List of top Questions asked in JEE Main

If $f(x)=\begin{cases} x+a, & x \leq 0 \\ |x-4|, & x\gt0\end{cases}$ and
$g(x)= \begin{cases}x+1 & , x\lt0 \\ (x-4)^2+b, & x \geq 0\end{cases}$
are continuous on $R$, then $(gof) (2)+(fog)(-2)$ is equal to:

If the minimum value of $f(x)=\frac{5 x^2}{2}+\frac{\alpha}{x^5}, x>0$, is 14 , then the value of $\alpha$ is equal to:

If force $\vec F=3\hat i+4\hat j−2\hat k$ acts on a particle having position vector $2\hat i+\hat j+2\hat k$ then, the torque about the origin will be

The pair, in which ions are isoelectronic with $Al^{3+}$ is:

Phenol on reaction with dilute nitric acid, gives two products. Which method will be most efficient for large scale separation?

Among the following species
N₂,N₂⁺,N₂⁻,N₂²⁻,O₂,O₂⁺,O₂⁻,O₂²⁻
the number of species showing diamagnetism is ________.

A tower PQ stands on a horizontal ground with base Q on the ground. The point R divides the tower in two parts such that QR = 15 m. If from a point A on the ground the angle of elevation of R is 60° and the part PR of the tower subtends an angle of 15° at A, then the height of the tower is :

The number of solutions of the equation sin x = cos² x in the interval (0, 10) is _____.

The value of
$\lim_{{n \to \infty}} 6\tan\left\{\sum_{{r=1}}^{n} \tan^{-1}\left(\frac{1}{{r^2+3r+3}}\right)\right\}$
is equal to :

The major product in the reaction is:

The major product in the reaction with product2-Methyl prop-1-ene

If α, β, γ, δ are the roots of the equation x⁴ + x³ + x² + x + 1 = 0, then α²⁰²¹ + β²⁰²¹ + γ²⁰²¹ + δ²⁰²¹ is equal to

In the following reaction:

The compound A and B respectively are:

If K₁ and K₂ are the thermal conductivities, L₁ and L₂ are the lengths and A₁ and A₂ are the cross sectional areas of steel and copper rods respectively such that $\frac{K_2}{K_1}=9,\frac{A_1}{A_2}=2,\frac{L_1}{L_2}=2.$

Then, for the arrangement as shown in the figure, the value of temperature T of the steel-copper junction in the steady state will be

lf the work function of a metal is 6.63 × 10^–19 J, the maximum wavelength of the photon required to remove a photoelectron from the metal is ______ nm. (Nearest integer)
[Given : h = 6.63 × 10^–34 J s, and c = 3 × 10⁸ m s^–1]

The mean and standard deviation of 15 observations are found to be 8 and 3, respectively. On rechecking, it was found that, in the observations, 20 was misread as 5. Then, the correct variance is equal to _______.

A deuteron and a proton moving with equal kinetic energy enter into a uniform magnetic field at right angle to the field. If $r_d$ and $r_p$ are the radii of their circular paths respectively, then the ratio $\frac{r_d}{r_p}$ will be $\sqrt x:1$ where $x$ is__________

The mean of the numbers a, b, 8, 5, 10 is 6 and their variance is 6.8. If M is the mean deviation of the numbers about the mean, then 25 M is equal to:

The number of terminal oxygen atoms present in the product B obtained from the following reaction is ______.
FeCr₂O₄ + Na₂CO₃ + O₂ → A + Fe₂O₃ + CO₂
A + H⁺ → B + H₂O + Na⁺

Let a > 0, b > 0. Let e and l respectively be the eccentricity and length of the latus rectum of the hyperbola
$\frac{x^2}{a^2}−\frac{y^2}{b^2}=1$
Let e′ and l′ respectively be the eccentricity and length of the latus rectum of its conjugate hyperbola. If
$e^2=\frac{11}{14}l$ and $(e^′)^2=\frac{11}{8}l^′$
then the value of 77a + 44b is equal to :

Let H: $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1, a > 0, b > 0,$ be a hyperbola such that the sum of lengths of the transverse and the conjugate axes is $4(2\sqrt 2 + \sqrt {14}).$ If the eccentricity H is $\frac{\sqrt {11}}{2}$, then the value of $a^2 + b^2 $ is equal to ______.

A circle touches both the y-axis and the line x + y = 0. Then the locus of its center is

The ratio for the speed of the electron in the 3^rd orbit of He⁺ to the speed of the electron in the 3^rd orbit of hydrogen atom will be :

‘A’ and ‘B’ respectively are: $A\xrightarrow[(2)Zn-H_2O]{(1)O_3}$
$Ethane-1, 2-dicarbaldehyde + Glyoxal/Oxaldehyde$
$B \xrightarrow[(2)Zn-H_2O]{(1)O_3} 5 - oxohexanal$

Five numbers, $x_1, x_2, x_3, x_4, x_5$ are randomly selected from the numbers $1, 2, 3$,….., $18$ and are arranged in the increasing order $(x_1<x_2<x_3<x_4<x_5)$. The probability that $x_2 = 7$ and $x_4 = 11$ is:

Which one of the following compounds is inactive towards S_N1 reaction?