EMRS PGT Mathematics Mock Test - 6 - EMRS MCQ

The Correct Answer is Option 3 i.e India.

• India:
  • It shares a border with seven countries, namely China, Pakistan, Bhutan, Myanmar, Afghanistan, Nepal, and Bangladesh.
  • India shares the longest border with Bangladesh.
  • It is the largest democracy in the world, the representative with the most number of votes gets the power.
  • New Delhi is the capital of India.
  • Droupadi Murmu is the current President of India and Narendra Modi is the current PM of India.
• Sweden:
  • It is a country in Europe.
  • Sweden is a constitutional monarchy with a parliamentary democracy.
  • Stockholm is the capital of Sweden.
  • Incumbent Magdalena Andersson is the current PM of Sweden.
• Iceland:
  • It is an Island country in Europe.
  • Iceland is a constitutional republic with a multi-party system and is considered as the worlds' oldest parliamentary democracy.
  • Reykjavik is the capital of Iceland.
  • Guoni Thorlacius Johannesson is the current President of Iceland.
• Norway:
  • It is located in Northwestern Europe.
  • It is a constitutional monarchy.
  • Jonas Gahr Støre is the current Prime Minister of Norway.
  • Oslo is the capital city of Norway.

Q, R, S, T, U, and V are seated in a straight line facing North.

i) S is second to the right of T.

ii) T is second to the right of Q.

iii) R is to the immediate left of Q

iv) R is to the immediate left of Q and is second to the left of V.

Thus we can see there are two persons seating between S and V.

Hence, the correct answer is "Two".

Given:

Five years ago, father's age was 5 times that of his son

After 3 years father will be 3 times as old as his son

Calculation:

Let the present age of son be x years 

Present age of father be y years 

According to the question,

Five years ago, father's age was 5 times that of his son

(y - 5) = 5 (x - 5)

⇒ y - 5 = 5x - 25 

⇒ y - 5x + 20 = 0     ---- (i)

After 3 years father will be 3 times as old as his son

(y + 3) = 3(x + 3)

⇒ y + 3 = 3x + 9

⇒ y - 3x - 6 = 0      ---- (ii)

Solving equation (i) and (ii) we get,

x = 13

∴ Present age of son is 13 years

Shortcut key to create a new document in MS-Word:
To create a new document in MS-Word, you can use the following shortcut key:
Answer: A - Ctrl + N
Explanation:
- To create a new document in MS-Word, you can use the Ctrl + N shortcut key combination.
- Here, "Ctrl" refers to the Control key on your keyboard.
- Press and hold the Control key (Ctrl) and then press the "N" key.
- This combination will create a new blank document in MS-Word.
Steps to create a new document:
1. Open MS-Word on your computer.
2. Press and hold the Ctrl key on your keyboard.
3. While holding the Ctrl key, press the N key.
4. A new blank document will be created in MS-Word.
Additional Information:
- The Ctrl + M shortcut key combination is used to indent a paragraph in MS-Word.
- The Ctrl + O shortcut key combination is used to open an existing document in MS-Word.
- The Ctrl + A shortcut key combination is used to select the entire document in MS-Word.

'If you are given 100 rupees, what will you do?' The objective of asking this type of question is to give place to child's experience and thinking. The child will think how he can use 100 rupees judiciously and take into account his previous experience in doing so. Through the use of 100 rupees the priorities of the child will reflect which he/she gained from the past experiences. There can be a child who believes more in saving the money or there may be some who prefer spending. Hence the thinking of the child can reflect.

cos2θ = cos2θ − sin2θ
And: cos2θ + sin2θ=1
we find:
cos2θ=(1−sin2θ)−sin2θ=1−2sin2θ
θ = θ/4
cosθ/2 = 1−2sin²θ/4

 By L-Hospital rule

Center of such circle in the case of parabolas  y² = 4ax, x² = 4ay is 

Centre and radius of the given circle are C(2,1) and √4+1+20 = 5 respectively.
Now CP=√8²+6²=10. Hence greatest distance of point P from the given circle is =10+r=15

We can write the given equation as
(x – a)² = 3 – a
This shows that 
Both the roots of the given equation will be less than 3 if the larger of the two roots is less than 3, that is, if 


⇒ 3 - a > 1 or a < 2
Thus a > 3 and a < 2 ⇒ a < 2

where n is order of matrix. Here n = 3.

