List of top Mathematics Questions asked in JEE Main

If \[ \alpha=\frac14+\frac18+\frac1{16}+\cdots \text{ up to infinity} \] \[ \beta=\frac13+\frac19+\frac1{27}+\cdots \text{ up to infinity} \] Then value of \[ (0.2)^{\log_5\alpha}+(0.04)^{\log_5\beta} \] is

If \[ f(x)=\int_{0}^{x}\tan(t-x)\,dt+\int_{0}^{x}f(t)\tan t\,dt \] then the value of \[ f''\left(\frac{\pi}{6}\right)-12f'\left(-\frac{\pi}{6}\right)+f\left(\frac{\pi}{6}\right) \] is

If \(f(x)\) satisfies the functional equation \[ f(x+y)=f(x)+2y^2+y+\alpha xy \] where \(x,y\) are whole numbers, such that \(f(0)=-1\) and \(f(1)=2\), then the value of \[ \sum_{i=1}^{5}\big(f(i)+\alpha\big) \] is

Let \[ S=\{z: z^2+4z+16=0,\; z\in\mathbb{C}\} \] then the value of \[ \sum_{z\in S}|z+\sqrt{3}i|^2 \] is

Evaluate \[ \int_{0}^{1}\cot^{-1}(1+x+x^2)\,dx \]

The maximum value of \[ E = 16\sin\frac{x}{2}\cos^3\frac{x}{2} \] where \(x\in[0,\pi]\), is

If function \(y(x)\) satisfies the differential equation \[ \frac{dy}{dx}+\left[\frac{6x^2+e^{-2x}(3x^2+2x^3+4)}{(x^3+2)(2+e^{-2x})}\right]y = e^{-2x}+2 \] such that \(y(0)=\frac{3}{2}\) and \[ y(1)=\alpha(e^{-2}+2) \] then \(\alpha\) is equal to

If the quadratic equation \[ (\lambda + 2)x^2 - 3\lambda x + 4\lambda = 0 \quad (\lambda \ne -2) \] has two positive roots then the number of possible integral values of \(\lambda\) is

From point \(B(4,8)\) on the parabola \(y^2 = 16x\), two perpendicular chords \(BA\) and \(BC\) are drawn. Given that the locus of the centroid of triangle \(BAC\) is another parabola with length of the latus rectum equal to \(\ell\), then \(3\ell\) is equal to

Area bounded between the curves \[ x = -2y^2 \] \[ x = 1 - 4y^2 \] is

If the system of equations \[ x + y + z = 5 \] \[ x + 2y + 3z = 9 \] \[ x + 3y + \lambda z = \mu \] has infinitely many solutions, then value of \( \lambda + \mu \) is

If \( \sum_{i=1}^{10} (x_i + 2)^2 = 180 \) and \( \sumᵢ=1¹0 (xᵢ - 1)² = 90 , then the Standard Deviation is equal to

If the matrix \[ \begin{bmatrix} 1 & 3 & 1 \\ 2 & 1 & \alpha \\ 0 & 1 & -1 \end{bmatrix} \] is singular. Given a function \( f(x) = \int_{0}^{x} (t^2 + 2t + 3)\, dt \), \( \forall x \in [1, \alpha] \). If \( m \) and \( n \) are the maximum and minimum values of the function \( f(x) \), then the value of \( 3(m - n) \) is:

If \(\sqrt{3}i, 1\) are the roots of \(x^{3} + ax^{2} + bx + c = 0\) where \(a, b, c \in \mathbb{R}\). Then \(\int_{-1}^{1} (x^{3} + ax^{2} + bx + c)dx\) is

The value of \( x \) which satisfies the equation \( \sin^{-1}\left(\frac{2}{3}\sqrt{1 - x^2}\right) = \cot^{-1}\left(2\sqrt{x}\right) \), is

Let \( f : \mathbb{R} \to \mathbb{R} \), \( f(x) = \frac{2x^2 - 3x + 2}{3x^2 + x + 3} \), then \( f(x) \) is

Let \( R \) be a relation such that \( R = \{ (x, y) \in \mathbb{N} \times \mathbb{N} \mid x + y \le 7 \} \). Minimum number of elements to be added in \( R \) so that it becomes transitive is:

If \( (1 - x)^{10} = \sum_{r=0}^{10} a_r \, x^r (1 - x)^{30 - 2r} \), then find \( \frac{9a_9}{a_{10}} \).

Given that quadratic equation \( (k^2 - 15k + 27) x^2 + 9(k - 1)x + 18 = 0 \) has one root twice of other. Then find the length of the latus rectum of the parabola \( y^2 = 6kx \):

Given vectors \( \vec{a} = \hat{i} + \hat{j} + \hat{k} \) and \( \vec{b} = \hat{j} - \hat{k} \). Another vector \( \vec{c} \) satisfy equations \( \vec{a} \cdot \vec{c} = 3 \) and \( \vec{a} \times \vec{c} = \vec{b} \), then find \( \vec{a} \cdot (\vec{c} - 2\vec{b}) \):

Consider \( e_1 \) and \( e_2 \) be roots of the equation \( x^2 - a x + 2 = 0 \). Set of exhaustive values of 'a' for which \( e_1 \) and \( e_2 \) are eccentricities of hyperbolas then \( a \in [\alpha, \beta) \) and set of values of 'a' for which \( e_1 \) and \( e_2 \) are eccentricity of the parabola and ellipse is \( (\gamma, \infty) \) then \( (\alpha^2 + \beta^2 + \gamma^2) \) equal:

Solution of differential equation \( \frac{dy}{dx} + \frac{y(x - \sqrt{x^2 - 1})}{x^2 - x\sqrt{x^2 - 1}} = \frac{x}{x^2 - x\sqrt{x^2 - 1}} \) satisfies the condition \( y(1) = 1 \), then find \( [y(\sqrt{5})] \). (Here [·] denotes greatest integer function):

Find the area bounded by \( 0 \le y \le 6 - x \), \( y^2 + 3 \le 4x \) and \( x>0 \):

If domain of \( f(x) = \sin^{-1} \left( \frac{x + |x|}{3} \right) \) is \( [\alpha, \beta) \), then \( (\alpha^2 + \beta^2) \) is:

If the ratio of y-ordinates of points on the parabola \( y^2 = 12x \) is 1 : 2 and the length of the chord joining these points is \( 3\sqrt{13} \), then find the angle subtended by the chord at the focus of the parabola: