List of top Mathematics Questions asked in JEE Main

Find the equation of normal to the curve$$y=(1+x)y+{\sin }^{-1}({\sin }^{2}x)\text{ at }x=0$$

If $a{x}^2+bx+c=0$ and $c{x}^2+bx+a=0$ $(a,b,c\in R)$ have a common non - real root, then

The value of $\underset{x\to 0}{lim}\frac{{\int }_0^{x^2}{\sec }^{2}tdt}{x\sin x}$ is

The integral $\int \frac{{\sin }^{2}x{\cos }^{2}x}{{({\sin }^{5}x+{\cos }^{3}x{\sin }^{2}x+x{\cos }^{2}x+{\cos }^{5}x)}^2}dx$ is equal to:

A function y = f(x) has a second order derivative f''(x) = 6(x - 1).  If its graph passes through the point (2, 1) and at that point the tangent to the graph is y = 3x -5.  then the function is :

The 315th word in dictionary arranged in order for the word ‘NAGPUR’ is

Find area bounded by $y^2 ≤ 2x$ and $y ≥ 4x – 1$

Given \(f(x) =   \begin{cases}     \frac{tan((a+1)x)+tanx\cdot b}{x}       & \quad x\lt 0\\     3  & \quad x=0\\ \frac{\sqrt{ax+b^2x^2}-\sqrt{ax}}{\sqrt{a}bx\sqrt{x}}  & \quad x\gt 0\end{cases}\) It is a continuous function at x=0, then find \(\frac{b}{a}\)

All the letters of the word PUBLIC are written in all possible orders and these words are written as in a dictionary with serial numbers. Then the serial number of the word PUBLIC is: \\ \\

Let line L pass through the point \( (0, 1, 2) \), intersect the line \( {2 = {3 = {4 \), and be parallel to the plane \( 2x + y - 3z = 4 \). Find the distance of the point \( P(1, -9, 2) \) from line L. \\

Let the vectors \( , , \) represent three coterminous edges of a parallelepiped of volume \( V \). Then the volume of the parallelepiped, whose coterminous edges are represented by \( , + \) and \( + 2 + 3 \) is equal to: \\ \\

If the domain of \(f(x)=\sin^{-1}(\frac{x-1}{2x+3})\) is R – (α, β] then find the value of 12αβ.

Let the solution curve $y=y(x)$ of the differential equation $\frac{d y}{d x}-\frac{3 x^5 \tan ^{-1}\left(x^3\right)}{\left(1+x^6\right)^{3 / 2}} y=2 x \exp \left\{\frac{x^3-\tan ^{-1} x^3}{\sqrt{\left(1+x^6\right)}}\right\}$ pass through the origin Then $y(1)$ is equal to :

R = (a, b) : a + 5b = 42 and a, b ∈ N has m elements and \(\sum\limits_{n=1}^{m}(1+i^{n!})\) = x + iy (where i = √-1). Find x + y + m.

If set A = { z: |z - 1| ≤ 1} and set B = { z: |z - 5i| ≤ |z - 5| }, if z = a + ib, where a, b ∈ I, then find the sum of modulus squares of A ∩ B.

\(I(x)=\int\frac{6dx}{sin^2x(1+\cot x)^2}\)and I(0) then I (\(\frac{\pi}{2}\)) is equal to

If the length of focal chord of y² = 12x is 15 and if the distance of the focal chord from origin is p then 10p² is equal to:

If $f(x)= 3\sqrt{(x-2)}+\sqrt{4-x }$ If minimum value = α Maximum value = β find $α2 + β2 $.

If the normal at point P $$$(a{t}_1^2,2a{t}_1)$ and $Q$$(a{t}_2^2,2a{t}_2)$ on the parabola $y^2=4ax$ meet on the parabola, the$t_1{t}_2$ equals

$PQ$ and $RS$ are two perpendicular chords of the rectangular hyperbola $xy=c^2$. If $C$ is the centre of the rectangular hyperbola, then the product of the slopes of $CP,CQ,CR$ and $CS$ is equal to:

The circle $x^2+y^2+4x-7y+12=0$ cuts an intercept on $y$ -axis of length

Find the equation of normal to the curve$$y=(1+x{)}^y+{\sin }^{-1}({\sin }^{2}x)\text{at}x=0$$

The derivative of $se{c}^{-1} \left(\frac{1}{2x^2-1}\right)$ with respect to $\sqrt{1-x^2}$ at $x=\frac{1}{2}$ is:

The rate of change of volume of a sphere with respect to its surface area when the radius is 4 cm is:

If A = {1, 2, 3, 4, 6} and R is a relation on A such that R = {(a, b) : a, b ∈ A and b is exactly divisible by a} then find the number of elements present in the range of R?