KTET Paper 2: Science and Mathematics Test - 4 - KTET MCQ

(5(6x - 10) - (15x - 25))/ 5 
⇒ 30x - 50 - 15x + 25 / 5
⇒ 15x - 25/ 5 
⇒ 3x - 5 
Hence, Option 1 is correct.

Given:
The given values =  a + 4, a – 3.5, a – 2.5, a – 3, a – 2, a + 0.5, a + 5 and a – 0.5
Concept used:
If n is odd
Median = [(n + 1)/2]^th observations
If n is even
Median = [(n/2)^th + (n/2 + 1)^th observations]/2
Calculation:
a + 4, a – 3.5, a – 2.5, a – 3, a – 2, a + 0.5, a + 5 and a – 0.5
Arrange the data in ascending order
⇒ a – 3.5, a – 3, a – 2.5, a – 2, a – 0.5, a + 0.5, a + 4, a + 5
Here, the n is 8, which is even
Median =  [(n/2)^th + (n/2 + 1)^th observations]/2
⇒ [(8/2) + (8/2 + 1)/2] term
⇒ 4^th + 5^th term
⇒ [(a – 2 + a – 0.5)/2]
⇒ [(2a – 2.5)/2]
⇒ a – 1.25
∴ The median of the data set is a – 1.25.

The reason behind preparing a frequency distribution is to provide a systematic way of “looking at” and understanding data. To understand, the information contained in a frequency distribution often is displayed in a graphic and/or diagrammatic form.
Pictographs are also known as picture grams, which are very frequently used in representing statistical data. They are drawn with the help of pictures usually and diagrams indicate the nature of the represented facts. Pictograms are attractive and easy to comprehend.

a² - 3a + 1 = 0
Dividing both sides by 'a', we get
a - 3 + (1/a) = 0
or, a + (1/a) = 3

Some dinosaurs had feathers although they could not fly, but birds have feathers that help them to fly. In the context of evolution, this means that feathers are homologous structures in both the organisms.

The S.I. unit of potential difference is volt and is denoted as V.

Given :
Base of the prism is trapezium parallel sides of trapezium are 11 cm and 15 cm
Height of the trapezium = 9 cm
Volume of the prism = 1614.6 cm³
Formula used :
Area of trapezium = (1/2) × (sum of parallel sides) × height        ------ (1)
Volume of prism = Area of the base × height         ----- (2)
Calculations :
Using equation (1), we get
Area of trapezium = (1/2) × (11 + 15) × 9
⇒ (1/2) × 26 × 9
⇒ 13 × 9 
⇒ 117 cm²
Using equation (2)
Let h be the height of the prism
⇒ Volume of prism with base as trapezium =  Base area of trapezium × height
⇒ 1614.6 = 117 × h
⇒ h = 1614.6/117
⇒ h = 13.8 cm
∴ The height (in cm) of the prism is 13.8 cm.

Given:
32400 = 2^p × 3^q × 5^r
Concept:
"Prime Factorization" is the finding which prime numbers multiply together to make the original number.
Calculation:
32400 = 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3 × 5 × 5
32400 = 2⁴ × 3⁴ × 5²
Now comparing 2⁴ × 3⁴ × 5² with 2^p × 3^q × 5^r
We get, p = 4, q = 4 and r = 2
⇒ 2pq + 3qr = 2 × 4 × 4 + 3 × 4 × 2
∴ 2pq + 3qr = 32 + 24 = 56

• Food preservation is the method of preventing food such as fruits and vegetables from spoiling.
• Food spoilage is caused by microbial growth.
• Food preservation allows one to extend the life of food and store it for a lengthy period of time.
• Food preservation plays an important role in businesses.
• The most commonly used preservatives are common salt, sugar, vinegar, vegetable oils, etc.

0.33 ÷ 0.11 = 33/11
To convert a fraction into a percentage we multiply by 100
Required answer = (33/11) x 100 = 300

Cost of cricket ball = Rs. 36
Cost of cricket bat = 12.5 × cost of cricket ball = 12.5 × 36 = Rs. 450

A pinhole camera is a simple camera without lens and with a single small aperture. Light from a scene passes through this single point and projects a real and inverted image on the opposite side of the box.

A regular octagon has 8 lines of symmetry as it has 8 sides.

Every regular polygon has as many lines of symmetry as the number of sides.
Hence, both assertion and reason are true. 

Friction: The property of a surface that opposes the relative motion between two surfaces is called friction.

Friction (f) = μ N
where μ is the coefficient of friction and N is the normal force.

Prime numbers from 4 to 15 are 5, 7, 11 and 13.
So, Probability = Number of favourable outcomes/Total outcomes = 4/12 = 1/3

Isotones are the elements having same number of neutrons. In ⁶C₁₃ and ⁷N₁₄, the numbers of neutrons are the same (that is 7).

Given:
The sum of the digits of the minimum number by which 1800 is multiplied to get a perfect cube number
Calculations:
1800 = 2 × 3 × 3 × 10 × 10  
To get perfect cube 
3 × 5 
so, that the number will be perfect cube 
1800 ×  5 × 3 = 2 × 2 × 2 × 3 × 3 × 3 × 5 × 5
1800 × 15 = 
So, the number multiplied by 1800 to get perfect square is 15
⇒ the sum of the digits of the numbers 6

Given:
Length of the room = 13 m
The breadth of the room = 12 m 
The height of the room = 15 m
The cost of whitewashing = 9 per m²
Formula used:
Area of four wall = 2 (l + b) × h
Calculation:
Area of four wall = 2 (13 + 12) × 15
⇒ 2 × 25 × 15
⇒ 750 m²
The cost of whitewashing the four walls of the room = 750 × 9 
⇒ 6750 
∴ The cost of whitewashing the four walls of the room is Rs. 6750

Teaching method: Different teaching methods are used by teachers as per the requirements of students. For choosing the one, the teacher may classify students based on their abilities (ability grouping) or he can choose it based on the compatibility of the topic.

• To connect Mathematics with real life, field trip, survey, and projects are more helpful. By involving students actively in learning interesting Mathematics, they will be more successful than more conventional courses in promoting a positive attitude toward Mathematics. 

Science is a cumulative and endless series of empirical observations which result in the formation of concepts & theories, with both concepts & theories being subject to modification in the light of the further empirical observation. Science is both a body of knowledge & the process of acquiring & refining knowledge.

The students will be able to formulate the mathematical ideas by themselves. They will collect the knowledge, and will reflect upon it, to formulate their own mathematical ideas and views.

Learning by doing is the concept of laboratory method.

The project method of teaching is best associated with the philosophy of B.F. Skinner.

A phase named 'Zone of Proximal Development (ZPD)' is a part of the strategy of reciprocal teaching. Reciprocal teaching refers to an instructional activity in which students become the teacher in small group reading sessions. Teachers model, then help students learn to guide group discussions using four strategies: summarising, question generating, clarifying, and predicting.

In the preparation of the Herbartian lesson plan, the stage after generalisation is application.

The maximum score is 1000 for Hunter's Score Card. The weightage given to content is 250 out of 1000 or 25%. The weightage given to author's educational level is 50 out of 1000 or 5%.

1 is not the smallest prime number.-- 2 is the smallest prime number.
The Sum of two prime numbers is always a prime number. -- Take an example to understand it better. Two prime numbers are 5+7=12. 12 is not a prime number.
There is no even prime number. -- 2 is even prime number.
A composite number can be odd. -- Yes, a composite number can be odd. Composite numbers are numbers with more than two factors. The smallest odd composite number is 9. 

The method of teaching science should be adopted according to the cognitive ability and stage of the students. Students at the upper primary stage should be delivered the content in different ways according to their stage and abilities as they would have gained basic knowledge already at the primary level.

Given:
The ratio of two numbers is 5 ∶ 6
The product of their HCF and LCM is 270
Formula used:
Product of two numbers = HCF × LCM
Calculation:
Let the numbers be 5x and 6x
Product of them = 5x × 6x = 30x²
⇒ 30x² = 270
⇒ x² = 9
⇒ x = 3
Now, the sum of them = (5x + 6x) = 11x
After putting the value of x
⇒ 11 × 3
⇒ 33
∴ The sum of the two numbers is 33

Seeking higher aims of teaching mathematics in school is the meaning of ambitious as per 2005 NCF.