CTET - Mathematics and Science
Central Teacher Eligibility Test - Mathematics and Science
1. This Section consists of 60 questions.
2. All questions are compulsory and carry equal marks.
3. Answer the questions quickly and as carefully as you can.
4. Some questions may be difficult and others easy.
5. Do not spend too much time on any question.
6. We recommend the candidates should aim to score atleast 70% questions right out of 60 questions to enable passing.
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Question 1 |
Directions—Answer the following questions by selecting the most appropriate option.
31. LCM of two prime numbers x and y, (x > y), is 161. The value of 3y – x is—
A | 62 |
B | 2 |
C | – 2 |
D | – 5 |
Question 1 Explanation:
LCM of x and y = 161
x × y = 161 = 23 × 7
Now, x = 23
and y = 7
Then, 3y – x = 3 × 7 – 23
= 21 – 23 = – 2
Question 2 |
32. In standard form, the number 829030000 is expressed as k × 10n. The value of k + n is—
A | 91·903 |
B | 90·903 |
C | 16·2903 |
D | 15·2903 |
Question 2 Explanation:
In standard form
= 8·2903 × 108
Now, here k = 8·2903
and n = 8
Then, k + n = 8·2903 + 8
= 16·2903
Question 3 |
33. If a, b and c are different integers such that a < b < c < 0, then which of the following statements is true ?
A | ac > ab |
B | a + c < b |
C | ab < c |
D | a + b > c |
Question 3 Explanation:
Let a = – 3, b = – 2, c = – 1
Then, a + c < b
– 3 – 1 < – 2
– 4 < – 2
Question 4 |
34. What should be subtracted from –5/7 to get – 1 ?
A | – 4/7 |
B | – 2/7 |
C | 4/7 |
D | 2/7 |
Question 4 Explanation:
Required number
= – 5/7 – (– 1)
= – 5/7 + 1
= 2/7
Question 5 |
35. Numbers –11/20, 7/–15, 17/–30 and –3/10 are written in descending order as—
A | –11/20 > 17/–30 > –3/10 > 7/–15 |
B | 17/–30 > –11/20 > –3/10 > 7/–15 |
C | –3/10 > 7/–15 > –11/20 > 17/–30
|
D | –3/10 > –11/20 > 7/–15 > 17/–30 |
Question 5 Explanation:
–11/20 = –0·55, 7/–15 = –0·46
17/–30 = –0·56
–3/10 = –0·3
In descending order—
–3/10 > 7/–15 > –11/20 > 17/–30
Question 6 |
36. If a =
, then the value of a is—

A | 2014 |
B | 1002 |
C | 1007 |
D | 2013 |
Question 7 |
37. The base of an isosceles ΔABC is 48 cm and its area is 168 cm2. The length of one of its equal sides is—
A | 25 cm |
B | 8 cm |
C | 15 cm |
D | 17 cm |
Question 8 |
38. 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 | Rs 2,10,000 |
B | Rs 1,75,800 |
C | Rs 1,80,000 |
D | Rs 2,00,000 |
Question 8 Explanation:
Purchased price
= 145800 × 100 × 100 × 100 / 90 × 90 × 90
= Rs 2,00,000
Question 9 |
39. Cost price of 20 articles is equal to selling price of x articles. If the profit is 25%, then the value of x is—
A | 25 |
B | 15 |
C | 16 |
D | 18 |
Question 9 Explanation:
Cost price of 20 articles = Selling price of x articles.
