Previous year questions · Central Teacher Eligibility Test

Central Teacher Eligibility Test Mathematics — Previous Year Questions

180 Mathematics questions asked in past Central Teacher Eligibility Test papers, split into 18 timed practice sets — every question with its answer and explanation.

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About Central Teacher Eligibility Test Mathematics previous year questions

This page collects every Mathematics question that has appeared in past Central Teacher Eligibility Test papers on AajExam — 180 questions in total, organised into 18 short, timed practice sets. Each question is shown with its four options, the correct answer, and an explanation of the reasoning, so you can use the page either as a self-test or as a revision reference. Why previous year questions are the highest-value Mathematics preparation you can do for Central Teacher Eligibility Test: recruitment boards reuse a stable pool of concepts across cycles. The wording changes, the underlying idea rarely does. Working through a few hundred genuine past Mathematics questions teaches you which sub-topics the paper actually rewards, how the examiner likes to frame distractors, and roughly how long each question type should take — none of which a syllabus document can tell you. How to use this page: attempt questions in blocks of ten without looking at the answers, then review every question you got wrong or guessed. Read the explanation for the concept, not just the answer letter. When a concept keeps catching you out, open the related topic page linked below and drill that single area before returning here. Repeat across the full bank, and track how your accuracy on the second pass compares with your first — a 15-20% improvement is normal and is the clearest sign your preparation is working. What is in this bank: the questions are transcribed from actual Central Teacher Eligibility Test question papers, kept in the original order and wording, with solutions written by subject specialists. Sets are free to attempt, work on mobile, and need no login to read. If you would rather practise a complete paper end to end under exam conditions, the full Central Teacher Eligibility Test previous-year papers are linked below as well.

Mathematics PYQs asked in Central Teacher Eligibility Test

A sample of 30 questions from the full bank of 180. Try each one before opening the solution — the remaining questions are in the timed practice sets below.

Q1.In how many ways, 48 small squares of 1 cm × 1 cm can be arranged so that the resulting area is 48 cm²
- A.6
- B.4
- C.5
- D.2
Show answer
Answer: C. 5
Q2.In school assembly, students of a class are standing in a line. Ruhi is 19th from both ends. How many students are present in that class
- A.38
- B.37
- C.36
- D.40
Show answer
Answer: B. 37
Q3.Asmita reaches school for a meeting 15 minutes before 8.30 am. She reached half an hour earlier than her colleague who is 40 minutes late for meeting. What is the scheduled time of the meeting
- A.8.15 am
- B.9.10 am
- C.8.45 am
- D.8.05 am
Show answer
Answer: D. 8.05 am
Q4.A number is larger than half of 100. It is more than 6 tens and less than 8 tens. The sum of its digits is 9. The tens digit is the double of the ones digit. What is the number
- A.72
- B.63
- C.54
- D.81
Show answer
Answer: B. 63
Q5.The rates of various stationery items are given below : A packet of crayons - ₹ 15.50 A packet of pencils - ₹ 14.00 A packet of sketch pens ₹ 22.50 One scissors - ₹ 17.00 One eraser - ₹ 2.00 One sheet of glazed paper ₹ 2.50 A pack of decorative stickers ₹ 5.00 Sohail buys one packet of crayons, two packets of pencils, one packet of sketch pens, one scissors, 5 sheets of glazed papers and one pack of decorative stickers. How much would he be required to pay
- A.₹ 98.00
- B.₹ 86.50
- C.₹ 100.50
- D.₹ 102.00
Show answer
Answer: C. ₹ 100.50
Q6.A train starts from Patna on 30th May, 2020 at 23:40 hours and reaches Mumbai on 1st June, 2020 at 5:15 hours. What is the total travel time of train
- A.28 hours 20 minutes
- B.29 hours 35 minutes
- C.29 hours 15 minutes
- D.28 hours 25 minutes
Show answer
Answer: B. 29 hours 35 minutes
Q7.In a five digit number, the digit at the hundreds place is three-fourth of the digit at ten thousands place and the digit at tens place is two-third of the digit at hundreds place. The digit at tens place is square of the smallest prime number and the digit at thousands place is the largest single digit prime number. If the digit at unit place is the largest single digit odd number, then the number is
- A.87649
- B.49327
- C.83419
- D.42937
Show answer
Answer: A. 87649
Q8.What should be subtracted from the sum of 8008, 8088 and 8808 to obtain 17863
- A.6121
- B.6131
- C.7041
- D.7141
Show answer
Answer: C. 7041
Q9.A bucket of 16 litres capacity is filled to the brim with water. Water from this bucket is to be transferred into smaller utensils. A mug filled to capacity has to be dipped 50 times to completely transfer the water in the bucket into the utensils. What is the capacity of the mug
- A.225 mL
- B.250 mL
- C.275 mL
- D.320 mL
Show answer
Answer: D. 320 mL
Q10.A taxi meter shows charges of ₹ 50 for the first two kilometres of journey and ₹ 16 for every subsequent kilometre travelled. Manju pays ₹ 258 as fare to travel from her house to the railway station. How far is the railway station from her home
- A.12 km
- B.13 km
- C.15 km
- D.18 km
Show answer
Answer: C. 15 km
Q11.Which of the following statements is/are correct? A) Mathematical knowledge can be created by primary school students by observing and identifying relations B) Learning mathematics is a social process involving dialogue and negotiation C) Argumentation plays an important role in learning of mathematics D) Culture has no role in creating mathematical understanding in classroom
- A.A, B
- B.B, C, D
- C.A, B, C
- D.A, B, D
Show answer
Answer: C. A, B, C
Q12.Which of the following statements is/are true regarding Geometry curriculum at Primary level? A) Geometry needs to be limited to recognition of 2-D shapes like circle, square, triangle etc. B) Proper definitions should be introduced C) Intuitive understanding of space should be developed
- A.A & B
- B.B & C
- C.Only C
- D.Only A
Show answer
Answer: C. Only C
Q13.Which of the following statements is/are true regarding mathematical skills and competencies used by street vendors and shopkeepers? A) They are not useful to solve mathematical problem in class B) They are ambiguous and illogical C) They help in developing alternate strategies in solving mathematical problems
- A.A & B
- B.Only B
- C.Only A
- D.Only C
Show answer
Answer: D. Only C
Q14.Which of the following activities is least likely to develop spatial reasoning among students?
- A.Drawing pictographs to represent data
- B.Working on tangram puzzles
- C.Identifying the nets of different solid shapes
- D.Identifying the axes of symmetry of given shapes
Show answer
Answer: A. Drawing pictographs to represent data
Q15.Which of the following strategies is best suited to introduce the multiplication of 3 and 5?
- A.Building rectangular arrays of 3 by 5 using certain objects
- B.Reciting the tables of 3 and 5 to find the answer
- C.Finding out the answer with the help of a calculator
- D.Providing practice in skip counting
Show answer
Answer: A. Building rectangular arrays of 3 by 5 using certain objects
Q16.Which of the following is NOT acceptable with regard to teaching students to solve problems based on mathematical operations?
- A.The problems chosen should be realistic
- B.Simple examples with smaller numbers should be taken up first
- C.Concrete materials may be used to support students' understanding of the steps of the algorithm
- D.Only one method of solving a particular type of problem should be emphasised
Show answer
Answer: D. Only one method of solving a particular type of problem should be emphasised
Q17.In which of the following statements number 'four' is used in (cardinal) sense?
- A.My office is on the fourth floor of this building
- B.My son ranked fourth in the competition
- C.The fourth chapter of this book is very interesting
- D.Four teams participated in the show
Show answer
Answer: D. Four teams participated in the show
Q18.Identify the correct statement. A. Multiplying a number by another always increases its value B. Dividing a number by another always decrease its value C. A number multiplied by 10 always has a zero at the units place D. Multiplication is the inverse of division
- A.A & B
- B.C & D
- C.Only C
- D.Only D
Show answer
Answer: D. Only D
Q19.Identify the correct statement from among the following
- A.Estimation of quantities is not a mathematical skill
- B.Mathematics can be equated with a list of standard formulae
- C.Mathematics involves identification of patterns
- D.Mathematics can be equated with a set of mechanical procedures
Show answer
Answer: C. Mathematics involves identification of patterns
Q20.Which of the following is the most suitable strategy for introducing the concept of symmetry?
- A.Engaging students in paper folding activities
- B.Giving clear definition of the concept
- C.Involving students in discussions
- D.Encourage students to observe squares and rectangles
Show answer
Answer: A. Engaging students in paper folding activities
Q21.The largest three digit number is multiplied by the largest two digit number. The product is divided by the smallest two digit odd number. What is the quotient?
- A.8991
- B.10989
- C.9999
- D.1089
Show answer
Answer: A. 8991
Q22.A number is larger than half of 50. It is more than three tens and less than four tens. The ones digit is two times the tens digit. What is the number?
- A.28
- B.32
- C.36
- D.38
Show answer
Answer: C. 36
Q23.The dimensions of a godown are 5 m × 7 m × 4 m. What is the largest number of parcels of dimensions 25 cm × 50 cm × 25 cm can be accommodated in the godown?
- A.2912
- B.4480
- C.1456
- D.896
Show answer
Answer: B. 4480
Q24.An auto rickshaw meter shows charges of ₹ 25 for the first two kilometres of journey and ₹ 8 for every subsequent kilometre travelled. Manas pays ₹ 249 as fare to travel from his house to his workplace. How far is his workplace from his home?
- A.24 km
- B.27 km
- C.30 km
- D.33 km
Show answer
Answer: C. 30 km
Q25.The following table shows marks obtained out of 100 by Sunita and Jessica in five subjects: Maths — Sunita 68, Jessica 74; English — Sunita 72, Jessica 60; Social Science — Sunita 85, Jessica 78; Science — Sunita 78, Jessica 84; Hindi — Sunita 79, Jessica 69. Based on the table above identify the correct statement from the following:
- A.Sunita has scored more marks than Jessica in all the subjects except the languages.
- B.Sunita's aggregate marks in maths and science are more than Jessica's aggregate marks in these subjects.
- C.Jessica has scored more than Sunita in three subjects.
- D.The aggregate marks of Sunita and Jessica would have been equal if Jessica had scored 17 more marks.
Show answer
Answer: D. The aggregate marks of Sunita and Jessica would have been equal if Jessica had scored 17 more marks.
Q26.Which of the following is NOT a feature of constructive practice in teaching - learning of mathematics
- A.starting the class by assessing learners' initial understanding
- B.encouraging intuitive solution
- C.presenting opportunity for cognitive conflict
- D.encouraging problem solving in prescribed manner
Show answer
Answer: D. encouraging problem solving in prescribed manner
Q27.Following questions are posed by the teacher in the mathematics classroom: A) Find two numbers whose sum is 8? B) Draw a triangle with perimeter 50 cm? C) What are factors of 25? D) Define 'Perimeter'
- A.A & B are open ended and C & D are closed ended questions
- B.A & C are closed ended and B & D are open ended question
- C.A, B, C are closed ended and D is open ended question
- D.A, C, D are closed ended and B is open ended question
Show answer
Answer: A. A & B are open ended and C & D are closed ended questions
Q28.Which of the following is an important indicator of creative thinking in mathematics?
- A.Standardized Problem solving
- B.Problem Posing
- C.error-free calculation
- D.recall of correct formula
Show answer
Answer: B. Problem Posing
Q29.At what level of Van Heile's spatial/geometrical understanding, a child is likely to accept that a square is also a rectangle
- A.Level 0 (Visualization)
- B.Level 1 (Analysis)
- C.Level 2 (Relationship)
- D.Level 3 (Deduction)
Show answer
Answer: C. Level 2 (Relationship)
Q30.Which of the following is referred to as additive identity for whole numbers?
- A.zero
- B.one
- C.The number itself
- D.The negative of the number
Show answer
Answer: A. zero

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Frequently Asked Questions

How many Central Teacher Eligibility Test Mathematics previous year questions are available?

180 Mathematics questions from past Central Teacher Eligibility Test papers are available on AajExam, split into 18 practice sets. New questions are added as fresh papers are released.

Are the answers and explanations free?

Yes. Every question on this page shows its correct answer and explanation free of charge, and you do not need an account to read them. A free account only adds attempt tracking and performance analytics.

Do Central Teacher Eligibility Test repeat questions from previous years?

Exact repeats do occur, but the more reliable pattern is conceptual: the same Mathematics sub-topics reappear cycle after cycle with reworded questions. That is why working through past questions raises your score more reliably than reading theory alone.

How should I use these questions in my Central Teacher Eligibility Test preparation?

Attempt a set of ten cold, review every wrong and guessed question with its explanation, then drill the weak sub-topic on its topic page before moving on. Revisit the same set after a few days — your second-attempt accuracy is the honest measure of whether the concept stuck.

Central Teacher Eligibility Test Mathematics practice sets

Each set is a timed 10-question drill drawn from the same question bank.

About Central Teacher Eligibility Test Mathematics previous year questions

Mathematics PYQs asked in Central Teacher Eligibility Test

Q1.In how many ways, 48 small squares of 1 cm × 1 cm can be arranged so that the resulting area is 48 cm²

Q2.In school assembly, students of a class are standing in a line. Ruhi is 19th from both ends. How many students are present in that class

Q3.Asmita reaches school for a meeting 15 minutes before 8.30 am. She reached half an hour earlier than her colleague who is 40 minutes late for meeting. What is the scheduled time of the meeting

Q4.A number is larger than half of 100. It is more than 6 tens and less than 8 tens. The sum of its digits is 9. The tens digit is the double of the ones digit. What is the number

Q6.A train starts from Patna on 30th May, 2020 at 23:40 hours and reaches Mumbai on 1st June, 2020 at 5:15 hours. What is the total travel time of train

Q8.What should be subtracted from the sum of 8008, 8088 and 8808 to obtain 17863

Q9.A bucket of 16 litres capacity is filled to the brim with water. Water from this bucket is to be transferred into smaller utensils. A mug filled to capacity has to be dipped 50 times to completely transfer the water in the bucket into the utensils. What is the capacity of the mug

Q10.A taxi meter shows charges of ₹ 50 for the first two kilometres of journey and ₹ 16 for every subsequent kilometre travelled. Manju pays ₹ 258 as fare to travel from her house to the railway station. How far is the railway station from her home

Q12.Which of the following statements is/are true regarding Geometry curriculum at Primary level? A) Geometry needs to be limited to recognition of 2-D shapes like circle, square, triangle etc. B) Proper definitions should be introduced C) Intuitive understanding of space should be developed

Q14.Which of the following activities is least likely to develop spatial reasoning among students?

Q15.Which of the following strategies is best suited to introduce the multiplication of 3 and 5?

Q16.Which of the following is NOT acceptable with regard to teaching students to solve problems based on mathematical operations?

Q17.In which of the following statements number 'four' is used in (cardinal) sense?

Q18.Identify the correct statement. A. Multiplying a number by another always increases its value B. Dividing a number by another always decrease its value C. A number multiplied by 10 always has a zero at the units place D. Multiplication is the inverse of division

Q19.Identify the correct statement from among the following

Q20.Which of the following is the most suitable strategy for introducing the concept of symmetry?

Q21.The largest three digit number is multiplied by the largest two digit number. The product is divided by the smallest two digit odd number. What is the quotient?

Q22.A number is larger than half of 50. It is more than three tens and less than four tens. The ones digit is two times the tens digit. What is the number?

Q23.The dimensions of a godown are 5 m × 7 m × 4 m. What is the largest number of parcels of dimensions 25 cm × 50 cm × 25 cm can be accommodated in the godown?

Q24.An auto rickshaw meter shows charges of ₹ 25 for the first two kilometres of journey and ₹ 8 for every subsequent kilometre travelled. Manas pays ₹ 249 as fare to travel from his house to his workplace. How far is his workplace from his home?

Q26.Which of the following is NOT a feature of constructive practice in teaching - learning of mathematics

Q27.Following questions are posed by the teacher in the mathematics classroom: A) Find two numbers whose sum is 8? B) Draw a triangle with perimeter 50 cm? C) What are factors of 25? D) Define 'Perimeter'

Q28.Which of the following is an important indicator of creative thinking in mathematics?

Q29.At what level of Van Heile's spatial/geometrical understanding, a child is likely to accept that a square is also a rectangle

Q30.Which of the following is referred to as additive identity for whole numbers?

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