Geometry PYQ — Page 5

In a square, lengths of the diagonals are $(4k + 6)$ cm and $(7k − 3)$ cm. The area of the square (in cm²) is:

The volume of a cylinder having base radius 3 cm is 396 cm³. Find its curved surface area (in cm²):

In triangle $ABC$, points $D$ and $E$ are on $AB$ and $AC$ respectively such that $DE$ is parallel to $BC$. If $AD = 6$ cm, $DB = 4$ cm, $AE = 9$ cm, then the length of $EC$ (in cm) is:

The point (-2, 3) lies in which quadrant?

From the figure, what is the value of x? 

An interior angle of a regular polygon is 135$^\circ$. The polygon is a/an:

A cuboidal slab of copper having dimensions 22 cm $\times$ 10 cm $\times$ 5 cm is melted and recasted in the form of a wire of 1 mm diameter. The wire is rubber coated at the rate of Rs. 1.50 per meter. Find the cost of rubber coating (in Rs.) Use $\pi = \frac{22}{7}$.

Find how many triangle are there in the given figure? 

If in $\triangle ABC$ $\angle A + \angle B = 90^\circ$ and $\sin B = \frac{4}{5}$, then find the value of $\cos A$.

A toy is made in the shape of a hemisphere of diameter 7 cm surmounted by a cone. If this 15.5 cm high toy is polished at 20 paise per cm$^2$, then find the cost of polishing. Take $\pi = \frac{22}{7}$

A solid metallic sphere of radius 8 cm is melted and recasted as a cone of height 8 cm. Find the base radius of the cone (in cm).

A ladder 25 feet long is leaning against a wall such that it touches 24 feet high window. How far is the foot of the ladder from the wall ?

A point on the y-axis which is equidistant from the points A(6, 5) and B(-4, 3) is:

A cone of height 24 cm and base radius 6 cm is made of modelling clay. A child reshapes it in the form of a sphere. The radius of the sphere is :

In $\triangle ABC$ with AB = 5 cm, BC = 12 cm, AC = 13 cm and $\angle B = 90^\circ$, which of the following is/are not correct? (a) $\tan C = \frac{12}{13}$ (b) $\text{cosec} A = \frac{13}{12}$ (c) $\sin B = \frac{5}{13}$ (d) $\tan A = \frac{12}{15}$ (e) $\cos C = \frac{12}{13}$ Choose the correct answer from the options given below:

AB is a diameter of a circle with centre (3, 4). If coordinates of A is the point (4, 9), then find the coordinates of B.

The angle of elevation of the sun, when the length of the shadow of a tree is equal to the height of the tree is :

Match List - I with List - II. | List - I (Shape) | List - II (Area) | |---|---| | (A) Square | (I) $\pi a^2$ | | (B) Triangle | (II) $b \times h$ | | (C) Circle | (III) $a \times a$ | | (D) Parallelogram | (IV) $\frac{1}{2} b \times h$ | Choose the correct answer from the options given below :

A, B, C, are three points on the circumference of a circle and if $AB = AC = 5\sqrt{2}$, angle $BAC = 90$ degrees then radius of the circle is __________.

A well has to be dug out 20 m deep and its radius is 3.5 m. Find the cost of plastering the inner curved surface at Rs 5 per square meter.

The area of a right-angled triangle with base 3 m and hypotenuse 5 m is :

Find the angle of elevation of the Sun, when the length of the shadow of a tree is $\frac{1}{\sqrt{3}}$ times the height of the tree.

The area of a circle is numerically equal to its circumference. Find the diameter of the circle.

Find the perimeter of a rhombus whose one diagonal is 16 cm long and area is 240 cm$^2$.