KTET Paper 2: Science and Mathematics Test - 6 - KTET MCQ

Given:
The square root of 18225
Concept used:
Square root: A number that produces another particular number when it is multiplied by itself.
Calculation:

⇒ √(5 × 5 × 9 × 9 × 3 × 3)
⇒ 5 × 9 × 3 = 135
∴ The required answer is 135.

The teaching-learning of mathematics stresses much on developing the skill of mathematization. It is expected that children should expand the horizon of cognition by incorporating abilities that help them to manage situations mathematically.

• For a plano-convex lens, one of the surfaces is flat (Plano) and the other is curved (convex).
• The radius of curvature of the curved surface is given as 20 cm, and the refractive index of the material of the lens is 1.5.
• The focal length of the lens can be calculated using the lens maker's formula:

1/f = (n - 1) × (1/R1 - 1/R2)
where
f is the focal length of the lens,
n is the refractive index of the lens material,
R₁ is the radius of curvature of the first surface (the flat surface in this case, which is infinite), and
R₂ is the radius of curvature of the second surface (the curved surface in this case).
Since the first surface is flat, the radius of curvature R1 is infinite, and the term (1/R1) becomes zero. Therefore, the lens maker's formula simplifies to:
1/f = (n - 1) ×  (1/R2)------(1)
Calculation:
Substituting the values in equation (1), we get:
1/f = (1.5 - 1) × (1/20)
1/f = 0.025
f = 1/0.025
f = 40 cm
Therefore, the focal length of the plano-convex lens is 40 cm.
The correct answer is option (4)

Let the purchase price of the machine three years ago = Rs. P
So, (0.90)³ P = 145800
Or, P = 145800/0.729 = 200000
Thus, the purchase price of the machine three years ago = Rs. 2,00,000
Hence, option (3) is correct.

Peripheral nerves control the functions of the rest of the body. In humans, there are 31 pairs of spinal nerves: 8 cervical, 12 thoracic, 5 lumbar, 5 sacral and 1 coccygeal.

Symbiosis is a close and often long-term interaction between two different biological species.

Given:
MN = 70 cm
Diameter = 74 cm
Concept used:
Diameter = Radius × 2
The perpendicular distance of a chord from the center bisects the chord itself.
Pythagoras Theorem.
(Hypotenuse)2 = (Base)2 + (Height)2
Calculation:

Let OM and OP be the radius and the perpendicular distance from the chord respectively. 
Hence, MP = 70 ÷ 2 = 35 cm
ΔOMP is a right-angled triangle at P.
Hence,
OP = √(OM² - MP²)
⇒ √(37² - 35²) = √144 
⇒ 12
∴ The perpendicular distance of the chord from the center is 12 cm.

Bile juice

• Bile is a dark-green to yellowish-brown fluid produced by the liver that helps in the digestion of lipids/Fats in the small intestine.
• In human beings, bile is produced by the liver continuously and stored in the gallbladder.
• After eating the food, this stored bile gets discharged into the duodenum.
• The two main pigments of bile are bilirubin and biliverdin.
• The secretion of bile juice is essential for fat digestion and absorption of lipids.
• The bile is secreted from hepatocytes cells of the liver and makes up 80% of the liver's mass.
• The liver comprises two lobes.
• Hepatocytes are its structural and functional unit.
• It is present below the lungs near the stomach.
• It is released via the common hepato-pancreatic duct into the duodenum.
• It helps in the emulsification of fats in the intestine.

Indicators:

• Indicators are the substances that are used to identify whether the given substance is an Acid or a Base.
• When indicators are added to acidic or basic solutions, they change their color accordingly.

There are two types of indicators:
Natural: These indicators are obtained from natural sources like plants.

• Turmeric, litmus, china rose petals, etc., are some of the naturally occurring indicators.
• The most commonly used natural indicator is Litmus. It is extracted from lichens. It is available in the form of a solution, or in the form of strips of paper, known as litmus paper. Generally, it is available as red and blue litmus paper.
• Natural indicators are used to detect the hydrogen ions (H+) and hydroxyl ions (OH-) in a solution.

Man-made: Phenolphthalein, Methyl orange are some of the man-made indicators.

Number of cubes = Capacity of box ÷ volume of cube
Volume of cube = 2.5 × 2.5 × 2.5 cu. cm = 15.625 cu. cm
Capacity of box = 15 × 12.5 × 7.5 cu. cm = 1406.25 cu. cm
Hence, 1406.25/15.625 = 90

Myopia occurs when the eyeball is too long, relative to the focusing power of the cornea and lens of the eye.

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 in the back.

