CTET Solved Question Paper - 2 (08 Dec - 2019) | Mathematics & Pedagogy Paper 2 for CTET & TET Exams - CTET & State TET PDF Download

 Page 1


Directions (Q. Nos. 1-30) Answer the following questions by selecting the most appropriate
options.
1. Which of the following aligns with the
overall objective of achieving ‘Mathematics
for All’ as per NCF-2005 ?
(1) Mathematically talented students should be
groomed in isolation
(2) It should be acknowledged that Mathematics is
meant for selected few students
(3) Textbooks should only include problems of
average difficulty
(4) Contributions of Mathematicians from
different regions and different social groups
should be highlighted
2. Which of the following is considered as a
characteristic of an effective Mathematics
classroom?
(1) Steps for solving a new problem are neatly
demonstrated on the board by the teacher
(2) Group work and group problem solving is
discouraged
(3) It is emphasized that, Mathematics is
essentially a concrete subject
(4) Multiple ways of approaching a problem are
encouraged
3. Which of the following is a desirable
practice in the context of teaching and
learning of measurement of volume?
(1) Encourage students to figure out ways to
calculate the volume of different objects
(2) Begin by writing the formula of volume of a
cube
(3) Encourage precise calculation right from the
beginning
(4) Begin by introducing students to the volume of
2-D figures
4. Which of the following is not true according
to Piaget’s view of children’s understanding
of space?
(1) Co-ordination of different visual and tactile
experiences is required for understanding
projective space
(2) Progression of geometric ideas follows a
definite order
(3) Progression of geometric ideas follows a
historical rather than a logical order
(4) Early understanding of space is formed by
child’s sensory motor experiences
CTET SOLVED PAPERS
Paper - 2 (Mathemati cs)
08 December, 2019
Page 2


Directions (Q. Nos. 1-30) Answer the following questions by selecting the most appropriate
options.
1. Which of the following aligns with the
overall objective of achieving ‘Mathematics
for All’ as per NCF-2005 ?
(1) Mathematically talented students should be
groomed in isolation
(2) It should be acknowledged that Mathematics is
meant for selected few students
(3) Textbooks should only include problems of
average difficulty
(4) Contributions of Mathematicians from
different regions and different social groups
should be highlighted
2. Which of the following is considered as a
characteristic of an effective Mathematics
classroom?
(1) Steps for solving a new problem are neatly
demonstrated on the board by the teacher
(2) Group work and group problem solving is
discouraged
(3) It is emphasized that, Mathematics is
essentially a concrete subject
(4) Multiple ways of approaching a problem are
encouraged
3. Which of the following is a desirable
practice in the context of teaching and
learning of measurement of volume?
(1) Encourage students to figure out ways to
calculate the volume of different objects
(2) Begin by writing the formula of volume of a
cube
(3) Encourage precise calculation right from the
beginning
(4) Begin by introducing students to the volume of
2-D figures
4. Which of the following is not true according
to Piaget’s view of children’s understanding
of space?
(1) Co-ordination of different visual and tactile
experiences is required for understanding
projective space
(2) Progression of geometric ideas follows a
definite order
(3) Progression of geometric ideas follows a
historical rather than a logical order
(4) Early understanding of space is formed by
child’s sensory motor experiences
CTET SOLVED PAPERS
Paper - 2 (Mathemati cs)
08 December, 2019
5. If - × - + ÷ - - - ÷ 12 3 20 4 24 8 ( ) [ ( ) ( ) ]
- ÷ - [ ( )] 16 2 = - ÷ + ( ) , 28 7 x then the value of
x is
(1) 47 (2) 29 (3) 39 (4) 46
6. If a 8-digit number 30 0867 x y is divisible by
88, then what is the value of ( ) 3x y + ?
(1) 7 (2) 4 (3) 5 (4) 6
7. The value of
6
2
3
2
1
2
3
3
4
5
1
2
4
1
4
1
2
3
7
8
3
4
2
3
÷ × - × + + ×
?
?
?
?
?
? is
(1) -6
1
2
(2) -11
1
12
(3) 11
1
12
(4) 6
1
2
8. How many pairs of twin primes are there
between the integers 1 to 100?
(1) 8 (2) 5
(3) 6 (4) 7
9. If 21168 2 3 7 = × ×
a b c
, where a b , and c are
natural numbers, then what is the value of
( ) 4 5 a b c - + ?
(1) 3 (2) 0
(3) 1 (4) 2
10. Let x be the least number which when
divided by 8, 12, 20, 28, 35 leaves a
remainder 5 in each case. What is the sum
of digits of x ?
(1) 17 (2) 11
(3) 14 (4) 15
11. What number should be subtracted from
each of 50, 61, 92, 117 so that the numbers,
so obtained in this order are in proportion?
(1) 23 (2) 14
(3) 17 (4) 19
12. A sum of` 1710 is divided in A B , and C
such that 4 times of A, 6 times of B and 9
times of C are equal. What is the difference
between A and C?
(1)` 540 (2)` 360
(3)` 450 (4)` 480
13. The number of fruits in baskets A and B are
in the ratio 7 : 9. If six fruits are taken out
from A and put in B, then this ratio
becomes 1 : 3. The total number of fruits in
A and B is
(1) 40 (2) 28
(3) 32 (4) 36
14. ?ABC and ?ADB are on the common base
AB and on the same side of AB. DA AB ? ,
CB AB ? and AC DB = . Which of the
following is true?
(1) ? ? ? ABC BDA (2)? ? ? ABC ABD
(3) ? ? ? ABC ADB (4) ? ? ? ABC BAD
15. The sides of four triangles are given below
(i) 20 cm, 22 cm, 24 cm
(ii) 15 cm, 32 cm, 37 cm
(iii) 11 cm, 60 cm, 61 cm
(iv) 19 cm, 40 cm, 41 cm
Which of them forms a right triangle?
(1) (iv) (2) (i)
(3) (ii) (4) (iii)
16. The angles of a quadrilateral are in the ratio
3 : 5 : 7 : 9. What is the difference between
the least and the greatest angles of the
quadrilateral?
(1) 90° (2) 50°
(3) 60° (4) 72°
17. The perimeter of a triangle is 12 cm. If all
the three sides have lengths (in cm), in
integers, then how many such different
triangles are possible?
(1) 5 (2) 2 (3) 3 (4) 4
18. A godown is in the shape of a cuboid whose
length, breadth and height are 56 m, 42 m
and 10 m respectively. How many
(maximum) cuboidal boxes each measuring
2.8 m 2. 5 m 70 cm × × can be stored into the
godown?
(1) 5400 (2) 2400
(3) 3600 (4) 4800
19. The circumference of the base of a right
circular cylinder is 528 cm and its height is
2 m. What is the volume of the cylinder ?
Take p =
?
?
?
?
?
?
22
7
(1) 6.6528 m
3
(2) 2.2176 m
3
(3) 3.3264 m
3
(4) 4.4352 m
3
20. The area of a quadrilateral is 227.2 cm
2
and
the length of the perpendiculars from the
opposite vertices to a diagonal are 7.2 cm
and 8.8 cm. What is the length of the
diagonal ?
(1) 32.6 cm (2) 26.8 cm
(3) 28.4 cm (4) 30.2 cm
02
2019DECPAPERII (CLASS VI-VIII)SOLVEDPAPER CTET
Page 3


Directions (Q. Nos. 1-30) Answer the following questions by selecting the most appropriate
options.
1. Which of the following aligns with the
overall objective of achieving ‘Mathematics
for All’ as per NCF-2005 ?
(1) Mathematically talented students should be
groomed in isolation
(2) It should be acknowledged that Mathematics is
meant for selected few students
(3) Textbooks should only include problems of
average difficulty
(4) Contributions of Mathematicians from
different regions and different social groups
should be highlighted
2. Which of the following is considered as a
characteristic of an effective Mathematics
classroom?
(1) Steps for solving a new problem are neatly
demonstrated on the board by the teacher
(2) Group work and group problem solving is
discouraged
(3) It is emphasized that, Mathematics is
essentially a concrete subject
(4) Multiple ways of approaching a problem are
encouraged
3. Which of the following is a desirable
practice in the context of teaching and
learning of measurement of volume?
(1) Encourage students to figure out ways to
calculate the volume of different objects
(2) Begin by writing the formula of volume of a
cube
(3) Encourage precise calculation right from the
beginning
(4) Begin by introducing students to the volume of
2-D figures
4. Which of the following is not true according
to Piaget’s view of children’s understanding
of space?
(1) Co-ordination of different visual and tactile
experiences is required for understanding
projective space
(2) Progression of geometric ideas follows a
definite order
(3) Progression of geometric ideas follows a
historical rather than a logical order
(4) Early understanding of space is formed by
child’s sensory motor experiences
CTET SOLVED PAPERS
Paper - 2 (Mathemati cs)
08 December, 2019
5. If - × - + ÷ - - - ÷ 12 3 20 4 24 8 ( ) [ ( ) ( ) ]
- ÷ - [ ( )] 16 2 = - ÷ + ( ) , 28 7 x then the value of
x is
(1) 47 (2) 29 (3) 39 (4) 46
6. If a 8-digit number 30 0867 x y is divisible by
88, then what is the value of ( ) 3x y + ?
(1) 7 (2) 4 (3) 5 (4) 6
7. The value of
6
2
3
2
1
2
3
3
4
5
1
2
4
1
4
1
2
3
7
8
3
4
2
3
÷ × - × + + ×
?
?
?
?
?
? is
(1) -6
1
2
(2) -11
1
12
(3) 11
1
12
(4) 6
1
2
8. How many pairs of twin primes are there
between the integers 1 to 100?
(1) 8 (2) 5
(3) 6 (4) 7
9. If 21168 2 3 7 = × ×
a b c
, where a b , and c are
natural numbers, then what is the value of
( ) 4 5 a b c - + ?
(1) 3 (2) 0
(3) 1 (4) 2
10. Let x be the least number which when
divided by 8, 12, 20, 28, 35 leaves a
remainder 5 in each case. What is the sum
of digits of x ?
(1) 17 (2) 11
(3) 14 (4) 15
11. What number should be subtracted from
each of 50, 61, 92, 117 so that the numbers,
so obtained in this order are in proportion?
(1) 23 (2) 14
(3) 17 (4) 19
12. A sum of` 1710 is divided in A B , and C
such that 4 times of A, 6 times of B and 9
times of C are equal. What is the difference
between A and C?
(1)` 540 (2)` 360
(3)` 450 (4)` 480
13. The number of fruits in baskets A and B are
in the ratio 7 : 9. If six fruits are taken out
from A and put in B, then this ratio
becomes 1 : 3. The total number of fruits in
A and B is
(1) 40 (2) 28
(3) 32 (4) 36
14. ?ABC and ?ADB are on the common base
AB and on the same side of AB. DA AB ? ,
CB AB ? and AC DB = . Which of the
following is true?
(1) ? ? ? ABC BDA (2)? ? ? ABC ABD
(3) ? ? ? ABC ADB (4) ? ? ? ABC BAD
15. The sides of four triangles are given below
(i) 20 cm, 22 cm, 24 cm
(ii) 15 cm, 32 cm, 37 cm
(iii) 11 cm, 60 cm, 61 cm
(iv) 19 cm, 40 cm, 41 cm
Which of them forms a right triangle?
(1) (iv) (2) (i)
(3) (ii) (4) (iii)
16. The angles of a quadrilateral are in the ratio
3 : 5 : 7 : 9. What is the difference between
the least and the greatest angles of the
quadrilateral?
(1) 90° (2) 50°
(3) 60° (4) 72°
17. The perimeter of a triangle is 12 cm. If all
the three sides have lengths (in cm), in
integers, then how many such different
triangles are possible?
(1) 5 (2) 2 (3) 3 (4) 4
18. A godown is in the shape of a cuboid whose
length, breadth and height are 56 m, 42 m
and 10 m respectively. How many
(maximum) cuboidal boxes each measuring
2.8 m 2. 5 m 70 cm × × can be stored into the
godown?
(1) 5400 (2) 2400
(3) 3600 (4) 4800
19. The circumference of the base of a right
circular cylinder is 528 cm and its height is
2 m. What is the volume of the cylinder ?
Take p =
?
?
?
?
?
?
22
7
(1) 6.6528 m
3
(2) 2.2176 m
3
(3) 3.3264 m
3
(4) 4.4352 m
3
20. The area of a quadrilateral is 227.2 cm
2
and
the length of the perpendiculars from the
opposite vertices to a diagonal are 7.2 cm
and 8.8 cm. What is the length of the
diagonal ?
(1) 32.6 cm (2) 26.8 cm
(3) 28.4 cm (4) 30.2 cm
02
2019DECPAPERII (CLASS VI-VIII)SOLVEDPAPER CTET
03
21. If 5 3 4 8 6 7 9 8 ( ) ( ) x x x + - + = - , then what is
the value of ( ) x x
2
2 1 - + ?
(1)
25
9
(2)
2
3
(3)
4
9
(4)
5
3
22. What is the value of
a a b c b a b c c a b ( ) ( ) ( ) + + + + + - +
2 2 2 2 2 2
,
when a b = = - 1 3 , and c = -2 ?
(1) 176 (2) 138
(3) 154 (4) 162
23. The expression
( )( ) ( )( ) x y x xy y x y x xy y - + + + + - +
2 2 2 2
- + - ( ) ( ) x y x y
2 2
is equal to
(1)x y xy x y
3 3
+ + - ( ) (2)x y xy x y
3 3
- + + ( )
(3) y x xy x y
3 3
- + + ( ) (4)x y xy y x
3 3
+ + - ( )
24. What is the mean of the median, mode and
range for the data given below?
11, 25, 0, 8, 25, 30, 44, 50, 30, 18, 20, 17, 11,
9, 24, 25, 29
(1) 34 (2) 31 (3) 32 (4) 33
25. A mathematical theorem is
(1) a statement without sufficient evidence for
proof
(2) a statement that has been proven by logical
arguments based on axioms
(3) a statement which is always true and doesn’t
need proof
(4) a statement whose truth or falsity is not known
26. ‘‘Things which are equal to the same thing
are equal to one another.’’ This axiom which
is basis to Arithmetic and Algebra is given
by
(1) Euler (2) Euclid
(3) Pythagoras (4) Descartes
27. Which of the following can be used as
assessment strategy to encourage
interdisciplinary in Mathematics?
A. Projects B. Field trips
C. Anecdotal records D. Olympiad
(1) C & D
(2) A & B
(3) A & C
(4) B & C
28. Which method can be used to prove ‘‘The
sum of two even integers is always even’’ ?
(1) Counter positive proof
(2) Proof by induction
(3) Direct proof
(4) Proof by contradiction
29. Which of the following skills are promoted
by Mathematics at upper primary stage?
A. Visualisation B. Transposition
C. Memorisation D. Generalisation
E. Estimation
(1) A, C, D, E (2) A, B, D, E
(3) A, B, C, D (4) B, C, D, E
30. Which of the following tasks is least likely
to develop critical thinking among
students ?
(1) Calculate the volume of a right circular cylinder
of radius 3.5 cm and height 10 cm.
(2) Evaluate 72 73 × in three different ways and
compare the result.
(3) Formulate any two situations to represent the
equation 7 3 24 x + =
(4) A student calculated the volume of a right
circular cylinder of radius 3.5 cm and height 10
cm is 385
3
. cm . Where did he go wrong?
2019DECPAPERII (CLASS VI-VIII)SOLVEDPAPER CTET
Answers
1 (4) 2 (4) 3 (1) 4 (3) 5 (4) 6 (3) 7 (2) 8 (1) 9 (1) 10 (1)
11 (3) 12 (3) 13 (3) 14 (4) 15 (4) 16 (1) 17 (3) 18 (4) 19 (4) 20 (3)
21 (1) 22 (3) 23 (4) 24 (4) 25 (2) 26 (2) 27 (4) 28 (3) 29 (2) 30 (1)
Page 4


Directions (Q. Nos. 1-30) Answer the following questions by selecting the most appropriate
options.
1. Which of the following aligns with the
overall objective of achieving ‘Mathematics
for All’ as per NCF-2005 ?
(1) Mathematically talented students should be
groomed in isolation
(2) It should be acknowledged that Mathematics is
meant for selected few students
(3) Textbooks should only include problems of
average difficulty
(4) Contributions of Mathematicians from
different regions and different social groups
should be highlighted
2. Which of the following is considered as a
characteristic of an effective Mathematics
classroom?
(1) Steps for solving a new problem are neatly
demonstrated on the board by the teacher
(2) Group work and group problem solving is
discouraged
(3) It is emphasized that, Mathematics is
essentially a concrete subject
(4) Multiple ways of approaching a problem are
encouraged
3. Which of the following is a desirable
practice in the context of teaching and
learning of measurement of volume?
(1) Encourage students to figure out ways to
calculate the volume of different objects
(2) Begin by writing the formula of volume of a
cube
(3) Encourage precise calculation right from the
beginning
(4) Begin by introducing students to the volume of
2-D figures
4. Which of the following is not true according
to Piaget’s view of children’s understanding
of space?
(1) Co-ordination of different visual and tactile
experiences is required for understanding
projective space
(2) Progression of geometric ideas follows a
definite order
(3) Progression of geometric ideas follows a
historical rather than a logical order
(4) Early understanding of space is formed by
child’s sensory motor experiences
CTET SOLVED PAPERS
Paper - 2 (Mathemati cs)
08 December, 2019
5. If - × - + ÷ - - - ÷ 12 3 20 4 24 8 ( ) [ ( ) ( ) ]
- ÷ - [ ( )] 16 2 = - ÷ + ( ) , 28 7 x then the value of
x is
(1) 47 (2) 29 (3) 39 (4) 46
6. If a 8-digit number 30 0867 x y is divisible by
88, then what is the value of ( ) 3x y + ?
(1) 7 (2) 4 (3) 5 (4) 6
7. The value of
6
2
3
2
1
2
3
3
4
5
1
2
4
1
4
1
2
3
7
8
3
4
2
3
÷ × - × + + ×
?
?
?
?
?
? is
(1) -6
1
2
(2) -11
1
12
(3) 11
1
12
(4) 6
1
2
8. How many pairs of twin primes are there
between the integers 1 to 100?
(1) 8 (2) 5
(3) 6 (4) 7
9. If 21168 2 3 7 = × ×
a b c
, where a b , and c are
natural numbers, then what is the value of
( ) 4 5 a b c - + ?
(1) 3 (2) 0
(3) 1 (4) 2
10. Let x be the least number which when
divided by 8, 12, 20, 28, 35 leaves a
remainder 5 in each case. What is the sum
of digits of x ?
(1) 17 (2) 11
(3) 14 (4) 15
11. What number should be subtracted from
each of 50, 61, 92, 117 so that the numbers,
so obtained in this order are in proportion?
(1) 23 (2) 14
(3) 17 (4) 19
12. A sum of` 1710 is divided in A B , and C
such that 4 times of A, 6 times of B and 9
times of C are equal. What is the difference
between A and C?
(1)` 540 (2)` 360
(3)` 450 (4)` 480
13. The number of fruits in baskets A and B are
in the ratio 7 : 9. If six fruits are taken out
from A and put in B, then this ratio
becomes 1 : 3. The total number of fruits in
A and B is
(1) 40 (2) 28
(3) 32 (4) 36
14. ?ABC and ?ADB are on the common base
AB and on the same side of AB. DA AB ? ,
CB AB ? and AC DB = . Which of the
following is true?
(1) ? ? ? ABC BDA (2)? ? ? ABC ABD
(3) ? ? ? ABC ADB (4) ? ? ? ABC BAD
15. The sides of four triangles are given below
(i) 20 cm, 22 cm, 24 cm
(ii) 15 cm, 32 cm, 37 cm
(iii) 11 cm, 60 cm, 61 cm
(iv) 19 cm, 40 cm, 41 cm
Which of them forms a right triangle?
(1) (iv) (2) (i)
(3) (ii) (4) (iii)
16. The angles of a quadrilateral are in the ratio
3 : 5 : 7 : 9. What is the difference between
the least and the greatest angles of the
quadrilateral?
(1) 90° (2) 50°
(3) 60° (4) 72°
17. The perimeter of a triangle is 12 cm. If all
the three sides have lengths (in cm), in
integers, then how many such different
triangles are possible?
(1) 5 (2) 2 (3) 3 (4) 4
18. A godown is in the shape of a cuboid whose
length, breadth and height are 56 m, 42 m
and 10 m respectively. How many
(maximum) cuboidal boxes each measuring
2.8 m 2. 5 m 70 cm × × can be stored into the
godown?
(1) 5400 (2) 2400
(3) 3600 (4) 4800
19. The circumference of the base of a right
circular cylinder is 528 cm and its height is
2 m. What is the volume of the cylinder ?
Take p =
?
?
?
?
?
?
22
7
(1) 6.6528 m
3
(2) 2.2176 m
3
(3) 3.3264 m
3
(4) 4.4352 m
3
20. The area of a quadrilateral is 227.2 cm
2
and
the length of the perpendiculars from the
opposite vertices to a diagonal are 7.2 cm
and 8.8 cm. What is the length of the
diagonal ?
(1) 32.6 cm (2) 26.8 cm
(3) 28.4 cm (4) 30.2 cm
02
2019DECPAPERII (CLASS VI-VIII)SOLVEDPAPER CTET
03
21. If 5 3 4 8 6 7 9 8 ( ) ( ) x x x + - + = - , then what is
the value of ( ) x x
2
2 1 - + ?
(1)
25
9
(2)
2
3
(3)
4
9
(4)
5
3
22. What is the value of
a a b c b a b c c a b ( ) ( ) ( ) + + + + + - +
2 2 2 2 2 2
,
when a b = = - 1 3 , and c = -2 ?
(1) 176 (2) 138
(3) 154 (4) 162
23. The expression
( )( ) ( )( ) x y x xy y x y x xy y - + + + + - +
2 2 2 2
- + - ( ) ( ) x y x y
2 2
is equal to
(1)x y xy x y
3 3
+ + - ( ) (2)x y xy x y
3 3
- + + ( )
(3) y x xy x y
3 3
- + + ( ) (4)x y xy y x
3 3
+ + - ( )
24. What is the mean of the median, mode and
range for the data given below?
11, 25, 0, 8, 25, 30, 44, 50, 30, 18, 20, 17, 11,
9, 24, 25, 29
(1) 34 (2) 31 (3) 32 (4) 33
25. A mathematical theorem is
(1) a statement without sufficient evidence for
proof
(2) a statement that has been proven by logical
arguments based on axioms
(3) a statement which is always true and doesn’t
need proof
(4) a statement whose truth or falsity is not known
26. ‘‘Things which are equal to the same thing
are equal to one another.’’ This axiom which
is basis to Arithmetic and Algebra is given
by
(1) Euler (2) Euclid
(3) Pythagoras (4) Descartes
27. Which of the following can be used as
assessment strategy to encourage
interdisciplinary in Mathematics?
A. Projects B. Field trips
C. Anecdotal records D. Olympiad
(1) C & D
(2) A & B
(3) A & C
(4) B & C
28. Which method can be used to prove ‘‘The
sum of two even integers is always even’’ ?
(1) Counter positive proof
(2) Proof by induction
(3) Direct proof
(4) Proof by contradiction
29. Which of the following skills are promoted
by Mathematics at upper primary stage?
A. Visualisation B. Transposition
C. Memorisation D. Generalisation
E. Estimation
(1) A, C, D, E (2) A, B, D, E
(3) A, B, C, D (4) B, C, D, E
30. Which of the following tasks is least likely
to develop critical thinking among
students ?
(1) Calculate the volume of a right circular cylinder
of radius 3.5 cm and height 10 cm.
(2) Evaluate 72 73 × in three different ways and
compare the result.
(3) Formulate any two situations to represent the
equation 7 3 24 x + =
(4) A student calculated the volume of a right
circular cylinder of radius 3.5 cm and height 10
cm is 385
3
. cm . Where did he go wrong?
2019DECPAPERII (CLASS VI-VIII)SOLVEDPAPER CTET
Answers
1 (4) 2 (4) 3 (1) 4 (3) 5 (4) 6 (3) 7 (2) 8 (1) 9 (1) 10 (1)
11 (3) 12 (3) 13 (3) 14 (4) 15 (4) 16 (1) 17 (3) 18 (4) 19 (4) 20 (3)
21 (1) 22 (3) 23 (4) 24 (4) 25 (2) 26 (2) 27 (4) 28 (3) 29 (2) 30 (1)
1. (4) Contributions of Mathematicians from different
regions and different social groups should be highlighted
with the overall objective of achieving ‘Mathematics for
All’ as per NCF - 2005.
2. (4) Multiple ways of approaching a problem are
encouraged by teacher is considered as a characteristic of
an effective Mathematics classroom.
3. (1) Encourage students to figure out ways to calculate
the volume of different objects is a desirable practice in
the context of teaching and learning of measurement of
volume.
4. (3) According to Piaget’s view of children’s
understanding of space following statements are true
(1) Co-ordination of different visual and tactile
experiences is required for understanding projective
space
(2) Progression of geometric ideas follows a definite
order
(4) Early understanding of space is formed by child’s
sensory motor experiences
5. (4) Given, - × - + ÷ - - - ÷ 12 3 20 4 24 8 ( ) [ ( ) ( ) ]
- ÷ - [ ( )] 16 2 = - ÷ + ( ) 28 7 x
? 36
20
4
24
8
16
2
28
7
+
-
-
- ?
?
?
?
?
?
?
?
?
?
?
?
-
-
?
?
?
?
?
?
=
- ?
?
?
?
?
? +x
? 36 5 3 8 4 + - + - - = - + [ ] ( ) ( ) x
? 36 2 8 4 - + = - + x
? x = + 42 4
? x = 46
6. (3) Number 30 0867 x y should follow the divisibility
rule of ( ) 88 8 = and 11
For 8, the number made by last three digits of the given
number (67y) is divisible by 8.
8) 67y (84
64
3y
32
×
? y = 2
For 11, if the difference of the sum of digits at even
places ( ) 3 8 7 + + + x and the sum of digits at odd places
( ) 0 0 6 + + + y is 0 or a multiple of 11.
( ) ( ) 3 8 7 0 0 6 0 + + + - + + + = x y or 11
? 18 6 2 0 + - + = x ( ) or 11
? 18 8 0 11 + - = x or
? x = - = 11 10 1
? 3 3 1 2 5 x y + = × + =
7. (2) Given,
6
2
3
2
1
2
3
3
4
5
1
2
4
1
4
1
2
3
7
8
3
4
2
3
÷ × - × + + ×
?
?
?
?
?
? = ?
(According to VBODMAS)
?
20
3
5
2
15
4
11
2
17
4
5
3
7
8
1
2
÷ × - × + +
?
?
?
?
?
? = ?
?
20
3
2
5
15
4
187
8
5
3
7 4
8
× × - +
+ ?
?
?
?
?
? = ?
? 10
187
8
55
24
- + =?
?
240 561 55
24
- +
= ?
?
295 561
24
-
= ?
? - =
266
24
?
? ? =
-
= -
133
12
11
1
12
8. (1) Total pairs of twin primes between the integers 1 to
100 = 8[ (3, 5), (5, 7), (11, 13), (17, 19), (29, 31),
(41, 43), (59, 61) and (71, 73)]
Note Two consecutive prime numbers with the
difference of 2 are called ‘‘Twin primes ’’.
9. (1) Prime factors of 21168 ,
2 21168
2 10584
2 5292
2 2646
3 1323
3 441
3 147
7 49
7 7
1
= × × × × × × × × 2 2 2 2 3 3 3 7 7
= × × 2 3 7
4 3 2
On comparing,
2 3 7 2 3 7
4 3 2
× × = × ×
a b c
? a = 4,b = 3 andc = 2
2019DCPAPERII ( CLASS VI-VIII ) SOLVEDPAPER CTET
sOLVEDPAPER2019 Hints&Solutions
Page 5


Directions (Q. Nos. 1-30) Answer the following questions by selecting the most appropriate
options.
1. Which of the following aligns with the
overall objective of achieving ‘Mathematics
for All’ as per NCF-2005 ?
(1) Mathematically talented students should be
groomed in isolation
(2) It should be acknowledged that Mathematics is
meant for selected few students
(3) Textbooks should only include problems of
average difficulty
(4) Contributions of Mathematicians from
different regions and different social groups
should be highlighted
2. Which of the following is considered as a
characteristic of an effective Mathematics
classroom?
(1) Steps for solving a new problem are neatly
demonstrated on the board by the teacher
(2) Group work and group problem solving is
discouraged
(3) It is emphasized that, Mathematics is
essentially a concrete subject
(4) Multiple ways of approaching a problem are
encouraged
3. Which of the following is a desirable
practice in the context of teaching and
learning of measurement of volume?
(1) Encourage students to figure out ways to
calculate the volume of different objects
(2) Begin by writing the formula of volume of a
cube
(3) Encourage precise calculation right from the
beginning
(4) Begin by introducing students to the volume of
2-D figures
4. Which of the following is not true according
to Piaget’s view of children’s understanding
of space?
(1) Co-ordination of different visual and tactile
experiences is required for understanding
projective space
(2) Progression of geometric ideas follows a
definite order
(3) Progression of geometric ideas follows a
historical rather than a logical order
(4) Early understanding of space is formed by
child’s sensory motor experiences
CTET SOLVED PAPERS
Paper - 2 (Mathemati cs)
08 December, 2019
5. If - × - + ÷ - - - ÷ 12 3 20 4 24 8 ( ) [ ( ) ( ) ]
- ÷ - [ ( )] 16 2 = - ÷ + ( ) , 28 7 x then the value of
x is
(1) 47 (2) 29 (3) 39 (4) 46
6. If a 8-digit number 30 0867 x y is divisible by
88, then what is the value of ( ) 3x y + ?
(1) 7 (2) 4 (3) 5 (4) 6
7. The value of
6
2
3
2
1
2
3
3
4
5
1
2
4
1
4
1
2
3
7
8
3
4
2
3
÷ × - × + + ×
?
?
?
?
?
? is
(1) -6
1
2
(2) -11
1
12
(3) 11
1
12
(4) 6
1
2
8. How many pairs of twin primes are there
between the integers 1 to 100?
(1) 8 (2) 5
(3) 6 (4) 7
9. If 21168 2 3 7 = × ×
a b c
, where a b , and c are
natural numbers, then what is the value of
( ) 4 5 a b c - + ?
(1) 3 (2) 0
(3) 1 (4) 2
10. Let x be the least number which when
divided by 8, 12, 20, 28, 35 leaves a
remainder 5 in each case. What is the sum
of digits of x ?
(1) 17 (2) 11
(3) 14 (4) 15
11. What number should be subtracted from
each of 50, 61, 92, 117 so that the numbers,
so obtained in this order are in proportion?
(1) 23 (2) 14
(3) 17 (4) 19
12. A sum of` 1710 is divided in A B , and C
such that 4 times of A, 6 times of B and 9
times of C are equal. What is the difference
between A and C?
(1)` 540 (2)` 360
(3)` 450 (4)` 480
13. The number of fruits in baskets A and B are
in the ratio 7 : 9. If six fruits are taken out
from A and put in B, then this ratio
becomes 1 : 3. The total number of fruits in
A and B is
(1) 40 (2) 28
(3) 32 (4) 36
14. ?ABC and ?ADB are on the common base
AB and on the same side of AB. DA AB ? ,
CB AB ? and AC DB = . Which of the
following is true?
(1) ? ? ? ABC BDA (2)? ? ? ABC ABD
(3) ? ? ? ABC ADB (4) ? ? ? ABC BAD
15. The sides of four triangles are given below
(i) 20 cm, 22 cm, 24 cm
(ii) 15 cm, 32 cm, 37 cm
(iii) 11 cm, 60 cm, 61 cm
(iv) 19 cm, 40 cm, 41 cm
Which of them forms a right triangle?
(1) (iv) (2) (i)
(3) (ii) (4) (iii)
16. The angles of a quadrilateral are in the ratio
3 : 5 : 7 : 9. What is the difference between
the least and the greatest angles of the
quadrilateral?
(1) 90° (2) 50°
(3) 60° (4) 72°
17. The perimeter of a triangle is 12 cm. If all
the three sides have lengths (in cm), in
integers, then how many such different
triangles are possible?
(1) 5 (2) 2 (3) 3 (4) 4
18. A godown is in the shape of a cuboid whose
length, breadth and height are 56 m, 42 m
and 10 m respectively. How many
(maximum) cuboidal boxes each measuring
2.8 m 2. 5 m 70 cm × × can be stored into the
godown?
(1) 5400 (2) 2400
(3) 3600 (4) 4800
19. The circumference of the base of a right
circular cylinder is 528 cm and its height is
2 m. What is the volume of the cylinder ?
