CTET 2014 September Paper-2 Question with Answer

CTET 2014 September Paper-2 Question with Answer
Child Development	Math and Science	Social Science
Language-I (Eng)		Language-II (Hindi)

The candidate has to do questions number 31 to 90 either from Part-II ( Mathematics and Science ) or from Part-III ( Social Studies/ Social Science):

Part-II: Math and Science

Directions (Q. 31-90): Answer the following questions by selecting the most appropriate option.

Q31. Numbers $\frac{-11}{20}, \frac{7}{-15}, \frac{17}{-30}\,\,and\,\,\frac{-3}{10}$ are written in descending order ass

(a) $\frac{17}{-20}>\,\,\frac{-11}{20}>\frac{-3}{10}>\frac{7}{15}$

(b) $\frac{-3}{10}>\frac{7}{-15}>\frac{-11}{20}>\frac{17}{-30}$

(d) $\frac{-11}{20}>\frac{17}{-30}>\frac{-3}{10}>\frac{7}{-15}$

Answer: (b) $\frac{-3}{10}>\frac{7}{-15}>\frac{-11}{20}>\frac{17}{-30}$

Solution: LCM of 20, 15, 30 and 10 = 60

Now, $\frac{-11}{20}=\frac{-11\times 60}{20}=-33$

$\frac{7}{-15}=\frac{7\times 60}{-15}=-28$

$\frac{17}{-30}=\frac{17\times 60}{-30}=-34$

$\frac{-3}{10}=\frac{-3\times 60}{10}=-18$

∴ – 18 > –28 > –33 > –34

$\Rightarrow \frac{-3}{10}>\frac{7}{-15}>\frac{-11}{20}>\frac{17}{-30}$

Q32. What should be subtracted from $\frac{-5}{7}$ to get-1?

(a) $\frac{-2}{7}$

(b) $\frac{4}{7}$

(d) $\frac{-4}{7}$

Answer: (c) $\frac{2}{7}$

Solution: Let x be subtracted.

$\frac{-5}{7}-x=\,\,-1$

$\Rightarrow x=\,\,1-\frac{5}{7}=\frac{2}{7}$

Q33. If a =$\sqrt{\left( 2013 \right) ^2+2013+2014}$, then the value of a is

(a) 1002

(b) 1007

(d) 2014

Answer: (d) 2014

Solution:

$\sqrt{\left( 2013 \right) ^2+2013+2014}\\=\sqrt{\left( 2013 \right) ^2+2013+2013+1}\\=\sqrt{\left( 2013 \right) ^2+2.2013+1}\\=\sqrt{\left( 2013+1 \right) ^2}\\=2013+1 =2014$

Q34. If a, b and c are different integers such that a < b < c <0, then which of the following statements is true?

(a) a + c < b

(b) ab < c

(d) ac > ab

Answer: (a) a + c < b

Solution: a is less than b and when a negative number added with another negative then it less. So a + c < b

Q35. In standard form, the number 829030000 is expressed as k x 10ⁿ. The value of k + n is

(a) 90.9003

(b) 16.2903

(d) 91.903

Answer: (b) 16.2903

Solution: 829030000 is expressed as 8.2903 × 10⁸

∴ k = 8.2903 and n = 8

∴ k + n = 8.2903 + 8 = 16.2903

Q36. LCM of two prime numbers x and y, (x > y), is 161. The value of 3y- x is

(a) 2

(b) –2

(d) 62

Answer: (b) –2

Solution: LCM of two prime numbers = product of two prime numbers

∴ xy = 161

Now 161 = 7 × 23

∴ Two prime numbers are 7 and 23

∴ x = 23 and y = 7 ( x > y)

3y- x = 21 – 23 = –2

Q37. What is the probability that a randomly selected factor from positive factors of 72 is less than 11?

(a) $\frac{5}{12}$

(b) $\frac{7}{11}$

(d) $\frac{7}{10}$

Answer: (c) $\frac{7}{12}$

Solution: positive factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36 and 72

∴ Total number of positive factors = 12

Total number of positive factors less than 11 = 7

∴ required probability = $\frac{7}{12}$

Q38. The value of $\sqrt[3]{500}\,\,\times \,\,\sqrt[3]{16}$ is

(a) 16

(b) 25

(d) 18

Answer: (c) 20

Solution:

