# CTET Question paper: 2013 July Paper-1

### Section -II: Mathematics

Directions: Answer the following questions by selecting the most appropriate option

Q31. Perimeter of a square is 24 cm and length of a rectangle is 8 cm. If the perimeters of the square and the rectangle are equal, then the area (in square cm) of the rectangle is

(a) 16

(b) 24

(c) 32

(d) 64

 Answer: (c) 32Solution: perimeters of the rectangle = perimeters of the square⇒ 2( a + b) = 24 ( a = length of a rectangle and b = breadth of a rectangle)⇒ 16 + 2b = 24⇒ b = (24 – 16)/2 = 4 cm∴ Area of rectangle = 8 × 4 = 32 cm2

Q32. The difference of the place value and the face value of the number 3 in 12345 is

(a) 0

(b) 295

(c) 297

(d) 305

 Answer: (c) 297Solution: Place value of 3 in 12345 is 300 and face value of 3 in 12345 is 3.∴ Difference = 300 – 3 = 297

Q33. Which one of the following is not correct?

(a) 56.7 kilogram = 5670grams

(b) A cube has six faces.

(c) One millimeter = 0.1 cm

(d) 0.10 is same as 0.1

 Answer: (a) 56.7 kilogram = 5670gramsSolution: 56.7 Kg = 56.7 × 1000 = 56700 gmSo (a) is not correct.

Q34. The speed of a boat in a river is 20 km per hour and the speed of another boat is 23 km per hour. They travel in the same direction from the same place at the same time. The distance between the boats after three and half hours is

(a) 10 km

(b) 10.5 km

(c) 11 km

(d) 11.5knm

 Answer: (b) 10.5 kmSolution: Distance travel by 2nd  boat= speed × time= 20 × $3\frac{1}{2}\,\,=\,\,20\times \frac{7}{2}=70$  kmDistance travel by 2nd  boat= speed × time= 20 × $3\frac{1}{2}\,\,=\,\,23\times \frac{7}{2}=80.5$  kmThe distance between the boats = 80.5 – 70 = 10.5 km

[ Read More: Mathematics and Pedagogy MCQ Questions with Answer ]

Q35. When 90707 is divided by 9, the remainder is

(a) 3

(b) 5

(c) 6

(d) 7

 Answer: (b) 5Solution: Use simple divide rule and get remainder.

Q36. When a fresh fish is dried it becomes 1/3 of its weight. Sunita buys 1500 kg fresh fish for 25 per kg and sell them, when dried, for 80 per kg. How much does she earn?

(a) Rs. 2,500

(b) Rs. 2,700

(c) Rs. 3,500

(d) Rs. 3,000

 Answer: (a) 2,500Solution: C.P of fresh fish = 1500 × 25 = Rs. 37500Weight dried fish = $\frac{1}{3}\times 1500=500$ kgS.P of dried fish = 500 × 80 = Rs. 40000Profit = 40000 – 37500 = Rs. 2500

Q37. Look at the following pattern

(9 – 1)  ÷ 8 = 1

(98 – 2)  ÷ 8 = 12

(987 – 3) ÷ 8 =  123

(9876 – 4) ÷ 8 = 1234

According to this pattern: (987654 – 6) ÷ 8 = ?

(a) 12345

(b) 123456

(c) 123465

(d) 123467

 Answer: (b) 123456Solution: According to pattern result is consecutive number up to 6(987654 – 6) ÷ 8 = 123456

Q38. 750 ml juice is filled in one bottle and six such bottles are packed in one carton. The number of cartons needed for 450 liters of juice is

(a) 75

(b) 80

(c) 9

(d) 100

 Answer: (d) 100Solution: number of cartons needed = $\frac{450\times 1000}{750\times 6}=100$

Q39. Internal length, breadth and depth of a (rectangular) box are 4 cm, 3 cm and 2 cm respectively. How many such boxes are needed to pack 8664 centimeter cubes?

(a) 351

(b) 361

(c) 391

(d) 722

 Answer: (b) 361Number of boxes are needed = $\frac{8644}{4\times 3\times 2}=360.167$  = 361 ( next round off)

Q40. Write the equivalent fraction of 1/3″. The above question asked to students of Class IV refers to

(a) lower-level demand task as it requires procedural skills

(b) lower-level demand task as it is based on memorization only.

(c) higher-level demand task as it is based on procedure with connection

(d) higher-level demand task as it is based on procedure without connection

 Answer: (a) lower-level demand task as it requires procedural skills

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Q41. Students often make a mistake in comparing the decimal numbers. For example, 0.50 is larger than 0.5. The most probable reason for this error is

(a) lack of practice of these types of questions in the class.

(b) lack of concrete experience of representation of decimal number on the number line

(c) a careless attempt by the students

(d) misconception regarding the significance of zero in ordering decimal

 Answer: (d) misconception regarding the significance of zero in ordering decimal

Q42. A teacher prompts the students to prepare Mathematical journals with the theme “Application of Mathematics in Daily life”. This activity is

(a) to test the students understanding of Mathematical concepts

(b) to provide an opportunity to students share their ideas and knowledge

(c) to help students to a sense of Mathematics

(d) to help students to connect Mathematical concepts and its applications and to share their knowledge and ideas

 Answer: (d) to help students to connect Mathematical concepts and its applications and to share their knowledge and ideas

Q43. According to Van Hiele level of geometric thought, the five levels are- visualization, analysis, informal deduction. Formal deduction and rigor. Some polygons are given to a child of Class III for sorting

He classified the polygons on the basis of the number of sides This child is at level …………. Of Van-Hiele Geometrical thought.

(a) Visualization

(b) Analysis

(c) Informal deduction

(d) Formal deduction

Q44. A child displays difficulty in differentiating between numbers, operations, and symbols, two clock hands, different coins, etc. This implies that the species barrier affecting his learning is

(a) poor verbal, visual, auditory and working memory

(b) poor visual processing ability i.e. visual discrimination, spatial organization, and visual coordination

(c) poor language processing ability. i.e. expression, vocabulary and auditory processing

(d) poor motor skills, reading and writing skills.

 Answer: (b) poor visual processing ability i.e. visual discrimination, spatial organization and visual coordination

Q45. NCF 2005 emphasizes on Constructivist Approach of learning as it focuses on

(a) memorization of definitions and formulae.

(b) submission of regular homework

(c) active participation of learner through engaging activities

(d) effective lecture and instructions by the teacher

 Answer: (c) active participation of learner through engaging activities

Q46. Following are array diagram bindis to represent 15

The way of representing 15 or any other number in the above manner can be used to teach the concept of

(a) area and commutative property

(b) commutative property of multiplication, identification of prime and composite numbers, area of a rectangle

(c) representation of a number as a product of two numbers, commutative property of multiplication, multiplicative identity, identification of prime and composite number area of a rectangle using units quantity

(d) representation of a number as a product of two numbers, commutative property of multiplication, multiplication identity, identification of the prime and composite number

 Answer: (b) commutative property of multiplication, identification of prime and composite numbers, area of a rectangle

Q47. Which of the following questions is open-ended

(a) Write the numbers 25, 71, 19,9, 8, 17, 85 in ascending

(b) Which is more? 1/3 or 7/5

(c) Write any four number greater than 2.7

(d) What is 7 more than 2/7?

 Answer: (c) Write any four number greater than 2.7Explain: open-ended questions offer children the opportunity to freely express feelings, motives, and ideas.

Q48. The most appropriate tool to expose the students of class-II to plane figures, its vertices and edges is

(a) Geo-Board

(b) Nets of 3D solids

(c) Cubes

(d) Black-board surface

Q49. Following is a problem from textbook of class V

“There are 4 poles of measure 105 cm, 215 cm, 150 cm, and 235 cm respectively. If they have to be cut into places of equal length, what is the maximum length of each piece ?”

