List of top Questions asked in JEE Main

For a solid rod, the Young's modulus of elasticity is $32 \times 10^{11} Nm ^{-2}$ and density is $8 \times 10^3 kg m ^{-3}$ The velocity of longitudinal wave in the rod will be

A particle of mass 250 g executes a simple harmonic motion under a periodic force F=(−25𝑥)N. The particle attains a maximum speed of 4 m/s during its oscillation. The amplitude of the motion is ______ cm.

A metal block of base area $0.20 \,m^2$ is placed on a table, as shown in figure. A liquid film of thickness $0.25\, mm$ is inserted between the block and the table. The block is pushed by a horizontal force of 0.1 N and moves with a constant speed. If the viscosity of the liquid is $5.0×10^{−3}Pl$, the speed of block is ________ $×10^{−3}m/s$

An inductor of inductance $2\mu H$ is connected in series with a resistance, a variable capacitor and an AC source of frequency $7\ kHz$. The value of capacitance for which maximum current is drawn into the circuit is $\frac 1x$ F, where the value of $𝑥 $ is ______. (Take $\pi=\frac {22}{7}$ )

A car is moving on a circular path of radius $600\ m$ such that the magnitudes of the tangential acceleration and centripetal acceleration are equal. The time taken by the car to complete first quarter of revolution, if it is moving with an initial speed of $54 \ km/hr$ is $𝑡(1−𝑒^{−\frac \pi2})\ 𝑠$. The value of $t$ is _____ .

Match List I with List II

List I		List II
A.	Microwaves	I.	Physiotherapy
B.	UV rays	II.	Treatment of cancer
C.	Infra-red rays	III.	Lasik eye surgery
D.	X-rays	IV.	Aircraft navigation

Choose the correct answer from the options given below:

For a charged spherical ball, electrostatic potential inside the ball varies with 𝑟 as $V=2𝑎𝑟^2+𝑏$. Here, 𝑎 and 𝑏 are constant and r is the distance from the center. The volume charge density inside the ball is −𝜆𝑎𝜀. The value of 𝜆 is ______.
(𝜀= permittivity of the medium)

The number of real solutions of the equation $3\left(x^2+\frac{1}{x^2}\right)-2\left(x+\frac{1}{x}\right)+5=0$, is

In an experiment of measuring the refractive index of a glass slab using travelling microscope in physics lab, a student measures real thickness of the glass slab as 5.25 mm and apparent thickness of the glass slab as 5.00 mm. Travelling microscope has 20 divisions in one cm on main scale and 50 divisions on vernier scale is equal to 49 divisions on main scale. The estimated uncertainty in the measurement of refractive index of the slab is $\frac{𝑥}{10} ×10^{−3}$, where 𝑥 is _______.

A particle of mass 100 g is projected at time $𝑡=0$ with a speed $20\,ms^{−1}$ at an angle $45°$ to the horizontal as given in the figure. The magnitude of the angular momentum of the particle about the starting point at time $𝑡=2 s$ is found to be $\sqrt{K}\ kgm^2/s.$ The value of $K$ is ________. (Take $g=10$ $ms^{−2}$)

When two resistances 𝑅₁ and 𝑅₂ connected in series and introduced into the left gap of a meter bridge and a resistance of 10Ω is introduced into the right gap, a null point is found at 60 cm from left side. When 𝑅₁ and 𝑅₂ are connected in parallel and introduced into the left gap, a resistance of 3Ω is introduced into the right-gap to get null point at 40 cm from left end. The product of 𝑅₁𝑅₂ is _______ Ω².

A square loop of area $25\ cm^2$ has a resistance of $10\ Ω$. The loop is placed in uniform magnetic field of magnitude $40.0 \ T$. The plane of loop is perpendicular to the magnetic field. The work done in pulling the loop out of the magnetic field slowly and uniformly in $1.0$ sec, will be

Let $f(x)$ be a function such that $f(x+y)=f(x) \cdot f(y)$ for all $x, y \in$ N If $f(1)=3$ and $\displaystyle\sum_{k=1}^n f(k)=3279$, then the value of $n$ is

The equation of a circle is given by $𝑥^2+𝑦^2=𝑎^2$, where 𝑎 is the radius. If the equation is modified to change the origin other than (0,0) then. find out the correct dimensions of A and B in a new equation : $(𝑥−𝐴𝑡)^2+(𝑦−𝑡 𝐵 )^2 =𝑎^2$. The dimensions of 𝑡 is given as $[T^{−1}]$.

A body of mass $10 kg$ is moving with an initial speed of $20 m / s$ The body stops after $5 s$ due to friction between body and the floor The value of the coefficient of friction is: (Take acceleration due to gravity $g =10 ms ^{-2}$ )

The time period of a satellite of earth is 24 hours. If the separation between the earth and the satellite is decreased to one fourth of the previous value, then its new time period will become.

For the given figures, choose the correct options:

The rms current in circuit (b) can never be larger than that in (a)

If the two metals $A$ and $B$ are exposed to radiation of wavelength $350 mm$. The work functions of metals $A$ and $B$ are $4.8 eV$ and $2.2 eV$. Then choose the correct option

A microscope is focused on an object at the bottom of a bucket If liquid with refractive index $\frac{5}{3}$ is poured inside the bucket, then microscope have to be raised by $30\, cm$ to focus the object again The height of the liquid in the bucket is :

Heat energy of 184 kJ is given to ice of mass $600 g$ at −12°C. Specific heat of ice is $ 2222.3 J kg^{−1}C^{−1}$ and latent heat of ice in $ 336 kJkg^{−1} $
A. Final temperature of system will be 0°C.
B. Final temperature of the system will be greater than 0°C.
C. The final system will have a mixture of ice and water in the ratio of 5:1.
D. The final system will have a mixture of ice and water in the ratio of 1:5.
E. The final system will have water only.
Choose the correct answer from the options given below:

If $\int \limits_0^\pi \frac{5^{\cos x}\left(1+\cos x \cos 3 x+\cos ^2 x+\cos ^3 x \cos 3 x\right) d x}{1+5^{\cos x}}=\frac{ k \pi}{16}$, then $k$ is equal to

Given below are two statements:
Statement I: Electromagnetic waves are not deflected by electric and magnetic field.
Statement II: The amplitude of electric field and the magnetic field in electromagnetic waves are related to each other as $E_0 = \sqrt{\frac{\mu_0}{E_0}}B_0$.
In the light of the above statements, choose the correct answer from the options given below:

A scientist is observing a bacteria through a compound microscope. For better analysis and to improve its resolving power he should. (Select the best option)

With the help of potentiometer, we can determine the value of emf of a given cell. The sensitivity of the potentiometer is
(A) directly proportional to the length of the potentiometer wire
(B) directly proportional to the potential gradient of the wire
(C) inversely proportional to the potential gradient of the wire
(D) inversely proportional to the length of the potentiometer wire
Choose the correct option for the above statements:

The electric current in a circular coil of four turns produces a magnetic induction 32 T at its centre. The coil is unwound and is rewound into a circular coil of single turn, the magnetic induction at the centre of the coil by the same current will be :