Quiz-6: Maths, Science and Pedagogy MCQ Questions with Answer

Explanation: aⁿ – bⁿ is always divisible by (a + b) if n is even.

2¹⁴ – 1= 2¹⁴ – 1¹⁴ ; As 14 is even, 2¹⁴ – 1¹⁴ is divisible by 2 + 1= 3

Explanation: x = 2³ x 3² x 5²

y = 2² x 3 x 5²

z = 2⁴ x 3³ x 5

2 – Lowest occurrence is 2 times.

3 – Lowest occurrence is 1 time.

5 – Lowest occurrence is 1 time.

H.C.F. = 2² x 3 x 5

Explanation: $\frac{\frac{1946}{-1a}}{19b7}$

Here, 7 is greater than 6.

There must be a carry-over of digits from 4 to 6.

If 6 becomes 16 and ‘a’ is subtracted from 16, we get 7.

∴ a = 16-7= 9

Now, 4 becomes 3 and 1 is subtracted from it.

∴  b= 3-1 = 2

Hence, a + b = 9+ 2 = 11

Explanation: On adding 331x + 337y = 360 and 337x + 331y = 308,

We get

668x + 668y = 668

⇒ x + y = 1 … (a)

On subtracting both equations, we get

–6x +6y = 52

⇒ –3x + 3y = 26 … (b)

From (a) × 3 + (b), we get

3x + 3y = 3
–3x + 3y = 26
____________
6у = 29

⇒ y = 29/6

Now, x + y = 1

⇒ x = $1-\frac{29}{6}=-\frac{23}{6}$

Explanation: Putting p(x) = 0, we have

2x²-8=0

⇒ 2x² = 8

⇒ x² = 4

⇒ x = ±2

Explanation: Since x – 2 is a factor of p(x), p(b) should be equal to zero.

Here, for p(x) = 2x² – 3x – 2

p(b) = 0

As 2(b)² – 3(b)-2 = 8-6-2 = 0

Explanation: If p(x) is divided by x – 3, the remainder is p(c).

p(c) = (c)⁴ + 3(c)² – 2(c)+7

= 81 +27 – 6 +7

= 109

Explanation: Two angles are complementary if they add up to 90 degrees.

72° + 18° = 90°

Explanation: 1 right angle = 90°

∴ 5 right angles = 90° 5 = 450°

Explanation: Mean =$\frac{\sum{x}}{N}$

= $\frac{42+45+50+52+55+56+60+62+64+66+68+70+71+72+74+80+82+85+90+92}{20}$

= $\frac{1336}{20}=66.8$

Explanation: Marks of 11 students in ascending order are:

10, 11, 15, 17, 20, 21, 32, 32, 33,

35, 41

Median = Size of $\left( \frac{N+1}{2} \right) ^{th}$item

Here, N = 11

M= $\left( \frac{11+1}{2} \right) ^{th}=6^{th}$ item

= Size of 6th item, i.e. 21

Therefore, median = 21

Explanation: The height of the bar corresponding to 4-5 is the maximum

So, the maximum number of students watched TV for 4-5 hours

Explanation: Area of equilateral triangle = $\frac{\sqrt{3}}{4}\left( side \right) ^2$

⇒  $4\sqrt{3}=\frac{\sqrt{3}}{4}\left( side \right) ^2$

⇒ (Side)² = 16

⇒ Side = 4

Perimeter = 3 x Side= 12 cm

Explanation: Let the original length and breadth be L and B

Area of original rectangle = LB

Length of new rectangle = $\frac{100-x}{100}L$

Breadth of new rectangle = $\frac{105+x}{100}B$

Area of new rectangle = $\left( \frac{100-x}{100}L \right) \left( \frac{105+x}{100}B \right) $

= $\frac{10500-5x-x^2}{10000}LB$

Now, $\frac{10500-5x-x^2}{10000}LB$ = LB

⇒ 10500 – 5x – x² = 10000

⇒ x² + 5x -500 = 0

⇒ (x + 25)(x-20) = 0

⇒ x = 20

Explanation: Volume of cone = $\frac{1}{3}\pi r^2h$

= $\frac{1}{3}\times \frac{22}{7}\times 14\times 14\times 24=4928$ m³

Explanation: $\frac{2}{5}\times 5\frac{1}{4}=\frac{2}{5}\times \frac{21}{4}=\frac{21}{10}$

Explanation: The portion between 0 and 1 is divided into 3 equal parts

Therefore, a = 1/3

Explanation: We have,

S= 2-3+4-5+ 6-7+8-9+…+50-51

= (2-3)+(4-5)+(6 – 7)+(8-9) +…+(50-51)

= (-1)+(-1)+(-1) + up to 25^th term

= -25

Therefore, additive inverse of S is 25.

Explanation: Since 4 is a composite number, 2 × 4 × 5 are not prime factors.

Explanation: The Square of an even number is even and the square of an odd number is odd. However, in the case of square root, it may not be true. For example, the square root of 3 is a fraction but not an odd number, and the square root of 6 is a decimal number but not an even number.

Explanation: The student knows the regrouping process after carrying over or borrowing, but he is careless, and most of the mistakes he makes are due to his absentmindedness. Though punishments and rewards may help sometimes, a habit of working carefully and ensuring that the sums are correctly solved can be developed through practice. The habit of self-checking answers helps minimise such errors.

Explanation: The discipline of mathematics has a logical structure because its most fundamental concepts include numbers, symbols, shapes, algorithms, axioms, theorems, proofs, etc. The understanding of mathematics requires critical thinking and reasoning.

Explanation: NCERT has suggested some directions in which action needs to be taken to overcome the problems of teaching. It has grouped these directions into four central themes. The Mathematisation of a learner’s mind is not stated as a central theme in the NCF document on teaching mathematics.

Explanation: The given approach is a constructivist approach. Under constructivism, students construct their own knowledge by testing ideas and approaches, based on their prior knowledge and experience.

In contextual learning, students plan and use their own experiences and process new knowledge with reference to their memory and everyday life experiences.

In cooperative learning, students carry out activities in groups under the supervision and guidance of a teacher. They exchange ideas through discussions in order to solve a problem.

In mastery learning, the whole curriculum content is broken down into small units and each unit is mastered one by one. The teacher makes sure that all students have mastered a unit taught before proceeding to the next unit.

Explanation: Adopting an exploratory approach, i.e. providing opportunities to explore problem situations using various manipulative and discussions with teachers and the peer group, provides a certain way of thinking and reasoning’ to the students. These not only help in developing manipulative skills and achieving narrow aims of education but also help students move towards achieving the higher aim of education. Rewriting a hundred textbooks or worksheets or providing special coaching is of little use if the students are not given hands-on experiences to which they can connect with real-life situations.

Explanation: Inductive method of teaching is always more helpful than the deductive method. Rather than loading and burdening a student with heavy terms or concepts, which they are not aware of, a teacher should try to make them draw conclusions by observing and exploring the situation.

Explanation: Roona has misaligned the numerals in columns for calculation. She seems to have problems with place value, which requires the understanding of the base ten systems, i.e. aligning numbers correctly before performing a mathematical operation.

Explanation: The competence of arranging numbers in ascending or descending order comes when students understand the concept of greater and smaller numbers. So, a student answering this question exhibits his/her “comprehension’ skill.

Explanation: The teacher is trying to develop an understanding of multiplication in her students. Multiplication as repeated addition is shown using a number of objects and activities. The students can learn by doing the operations on their own. The class in which students are engaged in activities is surely going to be interesting. Since only one type of activity is being done using different objects, we cannot say that the need of students for different learning styles is being catered to. Since the diagnosis of students’ problems will come after this phase is over, remedial teaching can be planned after that.

Explanation: Defective speech is the odd one among the given options because it is a subtype of physically exceptional children, while rapport building, individual traits and involvement or participation are attributes used during remedial teaching.