List of top Questions asked in JEE Main

Concrete mixture is made by mixing cement, stone and sand in a rotating cylindrical drum. If the drum rotates too fast, the ingredients remain stuck to the wall of the drum and proper mixing of ingredients does not take place. The maximum rotational speed of the drum in revolutions per minute $(rpm)$ to ensure proper mixing is close to : (Take the radius of the drum to be $1.25\, m$ and its axle to be horizontal) :

Velocity-time graph for a body of mass $10\, kg$ is shown in figure. Work-done on the body in first two seconds of the motion is :

The main oxides formed on combustion of $Li, Na$ and $K$ in excess of air are, respectively :

The amount of arsenic pentasulphide that can be obtained when 35.5 g arsenic acid is treated with excess ${H_2S}$ in the presence of conc. HCl ( assuming 100% conversion) is :

At very high pressures, the compressibility factor of one mole of a gas is given by :

The total number of orbitals associated with the principal quantum number 5 is :

A Carnot freezer takes heat from water at $0^{\circ}C$ inside it and rejects it to the room at a temperature of $27^{\circ}C$. The latent heat of ice is $336 \times 10^3 J \, kg^{-1}$. If $5\, kg$ of water at $0^{\circ}C$ is converted into ice at $0^{\circ}C$ by the freezer, then the energy consumed by the freezer is close to :

A galvanometer having a coil resistance of $100 \, \Omega$ gives a full scale deflection, when a current of $1 \,mA$ is passed through it. The value of the resistance, which can convert this galvanometer into ammeter giving a full scale deflection for a current of $10\, A$ is :

If a curve $y = f(x)$ passes through the point $(1, -1)$ and satisfies the differential equation, $y(1 + xy) dx = x \,dy$, then $f \left( - \frac{1}{2} \right)$ is equal to :

The sum of all real values of $x$ satisfying the equation $(x^2 - 5x + 5)^{x^2 + 4x -60} = 1 $ is

If $A = \begin{bmatrix}5a &-b\\ 3&2\end{bmatrix}$ and $A$ adj $A$ = $AA^T$ , then $5a + b$ is equal to :

The system of linear equations $x + \lambda y - z = 0$ $\lambda x -y - z = 0$ $x + y - \lambda z = 0$ has a non-trivial solution for :

If all the words (with or without meaning) having five letters, formed using the letters of the word $SMALL$ and arranged as in a dictionary; then the position of the word $SMALL$ is:

If the number of terms in the expansion of $\left( 1 - \frac{2}{x} + \frac{4}{x^2} \right)^n , x \neq 0$ , is $28$ , then the sum of the coefficients of all the terms in this expansion, is :

If the $2^{nd}, 5^{th}$ and $9^{th}$ terms of a non-constant $A.P.$ are in $G.P.$, then the common ratio of this $G.P.$ is :

If the sum of the first ten terms of the series $\left(1 \frac{3}{5}\right)^{2} + \left(2 \frac{2}{5}\right)^{2} + \left(3 \frac{1}{5}\right)^{2} + 4^{2} + \left(4 \frac{4}{5}\right)^{2} + .... , $ is $\frac{16}{5} m , $ then $m$ is equal to :

Let $p = \displaystyle\lim_{x \to 0^+ } ( 1 + \tan^2 \sqrt{x} )^{\frac{1}{2x}}$ then $log \,p$ is equal to

For $ x \epsilon R , f (x) = | \log 2 - \sin x|$ and $g(x) = f(f(x))$, then :

For $x \, \in \, R , x \neq 0, x \neq 1,$ let $f_0(x) = \frac{1}{1-x}$ and $f_{n+1} (x) | = f_0 (f_n(x)), n = 0 , 1 , 2 , ...$ Then the value of $f_{100}(3) + f_1 \left(\frac{2}{3} \right) + f_2 \left( \frac{3}{2} \right)$ is equal to :

A particular adsorption process has the following characteristics : (i) It arises due to van der Waals forces and (ii) it is reversible. Identify the correct statement that describes the above adsorption process :

A pendulum clock loses $12\,s$ a day if the temperature is $40^{\circ}C$ and gains $4\,s$ a day if the temperature is $20^{\circ}C$. The temperature at which the clock will show correct time, and the co-efficient of linear expansion $(\alpha)$ of the metal of the pendulum shaft are respectively :

A roller is made by joining together two cones at their vertices $O$. It is kept on two rails $AB$ and $CD$ which are placed asymmetrically (see figure), with its axis perpendicular to $CD$ and its centre $O$ at the centre of line joining $AB$ and $CD$ (see figure). It is given a light push so that it starts rolling with its centre $O$ moving parallel to $CD$ in the direction shown. As it moves, the roller will tend to :

A satellite is revolving in a circular orbit at a height ' $h$' from the earth's surface (radius of earth $R ; h < < R$). The minimum increase in its orbital velocity required, so that the satellite could escape from the earth?s gravitational field, is close to : (Neglect the effect of atmosphere.)

A screw gauge with a pitch of $0.5\, mm$ and a circular scale with $50$ divisions is used to measure the thickness of a thin sheet of Aluminium. Before starting the measurement, it is found that when the two jaws of the screw gauge are brought in contact, the $45^{th}$ division coincides with the main scale line and that the zero of the main scale is barely visible. What is the thickness of the sheet if the main scale reading is $0.5\, mm$ and the $25^{th}$ division coincides with the main scale line ?

A modulated signal $C_m(t)$ has the form $C_m(t)=30$ sin $300 \pi t + 10$ (cos $200 \pi t -$ cos $400 \pi t$). The carrier frequency $f_{c}$, the modulating frequency (message frequency) $f_{\omega}$, and the modulation index $\mu$ are respectively given by :