List of top Questions asked in JEE Main

The correct set of four quantum numbers for the valence electrons of rubidium atom $(Z = 37)$ is

The maximum area of a right angled triangle with hypotenuse $h$ is :

The $x$-coordinate of the incentre of the triangle that has the coordinates of mid-points of its sides as $(0, 1), (1, 1)$ and $(1,0)$ is

Two blocks of masses $m$ and $M$ are connected by means of a metal wire of cross-sectional area $A$ passing over a frictionless fixed pulley as shown in the figure. The system is then released. If $M \,= \,2 m$, then the stress produced in the wire is:

Equimolar solutions of the following compounds are prepared separately in water. Which will have the lowest pH value ?

A vessel contains a mixture of $1$ mole of oxygen and two moles of nitrogen at $300 \,K$. The ratio of the rotational kinetic energy per $ O_{2} $ molecule to that per $ N_{2} $ molecule is

In which of the following exothermic reactions, the heat liberated per mole is the highest ?

If the three lines $x - 3y = p, \,ax + 2y = q$ and $ax + y = r$ form a right-angled triangle then :

On the sides $AB, BC, CA$ of a $\Delta ABC, 3, 4, 5$ distinct points (excluding vertices $A, B, C$) are respectively chosen. The number of triangles that can be constructed using these chosen points as vertices a re :

Let $R=\left\{ \left(3,3\right) \left(5,5\right), \left(9,9\right), \left(12,12\right), \left(5,12\right), \left(3,9\right), \left(3,12\right), \left(3,5\right)\right\}$ be a relation on the set $A=\left\{3,5,9,12\right\}$. Then, $R$ is:

A light ray emerging from the point source placed at $P( 1,3)$ is reflected at a point $Q$ in the axis of $x$. If the reflected ray passes through the point $R (6, 7)$, then the abscissa of $Q$ is:

All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of $10$ to each of the students. Which of the following statistical measures will not change even after the grace marks were given?

The integral $\int \frac{xdx}{2-x^{2}+\sqrt{2-x^{2}}}$ equals

The real number $k$ for which the equation $2x^3 + 3x + k = 0$ has two distinct real roots in $[0, 1]$

If the surface area of a sphere of radius $r$ is increasing uniformly at the rate $8\, cm^2/s$, then the rate of change of its volume is :

The term independent of $x$ in expansion of $\bigg(\frac{x+1}{x^{2/3}-x^{1/3}+1}-\frac{x-1}{x-x^{1/2}}\bigg)^{10}$ is

The sum of first $20$ terms of the sequence $0.7, 0.77, 0.777,....,$ is

If the x-intercept of some line $L$ is double as that of the line, $3x+4y = 12$ and the $y$-intercept of $L$, is half as that of the same line, then the slope of $L$ is:

Let $T_n$ be the number of all possible triangles formed by joining vertices of an $n$-sided regular polygon. If $T_{n+1}-T_n =10$ then the value of $n$ is

If $\int \frac{dx}{x+x^{7}} = p\left(x\right)$ then, $\int \frac{x^{6}}{x+x^{7}}dx$ is equal to:

If $f(x) = sin\, (sin\, x)$ and $f'' (x) + tan \,x\,f'(x)+ g(x) = 0,$ then $g(x) $ is :

Let $a=Im\left(\frac{1+z^{2}}{2iz}\right),$ where $z$ is any non-zero complex number. The set $A=\left\{a:\left|z\right|=1\,and\,z\ne\pm1\right\}$ is equal to:

The line $x - 2y = 2$ meets the parabola, $y^2 + 2x = 0$ only at the point $(- 2,-2)$. The line $ y=mx-\frac{1}{2m}\left(m\ne0\right)$ is tangent to the parabola, $y^{2} = - 2x$ at the point $\left(-\frac{1}{2m^{2}}, -\frac{1}{m}\right).$

If $\vec{a}$ and $\vec{b}$ are non-collinear vectors, then the value of a for which the vectors $\vec{u}=\left(\alpha-2\right)\vec{a}+\vec{b}$ and $\vec{v}=\left(2+3\alpha\right)\vec{a}-3\vec{b}$ are collinear is :

Statement 1 : The only circle having radius $\sqrt{10}$ and a diameter along line $2 x+y=5 \, is\, x^{2}+y^{2}-6x+2y=0.$ Statement 2 : $2x + y = 5$ is a normal to the circle $x^{2}+y^{2}-6x+2y=0.$