List of top Mathematics Questions on Geometry asked in JEE Main

Let A, B be points on the two half-lines $x - \sqrt{3}|y| = \alpha, \alpha>0$ at a distance of $\alpha$ from their point of intersection P. The line segment AB meets the angle bisector of the given half-lines at the point Q. If $PQ = \frac{9}{2}$ and R is the radius of the circumcircle of $\Delta PAB$, then $\frac{\alpha^2}{R}$ is equal to ________

Identify the Mirror image of the given figure along X – X' axis.

Let the midpoints of the sides of a triangle $ABC$ be $ \left(\frac{5}{2},7\right), \left(\frac{5}{2},3\right)$ and $ (4,5) $. If its incentre is $(h,k)$, then $3h+k$ is equal to:

The question figure shows the 3D view of the object. Choose the correct 2D view (Elevation) of the object looking in the direction of the arrow

Identify the total number of surfaces in the given 3D object.

Find out the odd one.

If you draw an object measuring 1 cm on the paper, what would it be equivalent to at a scale of 1:100?

P is the point of intersection of the two half-lines \[ x-\sqrt{3}y=\alpha, \quad \alpha>0 \] Points $A$ and $B$ lie on these lines at a distance $\alpha$ from $P$. If the length of perpendicular from $P$ on $AB$ is $\frac{\alpha}{2}$ and the radius of the circumcircle of $\triangle PAB$ is $R$, then find \[ \frac{\alpha^2}{R} \]

The value of $ \int_{0}^{\infty} \frac{\ln x}{x^2 + 4} \, dx $ is equal to:

If $ S_1: x^2 + y^2 - 6x - 8y + 21 = 0 $ and $ S_2: x^2 + y^2 + 6x + 8y + \lambda = 0 $, then the distance of the centre of $ S_2 $ to the farthest point on $ S_1 $ is:

A rectangle is formed by the lines $ x = 0,\ y = 0,\ x = 3,\ 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 $ L_1 $ and $ L_2 $ are two parallel lines and $ \triangle ABC $ is an equilateral triangle as shown in the figure, then the area of triangle $ ABC $ is:

If \[ \lim_{x \to 0} \frac{e^{a(x-1)} + 2\cos(bx) + e^{-x}(c - 1)}{x \cos x - \ln(1 + x)} = 2, \] Then the value of $ a^2 + b^2 + c^2 $ is:

If $ P(10, 2\sqrt{15}) $ lies on the hyperbola $ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 $ and the length of the latus rectum is 8, then the square of the area of $ \Delta PS_1S_2 $ is [where $ S_1 $ and $ S_2 $ are the foci of the hyperbola].

If $ \cos(\alpha + \beta) = -\frac{1}{10} $ and $ \sin(\alpha - \beta) = \frac{3}{8} $, where \[ 0<\alpha<\frac{\pi}{3} \quad \text{and} \quad 0<\beta<\frac{\pi}{4}, \] and \[ \tan(2\alpha) = \frac{3\left(1 - \sqrt{55}\right)}{\sqrt{11} \left(s + \sqrt{5}\right)}, \] and $ r, s \in \mathbb{N} $, then $ r^2 + s $ is:

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

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

The line $y = x + 1$ intersects the ellipse \[ \frac{x^2}{2} + \frac{y^2}{1} = 1 \] at points $A$ and $B$. Find the angle subtended by the segment $AB$ at the centre of the ellipse.

Let a circle $ C $ with radius $ r $ passes through four distinct points $ (0, 0), (k, 3k), (2, 3), (-1, 5) $, such that $ k \neq 0 $, then $ (10k + 2r^2) $ is equal to:

Let $ ABCD $ be a tetrahedron such that the edges $ AB $, $ AC $, and $ AD $ are mutually perpendicular. Let the areas of the triangles $ ABC $, $ ACD $, and $ ADB $ be 5, 6, and 7 square units respectively. Then the area (in square units) of the $ \triangle BCD $ is equal to:

Let for two distinct values of $ p $, the lines $ y = x + p $ touch the ellipse $ E: \frac{x^2}{4} + \frac{y^2}{9} = 1 $ at the points $ A $ and $ B $. Let the line $ y = x $ intersect $ E $ at the points $ C $ and $ D $. Then the area of the quadrilateral $ ABCD $ is equal to:

Let $ A(4, -2), B(1, 1) $ and $ C(9, -3) $ be the vertices of a triangle ABC. Then the maximum area of the parallelogram AFDE, formed with vertices D, E and F on the sides BC, CA and AB of the triangle ABC respectively, is __________.

Let the three sides of a triangle ABC be given by the vectors $$ 2\hat{i} - \hat{j} + \hat{k}, \quad \hat{i} - 3\hat{j} - 5\hat{k}, \quad \text{and} \quad 3\hat{i} - 4\hat{j} - 4\hat{k}. $$ Let G be the centroid of the triangle ABC. Then $$ 6 \left( |\vec{AG}|^2 + |\vec{BG}|^2 + |\vec{CG}|^2 \right) \text{ is equal to}$$ _______

The center of a circle $ C $ is at the center of the ellipse $ E: \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 $, where $ a>b $. Let $ C $ pass through the foci $ F_1 $ and $ F_2 $ of $ E $ such that the circle $ C $ and the ellipse $ E $ intersect at four points. Let $ P $ be one of these four points. If the area of the triangle $ PF_1F_2 $ is 30 and the length of the major axis of $ E $ is 17, then the distance between the foci of $ E $ is:

Let the sum of the focal distances of the point $ P(4, 3) $ on the hyperbola $ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 $ be $ 8\sqrt{\frac{5}{3}} $. If for $ H $, the length of the latus rectum is $ \ell $ and the product of the focal distances of the point $ P $ is $ m $, then $ 9\ell^2 + 6m $ is equal to: