List of top Mathematics Questions asked in JEE Main

If \( L_1 \) and \( L_2 \) are two parallel lines and \( \triangle ABC \) is an equilateral triangle, then the area of triangle ABC is

The locus of point of intersection of tangent drawn to the circle \( (x - 2)^2 + (y - 3)^2 = 16 \), which subtends an angle of \( 120^\circ \) is

If \( O \) is the vertex of the parabola \( x^2 = 4ay \), \( Q \) is the point on the parabola. If \( C \) is the locus of the point which divides \( OQ \) in ratio 2:3, the equation of the chord of \( C \) which is bisected at point \( (1, 2) \) is

Orthocentre of equilateral \(\Delta ABC\) is at the origin. If side \(BC\) lies along \(x + 2\sqrt{2}y = 4\). If coordinates of vertex \(A\) are (a,b). Find the value of \(\lfloor |a + \sqrt{2}b| \rfloor\), where \([ \cdot ]\) denotes G.I.F. :

Rhombus \( ABCD \) is given with vertices \( A(1,2) \), \( C(-3,-6) \) and sides \( AD \) and \( BC \) are parallel to the line \( 7x - y = 14 \). If coordinates of \( B \) and \( D \) are \( (\alpha,\beta) \) and \( (\gamma,\delta) \) respectively, then find \( \alpha + \beta + \gamma + \delta \):

If the point of intersection of the ellipses \[ x^2 + 2y^2 - 6x - 12y + 23 = 0 \] \[ 4x^2 + 2y^2 - 20x - 12y + 35 = 0 \] lie on a circle of radius \( r \) and centre \( (a,b) \), then the value of \( ab + 18r^2 \) is:

The value(s) of \( \alpha \) for which the line \( \alpha x + 2y = 1 \) never touches the hyperbola \[ \frac{x^2}{9} - \frac{y^2}{1} = 1 \] is/are:

If $P(h,k)$ is a variable point on $x^2 + y^2 = 4$ and $Q(2h+1,\,3k+3)$ always lies on an ellipse, if eccentricity of the ellipse is $e$, then $\dfrac{5}{e^2}$ is equal to

Given triangle $OAB$ where $O$ is the origin, $A=(0,-\sqrt{3}a)$ and $B=(-\sqrt{2}b,0)$. Let the circumradius of $\triangle OAB$ be $4$ units. If the locus of the centroid of $\triangle OAB$ is a circle, then its radius is:

If two circles \(x^2 + y^2 - 4x - 2y - 4 = 0\) \& \((x+1)^2 + (y+4)^2 = r^2\) intersect at two distinct points and range of r \(\in (\alpha, \beta)\), then the value of \(\alpha\beta\) is :

Let \( A(1, 6, 3) \) and point \( B \) and \( C \) lie on the line \[ \frac{x - 1}{1} = \frac{y - 1}{2} = \frac{z - 2}{3} \] where \( B(4, 9, \alpha) \) and point \( C \) is 10 units from \( B \). Find the area of \( \triangle ABC \):

An equilateral triangle \( OAB \) is inscribed in the parabola \( y = 4x^2 \) whose vertex is \( O \). Find the least distance of the circle described on \( AB \) as diameter from the origin.

Let \( O \) be the vertex of the parabola \( y^2 = 16x \). The locus of centroid of \( \triangle OPA \) when \( P \) lies on the parabola and \( A \) lies on the x-axis and \( \angle OPA = 90^\circ \).

Let \( \frac{x^2}{2} + \frac{y^2}{1} = 1 \) and \( y = x + 1 \) intersect each other at points A & B, then \( \angle AOB \) (where O is the centre of the ellipse) is:

If $P(h,k)$ is a variable point on $x^2 + y^2 = 4$ and $Q(2h+1,\,3k+3)$ always lies on an ellipse, if eccentricity of the ellipse is $e$, then $\dfrac{5}{e^2}$ is equal to

Let one end of a focal chord of the parabola \( y^{2} = 20x \) be \( (20, -20) \). If \( P(\alpha, \beta) \) divides the chord internally in the ratio \( 2 : 3 \), find the minimum value of \( \alpha + \beta \).

Given conic \(x^2 - y^2 \sec^2 \theta = 8\) whose eccentricity is '\(e_1\)' & length of latus rectum '\(l_1\)' and for conic \(x^2 + y^2 \sec^2 \theta = 6\), eccentricity is '\(e_2\)' & length of latus rectum '\(l_2\)'. If \(e_1^2 = e_2^2 (1 + \sec^2 \theta)\) then value of \(\frac{e_1 l_1}{e_2 l_2} \tan \theta\)

A rectangle is formed by lines \( x = 0, y = 0, x = 3 \) and \( y = 4 \). A line perpendicular to \( 3x + 4y + 6 = 0 \) divides the rectangle into two equal parts. Then the distance of the line from the point \( \left( -1, \frac{3}{2} \right) \) is:

If \( PQ \) is a chord perpendicular to the transverse axis of \[ \frac{x^2}{4} - \frac{y^2}{b^2} = 1 \] of eccentricity \( \sqrt{3} \) such that \( \triangle OPQ \) is an equilateral triangle (where \( O \) is the origin), then the area of \( \triangle OPQ \) is:

Let \( A \) be a \( 3 \times 3 \) matrix such that \( A + A^{T} = O \). If

\[ A \begin{bmatrix} 1 \\ -1 \\ 0 \end{bmatrix} = \begin{bmatrix} 3 \\ 3 \\ 2 \end{bmatrix}, \quad A^{2} \begin{bmatrix} 1 \\ -1 \\ 0 \end{bmatrix} = \begin{bmatrix} -3 \\ 19 \\ -24 \end{bmatrix} \] and

\[ \det\!\big(\operatorname{adj}(2\,\operatorname{adj}(A+I))\big) = 2^{\alpha}\,3^{\beta}\,11^{\gamma}, \] where \( \alpha, \beta, \gamma \) are non-negative integers, then the value of
\( \alpha + \beta + \gamma \) is ________.

The number of distinct real solutions of the equation \[ x|x + 4| + 3|x + 2| + 10 = 0 \] is

The coefficient of \(x^{48}\) in \[ (1+x) + 2(1+x)^2 + 3(1+x)^3 + \cdots + 100(1+x)^{100} \] is equal to

If the sum of the first four terms of an A.P. is \(6\) and the sum of its first six terms is \(4\), then the sum of its first twelve terms is