CTET Solved Question Paper - 2 (31 Jan - 2021) | Mathematics & Pedagogy Paper 2 for CTET & TET Exams - CTET & State TET PDF Download

 Page 1


Directions (Q. Nos. 1-30)Answerthe
followingquestionsbyselectingthe
correct/mostappropriateoptions.
1. Which of the following is most appropriate
strategy for introducing the concept of
multiplication of two decimal numbers in
the middle school?
(a) Multiplication as repeated addition should be
emphasised
(b) Multiplication as inverse of division should be
emphasised
(c) The algorithm should be used to introduce the
concept
(d) The process should be visually represented
2. Which of the following is a narrow aim of
teaching Mathematics?
(a) To make students proficient in handling
numbers and number operations.
(b) To develop students’ generalisation abilities.
(c) To encourage systematic reasoning among
students.
(d) To develop students’ ability to argue the truth
and falsity of statements.
3. Which of the following is most appropriate
strategy for teaching students to solve
mathematical problems?
(a) Teacher should begin by explaining the steps
required for obtaining the solutions of the
problems.
(b) Students should be encouraged to view a
problem from many perspectives.
(c) Guess and verify approach should be strictly
discouraged.
(d) The list of formulae required for solving the
given set of problems should be provided in
the beginning.
4. Identify the incorrect statement from
among the following
(a) Mathematical communication involves precise
use of language.
(b) Conjectures do not have utility in constructing
mathematical knowledge.
(c) Hypothesis have a role in construction of
mathematical knowledge.
(d) The notion of argumentation is central to
Mathematics.
5. Which of the following is a desirable
strategy for assessing students’ learning in
Mathematics ?
(a) Students’ justification of their responses should
be an important basis of assessment.
(b) Development of' mathematical vocabulary
should not be a basis of assessment.
CTET SOLVED PAPERS
Paper - 2 (Mathemati cs)
31 Janua r y, 2021
Page 2


Directions (Q. Nos. 1-30)Answerthe
followingquestionsbyselectingthe
correct/mostappropriateoptions.
1. Which of the following is most appropriate
strategy for introducing the concept of
multiplication of two decimal numbers in
the middle school?
(a) Multiplication as repeated addition should be
emphasised
(b) Multiplication as inverse of division should be
emphasised
(c) The algorithm should be used to introduce the
concept
(d) The process should be visually represented
2. Which of the following is a narrow aim of
teaching Mathematics?
(a) To make students proficient in handling
numbers and number operations.
(b) To develop students’ generalisation abilities.
(c) To encourage systematic reasoning among
students.
(d) To develop students’ ability to argue the truth
and falsity of statements.
3. Which of the following is most appropriate
strategy for teaching students to solve
mathematical problems?
(a) Teacher should begin by explaining the steps
required for obtaining the solutions of the
problems.
(b) Students should be encouraged to view a
problem from many perspectives.
(c) Guess and verify approach should be strictly
discouraged.
(d) The list of formulae required for solving the
given set of problems should be provided in
the beginning.
4. Identify the incorrect statement from
among the following
(a) Mathematical communication involves precise
use of language.
(b) Conjectures do not have utility in constructing
mathematical knowledge.
(c) Hypothesis have a role in construction of
mathematical knowledge.
(d) The notion of argumentation is central to
Mathematics.
5. Which of the following is a desirable
strategy for assessing students’ learning in
Mathematics ?
(a) Students’ justification of their responses should
be an important basis of assessment.
(b) Development of' mathematical vocabulary
should not be a basis of assessment.
CTET SOLVED PAPERS
Paper - 2 (Mathemati cs)
31 Janua r y, 2021
(c) Same tasks should be given to all students for
parity.
(d) Students’ incorrect answers should be ignored.
6. For a given figure to be a triangle, the
condition that it is a union of three
segments is
(a) both necessary and sufficient condition.
(b) neither necessary nor sufficient condition.
(c) a necessary but not a sufficient condition.
(d) a sufficient but not a necessary condition.
7. Consider the following statements:
A= Ifn is even, then n
2
is even.
B= Ifn
2
is not even,n is not even.
C = Ifn
2
is even, then n is even.
D= Ifn is not even, then n
2
is not even.
Which of the following statements is true?
(a) B is inverse of A.
(b) D is contraposition of A.
(c) C is converse of A.
(d) D is converse of A.
8. Which of the following teaching- learning
resources in mathematics cannot be used
for visually challenged students?
(a) Tiles
(b) GeoBoard
(c) GeoGebra
(d) Taylor’s abacus
9. Which of the following statements is true?
(a) Intuition has no role in generating
mathematical knowledge.
(b) Mathematical statements can be conditional.
(c) Mathematics consists of all the theorems
proved in Mathematics books.
(d) A person good in arithmetical computation is
also good in Mathematics andvice-versa.
10. Which of the following statements is not
correct regarding differently abled children
of dyslexia in Mathematics learning in an
inclusive classroom?
(a) Dyslexic children may have difficulty in
writing down their ideas in systematic and
organised manner.
(b) Dyslexia impacts only language learning not
Mathematics learning.
(c) Dyslexia has an impact in a person’s
co-ordination of verbal and spatial aspects of
numbers.
(d) Visual patterns in Mathematics help in
overcoming difficulties experienced by
dyslexic children.
11. The number of distinct prime factors of the
largest 6-digits number is
(a) 5 (b) 6
(c) 3 (d) 4
12. If the 8-digits number 179 091 x y is divisible
by 88, then what is the value of ( ) x y - ?
