The Odisha Teacher Eligibility Test (OTET) is a critical step for aspiring teachers in Odisha. The examination, conducted by the Board of Secondary Education (BSE) Odisha, assesses the eligibility of candidates for teaching in schools affiliated with the board. OTET Paper 2 is aimed at candidates aspiring to teach Classes VI to VIII and includes a section on Mathematics, which is crucial for evaluating the candidates’ proficiency in the subject. Here, we present the top 30 Mathematics Multiple Choice Questions (MCQs) that are likely to aid in your preparation for the OTET Paper 2 Exam.
Top 30 Mathematics MCQs For OTET Paper 2 Exam
- Which of the following is the correct representation of the number five in binary?
A) 101
B) 100
C) 110
D) 111
ANS:- B) 101
Sol:- In binary, the number 5 is represented as 101, which corresponds to
= 1 x 22 + 0 x 21 + 1 x 20
= [1 x (2 x 2)] + [0 x (2 x 1)] + [1 x 20]
= (1 x 4) + (0 x 2) + (1)
= 4 + 0 + 1
= 5 - Which of the following is an irrational number?
A) 0.5
B) √16
C) 3/4
D) 2.5
E) None of the above.
Ans: E) None of the above
Sol:- An irrational number is a number that cannot be expressed as a fraction of two integers and cannot be represented as a terminating or repeating decimal.
Let’s analyze each option:
A) 0.5: Rational number, as it can be expressed as the fraction 1/2.
B) √16: Rational number, as the square root of 16 is 4, which is a rational number.
C) 3/4: Rational number, as it is a fraction of two integers.
D) 2.5: Rational number, as it can be expressed as the fraction 5/2.
Therefore, the irrational number among the options given is E) None of the above. - What is the value of the binary number 1101 in decimal?
A) 13
B) 12
C) 11
D) 14
ANS:- A) 13.
Sol:- The binary number 1101 can be converted to decimal by multiplying each digit by its corresponding power of 2 and then adding up the results:
= (1 x 23) + (1 x 22) + (0 x 21) + (1 x 20)
= [1 x (2 x 2 x 2)] + [1 x (2 x 2)] + [0 x (2 x 1)] + [1 x 20]
= (1 x 8) + (1 x 4) + (0 x 2) + (1 x 1)
= 8 + 4 + 0 + 1
= 13
So, the correct answer is A) 13. - What is the primary characteristic of mathematical knowledge that ensures its accuracy and reliability?
A) It is based on empirical observations.
B) It is universally accepted and can be tested anywhere, anytime.
C) It is dependent on individual interpretation.
D) It varies according to cultural contexts.
Answer: B) It is universally accepted and can be tested anywhere, anytime.
Explanation:
Mathematical knowledge is considered accurate and reliable because its principles, formulas, and rules are universally accepted and can be verified through testing at any time and in any location. This universal consistency is a key characteristic of mathematics. - Which of the following best describes the role of mathematical definitions?
A) They provide examples of mathematical concepts.
B) They describe procedures for solving problems.
C) They describe concepts accurately and precisely.
D) They offer counterexamples to refute incorrect statements.
Answer: C) They describe concepts accurately and precisely.
Explanation:
Mathematical definitions are crucial because they describe concepts accurately and precisely, ensuring clear communication and understanding of mathematical ideas. - How does mathematics contribute to the development of logical reasoning skills in children?
A) By teaching them to memorize formulas.
B) By encouraging rote learning of mathematical facts.
C) By engaging them in problem-solving and comparison of different scenarios.
D) By allowing them to guess answers to problems.
Answer: C) By engaging them in problem-solving and comparison of different scenarios.
Explanation:
Mathematics enhances logical reasoning skills by engaging children in problem-solving activities that require them to compare and contrast different scenarios, fostering critical thinking and analytical abilities. - What is a mathematical conjecture?
A) A proven statement or theorem.
B) A mathematical statement that appears plausible and requires proof.
C) An example illustrating a procedure.
D) A counterexample refuting an incorrect statement.
Answer: B) A mathematical statement that appears plausible and requires proof.
Explanation:
A mathematical conjecture is a statement that appears plausible based on observations but has not yet been proven. It requires a proof to be accepted as a valid mathematical statement. - Which of the following strategies is effective in inculcating creative thinking in children through mathematics?
A) Focusing solely on theoretical aspects of mathematics.
B) Encouraging passive listening during lessons.
C) Providing challenges with multiple solutions and promoting experimentation.
D) Discouraging questions and challenges from students.
Answer: C) Providing challenges with multiple solutions and promoting experimentation. - What is the L.C.M. of 25, 30, 35 and 40?
A. 4500
B. 4900
C. 5500
D. 4200
Ans: D. 4200
Solution:
L.C.M. of 25, 30, 35 and 40
Let us find LCM by prime factorisation.
Prime factorisation of 25 = 5 x 5 = 52
Prime factorisation of 30 = 2 x 3 x 5
Prime factorisation of 35 = 5 x 7
Prime factorisation of 40 = 2 x 2 x 2 x 5 = 23 x 5
Thus,
LCM (25, 30, 35, 40) = 2 x 2 x 2 x 3 x 5 x 5 x 7 = 4200 - The HCF of the two numbers is 29 & their sum is 174. What are the numbers?
A. 29,145
B.30, 155
C. 22, 160
D. 21, 130
Ans:
Solution: A. 29,145
Let the two numbers be 29x and 29y.
Given, 29x + 29y = 174
29(x + y) = 174
x + y = 174/29 = 6
Since x and y are co-primes, therefore, possible combinations would be (1,5), (2,4), (3,3).
The only combination that follows the co-prime part is (1,5)
For (1,5): 29 x = 29 x 1 and 29 y = 29 (5) = 145
Therefore, the required numbers are 29 and 145. - What is the GCF of 24 and 36?
A. 13
B. 12
C. 14
D. 15
Ans: B. 12
Sol: By prime factorisation, we know;
Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18 and 36
Factors of 24 = 1, 2, 3, 4, 6, 8, 12 and 24
HCF of (24,36) = 12 - If 20% of x = y, what is the value of y% of 20 in terms of x?
A. 4%
B. 5%
C. 6%
D. 7%
Ans: A. 4%
Solution: Given,
20% of x = y
⇒ (20/100) x = y
y% of 20
=(y/100). 20
= [(20x/100) / 100] x 20
= 4x/100
= 4% of x - Three students contested an election and received 1000, 5000 and 10000 votes, respectively. What is the percentage of the total votes the winning student gets?
A. 60%
B. 65%
C. 62.5%
D. 70%
Ans: 62.5%
Solution: Total number of votes = 1000 + 5000 + 10000 = 16000
The student who won the votes got 10000 votes
Hence, the percentage will be:
(10000/16000) x 100% = 62.5% - If the price of a product is first decreased by 25% and then increased by 20%, then what is the percentage change in the price?
A. 10%
B. 15%
C. 20%
D. 25%
Ans: A. 10%
Solution: Let the original price be Rs. 100.
New final price = 120 % of (75 % of Rs. 100)
= Rs. [(120/100) x (75/100) x 100]
= Rs. 90
Therefore, the net change in price is 100 – 90 = 10.
Percentage decrease = 10% - The value of a washing machine depreciates at the rate of 10% every year. If its present value is Rs. 8748, then what was the price of the washing machine three years ago?
A. Rs.13000
B. Rs.14000
C. Rs.16000
D. Rs.12000
Ans: D. Rs.12000
Solution: Given,
Current price of the washing machine = Rs.8748
The price of the machine depreciated at the rate of 10% every year
Therefore, the price of the washing machine three years ago = 8748 ÷ (1 – 10/100)3
= Rs. [8748 x (10/9) x (10/9 ) x (10/9)]
= Rs.12000 - What is the primary characteristic of inductive reasoning in mathematics?
A) It starts with a general law and applies it to specific cases.
B) It involves forming a general law from specific observations.
C) It uses already proven axioms and definitions to arrive at a conclusion.