Take p =
?
?
?
?
?
?
22
7
(1) 6.6528 m
3
(2) 2.2176 m
3
(3) 3.3264 m
3
(4) 4.4352 m
3
20. The area of a quadrilateral is 227.2 cm
2
and
the length of the perpendiculars from the
opposite vertices to a diagonal are 7.2 cm
and 8.8 cm. What is the length of the
diagonal ?
(1) 32.6 cm (2) 26.8 cm
(3) 28.4 cm (4) 30.2 cm
02
2019DECPAPERII (CLASS VI-VIII)SOLVEDPAPER CTET
03
21. If 5 3 4 8 6 7 9 8 ( ) ( ) x x x + - + = - , then what is
the value of ( ) x x
2
2 1 - + ?
(1)
25
9
(2)
2
3
(3)
4
9
(4)
5
3
22. What is the value of
a a b c b a b c c a b ( ) ( ) ( ) + + + + + - +
2 2 2 2 2 2
,
when a b = = - 1 3 , and c = -2 ?
(1) 176 (2) 138
(3) 154 (4) 162
23. The expression
( )( ) ( )( ) x y x xy y x y x xy y - + + + + - +
2 2 2 2
- + - ( ) ( ) x y x y
2 2
is equal to
(1)x y xy x y
3 3
+ + - ( ) (2)x y xy x y
3 3
- + + ( )
(3) y x xy x y
3 3
- + + ( ) (4)x y xy y x
3 3
+ + - ( )
24. What is the mean of the median, mode and
range for the data given below?
11, 25, 0, 8, 25, 30, 44, 50, 30, 18, 20, 17, 11,
9, 24, 25, 29
(1) 34 (2) 31 (3) 32 (4) 33
25. A mathematical theorem is
(1) a statement without sufficient evidence for
proof
(2) a statement that has been proven by logical
arguments based on axioms
(3) a statement which is always true and doesn’t
need proof
(4) a statement whose truth or falsity is not known
26. ‘‘Things which are equal to the same thing
are equal to one another.’’ This axiom which
is basis to Arithmetic and Algebra is given
by
(1) Euler (2) Euclid
(3) Pythagoras (4) Descartes
27. Which of the following can be used as
assessment strategy to encourage
interdisciplinary in Mathematics?
A. Projects B. Field trips
C. Anecdotal records D. Olympiad
(1) C & D
(2) A & B
(3) A & C
(4) B & C
28. Which method can be used to prove ‘‘The
sum of two even integers is always even’’ ?
(1) Counter positive proof
(2) Proof by induction
(3) Direct proof
(4) Proof by contradiction
29. Which of the following skills are promoted
by Mathematics at upper primary stage?
A. Visualisation B. Transposition
C. Memorisation D. Generalisation
E. Estimation
(1) A, C, D, E (2) A, B, D, E
(3) A, B, C, D (4) B, C, D, E
30. Which of the following tasks is least likely
to develop critical thinking among
students ?
(1) Calculate the volume of a right circular cylinder
of radius 3.5 cm and height 10 cm.
(2) Evaluate 72 73 × in three different ways and
compare the result.
(3) Formulate any two situations to represent the
equation 7 3 24 x + =
(4) A student calculated the volume of a right
circular cylinder of radius 3.5 cm and height 10
cm is 385
3
. cm . Where did he go wrong?
2019DECPAPERII (CLASS VI-VIII)SOLVEDPAPER CTET
Answers
1 (4) 2 (4) 3 (1) 4 (3) 5 (4) 6 (3) 7 (2) 8 (1) 9 (1) 10 (1)
11 (3) 12 (3) 13 (3) 14 (4) 15 (4) 16 (1) 17 (3) 18 (4) 19 (4) 20 (3)
21 (1) 22 (3) 23 (4) 24 (4) 25 (2) 26 (2) 27 (4) 28 (3) 29 (2) 30 (1)
1. (4) Contributions of Mathematicians from different
regions and different social groups should be highlighted
with the overall objective of achieving ‘Mathematics for
All’ as per NCF - 2005.
2. (4) Multiple ways of approaching a problem are
encouraged by teacher is considered as a characteristic of
an effective Mathematics classroom.
3. (1) Encourage students to figure out ways to calculate
the volume of different objects is a desirable practice in
the context of teaching and learning of measurement of
volume.
4. (3) According to Piaget’s view of children’s
understanding of space following statements are true
(1) Co-ordination of different visual and tactile
experiences is required for understanding projective
space
(2) Progression of geometric ideas follows a definite
order
(4) Early understanding of space is formed by child’s
sensory motor experiences
5. (4) Given, - × - + ÷ - - - ÷ 12 3 20 4 24 8 ( ) [ ( ) ( ) ]
- ÷ - [ ( )] 16 2 = - ÷ + ( ) 28 7 x
? 36
20
4
24
8
16
2
28
7
+
-
-
- ?
?
?
?
?
?
?
?
?
?
?
?
-
-
?
?
?
?
?
?
=
- ?
?
?
?
?
? +x
? 36 5 3 8 4 + - + - - = - + [ ] ( ) ( ) x
? 36 2 8 4 - + = - + x
? x = + 42 4
? x = 46
6. (3) Number 30 0867 x y should follow the divisibility
rule of ( ) 88 8 = and 11
For 8, the number made by last three digits of the given
number (67y) is divisible by 8.
8) 67y (84
64
3y
32
×
? y = 2
For 11, if the difference of the sum of digits at even
places ( ) 3 8 7 + + + x and the sum of digits at odd places
( ) 0 0 6 + + + y is 0 or a multiple of 11.
( ) ( ) 3 8 7 0 0 6 0 + + + - + + + = x y or 11
? 18 6 2 0 + - + = x ( ) or 11
? 18 8 0 11 + - = x or
? x = - = 11 10 1
? 3 3 1 2 5 x y + = × + =
7. (2) Given,
6
2
3
2
1
2
3
3
4
5
1
2
4
1
4
1
2
3
7
8
3
4
2
3
÷ × - × + + ×
?
?
?
?
?
? = ?
(According to VBODMAS)
?
20
3
5
2
15
4
11
2
17
4
5
3
7
8
1
2
÷ × - × + +
?
?
?
?
?
? = ?
?
20
3
2
5
15
4
187
8
5
3
7 4
8
× × - +
+ ?
?
?
?
?
? = ?
? 10
187
8
55
24
- + =?
?
240 561 55
24
- +
= ?
?
295 561
24
-
= ?
? - =
266
24
?
? ? =
-
= -
133
12
11
1
12
8. (1) Total pairs of twin primes between the integers 1 to
100 = 8[ (3, 5), (5, 7), (11, 13), (17, 19), (29, 31),
(41, 43), (59, 61) and (71, 73)]
Note Two consecutive prime numbers with the
difference of 2 are called ‘‘Twin primes ’’.
9. (1) Prime factors of 21168 ,
2 21168
2 10584
2 5292
2 2646
3 1323
3 441
3 147
7 49
7 7
1
= × × × × × × × × 2 2 2 2 3 3 3 7 7
= × × 2 3 7
4 3 2
On comparing,
2 3 7 2 3 7
4 3 2
× × = × ×
a b c
? a = 4,b = 3 andc = 2
2019DCPAPERII ( CLASS VI-VIII ) SOLVEDPAPER CTET
sOLVEDPAPER2019 Hints&Solutions
05
Now, 4 5 4 4 5 3 2 a b c - + = × - × +
= - + 16 15 2 = 3
10. (1) LCM of 8, 12, 20, 28, 35
2 8, 12, 20, 28, 35
2 4, 6, 10, 14, 35
5 2, 3, 5, 7, 35
2, 3, 1, 7, 7
= × × × × × 2 2 2 3 5 7 = 840
?Required number = LCM of 8, 12, 20, 28, 35 5 +
= + = 840 5 845
Now, sum of number = + + = 8 4 5 17
11. (3) Let the number be ‘x’.
According to the question,
( ) : ( ) : :( ) : ( ) 50 61 92 117 - - - - x x x x
? ( ) ( ) ( ) ( ) 50 117 61 92 - × - = - × - x x x x
? 5850 50 117
2
- - + x x x = - - + 5612 61 92
2
x x x
? 5612 153 5850 167 - = - x x
? 167 153 5850 5612 x x - = -
? 14 238 x =
? x = =
238
14
17
12. (3) Given, 4 6 9 × = × = × = A B C k (Let)
? A
k
B
k
= =
4 6
, andC
k
=
9
? A B C
k k k
: : : : =
4 6 9
=
36
4
36
6
36
9
: :
[Q LCM of 4, 6 and 9 = 36]
= 9 6 4 : :
A’s amount = ×
+ +
1710
9
9 6 4
= × = 1710
9
19
` 810
C’s amount = ×
+ +
1710
4
9 6 4
= × = 1710
4
19
` 360
Hence, required difference = - 810 360 =` 450
13. (3) Let the fruits in basketsA andB be 7x and 9x
respectively.
According to the question,
7 6
9 6
1
3
x
x
-
+
=
? 21 18 9 6 x x - = + ? 12 24 x =
? x = 2
Hence, total fruits in basketsA andB = + 7 9 x x
= × + × 7 2 9 2 = + = 14 18 32
14. (4) Given
In ?ABC and ?ABD,
? a common sideAB (given)
? AC BD = (given)
? a common angle 90°
Hence, ? ? ? ABC BAD
15. (4) We know that, sides of right angle triangle always
follows Pythagoras theorem.
By Statement (i), ( ) ( ) ( ) 24 20 22
2 2 2
= +
? 576 400 484 = +
? 576 884 ?
By Statement (ii), ( ) ( ) ( ) 37 15 32
2 2 2
= +
? 1369 225 1024 = +
? 1369 1249 ?
By Statement (iv), ( ) ( ) ( ) 41 40 19
2 2 2
= +
? 1681 1600 361 = +
? 1681 1961 ?
By Statement (iii), ( ) ( ) ( ) 61 60 11
2 2 2
= +
? 3721 3600 121 = + ? 3721 3721 =
Hence, sides given in Statement (iii) forms a right
triangle.
16. (1) Let the angles of quadrilateral be 3 5 7 x x x , , and 9x.
According to the question,
Sum of quadrilateral = ° 360
? 3 5 7 9 360 x x x x + + + = °
? 24 360 x = °
? x = ° 15
Hence, required difference
= × - × 9 15 3 15 = ° - ° = ° 135 45 90
17. (3) We know that,
Sum of any two sides of triangle > Third side
Q Sum of any two sides > 6
?Only possible combinations are as below.
= 3[(2, 5, 5), (3, 4, 5), and (4, 4, 4)].
18. (4) Volume of godown
= Length × Breadth × Height = × × ( ) 56 42 10 m
3
Volume of box
= × × 28 25
70
100
. . Q1
1
100
cm m =
?
?
?
?
?
?
= × × ( . . . ) 28 25 0 70 m
3
2019DECPAPERII (CLASS VI-VIII)SOLVEDPAPER CTET
C
B A
D