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KVS TGT Math Mock Test - 6 - KVS PGT/TGT/PRT MCQ


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30 Questions MCQ Test KVS TGT Exam Mock Test Series 2024 - KVS TGT Math Mock Test - 6

KVS TGT Math Mock Test - 6 for KVS PGT/TGT/PRT 2024 is part of KVS TGT Exam Mock Test Series 2024 preparation. The KVS TGT Math Mock Test - 6 questions and answers have been prepared according to the KVS PGT/TGT/PRT exam syllabus.The KVS TGT Math Mock Test - 6 MCQs are made for KVS PGT/TGT/PRT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for KVS TGT Math Mock Test - 6 below.
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KVS TGT Math Mock Test - 6 - Question 1

Direction: In the following question, a sentence has been given in Active/Passive Voice. Out of the four alternative suggested, select the one which best expresses the same sentence in Passive/Active Voice.

Sita was reading the Gita.

Detailed Solution for KVS TGT Math Mock Test - 6 - Question 1

Note: Assume if we had “Someone was reading the Gita”, then active voice would be, The Gita was being read.
We can say that ,
The above given sentence is given in Passive Voice :-
Use structure “subject + auxiliary + past participle + by + object”
The Gita was being read by Sita.
Hence , option A is correct sentence .

KVS TGT Math Mock Test - 6 - Question 2

Fill in the blanks with the correct modal verb.

You _________ smoke near children.

Detailed Solution for KVS TGT Math Mock Test - 6 - Question 2

Correct Answer:

  • C: shouldn't

Explanation:

  • The correct modal verb in this case is "shouldn't" because it expresses a recommendation or advice not to perform an action.
  • "Have to" is used for expressing obligation, "may" is used for expressing permission, and "couldn't" is used for expressing impossibility or inability, which are not suitable in this context.
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KVS TGT Math Mock Test - 6 - Question 3

'जब शाम हो  तब लौट आना' सरल वाक्य में बदलिए। 

Detailed Solution for KVS TGT Math Mock Test - 6 - Question 3

शाम होते ही लौट आना
Explanation: इस वाक्य मै शाम होते ही लौट आने के लिए कहा गया है, जिसका मतलब है कि जिस समय शाम हो जाए उसी समय लौट आना होगा।

KVS TGT Math Mock Test - 6 - Question 4

रमेश सरकारी नौकरी के लिए इधर उधर..................... रहा हैं। उपयुक्त मुहावरे से रिक्त स्थान की पूर्ति कीजिए।

KVS TGT Math Mock Test - 6 - Question 5
किस वाक्य में निपात का प्रयोग नहीं हुआ है?
Detailed Solution for KVS TGT Math Mock Test - 6 - Question 5
मैं कल परिवार सहित घूमने गया इस वाक्य में निपात का प्रयोग नहीं हुआ है। Key Points
  • किसी भी बात पर अतिरिक्त भार देने के लिए जिन शब्दों का प्रयोग किया जाता है उसे निपात कहते है।
  • जो अव्यय किसी शब्द के बाद लगकर उसके अर्थ को बल प्रदान करते हैं, वे निपात कहलाते हैं।
  • निपात को अवधारक भी कहते हैं।
  • निपात किसी बात पर जोर देने के लिए प्रयोग किये जाते हैं।

निपात के उदाहरण

  • हमने ही यह कार्य पूरा किया है ।
  • कल मेरा मित्र भी आएगा।

Additional Information

  • बात अपने तक ही रखना।
  • ही निपात है
  • तुम भी कल चले आओ।
  • भी निपात है।
  • शिक्षा केवल साधन है
  • केवल निपात है।
KVS TGT Math Mock Test - 6 - Question 6

व्याकरण की दृष्टि से दिए गए वाक्य के किस भाग में अशुद्धि है?

