31.

ABCD is a square with AB = (x+16)cm and BC = (3x)cm. The perimeter (in cm²) is 

• 16

• 24

• 32

• 96

The circumference of the base of a right circular cylinder is 44 cm and its height is 15 cm. The volume (in cm³) of the cylinder is $\left(\mathrm{use\pi }=\frac{22}{7}\right)$

• 770

• 1155

• 1540

• 2310

A Class VII teacher wants to discuss the following problem in the class.

"A square is divided into four congruent rectangles. The perimeter of each rectangle is 40 units. What is the perimeter of given square?" Key Mathematical concepts required to solve this problem is

• area of square and rectangle, perimeter of square and rectangle and definition of square and rectangle

• meaning of the terms square, rectangle, congruent, perimeter etc.

• area of rectangle, perimeter of square

• formation of algebraic equation to solve the problem

According to Van Hiele level of Geometric thought the five levels of geometric understanding are visualization, analysis, informal deduction, formal deduction, and rigour. Students of class VII are asked to classify the quadrilaterals according to their properties. These students are at ________ level of Van Hiele Geometrical thought.

• visualization

• analysis

• informal deduction

• formal deduction

A task is assigned to the Class VIII student is as follows. An open box is to be made out of a metallic sheet of 50 cm x 65 cm. Length and breadth of the box is 30 cm and 15 cm respectively. What is the possible height of the box? Also, find the volume of this box.

This task refers to

• lower level congnitive demand as it requires the knowledge of formulae of volume of cuboid

• lower level of cognitive demand as there is no connection between concepts involved and procedure required

• higher level of cognitive demand as the problem can be solved by making diagrams and connections between many possible situations

• higher level of cognitive demand as it requires the use of conceptual understanding that underline the procedure to complete the task

A child of Class VII defined the rectangle as follows
"Rectangle is a quadrilateral whose opposite sides are parallel and equal"
The definition reflects that the child

• cannot recognize the shape

• do not know the correct properties of the shape

• knows the properties of the shape, but repeated some properties in definition

• knows some properties, but missed some important to complete the definition

The base of an isosceles ABC is 48 cm and its area is 168 cm. The length of one of its equal sides is

• 8 cm

• 15cm

• 17cm

• 25 cm

The area of a square is$\frac{16}{\mathrm{\pi }}$ of the area of a circle. The ratio of the side of the square to the diameter of the circle is

• 3:1

• 2:1

• n:1

• $\sqrt{2}\mathrm{\pi }$:1

The sum of all interior angles of a polygon is 1440°. The number of sides of the polygon is

• 8

• 10

• 9

• 12

If a, b and c are respectively the number of faces, edges, and vertices of a pentagonal pyramid, then the value of ${\left(\frac{\mathrm{a}-\mathrm{b}+\mathrm{c}}{2}\right)}^2-2$ is 

• -1.5

• 2

• 1.75

• -1