KTET Paper 2: Science and Mathematics Test - 3 - KTET MCQ

Let C.P. be Rs. 100.
Then, S.P. = Rs. 123.50
Let marked price be Rs. x.
Then, (95/100) x = 123.50
x = 12350/95 = Rs. 130
Now, S.P. = Rs. 130
C.P. = Rs. 100
Profit % = 30%

The number of atoms = (given mass/molar mass) x Avogadro number
N = (10/40) x 6.022 x 10²³
N = 1.5 x 10²³

Given :
CD || EF || AB , in the figure
Concept used :
The sum of adjacent angles between two parallel lines is 180°
Calculation :
In quadrilaterals CEFD,
∠E+∠F+∠ECD+∠D = 360
∠C = 360−(140+2y+x)
∠ECD = 220−2y−x
As CD || AB,
∠ABC=∠BCD=70°
∠BCD = ∠ECD + ∠BCE = 70° 
⇒ 220 - 2y - x + y = 70°  
⇒ x + y = 150°    -----(1)
As  EF || AB,
So, 2y + x = 180°  -----(2)
On solving (1) and (2), we get
x = 120° and y = 30°
∴ The answer is 120°.

Heuristics: The word "heuristic" is derived from the Greek word "Heurisco" meaning "I find out" 

• Heuristic Method" is one in which the students are left to find out things for themselves.
• The heuristic method is a method of teaching which involves placing children as far as possible in the attitude of a discoverer.
• In the heuristic method, the teacher is a guide and also a working partner.
• As a friend of students, this teacher should proceed on the way to discovering facts.
• He is to see that this classroom is pervaded by an atmosphere of freedom and that the work provided to the students encourages self-development, spontaneity, and self-expression.

Concept used:
Supplementary angles are those angles that sum up to 180 degrees. For example, angle 130° and angle 50° are supplementary angles because sum of 130° and 50° is equal to 180°
Calculations:
In a triangle, if angle A measures 60°, the measure of the adjacent angle to A is 120°.
These angles are called supplementary angles.
Hence, Option 2 is Correct.

Given:
Nitara has 20 pencils of 4 different colours
1. Nitara has red coloured pencils = 5
2. Nitara has blue coloured pencils = 4
3. Number of green coloured pencils = Twice that of blue coloured pencils
Calculation:
According to the question
Number of green coloured pencils = twice that of blue coloured pencils = (2 × 4)
⇒ 8
So, Number of black coloured pencils = [20 – (5 + 4 + 8)]
⇒ (20 – 17)
⇒ 3
∴ Statements 1, 2 and 3 all together are sufficient.

8 + (1/2 + 1/4) x 16
Concept:

Calculation

⇒ 8 + 12
⇒ 20
∴ The value of  8 + (1/2 + 1/4) x 16 is 20.

Vitamin-D:

• The chemical name of Vitamin D is Cholecalciferol.
• Its deficiency causes rickets.
• It was discovered by Edward Mellanby.
• It is fat-soluble.
• It is found in Fish, eggs, liver, mushrooms.

By calculating the values, we get
 = 0.1
 = 0.9
 = 1.1
 = 0.03
So, 0.1 + 0.9 + 1.1 + 0.03 = 2.13

The given numbers are 5.007, 5.018, 5.02, 5.12, and 5.18.
Median = 5.02
Mean = (5.007 + 5.018 + 5.02 + 5.12 + 5.18)/5 = 5.069
Thus, the required sum is 5.02 + 5.069 = 10.089
Hence, option (1) is correct.

Usually, the voice of a woman has a higher frequency and is shriller than that of a man.

Given:
Speed of the boat in still water = 15 kmph
The time taken by the boat to travel downstream is 1/5th the time taken to travel upstream
Concept:
(s₁)/(s₂) = (t₂)/(t₁), where s is the speed and t is the time.
Downstream = speed of boat + speed of stream
Upstream = Speed of boat - speed of stream
Calculation:
(upstream speed)/(downstream speed) = (downstream time)/(upstream time)
Then, ratio of upstream speed and downstream speed = 1 : 5
Let the upstream speed and downstream speed are x and 5x
Speed of the boat in still water = (5x + x)/2
⇒ 3x
3x = 15
⇒ x = 5
speed of stream = (5x - x)/2
⇒ 2x
⇒ 10 kmph
∴ The Speed of the stream is 10 kmph.

Critical angle:

• When the light rays pass from denser to rarer medium and due to a certain angle of incidence, the angle of refraction becomes 90o.This angle of incidence is called the Critical angle.

Total Internal reflection:

• Total internal reflection is a phenomenon of reflection of ray back to the same medium when passing from a denser medium to a rarer medium in such a way that the angle of incidence is greater than its critical angle.

Condition of Total internal reflection is-

• The light must travel from a denser medium to a rarer medium.
• The angle of incidence inside the denser medium must be greater than the critical angle.

Theorem used is: Lengths of tangents drawn from external points to a circle are equal.
Let AB touches the circle at point P, BC at Q, CD at R, DA at S.
So, AP = AS ---(i)
BP = BQ ---(ii)
CR = CQ ---(iii)
DR = DS ---(iv)
Adding (i), (ii), (iii), (iv), we get
AP + BP + CR + DR = AS + DS + BQ + CQ
AB + CD = AD + BC
AB + CD = AD + BC

mg_eh_e = mg_mh_m
We know,
g_m = (1/6) g_e
h_e = 1.5 m
h_m = ?
Putting values in equation,
h_m = 9 m

Calculation:
Let the number be x
Now, A/Q
⇒ x/8 + 5 = x/6 – 5
⇒ x/6 – x/8 = 10
⇒ x/24 = 10
⇒ x = 240
∴ The required number is 240

cos 132º + cos 12º + cos 156º + cos 84º
= 2 cos 72º cos 60º + 2 cos 120º cos 36º

= - (1/2)
The value of cos 12º + cos 84º + cos 132º + cos 156º = -(1/2)

Given:
The product of the two digits is 72.
The sum of two-digit is 17.
Calculation:
Let the unit place be x.
Let the ten's place be y.
According to the question:
The sum of two digit is 17.
⇒ x + y = 17
⇒ x = 17 - y
The product of the two digits is 72.
⇒ x × y = 72
⇒ (17 - y)y = 72
⇒ y² - 17y + 72 = 0
⇒ y = 9, 8
The ten's place = 8
The unit place = 17 - 8 = 9
The two digit number = 89
∴ The number is 89.

The teaching method is a way to put theory into practice with the help of principles, pedagogy, and management strategies. It helps the teachers to plan and present the lesson coherently.
There are different kinds of teaching-learning methods that make learning a fruitful process and the 'interactive method' is one of them.

An explanation method consists of one person talking to many about a topic or theme. The main purposes of an explanation method are to convey information, generate understanding, and stimulate interest.

In the words of David Wheeler, "It is more useful to know how to mathematise than to know a lot of Mathematics. The higher aim is to develop the child's resources to think and reason mathematically, to pursue assumptions to their logical conclusion and to handle abstraction." It includes a way of doing things, and the ability and the attitude to formulate and solve problems (NCF, 2005).

The teacher try to promote honesty through this problem as honesty refers to a facet of moral character and connotes positive and virtuous attributes such as integrity, truthfulness, straightforwardness, including straightforwardness of conduct, along with the absence of lying, cheating, theft, etc.

Neutralisation is a chemical reaction in which an acid and a base react quantitatively with each other. By helping the learner to experience daily life situations in which neutralisation is involved, students will identify neutralisation reactions and summarize observations with respect to behaviour of indicators in acidic and basic solutions and its characteristics on their own. So, this is the best teaching strategy followed by a physical science teacher who is most concerned about a visually challenged learner to teach neutralisation.

The Regional College of Education, Mysore (R.C.E.M) developed its system known as the R.C.E.M. In this system, mental skills are also considered very important. It accepted Bloom's Taxonomy as its foundation. Bloom has divided the cognitive objectives into six objectives, but the R.C.M.E. approach has transformed the six cognitive goals of Bloom into only four objectives. Bloom’s three most recent goals, namely analysis, synthesis, and evaluation have been termed ‘creativity, in the R.C.E.M. system. All mental abilities, involved in these four objectives, are grouped into 17 categories. Thus, we see that all human learning activities are divided into 17 mental skills.
Following are some examples of writing objectives in behavioral terms according to R.C.E.M. System-

• Cognitive Objective: The pupils can recall the definition of the term 'Motivation'.
• Understanding Objective: The pupils can differentiate teaching and training.

NCERT recommended that teaching and learning methods of science should totally shift from traditional approach and rote memorization. Viewing the student as an young explorer and scientist is one of the recommendations of NCERT.

Student draws neat and accurate figures. This specification relates to skill. As the skill is good, that is why the student is able to draw all figures neatly.

The correct sequence of making an electromagnet to achieve the desired result is as follows:
c. Wind a copper wire tightly around an iron nail.
d. Connect free ends of the wire to the terminals of a cell.
a. Place some pins near the end of a nail.
b. Switch on the current and observe what happens.

Given :  
(x² + 7x + 10) ÷ (x + 2)
Concept: 
The coefficient is the number multiplied by a variable.
Solution :

∴  the coefficient of x is 1.

One question of value 2 marks