KTET Paper 2: Science and Mathematics Test - 8 - KTET MCQ

Given:
The diagonal of a rectangle = 17 cm
The area of the rectangle = 120 cm²
Formula used:
The diagonal of a rectangle = √(Length² + Width²)
The area of a rectangle = Length × Width
The perimeter of a rectangle = 2 (Length + Width)
Calculation:
Let, the length of the rectangle = L
The width of the rectangle = W
Then, L × W = 120   .....(1)
Also, √(L² + W²) = 17
⇒ (L² + W²) = 17²  [Squaring on both sides]
⇒ (L² + W²) = 289
⇒ (L + W)² - 2 × L × W = 289  [By using a² + b² = (a + b)² - 2ab formula]
⇒ (L + W)² - 2 × 120 = 289  [From the equation (1), L × W = 120]
⇒ (L + W)² - 240 = 289
⇒ (L + W)² = 289 + 240
⇒ (L + W)² = 529
⇒ (L + W) = √529  [Taking square root of both sides]
⇒ (L + W) = 23   .....(2)
Now, The perimeter of the rectangle = 2 (L + W)
= 2 × 23  [∵ (L + W) = 23]
= 46 cm
∴ The perimeter of the rectangle is 46 cm.

The concept of micro-teaching is a training concept that can be applied at various pre-service and in-service stages in the professional development of teachers.

Average speed:

• The average speed is the total distance traveled by the object in a particular time interval.
• The average speed is a scalar quantity.
• It is represented by the magnitude and does not have direction.​
• Formula, average speed, s_avg = total distance/total time

Average velocity:​

• It is defined as the change in position or displacement (∆x) divided by the time intervals (∆t) in which the displacement occurs.
• Formula, average velocity, v_avg  = Δx/Δt
• The average velocity can be positive or negative depending upon the sign of the displacement.
• Average velocity is a vector quantity.
• The SI unit of average velocity is meters per second (m/s).

Instantaneous speed and instantaneous velocity:

• Instantaneous velocity is defined as the rate of change of position for a time interval that is very small (almost zero). 
• Instantaneous speed is the magnitude of the instantaneous velocity.
• It has the same value as that of instantaneous velocity but does not have any direction.

A fresh solution of sodium hydroxide is prepared in a test tube by dissolving 3-4 pellets of it in 5 ml of water. A piece of aluminium foil is dropped into it. A burning match stick is brought near the mouth of the test tube. Then, a pop sound comes. As before, the 'pop' sound indicates the presence of hydrogen gas. Metals react with sodium hydroxide to produce hydrogen gas. So, burning match stick extinguishes.

The taste buds for "sweet" are on the tip of the tongue; the "salt" taste buds are on either side of the front of the tongue; "sour" taste buds are behind this; and "bitter" taste buds are way in the back.

Given:
83¹⁷ + 52¹⁷ + 84¹⁷ + 53¹⁷ is divided by 68
Concept used:
aⁿ + bⁿ is divided by (a + b) when n is an odd number.
Calculation:
83¹⁷ + 52¹⁷ + 84¹⁷ + 53¹⁷
= (83¹⁷ + 53¹⁷) + (52¹⁷ + 84¹⁷)
Here, n = 17 is an odd number
Also, 83 + 53 = 52 + 84 = 136
The whole number is divisible by 136
So, the whole number is divisible by 68  [∵ 136 = 68 × 2]
Since the whole number is divisible by 68 the remainder must be 0
∴ The remainder is 0.

• Motion is a change of position.
• The motion of an object could be uniform or non-uniform depending on whether its velocity is constant or changing. 
• Newton's first law states that an object continues to be in a state of rest or of uniform motion along a straight line unless acted upon by an unbalanced force.
• The natural tendency of the object to resist a change in its state of rest or of uniform motion is called Inertia.
• Therefore, Newton's 1st law is also the called Law of Inertia.

Explanation:

• Rest refers to an object being stationary relative to a particular frame of reference or another object.
  • When the position of a body with respect to its surroundings does not change with the passage of time, it is said to be at rest. 
• Rest and motion are relative terms because they depend on the Viewer's frame of reference.
  • If an observer is at rest in his or her own frame of reference but he may be moving in another observer's frame of reference. 

Thus, the correct answer is both 1 and 2.

• The reactivity of elements towards water decreases towards the right in a period.
• It also increases down the group.
• Zinc is more reactive than Iron because Zn is more electropositive than Fe. Also, Number of electrons and atomic size of Zn is more than that of Fe.
• Hence the correct order is:

Iron< Zinc< Magnesium< Sodium

Human ear can hear two sounds separately only if they reach the ear after an interval of  1/10 of a second. So the time taken by the sound from P₁ to P₂ should be greater than (1/10)s = 0.1s

Rice, millet, maize, moong, turmeric, groundnut, cotton and sugarcane are some of the Kharif crops. Kharif crops or monsoon crops are domesticated plants that are cultivated and harvested in South Asia during the rainy season, which lasts from April to October, depending on the area.

Given:
20% of P + 40% of Q = 80% of Q
Formula Used:
Percentages can be expressed as fractions or decimals. For example, 20% can be written as 0.2 or 1/5.
Solution:
20% of P + 40% of Q = 80% of Q
0.2P + 0.4Q = 0.8Q
0.2P = 0.8Q - 0.4Q
0.2P = 0.4Q
Now we can solve for P/Q:
P/Q = 0.4 / 0.2
P/Q = 2
This tells us that P is equal to 2Q.
P is 200% of Q.

Transfer of Heat:

• Heat transfer mainly takes place due to temperature differences.
• There are 3 ways of transferring heat: Conduction, Convection, and Radiation.

Conduction:

• Conduction is the phenomenon of the transfer of heat in the solid medium in which the molecules of the solid vibrate without any permanent displacement.

Convection:

• Convection is the phenomenon of the transfer of heat in the fluid medium in which a layer of the molecules shifts from maximum temperature to minimum temperature.

Radiation:

• Radiation is the phenomenon of the transfer of heat in which no medium is required.

Explanation:

• Conduction is the movement of heat through a substance by the collision of molecules.
• Conduction occurs when two objects at different temperatures are in contact with each other.
• This process continues until heat energy from the warmer object spreads throughout the cooler object, like the heat from the milk spreading throughout the metal spoon dipped in it.

Therefore, a cold steel spoon is dipped in a cup of hot milk, then its other end becomes hot by the process of conduction.

• In this case, the given equation, y=mt shows that the velocity is linear with time.
• Therefore the particle is moving with constant acceleration because for a particle to acquire constant acceleration the graph of the velocity time graph should be linear with the time function.

The given expression becomes 300000 + 4000 + 700 + 5 = 304705
Hence, answer option 3 is correct.

Phenolphthalein is a colourless substance (indicator). In acidic solution, it remains colourless. However, adding a few drops of phenolphthalein to basic (alkaline) solution turns the solution pink.
Phenolphthalein + acidic solution (hydrochloric acid) → Colourless
Phenolphthalein + basic solution (sodium hydroxide) → Pink
Phenolphthalein + neutral solution (distilled water) → Colourless

Mathematics is the study of numbers, shapes, quantities, and patterns. It relies on logic and connects learning with children's day to day life. The assessment of mathematical learning refers to know the learning needs and filling the gap by remedial teaching.

• The mineral acids are also known as strong acids.
• They readily dissolve in water and release H⁺ ions.
• The examples of mineral acids are hydrochloric acid, sulphuric acid, nitric acid, phosphoric acid, Hydrobromic acid and hydroiodic acid etc.
• Ciric acid is obtained from citrus fruits.
• It is an organic acid.
• It is a weak acid and not does not release protons readily in water.
• Thus, citric acid is not a mineral acid based on its source.

Objectivity means looking at the things without any biases, prejudices or discrimination. It can be developed by understanding the importance and use of evidence.

• It includes open to others’ ideas and should respect others point of view based on sound logic
• Being flexible and ready to accept the pieces of evidence.

While content represents the what of early childhood mathematics education, the processes of problem solving, reasoning, communication and connections make it possible for children to acquire content knowledge.

This is the correct option because the teaching-learning process of Science in a classroom at any level of formal education is directed by values inherent in the subject as it cannot be changed by school, teacher or community.

The topic 'Separation of Substances' in Class VI can be taught most effectively by using hands on activities to be performed by students.

Mathematics trains the mind in seeking logic and reason which in turn helps in rational thinking ahd understanding. Mathematics is an important component of school education. Its influence has been so fundamental and widespread that being numerate is becoming more important than being literate. The following values justify its position. 

Lactobacillus:

• It is a genus of Gram-positive bacteria.
• These are rod-shaped and can be found in fermented foods and supplements.
• It is the bacteria that is used to convert milk into curd. 
• Conversion of milk into curd is done by the process called fermentation.

So, the correct option is Lactobacillus. 

The word Tentative means the possibility of a change and science is always considered as tentative as there are always different discoveries and inventions that prove better than existing principles or theories.

• Most of the theories in science can be revised or improved or changed or sometimes abandoned whenever there is some discovery or new pieces of evidence discovered which counter with the existing principles or theories.
• For example, the Geocentric theory was revised as the Copernican model displaced the geocentric model of Ptolemy that had prevailed for centuries, which had placed Earth at the center of the Universe.

Therefore, we can say that science is always tentative as the theories of science are revised when new things are founded.

Characteristic of simplicity relates to disciplinary value.

The definition "Science is the investigation and interpretation of events or phenomenon that occurs in natural environment and within our own body" is given by J. Jacobson. It is true as science is the study of structure and behaviour of the physical and natural things through observation and experimentation.

Open-ended questions are those which require more thought and more than a simple one-word answer. Thus, option (2) best describes the example of an open-ended question.