(a) 3 (b) 4
(c) 1 (d) 2
13. Leta =
11
13
,b =
13
14
andc =
15
17
be three
fractions. Which of the following is true?
(a)
11
13
15
17
13
14
< < (b)
11
13
13
14
15
17
< <
(c)
13
14
11
13
15
17
< < (d)
15
17
13
14
11
13
< <
14. If 0.139 0.75 2.105 (1.001) + + -
´ = - 1.1 2 k, then the value of k is
(a) 0.1071 (b) 0.1075
(c) 0.8925 (d) 0.982
15. Ifa = -
3
4
andb =
5
6
, then which of the
following does not lie betweena andb?
(a)-
2
5
(b)-
7
9
(c) 0 (d)-
1
2
16. The product of 1.7 ´ 10
4
and 12.5 ´
-
10
6
is
expressed in the standard form ask
n
´ 10 .
The value of ( ) 2k n + is
(a) 2.25 (b) 3.25 (c) 2.125 (d) 1.125
17. Two numbers are in the ratio 3 : 5. If 12 is
added to both the numbers, then the ratio
becomes 5 : 7. the sum of the given two
numbers is
(a) 48 (b) 56 (c) 32 (d) 40
18. The marked price of an article is ` 840. A
shopkeeper gives a discount of 15% on the
marked price and still makes a profit of
19%. What is the cost price of the article?
(a)` 600 (b)` 640 (c)` 540 (d)` 580
19. If
5 7
3
2
4 3
4
4
x x
x
-
+ =
-
+ , then the value of
( ) 8 5 x + is
(a) 9 (b) 13 (c) 6 (d) 7
20. LetP xy y x = - - 12 10 18
2 2
,
Q x y xy = + + 14 12 9
2 2
, and
R y x xy = - + 5
2 2
, then ( ) P Q R + - =
(a) 20 7 3
2 2
xy x y - - (b) 20 3 3
2 2
xy x y - -
(c) 22 3 3
2 2
xy x y - + (d) 22 3 3
2 2
xy x y + -
2 2021 January (CLASSVI-VIII)Solved Paper CTET
Page 3


Directions (Q. Nos. 1-30)Answerthe
followingquestionsbyselectingthe
correct/mostappropriateoptions.
1. Which of the following is most appropriate
strategy for introducing the concept of
multiplication of two decimal numbers in
the middle school?
(a) Multiplication as repeated addition should be
emphasised
(b) Multiplication as inverse of division should be
emphasised
(c) The algorithm should be used to introduce the
concept
(d) The process should be visually represented
2. Which of the following is a narrow aim of
teaching Mathematics?
(a) To make students proficient in handling
numbers and number operations.
(b) To develop students’ generalisation abilities.
(c) To encourage systematic reasoning among
students.
(d) To develop students’ ability to argue the truth
and falsity of statements.
3. Which of the following is most appropriate
strategy for teaching students to solve
mathematical problems?
(a) Teacher should begin by explaining the steps
required for obtaining the solutions of the
problems.
(b) Students should be encouraged to view a
problem from many perspectives.
(c) Guess and verify approach should be strictly
discouraged.
(d) The list of formulae required for solving the
given set of problems should be provided in
the beginning.
4. Identify the incorrect statement from
among the following
(a) Mathematical communication involves precise
use of language.
(b) Conjectures do not have utility in constructing
mathematical knowledge.
(c) Hypothesis have a role in construction of
mathematical knowledge.
(d) The notion of argumentation is central to
Mathematics.
5. Which of the following is a desirable
strategy for assessing students’ learning in
Mathematics ?
(a) Students’ justification of their responses should
be an important basis of assessment.
(b) Development of' mathematical vocabulary
should not be a basis of assessment.
CTET SOLVED PAPERS
Paper - 2 (Mathemati cs)
31 Janua r y, 2021
(c) Same tasks should be given to all students for
parity.
(d) Students’ incorrect answers should be ignored.
6. For a given figure to be a triangle, the
condition that it is a union of three
segments is
(a) both necessary and sufficient condition.
(b) neither necessary nor sufficient condition.
(c) a necessary but not a sufficient condition.
(d) a sufficient but not a necessary condition.
7. Consider the following statements:
A= Ifn is even, then n
2
is even.
B= Ifn
2
is not even,n is not even.
C = Ifn
2
is even, then n is even.
D= Ifn is not even, then n
2
is not even.
Which of the following statements is true?
(a) B is inverse of A.
(b) D is contraposition of A.
(c) C is converse of A.
(d) D is converse of A.
8. Which of the following teaching- learning
resources in mathematics cannot be used
for visually challenged students?
(a) Tiles
(b) GeoBoard
(c) GeoGebra
(d) Taylor’s abacus
9. Which of the following statements is true?
(a) Intuition has no role in generating
mathematical knowledge.
(b) Mathematical statements can be conditional.
(c) Mathematics consists of all the theorems
proved in Mathematics books.
(d) A person good in arithmetical computation is
also good in Mathematics andvice-versa.
10. Which of the following statements is not
correct regarding differently abled children
of dyslexia in Mathematics learning in an
inclusive classroom?
(a) Dyslexic children may have difficulty in
writing down their ideas in systematic and
organised manner.
(b) Dyslexia impacts only language learning not
Mathematics learning.
(c) Dyslexia has an impact in a person’s
co-ordination of verbal and spatial aspects of
numbers.
(d) Visual patterns in Mathematics help in
overcoming difficulties experienced by
dyslexic children.
11. The number of distinct prime factors of the
largest 6-digits number is
(a) 5 (b) 6
(c) 3 (d) 4
12. If the 8-digits number 179 091 x y is divisible
by 88, then what is the value of ( ) x y - ?
(a) 3 (b) 4
(c) 1 (d) 2
13. Leta =
11
13
,b =
13
14
andc =
15
17
be three
fractions. Which of the following is true?
(a)
11
13
15
17
13
14
< < (b)
11
13
13
14
15
17
< <
(c)
13
14
11
13
15
17
< < (d)
15
17
13
14
11
13
< <
14. If 0.139 0.75 2.105 (1.001) + + -
´ = - 1.1 2 k, then the value of k is
(a) 0.1071 (b) 0.1075
(c) 0.8925 (d) 0.982
15. Ifa = -
3
4
andb =
5
6
, then which of the
following does not lie betweena andb?
(a)-
2
5
(b)-
7
9
(c) 0 (d)-
1
2
16. The product of 1.7 ´ 10
4
and 12.5 ´
-
10
6
is
expressed in the standard form ask
n
´ 10 .
The value of ( ) 2k n + is
(a) 2.25 (b) 3.25 (c) 2.125 (d) 1.125
17. Two numbers are in the ratio 3 : 5. If 12 is
added to both the numbers, then the ratio
becomes 5 : 7. the sum of the given two
numbers is
(a) 48 (b) 56 (c) 32 (d) 40
18. The marked price of an article is ` 840. A
shopkeeper gives a discount of 15% on the
marked price and still makes a profit of
19%. What is the cost price of the article?
(a)` 600 (b)` 640 (c)` 540 (d)` 580
19. If
5 7
3
2
4 3
4
4
x x
x
-
+ =
-
+ , then the value of
( ) 8 5 x + is
(a) 9 (b) 13 (c) 6 (d) 7
20. LetP xy y x = - - 12 10 18
2 2
,
Q x y xy = + + 14 12 9
2 2
, and
R y x xy = - + 5
2 2
, then ( ) P Q R + - =
(a) 20 7 3
2 2
xy x y - - (b) 20 3 3
2 2
xy x y - -
(c) 22 3 3
2 2
xy x y - + (d) 22 3 3
2 2
xy x y + -
2 2021 January (CLASSVI-VIII)Solved Paper CTET
21. Ifx
x
x
4
4
1
322 0 + = ¹ , , then one of the values
of x
x
-
æ
è
ç
ö
ø
÷
1
is
(a) 6 (b) 8
(c) 2 (d) 4
22. If 15 26 8
2
x x Ax B - + = + ( )( ) Cx D + ,
where A andC are positive integers, then
what is the value of ( ) 2 2 A B C D + - - ?
(a) 2 (b) 3
(c) 0 (d) 1
23. In DABC and DDEF, if AB EF = ,BC DE =
andCA FD = , then
(a)D D ABC EFD @
(b)D D ABC DFE @
(c)D D ABC DEF @
(d)D D ABC FED @
24. Which of the following can be the sides of a
right angled triangle?
(a) 15 cm, 32 cm and 57 cm
(b) 65 cm, 72 cm and 97 cm
(c) 20 cm, 21 cm and 31 cm
(d) 35 cm, 77 cm and 88 cm
25. The number of edges of a polyhedron, which
has 7 faces and 10 vertices, is
(a) 15 (b) 17
(c) 13 (d) 14
26. In DABC, the side AB is produced toE and
sideCA is produced toD. If Ð = ° BAD 125
and Ð = ° EBC 100 , then which of the
following is true?
(a) Difference betweenÐABC andÐACB is 35°
(b) Difference betweenÐBAC andÐACB is 20°
(c)DABC is an isosceles triangle.
(d)AB BC >
27. In trapeziumPQRS PQ SR , | | and the ratio
ofPQ to SR is 3 : 2. If the area of the
trapezium is 480 cm
2
and the distance
betweenPQ and SR is 12 cm, then the
length of SR is
(a) 36 cm (b) 48 cm (c) 24 cm (d) 32 cm
28. A rectangular sheet of paper 88 10 cm cm ´
is folded without overlapping to make a
cylinder of height 10 cm. What is the
capacity (in litres) of the cylinder?
(Take p =
22
7
)
(a) 7.392 (b) 8.624 (c) 5.54 (d) 6.16
29. The volume of a cube is 2197 cm
3
. What is
its lateral surface area (in cm
2
) ?
(a) 845 (b) 1014 (c) 676 (d) 576
30. What is the mean of the range, mode and
median of the data given below?
5, 10, 3, 6, 4, 8, 9, 3, 15, 2, 9, 4, 19, 11, 4
(a) 10 (b) 12 (c) 8 (d) 9
3 2021 January (CLASSVI-VIII)Solved Paper CTET
Answers
1 (d) 2 (a) 3 (b) 4 (b) 5 (a) 6 (a) 7 (c) 8 (c) 9 (b) 10 (b)
11 (a) 12 (d) 13 (a) 14 (a) 15 (b) 16 (b) 17 (a) 18 (a) 19 (c) 20 (b)
21 (d) 22 (d) 23 (c) 24 (b) 25 (a) 26 (a) 27 (d) 28 (d) 29 (c) 30 (d)
Page 4


Directions (Q. Nos. 1-30)Answerthe
followingquestionsbyselectingthe
correct/mostappropriateoptions.
1. Which of the following is most appropriate
strategy for introducing the concept of
multiplication of two decimal numbers in
the middle school?
(a) Multiplication as repeated addition should be
emphasised
(b) Multiplication as inverse of division should be
emphasised
(c) The algorithm should be used to introduce the
concept
(d) The process should be visually represented
2. Which of the following is a narrow aim of
teaching Mathematics?
(a) To make students proficient in handling
numbers and number operations.
(b) To develop students’ generalisation abilities.
(c) To encourage systematic reasoning among
students.
(d) To develop students’ ability to argue the truth
and falsity of statements.
3. Which of the following is most appropriate
strategy for teaching students to solve
mathematical problems?
(a) Teacher should begin by explaining the steps
required for obtaining the solutions of the
problems.
(b) Students should be encouraged to view a
problem from many perspectives.
(c) Guess and verify approach should be strictly
discouraged.
(d) The list of formulae required for solving the
given set of problems should be provided in
the beginning.
4. Identify the incorrect statement from
among the following
(a) Mathematical communication involves precise
use of language.
(b) Conjectures do not have utility in constructing
mathematical knowledge.
(c) Hypothesis have a role in construction of
mathematical knowledge.
(d) The notion of argumentation is central to
Mathematics.
5. Which of the following is a desirable
strategy for assessing students’ learning in
Mathematics ?
(a) Students’ justification of their responses should
be an important basis of assessment.
(b) Development of' mathematical vocabulary
should not be a basis of assessment.
CTET SOLVED PAPERS
Paper - 2 (Mathemati cs)
31 Janua r y, 2021
(c) Same tasks should be given to all students for
parity.
(d) Students’ incorrect answers should be ignored.
6. For a given figure to be a triangle, the
condition that it is a union of three
segments is
(a) both necessary and sufficient condition.
(b) neither necessary nor sufficient condition.
(c) a necessary but not a sufficient condition.
(d) a sufficient but not a necessary condition.
7. Consider the following statements:
A= Ifn is even, then n
2
is even.
B= Ifn
2
is not even,n is not even.
C = Ifn
2
is even, then n is even.
D= Ifn is not even, then n
2
is not even.
Which of the following statements is true?
(a) B is inverse of A.
(b) D is contraposition of A.
(c) C is converse of A.
(d) D is converse of A.
8. Which of the following teaching- learning
resources in mathematics cannot be used
for visually challenged students?
(a) Tiles
(b) GeoBoard
(c) GeoGebra
(d) Taylor’s abacus
9. Which of the following statements is true?
(a) Intuition has no role in generating
mathematical knowledge.
(b) Mathematical statements can be conditional.
(c) Mathematics consists of all the theorems
proved in Mathematics books.
(d) A person good in arithmetical computation is
also good in Mathematics andvice-versa.
10. Which of the following statements is not
correct regarding differently abled children
of dyslexia in Mathematics learning in an
inclusive classroom?
(a) Dyslexic children may have difficulty in
writing down their ideas in systematic and
organised manner.
(b) Dyslexia impacts only language learning not
Mathematics learning.
(c) Dyslexia has an impact in a person’s
co-ordination of verbal and spatial aspects of
numbers.
(d) Visual patterns in Mathematics help in
overcoming difficulties experienced by
dyslexic children.
11. The number of distinct prime factors of the
largest 6-digits number is
(a) 5 (b) 6
(c) 3 (d) 4
12. If the 8-digits number 179 091 x y is divisible
by 88, then what is the value of ( ) x y - ?
(a) 3 (b) 4
(c) 1 (d) 2
13. Leta =
11
13
,b =
13
14
andc =
15
17
be three
fractions. Which of the following is true?
(a)
11
13
15
17
13
14
< < (b)
11
13
13
14
15
17
< <
(c)
13
14
11
13
15
17
< < (d)
15
17
13
14
11
13
< <
14. If 0.139 0.75 2.105 (1.001) + + -
´ = - 1.1 2 k, then the value of k is
(a) 0.1071 (b) 0.1075
(c) 0.8925 (d) 0.982
15. Ifa = -
3
4
andb =
5
6
, then which of the
following does not lie betweena andb?
(a)-
2
5
(b)-
7
9
(c) 0 (d)-
1
2
16. The product of 1.7 ´ 10
4
and 12.5 ´
-
10
6
is
expressed in the standard form ask
n
´ 10 .
The value of ( ) 2k n + is
(a) 2.25 (b) 3.25 (c) 2.125 (d) 1.125
17. Two numbers are in the ratio 3 : 5. If 12 is
added to both the numbers, then the ratio
becomes 5 : 7. the sum of the given two
numbers is
(a) 48 (b) 56 (c) 32 (d) 40
18. The marked price of an article is ` 840. A
shopkeeper gives a discount of 15% on the
marked price and still makes a profit of
19%. What is the cost price of the article?
(a)` 600 (b)` 640 (c)` 540 (d)` 580
19. If
5 7
3
2
4 3
4
4
x x
x
-
+ =
-
+ , then the value of
( ) 8 5 x + is
(a) 9 (b) 13 (c) 6 (d) 7
20. LetP xy y x = - - 12 10 18
2 2
,
Q x y xy = + + 14 12 9
2 2
, and
R y x xy = - + 5
2 2
, then ( ) P Q R + - =
(a) 20 7 3
2 2
xy x y - - (b) 20 3 3
2 2
xy x y - -
(c) 22 3 3
2 2
xy x y - + (d) 22 3 3
2 2
xy x y + -
2 2021 January (CLASSVI-VIII)Solved Paper CTET
21. Ifx
x
x
4
4
1
322 0 + = ¹ , , then one of the values
of x
x
-
æ
è
ç
ö
ø
÷
1
is
(a) 6 (b) 8
(c) 2 (d) 4
22. If 15 26 8
2
x x Ax B - + = + ( )( ) Cx D + ,
where A andC are positive integers, then
what is the value of ( ) 2 2 A B C D + - - ?
