List of top Mathematics Questions on Geometry asked in MET

Total number of regions in which 'n' coplanar lines can divide the plane, it is known that no two lines are parallel and no three of them are concurrent, is equal to

In a \(\triangle ABC\), if \(b = 2\), \(\angle B = 30^\circ\), then the area of the circumcircle of \(\triangle ABC\) (in sq units) is

In a \(\triangle ABC\), if \(\sin A \sin B = \frac{ab}{c^2}\), then the triangle is

The sum to \(n\) terms of the series \(\frac{3}{1^2} + \frac{5}{1^2+2^2} + \frac{7}{1^2+2^2+3^2} + ..........\) is

The area of the region enclosed by the curves \(y = x\), \(x = e\), \(y = \frac{1}{x}\) and the positive X-axis, is

Let \(\mathbf{a}, \mathbf{b}, \mathbf{c}\) be non-zero vectors such that no two are collinear and \((\mathbf{a} \times \mathbf{b}) \times \mathbf{c} = \frac{1}{3} |\mathbf{b}||\mathbf{c}|\mathbf{a}\). If \(\theta\) is the acute angle between the vectors \(\mathbf{b}\) and \(\mathbf{c}\), then \(\sin \theta\) equals

One possible condition for the three points \((a,b), (b,a)\) and \((a^2, -b^2)\) to be collinear, is

If the lines $a₁x+b₁y+c₁=0$, $a₁x+b₁y+c₂=0$, $a₂x+b₂y+d₁=0$ and $a₂x+b₂y+d₂=0$ are sides of a rhombus, then

If $t₁, t₂$ and $t₃$ are distinct, the points $(t₁, 2at₁+at₁³), (t₂, 2at₂+at₂³), (t₃, 2at₃+at₃³)$ are collinear if

A and B are two points on one bank of a straight river and C, D are two other points on the other bank... AB=a, $\angle CAD=α, \angle DAB=β, \angle CBA=γ$, then CD is equal to

In a triangle, if $r₁ > r₂ > r₃$ then

In a \( \Delta ABC \), \( \angle B = 90^\circ \), then \( \tan^2\left(\frac{A}{2}\right) \) is