KTET Paper 1: Mathematics Test - 3 - KTET MCQ

Half cm on the map implies 125 km in reality.
This implies that 1 cm on the map implies 250 km in reality.
Or, 250 km actual distance is represented by a distance of 1 cm on the map.
Thus, a distance of 2000 km should be represented by a distance of (2000/250) cm on the map = 8 cm
Hence, option (3) is correct.

We know that if a number is divisible by another number, then it is also divisible by all the factors of that number.
Thus, the number divisible by 12 will also be divisible by all the factors of 12.
Now, the factors of 12 are 1, 2, 3, 4, 6 and 12.
Among these factors, only 3 is given as an option.
Hence, the correct answer is 3.

Concept used:
Place Value: It is the position of the digit. For example, in the digit 789, 9 is at the unit place, 8 is at the ten's place and 7 is at the 100's place. It means that we can write 789 = 700 + 80 + 9.
Face value is simply defined as the digit itself within a number. For example, the Face value of 5 in 350 is 5.
Calculation
Let the number which comes in blank space be 'a'
The place value of 8 in 45876 = 800
The place value of 6 in 9864 = 60
As given, 800 - 60 = 37 × a
⇒ 740 = 37 × a
⇒ a = 740 ÷ 37
∴ a = 20

The concept of learning can be understood properly by the students if pictures of various sizes are presented by the teacher. Circles of different sizes help them to understand the way by which circles are drawn.

Given that, the area of the figure consists of five squares = 180 cm²
As we know, the area of a square = side²
According to the question, the area of five squares = 180 cm²
So, the area of one square Side² = 180/5 = 36 cm²
⇒ Side = √36
⇒ Side = 6
Side of one square = 6 cm 
Now, the perimeter of figure = 12 × 6 = 72 cm

Mathematics is the study of geometrical figures, their co-relation, and their dependency on each other. It deals with quantity, measurement, and spatial relationships.

• The National Policy of Education (1986) lays down the importance of "mathematics" as a vehicle for developing creativity.
• The teacher should use effective teaching methods of mathematics so that individualized discovery-oriented (or problem-solving) learning could be fostered.

The most effective method of teaching mathematics in the classroom is the presentation of content in the classroom. We cannot understand mathematical content by reading.

Given that,
The internal length, breadth and height of a rectangular box are 10 cm, 8 cm and 6 cm respectively.
The volume of the cubes = 6240
As we know,
The volume of the rectangular box = length × breadth × height = 10 cm × 8 cm × 6 cm = 480 cm³
According to the question,
The total number of the boxes required = Total volume of the cubes ÷ Volume of the rectangular box = 6240/480 = 13
Hence, the total number of boxes needed to pack 6240 centimetre cubes = 13
.

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

• It involves the mathematization of thoughts that develops through mathematical reasoning which consists of abstract statements and their proofs.
• In mathematics teaching, teachers should focus more on providing practical exercises and abstract knowledge to students to foster their individualized discovery-oriented learning.

This number lies between 49000 and 50000. As digit on hundreds position is 5, on the tens position the digit is 3, this means it is greater than 49500. So, it is rounded to 50000.

Sum of interior angles of a polygon = 1800° 

Concept:
Sum of the interior angles of a polygon = (n - 2) × 180° 
where, n is the number of sides of a polygon

Calculation:
We know that, 
Sum of the interior angles of a polygon = (n - 2) × 180° 
⇒ 1800° = (n - 2) × 180° 
⇒ 10° = n - 2
⇒ n = 10 + 2 = 12 
Hence, the number of sides of the polygon is 12.

According to the question we need to represent the fraction 1/8 of the given picture. It is clearly visible that the last option is correct because we have cut the rectangle into 8 equal halves and represented one of them as black that represents the fraction. The second option is symmetrical though the areas are different. At first, we cut the rectangle into 4 equal halves and then each of them in symmetrical wave structure. Hence, it correctly represents the fraction.
The first option is correct because four of them have equal area, another four of them have equal area and we use one of them. Hence, it also represents the fraction. But in the third option, all areas cut are different and without any relation between them. 

Number of days in 70 months = 70 x 30 = 2100 days
Therefore, number of weeks in 2100 days = 2100/7 = 300 weeks.

We know,
1 right angle = 90º
And, four and two-third means 4(2/3).
So, required angle:
= 4(2/3) x 90º
= (14/3) x 90º
= 14 x 30º
= 420º
Hence, the correct answer is 420º.

Given:
Next in the sequence: 2, 4, 10, 28, _?
Calculation:
Here,
⇒  2, 4, 10, 28, _
First term, 
⇒  2 × 3 - 2 = 4
Second term,
⇒ 4 × 3 - 2 = 10
Third term,
⇒ 10 × 3 - 2 = 28
Fourth term, 
⇒ 28 × 3 - 2 = 84 - 2 = 82
∴ Option 4 is correct.

To create interest in mathematics in lower classes, the teaching method used must be recreative and game related. By this, student will find an interest in learning and understanding Mathematics.

Children use abstractions to perceive relationships, to see structures, to reason out things, to argue the truth or falsity of the statement. The main goal of mathematics education in schools is the 'mathematization' of a child's thinking. Clarity of thought and pursuing assumptions to logical conclusions is central to the mathematical enterprise.
As in general it increases the knowledge and also social skills in a systematic way. In science, it is also considered as the basic language as every other field is heavily dependent on mathematics. Experimentally proven that general intelligence, cognitive ability is given more priority than special ability in mathematics.
Hence, the correct answer is "All of the above".

Visual-spatial skills provide the child with the ability to visually perceive two or more objects in relation to each other.

Put x = -2 in the given expression
3x³ + 4x² - x - 3
= 3 x (-8) + 4 x (4) - (-2) - 3
= -24 + 16 + 2 - 3
= - 8 + 2 -3
Remainder = -9

The given number is 5671
When we reverse the given number, then we will get = 1765
Similarly, We have the difference between them as
5671 − 1765 = 3906.

The given series is 1, 5, 2, 10....15, 4, 20.
It consists of two series, which are

• 1, 2, 3, 4
• 5, 10, 15, 20

Clearly, from the first series, the missing number is 3.
Hence, the missing number in the pattern is 3 (Three).

Learning mathematics totally depends on the interest of the learner and also on the attention of the learner to the given problem.

A rubric is a tool that is used to evaluate the work of the student and it is a scoring tool for subjective assessment. So, the rubrics of assessment for the geometry lesson on points and lines can differentiate between the line, a ray and the line segment. Also, can define them separately.

The logic follows here is:
The hands of a clock are at a right angle two times in an hour.

• 1 hour = 2 times (right angle)

So, the number of hours from 1 o'clock afternoon upto 10 o'clock at night = 9 hours.
Thus, the number of times the hands of a clock will be at the right angle = 9 × 2 = 18 times
Hence, the correct answer is "18".

The reason is that student had a misconception regarding the significance of zero in ordering decimal.

A word problem in maths is a problem given in an ordinary language, children have to read that problem and find out through which operation they will get the answer. But, if a child is not able to recognize which operation he has to apply that means he is not able to understand the language of the word problem.
Hence, the correct answer is, 'Rajan has problems in comprehending language.'

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

• It involves the mathematization of thoughts that develops through mathematical reasoning, consisting of abstract statements and their proofs.
• Any assumption, hypotheses, and argument in mathematics can be proved with the help of various methods of proof.

Albert Einstein was a German Physicist who quoted that "Pure mathematics is, in its way, the poetry of logical ideas".

As given in the question the complete height of the tank = 9 meter.
Height of the tank filled with the water = 6 meter.
Therefore, the height of the empty tank = 9−6
⇒ 3 meter.
Now, the ratio of the height of the empty tank to the total height of the tank will give the desired result
⇒ 3/9 = 1/3
Hence, the correct answer is 1/3.

Mathematics is one of the few subjects that have practical, cultural and disciplinary value. Mathematics has the potential to range across all three values.