KTET Paper 2: Science and Mathematics Test - 5 - KTET MCQ

Given:
The total simple interest got in Rs 500 in 8 years and Rs 300 in 16 years is Rs 1100
The rate of interest is the same for both cases.
Formula used:
Simple Interest (SI) = (Principal (P) × Rate of interest (R) × Time (T)) / 100
Calculation:
Let, the rate of interest be R
As per the question,
1100 = (500 × R × 8) / 100 + (300 × R ×16) / 100
⇒ 1100 = (4000 × R) / 100 + (4800 × R) / 100
⇒ 1100 = (40 × R + 48 × R) 
⇒ 88R = 1100
⇒ R = 1100 / 88
⇒ R = 100 / 8
⇒ R = 12.5 %
∴ The rate of interest is 12.5 %

Given:
-60 ÷ [(-4) × (-2) – (-3) × 4]
Concept used:
Simplify using BODMAS: Bracket – of – Division – Multiplication – Addition – Subtraction
Calculation:
-60 ÷ [(-4) × (-2) – (-3) × 4]
⇒ -60 ÷ [8 + 12]
⇒ -60 ÷ 20
⇒ (-3)

Food:  

• When we get hungry we take food items from plants and animals as a food and it provides energy which increases the working capacity of the body.
• It is a substance that when consumed its provide nutritional support to an organism.

Components of Food:

• The ingredients of food which are beneficial to our body's growth and development are called components of food:

Components of food are
a) Carbohydrate
b) protein
c) Fat
d) Vitamin
e) Minerals(salts)
f) water
g) Roughage

Rearranging the series,
S = (1 + 3 + 5 + 7 + 9 + ... + 49) + (- 2 - 4 - 6 - 8 - 10 - ... - 50)
Now, we get two arithmetic progressions with common difference of 2.
Using the formula for sum of A.P. to get
S = 25(1 + 49)/2 - [25(2 + 50)/2]
= 25(50)/2 - 25(52)/2
= 25 x 25 - 25 x 26 = 25(-1) = -25
Now, the additive inverse (same number with an opposite sign) is -(-25) = 25.

After vigorous exercise, muscles generate energy anaerobically. This energy comes from glucose through a process called glycolysis, in which glucose is broken down or metabolised into a substance called pyruvate through a series of steps. When the body has plenty of oxygen, pyruvate is shuttled to an aerobic pathway to be further broken down for more energy. But when oxygen is limited, the body temporarily converts pyruvate into a substance called lactate, which allows glucose breakdown and thus energy production to continue.

We usually think of plants being green. It sounds like green pigment 'chlorophyll' is important in photosynthesis. But there are actually many pigments that can trap light for photosynthesis. Pigments like carotenoids can capture energy not absorbed by chlorophyll. There are at least 600 known carotenoids, divided into yellow xanthophylls and red and orange carotenes. They absorb blue light and appear yellow, red, or orange to our eyes. Anthocyanin is another important pigment that is not directly involved in photosynthesis. That is why the statement given in option (1) is correct, i.e. irrespective of colour, all leaves carry out photosynthesis.

OY is the bisector of ∠AOC = 2 ∠COX.
∴ ∠BOC = 2 ∠COY
∴ ∠AOC + ∠BOC
⇒ 2∠COX + 2∠COY = 180°
⇒ 2(∠COX + ∠COY) = 180°
⇒ 2∠XOY = 180°
⇒ ∠XOY = 90°
∴ ∠AOX + ∠XOY + ∠BOY = 180°
⇒ ∠BOY = 180° - 20° - 90° = 70°.

Given:
The height of the tank = 10 m
The length of the tank = 20 m
The width of the tank = 15 m
Formula used:
The surface area of the cuboid = 2 × (ab + bc + ca)     Where, a = The length of the cuboid, b = The width of the cuboid and c = The height of the cuboid
Calculation:
Let us assume the total cost of the plastering be X
⇒ The total surface arae of the tank = 2 × (20 × 15 + 15 × 10 + 10 × 20) = 2 × (300 + 150 + 200) = 650 × 2 = 1300 m2
⇒ The surface for plastering = 1300 - (15 × 20) = 1000 m2
⇒ The cost of the plastering of the tank = 1000 × 0.80 = 800 rupees
∴ The required result will be 800. 

• An ammeter has very little resistance so that it passes maximum current through it.
• An ammeter is a device, which used to measure current in a circuit in the milliampere or microampere range.
• As it requires the maximum pass of current through the ammeter to measure the current correctly, the resistance is kept very low in it.
• It is attached in series of the circuit.

Area of trapezium = (1/2) x  (Sum of parallel sides) x Distance between the parallel sides
720 = 0.5 x (35 + y) x 20
72 = 35 + y
y = 72 - 35
y = 37 m

x² + 7x + 10 = x² + 2x + 5x + 10 = x(x + 2) + 5(x + 2) = (x + 5)(x + 2)
x² - 3x - 10 = x² - 5x + 2x - 10 = x(x - 5) + 2(x - 5) = (x + 2)(x - 5)
Thus, (x + 2) is a common factor.
Hence, option (3) is correct.

Let the polygon has 'n' sides.
So, (n - 2)180º = 1440º
Or, n = 10
Thus, option (3) is correct.

Sum of non-parallel sides is 20 cm and perimeter is 58 cm.
So, sum of parallel sides (2 bases) = 58 - 20 = 38 cm
Area of trapezium = 1/2 × sum of bases × height
Let distance between the parallel sides, i.e., height be H.
So, according to the question,
1/2 × 38 × H = 152
So, H = 8 cm

Formula Used:
Probability = Number of favorable event/Total number of event
Calculation:     
Prime number are 29, 31, 37, 41, 43, 47
Total number of events = 25
Favorable events = 6
⇒ Probability = 6/25 = 0.24
∴ The probability to be a prime number is 0.24
The correct option is 3 i.e. 0.24

Plane Mirror: A plane mirror is a mirror with a flat (planar) reflective surface.

The characteristics of an image formed in a plane mirror:

• The image formed by the plane mirror is virtual and erect i.e. image cannot be projected or focused on a screen.
• The distance of the image ‘behind’ the mirror is the same as the distance of the object in front of the mirror.
• The size of the image formed is the same as the size of the object.
• The image is laterally inverted, i.e. left hand appears to be right hand when seen from the plane mirror.
  
• If the object moves towards (or away from) the mirror at a certain rate, the image also moves towards (or away from) the mirror at the same rate.

From above it is clear that images are formed by the Plane mirror is virtual, erect, and laterally inverted.

Given:
The length of a rectangular field is twice its breadth.
The area of the field is 288 sq.m.
Concept used:
Area of a rectangle = Length × Breadth
Calculation:
Let the length and breadth of the rectangular field be 2d and d meter respectively.
According to the concept,
2d × d = 288
⇒ 2d² = 288
⇒ d² = 144
⇒ d = ± 12
⇒ d = +12 (length can't be negative)
⇒ 2d = 24
∴ The length of the field is 24 meter.

Perimeter of Rhombus = 4 × Side
⇒ 100 cm = 4 × side
⇒ Each Side of Rhombus = 100/4 =  25 cm

In triangle AOB;
(AB)² = (OB)² + (AO)² 
⇒ (25)² = (7)² + (AO)² 
⇒ (AO)² = 625 - 49
⇒ (AO)² = 576 cm2 
⇒ AO = 24 cm
The value of AC = 2 × AO
The value of AC = 2 × 24 = 48 cm
Area of Rhombus ABCD = (1/2) × 48 × 14 = 336 cm²
∴ The area of rhombus ABCD is 336 cm²

Assessment is the second stage of evaluating a student’s performance. It makes a student’s performance more meaningful. Summative assessment is used for assigning a grade or certifying a student’s achievement at the end of the course or a unit. It is created based on predetermined learning outcomes and used to determine whether or not students have met the learning objectives.

Science is any system of knowledge concerned with the physical world; it focuses on the natural world around us; it is a way of life-based on rational thought, and it is a way of life.

• The way to learn Science is to do Science. 
• Science cannot be taught through books alone. It is always experimented with, observed, and experienced through several practical activities done inside and outside the school by the learner.
• For effective science teaching, there is a need for co-curricular activities and various other approaches like the organization of field trips, organizing quizzes, and laboratory along with different activities.

A teacher asks the students to find the number of possible pentominoes using five squares and then further explore the number of possible hexominoes and so on. These types of activities help the child to identify relation between number pattern and shapes. For a long, geometry and trigonometry have wisely been regarded as the arena wherein students can learn to appreciate this pattern and shape best. In the elementary stage, if students have learned many shapes and know how to associate quantities and formulas with them, here they start reasoning about these shapes using the defined quantities and formulas.

A student verifies the outcome when two fractions are multiplied together. This specification belongs to the objective of understanding as it shows that student is verifying the understanding about the concept.

The purpose of the teacher to ask this question is to investigate students' prior ideas related to human body and digestion so that future teaching-learning sessions can be accordingly planned.

Given:
In ΔABC, D is a point on BC 
∠ADB = 2∠DAC
∠BAC = 70° and ∠B = 56°
Concept Used:
linear pair of angles 
Sum of linear pair of angles = 180° 
Sum of angles of triangle = 180° 
Calculation:

Let ∠DAC = x° 
So, ∠ADB = 2x° 
Since, ∠BAC = 70° 
So, ∠BAD = (70 - x°)
Now, In ΔABD 
56° + 2x° + 70 - x° = 180° 
⇒ x = 54° 
⇒ 2x = 108° 
Now, By linear pair of angles 
∠ADB + ∠ADC = 180° 
⇒ 2x + ∠ADC = 180° 
⇒ 108° + ∠ADC = 180° 
⇒ ∠ADC = 180° - 108°
⇒ ∠ADC = 72° 
∴ The required measurement of angle is 72°.

The teacher has the moral responsibility of taking into consideration the ability and aptitude of learners and guiding them accordingly. Teachers should try to make the class an environment that motivates learners to fare according to their capability and capacity.

Learning doesn't only mean taking place in the classroom with the guidance of the teacher but it can take place anywhere. Children come to school already with a lot of experiences, they learn through different processes. 

Absenteeism: It is a measure of students missing a defined number of school days for any reason, including both authorized and unauthorized absences.

Absenteeism could be tackled by:

• Making students aware of the benefits of attending regular classes.
• Promptly investigating absenteeism by coordinating frequently with the parents and enquiring about their child’s absence
• Employing different strategies to encourage good attendance by way of personal example by staff members
• Maintaining strict criteria on whether or not to authorize an absence

l = Lower limit of the median class, where median class is that class where (n/2)^th item is lying
C = Cumulative frequency of the class preceding the median class
f = Frequency of the median class
i = Class interval of the median class

Science involves the process of observation, experiments, research, analysis, and investigation. It is a subject that is purely based upon facts that are proven with the help of various scientific techniques. To solve a problem scientifically, one must have a scientific attitude or temper which will help a person to solve problems in a systematic and organized manner by being objective and realistic. Scientific attitude is the tendency to think creatively and behave practically by being realistic in nature. 

Key Points

• The major problem of copying verbatim from books and encyclopedias affects the learning and thought processes of students.
• Students should have good knowledge of the topic, can use books, articles, videos and other sources before starts writing to do research works.
• It may help the student to broaden their knowledge and enhance the capability to use their own thought or words ethically and intelligently. 
• The teacher must encourage students to behave ethically, they can use different sources to enhance their knowledge but it should not be copied from any sources.

Hence, when upper-grade children do research work, the major problem the teacher has to contend with is discouraging children from copying verbatim from books and encyclopedias and guiding them effectively.