Q6. Find the remainder on dividing p(x) = 4x4 + 2x2 9x + 7 by x + 3.
(a) -376
(b) 376
(c) 324
(d) -324
Answer: (b)
Explanation: If p(x) is divided by x + 3 then remainder is p(-3)
p(-3) = 4(-3) + 2(-3)2 – 9(-3) + 7
= 324 +18+27 +7= 376
∴ Remainder = 376
Q7. Find the HCF of (x – 5)2 and x2 – 25.
(a) (X – 5)2
(b) 1
(c) (X – 5)
(d) (X + 5)
Answer: (c)
Explanation: We have
(x – 5)2 = (x – 5)(x – 5)
x2 – 25 = (x + 5)(X – 5)
So, HCF = (x – 5)
Q8. What is the order of symmetry of a square?
(a)
(b) 2
(c) 4
(d) 5
Answer: (c)
Explanation: When we rotate a square, it takes four positions in one circular rotation where it takes the same shape and size.
Q9. Which of the following has an infinite order of symmetry?
(a) Square
(b) Circle
(c) Equilateral triangle
(d) Rectangle
Answer: (b)
Explanation: A circle is symmetrical about all of its diameters (which are infinite in number); therefore, it has an infinite number of symmetrical rotations.
Q10. The mean of 5 observations is 51. The mean of the first two observations is 38 and that of the last two observations is 25. What is the middle observation?
(a) 120
(b) 125
(c) 129
(d) 130
Answer: (c)
Explanation: Sum of five numbers = 5 x 51 = 255
Sum of first two numbers = 2 × 38 = 76
Sum of last two numbers = 2 x 25 = 50
Sum of five numbers = Sum of first two numbers + Middle number + Sum of last two numbers
Or, the middle number = 255 – 76 – 50 = 129
Q41. Reenu has 65, 75 and 85 marks in three English tests, respectively. How many marks must she obtain in the next test to have an average of exactly 75 for the four tests?
(a) 70
(b) 80
(c) 75
(d) 60
Answer: (c)
Explanation: Suppose she will obtain x marks on the next test
Mean = $\frac{Sum\,\,of\,\,all\,\,observations}{Total\,\,number\,\,of\,\,observations}$
⇒ 75 = $\frac{65+75+85+x}{4}$
⇒ 300 = x + 225
⇒ x = 300 – 225 = 75
Q12. If the median of 26, 29, x, x + 1, 39 and 59 is 25.5, find the value of x.
(a) 23
(b) 27
(c) 25
(d) 24
Answer: (c)
Explanation: Here, n is even, i.e. 6
Median = $\frac{\left( \frac{n}{2} \right) ^{th}observation\,\,+\left( \frac{n}{2}+1 \right) ^{th}observation\,\,}{2}$
Q13. A tank 12 m long, 13 m wide and 0.5 m deep is dug in a field that is 25 m long and 15 m wide. If the earth dug out is evenly spread out over the field, the rise in the level of the field will be
(a) 18 cm
(b) 3.6 cm
(c) 3.6 m
(d) 36 cm
Answer: (d)
Explanation: Volume of earth dug out = 12 x 13 x 0.5 = 78 m²
Area over which earth is spread = 25 x 15-12 x 13 = 219 m²
Rise in level = $\frac{Volume}{Area}$ = $\frac{78}{219}$ = 0.36 m or 36 cm
Q14. The perimeter of one face of a cube is 96 m. The volume of the cube will be
(a) 13248 m
(b) 13428 m
(c) 13842 m
(d) 13824 m
Answer: (d)
Explanation: Perimeter of one face of the cube =96m
4x Side = 96 ⇒ Side = 24m
Volume of cube = (Side)3 = (24)3 = 13824m
Q15. The edges of a cuboid are in the ratio of 2:5:7 and its surface area is 472 m2. Then, the volume of the cuboid is
(a) 440 m3
(b) 724 m3
(c) 247 m3
(d) 560 m3
Answer: (d)
Explanation: Let the length, breadth and height be 2x, 5xand7x, respectively
Total surface area of the cuboid = 472m²
⇒ 2(1b + bh + 1h) = 472
⇒ 2(10x² + 35x² + 14x²) = 472
⇒59x2 = 236 ⇒x2 = 4 ⇒ x = 2
Volume = Ibh = 4x10x14 = 560m
Q16. The number 0.00009753 is expressed in the standard form as
(a) 9.753 x 10.5
(b) 9753 x 108
(c) 9.753 x 108
(d) 9753 x 105
Answer: (a)
Explanation: When a number is written in standard form, it becomes
a x 10n, where 0 < a < 10
∴ 0.00009753 = 9.753 x 10–5
Q17. The smallest number greater than 3, which when divided by 4, 5 and 6 leaves the same remainder 3, is
Q19. The LCM of the two numbers is 12, while their HCF is 2. If the sum of the numbers is 10, find the difference.
(a) 2.
(b) 12
(c) 6
(d) 15
Answer: (a)
Explanation: Let the two numbers be a and b.
Then, ab = Product of LCM and HCF = 12 x 2 = 24
(a – b)2 = (a + b)2 – 4ab
= 102 – 4 x 24 = 4
∴ a – b= 2
Q20. The difference between the HCF and LCM of 12, 24 and 30 is
(a) 126
(b) 120
(c) 114
(d) 144
Answer: (c)
Explanation: 12 = 22 x 3
24 = 23 x 3
30 = 2 x 3 x 5
HCF = 2 x 3 = 6
LCM = 23 x 3 x 5 = 120
So, the difference between HCF and LCM = 120 – 6 = 114
Q21. “Mathematics puzzles‘ are most useful to
(a) Identify brilliant students of the class
(b) Provide interesting diversion to students
(c) Test problem-solving skills
(d) Promote problem-solving skills in students
Answer: (d)
Explanation: Mathematical puzzles are not only a fun way of learning the concepts of mathematics but also help in promoting problem-solving skills, which the learners can apply to non-puzzle problems as well.
Q32. Which of the following is the most necessary attribute for learning the language of Mathematics?
(a) Knowledge of the natural language
(b) Symbols and notations of mathematics
(c) Usage of the mathematical processes
(d) Knowledge of the English language
Answer: (b)
Explanation: Knowledge about the symbolism and notations used in mathematics is the most necessary aspect for learning the language of Mathematics. Other options are not specific to the language of mathematics.
Q23. Which of the following processes is responsible for creating fear and anxiety in the students learning mathematics?
(a) Visualisation and representation
(b) Mathematical communications
(c) Estimation of quantities
(d) Memorisation of important concepts
Answer: (d)
Explanation: Memorisation of important concepts is very difficult. Once students learn certain concepts by heart (without understanding), they tend to forget them very soon and this results in fear and anxiety among them.
Q24. The main goal of mathematics education is to
(a) Help the students to understand mathematics
(b) Develop capabilities useful for life
(c) Develop children’s abilities for mathematisation
(d) Formulate theorems of geometry
Answer: (c)
Explanation: The main goal of mathematics education is to develop children’s abilities for mathematisation. It means that children should learn to think about any situation using the language of mathematics and solve the problem by applying mathematical tools and techniques. Formulation of theorems of geometry is not at all a goal at the primary level. Helping students to understand mathematics and to develop their capabilities is a part of the main goal, i.e. mathematisation.
Q25. What is the meaning of the term ‘tyranny of the right answer‘?
(a) Putting the students under pressure to compare different methods of solving a problem
(b) Applying one algorithm that has been taught and getting that ‘one right answer
(c) Presenting too many ways to solve a problem and confusing the students
(d) Giving the students too much freedom to apply their mind
Answer: (b)
Explanation: Expecting all the students to understand the one algorithm taught in the class and getting that ‘one right answer’ is tyranny or cruelty to the students. Students think in multiple ways and have the potential to solve a problem in multiple ways. This potential of theirs should be encouraged. They should be left free to explore all the ways and then compare and decide which is the most appropriate one to solve the problem.
Q26. Which question can be answered with certainty after the evaluation of the course is completed?
(a) How to teach?
(b) Why to teach?
(c) What has been taught?
(d) What has been achieved?
Answer: (d)
Explanation: Evaluation helps ascertain what the students have achieved after the teaching activity has been completed.
Q27. Which of the following statements is incorrect?
(a) There are many ways of solving a problem.
(b) There are many procedures for computing a quantity
(c) Every problem in mathematics has only one specific algorithm to solve it.
(d) There are many ways of proving or presenting an argument.
Answer: (c)
Explanation: It is a wrong assumption that one problem has only one algorithm to solve it. There are many ways of solving a problem, many procedures for computing quantity, many ways of proving or presenting an argument. This is called ‘multiplicity of approaches’. Students should be given the freedom to use the approach that is most natural and easy for them.
Q28. 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)
Explanation: Communication in mathematics refers to expressing mathematical thinking by using mathematical language to present a problem, consolidate the given facts and organise them for analysis and interpretation.
Q29. What is regarded as the most important part of a mathematics teacher’s job?
(a) Covering all the topics mentioned in the curriculum
(b) Understanding the thinking of the children
(c) Instructional planning
(d) Both (b) and (c)
Answer: (d)
Explanation: Mathematics education focuses on explanation and demonstration methods. Therefore, the most important part of a mathematics teacher’s job is to understand the thinking of the children and engage in effective instructional planning.
Q30. A teacher is observing students working in groups. Her observation is focused on collaboration and cooperation in the group, the concentration and interest of each student and the participation of the individual students in the activity. Through this activity, she is trying to
(a) Do summative assessment of the students
(b) Do a formative assessment of the students
(c) Give training to the students to work in groups
(d) Give training to the students in life skills
Answer: (b)
Explanation: She is doing a formative assessment. Providing opportunities to students to work in groups and imparting training in life skills through such activities are part of the formative assessment itself.