Formula Used:
Sum of all angles in quadrilateral is 360°.
Calculation: 
⇒ ∠ DCB + ∠ DCX = 180°  [ Linear pair ]
⇒ ∠ DCB + 120° = 180°
⇒  ∠ DCB = 180° - 120° = 60° =∠ C 
In quadrilateral ABCD
Using above formula-
⇒ ∠ A + ∠ B + ∠ C + ∠ D = 360° 
⇒ 120° + 105° + 60° + ∠ D = 360° 
⇒ ∠ D = ∠ ADC = 360° - 120° - 105° - 60° = 75° 
∴ The correct answer is 75° 

• Liver is the largest gland in our body that is characterised by its reddish brown colour.
• Liver is the largest gland, located in the upper right side of the abdomen below the diaphragm.
• It secretes bile, which gets collected in gall bladder and is finally poured into the duodenum through the common bile duct.
• Besides secreting bile, which helps in digestion, the liver has numerous other functions.

• Mosses come under the group Bryophyta.
• Bryophyta is known as the Amphibian category of the plant kingdom.
• It is an informal group that consists of three divisions of non-vascular land plants mosses, hornworts, and liverworts.
• There is a lack of xylem and phloem tissues in this category of Plants.
• They also lack true roots, stems, and leaves.
• Thalophyta is the largest group in the plant kingdom.
• Pteridophyta plants are mainly found in wet shady plants, forests, and mountains.
• Thallophyta is the simplest of plants that do not have a well-differentiated body design.
• Angiosperm, pteridophyte, and gymnosperm possess well-differentiated stems, roots, and leaves.

(500)^1/3 x (16)^1/3
= (5 x 2 x 5 x 2 x 5)^1/3 x (2 x 2 x 2 x 2)^1/3
= (2⁶)^1/3 x (5³)^1/3
= 2² x 5
= 4 x 5
= 20
Thus, option (2) is correct.

In most youngsters, broken bones are either "greenstick" fractures, in which the bone bends like green wood and breaks only on one side, or "torus" fractures, in which the bone is buckled, twisted, and weakened, but not completely broken. A "bend" fracture refers to a bone that is bent but not broken, and is also relatively common among youngsters.

Velocity = Displacement/Time
If the displacement gap is changed, the velocity will also change as seen from the relation. It will increase on increasing the gap, not decrease.

Mathematics is a subject that deals with numbers from small to complex concepts. It includes basic addition as well as tricky trigonometry. It demands strong attention as well as understanding ability from the learner.

• If the learner understands the concept, then only he/she can apply it in an appropriate situation and can create connections between the concepts.
• Merely memorizing the formula or mugging up and solving the problem in less time will not create a “good” mathematician.

Thus, it can be inferred that to be a “good” mathematician one must be able to understand, apply and make connections across the concepts.

• An ohmmeter is an electrical device used to measure resistance.
• Ammeter is an instrument for measuring the current flowing in a branch of a circuit.
• Voltmeter is a measuring instrument used to measure the potential difference between any two points of a circuit.
• Galvanometer is used to detect the presence of current in a circuit.

A teacher's task in the classroom is not limited to the teaching of a subject or developing knowledge, skills, and understandings among students. Merely teaching facts does not help students to achieve their potential.

• Education should enable the students to think and solve problems. It should also enable them to understand the underlying meanings instead of memorizing facts for grades. As teachers, therefore, it is our duty to ensure that students think and reason on their own in a critical, creative and intelligent manner.

The properties of quadrilaterals do not directly help in the construction of quadrilaterals. The students need to be taught the method to construct quadrilaterals. This construction can help to explain students the properties of quadrilaterals later on. Hence, there is a difference between what was taught, and what is being asked, i.e. there is a gap between instructions given in class and the assessment conducted.

The most important stage in diagnosis is finding the nature of difficulties, then cause of these difficulties, and then remedial measures and its application.

Lesson planning in Life Sciences should be guided primarily by the consideration of the curriculum goals and learning outcomes.

Values Inculcated through mathematics: Values of Learning Mathematics Values are the outcomes or results achieved after teaching according to certain aims. They are the actual results of our teaching effort. They enable the students to acquire mathematical knowledge, skills, develop interests and attitudes. The various values are as follows:

• Practical or Utilitarian values
• Intellectual values
• Social values
• Moral values
• Disciplinary values
• Cultural values
• International values
• Aesthetic values
• Vocational values
• Psychological values

• The Gravitational Force is the weakest force. So option 1 is correct.
• Weak Nuclear force has a very short range and is 1025 times stronger than the Gravitational Force.

Scientific method is a method of solving problem scientifically. Training in the method is more important than the acquisition of information.

• According to Lundberg “Scientific method consists of systematic observation, classification, and interpretation of data”.

Inductive instruction makes use of student noticing. Instead of explaining a given concept and following this explanation with examples, the teacher presents students with many examples showing how the concept is used. The intent is for students to notice, by way of the examples, how the concept works.

Errors/difficulties in learning Science are identified using questionnaire because it is a set of printed or written questions with a choice of answers, devised for the purposes of a survey or statistical study that removes the chances of errors and difficulties.

National Curriculum Framework (NCF) strongly recommends that Science education at upper primary stage should follow constructivistic approach for teaching and learning of the subject which helps in the holistic development of the student.