List of top Mathematics Questions on Geometry asked in CBSE CLASS XII, CBSE Compartment XII

Two vertical light poles of height 22 m and 16 m stand on the opposite sides of a 20 m wide road as shown below in the figure. Two ladders of length \( l_1 \) and \( l_2 \) are placed from a common point R on the road at a distance of x m from the smaller pole. Based on the above information, answer the following questions :
A cylindrical water container has developed a leak at the bottom. The water is leaking at the rate of 5 cm$^3$/s from the leak. If the radius of the container is 15 cm, find the rate at which the height of water is decreasing inside the container, when the height of water is 2 meters.
If the sides $AB$ and $AC$ of $\triangle ABC$ are represented by vectors $\hat{i} + \hat{j} + 4 \hat{k}$ and $3 \hat{i} - \hat{j} + 4 \hat{k}$ respectively, then the length of the median through A on BC is :
The coordinates of the foot of the perpendicular drawn from the point $A(-2, 3, 5)$ on the y-axis are:
Surface area of a balloon (spherical), when air is blown into it, increases at a rate of 5 mm²/s. When the radius of the balloon is 8 mm, find the rate at which the volume of the balloon is increasing.
Let the volume of a metallic hollow sphere be constant. If the inner radius increases at the rate of 2 cm/s, find the rate of increase of the outer radius when the radii are 2 cm and 4 cm respectively.
A window is in the form of a rectangle surmounted by an equilateral triangle on its length. Let the rectangular part have length and breadth x and y metres respectively.