(a) 2 (b) 3
(c) 0 (d) 1
23. In DABC and DDEF, if AB EF = ,BC DE =
andCA FD = , then
(a)D D ABC EFD @
(b)D D ABC DFE @
(c)D D ABC DEF @
(d)D D ABC FED @
24. Which of the following can be the sides of a
right angled triangle?
(a) 15 cm, 32 cm and 57 cm
(b) 65 cm, 72 cm and 97 cm
(c) 20 cm, 21 cm and 31 cm
(d) 35 cm, 77 cm and 88 cm
25. The number of edges of a polyhedron, which
has 7 faces and 10 vertices, is
(a) 15 (b) 17
(c) 13 (d) 14
26. In DABC, the side AB is produced toE and
sideCA is produced toD. If Ð = ° BAD 125
and Ð = ° EBC 100 , then which of the
following is true?
(a) Difference betweenÐABC andÐACB is 35°
(b) Difference betweenÐBAC andÐACB is 20°
(c)DABC is an isosceles triangle.
(d)AB BC >
27. In trapeziumPQRS PQ SR , | | and the ratio
ofPQ to SR is 3 : 2. If the area of the
trapezium is 480 cm
2
and the distance
betweenPQ and SR is 12 cm, then the
length of SR is
(a) 36 cm (b) 48 cm (c) 24 cm (d) 32 cm
28. A rectangular sheet of paper 88 10 cm cm ´
is folded without overlapping to make a
cylinder of height 10 cm. What is the
capacity (in litres) of the cylinder?
(Take p =
22
7
)
(a) 7.392 (b) 8.624 (c) 5.54 (d) 6.16
29. The volume of a cube is 2197 cm
3
. What is
its lateral surface area (in cm
2
) ?
(a) 845 (b) 1014 (c) 676 (d) 576
30. What is the mean of the range, mode and
median of the data given below?
5, 10, 3, 6, 4, 8, 9, 3, 15, 2, 9, 4, 19, 11, 4
(a) 10 (b) 12 (c) 8 (d) 9
3 2021 January (CLASSVI-VIII)Solved Paper CTET
Answers
1 (d) 2 (a) 3 (b) 4 (b) 5 (a) 6 (a) 7 (c) 8 (c) 9 (b) 10 (b)
11 (a) 12 (d) 13 (a) 14 (a) 15 (b) 16 (b) 17 (a) 18 (a) 19 (c) 20 (b)
21 (d) 22 (d) 23 (c) 24 (b) 25 (a) 26 (a) 27 (d) 28 (d) 29 (c) 30 (d)
1. (d) Visual representation of process is the most
appropriate strategy for introducing the concept of
multiplication of two decimal numbers in the middle
school.
2. (a) If we make students proficient in handling
numbers and number operations, then this is the narrow
aim of teaching Mathematics.
3. (b) If students are encouraged to view a problem from
many perspectives, then it will be a most appropriate
strategy for teaching students to solve mathematical
problems.
4. (b) The statement “Conjectures do not have utility in
constructing mathematical knowledge” is correct
statement.
5. (a) If students justifies their responses with a proper
logic, then it will be a desirable strategy for assessing
student’s learning in Mathematics.
6. (a) For a given figure to be a triangle, the condition
that it is a union of three segments is both necessary and
sufficient.
7. (c) StatementC is converse ofA.
8. (c) GeoGebra cannot be used for visually challenged
students.
9. (b) The statement “Mathematical statements can be
conditional” is true.
10. (b) The statement “Dyslexia impacts only language
learning not Mathematics learning” is not correct.
11. (a) The largest number of 6-digits=999999
Now, LCM of 999999=
3 999999
3 333333
3 111111
11 37037
7 3367
13 481
37
Factors (Prime and distinct)
= ´ ´ ´ ´ ´ ´ 3 3 3 11 7 13 37
= ´ ´ ´ ´ 3 7 11 13 37
3
So, there are 5 such factors.
12. (d) If the number179 091 x y is to be divided by 88,
then it must be divided by 8 and 11.
We know that if the difference between the sum of digits
at even and odd position is divisible by 11, then the
number is also divisible by 11.
( ) ( ) 7 9 1 9 0 1 + + + - + + + x y
= + + 5 x y
To make 5 + + x y divisible by 11,x y + must be equal
to 6. Now, we know that, if last three digits of a number
is divisible by 8, then the number is also divisible by 8.
Hence, if y = 2, then 912 is exactly divisible by 8.
\ y = 2 andx = - = 6 2 4
Þ x y - = - = 4 2 2
13. (a)
11
13
0 846 = . ,
13
14
0 928 = .
15
17
0 882 = .
We know that, 0 84 0 88 0 92 . . . < <
Þ
11
13
15
17
13
14
< <
14. (a) 0.139 2 .105 1.1 + + - ´ = - 0 75 1001 2 . ( . ) k
0.139 0.75 2 .105 1.1011 + + - = - 2 k
2 - = k 1.8929
k = - 2 1.8929
k = 0.1071
15. (b)a =
-
= -
3
4
0.75, b= =
5
6
0 83 .
