List of top Questions asked in JEE Main

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 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 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 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 :

A solid XY kept in an evacuated sealed container undergoes decomposition to form a mixture of gases X and Y at temperature T. The equilibrium pressure is 10 bar in this vessel. $K_p$ for this reaction is :

A student measures the time period of $100$ oscillations of a simple pendulum four times. The data set is $90\, s, 91\, s, 95\, s$ and $92\, s$. If the minimum division in the measuring clock is $1 \,s$, then the reported mean time should be :

A wire of length $2$ units is cut into two parts which are bent respectively to form a square of side $= x$ units and a circle of radius $= r$ units. If the sum of the areas of the square and the circle so formed is minimum, then :

$ABC$ is a triangle in a plane with vertices $A(2, 3, 5), B(-1, 3, 2)$ and $C(\lambda , 5, \mu)$. If the median through $A$ is equally inclined to the coordinate axes, then the value of $(\lambda^3 + \mu^3 + 5)$ is :

An observer looks at a distant tree of height $10\, m$ with a telescope of magnifying power of $20$. To the observer the tree appears :

An arc lamp requires a direct current of $10\, A$ at $80 \,V$ to function. If it is connected to a $220 \,V \,(rms)$, $50 \,Hz\, AC$ supply, the series inductor needed for it to work is close to :

An experiment succeeds twice as often as it fails. The probability of at least $5$ successes in the six trials of this experiment is :