When two or more two positive fractions have equal differences between their numerators and denominators, then the fraction with the greater numerator is a greater fraction, and the fraction with a smaller numerator is a smaller fraction.
Q6. Which of the following expressions is a polynomial?
(a) $\sqrt{2}$ xy2 + 3x2y – 9xy
(b) xy2 – 7$\sqrt{xy}$ – 2xy
(c) 3x² + 7x$\sqrt{y}$ – 11
(d) $\sqrt[3]{x}+\sqrt[4]{y}$
Answer: (a) $\sqrt{2}$ xy2 + 3x2y – 9xy
Explanation: The exponents of x and y in $\sqrt{2}$ xy2 + 3x2y – 9xy are whole numbers.
Hence, it is a polynomial.
Q7. Find the remainder when x4 – x3 – x² – X + 1 is divided by x2 – 2x – 1.
(a) 2x2 +1
(b) 4x + 3
(c) 4x – 3
(d) 2x² – 4x – 2
Answer: (b) 4x + 3
Explanation:
Q8. The degree of rotation of “O” is
(a) 1
(b) 2
(c) 4
(d) Infinite
Answer: (b) 2
Explanation: When we rotate 0, it takes two identical positions in one revolution. It is important to note that the shape of “0” is different from the shape of a circle.
Q9. If F, E and V are the numbers of faces, edges and vertices of a pentagonal pyramid, then the value of (F – E + V)2 – 4 is
(a) – 4
(b) – 2
(c) 0
(d) 4
Answer: (c) 0
Explanation: For any polyhedron that doesn’t intersect itself,
F + V – E = 2
Where
F is the number of faces, V is the number of vertices and E is the number of edges.
∴ (F-E + V)2 -4
= (F+V –E)2 – 4
= 22 – 4
= 4 – 4
= 0
Q10. Find the median in 21, 12, 11, 13, 14, 15, 27 and 26.
(a) 14
(b) 15
(c) 14.5
(d) 21
Answer: (c) 14
Explanation: By arranging all the numbers in an ascending order, we get 11, 12, 13, 14, 15, 21, 26 and 27
Q11. The mean of 5 observations is 7. Later on, it was found that two observations 4 and 8 were wrongly taken instead of 5 and 9. Find the correct mean.
Q14. The sides of a rectangle are in the ratio of 5:3. Find the area of the rectangle, if its perimeter is 96 cm.
(a) 540 cm2
(b) 5400 cm2
(c) 72 cm2
(d) 720 cm2
Answer: (a)540 cm2
Explanation: Let the length and breadth of the rectangle be 5x and 3x.
Now, Perimeter = 96
⇒ 2(5x+3x) = 96
⇒ 8x = 48
⇒ x = 6
Length = 5×6 = 30 cm
Breadth = 3 x 6 = 18 cm
Area = L x B = 30 x 18 = 540 cm2
Q15. The base of a triangle is twice its height. Find the height of the triangle, if its area is 25 cm2.
(a) 5 cm
(b) 6 cm
(c) 7 cm
(d) 8 cm
Answer: (a) 5 cm
Explanation: Let h be the height of triangle
Area of triangle = 25 cm2
⇒ $\frac{1}{2}$× Base × Height = 25
⇒ $\frac{1}{2}$× 2h × h = 25
⇒ h2 = 25
⇒ h = 5 cm
Q16. 9 – (6 – 2)0 + 42 + 8 + 7 is equal to
(a) 17
(b) 15
(c) 13
(d) 11
Answer: (a) 17
Explanation: On applying ‘BODMAS’, we get
9 – (6-2)0+ 42 + 8 + 7
= 9 – 40+ 42 + 8 + 7
= 9 – 1 + 16 + 8 + 7 (any non-zero number raised to the power of 0 is equal to 1)
= 9 – 1 + 2 + 7
= 18 – 1
= 17
Q17. The product of the two numbers is 60. If their LCM is 30, find the HCF.
(a) 4
(b) 2
(c) 30
(d) 5
Answer: (b)2
Explanation: Product of two numbers = LCM X HCF
∴HCF = $\frac{Product\,\,of\,\,numbers}{LCM}$
= $\frac{60}{30}=2$
Q18. The lowest factor of any number is
(a) Number itself
(b) 5
(c) Different for different numbers
(d) 1
Answer: (d)1
Explanation: 1 is the lowest factor of every number
Q19. What will be the sum of the greatest and least 4-digit numbers using the digits 1, 3, 5 and 9?
(a) 9531
(b) 1359
(c) 8172
(d) 10890
Answer: (d)10890
Explanation: Here, 1 < 3 < 5 < 9
Therefore, greatest 4-digit number 9531 and Least 4-digit number = 1359;
Sum = 9531 + 1359 =10890
Q20. What will be the difference between the greatest and least 4-digit numbers using the digits 0, 2, 5 and 9?
(a) 2095
(b) 7641
(c) 9025
(d) 7461
Answer: (d)7461
Explanation: Here, 0 < 2 < 5 < 9
Therefore, greatest 4-digit number = 9520 and Least 4-digit number
2059 (0 cannot be at the first place);
Difference = 9520 – 2059 = 7461
Q21. Communication in a mathematics class refers to developing the ability to
(a) Give prompt response to questions asked in the class
(b) Contradict the views of others on problems of mathematics
(c) Organise, consolidate and express mathematical thinking
(d) Interpret data by looking at bar graphs
Answer: (c)Organise, consolidate and express mathematical thinking
Explanation: Communication in mathematics refers to expressing mathematical thinking by using mathematical language to present a problem, consolidate the given facts, organise them for analysis and interpretation.
Q22. How many rectangles are there in the following figure?
The above question is testing of
(a) Knowledge
(b) Understanding
(c) Creativity
(d) Memory
Answer: (b)Understanding
Explanation: The question tests the understanding of the learner. Only with a thorough understanding and good observatory skills, the learner will be able to count up to 13 rectangles. Knowledge is essential for understanding. However, the question allows very little scope for creativity. The learner’s memory will not help either because the problem calls for active thinking.
Q23. Which of the following statements about evaluation is in accordance with the definition given by NCERT?
(a) It is a systematic process of determining the extent to which educational objectives are achieved by the pupils.
(b) It is introduced to designate a more comprehensive concept of measurement than what is done through the conventional tests.
(c) It is a process that is systematic and continuous, and can be used to find the effectiveness of the learning experiences of students.
(d) It is a process of ascertaining the importance of a careful appraisal process.
Answer: (c)It is a process that is systematic and continuous, and can be used to find the effectiveness of the learning experiences of students.
Explanation: According to NCERT, evaluation is a systematic and continuous process of determining the effectiveness of the learning experiences provided in the classroom.
Q24. In learning mathematics pictures and graphs are used as
(a) Audio aids
(b) Visual aids
(c) Audio-visual aids
(d) Psychological aids
Answer: (b)Visual aids
Explanation: Pictures, charts and diagrams are used as visual aids in learning. For example, teaching geometry requires the use of teaching aids, diagrams, graphs etc.
Q25. Which of the following statements about mathematics is incorrect?
(a) For naming various parameters and variables, Latin alphabets are used
(b) It is independent of the structure of a language
(c) It has its own terminology and naming conventions, symbols, words and its own set of rules
(d) It acts as a natural concomitant to any subject involving analysis and reasoning
Answer: (b)It is independent of the structure of a language
Explanation: Mathematics is not independent of language structure. In fact, it is a language in itself.
Q26. Which of the following statements about criterion-referenced tests is true?
(a) They are used to determine whether each student has achieved a specific skill or not
(b) They can be used to discriminate between high achievers and low achievers.
(c) They cannot be used as part of formative assessments.
(d) They are used as part of surveys and research work.
Answer: (a)They are used to determine whether each student has achieved a specific skill or not
Explanation: Criterion-referenced tests, also called the interim tests, are designed to determine if a student has achieved a specific skill or concept. These are generally conducted as part of formative assessments at the end of each unit.
Q27. The reason some of the students cannot solve certain problems consistently is that
(a) They lack conceptual knowledge
(b) The errors occur due to norms
(c) The errors occur due to trait
(d) They are not intelligent enough
Answer: (a)They lack conceptual knowledge
Explanation: Lack of knowledge and conceptual understanding in students could be one of the major reasons that they cannot solve certain problems consistently.
Q28. A debate was conducted, in a mathematics class, on Zero is the most powerful number”. This activity encourages the child to
(a) Write numbers containing zero(es)
(b) Solve problems containing numbers ending with zero(es)
(c) Collaborate with friends
(d) Analyse and communicate
Answer: (d) Analyse and communicate
Explanation: Debates and discussions are organised to analyse a given problem and to develop the communication skills of students.
Q29. Computational skills in mathematics can be enhanced by
(a) Conducting hands-on activities in class
(b) Clarifying concepts and procedures followed by lots of practice
(c) Giving conceptual knowledge alone
(d) Describing algorithm only
Answer: (a)Conducting hands-on activities in class
Explanation: Conducting hands-on activities in class helps students in learning. The students at this age are at the concrete operational stage, so giving them concrete objects in their hands always helps them sharpen their computational skills. Clarifying concepts and procedures or giving conceptual knowledge alone or describing algorithms only involves abstract thinking. Students may grasp the algorithm by repeated practice, they will still require time to understand the concept.
Q30. The highlights of a good textbook are that
A. they contain numerous exercises to give rigorous practice.
B. all concepts can be introduced through situations.
C. only solved examples are included.
D. they must be thick and heavy.
(a) A and B
(b) C and D
(c) A and C
(d) B and D
Answer: (a)A and B
Explanation: Good textbooks have concepts illustrated through real-life or hypothetical situations for a clear understanding as well as provide exercises so that learnt concepts are reinforced by practice.
