List of top Mathematics Questions asked in JEE Main

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 :

Let the length of the latus rectum of an ellipse with its major axis along x-axis and centre at the origin, be 8. If the distance between the foci of this ellipse is equal to the length of its minor axis, then which one of the following points lies on it?

Let a function \(f : (0, \infty) \to (0, \infty)\) be defined by \(f(x) = \left|1 - \frac{1}{x}\right|\). Then f is :

If the area of the triangle whose one vertex is at the vertex of the parabola, \(y^2 + 4(x - a^2) = 0\) and the othertwo vertices are the points of intersection of the parabola and y-axis, is 250 sq. units, then a value of 'a' is :

The area (in sq. units) in the first quadrant bounded by the parabola, \(y = x^2 + 1\), the tangent to it at the point (2, 5) and the coordinate axes is :

All x satisfying the inequality \((\cot^{-1}x)^2 - 7(\cot^{-1}x) + 10 \gt 0\), lie in the interval :

Let K be the set of all real values of x where the function \(f(x) = \sin |x| - |x| + 2(x - \pi)\cos |x|\) is not differentiable. Then the set K is equal to :

Let \(S = \{1, 2, \ldots\ldots, 20\}\). A subset B of S is said to be "nice", if the sum of the elements of B is 203. Then the probability that a randonly chosen subset of S is "nice" is :

The value of \(r\) for which \({}^{20}C_r\,{}^{20}C_0 + {}^{20}C_{r-1}\,{}^{20}C_1 + {}^{20}C_{r-2}\,{}^{20}C_2 + \ldots + {}^{20}C_0\,{}^{20}C_r\) is maximum, is

If \(q\) is false and \(p \wedge q \leftrightarrow r\) is true, then which one of the following statements is a tautology ?

The direction ratios of normal to the plane through the points \((0, -1, 0)\) and \((0, 0, 1)\) and making an angle \(\frac{\pi}{4}\) with the plane \(y - z + 5 = 0\) are :

If tangents are drawn to the ellipse \(x^2 + 2y^2 = 2\) at all points on the ellipse other than its four vertices then the mid points of the tangents intercepted between the coordinate axes lie on the curve :

In a triangle, the sum of lengths of two sides is \(x\) and the product of the lengths of the same two sides is \(y\). If \(x^2 - c^2 = y\), where \(c\) is the length of the third side of the triangle, then the circumradius of the triangle is :

The plane containing the line \(\frac{x-3}{2} = \frac{y+2}{-1} = \frac{z-1}{3}\) and also containing its projection on the plane \(2x + 3y - z = 5\), contains which one of the following points ?

Let \(\vec{a} = \hat{i} + 2\hat{j} + 4\hat{k}\), \(\vec{b} = \hat{i} + \lambda\hat{j} + 4\hat{k}\) and \(\vec{c} = 2\hat{i} + 4\hat{j} + (\lambda^2 - 1)\hat{k}\) be coplanar vectors. Then the non-zero vector \(\vec{a} \times \vec{c}\) is :

Equation of a common tangent to the parabola \(y^2 = 4x\) and the hyperbola \(xy = 2\) is :

If \(x\log_e(\log_e x) - x^2 + y^2 = 4\ (y \gt 0)\), then \(\frac{dy}{dx}\) at \(x = e\) is equal to :

Let \(\left(-2 - \frac{1}{3}i\right)^3 = \frac{x + iy}{27}\ (i = \sqrt{-1})\), where x and y are real numbers, then \(y - x\) equals :

Let \(f_k(x) = \frac{1}{k}\left(\sin^k x + \cos^k x\right)\) for \(k = 1, 2, 3, \dots\) Then for all \(x \in \mathbb{R}\), the value of \(f_4(x) - f_6(x)\) is equal to

The sum of the real values of \(x\) for which the middle term in the binomial expansion of \(\left(\frac{x^3}{3} + \frac{3}{x}\right)^8\) equals 5670 is :

If \(y(x)\) is the solution of the differential equation \(\frac{dy}{dx} + \left(\frac{2x+1}{x}\right)y = e^{-2x},\ x \gt 0\), where \(y(1) = \frac{1}{2}e^{-2}\), then

Let \(f : \mathbb{R} \to \mathbb{R}\) be defined by \(f(x) = \frac{x}{1+x^2},\ x \in \mathbb{R}\). Then the range of f is :

The maximum value of the function \(f(x) = 3x^3 - 18x^2 + 27x - 40\) on the set \(S = \{x \in \mathbb{R} : x^2 + 30 \le 11x\}\) is :

Let \(f(x) = \begin{cases} -1, & -2 \le x \lt 0 \\ x^2 - 1, & 0 \le x \le 2 \end{cases}\) and \(g(x) = |f(x)| + f(|x|)\). Then, in the interval \((-2, 2)\), g is :

Let \([x]\) denote the greatest integer less than or equal to \(x\). Then \(\lim_{x \to 0} \frac{\tan(\pi \sin^2 x) + \left(|x| - \sin(x[x])\right)^2}{x^2}\)