List of top Questions asked in JEE Main

A uniform cable of mass $'M'$ and length $'L'$ is placed on a horizontal surface such that its $\bigg(\frac{1}{n}\bigg)^{th}$ part is hanging below the edge of the surface. To lift the hanging part of the cable upto the surface, the work done should be :

An alpha-particle of mass m suffers 1-dimensional elastic coolision with a nucleus at rest of unknown mass. It is scattered directly backwards losing, $64\%$ of its initial kinetic energy. The mass of the nucleus is :

A string of length $1\, m$ and mass $5\, g$ is fixed at both ends. The tension in the string is $8.0\, N$. The siring is set into vibration using an external vibrator of frequency $100\, Hz$. The separation between successive nodes on the string is close to :

A travelling harmonic wave is represented by the equation $y (x, t) = 10^{-3} sin (50 t + 2x)$, where $x$ and $y$ are in meter and $t$ is in seconds. Which of the following is a correct statement about the wave? The wave is propagating along the

A tuning fork of frequency $480\, Hz$ is used in an experiment for measuring speed of sound (n) in air by resonance tube method. Resonance is observed to occur at two successive lengths of the air column, $l_1$ = 30 cm and $l_2$ = $70 \,cm$. Then, $v$ is equal to :

Equation of travelling wave on a stretched string of linear density $5\, g/m$ is $y\, =\, 0.03\, sin(450\, t - 9x)$ where distance and time are measured is SI units. The tension in the string is :

The IUPAC symbol for the element with atomic number $119$ would be :

Two identical spherical balls of mass $M$ and radius $R$ each are stuck on two ends of a rod of length $2R$ and mass $M$ (see figure). The moment of inertia of the system about the axis passing perpendicularly through the centre of the rod is :

The correct decreasing order for acid strength is :

The correct order of hydration enthalpies of alkali metal ions is -

A solution containing $62\, g$ ethylene glycol in $250 \,g$ water is cooled to $-10^{\circ}C$. If $K_f$ for water is $1.86\, K\, kg \,mol^{-1}$, the amount of water (in g) separated as ice is :

The effect of lanthanoid contraction in the lanthanoid series of elements by and large means :

When $M_1$ gram of ice at $-10^{\circ}C$ (specific heat = $0.5 \; cal \; g^{-1 \circ } C^{-1}$) is added to $M_2$ gram of water at $50^{\circ}C$, finally no ice is left and the water is at $0^{\circ}C$. The value of latent heat of ice, in cal $g^{-1}$ is:

The mean and the median of the following ten numbers in increasing order $10, 22, 26, 29, 34, x 42, 67, 70,\, y$ are $42$ and $35$ respectively, then $\frac{y}{x}$ is equal to :

A particle starts from origin $O$ from rest and moves with a uniform acceleration along the positive $x$-axis. Identify all figures that correctly represent the motion qualitatively. (a = acceleration, v = velocity, x = displacement, t = time)

A circular disc $D_1$ of mass $M$ and radius $R$ has two identical discs $D_2$ and $D_3$ of the same mass $M$ and radius $R$ attached rigidly at its opposite ends (see figure). The moment of inertia of the system about the axis $OO'$, passing through the centre of $D_1$, as shown in the figure, will be :

A rectangular solid box of length $0.3\, m$ is held horizontally, with one of its sides on the edge of a platform of height $5\,m$. When released, it slips off the table in a very short time $\tau = 0.01\,s$, remaining essentially horizontal. The angle by which it would rotate when it hits the ground will be (in radians) close to :

A string is wound around a hollow cylinder of mass $5\, kg$ and radius $0.5\, m$. If the string is now pulled with a horizontal force of $40\, N$, and the cylinder is rolling without slipping on a horizontal surface (see figure), then the angular acceleration of the cylinder will be (Neglect the mass and thickness of the string) :

Two materials having coefficients of thermal conductivity '3K' and 'K' and thickness 'd' and '3d', respectively, are joined to form a slab as shown in the figure. The temperatures of the outer surfaces are $'\theta_2'$ and $' \theta_1'$ respectively, $(\theta_2 > \theta_1)$. The temperature at the interface is :-

A resonance tube is old and has jagged end. It is still used in the laboratory to determine velocity of sound in air. A tuning fork of frequency $512\, Hz$ produces first resonance when the tube is filled with water to a mark $11\, cm$ below a reference mark, near the open end of the tube. The experiment is repeated with another fork of frequency $256\, Hz$ which produces first resonance when water reaches a mark $27\, cm$ below the reference mark. The velocity of sound in air, obtained in the experiment, is close to:

A $20$ Henry inductor coil is connected to a $10$ ohm resistance in series as shown in figure. The time at which rate of dissipation of energy (joule's heat) across resistance is equal to the rate at which magnetic energy is stored in the inductor is :

A hydrogen atom, initially in the ground state is excited by absorbing a photon of wavelength 980$\mathring A $. The radius of the atom in the excited state, it terms of Bohr radius $a_0$, will be : ($h_c$ = $12500\, eV - \mathring A $)

A metal ball of mass $0.1\, kg$ is heated upto $500^{\circ}C$ and dropped into a vessel of heat capacity $800 \; JK^{-1}$ and containing $0.5\, kg$ water. The initial temperature of water and vessel is $30^{\circ}C$. What is the approximate percentage increment in the temperature of the water ? [Specific Heat Capacities of water and metal are, respectively, $4200 \; Jkg^{-1} K^{-1}$ and $400 \; JKg^{-1} K^{-1}$]

If $x = 3 \,tan \,t $ and $y = 3 \,sec \,t$, then the value of $\frac{d^2 y}{dx^2}$ at $t = \frac{\pi}{4}$, is :

Let $f : (-1,1) \to R$ be a function defined by $f(x) = max \{- | x |,- \sqrt{ 1- x^2} \}$. If $K$ be the set of all points at which $f$ is not differentiable, then $K$ has exactly :