$\sqrt[3]{500}\times \sqrt[3]{16}\\=\sqrt[3]{8000}\,\,=20$

Q39. If x is an integer, then (x + 1)⁴ – (x – 1)⁴ is always divisible by

(a) 6

(b) 8

(d) 12

Answer: (b) 8

Solution: (x + 1)⁴ – (x – 1)⁴

= {(x +1)²}² – {(x –1)²}²

= {(x +1)² + (x –1)²}{(x +1)² – (x –1)²}

= 2(x² + 1) 4x

= 8x(x² + 1)

∴ Expression is always divisible by 8

Q40. The hundreds digit of a three-digit number is 7 more than the unit digit. The digits of the number are reversed, and the resulting number is subtracted from the original three-digit number. The unit digit of the final number so obtained is

(a) 0

(b) 1

(d) 3

Answer: (d) 3

Solution: Let unit digit = x and ten digit = y

Hundreds digit = x + 7

∴ The number = (x + 7) × 100 + 10y + x = 100x + 700 + 10y + x

digits of the number are reversed then the number = 100x + 10 y + x + 7

The difference = 100x + 700 + 10y + x – (100x + 10 y + x + 7)

= 100x + 700 +10y + x – 100x –10y – x – 7 = 693

unit digit of 693 = 3

Q41. A has 20% more money than B, and C has 20% less money than B. What percent more money does A have than C?

(a) 30

(b) 50

(d) 43

Answer: (b) 50

Solution: Let B has 100 money. A has 120 money and C has 80 money

A has 120 – 80 = 40 more money than A

A has $\frac{40}{80}\times 100=50$

Q42. Rani, y years old at present, is x years older than Hamid. Fifteen years ago, Hamid’s age was 1/4 of the age of Rani. Which of the following is true?

(a) 3y – 4x = 45

(b) 2y – x =15

(d) 3x – 4y = 45

Answer: (a) 3y – 4x = 45

Solution: Rani’s present age = y years, Hamid present age = y – x

y – x – 15 = $\frac{1}{4}\left( y-15 \right) $

⇒ 4y – 4x – 60 = y – 15

⇒ 3y – 4x = 45

Q43. The cost price of 20 articles is equal to the selling price of x articles. If the profit is 25%, then the value of x is

(a) 15

(b) 16

(d) 25

Answer: (b) 16

Solution: profit percentage = $\frac{20-x}{x}\times 100$

⇒ 25x = 2000 – 100x

⇒125x = 2000

⇒x = 16

Trick: Percentage of Profit/loss = $\frac{ad-bc}{bc}\times 100

Profit for positive sign and loss for the negative sign

Q44. The value of a machine depreciates at the rate of 10% per year. It was purchased 3 years ago. If its present value is Rs. 1,45,800, for how much was it purchased?

(a)1,75,800

(b) 1,80,000

(d) 2,10,000

Answer: (c) 2,00,000

Solution: Let machine purchased 3 years ago at Rs x

Then 145800 = $x\times \frac{90}{100}\times \frac{90}{100}\times \frac{90}{100}$

⇒ x = $\frac{145800\times 100\times 100\times 100}{90\times 90\times 90}=200000$

Q45. The base of an isosceles Δ ABC is 48 cm and its area is 168 cm². The length of one of its equal sides is

(a) 8 cm

(b) 15 cm

(d) 25 cm

Answer: (d) 25 cm

Solution: let length of equal side = x

s = (48 + x + x)/2 = 24 + x

Then area = $\sqrt{s\left( s-48 \right) \left( s-x \right) \left( s-x \right)}$

⇒168 = $\sqrt{24+x\left( 24+x-48 \right) \left( 24+x-x \right) \left( 24+x-x \right)}$

⇒168 = $24\sqrt{\left( 24+x \right) \left( x-24 \right)}$

⇒$\sqrt{x^2-576}$= 7

⇒ x² = 49 + 576 = 625

⇒ x = 25

Q46. The area of a square is $\frac{16}{\pi}$ of the area of a circle. The ratio of the side of the square to the diameter of the circle is

(a) 3:1

(b) 2:1

(d)

Answer: (b) 2:1

Solution: Let side of square = s and diameter of circle = d

Area of square = $\frac{16}{\pi}$ of the area of a circle

⇒ s² = $\frac{16}{\pi}\times \frac{\pi d^2}{4}$

⇒ $\left( \frac{s}{d} \right) ^2$= 4

⇒$\frac{s}{d}$= 2

⇒ s : d = 2 : 1

Q47. The sum of all interior angles of a polygon is 1440°. The number of sides of the polygon is

