Mathematics, Science and Pedagogy MCQ Questions | ||
Quiz-1 | Quiz-2 | Quiz-3 |
Directions (Q. 1-60): Answer the following questions by selecting the most appropriate option.
Q1. Which of the following fractions is greater than and less than
(a)
(b)
(c)
(d)
Answer: (b) Explanation: Make the denominators same in all the given fractions LCM of 5, 10, 15 = 30 $\frac{3}{5}=\frac{18}{30}$, $\frac{11}{15}\,\,=\frac{22}{30}$, $\frac{9}{10}=\frac{27}{30}$, $\frac{12}{15}=\frac{24}{30}$ Fraction between $\frac{2}{3}=\frac{20}{30}\,\,and\,\,\frac{4}{5}=\frac{24}{30}$ is $\frac{22}{30}=\frac{11}{15}$ |
Q2. 2 × 10^{5} + 3 × 10^{3} + 5 × 10^{2} + 6 is equal to
(a) 2003005006
(b) 2356 x 10^{5}
(c) 203506
(d) 2030506
Answer: (c) Explanation: 2 x 10^{5} + 3 x 10^{3} + 5 x 10^{2} + 6 = 200000 + 3000 + 500 + 6 = 203506 |
Q3. The greatest number of four digits that is divisible by 3, 7, 15 and 18 is
(a) 9450
(b) 9999
(c) 9500
(d) 9834
Answer: (a) Explanation: The greatest number of four digits is 9999 LCM of 3, 7, 15 and 18 is 630. On dividing 9999 by 630, the remainder comes out to be 549. Required number = 9999 – 549 = 9450 |
Q34. Factorise 25x² + 80x + 64.
(a) (X + 8)^{2}
(b) (5x–8)^{2}
(c) (5x+8)^{2}
(d) (x – 8)^{2}
Answer: (c) Explanation: 25x² +80x + 64 = (5x)^{2} + 2(5x)(8)+(8) = (5x+8)² |
Q5. Find the zeros of the polynomial p(x) = 2x^{2} – 7x-4.
(a) 0.5 and 4
(b) -0.5 and -4
(c) -4 and 0.5
(d) -0.5 and 4
Answer: (d) Explanation: Putting p(x) = 0 we have 2x^{2} – 7x – 4= 0 ⇒2x² – 8x + x – 4= 0 ⇒ 2x(x – 4) + 1(x – 4) = 0 ⇒ (x-4) (2x+1) = 0 ⇒ x = 4, or 2x = –1 or x = – 0.5 |
Q6. The sum of three consecutive even integers is 36.
Find the largest integer.
(a) 10
(b) 12
(c) 14
(d) 16
Answer: (c) Explanation: Let the smallest integer be x Therefore two other integers are x + 2 and x + 4 x + x + 2 + x + 4 = 36 ⇒3x + 6 = 36 ⇒3x = 30 ⇒ X = 10 So, the three integers are 10, 12 and 14 Hence, the largest integer is 14 |
Q7. The length of a rectangle is 3 cm more than its breadth. If its perimeter is 34 cm, find its length.
(a) 7 cm
(b) 10 cm
(c) 17 cm
(d) 13 cm
Answer: (b) Explanation: Let the breadth of the rectangle be x Then, the length of the rectangle = x + 3 Perimeter = 34 cm ⇒ 2(x + x + 3) = 34 ⇒ 2x + 3 = 17 ⇒ 2x = 14 ⇒ x = 7 cm Breadth = 7 cm Length = 7+3= 10 cm |
Q8. The sum of all exterior angles of a convex polygon having 5 sides is
(a) 540°
(b) 360°
(c) 720°
(d) 900°
Answer: (b) Explanation: The sum of all the exterior angles of any polygon is 360°. |
Q9. A polygon with the minimum number of sides is a/an
(a) Pentagon
(b) Square
(c) Triangle
(d) Angle
Answer: (c) Explanation: A pentagon has 5 sides, a square has 4 sides, and a triangle has 3 sides. An angle is not a polygon. So, a polygon with the minimum number of sides is a triangle. |
Q10. The sides of a triangle are 3.4 cm, 5 cm and x cm, where x is a positive number. What is the greatest possible value of x among the following?
(a) 7.9
(b) 8.0
(c) 8.1
(d) 8.2
Answer: (d) Explanation: We know that the largest side of a triangle is less than the sum of its two other sides. In the given options, the greatest value that is less than 8.4 is 8.2. |
Q11. Which of the following is an acute angle?
(a) 54°
(b) 95°
(c) 172°
(d) 90°
Answer: (a) Explanation: An angle less than 90° is an acute angle. |
Q12. Find the volume of a hemisphere whose radius is 21 cm.
(a) 14553 cm^{3}
(b) 29106 cm^{3}
(c) 19404 cm^{3}
(d) 1525 cm^{3}
Answer: (c) Explanation: Volume of hemisphere = $\frac{2}{3}\pi r^3$ =$\frac{2}{3}\times \frac{22}{7}\times 21^3$ = 19404 cm^{3} |
Q13. Find the curved surface area of a right circular cylinder whose radius is 14 cm and height is 12 cm.
(a) 1056 cm^{2}
(b) 528 cm^{2}
(c) 2112 cm^{2}
(d) 3145 cm^{2}
Answer: (a) Explanation: Curved surface area of cylinder = 2nrh = $2\times \frac{22}{7}\times 14\times 12$ = 1056 cm^{2} |
Q14. The radii of two spherical balls are in the ratio of 2:3. What is the ratio of their volumes?
(a) 2:3
(b) 4:9
(c) 8:27
(d) 3:2
Answer: (c) Explanation: Let the radii of two spheres be 2r and 3r. Volume of the first spherical ball, V_{1} = $\frac{4}{3}\pi \left( 2r \right) ^3$ Volume of the second spherical ball, V_{2} = $\frac{4}{3}\pi \left( 3r \right) ^3$ Ratio = $\frac{\frac{4}{3}\pi \left( 2r \right) ^3}{\frac{4}{3}\pi \left( 3r \right) ^3}=\frac{8}{27}$ = 8 : 27 |
Q15. If the median of 15, 18, 21, x, x + 2, 30, 35 and 40 is 25, find the value of x.
(a) 21
(b) 23
(c) 19
(d) 24
Answer: (d) Explanation: Here, n is even, i.e., 8 ∴ Median = $\frac{\left( \frac{n}{2} \right) ^{th}observation\,\,+\left( \frac{n}{2}+1 \right) ^{th}observation\,\,}{2}$ ⇒ 25 = $\frac{\left( \frac{8}{2} \right) ^{th}observation\,\,+\left( \frac{8}{2}+1 \right) ^{th}observation\,\,}{2}$ ⇒ 25 = $\frac{4^{th}observation\,\,+5^{th}observation\,\,}{2}$ ⇒50 = x + x + 2 ⇒48 = 2x ⇒ X = 24 |
Q16. The mean of 50 observations was found to be 45. Afterwards, it was discovered that the values of two items were misread as 12 and 19, instead of 21 and 91 respectively. Find the correct mean.
(a) 46
(b) 47
(c) 46.62
(d) 46.52
Answer: (c) Explanation: Sum of 50 numbers = 50 x 45 = 2250 Correct sum of 50 observations = 2250 – (12 + 19) + (21 + 91) = 2331 Correct mean = $\frac{2331}{50}$ = 46.62 |
Q17. Four positive integers a, b, c and d are such that a + b = 15, b + c = 17, c + d = 21 and d + a = 23. What is the mean of a, b, c and d?
(a) 8
(b) 9
(c) 10
(d) 9.5
Answer: (d) Explanation: a+b = 15 b+c=17 C + d = 21 d + a= 23 Adding all these, we get 2a + 2b + 2c + 2d= 76 a + b + c + d = 38 Mean = $\frac{Sum\,\,of\,\,all\,\,observations}{Total\,\,number\,\,of\,\,observations}$ = $\frac{38}{4}=9.5$ |
Q18. The largest factor of 280 is
(a) 140
(b) 280
(c) 2
(d) 279
Answer: (b) Explanation: The largest factor of any number is that number itself. |
Q19. Shown below are expressions given to Nishima, Shweta, Rahul and Pranjal, with their answers:
Nishima: 4 – 16 ÷ 8 + 2 = 0
Shweta: 12 – 6 ÷ 2 x 8 = 0
Rahul: 12 ÷ 6 – 2 x 8 = 1
Pranjal: 24 ÷ 8 – 3 × 1 = 0
Who has got the correct answer?
(a) Nishima
(b) Shweta
(c) Rahul
(d) Pranjal
Answer: (d) Explanation: As per the rule of BODMAS, first divide, then multiply, then add and then subtract ∴ 24 ÷ 8 – 3 × 1 = 3 – 3 = 0 Thus, Pranjal has got the correct answer |
Q20. The value of $7+\frac{7}{10}+\frac{7}{100}+\frac{7}{1000}$ is
(a) 7.777
(b) 7.077
(c) 7.707
(d) 7.007
Answer: (a) Explanation: $7+\frac{7}{10}+\frac{7}{100}+\frac{7}{1000}$ = 7 +0.7 +0.07 +0.007 =7.777 |
Q21. Which one of the following is the correct reason to assign homework to the students of upper primary classes?
(a) To relieve the teacher from teaching some part of the syllabus in the class
(b) To make students practice
(c) To ensure that the students do not have too much of leisure time available at home
(d) To deal with the problem of covering all topics and sub-topics mentioned in the curriculum
Answer: (b) Explanation: Homework is given to students primarily to inculcate the habit of self-study and to practice the lesson taught in school. |
Q22. “All students can learn mathematics and that all students need to learn mathematics.” This expectation reflected in NCF 2005 can be achieved by
(a) Grouping the students ‘ability wise’ and adopting different methods of teaching
(b) Developing an easy curriculum for weak students
(c) Providing situations that engage and challenge students
(d) Assigning more periods to mathematics in the school timetable
Answer: (c) Explanation: The students need to be involved in challenging tasks. There should be adrift from the focus on repetitive tasks (which are often boring) to challenge students with meaningful problems. Hands-on activities, group work, problem-solving etc. provide an environment where students can indulge in intense and joyful mathematical learning. |
Q23. Which of the following statements about mathematics is least appropriate?
(a) It is a language in itself.
(b) It is based on a set of assumptions that are built using logic.
(c) It has its own set of symbols, words and syntax.
(d) It is independent of any understanding of a language.
Answer: (d) Explanation: If a student does not understand language, he would probably not understand mathematics. Mathematics is a language in itself and has its own set of symbols, words and rules of syntax. |
Q24. A student was asked to express 5 m in cm. His answer was 50 cm. What type of error is it?
(a) Regrouping error
(b) Basic fact error
(c) Wrong algorithm
(d) Incorrect operation
Answer: (b) Explanation: It is a basic fact error. The student does not know that 1 m = 100 cm. |
Q25. Who said that “Mathematics is the classification and study of all possible patterns”?
(a) Bertrand Russell
(b) Walter Sawyer
(c) J. J. Sylvester
(d) John Locke
Answer: (b) Explanation: It was Walter Warwick Sawyer who said that mathematics “is the classification and study of all possible patterns”. |
Q26. The problem sums like “Mother made 180 puris, 5 people ate 32 puris each, and how many were left?”
Provide
(a) Scope for promoting gender bias
(b) An easy way to understand word problems
(c) No correlation to real-life situations
(d) Increased difficulty level of problems
Answer: (b) Explanation: Such problem sums are related to real-life situations and so are easy to understand. |
Q27. It is argued that mathematics should be the first subject to be taught to children because
(a) It helps in making the brain think more logically than creatively
(b) It inculcates the habit of reasoning at an early stage
(c) It enables them to become mathematicians
(d) It helps them qualify for higher studies
Answer: (b) Explanation: To turn the children into mathematicians or to enable them to qualify for higher studies is not the qualifying reason for teaching mathematics at an early stage. Mathematics also does not hinder Mathematics helps in shaping the brain to think logically in order to inculcate the habit of reasoning. |
Q28. Which one of the following techniques is not appropriate for students to learn mathematics in a class?
(a) Listening to the teacher carefully
(b) Observing how the teacher solves a problem
(c) Trying to solve the problems on their own
(d) Thinking about a problem deeply
Answer: (d) Explanation: Merely thinking about a problem does not necessarily lead to working out a solution to the problem. Moreover, thinking about a problem is not a part of the methods on which the techniques of teaching mathematics are based. |
Q29. A teacher divides the class into groups of 4 children each and gives a squared paper to each group. She gives them the following instructions, “Cut as many rectangles as possible of 24 square units each. After cutting out such rectangles from the squared paper, find out their perimeters and try to see which rectangle has got the biggest perimeter?”
What is the purpose of this activity?
(a) To engage the students in an activity so that they can finish their work
(b) To make the students work in groups so that they may socialise
(c) To assess the understanding of the students about the area and perimeter of rectangles
(d) To prepare material for the mathematical wall
Answer: (c) Explanation: Assessing the understanding of her students about the area and perimeter of rectangles is what the teacher targets through this activity. She is in fact doing a formative assessment to find out how much the students have assimilated and how to proceed next on this topic. |
Q30. A teacher explained the concept of similarity and congruence of triangles to her class. The next day, she drew two triangles on the blackboard and asked the students, “How do you know if these two triangles are similar or congruent?” To her surprise, she found that only a few students were able to answer the question correctly. What could be the reason for this?
(a) The concept was not taught properly to the class
(b) The teacher could not come up with an effective instructional strategy appropriate for the students
(c) The teacher did not draw the two triangles in the previous class while explaining the concept.
(d) Students were not willing to learn the concept
Answer: (b) Explanation: As only a few students were able to answer the question, the teacher has to change her instructional strategy to attain the teaching objective of the class. She needs to redesign her instructions in such a way that students are able to understand the concept effectively. |