List of top Questions asked in JEE Main

The value of $\underset{x\to 0}{lim}\frac{{\int }_0^{x^2}{\sec }^{2}tdt}{x\sin x}$ is

The integral $\int \frac{{\sin }^{2}x{\cos }^{2}x}{{({\sin }^{5}x+{\cos }^{3}x{\sin }^{2}x+x{\cos }^{2}x+{\cos }^{5}x)}^2}dx$ is equal to:

A function y = f(x) has a second order derivative f''(x) = 6(x - 1).  If its graph passes through the point (2, 1) and at that point the tangent to the graph is y = 3x -5.  then the function is :

The 315th word in dictionary arranged in order for the word ‘NAGPUR’ is

Find area bounded by $y^2 ≤ 2x$ and $y ≥ 4x – 1$

Given \(f(x) =   \begin{cases}     \frac{tan((a+1)x)+tanx\cdot b}{x}       & \quad x\lt 0\\     3  & \quad x=0\\ \frac{\sqrt{ax+b^2x^2}-\sqrt{ax}}{\sqrt{a}bx\sqrt{x}}  & \quad x\gt 0\end{cases}\) It is a continuous function at x=0, then find \(\frac{b}{a}\)

Assertion (A): Object at radius of curvature of biconvex lens made by glass (u = 1.5) form image at same distance an other side of the lens.
Reason (R): Image of a real object formed by concave lens is always virtual and erect.

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason $R$
Assertion A: Amongst $He, Ne, Ar$ and $Kr$; $1 g$ of activated charcoal adsorbs more of $Kr$
Reason R: The critical volume $V_c\left( cm ^3 mol ^{-1}\right)$ and critical pressure $P_e$ (atm) is highest for Krypton but the compressibility factor at critical point $Z_c$ is lowest for Krypton 
In the light of the above statements, choose the correct answer from the options given below

Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$
Assertion A : Hydrogen is an environment-friendly fuel
Reason R : Atomic number of hydrogen is 1 and it is a very light element
In the light of the above statements, choose the correct answer from the options given below

Which of the following represents the lattice structure of \(A _{0.95} O\) containing \(A ^{2+}, A ^{3+}\) and \(O ^{2-}\) ions?

Which of the following are the example of double salt?
A $FeSO _4 \left( NH _4\right)_2 SO _4 \cdot 6 H _2 O$
B $CuSO _4 4 NH _3 H _2 O$
C $K _2 SO _4 \cdot Al _2\left( SO _4\right)_3 \cdot 24 H _2 O$
D $Fe ( CN )_2 \cdot 4 KCN$
Choose the correct answer

Resonance in carbonate ion $\left( CO _3{ }^{2-}\right)$ is

Which of the following is true?

Given below are two statements:
Statement I : Chlorine can easily combine with oxygen to form oxides; and the product has a tendency to explode
Statement II : Chemical reactivity of an element can be determined by its reaction with oxygen and halogens
In the light of the above statements, choose the correct answer from the options given below

Let line L pass through the point \( (0, 1, 2) \), intersect the line \( {2 = {3 = {4 \), and be parallel to the plane \( 2x + y - 3z = 4 \). Find the distance of the point \( P(1, -9, 2) \) from line L. \\

Let the vectors \( , , \) represent three coterminous edges of a parallelepiped of volume \( V \). Then the volume of the parallelepiped, whose coterminous edges are represented by \( , + \) and \( + 2 + 3 \) is equal to: \\ \\

All the letters of the word PUBLIC are written in all possible orders and these words are written as in a dictionary with serial numbers. Then the serial number of the word PUBLIC is: \\ \\

A solution of $FeCl _3$ when treated with $K _{ t }\left[ Fe ( CN )_6\right]$ gives a prussiun blue precipitate due to the formation of

If the domain of \(f(x)=\sin^{-1}(\frac{x-1}{2x+3})\) is R – (α, β] then find the value of 12αβ.

Find out the major products from the following reactions

Let the solution curve $y=y(x)$ of the differential equation $\frac{d y}{d x}-\frac{3 x^5 \tan ^{-1}\left(x^3\right)}{\left(1+x^6\right)^{3 / 2}} y=2 x \exp \left\{\frac{x^3-\tan ^{-1} x^3}{\sqrt{\left(1+x^6\right)}}\right\}$ pass through the origin Then $y(1)$ is equal to :

R = (a, b) : a + 5b = 42 and a, b ∈ N has m elements and \(\sum\limits_{n=1}^{m}(1+i^{n!})\) = x + iy (where i = √-1). Find x + y + m.

If set A = { z: |z - 1| ≤ 1} and set B = { z: |z - 5i| ≤ |z - 5| }, if z = a + ib, where a, b ∈ I, then find the sum of modulus squares of A ∩ B.