List of top Mathematical Ability Questions on Geometry

A straight line \(ax+by=1\) passes through the points \((1,2)\) and \((2,1)\). Then \(9(a^{2}+b^{2})=\)

If the line \(y=mx+c\) makes intercepts \(a,b\) on coordinate axes respectively, such that \(a+b=10\) and \(ab=24\) with \(a>b\), then \(3m+5c=\)

If a line with slope 3 passing through the point \((4,-5)\) makes intercepts \(a,b\) on the coordinate axes, then \(3a^2+4b^2=\)

Two circles of radii 9 cm and 4 cm touch each other externally. A line touches the two circles at P and Q respectively. Then length of PQ, in cm, is

The quadrilateral ABCD with \(A(-5,12)\), \(B(-2,-3)\), \(C(9,-10)\), \(D(6,5)\) is a

The ratio in which the point (4,5) divides the line joining the points (2,3) and (7,8) is

In triangle ABC, \(B(10,9)\) and \(C(5,3)\). If D, E are mid points of AB, AC respectively, then slope of DE is

If the slope of the line \((\sqrt{3}+\sqrt{2})y+(\sqrt{8}-\sqrt{12})x=0\) is \(a-\sqrt{b}\), then \(a^2+b=\)

The equation of the line passing through the origin and having a slope of \(\frac{1}{\sqrt{3}}\) is

The angle of elevation of a tower PQ from a point A on the ground is observed as $30^\circ$. After walking 12 m towards the foot of the tower, the angle of tower is observed as $60^\circ$. Then the height of the tower in meter is

If ABC is an isosceles triangle with $AB=AC$ and $\angle BAC=70^\circ$, then the external angle at C is

In triangle ABC, the lengths of the sides are 5 cm, 8 cm and 9 cm. If D, E and F are the midpoints of BC, CA and AB respectively, then the area of triangle DEF, in $cm^2$, is

ABCD is a quadrilateral whose diagonal BD is of length 26 cm. The lengths of the perpendiculars drawn from A and C on BD are 14 cm and 8 cm respectively. The area of the quadrilateral in sq. cm. is

In the adjoining figure, \(AD \parallel BC\). What is the perimeter of the quadrilateral \(ABCD\)?

Two concentric circles are of radii 5 cm and 3 cm. The length of the chord of the larger circle which touches the smaller circle (in cm) is

If $\tan\theta,\;2\tan\theta+2,\;3\tan\theta+3$ are in geometric progression and $\tan\theta\neq -1$, then $\tan\theta=$

The floor of hall of dimensions \(18\,m \times 12\,m\) is to be fixed by tiles of size \(45\,cm \times 15\,cm\). The number of tiles required for the floor of the hall is:

A solid metallic sphere of 16 cm diameter is melted and cast into smaller solid spheres of diameter 4 cm. The number of smaller spheres formed is:

In triangle ABC, \( AB=26 \) cm, \( AC=24 \) cm and \( \angle C=90^{\circ} \). If \( r_1, r_2, r_3 \) are the areas of the semi-circles with AB, AC, BC as diameters respectively, then \( \frac{1}{\pi}(r_1 + 2r_2 + 3r_3) \) (in \( cm^2 \)) is

The length of a rectangle is 8 cm more than its breadth. If the area of the rectangle is 209 \( cm^2 \), then the perimeter of the rectangle, in cm, is

If the total surface area of a cone is \(384\pi \, cm^2\) and its height is 16 cm, then volume of the cone, in \(cm^3\) is

The height of a cylinder is 7 cm and the area of its curved surface is 264 sq.cm. Then the volume of the cylinder in cu.cm. is (take value of \( \pi=\frac{22}{7} \))

The perimeter of the longest circle that can be inscribed in a rectangle of sides \(161 \, \text{cm}\) and \(296 \, \text{cm}\), in cm, is (take \( \pi \approx \frac{22}{7} \)).