List of top Questions asked in JEE Main

Let a tangent to the curve $y^2=24 x$ meet the curve $x y=2$ at the points $A$ and $B$ Then the mid points of such line segments $A B$ lie on a parabola with the

Let $f(x)=2 x+\tan ^{-1} x$ and $g(x)=\log _e\left(\sqrt{1+x^2}+x\right), x \in[0,3]$ Then

Let $𝑎_1=𝑏_1=1$and $𝑎_𝑛=𝑎_{𝑛−1}+(𝑛−1)$, $𝑏_𝑛=𝑏_{𝑛−1}+𝑎_{𝑛−1}$, $∀𝑛≥2$. If $𝑆= \displaystyle\sum_{ 𝑛=1}^{10}\frac {𝑏_𝑛}{2^𝑛}$ and $𝑇= \displaystyle\sum_{𝑛=1}^{8} \frac {𝑛}{2^{𝑛−1}}$, then $2^7(2𝑆−𝑇)$ is equal to ____ .

Let $\vec{a}=5 \hat{i}-\hat{j}-3 \hat{k}$ and $\vec{b}=\hat{i}+3 \hat{j}+5 \hat{k}$ be two vectors Then which one of the following statements is TRUE ?

Some amount of dichloromethane $\left( CH _2 Cl _2\right)$ is added to $671.141 \,mL$ of chloroform $\left( CHCl _3\right)$ to prepare $2.6 \times 10^{-3} M$ solution of $CH _2 Cl _2$ (DCM) The concentration of DCM is ______$ppm$ (by mass) Given: atomic mass : $C =12$ $H =1$ $Cl =35.5$ density of $CHCl _3=1.49\, g \,cm ^{-3}$

The domain of $f(x)=\frac{log_{x+1}(x-2)}{e^{2logx}-(2x+3)}$, $x∈R$ is

As shown in figure, a $70 kg$ garden roller is pushed with a force of $\vec{F}=200 N$ at an angle of $30^{\circ}$ with horizontal. The normal reaction on the roller is (Given $g=10 m s ^{-2}$ )

Two billiard balls of mass $005\, kg$ each moving in opposite directions with $10 \, ms ^{-1}$ collide and rebound with the same speed If the time duration of contact is $t =0005 \, s$, then what is the force exerted on the ball due to each other?

Solid fuel used in rocket is a mixture of Fe₂O₃ and Al (in ratio 1 : 2) the heat evolved (KJ) per gram of the mixture is ______ (Nearest integer)
Given $\Delta H_f^{\circ}(Al_2O_3) = -1700 \, \text{KJ mol}^{-1}$
$\Delta H_f^{\circ}(Fe_2O_3) = -840 \, \text{KJ mol}^{-1}$ }

The set of all values of $a$ for which $\displaystyle\lim _{x \rightarrow a}([x-5]-[2 x+2])=0$,where $[\propto]$ denotes the greatest integer less than or equal to $\propto$ is equal to

A person forgets his 4-digit ATM pin code. But he remembers that in the code all the digits are different, the greatest digit is 7 and the sum of the first two digits is equal to the sum of the last two digits. Then the maximum number of trials necessary to obtain the correct code is

The number of functions $f:\{1,2,3,4\} \rightarrow\{ a \in: Z|a| \leq 8\}$ satisfying $f(n)+\frac{1}{n} f( n +1)=1, \forall n \in\{1,2,3\}$ is

If the x-intercept of a focal chord of the parabola $y^2=8 x+4 y+4$ is 3 , then the length of this chord is equal to ___

Total numbers of 3-digit numbers that are divisible by 6 and can be formed by using the digits 1, 2, 3, 4, 5 with repetition, is___.

Consider the above reaction and identify the product B.

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R)
Assertion (A): The first ionization enthalpy of $3d$ series elements is more than that of group 2 metals
Reason (R): In $3d$ series of elements successive filling of d-orbitals takes place
In the light of the above statements, choose the correct answer from the options given below :

A point charge of $10\, \mu C$ is placed at the origin At what location on the $X$-axis should a point charge of $40 \, \mu C$ be placed so that the net electric field is zero at $x=2 \, cm$ on the $X$-axis?

Match List I with List II

LIST I		LIST II
A	Gauss's Law in Electrostatics	I	$\oint \vec{E} \cdot d \vec{l}=-\frac{d \phi_B}{d t}$
B	Faraday's Law	II	$\oint \vec{B} \cdot d \vec{A}=0$
C	Gauss's Law in Magnetism	III	$\oint \vec{B} \cdot d \vec{l}=\mu_0 i_c+\mu_0 \in_0 \frac{d \phi_E}{d t}$
D	Ampere-Maxwell Law	IV	$\oint \vec{E} \cdot d \vec{s}=\frac{q}{\epsilon_0}$

Choose the correct answer from the options given below:

Let the plane x + 3y – 2z + 6 = 0 meet the co-ordinate axes at the points A,B,C. If the orthocentre of the triangle ABC is $(α,β,\frac{6}{7}),$ then 98(α + β)² is equal to___.

Given below are two statements:
Statement I: Area under velocity- time graph gives the distance travelled by the body in a given time.
Statement II: Area under acceleration-time graph is equal to the change in velocity- in the given time.
In the light of given statements, choose the correct answer from the options given below.

Number of 4-digit numbers that are less than or equal to 2800 and either divisible by 3 or by 11 , is equal to

If the mean deviation about median for the number $3,5,7,2 k , 12,16,21,24$ arranged in the ascending order, is 6 then the median is

Let $a_1=8, a_2, a_3, \ldots, a_n$ be an AP If the sum of its first four terms is $50$ and the sum of its last four terms is $170$ , then the product of its middle two terms is______

A particle moves in a circular path with uniform speed v. When it turns by 90°, find ratio of $\frac{v}{<\overrightarrow{v}>}$?

Let $ R = \{a, b, c, d, e\} $ and $ S = \{1, 2, 3, 4\} $. Total number of onto functions $ f: R \to S $ such that $ f(a) \neq 1 $, is equal to: