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

l || m 

Concept used:
For two parallel lines,
Corresponding angles are equal.
Vertically opposite angles are equal.
Calculation:
∠110° = ∠p (Vertically opposite angles) 
∠p + ∠r₁ + ∠r₂ + ∠110° = 360°
⇒ ∠110° + ∠r₁ + ∠r₂ + ∠110° = 360°  (∠r₁ = ∠r₂, vertically opposite angles)
⇒ 2∠r₁ = 140°
⇒ ∠r₁ = 70°
Now, ∠r₁ = ∠a (Corresponding angles)
∠a = 70°
Also, ∠a + ∠b = 180° (supplementary angles)
⇒ ∠b = 180° - 70° = 110°
∴ The measure of angles marked by a and b is 70° and 110° respectively.

​Mathematics is a study of patterns, numbers, geometrical objects, data, and information. It deals with data analysis, integration of various fields of knowledge, deductive and inductive reasoning, and generalizations.

• The teacher while asking questions in the mathematics classroom should focus more on providing practical exercises and abstract knowledge to students to foster their individualized discovery-oriented learning.

Mean of 10 numbers = 0
Sum of 10 numbers = 0
Sum of 12 numbers = 0 + 72 - 12 = 60
Mean of these 12 numbers = 60/12 = 5

g = GM_e/R_e²
D_s = 0.5 D_e; M_s = 0.1 M_e
g' = GM_s/R_s² = G x 0.1 M_e/0.25 R_e² = 0.4 g

Given:
Central angle for Hindi: 65° Central angle for Mathematics: 85°
Concept used:
To find the difference between the marks obtained in Mathematics and Science, we need to calculate the respective central angles for each subject and then use them to determine the marks obtained
Calculation:
Calculate the total of all central angles: Total of central angles = 65° + 53° + 85° + 81° + 76° = 360°
Calculate the marks obtained in Science and Mathematics using the central angles: Marks obtained in Science = (81° / 360°) ×  Total marks = (81/360) ×  630 = 141.75 (approximated to 114 marks)
Marks obtained in Mathematics = (85° / 360°) ×  Total marks = (85/360) × 630 = 148.75 (approximated to 149 marks)
Calculate the difference in marks between Mathematics and Hindi: Difference = Marks obtained in Mathematics - Marks obtained in Hindi Difference = 149 - 141 = 8 marks
Hence, the student obtained 35 more marks in Mathematics than in Science.

Given:
x² + (2x/5) + (1/25) = 0 
Formula used:
(a + b)² = a² + b² + 2ab 
Calculation:
x² + (2x/5) + (1/25) = 0 
⇒ x² + 1/(5²) + 2 × x × 1/5 = 0
⇒ (x + 1/5)² = 0
⇒ x = -1/5 
Now, (x−(2/3))² = (-1/5 -2/3)²
⇒ (- 13/15)²
⇒ 169/225 
∴ The required result is 169/225.

Given:
numbers are 
Concept used: 
To find ascending order of fraction we need to get the LCM of the denominator
Calculation:
LCM of -9, 18, -6, 3 = 18
Multiplying each fraction with 18
So, numbers are = - 8, 7, - 15, 12
So, order is = - 15, - 8, 7, 12
∴ Requried answer is is  - 5/6

• An adaptation seen in the camel is that it can close its nostril.
• This helps to prevent sand from entering the nasal cavity.
• Camels adapt very well methods for their survival in the desert. 
• To spread their weight on the sand Camels have a large and flat fleet.
• For shade Camels have thick fur on the top and thin fur elsewhere to allow easy heat loss.
• Camels have thick eyebrows and two rows of long eyelashes to protect their eyes from the desert sun.
• Camels have tough and large lips that enable them to pick at dry and thorny desert vegetation.
• Camels have three stomach compartments for the proper digestion of different kinds of food.

(x + 1)⁴ - (x - 1)⁴ = ((x + 1)² + (x - 1)²)((x + 1)² - (x - 1)²)
= (x² + 1 + 2x + x² + 1 - 2x)(x + 1 - (x - 1))(x + 1 + x - 1)
= 2(x² + 1)(2)(2x)
= 8x(x² + 1)
Now, let 'x' be an even number, say 2a.
The number becomes 8(2a)((2a)² + 1) = 16a(4a² + 1) = 16b
If 'x' is an odd number, say 2a + 1, the number becomes 8(2a + 1)((2a + 1)² + 1).
= 8(2a + 1)(4a² + 1 + 4a + 1)
= 8(2a + 1)(4a² + 4a + 2)
= 8(2a + 1)(2)(2a² + 2a + 1)
= 16(2a + 1)(2a² + 2a +1)
= 16c
Thus, the given expression is always a multiple of 16 and hence, divisible by 16.
Thus, option (1) is correct.

To represent equal numerical values, same type of diagrams are used in pictographs. A pictograph is a way of showing data using images. Each image stands for a certain number of things.

The deficiency in copper can cause many hematological manifestations, such as myelodysplasia, anemia, leukopenia (low white blood cell count) and neutropenia (low count of neutrophils, a type of white blood cell that is often called "the first line of defense" for the immune system).

Given:
 = Ax² + By² + Cxy
Formula used:
a³ - b³ = (a - b)(a² + b² + ab)
Calculation:

About Desert Oak:

• It is found in the dry and arid regions of Australia.
• It grows almost 10 ft tall.
• It has very few leaves
• Its roots go very deep in search of water.
• The depth of these roots is nearly 30 times the height of the tree. 
• This water is stored in the tree trunk. 
• Local people use a thin pipe to drink this water.

Time taken by the car to cover the 1st km = 1/30 hrs
Time taken by the car to cover the 2nd km = 1/40 hrs
Total time taken to cover 2 km =  hrs
Thus, average speed =   km/hr =  km/hr
Hence, answer option 2 is correct.

When an object is placed between C and F, the reflected rays meet at a point beyond C and the image is real, inverted and magnified.

For a convex lens, when the object is between F₁ and 2F₁, a real, inverted and enlarged image will form beyond 2F₂.

Given: 
Three positive numbers are in the ratio 2 ∶ 3 ∶ 4.
The sum of their squares is 2349.
The average of the first two numbers 
Calculation:
Let the numbers be 2x, 3x, 4x 
⇒ 4x² + 9x² + 16x² = 2349
⇒ 29x² = 2349 
⇒ x = √2349/29
⇒ √81 = 9
⇒  x = 9
⇒ Two numbers = 2x, 3x = 18 and 27
⇒ The average of the first two numbers = (18 + 27)/2 = 22.5
∴ The average of the first two numbers is 22.5.

The student needs to understand the concept related to the topic, he needs to comprehend what is asked and then have to apply a procedure to arrive at a solution. The knowledge of the concept only will help him to know about the procedure which should be used for the problem.

The Taj Mahal is a world renowned monument having symmetry both inside and outside. There is equal distance of windows and doors from one another, the formations of the minarets, and the proportions of the domes to the arch ways denote that it is constructed taking into consideration order, similarity and sequence. The stones lie in a distinctive pattern of four-pointed stars (red sandstone) and diamonds (marble).

Audio visual aids are those devices which are used in classrooms to encourage teaching learning process and make it easier and interesting. According to William. H. Burton, "Audio visual aids are those sensory objects or images which initiate or stimulate and reinforce learning".

Mathematics is a branch of science which deals with counting, calculating, and studying numbers, shapes, and structures. 
There is 6 Development Phase in Mathematics:

• Emergent Phase: Recognize that numbers may be used to signify quantity.
• Matching Phase: Understanding of counting or numeric values.
• Quantifying Phase: In this phase, the students are able to quantify the objects by automatic recognition.
• Partitioning Phase: Splitting of large numbers into smaller ones to solve easily.
• Factoring Phase: Factoring complex numbers into simple.
• Operating Phase: In this phase, the students are able to perform basic operations on whole numbers, fractions, and decimal numbers.

Thus, if a learner is able to perform the four basic operations on whole numbers, fractions, and decimal numbers, the learner is at the operating phase.

Biodiversity is the diversity of and in living nature. Diversity, at its heart, implies the number of different kinds of objects, such as species. It is a measure of the relative diversity among organisms present in different ecosystems. 

Given:
2460375= 3375 × 729
Calculation:
∛2460375= ∛(3375 × 729) 
= ∛(153 × 93) = 15 × 9 
∛2460375= 135

• The National Policy on Education 1986 proposed that “Mathematics should be visualized as the vehicle to train a child, to think, reason, analyze and to articulate logically.
• There is a shift in treating mathematics education as an instrument for the National development to the development of a child’s abilities.
• This has been carried forward further in the National Curriculum Framework 2005 wherein child’s active engagement in mathematics learning involving “inquiry, exploration, questioning, debates, application and reflection leading to theory building and creation of ideas/positions in Mathematics” is envisaged.

Science (from the Latin word Scientia, meaning knowledge) is the activity and application of knowledge and understanding of the social and natural world around us followed by systematic approach based on evidence.

• Technology is the application of scientific knowledge for practical purposes. To achieve goals, skills methods, and processes used is called technology.
• The science includes the study of the physical and biological world around us through several approaches like observation, experimenting, inference, etc while technology involves the application of that scientific knowledge for practical purposes.

Here, 'ambitious' refers to seek higher aims of teaching Mathematics in schools.

Hyperactive students find it difficult to concentrate for a long time. They need the freedom to learn in short spans. Hyperactive students usually refer to constant activity, being easily distracted, inability to concentrate, impulsiveness. Therefor, a tightly structured lesson of physics if taught with little flexibility is least conducive to the learning of the student who is hyperactive.

Concept:
Complementary angles: The pair of angles whose sum is equal to 90° are complementary angles.
Supplementary angles: The pair of angles whose sum is equal to 180° are supplementary angles.
Explanation:
Let the acute angle be a°.
⇒ Complementary angle of a° = (90 - a)° 
Also, Supplementary angle of a° = (180 - a)° 
∴ Difference between supplementary and complementary angles = (180 - a)° - (90 - a)° 
⇒ 180 - a - 90 + a 
⇒ 90° 
Hence, the difference between complementary and supplementary angles of a given acute angle is 90°. 

Multiple response type is the correct answer.
This is because we can get multiple combinations of numbers to get the answer 4.

The first stage would be speaking the numbers '1 to 10', then next stage would be counting 10 objects as 1, 2, 3, ..., then the next stage would be writing numbers 1 to 10 and simultaneously speaking, and the last stage would be practicing them by writing 10 times.