CTET 2024 Jan Paper 2 with answer keys (Mathematics)

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Q.31. BD is the diagonal of parallelogram ABCD such that \(\angle CBD=12x\), \(\angle ABD=7y\), \(\angle ADB=60^{\circ}\) and \(\angle CDB=28^{\circ}\). Then, the value of \(2x+3y\) is

1. \(20^{\circ}\)
2. \(21^{\circ}\)
3. \(22^{\circ}\)
4. \(23^{\circ}\)

3

Q.32. A student listed the following properties of Rational Numbers. Which one/ones is/are correct?
(a) A rational number includes integers.
(b) 0 (zero) is not a rational number.
(c) All fractions are rational numbers.

1. (a) and (c)
2. Only (b)
3. Only (c)
4. (a) and (b)

1

Q.33. One of the factors of \(p^{3}x+p^{2}(x-y)-p(y+z)-z\) is

1. \(p^{2}x-py+z\)
2. \(p^{2}x+py+z\)
3. \(p^{2}x-py-z\)
4. \(p^{2}x+py-z\)

3

Q.34. If the median of the data 30, 8, 7, 3, 17, 15, 21, 24, 29, 23 is \(x\) and the median of the data obtained by replacing 3 by 33 and 8 by 18 in the above data is \(y\), then what is the difference between \(y\) and \(x\)?

1. 1
2. 2
3. 3
4. 4

3

Q.35. Three numbers are in the ratio \(2:3:4\) and the sum of their cubes is 33957. What is the sum of the three numbers?

1. 54
2. 63
3. 72
4. 81

2

Q.36. The number of vertices (V), edges (E) and faces (F) of a polyhedron are respectively 10, 15 and \(x\). Then, the value of \((3x-12)\) is

1. 7
2. 9
3. 14
4. 18

2

Q.37. If \(\frac{x}{y}=(\frac{-1}{3})^{-3} \div (\frac{2}{3})^{-4}\), then what is the value of \((\frac{x}{y}+\frac{y}{x})^{-1}\)?

1. \(-\frac{3}{16}\)
2. \(\frac{19}{48}\)
3. \(\frac{38}{73}\)
4. \(-\frac{48}{265}\)

4

Q.38. Concept was labelled as 'Schema' by

1. Vygotsky
2. Piaget
3. Bruner
4. Van Hieles

2

Q.39. If \(x=1.011+10.11-12.101+0.1011\), then what should be added to \(x\) to get the sum as 1.1?

1. 1.9789
2. 0.3111
3. 0.2211
4. 1.1311

1

Q.40. Teacher conducted an oral assessment in class and found that Ram can speak definition of all types of numbers - odd, even, prime and composite accurately, but not able to identify the numbers accurately when given a set of numbers. Which of the following is most appropriate for the above situation?

1. Ram has good memory but lacks practice.
2. Ram has good memory but lacks concentration.
3. Ram has good memory but lacks conceptual understanding.
4. Ram has analytical ability.

3

Q.41. A shopkeeper sells an article for 324 after giving a discount of 28% on its marked price. The cost price of the article is 300. If he sells the article by giving 18% discount on its same marked price, then what will be his profit percent?

1. 10%
2. 19%
3. 23%
4. 24%

3

Q.42. The product of two rational numbers is \(-\frac{40}{3}\). If one of the two numbers is \(-\frac{5}{2}\), then the reciprocal of the other number lies between:

1. \(\frac{3}{20}\) and \(\frac{9}{50}\)
2. \(\frac{9}{50}\) and \(\frac{1}{5}\)
3. \(\frac{1}{5}\) and \(\frac{1}{4}\)
4. \(\frac{1}{4}\) and \(\frac{1}{3}\)

2

Q.43. A class VI mathematics teacher posed the following problem to her students: "In a morning walk, three persons started together. Their steps measure 70 cm, 85 cm and 95 cm respectively. What is the minimum distance each should walk so that all can cover the same distance in complete steps?" Which of the following concepts would be required to solve the given problem?

1. Concept of HCF
2. Concept of LCM
3. Concept of division
4. Concept of proportion

2

Q.44. A student was given the following problem on percentage: "Find the percentage of decrease if the population of a city decreased from 28,000 to 26,500." She wrote: % decrease \( = \frac{26,500}{28,000} \times 100\% = 94.6\% \). Which of the following is most appropriate with respect to the response of the student?

1. Student is able to understand the concept of percentage but is not able to understand percentage of which quantity is to be found.
2. Student has solved the question correctly but has used wrong symbols in solution.
3. Student does not know the concept of percentage.
4. Student has made a careless mistake.

1

Q.45. The difference between two supplementary angles is \(20^{\circ}\). If the smaller of these angles is \(p\), then the value of \(3p-50^{\circ}\) is

1. \(310^{\circ}\)
2. \(270^{\circ}\)
3. \(250^{\circ}\)
4. \(190^{\circ}\)

4

Q.46. \(x\) varies inversely as \(y\). When \(x=3.5\), then \(y=2.4\). What is the value of \(y\) when \(x=5.6\)?

1. 1.4
2. 1.5
3. 2.1
4. 2.8

2

Q.47. Which among the following Learning-Teaching Resources (LTRs) are most appropriate for visually challenged students in mathematics classroom?
(a) Geogebra
(b) Taylor's abacus
(c) Computer
(d) Spreadsheet

1. (a) and (b)
2. (c) and (d)
3. (b) and (c)
4. (b), (c) and (d)

3

Q.48. National Education Policy (NEP) 2020 recommends that Sports Integrated Pedagogy needs to be used in classroom teaching. Which among the following are correct in the context of using sports integrated pedagogy in mathematics classroom?
(a) Teaching-learning process shall become joyful.
(b) It is not possible to use sports for teaching mathematics.
(c) It will be time consuming and hence needs to be avoided.
(d) Apart from popular sports, there are many indigenous sports which can be used in teaching mathematics.

1. (a) and (c)
2. (b) and (c)
3. (a) and (d)
4. (b), (c) and (d)

3

Q.49. The area of the curved surface of a right circular cylinder is \(4400~cm^{2}\) and the circumference of its base is 110 cm. Its volume (in \(m^{3}\)) is: (Use \(\pi=\frac{22}{7}\))

1. 0.0284
2. 0.0385
3. 0.0285
4. 0.0382

2

Q.50. A box opened at the top is made of wood of thickness 3 cm. Its external length, breadth and height are respectively 1.48 m, 1.16 m and 83 cm (\(base = length \times breadth\)). What will be the cost of painting its inner surface at 150 per \(m^{2}\)?

1. 838.20
2. 839.10
3. 841.40
4. 842.50

2

Q.51. In triangles ABC and DEF; \(\angle B=90^{\circ}\), \(BC=8~cm\), \(\angle A=40^{\circ}\), \(DE=8~cm\), \(\angle F=40^{\circ}\) and \(\angle E=90^{\circ}\). Then, which of the following statements is true?

1. \(\Delta ABC \cong \Delta DEF\) by RHS
2. \(\Delta ABC \cong \Delta FED\) by RHS
3. \(\Delta ABC \cong \Delta DFE\) by AAS
4. \(\Delta ABC \cong \Delta FED\) by AAS

4

Q.52. Three consecutive integers are such that when they are taken in increasing order and multiplied by 3, 5 and 2, respectively, they add up to 99. What is the sum of the original first and third integers?

1. 16
2. 18
3. 20
4. 24

3

Q.53. A middle school mathematics teacher poses the following question: "Which type of graph would you use to show (a) heights of participants and (b) passengers boarding trains from 9:00 am to 9:00 pm?" The intention of the teacher is to:

1. Help learners understand the difference between bar graph and line graph.
2. Introduce the concept of pie charts.
3. Teach line graph through contextual situations.
4. Teach the use of histograms for data representation.

4

Q.54. If a 8-digit number 9 47 1 x 9 y 2 is divisible by 72, then which of the following statements is not true?

1. \(x=8\) and \(y=5\)
2. \(x=4\) and \(y=9\)
3. \(x=9\) and \(y=5\)
4. \(x=3\) and \(y=1\)

3

Q.55. Mathematics is a way of thinking since:
(a) It provides an opportunity for students to engage in proofs and examining patterns.
(b) Students reproduce formulae and symbols during problem solving.
(c) Students use appropriate strategies for solving various new problems.

1. (a) and (b)
2. (b) and (c)
3. (a) and (c)
4. Only (b)

3

Q.56. The following table shows the number of different fruits kept in a carton:

Type of fruits	Number
Mangoes	44
Apples	56
Oranges	42
Guavas	30
Pomegranates	38

If a pie chart is constructed, what will be the angle of the sector representing apples?

1. \(79.2^{\circ}\)
2. \(72^{\circ}\)
3. \(96^{\circ}\)
4. \(100.8^{\circ}\)

3

Q.57. The lengths of the parallel sides of a trapezium are 11 cm and 25 cm and the distance between them is 12 cm. Its area is equal to the area of a rectangle whose sides are in the ratio 3 : 2. What is the perimeter (in cm) of the rectangle?

1. 40
2. 50
3. 60
4. 70

3

Q.58. If \(A=-2x^{2}+12x\), \(B=11-8x+3x^{2}\), \(C=17-4x^{2}\) and \(D=x^{2}-x-3\), then what is the sum of the co-efficients of \(x^{2}\) and \(x\) in \((A+B+C-D)\)?

1. 0
2. -1
3. 1
4. 3

3

Q.59. Which of the following is not a dimension of assessment of mathematics learning?

1. Communication
2. Patterns and procedures
3. Disposition towards mathematics
4. Mathematical reasoning

3

Q.60. In triangle PQR, \(\angle P=55^{\circ}\) and \(QR=18~cm\). In which of the following cases, \(\Delta PQR\) can be an obtuse scalene triangle?

1. \(\angle R=25^{\circ}\) and \(PQ=18~cm\)
2. \(\angle R=15^{\circ}\) and \(PR > 18~cm\)
3. \(\angle R=65^{\circ}\) and \(PQ > 18~cm\)
4. \(\angle R=35^{\circ}\) and \(PR=18~cm\)

2