List of top Mathematics Questions asked in JEE Main

If \[ \sum_{r=1}^{25}\frac{r}{r^4+r^2+1}=\frac{p}{q}, \] where \(p\) and \(q\) are coprime positive integers, then \(p+q\) is equal to:
Find the value of \[ \tan\!\left[\left(2\sin^{-1}\frac{2}{\sqrt{13}}\right)-2\cos^{-1}\!\left(\frac{3}{\sqrt{10}}\right)\right] \]
Given \[ f(x)=\int \frac{dx}{x^{2/3}+2\sqrt{x}} \quad \text{and} \quad f(0)=-26+24\ln 2. \] If \(f(1)=A+B\ln 3\), then find \((A+B)\).
If the image of a point \(P(3,2,1)\) in the line \[ \frac{x-1}{1}=\frac{y}{2}=\frac{z-1}{1} \] is \(Q\), then the distance of \(Q\) from the line \[ \frac{x-9}{3}=\frac{y-9}{2}=\frac{z-5}{-2} \] is:
If \[ f(x)=1-2x+\int_{0}^{x} e^{x-t} f(t)\,dt \] and \[ g(x)=\int_{0}^{x} (f(t)+2)^{11}(t+12)^{17}(t-4)^4\,dt, \] If local minima and local maxima of \(g(x)\) occur at \(x=p\) and \(x=q\) respectively, find \(|p|+q\).
Consider two parabolas \(P_1,\ P_2\) and a line \(L\):
\[ P_1:\ y=4x^2,\qquad P_2:\ y=x^2+27,\qquad L:\ y=\alpha x \] If the area bounded by \(P_1\) and \(P_2\) is six times the area bounded by \(P_1\) and \(L\), find \(\alpha\).
Let \(L\) be the distance of point \(P(-1,2,5)\) from the line \[ \frac{x-1}{2}=\frac{y-3}{2}=\frac{z+1}{1} \] measured {parallel to a line having direction ratios \(4,\,3,\,-5\). Then \(L^2\) is equal to: }
If sum of first 4 terms of an A.P. is 6 and sum of first 6 terms is 4, then sum of first 12 terms of an A.P. is
Let \(\tan \left( \frac{\pi}{4} + \frac{1}{2} \cos^{-1} \frac{2}{3} \right) + \tan \left( \frac{\pi}{4} - \frac{1}{2} \sin^{-1} \frac{2}{3} \right) = k\). Then number of solution of the equation \(\sin^{-1}(kx - 1) = \sin x - \cos^{-1} x\) is/are :
The value of \(\lim_{x \to 0} \frac{\ln(\sec(ex) \cdot \sec(e^2x) \dots \sec(e^{10}x))}{e^2 - e^{2\cos x}}\) is :
Value of : \(\sum_{k=1}^{\infty} \frac{(-1)^k \cdot k(k+1)}{k!}\)
If \(f(x^2 + 1) = x^4 + 5x^2 + 1\), then find \(\int_{0}^{3} f(x) dx\) :
Area bounded by \(\{(x, y) : xy \le 8 ; y \le x^2, y \ge 1\}\) is :
Find possible no. of triplets (b, c, d), such that \(x^2 + 2\) is divisor of \(x^3 + bx^2 + cx + d\) & b, c, d \( \le \) 20 & b, c, d \( \in \) N :
In \(\Delta ABC\) if \(\frac{\tan(A-B)}{\tan A} + \frac{\sin^2 C}{\sin^2 A} = 1\) where \(A, B, C \in (0, \frac{\pi}{2})\) then
If \(g(x) = 3x^2 + 2x - 3, f(0) = -3, 4g(f(x)) = 3x^2 - 32x + 72\) then find \(f(g(2))\) where \(f(x)>0\) for all valid x:
Consider the 10 observations 2, 3, 5, 10, 11, 13, 15, 21, a and b such that mean of observation is a and variance is 34.2. Then the mean deviation about median, is :
The value of \(S = \sum_{r=1}^{20} \sqrt{\pi \int_{0}^{r} x |\sin \pi x| dx}\) is :
Given \(\frac{1}{\alpha} - \frac{1}{\beta} = \frac{1}{3}\) such that roots of the quadratic equation \(\lambda x^2 + (\lambda+1)x + 3 = 0\) are \(\alpha\) & \(\beta\), then sum of values of \(\lambda\) is equal to :

If \(\vec{a}, \vec{b} \& \vec{c}\) are unit vectors such that \((\vec{a}-\vec{b})^2 + (\vec{b}-\vec{c})^2 + (\vec{c}-\vec{a})^2 = 9\). Find positive k if \(|2\vec{a} + k\vec{b} + k\vec{c}| = 3\) :

Let x be the number of 9 digit numbers formed by taking digits from first 9 natural numbers, where only one digit is repeated twice & y be the number of 9 digit numbers formed from first 9 natural numbers, such that exactly 2 digits repeated twice then
Let \(\int \frac{1 - 5 \cos^2 x}{\sin^5 x \cos^2 x} dx = f(x) + c\) then find \(f\left(\frac{\pi}{4}\right) - f\left(\frac{\pi}{6}\right)\) :
Product of first 3 terms of a G.P. is 27 and sum is \(R - \{a,b\}\), then \(a^2 + b^2\) is equal to :
Let \(x \frac{dy}{dx} - \sin 2y = x^3(2 - x^3) \cos^2 y ; y(2) = 0\), then find \(\tan(y(1))\) :
Maximum value of $n$ for which $40^n$ divides $60!$ is