KTET Paper 1: Mathematics Test - 2 - KTET MCQ

Quantity of milk in 16 jars = 240 litres and 128 millilitres = 240.128 litres (As, 1 L = 1000 mL)
Quantity of milk in 1 jar = (240.128 ÷ 16) litres = 15.008 litres
Quantity of milk in 22 jars = (15.008 × 22) litres = 330.176 litres or 330 litres and 176 millilitres.

Given,
Principal (P) = ₹800
Time (t) = 2 years.
Rate (r) = 5%p.a
We know, SI = (P×t×r)/100.
∴ SI = (800×2×5)/100
SI = ₹80
Hence, the correct answer is ₹80.

Clock gains 12 minutes = 24 hours i.e. 1440 minutes.
Clock gains 1 minutes = 120 minutes.
i.e. 121 minutes = 120 minutes.
Now, from 10 p.m to 1 a.m = 3 hours = 180 minutes 
i.e. time loss = (120×180)/121 ≈ 178 minutes i.e. 2 hour. 58 minutes.
So the actual time is 12:58 a.m.
Hence, the correct answer is 12:58 a.m.

Mathematics has a nature of logical thinking.

One can involve a certain way of thinking and reasoning in mathematics by using exploratory learning that is an approach to teaching and learning that encourages learners to examine and investigate new material with the purpose of discovering relationships between existing background knowledge and unfamiliar content and concepts, by using maths manipulatives which make learning maths interesting and enjoyable. Give students the choice of working on a page of problems with colourful and interestingly shaped blocks, and there's no contest. By using real-life examples which can be linked with the maths concepts and by performing discussions in the classroom related to the mathematics topic.

Mathematics helps an individual to understand the world around us by exploring the hidden patterns in a systematic and organized manner as it has universal applicability.

• The concepts learned in mathematics are helpful to solve our daily-life problems, i.e., the knowledge of addition will help students while buying fruits or vegetables.

Making personal connection with others and solving real-world problems are the interpersonal skills of mathematics students.

Let the shaded part visualise and divide into two triangles as ΔABD and ΔBCD.

So, by adding the area of two triangles, we get the area of the shaded part in the given figure:
Area of the shaded part = Area of △ABD + Area of △BCD
= (1/2) × AB × BD + (1/2) × CE × BD
= (1/2) × 3 × 4 + (1/2) × 2 × 4 = 6 + 4 = 10 cm²
Hence, the area of the shaded part is 10 cm².

Mathematics is a branch of science, which deals with numbers and their operations. It involves calculations, computations, solving problems, etc.

• Mathematics is a subject of logic. Learning mathematics will help students to grow their problem-solving and logical reasoning skills.
• Solving mathematical problems is one of the best brain exercises. 
• It has a huge scope in every field of our life, such as medicine, engineering, finance, natural science, economics, etc. We are all surrounded by a mathematical world.
• It involves calculations, computations, solving problems, etc. Its dictionary meaning states that ‘Mathematics is the science of numbers and space’ or ‘Mathematics is the science of measurement, quantity, and magnitude’.
• The theories and concepts are given in mathematics help us understand and solve various types of problems in academic as well as in real-life situations.
• It is exact, precise, systematic, and a logical subject.

Hence, we can conclude that the right answer to this question is all of the above.

Distance between A and B = 3 × 42 = 126 km Distance between B and C = 128 km Total distance between A and C = 126 + 128 = 254 km Time taken in travelling from A to C = 5 hours Distance = Speed × TimeSpeed = 254 ÷ 5 = 50.8 km/hr.

LCM(a, b) = (a × b) ÷ GCD(a, b)
Calculation:
Prime factorization of 16 = 1 × 24
Prime factorization of 20 = 1 × 22 × 5
Prime factorization of 36 = 1 × 22 × 32
The smallest common multiple(or LCM) of 16, 20 and 36 = 24 × 32 × 5 = 720
The largest common factor(or GCD) of 16, 20 and 36 = 22 = 4
According to question, 
720 ÷ 4 = 180 

The working principle of this operator is like a pattern. The starting number before the operator denotes the starting number from where the sum will start. The number after the operator denotes the number of terms up to which summation will continue. Hence, the solution to n ⊕ 8 is
n+(n+1)+(n+2)+.......+(n+7) = (n+n+n+...8 times)+(1+2+.....+7) = 8n+28.

Suppose the cost of one apple is x and that of one orange is y .
Therefore, by the given conditions:
5x + 3y = 210 ............. (1)
4x + 2y = 160 ..............(2)
Multiply equation (2) with 5 and subtract it from equation (1) after multiplication with 4,
Therefore,
20x + 12y = 840
20x + 10y = 800
- - -
_____________
2y = 40
y = 20
Therefore,
x = 
= 
= 
= 150/5 = 30
Therefore, the cost of one apple is Rs. 30.
Hence, with Rs.120 we can buy (120/30) = 4 apples.

In the number 35362, the number 5 is at the thousands place.
So, the place value of 5 x 1000 = 5000
The difference of the place value and the face value of 5 in the number is:
5000− 5 = 4995
Hence, the correct answer is 4995.

Given:
Length of cuboid = 25 cm
Breadth of cuboid = 7.5 m
Height of cuboid = 85 cm
Formula Used:
The volume of cuboid = Length × Breadth × Height
1 m = 100 cm
Calculation:
1 m = 100cm 
7.5 m = 7.5 × 100 = 750 cm
The volume of cuboid = Length × Breadth × Height
⇒ The volume of cuboid = 25 × 750 × 85
⇒ The volume of cuboid = 1593750 cm³
∴ The volume of cuboid is 1593750 cm³
The correct option is 4 i.e. 1593750 cm³

Rubrics of assessment for the geometry lesson on points and lines in Class IV can differentiate between line and line segment, can mark a point and can draw a line segment of given length accurately.

The language of mathematics is always valuable for any section of science. It is heavily dependent on mathematical equations. Scientific ideas and data need mathematical analysis. It also enables the use of technology to open up new fields of investigation.
Every single syntax, vocab of this universal language is used to prove abstract ideas, theories of application, and their existence. For example, Cryptography which is the founding base of every little security that exists is based on mathematics. That is the language of mathematics in a nutshell.
Hence, the correct answer is "All of the above".

Mathematics includes the study of numbers, patterns, shapes, data, and statistics which helps an individual in solving and dealing with his real-life issues and problems.

• Statistics deals with the collection, classification, and tabulation of numerical facts as the basis for explanation description, and comparison of the phenomenon.

First 10 odd numbers are: 1, 3, 5, 7, 9, 11, 13, 15, 17, 19.
Here N = 10, which is an even number.
So, median = Mean of (n/2)th term + (n/2)+(1)th term
∴ Median = Mean of 5th term + 6th term

= 10

In the given term,
The place value of 6 at first place in 60606 is once place.
63600+6=63606
The place value of 6 in second place in 63606 is hundreds place.
63000+606=63606
The place value of 6 in third place in 63606 is ten thousands place.
60000+3606=63603
Hence, the sum of place value all 6 in 63606 = 60000+600+6=60606.

Now, the ratio of the number of working days in year R to the number of working days in year T
⇒ 160 : 210 = 16 : 21
∴ The ratio of the number of working days in year R to the number of working days in year T is 16 : 21.

Questions which start with how, what, when, where and why are open-ended questions.

According to van hiele theory states that how the young peoples learn geometry. According to van hiele theory, the students are at informal deduction level, because, at the informal deduction level the students are able to think about the fact that the angles opposite to each other when two line crosses. They are always equal and form when two lines intersect. And "vertical" refers to the vertex, means the cross.

The pattern followed here is:

Hence, '116' is the correct answer.

Most appropriate formative task to assess the students' understanding of data analysis is survey-based project.

In order to introduce a concept of area, a teacher must start with the basic things and then slowly explain them by relating. The teacher must compare the area of any figure with the help of objects like pencil, notebook, etc, i.e., comparing it with the things that look alike and explaining to them so that they get a clear concept and have a better understanding. This method will help them to find the area of those objects also which are not so common as they will be able to imagine the things clearly.
Hence, the correct answer is, 'comparing the area of any figure with the help of different objects like palm, leaf, pencil, notebook, etc.'

Logarithms, a device used to simplify calculations by "turning" complicated multiplications and divisions into additions and subtractions. Since logarithms make the solution easier, therefore, their usability in daily life can be seen quite often such as computing compound interest.

Activities involved in teaching of mathematics are Mathematics Quiz, Exhibitions and Mathematics Club activities etc.

As given in the question the perimeter of the square is 96 cm.
⇒ 4a = 96
⇒ a = 24 (side of the square)
Now, as given in the question the breadth 'b' = 24 - 4
⇒ b =20 cm.
Now, using the formula for the perimeter of the rectangle
⇒ 2(l+b) = 96
⇒ (l+b) = 48
⇒ l +20 = 48
⇒ l = 28 cm. where 'l' is the length of the rectangle.
Now, using the formula for the area of the rectangle
⇒ l × b = 28 × 20
⇒ 560 square cm.
Therefore, two times the area of the square = 2 × 560
⇒ 1120  square cm.
Hence, the correct answer is 1120 square cm.

Creativity has been described and defined in various ways. It is the ability to come up with or generate creative ideas and possibilities. It involves thinking in new and original ways to reach a solution.