CTET Paper 2 Maths Questions 2026 |Previous Year Questions for Primary Teacher Exam

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CTET – Part II (Mathematics & Science)

Questions 31–60

Disclaimer: The answer key provided in this post is not official. It is prepared for reference and practice purposes only. This is a tentative answer key . Students are advised to verify the answers after the official CTET answer key is released by the exam authority.

This post provides the Mathematics questions asked in CTET 2026 Paper–II conducted on 7th and 8th February 2026. In this article, we have included only the Mathematics section questions from the exam so that students preparing for CTET exam preparation, primary teacher eligibility test, and competitive exam mathematics practice can understand the exam pattern, question types, and level of difficulty.

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CTET – Part II (Mathematics & Science)

CTET Mathematics & Science – 7th Feb Paper

Questions 31–60

Q.31. If the multiplication

\( \begin{array}{c} 2A\\ \times A\\ \hline B2A \end{array} \)

where \(A\) and \(B\) are digits, then

1. \(A=1, B=6\)
2. \(A=1, B=5\)
3. \(A=5, B=1\)
4. \(A=6, B=1\)

Correct Answer: (3)

Q.32. If \(a-b=\displaystyle \frac{11}{5}\) and \(ab=\displaystyle \frac{3}{4}\), then one of the values of \((a+b)\) is

1. \(2\displaystyle \frac{4}{5}\)
2. \(3\displaystyle \frac{1}{5}\)
3. \(3\displaystyle \frac{2}{5}\)
4. \(2\displaystyle \frac{3}{5}\)

Correct Answer: (1)

Q.33. If \( \displaystyle \frac{7x-1}{4}-\displaystyle \frac{1}{3}\left(2x-\displaystyle \frac{1-x}{2}\right)=\displaystyle \frac{10}{3} \) then what is the value of \(\displaystyle \frac{11x+21}{2}\) ?

1. 29
2. 31
3. 32
4. 27

Correct Answer: (4)

Q.34. One of the factors of \( 5(2x-4y)+6(4x^2+16y^2-16xy)-6 \) is :

1. \(4x-8y+3\)
2. \(3x-6y+1\)
3. \(3x-6y-1\)
4. \(2x-4y-3\)

Correct Answer: (3)

Q.35. A shopkeeper buys a fan for ₹1500 and marks it for ₹2500. He sells it after giving a discount of \(20\%\) on its marked price and an additional discount of ₹250 on cash payment. What is the profit (in ₹) earned by the shopkeeper?

1. 225
2. 250
3. 300
4. 200

Correct Answer: (2)

Q.36. When \(x\) is added to each of the numbers 4, 10, 12 and 24, then the numbers so obtained in this order are in proportion. What is the value of \((3x+1)\)?

1. 13
2. 16
3. 19
4. 10

Correct Answer: (3)

Q.37. If \((3x-30^\circ)\) and \((2x+20^\circ)\) are two supplementary angles, then the value of \((2x-4^\circ)\) is :

1. 76°
2. 80°
3. 84°
4. 72°

Correct Answer: (4)

Q.38. Angles \(P\) and \(Q\) of a triangle \(PQR\) are respectively \(30^\circ\) and \(50^\circ\). If the bisectors of angles \(P\) and \(Q\) meet at point \(O\), then the value of \((2\angle POQ-10^\circ)\) is :

1. 190°
2. 270°
3. 250°
4. 150°

Correct Answer: (2)

Q.39. Which of the following measurements (in cm) cannot form the sides of a right triangle?

1. 12, 16, 20
2. 4.5, 6, 7.5
3. 8, 16, 12
4. 2.5, 6.5, 6

Correct Answer: (3)

Q.40. Which of the following letters does not have rotational symmetry?

1. O
2. E
3. N
4. H

Correct Answer: (2)

Q.41. Diagonals \(PR\) and \(QS\) of a parallelogram \(PQRS\) intersect at \(O\). If \(OP=(x+y)\), \(OQ=20\), \(OR=16\), \(OS=(y+7)\), then value of \((7x-y)\) is :

1. 8
2. 9
3. 13
4. 6

Correct Answer: (3)

Q.42. The perimeter and area of a trapezium are respectively 52 cm and 128 cm². If the sum of non-parallel sides is 20 cm, then the distance between parallel sides is :

1. 8 cm
2. 10 cm
3. 12 cm
4. 6 cm

Correct Answer: (3)

Q.43. The area of a rectangular field is \(48\,m^2\) and one of its sides is 6 m. How long will it take to cross the field diagonally at a speed of \(20\,m\) per minute?

1. 20 seconds
2. 30 seconds
3. 40 seconds
4. 15 seconds

Correct Answer: (2)

Q.44. Three metallic solid cubes of sides 8 cm, 6 cm and 10 cm are melted to form a cube. The side of the new cube formed is :

1. 20 cm
2. 18 cm
3. 12 cm
4. 24 cm

Correct Answer: (2)

Q.45. The mean of the median and mode of the observations 30, 61, 55, 56, 60, 20, 26, 45, 28, 56 is

1. 53
2. 55
3. 56
4. 52

Correct Answer: (1)

Q.46. A card is drawn from a well-shuffled deck of playing cards. What is the probability that the card drawn is a 10 or a red king?

1. \(\displaystyle \frac{1}{13}\)
2. \(\displaystyle \frac{3}{26}\)
3. \(\displaystyle \frac{2}{13}\)
4. \(\displaystyle \frac{1}{26}\)

Correct Answer: (1)

Q.47. The greatest number that divides 87 and 123 leaving respectively 7 and 3 as remainders is :

1. 36
2. 40
3. 80
4. 20

Correct Answer: (3)

Q.48. The value of \(0.\overline{4} + 0.\overline{6}\) is :

1. \(1\displaystyle \frac{1}{9}\)
2. \(1\displaystyle \frac{2}{9}\)
3. \(1\displaystyle \frac{1}{10}\)
4. 1

Correct Answer: (1)

Q.49. The difference between the largest and smallest fractions among \(\displaystyle \frac{4}{7}, \displaystyle \frac{9}{16}, 1\displaystyle \frac{2}{7}, \displaystyle \frac{3}{5}\) is :

1. \(\displaystyle \frac{81}{112}\)
2. \(\displaystyle \frac{25}{28}\)
3. \(\displaystyle \frac{31}{56}\)
4. \(\displaystyle \frac{2}{7}\)

Correct Answer: (1)

Q.50. The digit at units place of the square of a number is 2 more than the digit at units place of that number. Which of the following cannot be the digit at units place of that number?

1. 5
2. 6
3. 9
4. 4

Correct Answer: (3)

Q.51. Which of the following should not be a part of assessment of students in mathematics?

1. Reason out mathematical facts
2. Recalling the definitions of mathematical terms
3. Use abstractions to perceive mathematical relationships
4. Apply mathematical concepts learnt to solve problems related to daily life

Correct Answer: (2)

Q.52. ______ was the first Indian mathematician who explained that the square root of a negative number does not exist.

1. Baudhayana
2. Aryabhatta
3. Ramanujan
4. Mahavira

Correct Answer: (3)

Q.53. When asked to arrange the decimal numbers 1.5, 0.23, 1.6, 0.034, 1.13 in ascending order, one of the students arranged them as 0.23, 0.034, 1.5, 1.6, 1.13. Which among the following is most appropriate for the response of the student?

1. The student has made a careless mistake by arranging the decimal numbers in descending order
2. Teacher should ask the student to recall the rules of ordering decimal numbers and then arrange them
3. The student has developed a misconception of considering that decimal number as bigger number which has more digits in decimal part
4. The student has arranged the decimal numbers in the correct order

Correct Answer: (C)

Q.54. A teacher asked the children to cut out six squares of ‘one’ unit each and then asked, “How many different shapes can you make using these squares? Which shape formed would have the maximum perimeter?” The least appropriate objective of this activity is

1. to provide opportunities for developing creativity and analytical skills
2. to assess children’s learning about area and perimeter
3. to apply the formulae learnt in a new context
4. to engage children in group work

Correct Answer: (C)

Q.55. A child solved an equation \(x + 7 = 15\) as

\(x + 7 - 7 = 15\)
\(x = 15\)

The best remedial strategy for this child is

1. explain problems in simple language to the child
2. explain the concept of equality using alternate methods
3. ask the child to solve the same equation on the blackboard
4. give a lot of problems on solving equations to the child

Correct Answer: (B)

Q.56. According to the National Curriculum Framework, 2005, what are the important skills developed among learners while teaching arithmetic and algebra?

A. Looking for patterns in the relationships
B. Memorizing algebraic identities
C. Seeing relationship between numbers
D. Rigorous practice of writing algebraic notation

Choose the correct option.

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

Correct Answer: (A)

Q.57. After teaching ‘shapes’ in Class VIII, a teacher planned a trip to historical places. Which of the following is the most appropriate reason for this?

1. Teacher has completed most of the syllabus, so she planned the field trip just to have fun
2. Shapes are an integral part of any architecture and such trips encourage connections across the disciplines
3. It would be a break from the routine teaching of mathematics class and an opportunity to improve students’ communication skill
4. Field trips are the recommendations of CBSE

Correct Answer: (B)

Q.58. Uma, a mathematics teacher, asked a student, “How many edges are there in a cylinder?” The student answered, “Two”. What should Uma do?

1. praise the student for correct answer
2. draw picture of the cylinder on the blackboard and show the edges
3. give cylinder in the hands of that student and ask the question again
4. give punishment to the student for wrong answer

Correct Answer: (C)

Q.59. A teacher gives an image drawn on a square grid to children and asks them to draw enlarged and reduced size images. Which of the following would not be an objective of doing this exercise in a mathematics classroom?

1. To provide practice for application of fractions
2. To provide scope for integrating arithmetic and geometry
3. To introduce the concept of congruency and similarity
4. To apply the concept of ratio and proportion in different situations

Correct Answer: (C)

Q.60. Closed-ended questions in mathematics do not promote :

A. Divergent thinking
B. Convergent thinking
C. Creativity
D. Higher-order thinking skills

Choose the correct option.

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

Correct Answer: (C)

CTET Mathematics & Science – 8th Feb Paper

Disclaimer: The answer key provided in this post is not official. It is prepared for reference and practice purposes only. This is a tentative answer key . Students are advised to verify the answers after the official CTET answer key is released by the exam authority.

Q.31. The value of \(\displaystyle \displaystyle \frac{\sqrt{5043} \times \sqrt{50}}{\sqrt{32} \times \sqrt{1323}} \) is :

1. \(\displaystyle \displaystyle \frac{215}{84}\)
2. \(\displaystyle \displaystyle \frac{205}{42}\)
3. \(\displaystyle \displaystyle \frac{205}{84}\)
4. \(\displaystyle \displaystyle \frac{215}{42}\)

Correct Answer: (4)

Q.32. If \(5(3x+4) - 8(6x+7) = 9x - 8\), then what is the value of \(3x+4\) ?

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

Correct Answer: (3)

Q.33. Which of the following problems is inter-disciplinary in nature ?

1. Draw the lines of symmetry in a given geometrical figure.
2. Draw the mirror image of a given figure.
3. How many lines of symmetry are there in a given figure.
4. Write your name and draw the lines of symmetry in each alphabet wherever possible.

Correct Answer: (4)

Q.34. Which of the following measurements (in cm) can be the sides of a right triangle ?

1. 12, 50, 44
2. 14, 50, 48
3. 12, 20, 18
4. 16, 30, 32

Correct Answer: (2)

Q.35. A pie chart is constructed for the following data :

Month	Number of computers sold
January	500
February	700
March	840
April	750
May	890
June	820

What will be the difference between the central angles of the sectors representing the number of computers sold in March and January ?

1. 29°
2. 27.2°
3. 28°
4. 28.8°

Correct Answer: (1)

Q.36. Renu loses 15% by selling an article A for ₹382.50 and gains 12% by selling article B for ₹616. If she sells both articles for ₹1,180, then her percentage gain is :

1. 18%
2. 16.5%
3. 17%
4. 17.5%

Correct Answer: (1)

Q.37. Which of the following number is not divisible by 72 ?

1. 88704
2. 95112
3. 95142
4. 88848

Correct Answer: (3)

Q.38. Which of the following is an effective teaching-learning material to introduce basic concepts such as shapes, perimeter, area and characteristics of polygons ?

1. Tangrams
2. Geoboard
3. Hanoi Tower
4. Cuisenaire rods

Correct Answer: (1)

Q.39. Rajiv invested a sum of ₹7,000 at 20% p.a. for \(1 \displaystyle \frac{1}{2}\) years, compounded half yearly, and his friend Amit invested a sum of ₹8,000 at 10% p.a. for 2 years, compounded annually. What is the difference between the interest received by Rajiv and Amit, at maturity ?

1. ₹634
2. ₹637
3. ₹632
4. ₹638

Correct Answer: (3)

Q.40. On which numeration system the clocks are based ?

1. Binary System
2. Sexagesimal System
3. Decimal System
4. Hexadecimal System

Correct Answer: (2)

Q.41. The height of a cylinder is three times the radius of its base. If the area of the base is 616 cm², then what is the capacity (in litres) of the cylinder ? Use \( \pi = \displaystyle \frac{22}{7} \)

1. 34.496
2. 12.936
3. 25.872
4. 17.248

Correct Answer: (3)

Q.42. A student was asked to arrange the following numbers in descending order, \(-20, -150, 0, 23, 46\).

The student wrote the following answer, \(-150, -20, 0, 23, 46\).

Which of the following is most appropriate for the response of the student ?

1. The student needs to recall the rules of addition of integers.
2. The student has written the numbers in correct order.
3. The student has understood the concept of arranging integers but has done a mistake by arranging them in increasing order.
4. The student does not know the concept of integers.

Correct Answer: (3)

Q.43. “While teaching the concept of ‘Discount on items’ a teacher can plan a trip to a local market.” The most appropriate reason for this is :

1. It is mandatory to have such type of field trip as suggested by National Curriculum Framework, 2005.
2. It would provide opportunity to the students to formally learn the mathematical concepts.
3. It would provide opportunity to students to see different advertisements related to ‘sales’ and to discuss with shopkeepers how to calculate it.
4. It would be a time for enjoyment for both teacher and students.

Correct Answer: (3)

Q.44. In a quadrilateral ABCD, if AB||DC, ∠B = 70° and AB = CD, then :

1. ∠A = 110°, ∠C = 110°
2. ∠A = 70°, ∠C = 70°
3. ∠A = 70°, ∠D = 110°
4. ∠C = 70°, ∠D = 110°

Correct Answer: (1)

Q.45. One of the factors of \(4x^2 + 9y^2 + 12xy - 5(2x + 3y) - 14\) is :

1. \(2x + 3y + 7\)
2. \(2x + 3y + 14\)
3. \(2x + 3y - 2\)
4. \(2x + 3y - 7\)

Correct Answer: (1)

Q.46. The product of two rational numbers is \( \displaystyle-\displaystyle \frac{40}{3} \). If one of them is \( \displaystyle -\displaystyle \frac{5}{2} \), and the reciprocal of the other is \(x\), then what is the value of \( (8x + 2\displaystyle \frac{1}{4}) \) ?

1. \(\displaystyle 3\displaystyle \frac{3}{4}\)
2. \(\displaystyle 4\displaystyle \frac{1}{2}\)
3. \(\displaystyle 4\displaystyle \frac{3}{4}\)
4. \(\displaystyle 3\displaystyle \frac{1}{2}\)

Correct Answer: (1)

Q.47. If \(x, y\) and \(z\) are respectively the number of faces, vertices and edges of a triangular pyramid, then :

1. \(3x + 3y - 2z = 6\)
2. \(2x + 3y - 2z = 8\)
3. \(3x + 2y - 3z = 4\)
4. \(2x + 2z - 3y = 6\)

Correct Answer: (1)

Q.48. If \(a + b = \displaystyle \frac{17}{6}\) and \(ab = 2\), then what is the value of \((a-b)\), where \(a>b\) ?

1. \(\displaystyle \displaystyle \frac{1}{12}\)
2. \(\displaystyle \displaystyle \frac{1}{3}\)
3. \(\displaystyle \displaystyle \frac{2}{3}\)
4. \(\displaystyle \displaystyle \frac{1}{6}\)

Correct Answer: (2)

Q.49.If \( \displaystyle \displaystyle \frac{x}{y} = \left(-\displaystyle \frac{1}{3}\right)^{-3} \div \left(\displaystyle \frac{2}{3}\right)^{-4} \), then the value of \(\displaystyle \left(\displaystyle \frac{x}{y} + \displaystyle \frac{y}{x}\right)^{-1} \times \left(\displaystyle \frac{y}{x}\right)^{-1} \) is : :

1. \(\displaystyle \displaystyle \frac{265}{9}\)
2. \(\displaystyle \displaystyle \frac{165}{48}\)
3. \(\displaystyle \displaystyle \frac{155}{3}\)
4. \(\displaystyle \displaystyle \frac{145}{9}\)

Correct Answer: (1)

Q.50. “Developing an understanding about patterns is considered essential for teaching algebra”. Which of the following represents correct reason for the given statement ?

1. Making patterns enhances creative mindset
2. Patterns are comparatively easier
3. Patterns have a lot of real-life application unlike algebra
4. Patterns are associated with generalization

Correct Answer: (4)

Q.51. A swimming pool is 20 m in length, 15 m in breadth and 4 m in depth. What is the cost of plastering its floor and walls at ₹ 42 per m² ?

1. ₹ 25,200
2. ₹ 24,276
3. ₹ 24,360
4. ₹ 24,780

Correct Answer: (1)

Q.52. The perimeters of two circular fields \(C_1\) and \(C_2\) are \(40\pi\) m and \(96\pi\) m, respectively. What is the radius of the third circular field \(C_3\) whose area is equal to the sum of the areas of \(C_1\) and \(C_2\) ?

1. 53 m
2. 68 m
3. 51 m
4. 52 m

Correct Answer: (3)

Q.53. Which of the following statement(s) is/are true ?

(a) A number never exceeds its square.

(b) All negative numbers exceeds their cubes.

(c) A number never exceeds its cube.

(d) The square root of a prime number is not a rational number.

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

Correct Answer: (2)

Q.54. A and D are two points lying on the same side of line segment BC, such that AB = 5 cm, AC = 8 cm, BC = 4 cm, BD = 8 cm and CD = 5 cm. Then,

1. ΔABC ≅ ΔDCB, by SSS
2. ΔABC ≅ ΔDBC, by SAS
3. ΔABC ≅ ΔDCB, by SAS
4. ΔABC ≅ ΔDBC, by SSS

Correct Answer: (1)

Q.55. Which among the following is the most appropriate ‘Method of Proof’ for proving \( \sqrt{2} \) is an irrational number ?

1. Induction
2. Direct Proof
3. Contrapositive
4. Contradiction

Correct Answer: (4)

Q.56. The following observations have been written in the ascending order :

\(28, 31, 47, 51, a, a + 3, 71, 74, 78, 90\)

If the median of the data is 61.5, then the mean of the data is :

1. 59.3
2. 58.1
3. 58.4
4. 59.2

Correct Answer: (1)

Q.57. Which among the following is/are the purpose of formative assessment ?

(a) Making assessment a part of teaching.

(b) Ranking and placement of children.

(c) Providing feedback to the children.

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

Correct Answer: (1)

Q.58. Which of the following statements related to project method in teaching of mathematics are correct ?

(a) It is a method based on learning by doing.

(b) It is a method in which the role of the learner is minimum.

(c) It is a method which turns the learners into a discoverer.

(d) It is always based on deduction.

Choose the correct option :

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

Correct Answer: (1)

Q.59. If \( (2x - 10°) \) and \( (3x - 50°) \) are complementary angles, then the value of \( (4x + 40°) \) is :

1. 180°
2. 120°
3. 150°
4. 160°

Correct Answer: (4)

Q.60. Tests which provide information about the relative performance of members of a specific group of students are called :

1. Diagnostic tests
2. Norm referenced tests
3. Criterion referenced tests
4. Achievement tests

Correct Answer: (2)