KTET Paper 1: Mathematics Test - 5 - KTET MCQ

Number of wooden boxes required to pack 10,290 books = 10290/98 = 105
Cost of 105 boxes = 105 x 518 = Rs. 54,390.

Given that,
4□3=4+5+6
5□4=5+6+7+8
6□4=6+7+8+9
So, we can see the left operand defines the starting number for the summation.
The right operand defines the number of consecutive digits that are being added.
∴ n□8
= n+(n+1)+(n+2)+(n+3)+(n+4)+(n+5)+(n+6)+(n+7)
= 8n+28.
Hence, the correct answer is 8n+28.

Concept used: 
Prime number:- The number which is divisible by one and itself 
Ex:- 2, 3, 5, 7 etc
2 is the even prime number 
Calculation:
Sum of the digit = 9
Tens digit + Unit digit = 9
⇒ 2 + Unit digit = 9
⇒ Unit digit = 7
∴ The number is 27.

The application of mathematics provides us with precise and real values to questions that are reliable in nature.

Role-play is one of the types of method of instruction in the field of addition that meets these needs like; individuals take on the roles of other people and act out the others feelings, thoughts, and behaviour by assuming or dictating as same as others.

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.

• The teaching of mathematics should be done in the way, in which a student learns the best i.e., following the child-centred approaches by engaging students actively in the learning process.
• The teacher should focus more on providing practical exercises and abstract knowledge to students to foster their individualized discovery-oriented learning.​

For each rational number x, one and only one of the following statements holds:
(i) x > 0
(ii) x = 0
(iii) x < 0
Therefore, all of the above options are incorrect.

Let us convert the given time according to the 24 hours clock system:
So,8.02 p.m + 12 : 00 = 20 : 02
According to the question,
20 : 0.2 − 6 : 14 = 13 hours and 48 minutes

Mathematics is the study of numbers, shape, quantity, and patterns. Mathematics is the ‘queen of all sciences’ and its presence is there in all the subjects. 

• The teaching of mathematics should be done in a pre-defined order that is psychologically organized as per the needs of the students. 
• An objective in teaching may better be defined "as the desired change in behavior in a person that we try to bring about through education". 

Number of boys in the school = 2/3 x 660 = 440
Number of girls in the school = 660 - 440 = 220
Number of players who are boys = 3/4 x 440 = 330
Number of players who are girls = 1/4 x 220 = 55
Total number of players = 330 + 55 = 385

Symmetry:- The state of having two halves that match each other exactly in size, shape, etc.
The imaginary line or axis along which you can fold a figure to obtain the symmetrical halves is called the line of symmetry.
Calculation:

∴ Isosceles trapezium has one line of symmetry.

To read any big number just follow the basic rules of writing any number. The least significant bit represents the unit place digit, then tens place, then hundred's place, then thousand and so on. Hence. unit place digit = 8, ten's place = 2, hundred's place = 9, thousand's place = 7, ten thousand's place = 0, lakh place = 4. Hence, the answer will be four lakh seven thousand nine hundred twenty-eight.

Total population of the village = 1320
Number of males in the village = (2/3) x 1320 = 880
Number of females in the village = 1320 - 880 = 440
Number of males who are farmers = (3/4) x 880 = 660
Number of females who are farmers (1/4) x 440 = 110
Therefore,
Total number of farmers in the village = 660 + 110 = 770

In order to enhance proficiency in Mathematical language, the problems should be presented in the following sequence:
Everyday Language means the unique way of explaining the problem in simple language. Mathematized situation language involves technical and subjective terminologies of that problem. Language of Mathematical problem-solving involves formulas and steps involved to solve that problem. Symbolic Language means the use of characters, signs, short forms, or images to represent concepts.
Hence, the correct answer is, 
'Everyday language → Mathematized situation language → Language of Mathematical problem-solving → Symbolic language'.

Let x be subtracted 560045 to get 505050
⇒ 560045 - x = 505050
⇒ x = 560045 - 505050 ⇒ x = 54995

GeoGebra is an interactive geometry, algebra, statistics and calculus application that is intended for learning and teaching mathematics and science from primary school to university level. GeoGebra is available on multiple platforms with its desktop applications for Windows, macOS and Linux, with its tablet apps for Android, iPad and Windows and with its web application based on HTML5 technology. It is an ICT based tool.

In a fraction, be it mixed or straight one needs to understand the concept about the denominator and numerator. They also need to understand how these two work and how a fraction is different from a whole number. So, identifying the fractional part of a number is the stepping stone of introducing the concept of fractions.
Hence, the correct answer is "Identifying fractional parts of things around them".

Learning outcomes describe the knowledge or skills a student should have attained by the end of a particular time period as a result of various assignments, courses, classes, or programs.

All the mentioned approaches are used to teach the concept of Maths.

Let's consider 1/2 is 'n' times 1/8.
n x (1/8) = 1/2
So,
n = (1/2) x 8 = 4
Hence, 4 times of (1/8) is equal to (1/2).

Given:
The time = 2:58 p.m.
Concept:
1 hour = 60 minutes
Calculation:
⇒ 2 hours 58 minutes = (2 × 60) + 58 = 120 + 58 = 178 minutes
⇒ 4 hours 59 minutes = (4 × 60) + 59 = 240 + 59 = 299 minutes
⇒ The difference between them = 299 - 178 = 121 minutes or (2 hours 1 minutes)
⇒ Now this 2 hours 1 minutes will be before 12 p.m. then, 
⇒ Required timing = (12 × 60) - 121 = 720 - 121 = 599 or (9 hours 59 minutes)
∴ The required result will be 9 : 59 a.m.

Suppose usual speed is x km/hr
Therefore,
The new speed is ( x + (x/20))= 21x/20 km/hr
Now,
Time taken to cover the distance with the usual speed = 300/x
Time taken to cover the distance with the new speed =  
By the given condition,

By asking the students to define a quadrilateral in different ways the teacher wants the students to learn the whole concept about a quadrilateral as the value of sides of a quadrilateral, angles made in a quadrilateral and the value of diagonals etc. So, the students understand all prospectives of the quadrilateral.

To make it a perfect square, we have to make pairs of its prime factors
125 = 5 × 5 × 5
Here, we have to multiply it with 5 to make two pairs of 5
125 × 5 = 625
625 = 5 × 5 × 5 × 5.
Hence, the least number is 5.

The teacher can help the child to understand the concept of LCM i.e., by using different teaching styles or teaching LCM again using different teaching materials. She can give extra revision of the concept of LCM. The teacher conducts several drill exercises and special practice exercises to help the students in acquiring a certain level of knowledge in a particular subject.

To find which bus takes the least time to reach Mathura from New Delhi we just need to find the difference in times of departure and Mathura arrival of all the buses and then compare them.
Bus 1 = (24:40 − 19:15)  = 5 hr 25 min
Bus 2 = (18:10−12:30) = 5 hr 40 min
Bus 3 = (21:55 − 16:45) = 5 hr 10 min
5 hr 10 min < 5 hr 25 min < 5 hr 40 min.

Mathematics is based on practical usability in all aspects of life as it applies in every aspect of our life from buying clothes to sharing and making our food. 

• Mensuration is that part of mathematics which has very vast applicability in our life. 
• It deals with quantifying and estimating different types of geometric figures and their attributes such as length, volume, shape, perimeter, area, etc.

Unlike an aptitude test that measures an ability of learning something, achievement test measures the overall knowledge of candidate on specific field. The most common exam of such a test is SAT.

The Van Hiele propounded the Model of Geometry Thinking. He has given five stages: Visualization, Analysis, Abstraction, Deduction, Rigor Children at the primary stage are ready to classify the given shapes that supported their appearance. According to Van Hiele's levels of geometry, they are at the Visualization stage. At this stage, children start comparing figures with their prototypes or everyday things (it looks like a ball.)
Hence, the correct answer is, 'Visualization stage.'

The National Curriculum Framework 2005, defines the aims of learning mathematics as broad and narrow aims.