(a) 8

(b) 9

(d) 12

Answer: (c) 10

Solution: let number of side of polygon = n

Sum of all interior angles = (n – 2) × 180°

(n – 2) × 180 = 1440

⇒180n = 1440 + 360

⇒n = 1800/180 = 10

Q48. If a, b and c are 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

(a) –1.5

(b) 2

(d) –1

Answer: (d) –1

Solution: We know F – E + V = 2 where F = number of faces, E = number of edges and V = number of vertices

∴ a – b + c = 2

⇒$\frac{a-b+c}{2}$=1

⇒$\left( \frac{a-b+c}{2} \right) ^2$= 1

⇒$\left( \frac{a-b+c}{2} \right) ^2$– 2 = 1 – 2 = –1

Q49. If one angle of a triangle is 130°, then the angle between the bisectors of the other two angles is

(a) 65°

(b) 115°

(d) 155°

Answer: (d) 155°

Solution:

Now ∠BAC + ∠ABC + ∠ ACB = 180°

∠ABC + ∠ ACB = 50°

½(∠ABC + ∠ ACB) = 25°

∠DBC + ∠ DCB = 25°

Again, ∠DBC + ∠ DCB + ∠BDC = 180°

∠BDC = 180° – 25° = 155°

Q50. Four times the area of the curved surface of a cylinder is equal to 6 times the sum of the areas of is bases. If its height is 12 cm, then its volume, in cm³, is

(a) 48 π

(b) 384 π

(d) 768 π

Answer: (d) 768 π

Solution: let radius = r

Curved surface = 2 π r 12 = 24 πr

Areas of is bases = 2 πr²

According to question,

12 πr² = 96 πr

⇒r = 8

Volume = πr².12 = 768π

Q51. “t is more useful to know how to mathematics than to know a lot of mathematics.” This statement is given b

(a) David Wheeler

(b) George Polya

(d) Vygotsky

Answer: (a) David Wheeler

Q52. As per NCF 2005, one main goal of mathematics education in schools is to

(a) Develop numeracy skills

(b) Enhance problem-solving skills

(d) Mathematics the child’s thought process

Answer: (d) mathematics the child’s thought process

Q53. As per NCF 2005, the Mathematics curriculum is ambitious coherent and teaches important Mathematics. Here ‘ambitious’ refers to

(a) Seek narrow aims of teaching mathematics in school

(b) Seek higher aims of teaching mathematics in school

(d) Teach a variety of mathematics like arithmetic, algebra, geometry, and data handling

Answer: (b) seek higher aims of teaching mathematics in school

Q54. Anil is able to answer all questions orally but commits mistakes while writing the solutions to problems. The best remedial strategy to remove errors in his writing is

(a) Giving him an assignment of 10 problems every day

(b) Calling him out to solve a problem on the black- board

(d) Giving him practice test after school hours, continuously for one month

Answer: (c) providing him with a worksheet with partially solved problems to complete the missing gaps

Q55. A teacher asked the students to collect leaves and to identify symmetry patterns. This task reflects the teacher’s efforts to

(a) Relate real-life experience with mathematical concepts

(b) Introduce an interdisciplinary approach

(d) Improve mathematical communication

Answer: (a) relate a real-life experience with mathematical concepts

Q57. The twin premises to fix the place of mathematics teaching in our school curriculum are

(a) how to engage the mind of every student” and” how to strengthen the student’s resources.

(b) “How to improve the reasoning ability of every student” and “how to enhance his spatial ability.”

(c) “How to raise the performance of every student in Mathematics and how to prepare meritorious students for international Olympiads.

(d) “How to make the Mathematics class more activity-oriented and “how to enhance the procedural skills and understanding of algorithms in every student.”

Answer: (a) how to engage the mind of every student” and” how to strengthen the student’s resources.

Q57. A teacher asked the students to “find the number of possible pentominoes using 5 squares and then turner explores the number of possible hexominoes and so on. These types of activities help the students to

(a) improve the observation skills

(b) identity relation between number pattern and shapes

(d) improve analytical ability

Answer: (c) improve spatial ability

Q58. As per the vision statement of NCF 2005, School mathematics does not take place in situations, where children

(a) learn to enjoy mathematics

(b) see mathematics as a part of their daily life experience

(d) memorize formulae and algorithms

Answer: (d) memorize formulae and algorithms

Q59. With the help of ‘Geogebra’ software, students can learn all concepts of geometry through

(a) Exploratory approach

(b) inquiry-based approach

(d) lecture-based approach

Answer: (a) exploratory approach

Q60. One of the major reasons for the student’s failure in mathematics at the school level is that our assessment process