D) It is primarily concerned with verifying hypotheses through experimentation.
Answer: B) It involves forming a general law from specific observations.
Explanation: Inductive reasoning in mathematics starts by observing specific instances and then generalizing a rule or law from these instances. This process is exploratory and experimental in nature. - Which of the following best describes the synthetic method in Euclidean geometry?
A) It breaks down complex problems into simpler parts.
B) It combines various elements to form a new whole.
C) It focuses on proving new hypotheses using axioms and previously proven statements.
D) It uses experimentation to derive conclusions from observed patterns.
Answer: C) It focuses on proving new hypotheses using axioms and previously proven statements.
Explanation: The synthetic method in Euclidean geometry is deductive, relying on established axioms, definitions, and previously proven propositions to prove new hypotheses. - What is the primary goal of the heuristic or discovery method in teaching mathematics?
A) To have students memorize mathematical facts through repetition.
B) To encourage students to find connections and discover relationships through activities and experiments.
C) To ensure students complete a high volume of practice problems.
D) To teach mathematics through lectures and direct instruction.
Answer: B) To encourage students to find connections and discover relationships through activities and experiments.
Explanation: The heuristic or discovery method focuses on meaningful learning where students actively engage in discovering concepts and relationships themselves, fostering deeper understanding and retention. - Which statement is true about the role of drill in learning mathematics?
A) Drills should be the primary method of teaching new mathematical concepts.
B) Drills should follow the understanding of basics to reinforce learning.
C) Drills should be lengthy and repetitive to ensure mastery.
D) Drills are mainly used to keep students busy.
Answer: B) Drills should follow the understanding of basics to reinforce learning.
Explanation: Effective drill practices are employed after students have understood the fundamental concepts to help reinforce and solidify their learning through repetition and practice. - What is one of the key benefits of using teaching aids such as concrete materials and audiovisual tools in teaching mathematics?
A) They replace the need for a textbook entirely.
B) They help students memorize facts more quickly.
C) They provide interactive and engaging ways to understand abstract concepts.
D) They are used to occupy students during free time.
Answer: C) They provide interactive and engaging ways to understand abstract concepts. - Calculate the sum of lengths: 21 m 13 cm, 33 m 55 cm and 45 m 6 cm.
A. 90 m 74 cm
B. 70 m 74 cm
C. 99 m 74 cm
D. 74 m 99 cm
Ans: C. 99 m 74 cm
Solution:
21 m 13 cm + 33 m 55 cm + 45 m 6 cm
= (21 + 33 + 45) m (13 + 55 + 6) cm
= 99 m 74 cm
Therefore, the sum of given lengths = 99 m 74 cm. - Beena bought 3 kg 760 grams of wool to make a carpet. How much more wool does she need to make the weight 4 kg?
A. 241 grams
B. 250 grams
C. 270 grams
D. 240 grams
Ans: D. 240 grams
Solution:
Given the weight of wool = 3 kg 760 grams
Let us convert this weight into grams.
3 kg 760 grams = (3 × 1000 + 760) grams
= (3000 + 760) grams
= 3760 grams
4 kg = (4 × 1000) grams = 4000 grams
Difference = (4000 – 3760) grams = 240 grams
Therefore, 240 grams of more wool is required. - A pile of 10 books is 10 cm high. What is the thickness of each book?
A. 10 mm
B. 50mm
C. 20 MM
D. 10 mm
Ans: D. 10 mm
Solution:
As we know,
1 cm = 10 mm
Given that the height of a pile of 10 books = 10 cm
10 books = 10 cm
= 10 x 10 mm
= 100 mm
1 book = 100/10
= 10 mm
Therefore, the thickness of each book = 10 mm. - The cost of 1 litre of syrup is Rs. 840.80. Find the cost of 600 ml of the syrup.
A. C. Rs. 504.88
B. C. Rs. 507.48
C. Rs. 504.48
D. C. Rs. 502.48
Ans: C. Rs. 504.48
Solution:
Given,
The cost of 1 litre of syrup = Rs. 840.80
As we know,
1 litre = 1000 ml
The cost of 600 ml of the syrup = (600/1000) × Rs. 840.80 = Rs. 504.48 - What is the formula for the surface area of a cuboid?
A) a √3
B) a³
C) 6a²
D) 2πr²
ANS:- C) 6a²
Sol:- The formula for the surface area of a cuboid is calculated by finding the sum of the areas of all its faces. Since a cuboid has 6 faces, each with an area equal to the product of its length and breadth, the total surface area A can be calculated as:
A = 2 (lw + wh + lh)
where l, w, and h represent the length, width, and height of the cuboid respectively. Simplifying this formula, we get:
A = 2lw + 2wh + 2lh
A = 2 (lw + wh + lh)
In a cuboid, opposite faces have the same area, so each term appears twice, leading to the simplified formula:
A = 2 (lw + wh + lh) = 2 × area of one face × 6
A = 6a².
Therefore, the correct answer is C) 6a². - Calculate the area of a rhombus with diagonals of lengths 10 cm and 12 cm.
A) 120 square cm
B) 60 square cm
C) 100 square cm
D) 150 square cm
ANS:- B) 60 square cm
Sol:- To calculate the area of a rhombus given the lengths of its diagonals, you can use the formula:
Area= ½ × Product of Diagonals
Given that the diagonals are 10 cm and 12 cm, the area can be calculated as:
Area = ½ × 10 × 12
Area = ½ × 120
Area = 60 square cm
Area = 60 square cm
So, the correct answer is B) 60 square cm - What is the formula for the space diagonal of a cuboid?
A) √ l² + b² + h²
B) √3a
C) a √2
D) √(l² + b²)
ANS:- A) √ l² + b² + h²
Sol:- The space diagonal of a cuboid is the diagonal that runs from one corner of the cuboid to the opposite corner through the interior. It can be calculated using the Pythagorean theorem in three dimensions, considering the length (l), breadth (b), and height (h) of the cuboid. Therefore, the correct formula is the square root of the sum of the squares of these three dimensions. The correct formula for the space diagonal of a cuboid is A) √ l² + b² + h² - Calculate the volume of a cone with a radius of 6 cm and a height of 9 cm. (Take π = 3.14)
A) 254.52 cubic cm
B) 339.12 cubic cm
C) 377.52 cubic cm
D) 452.16 cubic cm
ANS:- B) 339.12 cubic cm
Sol:- The formula for the volume of a cone is given by: Volume= 1/3 πr²h
Where: r is the radius of the base of the cone h is the height of the cone π is approximately 3.14
Given that the radius r is 6 cm and the height h is 9 cm, we can plug these values into the formula:
Volume = 1/3 × 3.14 × 6² × 9
Volume = 1/3 × 3.14 × 36 × 9
Volume = 1/3 × 3.14×324
Volume = 1017.36 / 3
Volume = 339.12 cubic cm
So, the volume of the cone with a radius of 6 cm and a height of 9 cm is 339.12 cubic cm.
Therefore, the correct option is B) 339.12 cubic cm. - Which geometric figure is defined by two linearly independent points in a two-dimensional surface?
A) Line
B) Plane
C) Circle
D) Triangle
ANS:- B) Plane
Sol:- A plane in geometry is defined as a two-dimensional flat surface that extends indefinitely in all directions. It is characterized by its lack of thickness and strict two-dimensionality. A plane is uniquely determined by any two points that are not collinear (linearly independent) within the plane. Therefore, a plane is defined by two linearly independent points on a two-dimensional surface. So the correct answer is B) Plane - What is the perimeter of a square with a side length of 5 units?
A) 20 units
B) 15 units
C) 25 units
D) 10 units
ANS:- A) 20 units.
Sol:- The perimeter of a square is the sum of the lengths of all its sides. Since all sides of a square are equal, you can find the perimeter by multiplying the length of one side by 4.
Given that the side length of the square is 5 units:
Perimeter = 4 × side length
Perimeter = 4 × 5
Perimeter = 20 units
So, the perimeter of the square with a side length of 5 units is 20 units.
Therefore, the correct option is A) 20 units.
