List of top Questions asked in JEE Main

The following reaction is performed at $298\, K ?$ $2 NO ( g )+ O _{2}( g ) \rightleftharpoons 2 NO _{2}( g )$ The standard free energy of formation of $NO ( g )$ is $86.6 \,kJ /\, mol$ at $298 \,K .$ What is the standard free energy of formation of $NO _{2}( g )$ at $298 \,K ?\left( K _{n}=1.6 \times 10^{12}\right)$

The set of all values of \(\lambda\) for which the system of linear equations 
\(2x_1-2x_2+x_3=\lambda x_1\)
 \(2x_1-3x_2+2x_3=\lambda x_2\)
\(-x_1+2x_2=\lambda x_3\) has a non-trivial solution

In a certain town, $25\%$ of the families own a phone and $15\%$ own a car $65\%$ families own neither a phone nor a car and $2,000$ families own both a car and a phone. Consider the following three statements : (a) $5\%$ families own both a car and a phone. (b) $35\%$ families own either a car or a phone. (c) $40,000$ families live in the town. Then,

The molecular formula of a commercial resin used for exchanging ions in water softening is $C_8H_7SO_3Na$ (molecular weight = $206$). What would be the maximum uptake of $Ca^{2+}$ ions by the resin when expressed in mole per gram resin

The AC voltage across a resistance can be measured using a :

Two long current carrying thin wires, both with current $I$, are held by insulating threads of length $L$ and are in equilibrium as shown in the figure, with threads making an angle $'\theta'$ with the vertical. If wires have mass $\lambda$ per unit length then, the value of $I$ is : ( $g =$ gravitational acceleration)

The period of oscillation of a simple pendulum is $T=2 \pi \sqrt{\frac{L}{g}}$. Measured value of $L$ is $20.0\, cm$ known to $1\, mm$ accuracy and time for $100$ oscillations of the pendulum is found to be $90\, s$ using a wrist watch of $1\, s$ resolution. The accuracy in the determination of $g$ is

A $25\, cm$ long solenoid has radius $2\, cm$ and $500$ total number of turns. It carries a current of $15\, A$. If it is equivalent to a magnet of the same size and magnetization $|\bar{M}|$ (magnetic moment/volume), then $|\bar{M}|$ is :

If the angles of elevation of the top of a tower from three collinear points $A , B$ and $C$ on a line leading to the foot of the tower are $ 30^\circ, \, 45^\circ$ and $ 60^\circ$ respectively, then the ratio $AB : BC$ is

Let k be a non-zero real number. If $f(x) = \begin{cases} \frac{\left(e^x-1\right)^2}{sin\left(\frac{x}{k}\right)log\left(1+\frac{x}{4}\right)}, & \text{x $\ne$ 0} \\[2ex] 12, & \text{x = 0} \end{cases}$ is a continuous function, then the value of $k$ is :

The de - Broglie wavelength associated with the electron in the $n = 4$ level is :

The value of $ \displaystyle \sum^{30}_{r = 16} (r + 2)(r - 3)$ is equal to :

A complex number $z$ is the said to be unimodular if $|z|=1 .$ Suppose $z_{1}$ and $z_{2}$ are complex number such that $\frac{z_{1}-2 z_{2}}{2-z_{1} z_{2}}$ is unimodular and $z _{2}$ is not unimodular. Then the point $z_{1}$ lies on a :

The solution of the differential equation $ydx - (x + 2y^2)dy = 0$ is $x = f(y)$. If $f(- 1) = 1$, then $f(1)$ is equal to :

If $\begin{vmatrix}x^{2}+x&x+1&x-2\\ 2x^{2}+3x-1&3x&3x-3\\ x^{2}+2x+3&2x-1&2x-1\end{vmatrix}=ax-12,$ then 'a' is equal to :

The term independent of $x$ in the binomial expansion of $\left(1-\frac{1}{x}+3x^{5}\right)\left(2x^{2}-\frac{1}{x}\right)^{8}$ is :

The mean of the data set comprising of $16$ observations is $16$. If one of the observatio $d$ three new observations valued $3,4$ and $5$ added to the data, then the mean of the resultant data is

The number of integers greater than $6,000$ that can be formed using the digits $3, 5, 6, 7$ and $ 8$ without repetition is

The number of common tangents to the circles $x^2+y^2-4x-6y-12=0$ and $x^2+y^2+6x+18y+26=0$

From a solid sphere of mass $M$ and radius $R$, a spherical portion of radius $\frac{R}{2}$ is removed, as shown in the figure. Taking gravitational potential $V = 0$ at $r = \infty$, the potential at the centre of the cavity thus formed is ($G =$ gravitational constant)

Arrange the following amines in the order of increasing basicity.

A pendulum made of a uniform wire of cross sectional area $A$ has time period $T$. When an additional mass $M$ is added to its bob, the time period changes to $T_M$. If the Young's modulus of the material of the wire is $Y$ then $\frac{1}{Y}$ is equal to ( $g =$ gravitational acceleration)

A simple harmonic oscillator of angular frequency $2 \,rad \,s^{-1}$ is acted upon by an external force $F= \sin\, t \,N$. If the oscillator is at rest in its equilibrium position at $t\, =\, 0$, its position at later times is proportional to :

The equation of the plane containing the lines $2x - 5y + z = 3, x + y + \, z = 5$ and parallel to the plane $x + 3 y+ 6 z = 1$ is

If in a regular polygon the number of diagonals is $54$, then the number of sides of this polygon is :