CTET Solved Question Paper - 2 (07 Jul - 2019) | Mathematics & Pedagogy Paper 2 for CTET & TET Exams - CTET & State TET PDF Download

 Page 1


Directions (Q. Nos. 1-30)Answerthefollowingquestionsbyselectingthecorrect/most
appropriateoptions.
1. Which of the following statements reflects
a desirable assessment practice in the
context of Mathematics learning?
(1) Incorrect answers of children should largely
be ignored because we need to focus on
children’s strengths
(2) Only paper-pencil tasks are suited to
assess students because they require precise
answers
(3) Holding conversations and one to one
discussion with children can also be helpful in
assessing them
(4) Assessment should be product oriented and
focus on the right answer of the child
2. Which of the following statements is true
of learning Mathematics?
(1) Informal algorithms are inferior to formal
Mathematics
(2) Everyone can learn and succeed in
Mathematics
(3) Girls need extra attention because they are
weaker in Mathematics
(4) Mathematics is a specialised subject meant for
a select few
3. The role of proportional reasoning in
understanding the concept related to ratio and
proportion was highlighted by
(1) Lev Vygotsky (2) Van Hiele
(3) Zoltan Dienes (4) Jean Piaget
4. A student is not able to solve those word
problems which involve transposition in
algebra. The best remedial strategy is to
(1) explain concept of equality using alternate method
(2) give lot of practise questions on transposition of
numbers
(3) give lot of practise questions of word problems in
another language
(4) explain him/her word problem in simple language
5. Contemporary understanding of Mathematics
Pedagogy encourages teachers to do all of the
following, except
(1) Develop the skill of systematic reasoning in
students
(2) Encourage the ability to approximate solutions
(3) Introduce computation of problems before
development of conceptual understanding
(4) Create opportunities for students to guess and
verify the solutions to problems
CTET SOLVED PAPERS
Paper - 2 (Mathemati cs)
0 7 Jul, 201 9
Page 2


Directions (Q. Nos. 1-30)Answerthefollowingquestionsbyselectingthecorrect/most
appropriateoptions.
1. Which of the following statements reflects
a desirable assessment practice in the
context of Mathematics learning?
(1) Incorrect answers of children should largely
be ignored because we need to focus on
children’s strengths
(2) Only paper-pencil tasks are suited to
assess students because they require precise
answers
(3) Holding conversations and one to one
discussion with children can also be helpful in
assessing them
(4) Assessment should be product oriented and
focus on the right answer of the child
2. Which of the following statements is true
of learning Mathematics?
(1) Informal algorithms are inferior to formal
Mathematics
(2) Everyone can learn and succeed in
Mathematics
(3) Girls need extra attention because they are
weaker in Mathematics
(4) Mathematics is a specialised subject meant for
a select few
3. The role of proportional reasoning in
understanding the concept related to ratio and
proportion was highlighted by
(1) Lev Vygotsky (2) Van Hiele
(3) Zoltan Dienes (4) Jean Piaget
4. A student is not able to solve those word
problems which involve transposition in
algebra. The best remedial strategy is to
(1) explain concept of equality using alternate method
(2) give lot of practise questions on transposition of
numbers
(3) give lot of practise questions of word problems in
another language
(4) explain him/her word problem in simple language
5. Contemporary understanding of Mathematics
Pedagogy encourages teachers to do all of the
following, except
(1) Develop the skill of systematic reasoning in
students
(2) Encourage the ability to approximate solutions
(3) Introduce computation of problems before
development of conceptual understanding
(4) Create opportunities for students to guess and
verify the solutions to problems
CTET SOLVED PAPERS
Paper - 2 (Mathemati cs)
0 7 Jul, 201 9
6. The value of
[( ) ] ( ) ( )[( ) ( ) ] - ÷ × - - - - × - - 4 2 3 3 3 7 8
+ - ÷ ( ) [( ) ] 4 48 6 is
(1) - 16 (2) 9
(3) - 11 (4) 13
7.
The fractions
44
49
33
38
22
25
, , and
24
29
are
written in descending order as
(1)
44
49
33
38
24
29
22
25
, , , (2)
24
29
33
38
22
25
44
49
, , ,
(3)
22
25
24
29
33
38
44
49
, , , (4)
44
49
22
25
33
38
24
29
, , ,
8. Which one of the following statements is
not true for integers?
(1) Subtraction is not commutative
(2) Multiplication is associative
(3) Division is commutative
(4) 1 is the multiplicative identity
9. Ifx = × × × 2 3 5 7
3 2 3 3
, y = × × × 2 3 5 7
2 3 4 3
, andz = × × × 2 3 5 7
4 4 2 5
, then HCF ofx y ,
and z is
(1) 30 7
5
× (2) ( ) 30 7
2 3
×
(3) ( ) 15 7
3 4
× (4) ( ) 30 7
3 3
×
10. If 52272
2 3 4
= × × p q r , where p q , andr are
prime numbers, then the value of
( ) 2p q r + - is
(1) 29 (2) 21 (3) 22 (4) 23
11. If the 7-digit number 134 58 x y is divisible
by 72, then the value of ( ) 2x y + is
(1) 9 (2) 6 (3) 7 (4) 8
12. Which of the following is not a Pythagorean
triplet?
(1) 13, 84, 85 (2) 7, 24, 25
(3) 8, 15, 17 (4) 11, 60, 63
13. The measure of an angle for which the
measure of the supplement is four times
the measure of the complement is
(1) 75° (2) 30° (3) 45° (4) 60°
14. If the angles, in degrees, of a triangle are
x x , 3 20 + and 6x, the triangle must be
(1) isosceles (2) obtuse
(3) acute (4) right
15. In triangles ABC andDEF, ? = ? C F,
AC DF = , andBC EF = . If AB x = - 2 1 and
DE x = - 5 4, then the value ofx is
(1) 4 (2) 1 (3) 2 (4) 3
16. One side of a triangle is 5 cm and the other
side is 10 cm and its perimeter isP cm, where
P is an integer. The least and the greatest
possible values ofP are, respectively.
(1) 22 and 27 (2) 19 and 29
(3) 20 and 28 (4) 21 and 29
17. Letx be the median of the data 13, 8, 15, 14,
17, 9, 14, 16, 13, 17, 14, 15, 16, 15, 14.
If 8 is replaced by 18, then the median of the
data is y. What is the sum of the values ofx
and y?
(1) 30 (2) 27 (3) 28 (4) 29
18. A bag contains 3 white, 2 blue and 5 red balls.
One ball is drawn at random from the bag.
What is the probability that the ball drawn is
not red?
(1)
1
2
(2)
4
5
(3)
3
10
(4)
1
5
19. The total surface area of a cuboid is 194 m
2
.
If its length is 8 m and breadth is 6 m, then
what is its volume (in m
2
)?
(1) 224 (2) 112 (3) 126 (4) 168
20. The area of a trapezium is 105 cm
2
and its
height is 7 cm. If one of the parallel sides is
longer than the other by 6 cm, then the length
of the longer side, (in cm) is
(1) 12 (2) 18 (3) 16 (4) 15
21. The curved surface area of a right circular
cylinder of base radius 3 cm is 94.2 cm
2
. The
volume (in cm
3
) of the cylinder is (take
p = 3 14 . )
(1) 113.04 (2) 138.6 (3) 141.3 (4) 125.6
22. Ifx is added to each of 14, 12, 34 and 30, the
numbers so obtained, in this order, are in
proportion. What is the value of 12 9 x + ?
(1) 13 (2) 8 (3) 9 (4) 11
23. Which one of the following statements is
true?
(1) An angle has two lines of symmetry
(2) A regular hexagon has only 4 lines of symmetry
(3) A regular polygon of 10 sides has 10 lines of
symmetry
(4) A circle has no line of symmetry
24. The value ofx which satisfies the equation
10 6 8 3 5 5 4 ( ) ( ) ( ) x x x + + - = -
also satisfies the equation
(1) 5 5 2 3 5 ( ) ( ) x x - = - +
2
CTET 2019 July (CLASSVI-VIII)Solved Paper
Page 3


Directions (Q. Nos. 1-30)Answerthefollowingquestionsbyselectingthecorrect/most
appropriateoptions.
1. Which of the following statements reflects
a desirable assessment practice in the
context of Mathematics learning?
(1) Incorrect answers of children should largely
be ignored because we need to focus on
children’s strengths
(2) Only paper-pencil tasks are suited to
assess students because they require precise
answers
(3) Holding conversations and one to one
discussion with children can also be helpful in
assessing them
(4) Assessment should be product oriented and
focus on the right answer of the child
2. Which of the following statements is true
of learning Mathematics?
(1) Informal algorithms are inferior to formal
Mathematics
(2) Everyone can learn and succeed in
Mathematics
(3) Girls need extra attention because they are
weaker in Mathematics
(4) Mathematics is a specialised subject meant for
a select few
3. The role of proportional reasoning in
understanding the concept related to ratio and
proportion was highlighted by
(1) Lev Vygotsky (2) Van Hiele
(3) Zoltan Dienes (4) Jean Piaget
4. A student is not able to solve those word
problems which involve transposition in
algebra. The best remedial strategy is to
(1) explain concept of equality using alternate method
(2) give lot of practise questions on transposition of
numbers
(3) give lot of practise questions of word problems in
another language
(4) explain him/her word problem in simple language
5. Contemporary understanding of Mathematics
Pedagogy encourages teachers to do all of the
following, except
(1) Develop the skill of systematic reasoning in
students
(2) Encourage the ability to approximate solutions
(3) Introduce computation of problems before
development of conceptual understanding
(4) Create opportunities for students to guess and
verify the solutions to problems
CTET SOLVED PAPERS
Paper - 2 (Mathemati cs)
0 7 Jul, 201 9
6. The value of
[( ) ] ( ) ( )[( ) ( ) ] - ÷ × - - - - × - - 4 2 3 3 3 7 8
+ - ÷ ( ) [( ) ] 4 48 6 is
(1) - 16 (2) 9
(3) - 11 (4) 13
7.
The fractions
44
49
33
38
22
25
, , and
24
29
are
written in descending order as
(1)
44
49
33
38
24
29
22
25
, , , (2)
24
29
33
38
22
25
44
49
, , ,
(3)
22
25
24
29
33
38
44
49
, , , (4)
44
49
22
25
33
38
24
29
, , ,
8. Which one of the following statements is
not true for integers?
(1) Subtraction is not commutative
(2) Multiplication is associative
(3) Division is commutative
(4) 1 is the multiplicative identity
9. Ifx = × × × 2 3 5 7
3 2 3 3
, y = × × × 2 3 5 7
2 3 4 3
, andz = × × × 2 3 5 7
4 4 2 5
, then HCF ofx y ,
and z is
(1) 30 7
5
× (2) ( ) 30 7
2 3
×
(3) ( ) 15 7
3 4
× (4) ( ) 30 7
3 3
×
10. If 52272
2 3 4
= × × p q r , where p q , andr are
prime numbers, then the value of
( ) 2p q r + - is
(1) 29 (2) 21 (3) 22 (4) 23
11. If the 7-digit number 134 58 x y is divisible
by 72, then the value of ( ) 2x y + is
(1) 9 (2) 6 (3) 7 (4) 8
12. Which of the following is not a Pythagorean
triplet?
(1) 13, 84, 85 (2) 7, 24, 25
(3) 8, 15, 17 (4) 11, 60, 63
13. The measure of an angle for which the
measure of the supplement is four times
the measure of the complement is
(1) 75° (2) 30° (3) 45° (4) 60°
14. If the angles, in degrees, of a triangle are
x x , 3 20 + and 6x, the triangle must be
(1) isosceles (2) obtuse
(3) acute (4) right
15. In triangles ABC andDEF, ? = ? C F,
AC DF = , andBC EF = . If AB x = - 2 1 and
DE x = - 5 4, then the value ofx is
(1) 4 (2) 1 (3) 2 (4) 3
16. One side of a triangle is 5 cm and the other
side is 10 cm and its perimeter isP cm, where
P is an integer. The least and the greatest
possible values ofP are, respectively.
(1) 22 and 27 (2) 19 and 29
(3) 20 and 28 (4) 21 and 29
17. Letx be the median of the data 13, 8, 15, 14,
17, 9, 14, 16, 13, 17, 14, 15, 16, 15, 14.
If 8 is replaced by 18, then the median of the
data is y. What is the sum of the values ofx
and y?
(1) 30 (2) 27 (3) 28 (4) 29
18. A bag contains 3 white, 2 blue and 5 red balls.
One ball is drawn at random from the bag.
What is the probability that the ball drawn is
not red?
(1)
1
2
(2)
4
5
(3)
3
10
(4)
1
5
19. The total surface area of a cuboid is 194 m
2
.
If its length is 8 m and breadth is 6 m, then
what is its volume (in m
2
)?
(1) 224 (2) 112 (3) 126 (4) 168
20. The area of a trapezium is 105 cm
2
and its
height is 7 cm. If one of the parallel sides is
longer than the other by 6 cm, then the length
of the longer side, (in cm) is
(1) 12 (2) 18 (3) 16 (4) 15
21. The curved surface area of a right circular
cylinder of base radius 3 cm is 94.2 cm
2
. The
volume (in cm
3
) of the cylinder is (take
p = 3 14 . )
(1) 113.04 (2) 138.6 (3) 141.3 (4) 125.6
22. Ifx is added to each of 14, 12, 34 and 30, the
numbers so obtained, in this order, are in
proportion. What is the value of 12 9 x + ?
(1) 13 (2) 8 (3) 9 (4) 11
23. Which one of the following statements is
true?
(1) An angle has two lines of symmetry
(2) A regular hexagon has only 4 lines of symmetry
(3) A regular polygon of 10 sides has 10 lines of
symmetry
(4) A circle has no line of symmetry
24. The value ofx which satisfies the equation
10 6 8 3 5 5 4 ( ) ( ) ( ) x x x + + - = -
also satisfies the equation
(1) 5 5 2 3 5 ( ) ( ) x x - = - +
2
CTET 2019 July (CLASSVI-VIII)Solved Paper
(2) 5 3 5 ( ) x x - = +
(3) 3 3 5 2 1 ( ) x x - = +
(4) 2 3 5 5 4 ( ) ( ) x x + = - +
25. What should be subtracted from
5 13 8 y x a - - to obtain 11 16 7 x y a - + ?
(1) 24 21 x y a - +
(2) 6 21 15 x y a + +
(3) 21 5 y x a - -
(4) 21 24 15 y x a - -
26. Which of the following statement(s) is
correct regarding children coming to school
from rural areas in the context of
Mathematics?
(1) They have poor communication skills in
Mathematics
(2) They need not learn formal Mathematics as it is
of no use to them
(3) They may have rich oral Mathematical
traditions and knowledge
(4) They do not know any Mathematics
27. Read the following statements
A. Axioms are propositions which are
assumed.
B. Axioms are special theorems.
C. Axioms are definitions.
D. Axioms, when proved becomes
theorems.
Which of the following statement(s) is
correct?
(1) Only A (2) A and C
(3) A and D (4) Only B
28. Which of the following statements does not
reflect contemporary view of students errors
in Mathematics?
(1) They can guide the teacher in planning her
classes
(2) They should be overlooked
(3) They are a part of learning
(4) They are a rich source of information
29. Which of the following statement(s)
regarding Mathematics is true?
A. Mathematics is a tool.
B. Mathematics is a form of art.
C. Mathematics is a language.
(1) A, B and C (2) A and B
(3) B and C (4) Only A
30. To prove that 2 is an irrational number, a
teacher begins by assuming that it is a
rational number and then proceeds to show
how this assumption is not feasible. This is
an example of proof by
(1) Verification (2) Induction
(3) Deduction (4) Contradiction
3
CTET 2019 July (CLASSVI-VIII)Solved Paper
Answers
1 (3) 2 (2) 3 (4) 4 (1) 5 (3) 6 (4) 7 (4) 8 (3) 9 (2) 10 (4)
11 (4) 12 (4) 13 (4) 14 (2) 15 (2) 16 (4) 17 (4) 18 (1) 19 (4) 20 (2)
21 (3) 22 (3) 23 (3) 24 (1) 25 (4) 26 (1) 27 (4) 28 (4) 29 (1) 30 (4)
1. (3) In the context of Mathematics,
given statement reflects a desirable
assessment practice learning, holding
conversations and one to one
discussion with children can also be
helpful in assessing them.
2. (2) Learning Mathematics everyone
can learn and succeed in Mathematics.
3. (4) The role of proportional
reasoning in understanding the
concept related to ratio and
proportion was highlighted by Jean
Piaget.
4. (1) A student is not able to solve
those word problems which involve
transposition in algebra. The best
remedial strategy is to explain
concept of equality using alternate
method.
5. (3) Contemporary understanding
of Mathematics Pedagogy encourages
teachers to do all of the following,
—
develop the skill of systematic
reasoning in students.
—
encourage the ability of
approximate solutions and
—
create opportunities for students
to guess and verify the solutions
to problems.
except introduce computation of
problems before development of
conceptual understanding.
sOLVEDPAPER2019 Hints & Solutions
Page 4


Directions (Q. Nos. 1-30)Answerthefollowingquestionsbyselectingthecorrect/most
appropriateoptions.
1. Which of the following statements reflects
a desirable assessment practice in the
context of Mathematics learning?
(1) Incorrect answers of children should largely
be ignored because we need to focus on
children’s strengths
(2) Only paper-pencil tasks are suited to
assess students because they require precise
answers
(3) Holding conversations and one to one
discussion with children can also be helpful in
assessing them
(4) Assessment should be product oriented and
focus on the right answer of the child
2. Which of the following statements is true
of learning Mathematics?
(1) Informal algorithms are inferior to formal
Mathematics
(2) Everyone can learn and succeed in
Mathematics
(3) Girls need extra attention because they are
weaker in Mathematics
(4) Mathematics is a specialised subject meant for
a select few
3. The role of proportional reasoning in
understanding the concept related to ratio and
proportion was highlighted by
(1) Lev Vygotsky (2) Van Hiele
(3) Zoltan Dienes (4) Jean Piaget
4. A student is not able to solve those word
problems which involve transposition in
algebra. The best remedial strategy is to
(1) explain concept of equality using alternate method
(2) give lot of practise questions on transposition of
numbers
(3) give lot of practise questions of word problems in
another language
(4) explain him/her word problem in simple language
5. Contemporary understanding of Mathematics
Pedagogy encourages teachers to do all of the
following, except
(1) Develop the skill of systematic reasoning in
students
(2) Encourage the ability to approximate solutions
(3) Introduce computation of problems before
development of conceptual understanding
(4) Create opportunities for students to guess and
verify the solutions to problems
CTET SOLVED PAPERS
Paper - 2 (Mathemati cs)
0 7 Jul, 201 9
6. The value of
[( ) ] ( ) ( )[( ) ( ) ] - ÷ × - - - - × - - 4 2 3 3 3 7 8
+ - ÷ ( ) [( ) ] 4 48 6 is
(1) - 16 (2) 9
(3) - 11 (4) 13
7.
The fractions
44
49
33
38
22
25
, , and
24
29
are
written in descending order as
(1)
44
49
33
38
24
29
22
25
, , , (2)
24
29
33
38
22
25
44
49
, , ,
(3)
22
25
24
29
33
38
44
49
, , , (4)
44
49
22
25
33
38
24
29
, , ,
8. Which one of the following statements is
not true for integers?
(1) Subtraction is not commutative
(2) Multiplication is associative
(3) Division is commutative
(4) 1 is the multiplicative identity
9. Ifx = × × × 2 3 5 7
3 2 3 3
, y = × × × 2 3 5 7
2 3 4 3
, andz = × × × 2 3 5 7
4 4 2 5
, then HCF ofx y ,
and z is
(1) 30 7
5
× (2) ( ) 30 7
2 3
×
(3) ( ) 15 7
3 4
× (4) ( ) 30 7
3 3
×
10. If 52272
2 3 4
= × × p q r , where p q , andr are
prime numbers, then the value of
( ) 2p q r + - is
(1) 29 (2) 21 (3) 22 (4) 23
11. If the 7-digit number 134 58 x y is divisible
by 72, then the value of ( ) 2x y + is
(1) 9 (2) 6 (3) 7 (4) 8
12. Which of the following is not a Pythagorean
triplet?
(1) 13, 84, 85 (2) 7, 24, 25
(3) 8, 15, 17 (4) 11, 60, 63
13. The measure of an angle for which the
measure of the supplement is four times
the measure of the complement is
(1) 75° (2) 30° (3) 45° (4) 60°
14. If the angles, in degrees, of a triangle are
x x , 3 20 + and 6x, the triangle must be
(1) isosceles (2) obtuse
(3) acute (4) right
15. In triangles ABC andDEF, ? = ? C F,
AC DF = , andBC EF = . If AB x = - 2 1 and
DE x = - 5 4, then the value ofx is
(1) 4 (2) 1 (3) 2 (4) 3
16. One side of a triangle is 5 cm and the other
side is 10 cm and its perimeter isP cm, where
P is an integer. The least and the greatest
possible values ofP are, respectively.
(1) 22 and 27 (2) 19 and 29
(3) 20 and 28 (4) 21 and 29
17. Letx be the median of the data 13, 8, 15, 14,
17, 9, 14, 16, 13, 17, 14, 15, 16, 15, 14.
If 8 is replaced by 18, then the median of the
data is y. What is the sum of the values ofx
and y?
(1) 30 (2) 27 (3) 28 (4) 29
18. A bag contains 3 white, 2 blue and 5 red balls.
One ball is drawn at random from the bag.
What is the probability that the ball drawn is
not red?
(1)
1
2
(2)
4
5
(3)
3
10
(4)
1
5
19. The total surface area of a cuboid is 194 m
2
.
If its length is 8 m and breadth is 6 m, then
what is its volume (in m
2
)?
(1) 224 (2) 112 (3) 126 (4) 168
20. The area of a trapezium is 105 cm
2
and its
height is 7 cm. If one of the parallel sides is
longer than the other by 6 cm, then the length
of the longer side, (in cm) is
(1) 12 (2) 18 (3) 16 (4) 15
21. The curved surface area of a right circular
cylinder of base radius 3 cm is 94.2 cm
2
. The
volume (in cm
3
) of the cylinder is (take
p = 3 14 . )
(1) 113.04 (2) 138.6 (3) 141.3 (4) 125.6
22. Ifx is added to each of 14, 12, 34 and 30, the
numbers so obtained, in this order, are in
proportion. What is the value of 12 9 x + ?
(1) 13 (2) 8 (3) 9 (4) 11
23. Which one of the following statements is
true?
(1) An angle has two lines of symmetry
(2) A regular hexagon has only 4 lines of symmetry
(3) A regular polygon of 10 sides has 10 lines of
symmetry
(4) A circle has no line of symmetry
24. The value ofx which satisfies the equation
10 6 8 3 5 5 4 ( ) ( ) ( ) x x x + + - = -
also satisfies the equation
(1) 5 5 2 3 5 ( ) ( ) x x - = - +
2
CTET 2019 July (CLASSVI-VIII)Solved Paper
(2) 5 3 5 ( ) x x - = +
(3) 3 3 5 2 1 ( ) x x - = +
(4) 2 3 5 5 4 ( ) ( ) x x + = - +
25. What should be subtracted from
5 13 8 y x a - - to obtain 11 16 7 x y a - + ?
(1) 24 21 x y a - +
(2) 6 21 15 x y a + +
(3) 21 5 y x a - -
(4) 21 24 15 y x a - -
26. Which of the following statement(s) is
correct regarding children coming to school
from rural areas in the context of
Mathematics?
(1) They have poor communication skills in
Mathematics
(2) They need not learn formal Mathematics as it is
of no use to them
(3) They may have rich oral Mathematical
traditions and knowledge
(4) They do not know any Mathematics
27. Read the following statements
A. Axioms are propositions which are
assumed.
B. Axioms are special theorems.
C. Axioms are definitions.
D. Axioms, when proved becomes
theorems.
Which of the following statement(s) is
correct?
(1) Only A (2) A and C
(3) A and D (4) Only B
28. Which of the following statements does not
reflect contemporary view of students errors
in Mathematics?
(1) They can guide the teacher in planning her
classes
(2) They should be overlooked
(3) They are a part of learning
(4) They are a rich source of information
29. Which of the following statement(s)
regarding Mathematics is true?
A. Mathematics is a tool.
B. Mathematics is a form of art.
C. Mathematics is a language.
(1) A, B and C (2) A and B
(3) B and C (4) Only A
30. To prove that 2 is an irrational number, a
teacher begins by assuming that it is a
rational number and then proceeds to show
how this assumption is not feasible. This is
an example of proof by
(1) Verification (2) Induction
(3) Deduction (4) Contradiction
3
CTET 2019 July (CLASSVI-VIII)Solved Paper
Answers
1 (3) 2 (2) 3 (4) 4 (1) 5 (3) 6 (4) 7 (4) 8 (3) 9 (2) 10 (4)
11 (4) 12 (4) 13 (4) 14 (2) 15 (2) 16 (4) 17 (4) 18 (1) 19 (4) 20 (2)
21 (3) 22 (3) 23 (3) 24 (1) 25 (4) 26 (1) 27 (4) 28 (4) 29 (1) 30 (4)
1. (3) In the context of Mathematics,
given statement reflects a desirable
assessment practice learning, holding
conversations and one to one
discussion with children can also be
helpful in assessing them.
2. (2) Learning Mathematics everyone
can learn and succeed in Mathematics.
3. (4) The role of proportional
reasoning in understanding the
concept related to ratio and
proportion was highlighted by Jean
Piaget.
4. (1) A student is not able to solve
those word problems which involve
transposition in algebra. The best
remedial strategy is to explain
concept of equality using alternate
method.
5. (3) Contemporary understanding
of Mathematics Pedagogy encourages
teachers to do all of the following,
—
develop the skill of systematic
reasoning in students.
—
encourage the ability of
approximate solutions and
—
create opportunities for students
to guess and verify the solutions
to problems.
except introduce computation of
problems before development of
conceptual understanding.
sOLVEDPAPER2019 Hints & Solutions
6. (4) Given expression,
[( ) ] ( ) ( ) - ÷ × - - - 4 2 3 3
[( ) ( ) ] - × - - 3 7 8 + - ÷ ( ) [( ) ] 4 48 6
= -
?
?
?
?
?
?
× - - -
4
2
3 3 ( ) ( )
[ ] 21 8 4
48
6
- + -
?
?
?
?
?
?
= - × - + × + - [ ] ( ) [ ] 2 3 3 13 4 8
= + - = 6 39 32 13
7. (4) To convert given fractions into
decimal fractions,
44
49
0 89
33
38
0 86 = = . , . ,
22
25
0 88 = . and
24
29
0 83 = .
? 0 89 0 88 0 86 0 83 . . . . > > >
Hence, required descending order is
44
49
22
25
33
38
24
29
, , , .
8. (3) By option (1), For integers,
subtraction is not commutative. (3)
By option (2), Every integer follows
the rule of commutative and
associative for addition and
multiplication. (3)
By option (3), For integers, division is
commutative. (7)
By option (4), Multiplicative identity
of integers is 1. (3)
9. (2) Given,x = × × × 2 3 5 7
3 2 3 3
y = × × × 2 3 5 7
2 3 4 3
and
z = × × × 2 3 5 7
4 4 2 5
Hence, HCF ofx y , and
z = × × × 2 3 5 7
2 2 2 3
[Qto take lowest power of common
factors]
= × × × ( ) 2 3 5 7
2 3
= × ( ) 30 7
2 3
10. (4) Given, 52272 = × × p q r
2 3 4
.
By prime factorisation of 52272,
2 5 2 2 7 2
2 2 6 1 3 6
2 1 3 0 6 8
2 6 5 3 4
3 3 2 6 7
3 1 0 8 9
3 3 6 3
11 1 2 1
11 11
1
2 2 2 2 3 3 3 11 11 × × × × × × × ×
= × × p q r
2 3 4
? 2 3 11
4 3 2 2 3 4
× × = × × p q r
? 11 3 2
2 3 4 2 3 4
× × = × × p q r
On comparing of both sides, we get
p = 11 ,q = 3 andr = 2
? 2 2 11 3 2 22 1 p q r + - = × + - = +
= 23
11. (4) Given, 7-digit number 134 58 x y
is divisible by 72 ( ) = × 8 9 factors of
72 2 = , 3, 6, 8, 9, 18, 24, 36 and 72.
? This 7-digit number divisible by 8
because 8 is a factor of 72. So, last
three digits of a number is divisible by
8, for y = 4
8)584(73
56
24
24
×
QThis 7-digit number also divisible
by 9. So, the sum of all the digits of
given number is divisible by 9.
Hence,
1 3 4 5 8 4 25 + + + + + + = + x x
so, x = 2
= + = 25 2 27, divisible by 9.
Hence,x = 2and y = 4
? 2 2 2 4 4 4 8 x y + = × + = + =
12. (4) From option (1),
( ) ( ) ( ) 85 84 13
2 2 2
= +
? 7225 7056 169 = +
? 7225 7225 =
Hence, 13, 84, 85 is a Pythagorean
triplet.
From option (2), ( ) ( ) ( ) 25 24 7
2 2 2
= +
? 625 576 49 = +
? 625 625 =
Hence, 7, 24, 25 is a Pythagorean
triplet.
From option (3), ( ) ( ) ( ) 17 15 8
2 2 2
= +
? 289 225 64 = +
? 289 289 =
Hence, 8, 15, 17 is a Pythagorean
triplet.
From option (4), ( ) ( ) ( ) 63 60 11
2 2 2
= +
? 3969 3600 121 = +
? 3969 3721 ?
Hence, 11, 60, 63 is not a Pythagorean
triplet.
13. (4) Let the angle be ?. Then,
Supplementary angle of ? ? = ° - 180
and complementary angle of
? ? = ° - 90
According to the question,
Supplementary angle = × 4
Complementary angle
? 180 4 90 ° - = × ° - ? ? ( )
? 180 360 4 ° - = ° - ? ?
? 3 180 ? = °
? ? = ° 60
14. (2) Given, the angles of triangle
= + x x , 3 20 and 6x.
We know that, sum of angles of
triangle = ° 180
? x x x + + + = ° 3 20 6 180
? 10 160 x = °
? x = ° 16
?Angles of triangle
= ° × + × 16 3 16 20 6 16 , ,
= ° ° ° 16 68 96 , ,
There is a angle (96°) is greater than
90.
Hence, the triangle must be obtuse
triangle.
15. (2) In ?ABC and ?DEF,
? = ? = C F AC DF , andBC EF =
? ? ? ABC DEF
~
= [Qby SAS
congruency]
? AB DE =
? 2 1 5 4 x x - = -
[QAB x = - 2 1 ,DE x = - 5 4]
? 5 2 4 1 x x - = - ? 3 3 x = ?x = 1
16. (4) Given, sides of a triangle be 5
cm and 10 cm.
Perimeter of triangle = P cm.
If third side of triangle is greatest
( ) > 10 , then maximum value of third
side = 14
[Qsum of any two sides > third side]
?Maximum value ofP = Sum of all
sides
= + + = 5 10 14 29 cm
If third side of triangle is less than 10.
Minimum value of third side = 6 cm.
? Minimum value of
P = + + = 5 10 6 21cm
4
CTET 2019 July (CLASSVI-VIII)Solved Paper
A
C B
D
F E
Page 5


Directions (Q. Nos. 1-30)Answerthefollowingquestionsbyselectingthecorrect/most
appropriateoptions.
1. Which of the following statements reflects
a desirable assessment practice in the
context of Mathematics learning?
(1) Incorrect answers of children should largely
be ignored because we need to focus on
children’s strengths
(2) Only paper-pencil tasks are suited to
assess students because they require precise
answers
(3) Holding conversations and one to one
discussion with children can also be helpful in
assessing them
(4) Assessment should be product oriented and
focus on the right answer of the child
2. Which of the following statements is true
of learning Mathematics?
(1) Informal algorithms are inferior to formal
Mathematics
(2) Everyone can learn and succeed in
Mathematics
(3) Girls need extra attention because they are
weaker in Mathematics
(4) Mathematics is a specialised subject meant for
a select few
3. The role of proportional reasoning in
understanding the concept related to ratio and
proportion was highlighted by
(1) Lev Vygotsky (2) Van Hiele
(3) Zoltan Dienes (4) Jean Piaget
4. A student is not able to solve those word
problems which involve transposition in
algebra. The best remedial strategy is to
(1) explain concept of equality using alternate method
(2) give lot of practise questions on transposition of
numbers
(3) give lot of practise questions of word problems in
another language
(4) explain him/her word problem in simple language
5. Contemporary understanding of Mathematics
Pedagogy encourages teachers to do all of the
following, except
(1) Develop the skill of systematic reasoning in
students
(2) Encourage the ability to approximate solutions
(3) Introduce computation of problems before
development of conceptual understanding
(4) Create opportunities for students to guess and
verify the solutions to problems
CTET SOLVED PAPERS
Paper - 2 (Mathemati cs)
0 7 Jul, 201 9
6. The value of
[( ) ] ( ) ( )[( ) ( ) ] - ÷ × - - - - × - - 4 2 3 3 3 7 8
+ - ÷ ( ) [( ) ] 4 48 6 is
(1) - 16 (2) 9
(3) - 11 (4) 13
7.
The fractions
44
49
33
38
22
25
, , and
24
29
are
written in descending order as
(1)
44
49
33
38
24
29
22
25
, , , (2)
24
29
33
38
22
25
44
49
, , ,
(3)
22
25
24
29
33
38
44
49
, , , (4)
44
49
22
25
33
38
24
29
, , ,
8. Which one of the following statements is
not true for integers?
(1) Subtraction is not commutative
(2) Multiplication is associative
(3) Division is commutative
(4) 1 is the multiplicative identity
9. Ifx = × × × 2 3 5 7
3 2 3 3
, y = × × × 2 3 5 7
2 3 4 3
, andz = × × × 2 3 5 7
4 4 2 5
, then HCF ofx y ,
and z is
(1) 30 7
5
× (2) ( ) 30 7
2 3
×
(3) ( ) 15 7
3 4
× (4) ( ) 30 7
3 3
×
10. If 52272
2 3 4
= × × p q r , where p q , andr are
prime numbers, then the value of
( ) 2p q r + - is
(1) 29 (2) 21 (3) 22 (4) 23
11. If the 7-digit number 134 58 x y is divisible
by 72, then the value of ( ) 2x y + is
(1) 9 (2) 6 (3) 7 (4) 8
12. Which of the following is not a Pythagorean
triplet?
(1) 13, 84, 85 (2) 7, 24, 25
(3) 8, 15, 17 (4) 11, 60, 63
13. The measure of an angle for which the
measure of the supplement is four times
the measure of the complement is
(1) 75° (2) 30° (3) 45° (4) 60°
14. If the angles, in degrees, of a triangle are
x x , 3 20 + and 6x, the triangle must be
(1) isosceles (2) obtuse
(3) acute (4) right
15. In triangles ABC andDEF, ? = ? C F,
AC DF = , andBC EF = . If AB x = - 2 1 and
DE x = - 5 4, then the value ofx is
(1) 4 (2) 1 (3) 2 (4) 3
16. One side of a triangle is 5 cm and the other
side is 10 cm and its perimeter isP cm, where
P is an integer. The least and the greatest
possible values ofP are, respectively.
(1) 22 and 27 (2) 19 and 29
(3) 20 and 28 (4) 21 and 29
17. Letx be the median of the data 13, 8, 15, 14,
17, 9, 14, 16, 13, 17, 14, 15, 16, 15, 14.
If 8 is replaced by 18, then the median of the
data is y. What is the sum of the values ofx
and y?
(1) 30 (2) 27 (3) 28 (4) 29
18. A bag contains 3 white, 2 blue and 5 red balls.
One ball is drawn at random from the bag.
What is the probability that the ball drawn is
not red?
(1)
1
2
(2)
4
5
(3)
3
10
(4)
1
5
19. The total surface area of a cuboid is 194 m
2
.
If its length is 8 m and breadth is 6 m, then
what is its volume (in m
2
)?
(1) 224 (2) 112 (3) 126 (4) 168
20. The area of a trapezium is 105 cm
2
and its
height is 7 cm. If one of the parallel sides is
longer than the other by 6 cm, then the length
of the longer side, (in cm) is
(1) 12 (2) 18 (3) 16 (4) 15
21. The curved surface area of a right circular
cylinder of base radius 3 cm is 94.2 cm
2
. The
volume (in cm
3
) of the cylinder is (take
p = 3 14 . )
(1) 113.04 (2) 138.6 (3) 141.3 (4) 125.6
22. Ifx is added to each of 14, 12, 34 and 30, the
numbers so obtained, in this order, are in
proportion. What is the value of 12 9 x + ?
(1) 13 (2) 8 (3) 9 (4) 11
23. Which one of the following statements is
true?
(1) An angle has two lines of symmetry
(2) A regular hexagon has only 4 lines of symmetry
(3) A regular polygon of 10 sides has 10 lines of
symmetry
(4) A circle has no line of symmetry
24. The value ofx which satisfies the equation
10 6 8 3 5 5 4 ( ) ( ) ( ) x x x + + - = -
also satisfies the equation
(1) 5 5 2 3 5 ( ) ( ) x x - = - +
2
CTET 2019 July (CLASSVI-VIII)Solved Paper
(2) 5 3 5 ( ) x x - = +
(3) 3 3 5 2 1 ( ) x x - = +
(4) 2 3 5 5 4 ( ) ( ) x x + = - +
25. What should be subtracted from
5 13 8 y x a - - to obtain 11 16 7 x y a - + ?
(1) 24 21 x y a - +
(2) 6 21 15 x y a + +
(3) 21 5 y x a - -
(4) 21 24 15 y x a - -
26. Which of the following statement(s) is
correct regarding children coming to school
from rural areas in the context of
Mathematics?
(1) They have poor communication skills in
Mathematics
(2) They need not learn formal Mathematics as it is
of no use to them
(3) They may have rich oral Mathematical
traditions and knowledge
(4) They do not know any Mathematics
27. Read the following statements
A. Axioms are propositions which are
assumed.
B. Axioms are special theorems.
C. Axioms are definitions.
D. Axioms, when proved becomes
theorems.
Which of the following statement(s) is
correct?
(1) Only A (2) A and C
(3) A and D (4) Only B
28. Which of the following statements does not
reflect contemporary view of students errors
in Mathematics?
(1) They can guide the teacher in planning her
classes
(2) They should be overlooked
(3) They are a part of learning
(4) They are a rich source of information
29. Which of the following statement(s)
regarding Mathematics is true?
A. Mathematics is a tool.
B. Mathematics is a form of art.
C. Mathematics is a language.
(1) A, B and C (2) A and B
(3) B and C (4) Only A
30. To prove that 2 is an irrational number, a
teacher begins by assuming that it is a
rational number and then proceeds to show
how this assumption is not feasible. This is
an example of proof by
(1) Verification (2) Induction
(3) Deduction (4) Contradiction
3
CTET 2019 July (CLASSVI-VIII)Solved Paper
Answers
1 (3) 2 (2) 3 (4) 4 (1) 5 (3) 6 (4) 7 (4) 8 (3) 9 (2) 10 (4)
11 (4) 12 (4) 13 (4) 14 (2) 15 (2) 16 (4) 17 (4) 18 (1) 19 (4) 20 (2)
21 (3) 22 (3) 23 (3) 24 (1) 25 (4) 26 (1) 27 (4) 28 (4) 29 (1) 30 (4)
1. (3) In the context of Mathematics,
given statement reflects a desirable
assessment practice learning, holding
conversations and one to one
discussion with children can also be
helpful in assessing them.
2. (2) Learning Mathematics everyone
can learn and succeed in Mathematics.
3. (4) The role of proportional
reasoning in understanding the
concept related to ratio and
proportion was highlighted by Jean
Piaget.
4. (1) A student is not able to solve
those word problems which involve
transposition in algebra. The best
remedial strategy is to explain
concept of equality using alternate
method.
5. (3) Contemporary understanding
of Mathematics Pedagogy encourages
teachers to do all of the following,
—
develop the skill of systematic
reasoning in students.
—
encourage the ability of
approximate solutions and
—
create opportunities for students
to guess and verify the solutions
to problems.
except introduce computation of
problems before development of
conceptual understanding.
sOLVEDPAPER2019 Hints & Solutions
6. (4) Given expression,
[( ) ] ( ) ( ) - ÷ × - - - 4 2 3 3
[( ) ( ) ] - × - - 3 7 8 + - ÷ ( ) [( ) ] 4 48 6
= -
?
?
?
?
?
?
× - - -
4
2
3 3 ( ) ( )
[ ] 21 8 4
48
6
- + -
?
?
?
?
?
?
= - × - + × + - [ ] ( ) [ ] 2 3 3 13 4 8
= + - = 6 39 32 13
7. (4) To convert given fractions into
decimal fractions,
44
49
0 89
33
38
0 86 = = . , . ,
22
25
0 88 = . and
24
29
0 83 = .
? 0 89 0 88 0 86 0 83 . . . . > > >
Hence, required descending order is
44
49
22
25
33
38
24
29
, , , .
8. (3) By option (1), For integers,
subtraction is not commutative. (3)
By option (2), Every integer follows
the rule of commutative and
associative for addition and
multiplication. (3)
By option (3), For integers, division is
commutative. (7)
By option (4), Multiplicative identity
of integers is 1. (3)
9. (2) Given,x = × × × 2 3 5 7
3 2 3 3
y = × × × 2 3 5 7
2 3 4 3
and
z = × × × 2 3 5 7
4 4 2 5
Hence, HCF ofx y , and
z = × × × 2 3 5 7
2 2 2 3
[Qto take lowest power of common
factors]
= × × × ( ) 2 3 5 7
2 3
= × ( ) 30 7
2 3
10. (4) Given, 52272 = × × p q r
2 3 4
.
By prime factorisation of 52272,
2 5 2 2 7 2
2 2 6 1 3 6
2 1 3 0 6 8
2 6 5 3 4
3 3 2 6 7
3 1 0 8 9
3 3 6 3
11 1 2 1
11 11
1
2 2 2 2 3 3 3 11 11 × × × × × × × ×
= × × p q r
2 3 4
? 2 3 11
4 3 2 2 3 4
× × = × × p q r
? 11 3 2
2 3 4 2 3 4
× × = × × p q r
On comparing of both sides, we get
p = 11 ,q = 3 andr = 2
? 2 2 11 3 2 22 1 p q r + - = × + - = +
= 23
11. (4) Given, 7-digit number 134 58 x y
is divisible by 72 ( ) = × 8 9 factors of
72 2 = , 3, 6, 8, 9, 18, 24, 36 and 72.
? This 7-digit number divisible by 8
because 8 is a factor of 72. So, last
three digits of a number is divisible by
8, for y = 4
8)584(73
56
24
24
×
QThis 7-digit number also divisible
by 9. So, the sum of all the digits of
given number is divisible by 9.
Hence,
1 3 4 5 8 4 25 + + + + + + = + x x
so, x = 2
= + = 25 2 27, divisible by 9.
Hence,x = 2and y = 4
? 2 2 2 4 4 4 8 x y + = × + = + =
12. (4) From option (1),
( ) ( ) ( ) 85 84 13
2 2 2
= +
? 7225 7056 169 = +
? 7225 7225 =
Hence, 13, 84, 85 is a Pythagorean
triplet.
From option (2), ( ) ( ) ( ) 25 24 7
2 2 2
= +
? 625 576 49 = +
? 625 625 =
Hence, 7, 24, 25 is a Pythagorean
triplet.
From option (3), ( ) ( ) ( ) 17 15 8
2 2 2
= +
? 289 225 64 = +
? 289 289 =
Hence, 8, 15, 17 is a Pythagorean
triplet.
From option (4), ( ) ( ) ( ) 63 60 11
2 2 2
= +
? 3969 3600 121 = +
? 3969 3721 ?
Hence, 11, 60, 63 is not a Pythagorean
triplet.
13. (4) Let the angle be ?. Then,
Supplementary angle of ? ? = ° - 180
and complementary angle of
? ? = ° - 90
According to the question,
Supplementary angle = × 4
Complementary angle
? 180 4 90 ° - = × ° - ? ? ( )
? 180 360 4 ° - = ° - ? ?
? 3 180 ? = °
? ? = ° 60
14. (2) Given, the angles of triangle
= + x x , 3 20 and 6x.
We know that, sum of angles of
triangle = ° 180
? x x x + + + = ° 3 20 6 180
? 10 160 x = °
? x = ° 16
?Angles of triangle
= ° × + × 16 3 16 20 6 16 , ,
= ° ° ° 16 68 96 , ,
There is a angle (96°) is greater than
90.
Hence, the triangle must be obtuse
triangle.
15. (2) In ?ABC and ?DEF,
? = ? = C F AC DF , andBC EF =
? ? ? ABC DEF
~
= [Qby SAS
congruency]
? AB DE =
? 2 1 5 4 x x - = -
[QAB x = - 2 1 ,DE x = - 5 4]
? 5 2 4 1 x x - = - ? 3 3 x = ?x = 1
16. (4) Given, sides of a triangle be 5
cm and 10 cm.
Perimeter of triangle = P cm.
If third side of triangle is greatest
( ) > 10 , then maximum value of third
side = 14
[Qsum of any two sides > third side]
?Maximum value ofP = Sum of all
sides
= + + = 5 10 14 29 cm
If third side of triangle is less than 10.
Minimum value of third side = 6 cm.
? Minimum value of
P = + + = 5 10 6 21cm
4
CTET 2019 July (CLASSVI-VIII)Solved Paper
A
C B
D
F E
Hence, possible maximum and
minimum value ofP is 29 and 21,
respectively.
17. (4) By first condition, ascending
order of given data,
8, 9, 13, 13, 14, 14, 14, 14, 15, 15, 15,
16, 16, 17, 17
Here,n = 15
?Median ( ) x
n
=
+ 1
2
th term
=
+ 15 1
2
th term
= 8th term = 14
By second condition, ascending order
of given data,
9, 13, 13, 14, 14, 14, 14, 15, 15, 15, 16,
16, 17, 17, 18
?Median ( ) y
n
=
+ 1
2
th term
=
+ 15 1
2
th term
= 8 th term = 15
? x y + = + = 14 15 29
18. (1) In the bag, number of white
balls = 3
Number of blue balls = 2
Number of red balls = 5
?Total balls in the bag
= + + = 3 2 5 10
?Total number of outcomesn S ( ) = 10
LetE be the event of selecting an red
ball.
Then, number of outcomes favourable
ton E ( ) = 5
?Probability of getting a red ballP E ( )
= = =
n E
n S
( )
( )
5
10
1
2
Hence, required probability of getting
a ball not red
= - = - = 1 1
1
2
1
2
P E ( )
19. (4) Given, length of cuboid ( ) l = 8
m and height of cuboid = h (let)
breadth of cuboid ( ) b = 6 m
QTotal surface area of cuboid
= 194 m
2
2 194 ( ) lb bh hl + + =
? 8 6 6 8 97 × + × + × = h h
? 14 49 h =
? h =
7
2
m
?Volume of cuboid
= × × = × × l b h 8 6
7
2
= 168 m
3
20. (2) Given, area of trapezium
= 105 cm
2
and height = 7 cm
Let the parallel sides of trapezium bex
cm and ( ) x + 6 cm. Then,
Area of trapezium
= ×
1
2
(sum of parallel sides) × height
? 105
1
2
6 7 = × + + × ( ) x x
?
105 2
7
2 6
×
= + x ? 30 6 2 - = x
? x = =
24
2
12cm
Hence, larger side = + = 12 6 18 cm
21. (3) Given, radius of right circular
cylinder
= 3cm
Let the height of cylinder = h cm
Curved surface area of cylinder
= 94 2 . cm
2
? 2p × radius × height = 94 2 .
? 2
22
7
3 94 2 × × × = h .
? h =
×
× ×
=
94 2 7
2 22 3
5
.
cm
?Volume of cylinder = pr h
2
= × × 314 3 5
2
. ( ) = 1413 . cm
3
22. (3) According to the question,
14
12
34
30
+
+
=
+
+
x
x
x
x
?( )( ) ( ) ( ) 14 30 34 12 + + = + + x x x x
? 420 14 30
2
+ + + x x x
= + 408 12x + + 34
2
x x
? 420 44 408 46 + = + x x
? 420 408 46 44 - = - x x
? 2 12 x =
? x = 6
Hence, the value of 12 9 x +
= × + = + 12 6 9 72 9 = = 81 9
23. (3) From option (1), an angle has
two lines of symmetry (?)
QAn angle has only one line of
symmetry.
From option (2), a regular hexagon
has only 4 lines of symmetry (?)
QA regular hexagon has 6 lines of
symmetry.
From option (3), a regular polygon of
10 sides has 10 lines of symmetry (? )
From option (4), a circle has no line of
symmetry (?)
QA circle has infinite line of
symmetry.
24. (1) Given,
10 6 8 3 5 5 4 ( ) ( ) ( ) x x x + + - = -
? 10 60 8 24 25 20 x x x + + - = -
? 18 36 25 20 x x + = -
? 7 56 x =
? x = 8
Put the value ofx in option (1),
5 8 5 2 8 3 5 ( ) ( ) - = - +
?5 3 2 5 5 × = × + ? 15 15 = (true)
25. (4) LetP be subtracted, then
5 13 8 11 16 7 y x a P x y a - - - = - +
? P y y x x a a = + - - - - 5 16 13 11 8 7
? P y x a = - - 21 24 15
26. (1) In the context of Mathematics,
children coming to school from rural
areas have poor communication skills
in Mathematics.
27. (4) Only statement (B) is correct.
Axioms are special theorems.
28. (4) Students errors in Mathematics
are rich sources of information, this
statement does not reflect
contemporary view.
29. (1) Statements (A), (B) and (C) are
true, Mathematics is a tool.
Mathematics is a form of art.
Mathematics is a language.
30. (4) To prove that 2 is an
irrational number, a teacher begins
by assuming that it is a rational
number and then proceeds to show
how this assumption is not feasible.
This is an example of proof by
contradiction.
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CTET 2019 July (CLASSVI-VIII)Solved Paper