List of top Questions asked in JEE Main

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?

How can photochemical smog be controlled?

Highest oxidation state of $Mn$ is exhibited in $Mn _2 O _7$ The correct statements about $Mn _2 O _7$ are
(A) Mn is tetrahedrally surrounded by oxygen atoms
(B) $Mn$ is octahedrally surrounded by oxygen atoms
(C) Contains $Mn-O-Mn$ bridge
(D) Contains $Mn - Mn$ bond
Choose the correct answer from the options given below:

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

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

Choose the correct statement(s):
A Beryllium oxide is purely acidic in nature
B Beryllium carbonate is kept in the atmosphere of $CO _2$
C Beryllium sulphate is readily soluble in water
D Beryllium shows anomalous behavior
Choose the correct answer from the options given below:

Let $R$ be a relation on $R$, given by $R=\{(a, b): 3 a-3 b+\sqrt{7}$ is an irrational number $\}$Then $R$ is

The sum to $10$ terms of the series $\frac{1}{1+1^2+1^4}+\frac{2}{1+2^2+2^4}+\frac{3}{1+3^2+3^4}+\ldots $ is

Let \(S=x: x∈R\) and $\left(\sqrt{3}+\sqrt{2})^{x^2-4}+(\sqrt{3}-\sqrt{2})^{x^2-4}=10\right\}$Then $n(S)$ is equal to

The mean and variance of $5$ observations are $5$ and $8$ respectively If $3$ observations are $1,3,5$, then the sum of cubes of the remaining two observations is

Let $S$ be the set of all solutions of the equation $\cos ^{-1}(2 x)-2 \cos ^{-1}\left(\sqrt{1-x^2}\right)=\pi$, $x \in\left[-\frac{1}{2}, \frac{1}{2}\right]$ Then $\displaystyle\sum_{x \in S} 2 \sin ^{-1}\left(x^2-1\right)$ is equal to

The value of $\frac{1}{1 ! 50 !}+\frac{1}{3 ! 48 !}+\frac{1}{5 ! 46 !}+\ldots +\frac{1}{49 ! 2 !}+\frac{1}{51 ! 1 !}$ is :

$\displaystyle \lim _{n \rightarrow \infty}\left[\frac{1}{1+n}+\frac{1}{2+n}+\frac{1}{3+n}+\ldots+\frac{1}{2 n}\right]$ is equal to

If the orthocentre of the triangle, whose vertices are $(1,2),(2,3)$ and $(3,1)$ is $(\alpha, \beta)$, then the quadratic equation whose roots are $\alpha+4 \beta$ and $4 \alpha+\beta$, is

A vernier caliper having least count \(\frac{1}{20N}\)cm and one main scale division is 1 mm, then value of one vernier scale division is

The diameter of a sphere having mass 8.635 gm is measured by a vernier scale. 10 divisions of vernier scale coincide with 9 divisions of main scale and main scale division is 1 mm. If the reading of the main scale is 2 cm & 2nd division of vernier coincide with a main scale division, the density of the sphere is

The momentum of an electron revolving in \(n ^{\text {th }}\) orbit is given by : (Symbols have their usual meanings)

A point source of light is placed at focus of convex lens, then what is the shape of wave front after passing through the lens?

$∫_{-\pi}^{\pi} \frac{2x(1+sinx)}{1+cos^2x}dx $ is equal to?

Sides of a triangle are AB = 9, BC = 7, AC = 8. Then cos 3C equals to

A circle passes through (0, 0) and (1, 0) and touches the circle x² + y² = 9. Then the locus of the centre of the circle is:

A ray of light coming from (3, 1) incident on 2x + y = 6 and deflected ray passing through (7, 2). If equation of incident ray is ax + by + 1 = 0, then a² + b² + 3ab =

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 :