mathrm{C}}_3={\mathrm{A}}_2+{\mathrm{B}}_2+{\mathrm{C}}_2>{\mathrm{A}}_1+{\mathrm{B}}_1+{\mathrm{C}}_1$

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

Three containers $C_1$, $C_2$ and $C_3$ have water at different temperatures. The table below shows the final temperature T when different amounts of water (given in litres) are taken from each containers and mixed (assume no loss of heat during the process) $$\begin{array}{cccc}{\mathrm{C}}_1& {\mathrm{C}}_2& {\mathrm{C}}_3& \mathrm{T}\\ 1l& 2l& -& 60^{\circ }\mathrm{C}\\ -& 1l& 2l& 30^{\circ }\mathrm{C}\\ 2l& -& 1l& 60^{\circ }\mathrm{C}\\ 1l& 1l& 1l& \theta \end{array}$$ The value of $\theta$ (in ${}^{\circ }\mathrm{C}$ to the nearest integer) is .........

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

1. A.10 V
2. B.5 V
3. C.zero
4. D.15 V

A mass of 10 kg is suspended by a rope of length 4 m, from the ceiling. A force F is applied horizontally at the mid point of the rope such that the top half of the rope makes an angle of $45^{\circ }$ with the vertical. Then F equal : (Take $\text{g}=10{\text{ ms}}^{-2}$ and the rope to be massless)

1. A.100 N
2. B.75 N
3. C.90 N
4. D.70 N

The sum of two forces $\vec{P}$ and $\vec{Q}$ is $\vec{R}$ such that $\left|\vec{R}\right|=\left|\vec{P}\right|$. The angle $\theta$ (in degrees) that the resultant of $2\vec{P}$ and $\vec{Q}$ will make with $\vec{Q}$ is .............

A shell is fired from a fixed artillery gun with an initial speed u such that it hits the target on the ground at a distance R from it. If $t_1$ and $t_2$ are the values of the time taken by it to hit the target in two possible ways, the product $t_1{t}_2$ is -

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

1. A.$16\Omega$
2. B.$1\Omega$
3. C.$8\Omega$
4. D.$6\Omega$

The number density of molecules of a gas depends on their distance r from the origin as, $n(r)=n_0{e}^{-\alpha r^4}$. Then the total number of molecules is proportional to :

1. A.$n_0{\alpha }^{-3/4}$
2. B.$n_0{\alpha }^{-3}$
3. C.$n_0{\alpha }^{1/4}$
4. D.$\sqrt{n_0}{\alpha }^{1/2}$

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

1. A.14 cm
2. B.18 cm
3. C.20 cm
4. D.26 cm