List of top Questions asked in JEE Main

Diameter of a plano-convex lens is $6 \,cm$ and thickness at the centre is 3 mm. If speed of light in material of lens is $2 \times 10^8$ m/s, the focal length of the lens is

The equation $x log x = 2 - x$ is satisfied by at least one value of $x$ lying between $1$ and $2$. The function $f(x) = x log x$ is an increasing function in $[1,2]$ and $g (x)=2-x$ is a decreasing function in $[1, 2]$ and the graphs represented by these functions intersect at a point in $[1,2]$

Distance between two parallel planes $2x+ y + 2z = 8$ and $4x + 2y + 4z + 5 = 0$ is

The expression$\frac{tan\, A}{1-cot\, A}+\frac{cot\, A}{1-tan \, A}$ can be written as

The molarity of a solution obtained by mixing $750\, mL$ of $0.5\, M \,HCl$ with $250\, mL$ of $2 \,M \,HCl$ will be

The order of basicity of amines in gaseous state is:

The image of an illuminated square is obtained on a screen with the help of a converging lens. The distance of the square from the lens is $40\, cm$. The area of the image is $9$ times that of the square. The focal length of the lens is :

Let $x \in \left(0,1\right).$ The set of all x such that $sin^{-1} x >\, cos^{-1} x, $ is the interval:

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

Sodium Carbonate cannot be used in place of $(NH_4)_2CO_3$ for the identification of $Ca^{2+},\, Ba^{2+}$ and $Sr^{2+}$ ions (in group V) during mixture analysis because :

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

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

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

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

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

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:

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:

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 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 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:

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:

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 :