CTET 2023 Paper 2 with answer keys (Mathematics)

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Q.31. A teacher in her class discusses various examples from daily life situations like a railway line crossing several other lines, a road crossing two or more roads, alphabets like 'H', 'Z', etc. Which of the following concept(s) can be introduced through these examples?
A. Line segment
B. Transversal
C. Parallel lines
D. Right angles

1. B and C
2. Only A
3. A and D
4. Only B

1

Q.32. Which among the following is the most appropriate way to teach mathematics?

1. Find the gaps in learning and address them only
2. Find the low performers and make them sit in the front row of the class
3. Teach every student with the same approach
4. Motivate the learners to develop their existing capabilities

4

Q.33. Which of the following is true for Continuous and Comprehensive Evaluation (CCE)?

1. In CCE, assessment process includes assessment of previous knowledge, understanding level and learning process.
2. For CCE, teachers feel that each one of them has to give some home assignment every day to assess children's learning.
3. CCE is all about converting marks into grades.
4. In CCE, there is more testing and less teaching.

1

Q.34. Which of the following is/are essential features of a concept map in mathematics?
A. It represents a conceptual analysis of a concept using contributory sub-concepts.
B. They are directional, with arrows showing which concepts are prerequisite for which others.
C. They cannot be used for diagnostic purposes to identify difficulties in learning a particular concept.
D. They cannot be used frequently as they are very time consuming.

1. B and D
2. Only C
3. C and D
4. A and B

4

Q.35. Which of the following is not true about nature of mathematics?

1. Mathematics at school level requires special aptitude in learners.
2. Primary concepts in mathematics are abstract in nature.
3. Mathematics is based on deductive reasoning.
4. Mathematics is much more abstract and hierarchic than most of the other subjects which children learn at the same age.

1

Q.36. Which of the following statements are appropriate regarding "Argumentation" in a mathematics classroom?
A. It can be understood as line of reasoning that intends to show or explain why a mathematical result is true.
B. It is always helpful in mathematics in the same manner as in other empirical disciplines.
C. It can also be a part of the heuristic approach in mathematics education.
D. It is less useful for elementary grade students as its assessment will be difficult.

1. A and C
2. B and C
3. A and B
4. A and D

1

Q.37. Which of the following statements is not correct with regard to a mathematics textbook?

1. Examples in a mathematics textbook should be related to daily life of the students.
2. A mathematics textbook should have solved examples only.
3. A textbook of mathematics should not be very thick or heavy.
4. A mathematics textbook should have varied exercises to give practice to students.

2

Q.38. A conjecture in mathematics is:

1. not important at all as it does not help in developing mathematical understanding.
2. a proposition or conclusion that has been proved.
3. important for students of secondary level only.
4. a proposition or conclusion that is assumed to be true on a tentative basis without proof.

4

Q.39. The statement "1 less than or 1 more than a multiple of 6 are prime numbers" is an example of:

1. Generalisation
2. Theorem
3. Conjecture
4. Axiom

3

Q.40. A mathematics teacher posed the following problems to her students:
A. Simrat pays ₹60,000 as rent for three months. How much will she have to pay for a whole year if the rent per month remains same?
B. Cost of three dozen bananas is ₹45. Calculate the number of bananas that can be purchased for ₹12.50.
C. Joey and Jenny are going to school. Joey started walking before Jenny. When Joey was at the third block, Jenny was at the first block. If both are walking with the same speed, then where would Jenny be if Joey is at the ninth block?
Which of the following is correct with respect to the above three questions?

1. Only A is based on unitary method.
2. B and C are daily life problems based on unitary method.
3. A and C are daily life problems based on unitary method.
4. A and B are daily life problems based on unitary method.

4

Q.41. The area of a rectangle whose sides are 176 cm and 56 cm is equal to the area of a circle. What is the circumference (in cm) of the circle? (Take \(\pi=\frac{22}{7}\))

1. 396
2. 352
3. 440
4. 308

2

Q.42. The cost of painting the surface of a solid cuboid of dimensions \(40~cm \times 36~cm \times x~cm\) at ₹20 per \(100~cm^{2}\) is ₹1,032. What is the value of x?

1. 20
2. 15
3. 24
4. 12

2

Q.43. PQRS is a quadrilateral in which \(PQ=PS\) and \(RQ=RS\). Which of the following statements is true about this quadrilateral?

1. Its diagonals are equal.
2. Its diagonals are perpendicular to each other.
3. Each diagonal bisects the angle at each vertex.
4. Its diagonals bisect each other.

2

Q.44. ABCD is a rhombus in which \(\angle ADB=25^{\circ}\). Then, the value of \((2\angle BAD-\angle ABC)\) is:

1. \(230^{\circ}\)
2. \(240^{\circ}\)
3. \(210^{\circ}\)
4. \(260^{\circ}\)

3

Q.45. What is the mean of the mode, median and range of the data given below?
17, 8, 11, 13, 9, 14, 10, 11, 16, 23, 15, 7

1. 13
2. 12.5
3. 13.5
4. 12

1

Q.46. If \(x=\sqrt{198} \times \sqrt{550}\) and \(y=\sqrt[3]{99} \times \sqrt[3]{363}\), then \(\frac{1}{x}+\frac{1}{y}\) is equal to:

1. \(0\cdot\overline{01}\)
2. \(0\cdot03\)
3. \(0\cdot33\)
4. \(0\cdot\overline{1}\)

2

Q.47. If \(p=(12\cdot34 \times 10^{10})-(5\cdot67 \times 10^{9})\), then p is expressed in standard form as:

1. \(1\cdot1773 \times 10^{11}\)
2. \(1\cdot1773 \times 10^{10}\)
3. \(1\cdot773 \times 10^{11}\)
4. \(1\cdot773 \times 10^{10}\)

1

Q.48. By which number should \((-\frac{1}{4})^{-1}\) be multiplied so that the product is the reciprocal of \((-\frac{7}{4})^{-1}\)?

1. \(\frac{7}{16}\)
2. \(\frac{16}{7}\)
3. \(-\frac{16}{7}\)
4. \(\frac{7}{16}\)

1

Q.49. If \(313632=p^{2} \times q^{5} \times r^{4}\), where p, q and r are prime numbers, then what is the value of \((p+q-2r)\)?

1. 8
2. 7
3. 9
4. 6

2

Q.50. Marks obtained by Sunita in her pre-board examination are as follows:

Subject	Marks
English	72
Hindi	84
Mathematics	96
Science	80
Social Science	68

If a pie chart is constructed for the above data, then what will be the angle of the sector representing marks obtained by Sunita in Mathematics?

1. \(75\cdot6^{\circ}\)
2. \(72^{\circ}\)
3. \(86\cdot4^{\circ}\)
4. \(64\cdot8^{\circ}\)

3

Q.51. The volume of a right circular cylinder of length 1.2 metres is \(4620~cm^{3}\). What is the curved surface area (in \(cm^{2}\)) of the cylinder? (Take \(\pi=\frac{22}{7}\))

1. 2640
2. 2200
3. 2860
4. 1980

1

Q.52. If F, V and E are respectively the number of faces, vertices and edges of a triangular prism, then which of the following statements is true?

1. \(4F+2V-3E=6\)
2. \(2F+3V-2E=10\)
3. \(2F+4V-3E=8\)
4. \(3F+2V-2E=11\)

2

Q.53. P is a point on line AB and PQ is a ray such that \(\angle QPA=7x\) and \(\angle QPB=5x\). Then, the value of \((8x-10^{\circ})\) is:

1. \(118^{\circ}\)
2. \(110^{\circ}\)
3. \(140^{\circ}\)
4. \(102^{\circ}\)

2

Q.54. S is a point on side PQ of a triangle PQR such that \(RS=PS=QS\). If \(\angle QPR=15^{\circ}\), then the value of \((2\angle PQR-\angle PRQ)\) is:

1. \(50^{\circ}\)
2. \(60^{\circ}\)
3. \(45^{\circ}\)
4. \(75^{\circ}\)

2

Q.55. When a shopkeeper sells item A for ₹384, then there is a loss of 20% and when he sells item B for ₹400, then there is a profit of 25%. What is the profit/loss percent, if he sells both items for a total of ₹852?

1. Profit, 6.5%
2. Loss, 5%
3. Loss, 7%
4. Profit, 7.5%

1

Q.56. A sum of ₹12,000 amounts to ₹15,972 at a certain rate percent per annum in \(1\frac{1}{2}\) years, when the interest is compounded half-yearly. What will be the amount of the same sum in same time and with the same rate, if interest is compounded annually?

1. ₹15,840
2. ₹15,420
3. ₹15,950
4. ₹14,520

1

Q.57. If \(5x^{2}-8y-20x+2xy=(x+a)(bx+2y)\), then the value of \((a-b)\) is:

1. 9
2. -1
3. -9
4. 1

3

Q.58. If \(A=x^{2}(1-3y^{2})\), \(B=x(xy^{2}-2x)\) and \(C=3y(y-4x^{2}y)\), then \(A+B-C=px^{2}+qx^{2}y^{2}+ry^{2}\). What is the value of \((5p+q-r)\)?

1. 12
2. 10
3. 18
4. 8

4

Q.59. Which of the following are divisible by 2, 3 and 11?
A. 8448
B. 9812
C. 9126
D. 9636

1. A and B
2. B and D
3. A and D
4. A and C

3

Q.60. The solution of the equation \(\frac{(x+1)-(2x+4)}{3-5x}=\frac{1}{23}\) is also the solution of the equation:

1. \(5(2x+1)=3(x+1)\)
2. \(3(2x+3)=2(x+3)\)
3. \(3(2x+3)=5(x+1)\)
4. \(2(2x-3)=3(x+1)\)

3