मैं दो घंटे से आपकी प्रतीक्षा देख रहा था।

Detailed Solution for KVS TGT Math Mock Test - 6 - Question 6

सही उत्तर है - “देख रहा था।

  • अशुद्ध वाक्य:- मैं दो घंटे से आपकी प्रतीक्षा देख रहा था।
  • शुद्ध वाक्य:- मैं दो घंटे से आपकी प्रतीक्षा कर रहा था

Key Points

  • मैं दो घंटे से आपकी प्रतीक्षा देख रहा था' वाक्य में ‘देख’ शब्द वाक्य अशुद्धि का कारण है।
  • अत: वाक्य में वर्तनी संबंधी अशुद्धता है।

Additional Information

  • अशुद्ध वाक्यों में एक से अधिक विषय और एक से अधिक क्रिया होती है।
  • दूसरी ओर, अशुद्ध वाक्यों में त्रुटियाँ या गलतियाँ हो सकती हैं।
  • शुद्ध वाक्यों में एक ही विषय और एक क्रिया होती है।
  • शुद्ध वाक्य वे हैं जो किसी भी त्रुटि या गलतियों से मुक्त हैं।

Important Points

  • वर्तनी वाले शब्द का अर्थ:- भाषा के किसी शब्द को को लिखने में प्रयुक्त वर्णों के सही क्रम को वर्तनी कहते हैं।
  • भाषा की समस्त ध्वनियोँ को सही तरीके से उच्चारण करने के लिए वर्तनी की एकरुपता स्थापित की जाती है।
KVS TGT Math Mock Test - 6 - Question 7
What are the Five Vows of Jainism?
Detailed Solution for KVS TGT Math Mock Test - 6 - Question 7
The Five Vows of Jainism include Non-violence, Truth, Stealing, Non-possession, and Celibacy.
KVS TGT Math Mock Test - 6 - Question 8

Which of the following TCP/IP protocols is used for transferring files form one machine to another.

Detailed Solution for KVS TGT Math Mock Test - 6 - Question 8
TCP/IP Protocol for Transferring Files

The TCP/IP protocol used for transferring files from one machine to another is FTP (File Transfer Protocol).


FTP is a standard network protocol that enables the transfer of files over a TCP/IP network. It allows users to upload, download, and manage files on a remote server.


Here are some key points about FTP:



  • FTP operates on the Application layer of the TCP/IP protocol stack.

  • It uses separate control and data connections for file transfer.

  • FTP supports authentication for secure file transfers.

  • It provides various commands for file manipulation, such as uploading, downloading, renaming, deleting, and creating directories.

  • FTP can be accessed using FTP client software, command-line interfaces, or web browsers.


Other TCP/IP protocols mentioned in the options are:



  • SNMP (Simple Network Management Protocol): Used for network management and monitoring, not file transfer.

  • SMTP (Simple Mail Transfer Protocol): Used for sending and receiving email, not file transfer.

  • RPC (Remote Procedure Call): Used for communication between programs on different computers, not specifically for file transfer.


Therefore, the correct answer is FTP (File Transfer Protocol).

KVS TGT Math Mock Test - 6 - Question 9

When integrating MS Word and Excel, the Word is usually the

Detailed Solution for KVS TGT Math Mock Test - 6 - Question 9
When integrating MS Word and Excel, the Word is usually the Client

Explanation:



  • Integration: Integration refers to the process of combining or merging two or more software applications to work together.

  • MS Word and Excel: MS Word is a word processing software, while MS Excel is a spreadsheet software.

  • Client-Server Model: In computing, the client-server model is a distributed application structure that partitions tasks or workloads between the providers of a resource or service, called servers, and service requesters, called clients.

  • Integrating MS Word and Excel: When integrating MS Word and Excel, the Word application is usually considered as the client.

  • Functionality: MS Word acts as a client to request data or perform operations on the Excel application, which acts as the server.

  • Examples: Some examples of integrating MS Word and Excel include importing data from Excel into Word for creating reports, generating mail merges using Excel as a data source, or embedding Excel charts or tables within Word documents.

  • Benefits: Integrating Word and Excel allows users to combine the features of both applications to enhance productivity and create more comprehensive documents.


Therefore, the correct answer is C: Client.

KVS TGT Math Mock Test - 6 - Question 10
The most common method of estimating internal consistency of a test reliability is the
Detailed Solution for KVS TGT Math Mock Test - 6 - Question 10

Reliability: An assessment is said reliable if there is consistency in the assessment of the knowledge, skills, abilities being assessed. For example, a student getting the same score on two different writing tests. Reliability refers to the consistency of a research study or measuring test. 

There are two types of reliability:

  • Internal reliability:- Assesses the consistency of results across items within the tests.
  • External reliability:- Refers to the extent to which a measure varies from one use to another.