This question is asked to

(a) test knowledge of factors and multiples

(b) check the skill of finding HCP

(c) enhance problem-solving skills using learned concepts

(d) give the practice of word problems based on HCF and LCM

 Answer: (c) enhance problem-solving skills using learned concepts

Q50. Following is a problem from the textbook of class III

“Which mathematical operation will be used to solve the following problem.?

A milkman sold 1410 liters of milk in 10 days. How many liters of milk did he sell in a day ?”

Which competence of Bloom’s cognitive domain is referred to in the above question?

(a) Knowledge

(b) Comprehension

(c) Analysis

(d) Synthesis

Q51. Rashid is studying in class V. He can classify various types of triangles in different categories but has difficulty in understanding the abstract proof for the sum of three angles in a triangle to be always 180. According to Piaget Cognitive Theory Rashid is at

(a) Concrete operational stage

(b) Formal operational stage

(c) Sensory-motor stage

(d) Pre-operational stage

 Answer: (a) Concrete operational stage

Q52. According to NCF 2005

“Developing children’s abilities for mathematization is the main goal of mathematics education The narrow aim of school mathematics is to develop ‘useful capabilities.”

Here mathematization refers to develop child’s abilities

(a) In performing all number operations efficiently including of finding square root and cube root

(b) To formulate Theorems of Geometry and their proofs independently

(c) To translate word problems into linear equations

(d) To develop the child’s resources to think and reason mathematically, to pursue assumptions to their logical conclusion and to handle abstraction

 Answer: (d) To develop the child’s resources to think and reason mathematically, to pursue assumptions to their logical conclusion and to handle abstraction

Q53. The highlights of a good textbook are that

A. They contain numerous exercises to give rigorous practice

B. All concepts can be introduced through situations

C. Only solved examples are included

D. They must” be thick and heavy

(a) A and B

(b) C and D

(c) A and C

(d) Band D

 Answer: (a) A and B

Q54. NCF 2005 emphasizes that

(a) Succeeding in Mathematics should be mandatory for every child.

(b) Students should be tested first for their logical-mathematical ability

(c) Maths curriculum shall be separate for low achievers

(d) Maths shall be taught to selective students

 Answer: (a) Succeeding in Mathematics should be mandatory for every child.

Q55. The difference between the smallest common multiple and biggest common factor of 5, 10 and 35 is

(a) 30

(b) 35

(c) 65

(d) 75

 Answer: (c) 65Solution:  LCM of 5, 10, and 35 =  70biggest common factor of 5, 10 and 35 = 5Difference = 70 – 5 = 65

Q56. The number of factors of 105 is

(a) 3

(b) 4

(c) 6

(d) 8

 Answer: (d) 8Solution: factors of 105 are 1, 3 , 5, 7, 15, 21, 35 and 105.∴  number of factors = 8

Q57. If the time now is 2: 17 PM. what will be the time 11 hours and 59 minutes from now?

(a) 11:57A.M

(b) 9:59 A.M

(c) 2: 16 A.M

(d) 2:17A.M

 Answer: (c) 2:16A.MSolution: 2.17 PM = 14 : 17Then 14 : 17 + 11: 59 = 26 : 16, After 24 hours next day start∴ 26 : 16 hrs = 2 : 16 A.M.

Q58. Number of degrees in three and one half right angles is

(a) 285°

(b) 295°

(c) 305°

(d) 315°

 Answer: (d) 315°Solution: right angles = 90°three and one half right angles= $3\frac{1}{2}\times 90=\frac{7}{2}\times 90=315$

Q59. 11 ones + 11 tens+11 hundreds equals

(a) 144

(b) 1221

(d) 111

(c) 12321

 Answer: (b) 1221Solution: 11 ones + 11 tens+11 hundreds = 11 + 110 + 1100 = 1221

Q60. The sum of five hundred nine and three thousand twenty eight is

(a) 3537

(b) 3087

(c) 837

(d) 387

 Answer: (a) 3537The sum of five hundred nine and three thousand twenty eight= 509 + 3028 = 3537

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