(a) emphasizes on testing of procedural knowledge than mathematization of abilities

(b) is gender-biased and asks problems relevant to boy’s interests

(d) gives more weightage to formative assessment than Summative assessment

Answer: (a) emphasizes on testing of procedural knowledge than mathematization of abilities

Q61. The image of a distant colored object formed in a pinhole camera is always

(a) virtual, erect, colored, and diminished

(b) real, erect, colored, and diminished

(d) real, inverted, colored, and diminished

Answer: (d) real, inverted, colored, and diminished

Q62. Study the following table

Group	Parts of stamen	Parts of pistil
A	Anther, filament	Ovary, stigma, style
B	Anther, petal	Anther, sepal, stigma
C	Stigma, filament	Style, stigma sepal
D	Style, ovary	Anther, filament, ovary

The group in which the parts of stamen and parts of pistil are correctly shown is

(a) A

(b) B

(d) D

Answer: (a) A

Q63. If you carefully dig a grass plant and observe its roots and leaves you will find that it has

(a) tap roots and parallel venation

(b) tap roots and reticulate venation

(d) fibrous roots and parallel venation

Answer: (d) fibrous roots and parallel venation

Q64. An animal pops out its stomach through its mouth to eat the soft material of those animals which are covered by hard shells of calcium carbonate. After opening the shell and eating the soft material the stomach goes back into the body of the animal to slowly digest the food. The name of this animal is

(a) Crocodile

(b) Octopus

(d) Starfish

Answer: (d) Starfish

Q65. The ratio between the lengths of the small intestine and large intestine in the human body is

(a) 8:2

(b) 5:1

(d) 1:8

Answer: (a) 8:2

Q66. The normal temperature of the human body on the Celsius and Fahrenheit scales is respectively

(a) 37°C and 98.6° F

(b) 37° F and 98.6° C

(d) 37° F and 96.8° C

Answer: (a) 37°C and 98.6° F

Q67. Select the group of poor conductors of heat from the following

(a) Air, water, plastic

(b) Wool, wood, iron

(d) Air, aluminum, wool

Answer: (a) Air, water, plastic

Q68. The reason behind the formation of the sea breeze is

(a) During the day, the land gets heated faster than the sea water

(b) During the day, the sea water gets heated faster than the land

(d) At night, the sea water co0ols down more slowly than the land

Answer: (a) During the day, the land gets heated faster than the sea water

Q69. You have phenolphthalein solution in three test tubes A, B, and C. On putting 2-3 drops of dilute hydrochloric acid in A, a solution of sodium hydroxide in B, and distilled water in C, if you immediately observe the color of the solution in each test tube, you will find that the solution in the test tube

(a) A is colorless, in B pink, and in C colorless

(b) A is pink, in B pale green, and in C colorless

(d) A is pale green, in B pink, and in C pink

Answer: (a) A is colorless, in B pink and in C colorless

Q70. A student puts a drop of the diluted solution of sodium hydroxide first on a blue litmus paper and then on a red litmus paper. He would observe that

(a) the blue litmus paper turns red and the red litmus paper turns blue

(b) there is no change in the blue litmus paper and the red litmus paper turns blue

(d) the blue litmus paper turns colorless and there is no change in the red litmus paper

Answer: (b) there is no change in the blue litmus paper and the red litmus paper turns blue

Q71. If we add a handful of garden soil to a beaker filled three-quarters with water, stir the contents with a stick to dissolve the soil and let it stand undisturbed for some time. We observe different layers. The order of these layers from the bottom to the top is

(a) gravel, clay, sand, humus, water

(b) sand, gravel, clay, water, humus

(d) gravel, sand, clay, water, humus

Answer: (d) gravel, sand, clay, water, humus

Q72. Cereals such as wheat and gram are grown in an area. The soil of this area must be

(a) both loamy and sandy

(b) clayey

(d) both clayey and loamy

Answer: (d) both clayey and loamy

Q73. When a copper plate is exposed to moist air for long, it acquires a dull green coating. The green material is

(a) copper sulfate

(b) a mixture of copper hydroxide and copper sulfate

(d) a mixture of copper carbonate and copper hydroxide

Answer: (d) a mixture of copper carbonate and copper hydroxide

Q74. In which of the following units is the calorific value of fuels generally expressed?

(a) Calories per gram

(b) Kilocalories per mol

(d) Kilojoules per kilogram

Answer: (d) Kilojoules per kilogram

Q75. The metamorphosis of tadpoles is not possible if the water in which they are growing does not contain sufficient

(a) Calcium

(b) Oxygen

(d) Minerals

Answer: (c) Iodine

Q76. Which of the following commonly used fuels has maximum calorific value?