Then, profit percentage = (20 – x) / x × 100
25 = (20 – x) / x × 100
x = 80 – 4x
⇒ 5x = 80
x = 16
Question 10 |
40. A teacher asked the students to “find the number of possible pentominoes using 5 squares and then further explore the number of possible hexaminoes and so on.” These types of activities help the child to—
A | improve analytical ability |
B | improve the observation skills |
C | identify relation between number pattern and shapes |
D | improve spatial ability |
Question 11 |
41. The twin premises to fix the place of Mathematics teaching in our school curriculum are—
A | “how to make the Mathematics class more activity oriented” and “how to enhance the procedural skills and understanding of algorithms in every student” |
B | “how to engage the mind of every student” and “how to strengthen the student’s resources” |
C | “how to improve the reasoning ability of every student” and “how to enhance his spatial ability” |
D | “how to raise the performance of every student in Mathematics” and “how to prepare meritorious students for international olympiads”
|
Question 12 |
42. One of the major reasons for student’s failure in Mathematics at school level is that our assessment process—
A | gives more weightage to formative assessment than summative assessment
|
B | emphasizes on testing of procedural knowledge than mathematisation of abilities |
C | is gender biased and asks problems relevant to boy’s interests
|
D | is more subjective in nature and less or no objective type of questions are included
|
Question 13 |
43. With the help of ‘Geogebra’ software, students can learn all concepts of geometry through—
A | lecture-based approach |
B | exploratory approach |
C | inquiry-based approach |
D | project-based approach |
Question 13 Explanation:
Geo Gebra is an interactive geometry, algebra, statistics and calculus application, intended for learning and teaching mathematics and science from primary school to university level. Geo Gebra is available on multiple platforms with its desktop applications for Windows, Mac OS and Linux, with its tablet apps for Android, iPad and Windows, and with its web application based on HTML5 technology.
Question 14 |
44. As per the vision statement of NCF 2005, School Mathematics does not takes place in a situation, where children—
A | memorize formulae and algorithms |
B | learn to enjoy Mathematics |
C | see Mathematics as a part of their daily life experience |
D | pose and solve meaningful problems |
Question 14 Explanation:
The National Curriculum Framework (NCF 2005) is one of four National Curriculum Frameworks published in 1975, 1988, 2000 and 2005 by the National Council of Educational Research and Training (NCERT).
Question 15 |
45. The value of
is—

A | 18 |
B | 16 |
C | 20 |
D | 25 |
Question 16 |
46. What is the probability that a randomly selected factor from positive factors of 72 is less than 11 ?
A | 7/10 |
B | 5/12 |
C | 7/11 |
D | 7/12 |
Question 16 Explanation:
Required probability =
7 / 12
Question 17 |
47. If a, b and c are respectively the number of faces, edges and vertices of a pentagonal pyramid, then the value of 

A | – 1 |
B | – 1·5 |
C | 2 |
D | 1·75 |
Question 18 |
48. The sum of all interior angles of a is 144°. The number of sides of the polygon is—
A | 12 |
B | 8 |
C | 9 |
D | 10 |
Question 18 Explanation:
Let number of sides of the polygon = n.
Then, (n – 2) × 180 = 1440
n – 2 = 8
n = 10
Question 19 |
49. The area of a square is 16/π of the area of a circle. The ratio of the side of the square to the diameter of the circle is—
A | √2 π : 1 |
B | 3 : 1 |
C | 2 : 1 |
D | π : 1
|
Question 19 Explanation:
Let side of the square = a
and, diameter of the circle = 2r
Then, a2 = 16/x × π r2
a2 = 16r2
a/r = 4
a/2r = 2
Hence, required ratio = 2 : 1.
Question 20 |
50. If x is an integer, then (x + 1)4 – (x – 1)4 is always divisible by—
A | 12 |
B | 6 |
C | 8 |
D | 9 |
Question 21 |
51. Anil is able to answer all questions orally, but commits mistakes while writing the solutions of problems. Thebest remedial strategy to remove errors in his writing is—
A | giving him practice test after school hours, continuously for one month |
B | giving him an assignment of 10 problems every day |
C | calling him out to solve a problem on the blackboard |
D | providing him with a worksheet with partially solved problems to complete the missing gaps |
Question 22 |
52. As per NCF 2005, Mathematics curriculum is ambitious, coherent and teaches important Mathematics. Here ‘ambitious’ refers to—
A | teach variety of Mathematics like arithmetic, algebra, geometry and data handling |
B | seek narrow aims of teaching Mathematics in school
|
C | seek higher aims of teaching Mathematics in school
|
D | teach more than one way of solving problems of Mathematics
|
Question 23 |
53. 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 | 43 |
B | 30 |
C | 50 |
D | 17 |
Question 23 Explanation:
Let B’s money = 100
Then, A = 120
and C = 80
Now, Required per cent = 120 – 80/80 × 100
= 40/80 × 100 = 50%
Question 24 |
54. A teacher asked the students to collect leaves and to identify symmetry patterns. This task reflects the teacher’s efforts to—
A | improve mathematical communication |
B | relate real life experience with mathematical concepts |
C | introduce an intradisciplinary approach |
D | enhance creativity amongst students |
Question 25 |
55. Rani, who is 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 | 3x – 4y = 45 |
B | 3y – 4x = 45 |
C | 2y – x = 15 |
D | y/x – 15 = 1/4 |
Question 25 Explanation:
Age of Hamid = (y – x)
Then, 15 years ago,
y – x – 15 = (y – 15) ×1/4
4y – 4x – 60 = y – 15
3y – 4x = 45
Question 26 |
56. The hundreds digit of a threedigit number is 7 more than the units digit. The digits of the number are reversed, and the resulting number is subtracted from the original three-digit number. The units digit of the final number so obtained is—
A | 3 |
B | 0 |
C | 1 |
D | 2 |
Question 26 Explanation:
Let hundred place values 7, 8 or 9
Then, unit place value unit 0 for 7, 1 for 8 and 2 for 9
real number – 700, 801, 902
On changing the order
– 007/693, –108/693, –209/693
Hence, unit digit of the final number is 3.
Question 27 |
57. As per NCF 2005, one main goal of Mathematics education in schools is to—
A | mathematise the child’s thought process |
B | develop numeracy skills |
C | enhance problem solving skills |
D | nurture analytical ability |
Question 27 Explanation:
The NCF 2005 document draws its policy basis from earlier government reports on education as Learning Without Burden and National Policy of Education 1986 1992 and focus group discussion.
Question 28 |
58. Four times the area of the curved surface of a cylinder is equal to 6 times the sum of the areas of its bases. If its height is 12 cm, then its volume, in cm3, is—
A | 768 π |
B | 48 π |
C | 384 π |
D | 546 π |
Question 28 Explanation:
Let radius of a cylinder = r cm.
Then, 4 × 2π r h = 2π r2 × 6
4 × 12 = r × 6
r = 8 cm
Hence, volume of a cylinder
= π r2h
= π (8)2 × 12
= 768 π cm3
Question 29 |
59. “It is more useful to know how to mathematise than to know a lot of Mathematics.” This state-ment is given by—
A | Vygotsky |
B | David Wheeler |
C | George Polya |
D | Van Hiele |
Question 29 Explanation:
David John Wheeler was a computer scientist. Wheeler’s contributions to the field included work on the EDSAC and the Burrows-Wheeler transform.
Question 30 |
60. If one angle of a triangle is 130°, then the angle between the bisectors of the other two angles is—
A | 155° |
B | 65° |
C | 115° |
D | 130° |
Question 30 Explanation:
Required angle = 90 + 130/2
= 90 + 65
= 155°
Question 31 |
61. Vandana is interested to focus more on acquisition of process skills of science by students of Class VIII. Which of the following combination of methods should she prefer to teach the topic on ‘Micro-organisms’ ?
A | Home assignment-cumquestioning method |
B | Assignment - cum - questioning method |
C | Project - cum - laboratory method |
D | Home assignment-cumscience quiz method
|
Question 32 |
62. While teaching correct method of measuring volume of a solid using a measuring cylinder, Kavita mentions the following
steps (not in correct sequence) to be followed :
1. Note the reading of level of water in the cylinder.
2. Suspend the solid with a thread inside water in the cylinder.
3. Record the least count of the measuring cylinder.
4. 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 | 4, 2, 3, 1 |
B | 1, 2, 3, 4 |
C | 3, 2, 4, 1 |
D | 3, 4, 2, 1 |
Question 33 |
63. The reason of sea breeze is—
A | At night, the sea water cools down more slowly than the land |
B | During the day, the land gets heated faster than the sea water |
C | During the day, the sea water gets heated faster than the land |
D | At night, the land cools down more slowly than the sea water
|
Question 33 Explanation:
A sea breeze is a gentle wind that develops over bodies of water near land due to differences in air pressure created by their different heat capacity. It is a common occurrence along coasts during the morning as solar radiation heats the land more quickly than the water.
Question 34 |
64. Good science education should be ‘true to the child’, implies that science we teach should—
A | engage the child in learning process skills |
B | relate to the environment of the child |
C | convey significant aspects of science content |
D | be understandable to the child |
Question 35 |
65. A student puts a drop of dilute 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 colourless and there is no change in the red litmus paper
|
B | the blue litmus paper turns red and the red litmus paper turns blue
|
C | there is no change in the blue litmus paper and the red litmus paper turns blue |
D | there is no change in the red litmus paper and the blue litmus paper turns red |
Question 35 Explanation:
Litmus is a water-soluble mixture of different dyes extracted from lichens, especially Roccella tinctoria. It is often absorbed onto filter paper to produce one of the oldest forms of pH indicator, used to test materials for acidity.
Question 36 |
66. 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 colour of the solution in each
test tube, you will find that the solution in test tube—
A | A is pale green, in B pink and in C pink |
B | A is colourless, in B pink and in C colourless
|
C | A is pink, in B pale green and in C colourless |
D | A is colourless, in B colourless and in C pink
|
Question 37 |
67. 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 cricket ball hit by a batsman |
B | Motion of a boy sitting in a moving car in relation to the car
|
C | Motion of a boy sitting in a merry-go-round
|
D | Motion of the hammer of an electric bell |
Question 38 |
68. Anjali asks the following tasks to be performed by students of Class VII while making an electromagnet (not in correct sequence) :
1. Place some pins near the end of a nail.
2. Switch on the current and observe what happens.
3. Wind a copper wire tightly around an iron nail.
4. 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 | 4, 3, 1, 2 |
B | 1, 2, 3, 4 |
C | 3, 4, 1, 2 |
D | 3, 1, 2, 4 |
Question 39 |
69. If you carefully dig a grass plant and observe its roots and leaves you will find that it has—
A | fibrous roots and parallel venation |
B | taproots and parallel venation |
C | taproots and reticulate venation |
D | fibrous roots and reticulate venation |
Question 40 |
70. The term ‘constructivism’ in relation to science education means that children should be—
A | given latest information on scientific developments |
B | given complete information about science |
C | actively involved in the process of learning science |
D | discouraged to raise questions in the classroom |
Question 40 Explanation:
Constructivism is a theory of knowledge that argues that humans generate knowledge and meaning from an interaction between their experiences and their ideas. Piaget’s theory of constructivist learning has had wide ranging impact on learning theories and teaching methods in education and is an underlying theme of many education reform movements.
Question 41 |
71. Study the following table :
The group in which the parts of stamen and parts of pistil are correctly shown is—

A | D |
B | A |
C | B |
D | C |
Question 42 |
72. The image of a distant coloured object formed in a pinhole camera is always—
A | real, inverted, coloured and diminished |
B | virtual, erect, coloured and diminished
|
C | real, erect, coloured and diminished |
D | real, inverted, black and white and diminished
|
Question 42 Explanation:
A pinhole camera is a simple camera without a lens and with a single small aperture, a pinhole— effectively a light-proof box with a small hole in one side. Light from a scene passes through this single point and projects an inverted image on the opposite side of the box.
Question 43 |
73. A person is suffering from a disease named ‘Goitre’. Which of the following glands of the person is not functioning properly ?
A | Thyroid |
B | Adrenal |
C | Pancreas |
D | Pituitary |
Question 43 Explanation:
The thyroid gland is one of the largest endocrine glands and
consists of two connected lobes. The thyroid gland is found in the neck, below the thyroid cartilage. The thyroid gland controls how quickly the body uses energy, makes proteins, and controls how sensitive the body is to other hormones.
Question 44 |
74. Select the one which is different from the others in the manner it is applied—
A | Magnetic force |
B | Electrostatic force |
C | Frictional force |
D | Gravitational force
|
Question 44 Explanation:
Fraction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each
other.
Question 45 |
75. When a copper plate is exposed to moist air for long, it acquires a dull green coating. The green material is—
A | a mixture of copper carbonate and copper hydroxide |
B | copper sulphate |
C | a mixture of copper hydroxide and copper sulphate |
D | a mixture of copper carbonate and copper sulphate
|
Question 46 |
76. 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 vapour combined together is about—
A | 78% |
B | 0·1% |
C | 1% |
D | 21% |
Question 47 |
77. Which of the following commonly used fuels has maximum calorific value ?
A | Petrol |
B | Compressed Natural Gas (CNG) |
C | Diesel |
D | Liquefied Petroleum Gas (LPG) |
Question 47 Explanation:
LPG is prepared by refining petroleum or ‘wet’ natural gas,
and is almost entirely derived from fossil fuel sources, being
manufactured during the refining of petroleum (crude oil), or
extracted from petroleum or natural gas streams as they emerge from the ground.
Question 48 |
78. The metamorphosis of tadpoles is not possible if the water in which they are growing does not contain sufficient—
A | Minerals |
B | Calcium |
C | Oxygen |
D | Iodine |
Question 48 Explanation:
Iodine and its compounds are primarily used in nutrition, and industrially in the produc-tion of acetic acid and certain polymers. Iodine’s relatively high atomic number, low toxicity, and ease of attachment to organic compounds have made it a part of many Xray contrast materials in modern medicine. Iodine has only one stable isotope. A number of
iodine radioisotopes are also used in medical applications.
Question 49 |
79. In which of the following units is the calorific value of fuels generally expressed ?
A | Kilojoules per kilogram |
B | Calories per gram |
C | Kilocalories per kilogram |
D | Joules
|
Question 50 |
80. Cereals such as wheat and gram are grown in an area. The soil of this area must be—
A | both clayey and loamy |
B | both loamy and sandy |
C | clayey |
D | both sandy and clayey |
Question 51 |
81. 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 then 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, sand, clay, water, humus |
B | Gravel, clay, sand, humus, water |
C | Sand, gravel, clay, water, humus |
D | Clay, sand, gravel, humus, water
|
Question 52 |
82. Which of the following endo-crine glands secretes sugar controlling hormone ?
A | Thyroid |
B | Adrenal |
C | Pancreas |
D | Pituitary |
Question 52 Explanation:
The pancreas is a glandular organ in the digestive system and endocrine system of vertebrates. In humans, it is located
in the abdominal cavity behind the stomach. It is an endocrine gland producing several important
hormones, including insulin, glucagon, somatostatin, and
pancreatic polypeptide which circulate in the blood. The
pancreas is also a digestive organ, secreting pancreatic juice
containing digestive enzymes that assist digestion and absorption of nutrients in the small intestine.
Question 53 |
83. ‘Cognitive validity’ of science curriculum at upper primary stage implies that it should—
A | enable the child to view science as a social enterprise |
B | convey significant and scientifically correct facts |
C | be age appropriate |
D | use appropriate pedagogical processes in teaching |
Question 54 |
84. 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 | Starfish |
B | Crocodile |
C | Octopus |
D | Tortoise |
Question 54 Explanation:
Starfish are marine invertebrates. They typically have a central disc and five arms, though some species have more than this. The amoral or upper surface may be smooth, granular or spiny, and is covered with overlapping plates.
Question 55 |
85. Select the group of poor conductors of heat from the following—
A | Air, aluminium, wool |
B | Air, water, plastic |
C | Wool, wood, iron |
D | Water, copper, wood |
Question 56 |
86. The ratio between the lengths of small intestine and large intestine in the human body is—
A | 1 : 8 |
B | 8 : 1 |
C | 5 : 1 |
D | 1 : 5 |
Question 57 |
87. National Curriculum Framework, 2005 recommends that science education at upper primary stage should focus on—
A | promoting human values and knowledge base for peaceful society |
B | helping students to connect classroom learning to life outside the school |
C | helping students to acquire international standards in learning of science |
D | minimizing social disparities in the students |
Question 57 Explanation:
The approach and recommendations of NCF-2005 are for the entire educational system. A number of its recommendations, for example, focus on rural schools. The syllabus and textbooks based on it are being used by all the CBSE schools.
Question 58 |
88. Which one of the following is the key expectation from teaching and learning of science at upper primary stage ?
A | To acquire academic excellence for competitive examinations |
B | To acquire questioning and inquiring skills |
C | To create literary literacy |
D | To appreciate the interrelationship between science and art |
Question 59 |
89. The normal temperature of human body on the Celsius scale and Fahrenheit scales is respectively—
A | 37°F and 96·8°C |
B | 37°C and 98·6°F |
C | 37°F and 98·6°C |
D | 37°C and 96·8°F |
Question 60 |
90. The topic ‘Separation of Substances’ in Class VI can be taught most effectively by—
A | organizing more group discussions on different sub-topics |
B | in depth explanation of related concepts |
C | using hands on activities to be performed by students |
D | using good home assignments |
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