List of top Mathematics Questions asked in JEE Main

Let $f(x)=\int \frac{2 x}{\left(x^2+1\right)\left(x^2+3\right)} d x$. If $f(3)=\frac{1}{2}\left(\log _e 5-\log _e 6\right)$, then $f(4)$ is equal to

If the system of linear equations $ 8 x+y+4 z=-2 $, $ x+y+z=0 $, $ \lambda x-3 y=\mu$ has infinitely many solutions, then the distance of the point $\left(\lambda, \mu,-\frac{1}{2}\right)$ from the plane $8 x + y +4 z +2=0$ is :

Let \(C\) be the centre of the circle \(x^2+y^2-x+2 y=\frac{11}{4}\) and \(P\) be a point on the circle A line passes through the point \(C\), makes an angle of \(\frac{\pi}{4}\) with the line CP and intersects the circle at the points \(Q\) and \(R\) Then the area of the triangle \(PQR\) (in unit \({ }^2\)) is :

From the top of 30 m tower AB the angle of depression to another tower’s QP base and top is 60º and 30º respectively. Another point C lies on tower AB such that CQ is parallel to BP (where B and P are the base of towers). Then the area of BCQP is?

If $\frac{\tan 3\theta -1}{\tan 3\theta +1}=\sqrt{3}$, then the general value of $\theta$ is: