11.

If y = $\frac{\mathrm{x}-2}{\mathrm{x}+1}$, y= 1 , then x equals

• $\frac{\mathrm{y}+2}{1-\mathrm{y}}$

• $\frac{\mathrm{y}+2}{\mathrm{y}-1}$

• $\frac{\mathrm{y}-2}{\mathrm{y}+1}$

• $\frac{2-\mathrm{y}}{1-\mathrm{y}}$

A square and a circle have equal perimeters. The ratio of the area of the square to the area of the circle is

• 1:1

• 1:4

• $\mathrm{\pi }$:2

• $\mathrm{\pi }$:4

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

• 16

• 24

• 32

• 96

The mean of 10 numbers is 0. If 72 and-12 are included in these numbers, the new mean will be

• 0

• 5

• 6

• 60

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

Algebra is introduced in the middle classes. According to Piagets' theory of cognitive development, it is appropriate to introduce algebra at this stage as

• the child is at sensorimotor stage and can understand with the help of lots of manipulatives

• the child is at pre-operational stage and can understand abstract concepts

• the child is at concrete-operational stage and he can understand and conceptualize concrete experiences by creating logical structure

• the child is at formal operational stage and is fully mature to grasp the abstract concepts

Mr. Sharma was assessing the students' work on exponents. One of the response sheets was as follows
(i) 2³ x 2⁵= 2⁸
(ii) 3² x 4²=(12)⁴
(iii) 3³ $÷$ 3⁵= 3^-2
(iv) 7²⁰ $÷$ 7¹⁴ = 7⁶
(v) 9³ $÷$ 18⁶ = ${\left(\frac{1}{2}\right)}^3$

On the basis of this response sheet, Mr. Sharma can make the following observations

• Child has understood the laws of exponents and can apply them well

• Child has understood the laws of exponents but has made clerical errors

• Child has understood the laws of exponents but has not practised the questions involving division of two numbers

• Child has understood the law of exponents for the cases where the base is same and has missed the concept for the case where the base is different

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