Option (a)= - = -
2
5
0 4 .
Option (b)= - = -
7
9
0 77 .
Option (c)= 0
Option (d)= - = -
1
2
0 5 .
Hence,- 0 77 . does not lie between
-3
4
and
5
6
.
16. (b) 17 10 125 10 21 25 10
4 6 2
. . . ´ ´ ´ = ´
- -
Comparing= ´
-
2.125 10
1
with
= ´ k
n
10 , we get
k= 2.125 ,n= -1
\ 2 2 1 k n + = ´ + - 2.125 ( )= - 4 25 1 . = 3 25 .
17. (a) Let the two numbers be 3x and 5x respectively.
According to question, if 12 is added to both the
numbers.
3 12
5 12
5
7
x
x
+
+
=
sOLVED PAPER 2021 Hints & Solutions
Page 5


Directions (Q. Nos. 1-30)Answerthe
followingquestionsbyselectingthe
correct/mostappropriateoptions.
1. Which of the following is most appropriate
strategy for introducing the concept of
multiplication of two decimal numbers in
the middle school?
(a) Multiplication as repeated addition should be
emphasised
(b) Multiplication as inverse of division should be
emphasised
(c) The algorithm should be used to introduce the
concept
(d) The process should be visually represented
2. Which of the following is a narrow aim of
teaching Mathematics?
(a) To make students proficient in handling
numbers and number operations.
(b) To develop students’ generalisation abilities.
(c) To encourage systematic reasoning among
students.
(d) To develop students’ ability to argue the truth
and falsity of statements.
3. Which of the following is most appropriate
strategy for teaching students to solve
mathematical problems?
(a) Teacher should begin by explaining the steps
required for obtaining the solutions of the
problems.
(b) Students should be encouraged to view a
problem from many perspectives.
(c) Guess and verify approach should be strictly
discouraged.
(d) The list of formulae required for solving the
given set of problems should be provided in
the beginning.
4. Identify the incorrect statement from
among the following
(a) Mathematical communication involves precise
use of language.
(b) Conjectures do not have utility in constructing
mathematical knowledge.
(c) Hypothesis have a role in construction of
mathematical knowledge.
(d) The notion of argumentation is central to
Mathematics.
5. Which of the following is a desirable
strategy for assessing students’ learning in
Mathematics ?
(a) Students’ justification of their responses should
be an important basis of assessment.
(b) Development of' mathematical vocabulary
should not be a basis of assessment.
CTET SOLVED PAPERS
Paper - 2 (Mathemati cs)
31 Janua r y, 2021
(c) Same tasks should be given to all students for
parity.
(d) Students’ incorrect answers should be ignored.
6. For a given figure to be a triangle, the
condition that it is a union of three
segments is
(a) both necessary and sufficient condition.
(b) neither necessary nor sufficient condition.
(c) a necessary but not a sufficient condition.
(d) a sufficient but not a necessary condition.
7. Consider the following statements:
A= Ifn is even, then n
2
is even.
B= Ifn
2
is not even,n is not even.
C = Ifn
2
is even, then n is even.
D= Ifn is not even, then n
2
is not even.
Which of the following statements is true?
(a) B is inverse of A.
(b) D is contraposition of A.
(c) C is converse of A.
(d) D is converse of A.
8. Which of the following teaching- learning
resources in mathematics cannot be used
for visually challenged students?
(a) Tiles
(b) GeoBoard
(c) GeoGebra
(d) Taylor’s abacus
9. Which of the following statements is true?
(a) Intuition has no role in generating
mathematical knowledge.
(b) Mathematical statements can be conditional.
(c) Mathematics consists of all the theorems
proved in Mathematics books.
(d) A person good in arithmetical computation is
also good in Mathematics andvice-versa.
10. Which of the following statements is not
correct regarding differently abled children
of dyslexia in Mathematics learning in an
inclusive classroom?
(a) Dyslexic children may have difficulty in
writing down their ideas in systematic and
organised manner.
(b) Dyslexia impacts only language learning not
Mathematics learning.
(c) Dyslexia has an impact in a person’s
co-ordination of verbal and spatial aspects of
numbers.
(d) Visual patterns in Mathematics help in
overcoming difficulties experienced by
dyslexic children.
11. The number of distinct prime factors of the
largest 6-digits number is
(a) 5 (b) 6
(c) 3 (d) 4
12. If the 8-digits number 179 091 x y is divisible
by 88, then what is the value of ( ) x y - ?
(a) 3 (b) 4
(c) 1 (d) 2
13. Leta =
11
13
,b =
13
14
andc =
15
17
be three
fractions. Which of the following is true?
(a)
11
13
15
17
13
14
< < (b)
11
13
13
14
15
17
< <
(c)
13
14
11
13
15
17
< < (d)
15
17
13
14
11
13
< <
14. If 0.139 0.75 2.105 (1.001) + + -
´ = - 1.1 2 k, then the value of k is
(a) 0.1071 (b) 0.1075
(c) 0.8925 (d) 0.982
15. Ifa = -
3
4
andb =
5
6
, then which of the
following does not lie betweena andb?
(a)-
2
5
(b)-
7
9
(c) 0 (d)-
1
2
16. The product of 1.7 ´ 10
4
and 12.5 ´
-
10
6
is
expressed in the standard form ask
n
´ 10 .
The value of ( ) 2k n + is
(a) 2.25 (b) 3.25 (c) 2.125 (d) 1.125
17. Two numbers are in the ratio 3 : 5. If 12 is
added to both the numbers, then the ratio
becomes 5 : 7. the sum of the given two
numbers is
(a) 48 (b) 56 (c) 32 (d) 40
18. The marked price of an article is ` 840. A
shopkeeper gives a discount of 15% on the
marked price and still makes a profit of
19%. What is the cost price of the article?
(a)` 600 (b)` 640 (c)` 540 (d)` 580
19. If
5 7
3
2
4 3
4
4
x x
x
-
+ =
-
+ , then the value of
( ) 8 5 x + is
(a) 9 (b) 13 (c) 6 (d) 7
20. LetP xy y x = - - 12 10 18
2 2
,
Q x y xy = + + 14 12 9
2 2
, and
R y x xy = - + 5
2 2
, then ( ) P Q R + - =
(a) 20 7 3
2 2
xy x y - - (b) 20 3 3
2 2
xy x y - -
(c) 22 3 3
2 2
xy x y - + (d) 22 3 3
2 2
xy x y + -
2 2021 January (CLASSVI-VIII)Solved Paper CTET
21. Ifx
x
x
4
4
1
322 0 + = ¹ , , then one of the values
of x
x
-
æ
è
ç
ö
ø
÷
1
is
(a) 6 (b) 8
(c) 2 (d) 4
22. If 15 26 8
2
x x Ax B - + = + ( )( ) Cx D + ,
where A andC are positive integers, then
what is the value of ( ) 2 2 A B C D + - - ?
(a) 2 (b) 3
(c) 0 (d) 1
23. In DABC and DDEF, if AB EF = ,BC DE =
andCA FD = , then
(a)D D ABC EFD @
(b)D D ABC DFE @
(c)D D ABC DEF @
(d)D D ABC FED @
24. Which of the following can be the sides of a
right angled triangle?
(a) 15 cm, 32 cm and 57 cm
(b) 65 cm, 72 cm and 97 cm
(c) 20 cm, 21 cm and 31 cm
(d) 35 cm, 77 cm and 88 cm
25. The number of edges of a polyhedron, which
has 7 faces and 10 vertices, is
(a) 15 (b) 17
(c) 13 (d) 14
26. In DABC, the side AB is produced toE and
sideCA is produced toD. If Ð = ° BAD 125
and Ð = ° EBC 100 , then which of the
following is true?
(a) Difference betweenÐABC andÐACB is 35°
(b) Difference betweenÐBAC andÐACB is 20°
(c)DABC is an isosceles triangle.
(d)AB BC >
27. In trapeziumPQRS PQ SR , | | and the ratio
ofPQ to SR is 3 : 2. If the area of the
trapezium is 480 cm
2
and the distance
betweenPQ and SR is 12 cm, then the
length of SR is
(a) 36 cm (b) 48 cm (c) 24 cm (d) 32 cm
28. A rectangular sheet of paper 88 10 cm cm ´
is folded without overlapping to make a
cylinder of height 10 cm. What is the
capacity (in litres) of the cylinder?
(Take p =
22
7
)
(a) 7.392 (b) 8.624 (c) 5.54 (d) 6.16
29. The volume of a cube is 2197 cm
3
. What is
its lateral surface area (in cm
2
) ?
(a) 845 (b) 1014 (c) 676 (d) 576
30. What is the mean of the range, mode and
median of the data given below?
5, 10, 3, 6, 4, 8, 9, 3, 15, 2, 9, 4, 19, 11, 4
(a) 10 (b) 12 (c) 8 (d) 9
3 2021 January (CLASSVI-VIII)Solved Paper CTET
Answers
1 (d) 2 (a) 3 (b) 4 (b) 5 (a) 6 (a) 7 (c) 8 (c) 9 (b) 10 (b)
11 (a) 12 (d) 13 (a) 14 (a) 15 (b) 16 (b) 17 (a) 18 (a) 19 (c) 20 (b)
21 (d) 22 (d) 23 (c) 24 (b) 25 (a) 26 (a) 27 (d) 28 (d) 29 (c) 30 (d)
1. (d) Visual representation of process is the most
appropriate strategy for introducing the concept of
multiplication of two decimal numbers in the middle
school.
2. (a) If we make students proficient in handling
numbers and number operations, then this is the narrow
aim of teaching Mathematics.
3. (b) If students are encouraged to view a problem from
many perspectives, then it will be a most appropriate
strategy for teaching students to solve mathematical
problems.
4. (b) The statement “Conjectures do not have utility in
constructing mathematical knowledge” is correct
statement.
5. (a) If students justifies their responses with a proper
logic, then it will be a desirable strategy for assessing
student’s learning in Mathematics.
6. (a) For a given figure to be a triangle, the condition
that it is a union of three segments is both necessary and
sufficient.
7. (c) StatementC is converse ofA.
8. (c) GeoGebra cannot be used for visually challenged
students.
9. (b) The statement “Mathematical statements can be
conditional” is true.
10. (b) The statement “Dyslexia impacts only language
learning not Mathematics learning” is not correct.
11. (a) The largest number of 6-digits=999999
Now, LCM of 999999=
3 999999
3 333333
3 111111
11 37037
7 3367
13 481
37
Factors (Prime and distinct)
= ´ ´ ´ ´ ´ ´ 3 3 3 11 7 13 37
= ´ ´ ´ ´ 3 7 11 13 37
3
So, there are 5 such factors.
12. (d) If the number179 091 x y is to be divided by 88,
then it must be divided by 8 and 11.
We know that if the difference between the sum of digits
at even and odd position is divisible by 11, then the
number is also divisible by 11.
( ) ( ) 7 9 1 9 0 1 + + + - + + + x y
= + + 5 x y
To make 5 + + x y divisible by 11,x y + must be equal
to 6. Now, we know that, if last three digits of a number
is divisible by 8, then the number is also divisible by 8.
Hence, if y = 2, then 912 is exactly divisible by 8.
\ y = 2 andx = - = 6 2 4
Þ x y - = - = 4 2 2
13. (a)
11
13
0 846 = . ,
13
14
0 928 = .
15
17
0 882 = .
We know that, 0 84 0 88 0 92 . . . < <
Þ
11
13
15
17
13
14
< <
14. (a) 0.139 2 .105 1.1 + + - ´ = - 0 75 1001 2 . ( . ) k
0.139 0.75 2 .105 1.1011 + + - = - 2 k
2 - = k 1.8929
k = - 2 1.8929
k = 0.1071
15. (b)a =
-
= -
3
4
0.75, b= =
5
6
0 83 .
Option (a)= - = -
2
5
0 4 .
Option (b)= - = -
7
9
0 77 .
Option (c)= 0
Option (d)= - = -
1
2
0 5 .
Hence,- 0 77 . does not lie between
-3
4
and
5
6
.
16. (b) 17 10 125 10 21 25 10
4 6 2
. . . ´ ´ ´ = ´
- -
Comparing= ´
-
2.125 10
1
with
= ´ k
n
10 , we get
k= 2.125 ,n= -1
\ 2 2 1 k n + = ´ + - 2.125 ( )= - 4 25 1 . = 3 25 .
17. (a) Let the two numbers be 3x and 5x respectively.
According to question, if 12 is added to both the
numbers.
3 12
5 12
5
7
x
x
+
+
=
sOLVED PAPER 2021 Hints & Solutions
7 3 12 5 5 12 ( ) ( ) x x + = +
21 84 25 60 x x + = +
4 24 x =
x = 6
\ The sum of given numbers= + 3 5 x x
= ´ 8 6= 48
18. (a) Marked Price (MP)=` 840
Discount=15%
Selling price (SP)= - ´ 840
15
100
840
= - 840 126=` 714
Now, profit= 19%
Cost Price (CP)=
+
æ
è
ç
ö
ø
÷
´
100
100 19
714
= ´
100
119
714= ` 600
19. (c)
5 7
3
2
4 3
4
4
x x
x
-
+ =
-
+
4 3
4
5 7
3
2 4
x x
x
-
-
-
= -
3 4 3 4 5 7
12
2 4
( ) ( ) x x
x
- - -
= -
12 9 20 28 24 48 x x x - - + = -
- = - + - 8 24 28 9 48 x x
40 5 x =
x =
1
8
Value of 8 5 x + = ´ + 8
1
8
5
= + 1 5= 6
20. (b)P xy y x = - - 12 10 18
2 2
Q x y xy = + + 14 12 9
2 2
R y x xy = - + 5
2 2
\ ( ) P Q R + -
= - - + + 12 10 18 14 12
2 2 2 2
xy y x x y
+ - - + 9 5
2 2
xy y x xy ( )
= - - + + 12 10 18 14 12
2 2 2 2
xy y x x y
+ - + - 9 5
2 2
xy y x xy
= - - 20 3 3
2 2
xy x y
21. (d)x
x
4
4
1
322 + =
(We know that,a b a b ab
2 2 2
2 + = + - ( ) )
x
x
2
2
1
2 322 2 + + = +
x
x
2
2
2
1
324 +
æ
è
ç
ö
ø
÷
=
x
x
2
2
1
18 + =
x
x
2
2
1
2 18 2 - - = -
x
x
-
æ
è
ç
ö
ø
÷ =
1
16
2
\ x
x
- =
1
4
22. (d) 15 26 8
2
x x Cx B x D - + = + + ( ) ( )
= - - + = + + 15 20 6 8
2
x x x Ax B C D ( ) ( )
= - - - = + + 5 3 4 2 3 4 x x x Ax B Cx D ( ) ( ) ( ) ( )
( ) ( ) ( ) ( ) 3 4 5 2 x x Ax B Cx D - - = + +
On comparing both sides,
A B C D = = - = = - 3 4 5 2 , , ,
Now, 2 2 A B C D + - -
= + - - - ´ - 2 3 4 5 2 2 ( ) ( ) ( )
= - - + 6 4 5 4
= - 10 9 = 1
23. (c) InDABC andDDEF, if
AB EF = ,BC DE = andCA FD =
then D D ABC DEF @
24. (b) From option (b),
65 4225
2
=
72 5184
2
=
97 9409
2
=
65 72 4225 5184
2 2
+ = +
= 9409= 97
2
Since, all the three sides of triangle satisfies Pythagoras
theorem, (Hypotenuse
2
= Base
2
+ Perpendicular
2
)
Therefore, this triangle is a right angle triangle.
25. (a) Faces ( ) F = 7
Vertices ( ) V = 10
Let the number of edges beE,
Then, according to Euler’s formula,
F V E + = + 2
7 10 2 + = + E
5 2021 January (CLASSVI-VIII)Solved Paper CTET
A
B C
D
E F