Important Points

Split -half method:

  • The split-half method assesses the internal consistency of a test, such as psychometric tests and questionnaires.
  • It measures the extent to which all parts of the test contribute equally to what is being measured.
  • It is done by comparing the results of one half of a test with the results from the other half.
  • A test can be spilt in half in several ways. e.g. first half and second half, or by odd and even numbers. If the two halves of the test provide similar results this would suggest that the test has internal reliability.
  • The split-half method is a quick and easy way to establish reliability.

Hence, we can conclude that the most common method of estimating internal consistency of test reliability is the Split-half method.

Additional Information

Test-retest method- The test-retest method assesses the external consistency of a test. It measures the stability of a test over time.

KVS TGT Math Mock Test - 6 - Question 11
Flexible time table and seating arrangement is a feature of
Detailed Solution for KVS TGT Math Mock Test - 6 - Question 11

Child-centered education-

  • ‘learner-centered’ approach in the teaching-learning process. In this approach, the ‘learner’ or ‘child’ and not the ‘teacher’ is the main focus of the educational program.
  • It emphasizes ‘learning’ rather than ‘teaching’.
  • The overall goal of education, according to this approach is all-around development of the child and not only that of acquiring knowledge.

Key Points

Ensuring a Child-friendly Environment- 

  • A safe, secure, and motivating child-friendly school environment that encourages child-centered practices of teaching-learning to ensure the participation of children, can help them learn better. The following points need to be kept in view:
    • It is a fact that every child is capable of learning. It is the responsibility of the teachers, to ensure that the child unfolds her or his potential to accomplish the expected learning outcomes for each stage and class as intended and spelled out.
    • Creating a fear-free environment is essential where each child can express freely, confide in her or his teacher, and can share her or his likes, dislikes, or problems without any hesitation.
    • Alternative strategies for maintaining positive discipline need to be practiced in classrooms. Parents or guardians, too, need to be convinced for the same.
    • Time-table needs to be flexible for teachers to plan and carry out the activities in a time span more than the duration allocated to a period if required.
    • Teachers may be free to change the seating arrangement according to the activity to be organized. 
    • For physical or emotional disturbances, the child may, if needed, be encouraged to approach counselors or medical practitioners, with the involvement of parents or guardians.
    • Recognizing the unique abilities of children and their pace of learning, teachers need to be patient to ensure their involvement in different activities to help them learn, progress and accomplish the class-wise learning outcomes promptly.  

Thus from the above-mentioned points, it is clear that a Flexible time table and seating arrangement is a feature of child-centered education.

KVS TGT Math Mock Test - 6 - Question 12
Which of the following is/are the area(s) that usually affected in mental retardation?
Detailed Solution for KVS TGT Math Mock Test - 6 - Question 12

When then is a lowed capacity for mental work of a permanent nature, it is called mental retardation or mental disability. Mental disability is a condition that slows down mental and physical growth. It is not an illness or a disease, but a condition due to inadequate development of the brain. Children who have this condition are called dull or mentally retarded. A child can be born mentally disabled, or become mentally disabled during or after birth.

Key Points

On the way of knowing that a child is retarded is that development in many areas of functioning would be affected. Development in many areas would proceed slower than what is expected of a child of that age. Some of the areas that are usually affected are:

  • Communication: The mentally disabled child has difficulty in communicating with others, both through speech and action In fact, a retarded child learns to speak later than other children. The child has poor vocabulary and has articulation problems. The speech may be unclear and, therefore, may be incomprehensible to the listener. 
  • Motor Development: There is a lack of coordination in gross and fine motor movements. The milestones of motor development are delayed. 
  • Self Care: The child with mental retardation takes longer to learn to look after her own daily needs, such as eating, bathing, dressing and going to the toilet.
  • Self-direction: There is a lack of direction in retarded children's actions. They may ho something without purpose, such as rock themselves while sitting or carry on doing something for no reason. 

Thus from the above-mentioned points, it is clear that Both (i) and (ii) are true.

Additional Information

  • Other affected areas are- Health and Safety, Academic Work, Leisure and Work, Social Skills, etc.
KVS TGT Math Mock Test - 6 - Question 13
Which of the following is not a measure that a school can adopt to prevent mental health problems?
Detailed Solution for KVS TGT Math Mock Test - 6 - Question 13

Mental health problems are increasingly at a very high rate in individuals of all age-group, especially school-going children or college-going children, due to education pressure and personal problems.

  • Suicide is also highly common in young children.

Key Points

  • Adopting effective and appropriate teaching practices in school can reduce mental health problems
  • Providing discipline education can also help in preventing mental health problems
  • Reducing educational pressure is also a great initiative.
  • Providing value education for the betterment of children is also useful.
  • Helping children gain sex education also prevents mental health education.
  • Understanding children and accepting them also prevent mental health problems

Thus, it can be concluded that option 4 is correct

KVS TGT Math Mock Test - 6 - Question 14

A large number of emotions and heightened emotionality in adolescence have been reported by Larson and Richards. Which of the following emotion is displayed by adolescents?

I. Feeling of happiness.

II. Ignored and terrified.

III. Unsure about some things.

Detailed Solution for KVS TGT Math Mock Test - 6 - Question 14

According to World Health Organization (WHO), "adolescence is a phase of life between 10 to 19 years of age characterized by physical growth, emotional, psychological, and behavioral changes thus bringing about transformation from childhood to adulthood."

  • These changes usually occur earlier in girls than in boys. Some of the changes are externally visible and some are internal. These changes are normal and natural and are due to the release of various hormones in both girls and boys.

Key Points

  • Reed Larson & Maryse H. Richards worked around the changing life space of early adolescence. They reported a large number of emotions and heightened emotionality in adolescence
  • The hormonal changes in adolescence lead to heightened emotions. They become more emotional and sensitive.

Emotional changes in adolescents reported by Reed Larson & Maryse H. Richards include:

  • ​These changes include both positive emotions like love, happiness, and joy, as well as negative emotions like sadness depression, and anxiety. 
  • Mood swings also occur quite frequently. Sometimes they're happy sometimes sad. This makes their behavior somewhat unpredictable.
  • They cannot think rationally about any activities and become unsure about some things.
  • Adolescents' sense of uniqueness makes them think that no one understands them or their feelings which makes them feel ignored.
  • Adolescent fails to think clearly and it creates great frustration and stress in their lives and leads to a terrifying state.

Hence, we conclude that I, II, and III, all are the emotions displayed by adolescents.

KVS TGT Math Mock Test - 6 - Question 15
Which of the following is helpful in facilitating conceptual understanding of a task among students?
Detailed Solution for KVS TGT Math Mock Test - 6 - Question 15

Conceptual knowledge or understanding refers to the knowledge of, or understanding of concepts, principles, theories, models, classifications, etc.

Key Points

  • Discussions and dialogue are helpful in facilitating conceptual understanding of a task among students.
  • Initiating and sustaining a lively, productive discussion is among the most challenging activities for an instructor.
  • In order for a discussion to be effective, students need to understand the value of actively listening to their peers, tolerating opposing viewpoints, and being open-minded.
  • Discussion and dialogue allow the students to interact with each other and help in understanding the concepts.

Thus, it is concluded that Discussions and dialogue is helpful in facilitating conceptual understanding of a task among students.

KVS TGT Math Mock Test - 6 - Question 16
Physical and emotional health of children ______ their learning.
Detailed Solution for KVS TGT Math Mock Test - 6 - Question 16

Learning may be defined as “any relatively permanent change in behaviour or behavioural potential produced by experience”. Learning is not a mere addition to the knowledge or acquisition of facts and skills through drill and repetition. It involves reorganization of experience.

Key Points 

Factors affecting learning:

  • Physiological Factors-
    • Among the organic factors considered to cause learning problems are genetics, brain injury. biochemical imbalances, intake of toxic substances like lead, oxygen deprivation, infectious diseases, drug intoxication, malnutrition and congenital defects. While considering these as factors influencing learning, it may be mentioned that attempts to correlate specific physiological factors with learning problems are not successful. 
    • Unless the body is physiologically mature and ready, academic learning cannot take place. 
  • Psychological Factors-
    • Several psychological factors such as intelligence, personality, attitude, interest, and aptitude have considerable influence on the learning of a child.
  • Socio-emotional Factors-
    • The family the child belongs to has a considerable influence on the learning. Family factors such as child-rearing practices, reward and punishment, the scope for freedom and independence in activities, play and study facilities, the ambitiousness of the parents, disorganization and discord among members, degree of maturity expected of the boy or the girl child, birth position such as eldest, youngest or single child have their definite influence on learning. 
    • Working mothers who also experience marital discord are not only physically absent from their children, they are also emotionally absent. Learner from such a home is usually found self-absorbed and inattentive. 

Thus from above-mentioned points, it is clear that the physical and emotional health of children plays an important role in their learning. 

KVS TGT Math Mock Test - 6 - Question 17
Which of the following factors hinders successful inclusion of students with locomotor disabilities?
Detailed Solution for KVS TGT Math Mock Test - 6 - Question 17

 Inclusion in education means education for all children in school as it refers to the inclusion of all children in the education system, regardless of their differences and disabilities.

  • ‘Locomotor Disability’ refers to a person’s inability to execute distinctive activities associated with the movement of self and manipulation of objects resulting from affliction of the musculoskeletal and/or nervous system.

Key Points Characteristics of the inclusive education:

  • Inclusive education can help break the cycle of poverty and exclusion.
  • It makes the curriculum flexible and easy to access the infrastructure for the students.
  •  It encourages children to stay with their families and communities.
  •  The school atmosphere can improve to the benefit of all the learners.
  • The practice can help overcome discrimination which is widespread in every sphere of society.
  • The evaluation of the students is a comprehensive way, not o a particular ability/disablility.
  • No segregation of children with learning/physical disabilities, children who are socially, economically, culturally, marginalized children, gifted, creative, and linguistically disadvantaged.
  • The education system will make suitable modifications to suit the needs of children.
  • Students are never made to feel inadequate as curricular and co-curricular activities are modified to the requirement of specific.
  • All the required support will be made available to the students in the regular classroom.
  • Thus we can say that if a student has a locomotor disability that he can not easily access the infrastructure of inclusive education.

Important PointsSome common conditions that can cause locomotor disability are

  • Soft Tissues
  • Muscular Dystrophies
  • Dwarfism
  • Spinal Injuries
  • Injuries of Head
  • Amputation
  • Fractures.
KVS TGT Math Mock Test - 6 - Question 18

If ‘2’ is the zero of both the polynomials 3x2+mx−14 and 2x3+nx2+x−2, then the value of m – 2n is

Detailed Solution for KVS TGT Math Mock Test - 6 - Question 18

According to the question, p (2) = 3x2 + mx - 14 = 0
⇒ 3(2)2 + m x 2 - 14 = 0
⇒ 12 + 2m - 14 = 0 ⇒ m = 1
 Also p(2) = 2x+ nx2 + x - 2 = 0


KVS TGT Math Mock Test - 6 - Question 19

Sohan draws a gate of a temple on the graph paper. He has following points :

(– 1, 0), (1, 0), (1, 1), (– 1, 1) and (0, 2)

Q. Which point from the following lies on Y-axis ?

Detailed Solution for KVS TGT Math Mock Test - 6 - Question 19
On Y-axis, x-co-ordinate is zero.
KVS TGT Math Mock Test - 6 - Question 20

Which of the following equations has no real roots ?

Detailed Solution for KVS TGT Math Mock Test - 6 - Question 20

(a) The given equation is x2 - 4x + 3√2 = 0.
On comparing with ax2 + bx + c = 0, we get
a = 1, b = -4 and c = 3√2
The discriminant of x2 - 4x + 3√2 = 0 is
D = b2 - 4ac
= (-4)2 - 4(1)(3√2) = 16 - 12√2 = 16 - 12 x (1.41)
= 16 - 16.92 = -0.92
⇒ b2 - 4ac < 0
(b) The given equation is x2 + 4x - 3√2 = 0
On comparing the equation with ax2 + bx + c = 0, we get
a = 1, b = 4 and c = -3√2
Then, D = b2 - 4ac = (-4)2 - 4(1)(-3√2)
= 16 + 12√2 > 0
Hence, the equation has real roots.
(c) Given equation is x2 - 4x - 3√2 = 0
On comparing the equation with ax2 + bx + c = 0, we get
a = 1, b = -4 and c = -3√2
Then, D = b2 - 4ac = (-4)2 - 4(1) (-3√2)
= 16 + 12√2 > 0
Hence, the equation has real roots.
(d) Given equation is 3x​2 + 4√3x + 4 = 0.
On comparing the equation with ax2 + bx + c = 0, we get
a = 3, b = 4√3 and c = 4
Then, D = b2 - 4ac = (4√3)2 - 4(3)(4) = 48 - 48 = 0
Hence, the equation has real roots.
Hence, x2 - 4x + 3√2 = 0 has no real roots.

KVS TGT Math Mock Test - 6 - Question 21

Ramesh’s salary in February 2008 is Rs. 10,000. If he’s promised an increase of Rs. 1000 every year, what would be his salary in Feb 2011?​

Detailed Solution for KVS TGT Math Mock Test - 6 - Question 21

So this is an AP with a=10,000 , d= 1000
So after 4 years
l=a+(n-1)d=10000+(4 -1)1000=10000+3000=13000

KVS TGT Math Mock Test - 6 - Question 22

If a + 1, 2a + 1, 4a – 1 are in A.P., then value of ‘a’ is:

Detailed Solution for KVS TGT Math Mock Test - 6 - Question 22

KVS TGT Math Mock Test - 6 - Question 23

The total number of propositions in the Euclid’s Elements are

Detailed Solution for KVS TGT Math Mock Test - 6 - Question 23

In the thirteen books that comprise Euclid's Elements there is a total of 465 propositions.

KVS TGT Math Mock Test - 6 - Question 24

Direction: Ladli Scheme was launched by the Delhi Government in the year 2008. This scheme helps to make women strong and will empower a girl child. This scheme was started in 2008.

Read the above bar graph and answer the following questions :

Q. In which year the budget was minimum?

Detailed Solution for KVS TGT Math Mock Test - 6 - Question 24
According to data, In 2007 - 08 the budget was minimum.
KVS TGT Math Mock Test - 6 - Question 25

An exterior angle of a triangle is 800 and the interior opposite angles are in the ratio 1 : 3. Measure of each interior opposite angle is :

Detailed Solution for KVS TGT Math Mock Test - 6 - Question 25
X+3x=80(exterior angle of triangle is equal to two interior opposite angles) 4x=80 x=80/4 x=20 So, x=20 and 3x=3*20=60 are two opposite interior angles.
KVS TGT Math Mock Test - 6 - Question 26

The angles of elevation of the top of a tower from two points at a distance of 4 m and 9 m from the base of the tower and in the same straight line with it are complementary. The height of the tower is:

Detailed Solution for KVS TGT Math Mock Test - 6 - Question 26

Given AB is the tower.

P and Q are the points at distance of 4m and 9m respectively.

From fig, PB = 4m, QB = 9m.

Let angle of elevation from P be α and angle of elevation from Q be β.

Given that α and β are supplementary. Thus, α + β = 90

In triangle ABP,

tan α = AB/BP – (i)

In triangle ABQ,

tan β = AB/BQ

tan (90 – α) = AB/BQ (Since, α + β = 90)

cot α = AB/BQ

1/tan α = AB/BQ

So, tan α = BQ/AB – (ii)

From (i) and (ii)

AB/BP = BQ/AB

AB^2 = BQ x BP

AB^2 = 4 x 9

AB^2 = 36

Therefore, AB = 6.

Hence, height of tower is 6m.

KVS TGT Math Mock Test - 6 - Question 27

Which of the following is a measure of central tendency?

Detailed Solution for KVS TGT Math Mock Test - 6 - Question 27

In statistics, a central tendency is a central or typical value for a probability distribution. It may also be called a center or location of the distribution. Colloquially, measures of central tendency are often called averages. So we have 3 measures of central tendencies namely, mean , median and mode. So mean is the answer as the other three options are the components of the given distribution.

KVS TGT Math Mock Test - 6 - Question 28

There are 50 numbers. Each number is subtracted from 53 and the mean of the numbers so obtained is found to be – 3.5. The mean of the given number is

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KVS TGT Math Mock Test - 6 - Question 29

If a is a non-zero rational and √b is irrational, then a√b is:

Detailed Solution for KVS TGT Math Mock Test - 6 - Question 29

If possible let a√b be rational. Then a√b = p/q, 
where p and q are non-zero integers, having no common factor other than 1.
Now, a√b = p/q ⇒ √b = p/aq……….(i)
But, p and aq are both rational and aq ≠ 0. 
∵ p/aq is rational.
Therefore, from eq. (i), it follows that √b is rational.
The contradiction arises by assuming that a√b is rational.
Hence, a√b is irrational.

KVS TGT Math Mock Test - 6 - Question 30

A wooden box of dimensions 8 m × 7 m × 6 m is to carry rectangular boxes of dimensions 8 cm × 7 cm × 6 cm. The maximum number of boxes that can be carried in the wooden box, is :

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