List of top Questions asked in JEE Main

$\alpha, \alpha + 2 \in Z$ and $n \in N$, where $\alpha, \alpha+2$ are roots of equation $x(x + 2) + (x + 1) (x + 3) + ... + (x + n-1) (x + n+1) = 4n$ then $\alpha + n =$

If eccentricity of an ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$, which passes through the point $(3, 4)$ is $\frac{\sqrt{5}}{3}$, then length of latus rectum of ellipse, is :

Consider $f(x) = \begin{cases} \frac{\sin x}{x}, & x \neq 0 \\ 1, & x = 0 \end{cases}$
Number of critical points of $f(x)$ in the interval $(-2\pi, 2\pi)$ is:

If probability that $ax^2 + 2\sqrt{2}bx + c > 0 \, \forall x \in R$ where $a, b, c \in {1, 2, 3, 4}$ is $\frac{m}{n}$ where $m$ & $n$ are coprime, then $(m + n)$ is:

Let $|a| = 2, |b| = 3$, then maximum value of $3|3a + 2b| + 4|3a - 2b|$ is :

A circle meets coordinate axes at 3 points and cuts equal intercepts. If it cuts a chord of length $\sqrt{14}$ unit on $x + y = 1$, then square of its radius is (centre lies in first quadrant):

Let $x \in [-\pi, \pi]$ & $S = \{ x : \sin x (\sin x + \cos x) = a, a \in I \}$, then number of elements in set $S$ is equal to :

The Range of $f(x) = \sin^{-1} \left( \frac{1}{x^2 - 2x + 2} \right)$ is:

Number of seven digits numbers which can be formed by using all the digits 1, 2, 3, 4, 5 with at least one digit repeated is _____.

The value of $\int_{0}^{3} \frac{e^x + e^{-x}}{[x]!} dx$ is equal to (where $[\, \cdot \,]$ denotes greatest integer function):

If $y = f(x)$ is the solution of the differential equation $(1 + \sin x) \frac{dy}{dx} + \cos x = 0$, such that $f(0) = 0$, then $f\left(\frac{\pi}{2}\right)$ is:

Which of the following is most basic?

Consider the reaction given below:

$\text{A gives positive Fehling's test. Choose the correct relation}$.

Write the correct order of rate of reaction of following compounds with $PhN_2Cl$
P: $N,N$-dimethylaniline
Q: $N,N$-dimethyl-3-methylaniline
R: $N,N$-dimethyl-2,6-dimethylaniline

If all the letters of the word 'UDAYPUR' are arranged in all possible permutations and these permutations are listed in dictionary order, then the rank of the word 'UDAYPUR' is

Dimensions of $G$ (Universal gravitational constant) in terms of $h$ (Planck's constant), $m$ (mass), $t$ (time) and $L$ (length) will be:

The value of $ \int_0^{2\pi} (\sin^4 x + \cos^4 x) \, dx $ is equal to:

5.33 gram of $CrCl_3 \cdot 6H_2O$ (1:3 electrolyte) is passed through cation exchanger. The resulting solution is then treated with an excess of $AgNO_3$, leading to formation of 8.61 gran of precipitate. Calculate :
$\frac{\text{number of moles of complex reacted}}{\text{number of moles of AgCl precipitated}} \times 100$

Most preferred site for electrophilic substitution in above example?
(Note: The molecule contains a nitrogen-containing ring and a carbonyl-containing ring, labels are U, S, R, P).

Statement-I : The correct increasing order of bond length among the following is $O_2^+ < O_2 < O_2^- < O_2^{2-}$.
Statement-II : The correct order of number of unpaired electrons is $O_2^{2-} < O_2^+ < O_2^- < O_2$.

Find the correct match.

Column-I (Complex compound)	Column-II ($\Delta_0$ (CFSE) $\text{cm}^{-1}$)
(i) $[Cr(CN)_6]^{3-}$	(P) 17000
(ii) $[Cr(H_2O)_6]^{3+}$	(Q) 15000
(iii) $[Cr(en)_3]^{3+}$	(R) 12000
(iv) $[CrF_6]^{3-}$	(S) 20000

Cation of salt A when treated in flame gives apple green colour. When salt A is heated with Chromate solution gives yellow precipitate & when salt is heated with conc $HNO_3$ & Ammionium molybdate it gives canary yellow ppt. Salt A contains :

Statement-I : The correct order of Ionization energy is $Na > Mg > Al > Ar$
Statement-II : Among the following elements $Sc, Ca$ and $Mg, Ca$ has highest $3^{rd}$ Ionisation Energy.

Statement-I : 1, 2, 3-trihydroxy propane can be separated from water by using simple distillation.
Statement-II : Azeotropic mixture cannot be separated by using fractional distillation.

Statement-1 : Benzyl chloride reacts faster than ethyl chloride towards $S_N1$.
Statement-2 : Positive charge on ethyl will be unstable.