List of top Mathematics Questions asked in JEE Main

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

Let \(P = \begin{bmatrix} 1 & 0 & 0\\ 3 & 1 & 0\\ 9 & 3 & 1\end{bmatrix}\) and \(Q = [q_{ij}]\) be two \(3 \times 3\) matrices such that \(Q - P^5 = I_3\). Then \(\frac{q_{21} + q_{31}}{q_{32}}\) is equal to :

An ordered pair \((\alpha, \beta)\) for which the system of linear equations
\((1 + \alpha)x + \beta y + z = 2\)
\(\alpha x + (1 + \beta)y + z = 3\)
\(\alpha x + \beta y + 2z = 2\)
has a unique solution, is :

If \(\lambda\) be the ratio of the roots of the quadratic equation in \(x\), \(3m^2x^2 + m(m - 4)x + 2 = 0\), then the least value of \(m\) for which \(\lambda + \frac{1}{\lambda} = 1\), is

A ratio of the 5th term from the beginning to the 5th term from the end in the binomial expansion of \(\left(2^{1/3} + \frac{1}{2(3)^{1/3}}\right)^{10}\) is :

Let \(S = \{1, 2, 3, \ldots, 100\}\). The number of non-empty subsets \(A\) of \(S\) such that the product of elements in \(A\) is even is :

Let \(P(4, -4)\) and \(Q(9, 6)\) be two points on the parabola, \(y^2 = 4x\) and let \(x\) be any point on the arc \(POQ\) of this parabola, where \(O\) is the vertex of this parabola, such that the area of \(\Delta PXQ\) is maximum. Then this maximum area (in sq. units) is :

Let \(f\) and \(g\) be continuous functions on \([0, a]\) such that \(f(x) = f(a - x)\) and \(g(x) + g(a - x) = 4\), then \(\int_0^a f(x)g(x)\,dx\) is equal to :

Let \(S\) be the set of all points in \((-\pi, \pi)\) at which the function, \(f(x) = \min\{\sin x, \cos x\}\) is not differentiable. Then \(S\) is a subset of which of the following ?

Let \(y = y(x)\) be the solution of the differential equation, \(x\frac{dy}{dx} + y = x\log_e x,\ (x > 1)\). If \(2y(2) = \log_e 4 - 1\), then \(y(e)\) is equal to :

The product of three consecutive terms of a G.P. is 512. If 4 is added to each of the first and the second of these terms, the three terms now form an A.P. Then the sum of the original three terms of the given G.P. is :

Two lines \( \frac{x-3}{1} = \frac{y+1}{3} = \frac{z-6}{-1} \) and \( \frac{x+5}{7} = \frac{y-2}{-6} = \frac{z-3}{4} \) intersect at the point R. The reflection of R in the xy-plane has coordinates :

If the point \( (2, \alpha, \beta) \) lies on the plane which passes through the points (3, 4, 2) and (7, 0, 6) and is perpendicular to the plane \( 2x - 5y = 15 \), then \( 2\alpha - 3\beta \) is equal to

Let \( S_n = 1 + q + q^2 + \ldots + q^n \) and \( T_n = 1 + \left(\frac{q+1}{2}\right) + \left(\frac{q+1}{2}\right)^2 + \ldots + \left(\frac{q+1}{2}\right)^n \) where q is a real number and \( q \ne 1 \). If \( {}^{101}C_1 + {}^{101}C_2 \cdot S_1 + \ldots + {}^{101}C_{101}\cdot S_{100} = \alpha T_{100} \) then \( \alpha \) is equal to

Contrapositive of the statement " If two numbers are not equal, then their squares are not equal." is :

Let \( f(x) = \frac{x}{\sqrt{a^2+x^2}} - \frac{d-x}{\sqrt{b^2+(d-x)^2}} \), \( x \in R \), where a, b and d are non-zero real constants. Then :

If \( \int \frac{x+1}{\sqrt{2x-1}}\,dx = f(x)\sqrt{2x-1} + C \), where C is a constant of integration, then \( f(x) \) is equal to :

If \(\begin{vmatrix} a-b-c & 2a & 2a \\ 2b & b-c-a & 2b \\ 2c & 2c & c-a-b \end{vmatrix} = (a+b+c)(x + a + b + c)^2\), \(x \ne 0\), then x is equal to :

If a hyperbola has length of its conjugate axis equal to 5 and the distance between its foci is 13, then the eccentricity of the hyperbola is :

If 19^th term of a non-zero A.P. is zero, then its (49^th term) : (29^th term) is :

The integral \(\int_{\pi/6}^{\pi/4}\frac{dx}{\sin 2x\left(\tan^5x + \cot^5x\right)}\) equals :

\( \lim_{x\to 0} \frac{x\cot(4x)}{\sin^2 x\,\cot^2(2x)} \) is equal to :

Let \(\sqrt{3}\,\hat{i} + \hat{j}\), \(\hat{i} + \sqrt{3}\,\hat{j}\) and \(\beta\hat{i} + (1-\beta)\hat{j}\) respectively be the position vectors of the points A, B and C with respect to the origin O. If the distance of C from the bisector of the acute angle between OA and OB is \(\frac{3}{\sqrt{2}}\), then the sum of all possible values of \(\beta\) is :

Let \(\alpha\) and \(\beta\) be the roots of the quadratic equation \(x^2\sin\theta - x(\sin\theta\cos\theta + 1) + \cos\theta = 0\) \((0 \lt \theta \lt 45^{\circ})\), and \(\alpha \lt \beta\). Then \(\sum_{n=0}^{\infty}\left(\alpha^n + \frac{(-1)^n}{\beta^n}\right)\) is equal to :

The number of functions f from \(\{1, 2, 3, \ldots, 20\}\) onto \(\{1, 2, 3, \ldots, 20\}\) such that f(k) is a multiple of 3, whenever k is a multiple of 4, is :