List of top Mathematics Questions asked in JEE Main

If a line intercepted between the coordinate axes is trisected at a point $A(4, 3)$, which is nearer to $x$-axis, then its equation is :

The number of terms in an $A.P$. is even; the sum of the odd terms in it is $24$ and that the even terms is $30$. If the last term exceeds the first term by $10 \frac{1}{2},$ then the number of terms in the $A.P$. is :

Let C be the circle with centre at (1, 1) and radius = 1. If T is the circle centred at (0, y) passing through origin and touching the circle $C$ externally, then the radius of$ T $is equal to

Let $L_1$ be the length of the common chord of the curves $x^2+y^2 = 9$ and $y^2 = 8x,$ and $L_2$ be the length of the latus rectum of $y^2 = 8x,$ then :

Let P $\left(3\, sec \,\theta, \,2 \,tan \,\theta\right)$ and Q $\left(3\, sec\, \phi, \,2 \,tan \,\phi\right)$ where $\theta + \phi = \frac{\pi}{2},$ be two distinct points on the hyperbola $\frac{x^{2}}{9} - \frac{y^{2}}{4} = 1.$ Then the ordinate of the point of intersection of the normals at P and Q is :

If $f$ and $g$ are differentiable functions in $(0, 1)$ satisfying $f (0) = 2 = g (1), g (0) = 0$ and $f (1) = 6$, then for some $c \in ] 0, 1 [$

For all complex numbers z of the form 1 + i$\alpha$, $\alpha$ $\epsilon$ R, if z = x + iy, then :

Let $z\ne-i$ be any complex number such that $\frac{z-i}{z+i}$ is a purely imaginary number. Then $z+\frac{1}{z}$ is :

Let $A$ and $B$ be two events such that $P\left(\overline{A\cup B}\right)=\frac{1}{6}, P\left(\overline{A \cap B}\right)=\frac{1}{4}$ and $P\left(\bar{A}\right)=\frac{1}{4}$ where $\overline{A}$ stands for the complement of the event $A$. Then , the events $A$ and $B$ are

A number $x$ is chosen at random from the set $\{1, 2, 3, 4, ....., 100\}$. Define the event: $A =$ the chosen number $x$ satisfies $\frac{\left(x-10\right)\left(x-50\right)}{\left(x-30\right)}\ge0$ Then $P(A)$ is :

Let $a ,b,c$ and $d$ be non-zero numbers. If the point of intersection of the lines $4ax+2ay+c = 0$ and $5bx + 2by+ d = 0$ lies in the fourth quadrant and is equidistant from the two axes, then

The contrapositive of the statement "if I am not feeling well, then I will go to the doctor" is :

The image of the line $\frac{x-2}{3}=\frac{y+1}{4} = \frac{z-2}{12}$ in the plane $2x - y + z + 3 = 0$ is the line

The image of the line $\frac{x-1}{3}=\frac{y-3}{1}=\frac{z-4}{-5}$ in the plane $2 x - y + z+ 3 = 0$ is the line.

The integral $\int x \,cos^{-1}\left(\frac{1-x^{2}}{1+x^{2}}\right) \,dx\, \left(x > 0\right)$ is equal to :

Two tangents are drawn from a point $(- 2, -1)$ to the curve, $y^{2}=4x.$ If $\alpha$ is the angle between them, then $|\tan \alpha|$ is equal to :

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

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

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

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

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 :

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

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: