List of top Questions asked in JEE Main

If the domain of the function $f(x)=\frac{[x]}{1+x^2}$, where $[x]$ is greatest integer $\leq x$, is $[2,6)$, then its range is

Let y = y(x) be a solution of the differential equation (x cos x)dy +(xy sin x + y cos x – l)dx = 0, 0 < x < $\frac{π}{2}$. If$\frac{π}{3}y(\frac{π}{3})=\sqrt3$, then $| \frac{π}{6 }y“( \frac{π}{6})+2 y'( \frac{π}{6})| $ is equal to______.

A body is moving with constant speed, in a circle of radius $10 m$ .The body completes one revolution in 4 s .At the end of 3 rd second, the displacement of body (in mi) from its starting point is :

If wavelength of the first line of the Paschen series of hydrogen atom is _____ nm, then the wavelength of the second line of this series is nm (Nearest integer)

Let D_k=$\begin{vmatrix} 1 & 2k & 2k-1\\ n & n^2+n+2 & n^2 \\ n & n^2+n & n^2+n+2 \end{vmatrix} $ If $∑^n_{k=1} D_k=96,$ The n is equal to

Let B =$\begin{bmatrix} 1 & 3 & α \\ 1 & 2& 3 \\ α & α & 4 \end{bmatrix}$ , α>2 be the adjoint of a matrix A and |A| = 2, then [α - 2α α] B$\begin{bmatrix} α \\ -2α \\ α \end{bmatrix}$is equal to

The number of real values $\lambda$, such that the system of linear equations $2 x-3 y+5 z=9 $ $ x+3 y-z=-18 $ $ 3 x-y+\left(\lambda^2-|\lambda|\right) z=16$ has no solution, is :-

Match List I with List II

Identify the correct order for the given property for following compounds.

Choose the correct answer from the option given below :

Number of hydrogen atoms per molecule of a hydrocarbon A having $858 \%$ carbon is_____ (Given: Molar mass of $A =84 g mol ^{-1}$ )

Match List I with List II:

List - I		List - II
A.	Torque	I.	kg m^-1 s^-2
B.	Energy Density	II.	kg ms^-1
C.	Pressure gradient	III.	kg m^-2 s^-2
D.	Impulse	IV.	kg m² s^-2

Choose the correct answer from the options given below :

Let $S=\{\theta \in[0,2 \pi): \tan (\pi \cos \theta)+\tan (\pi \sin \theta)=0\}$ Then $\displaystyle\sum_{\theta \in s } \sin ^2\left(\theta+\frac{\pi}{4}\right)$ is equal to _______

Rank of the word PUBLIC is?

Consider a function f:N→R, satisfying
$ f(1)+2f(2)+3f(3)+⋯+xf(x)=x(x+1)f(x);x≥2 with f(1)=1.$
Then $\frac{1}{f(2022)} + \frac{1}{f(2028)}$ is equal to $

Let $S =\{1,2,3,5,7,10,11\}$ The number of non-empty subsets of $S$ that have the sum of all elements a multiple of 3 , is _____

Let $A =\left[ a _{i j}\right], a _{i j} \in Z \cap[0,4], 1 \leq i, j \leq 2$ .
The number of matrices $A$ such that the sum of all entries is a prime number $p \in(2,13)$ is _____.

Let a and b are roots of x² – 7x – 1 = 0. The value of $\frac{a^{21} + b^{21} + a^{17} + b^{17}}{a^{19} + b^{19}}$ is?

if f(x)= $\frac{(tan1\degree)x+\log_e(123)}{x\log_e(1234)-(tan1\degree)},x>0$ , then the least value of $f(f(x))+f(f(\frac{4}{x}))$is

Expression for an electric field is given by $\overrightarrow{ E }=4000 x^2 i \frac{ V }{ m }$ The electric flux through the cube of side $20 cm$ when placed in electric field (as shown in the figure) is ___$V cm$

Let $a_1, a_2, a_3, \ldots$ be an AP If $a_7=3$, the product $a_1 a_4$ is minimum and the sum of its first $n$ terms is zero, then $n !-4 a_{n(n+2)}$ is equal to :

Let $ \alpha, \beta $ be the roots of the equation $ x^2 - \sqrt{2}x + 2 = 0 $, then $ \alpha^{14} + \beta^{14} $ is equal to:

As shown in the figure, a plane mirror is fixed at a height of 50 cm from the bottom of tank containing water (μ = 4/3). The height of water is the tank is 8 cm. A small bulb is placed at the bottom of the water tank. The distance of image of the bulb formed by mirror from the bottom of the tank is ____cm.

distance of image of the bulb formed by mirror

A pole is vertically submerged in swimming pool, such that it gives a length of shadow 2.15 m within water when sunlight is incident at an angle of 30o with the surface of water. If swimming pool is filled to a height of 1.5 m, then the height of the pole above the water surface in centimeters is (n-w = 4/3) ____________

An organization awarded 48 medals in event 'A', 25 in event 'B' and 18 in event 'C'. If these medals went to total 60 men and only five men got medals in all the three events, then how many received medals in exactly two of three events?

The density of $3 M$ solution of $NaCl$ is $10 \,g \,mL -1$. Molality of the solution is _______ $\times 10^{-2} m$ (Nearest integer). Given: Molar mass of Na and $Cl$ is $23$ and $355 \,g \,mol ^{-1}$ respectively.

List I (Current configuration)	List II(Magnetic field at point O)
A	i	\(B_0=\frac{\mu_0I}{4\pi r}[\pi+2]\)
B	ii	\(B_0=\frac{\mu_0}{4}\frac{I}{r}\)
C	iii	\(B_0=\frac{\mu_0I}{2\pi r}[\pi-1]\)
D	iv	\(B_0=\frac{\mu_0I}{4\pi r}[\pi+1]\)