List of top Mathematics Questions asked in JEE Main

\(\lim_{x\to\infty}\left(\dfrac{n}{n^2+1^2}+\dfrac{n}{n^2+2^2}+\dfrac{n}{n^2+3^2}+\ldots+\dfrac{1}{5n}\right)\) is equal to :

If the sum of the first 15 terms of the series \(\left(\frac{3}{4}\right)^3+\left(1\frac{1}{2}\right)^3+\left(2\frac{1}{4}\right)^3+3^3+\left(3\frac{3}{4}\right)^3+\ldots\) is equal to 225 k, then k is equal to :

If an angle between the line, \(\frac{x+1}{2}=\frac{y-2}{1}=\frac{z-3}{-2}\) and the plane, \(x-2y-kz=3\) is \(\cos^{-1}\left(\frac{2\sqrt{2}}{3}\right)\), then a value of k is :

The mean and the variance of five observations are 4 and 5.20, respectively. If three of the observations are 3, 4 and 4 ; then the absolute value of the difference of the other two observations, is :

If \(\sin^4\alpha+4\cos^4\beta+2=4\sqrt2\,\sin\alpha\cos\beta;\ \alpha,\beta\in[0,\pi]\), then \(\cos(\alpha+\beta)-\cos(\alpha-\beta)\) is equal to :

Let f be a differentiable function such that \(f(1)=2\) and \(f'(x)=f(x)\) for all \(x\in R\). If \(h(x)=f(f(x))\), then \(h'(1)\) is equal to :

The tangent to the curve \(y=x^2-5x+5\), parallel to the line \(2y=4x+1\), also passes through the point :

\(\lim_{x\to1^-}\dfrac{\sqrt\pi-\sqrt{2\sin^{-1}x}}{\sqrt{1-x}}\) is equal to :

In a class of 60 students, 40 opted for NCC, 30 opted for NSS and 20 opted for both NCC and NSS. If one of these students is selected at random, then the probability that the students selected has opted neither for NCC nor for NSS is :

The number of integral values of m for which the quadratic expression, \((1+2m)x^2-2(1+3m)x+4(1+m)\), \(x\in R\), is always positive, is :

If \(A=\begin{bmatrix}1&\sin\theta&1\\-\sin\theta&1&\sin\theta\\-1&-\sin\theta&1\end{bmatrix}\); then for all \(\theta\in\left(\frac{3\pi}{4},\frac{5\pi}{4}\right)\), \(\det(A)\) lies in the interval :

Let \(z_1\) and \(z_2\) be two complex numbers satisfying \(|z_1|=9\) and \(|z_2-3-4i|=4\). Then the minimum value of \(|z_1-z_2|\) is :

If the function f given by \(f(x)=x^3-3(a-2)x^2+3ax+7\), for some \(a\in R\) is increasing in (0, 1] and decreasing in [1, 5), then a root of the equation, \(\frac{f(x)-14}{(x-1)^2}=0\ (x\ne1)\) is :

If \(^nC_4,\ ^nC_5\) and \(^nC_6\) are in A.P., then n can be :

The integral \(\int_1^e \left\{\left(\frac{x}{e}\right)^{2x}-\left(\frac{e}{x}\right)^{x}\right\}\log_e x\,dx\) is equal to :

The sum of the distinct real values of \(\mu\), for which the vectors, \(\mu\hat{i} + \hat{j} + \hat{k},\ \hat{i} + \mu\hat{j} + \hat{k},\ \hat{i} + \hat{j} + \mu\hat{k}\) are co-planar, is :

Let \(C_1\) and \(C_2\) be the centres of the circles \(x^2 + y^2 - 2x - 2y - 2 = 0\) and \(x^2 + y^2 - 6x - 6y + 14 = 0\) respectively. If P and Q are the points of intersection of these circles, then the area (in sq. units) of the quadrilateral \(PC_1QC_2\) is :

If a variable line, \(3x + 4y - \lambda = 0\) is such that the two circles \(x^2 + y^2 - 2x - 2y + 1 = 0\) and \(x^2 + y^2 - 18x - 2y + 78 = 0\) are on its opposite sides, then the set of all values of \(\lambda\) is the interval :

The perpendicular distance from the origin to the plane containing the two lines, \(\frac{x+2}{3} = \frac{y-2}{5} = \frac{z+5}{7}\) and \(\frac{x-1}{1} = \frac{y-4}{4} = \frac{z+4}{7}\), is :

Let \(S_k = \frac{1 + 2 + 3 + \dots + k}{k}\). If \(S_1^2 + S_2^2 + \dots + S_{10}^2 = \frac{5}{12}A\), then A is equal to :

If the vertices of a hyperbola be at \((-2, 0)\) and \((2, 0)\) and one of its foci be at \((-3, 0)\), then which one of the following points does not lie on this hyperbola?

A tetrahedron has vertices \(P(1, 2, 1)\), \(Q(2, 1, 3)\), \(R(-1, 1, 2)\) and \(O(0, 0, 0)\). The angle between the faces OPQ and PQR is :

The area (in sq. units) of the region bounded by the parabola, \(y = x^2 + 2\) and the lines, \(y = x + 1\), \(x = 0\) and \(x = 3\), is

The maximum area (in sq. units) of a rectangle having its base on the x-axis and its other two vertices on the parabola, \(y = 12 - x^2\) such that the rectangle lies inside the parabola, is :

\(\displaystyle\lim_{x \to \pi/4} \frac{\cot^3 x - \tan x}{\cos\left(x + \frac{\pi}{4}\right)}\) is :