(a) Compressed Natural Gas (CNG)

(b) Diesel

(d) Petrol

Answer: (c) Liquefied Petroleum Gas (LPG)

Q77. Air is a mixture of many gases. The percentage by volume, of the gases other than nitrogen and oxygen, i.e. CO₂, methane, argon, ozone, and water vapor combined together is about

(a) 0.1%

(b) 1%

(d) 78%

Answer: (b) 1%

Q78. Which of the following endocrine glands secretes Sugar controlling hormone?

(a) Adrenal

(b) Pancreas

(d) Thyroid

Answer: (b) Pancreas

Q79. Select the one which is different from the others in the manner it is applied.

(a) Electrostatic force

(b) Frictional force

(d) Magnetic force

Answer: (b) Frictional force

Q80. A person is suffering from a disease named ‘Goitre’.

Which of the following glands of the person is not functioning properly

(a) Adrenal

(b) Pancreas

(d) Thyroid

Answer: (d) Thyroid

Q81. Good science education should be ‘true to the child‘, implies that the science we teach should

(a) relate to the environment of the child

(b) convey significant aspects of science content

(d) engage the child in learning process skills

Answer: (c) be understandable to the child

Q82. While teaching the correct method of measuring the volume of a solid using a measuring cylinder, Kavita mentions the following steps (not in the correct sequence) to be followed

a. Note the reading of the level of water in the cylinder.
b. Suspend the solid with a thread inside water in the cylinder.
c. Record the least count of the measuring cylinder.
d. Put sufficient water in the cylinder and note the reading

Which one of the following is the correct sequence of steps for the said purpose?

(a) a, b, c, d

(b) c, d, d, à

(d) d, b, c, a

Answer: (c) c, d, b, a

Q83. Vandana is interested to focus more on the acquisition of process skills of science by students of Class VII. Which of the following combination of methods should she prefer to teach the topic of “Micro-organisms’?

(a) Assignment-cum-questioning method

(b) Project-cum-laboratory method

(d) Home assignment-cum-questioning method

Answer: (b) Project-cum-laboratory method

Q84. Which one of the following is the key expectation teaching and learning of science at the upper primary stage?

(a) To acquire questioning and inquiring skills

(b) to create literarily

(d) To acquire academic excellence for competitive examinations

Answer: (a) To acquire questioning and inquiring skills

Q85. National Curriculum Framework, 2005 recommends that science education at the upper primary stage should focus on

(a) helping students to connect classroom learning to life outside the school

(b) helping students to acquire international standards in the learning science

(d) promoting human values and knowledge base for a peaceful society

Answer: (a) helping students to connect classroom learning to life outside the school

Q86. Cognitive validity’ of the science curriculum at the upper primary stage implies that it should

(a) convey Significant and scientifically correct facts

(b) be age-appropriate

(d) enable the child to view science as a social enterprise

Answer: (b) be age-appropriate

Q87. The topic “Separation of Substances’ in Class VI can be taught most effectively by

(a) an in-depth explanation of related concepts

(b) using hands-on activities to be performed by students

(d) organizing more group discussions on different sub-topics

Answer: (b) using hands-on activities to be performed by students

Q88. The term constructivism in relation to science education means that children should be

(a) given complete information about science

(b) actively involved in the process of learning science

(d) given the latest information on scientific developments

Answer: (b) actively involved in the process of learning science

Q89. Anjali asks the following tasks to be performed by students of Class VII while making an electromagnet (not in the correct sequence)

a. Place some pins near the end of a nail.
b. Switch on the current and observe what happens.
c. Wind a copper wire tightly around an iron nail.
d. Connect free ends of the wire to the terminals of a cell

Which one of the following is the correct sequence of tasks to be performed to achieve the desired result?

(a) a, b, c, d

(b) c, d, a, b

(d) d, c, a, b

Answer: (b) c, d, a, b

Q90. While teaching the topic on Motion and Time’ to Class VII students, Savita gave examples of different kinds of motion to the students. Which one of the following examples was quoted by her incorrectly?

(a) Motion of a boy sitting in a moving car in relation to the car

(b) Motion of a boy sitting in a merry-go-round

(d) Motion of a cricket ball hit by a batsman

Answer: (a) Motion of a boy sitting in a moving car in relation to the car

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CTET 2014 September Paper-2 Question with Answer

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Part-II: Math and Science

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