Solving x + y = k + 1 and y = x(1 – x) ⇒ x² – 2x + k + 1 = 0  and Δ = 0 

Divide the numerator and denominator by x, so that given function becomes
f(x)=1+sinx/x/(1+cosx/x)
Now as x→∞.sinx/x→0 , because sin x would oscillate between +1 and -1, which in either case divided by ∞ would be 0. Thus the limit of the numerator would be 1. Like wise the limit of the denominator would also be 1.
Thus limit as a whole would be 1

sin³10° + sin³50° - sin³70° 
= 1/4 [(3 sin 10° - sin 30°) + (3 sin 50° - sin 150°) - (3 sin 70° - sin 210°)]

L.H.S. is positive for all x ∈ R

Teachers must be aware of the fact that every child is different from each other. The differences occur from physical characteristics to learning style and ability. The objective of education is to provide the fullest possible development of learners. So, to address the individual differences in students a school should follow a child-centered curriculum and provide multiple learning opportunities to students. The teachers should find out the different strengths and weaknesses of students before adopting an appropriate curriculum.
Hence, the correct answer is, 'Follow a child-centered curriculum and provide multiple learning opportunities to students.'

A disorder is a disturbance in physical or mental health or functions. It may be caused by genetic factors, disease, or trauma.

Learning takes place by comparing previous knowledge and experience with the present learning experience through thinking and activities. Learning is a universal skill seen in all species. Thinking and Learning are two interwoven activities that help to develop knowledge, critical thinking, and creative thinking.

Key Points

•  Despite the addition of more specialized disciplines and subject instructors, experiential learning within each subject and investigations of relationships among different subjects will be encouraged and highlighted.
• Experiential learning will be implemented at all levels, with investigations of the connections between various disciplines as well as hands-on learning, education that incorporates the arts and sports, and pedagogy centered on telling stories, among others, as normal practices within each subject.
• Classroom activities will change to competency-based learning and teaching to address the achievement gap in learning outcomes. Additionally, the assessment instruments—including assessment "as," "of," and "for" learning—will be in line with the learning objectives, skills, and attitudes that are listed for each subject in a given class.
• Each subject's curriculum will be edited down to the fundamentals in order to allow room for critical thinking and more all-encompassing, inquiry-based, discovery-based, discussion-based, and analysis-based learning.

Hence, National Education Policy 2020 proposes that experiential learning should be encouraged to promote critical thinking. 

Clearly, (x, y)R(x, y),  
since xy = yx. This shows that R is reflexive.
Further, (x, y)R(u, v) ⇒ xv = yu ⇒ uy vx and hence (u, v)R(x, y). This shows that R is symmetric.
Similarly, (x, y)R(u, v) and (u, v)R(a, b) ⇒ xv = yu and ub = va ⇒ xb = ya and hence (x, y)R(a, b). Thus, R is transitive. Thus, R is an equivalent relation.

The correct spelling of the word would be 'Narcissism'. It is the characteristic of always being engrossed in one's own self.
Example- Certain historians claim Hilter's policies to be filled with narcissism.

Rule- The object in the active voice becomes the subject in the passive voice and the subject in the active voice becomes the object in the passive voice.This is valid in both ways (Active to passive and vice-versa). Further, the verb is changed to the past participle form. 

सही उत्तर है - ‘ह’।

• ‘ह’ व्यंजन ‘उष्म व्यंजन’ है।

Key Pointsव्यंजन:-

• जो वर्ण स्वरों की सहायता से बोले जाते हैं उन्हें व्यञ्जन कहते हैं। हर व्यंजन के उच्चारण में अ स्वर लगा होता है।
  अ के बिना व्यंजन का उच्चारण नहीं हो सकता।

वर्णमाला में कुल 39 व्यंजन होते हैं।

• क वर्ग : क , ख , ग , घ , ङ
• च वर्ग : च , छ , ज , झ , ञ
• ट वर्ग : ट , ठ , ड , ढ , ण
• त वर्ग : त , थ , द , ध , न
• प वर्ग : प , फ , ब , भ , म
• अन्तस्थ : य , र , ल , व
• उष्म : श , ष , स , ह
• संयुक्त व्यंजन : क्ष , त्र , ज्ञ , श्र
• उक्षिप्त व्यंजन- ड़, ढ़

क्ष व्यंजन 'संयुक्त व्यंजन' का उदाहरण है।

• क्ष = क् (स्वर रहित) + ष (स्वर सहित)
• क्ष से शब्द = क्षय, कक्षा, नक्षत्र, रक्षा आदि।
• दो या दो से अधिक असमान व्यंजनों के मिलने से बनने वाले व्यंजन को संयुक्त व्यंजन कहते हैं।

उदाहरण -

• त्र = त् + र
• ज्ञ = ज्+ ञ
• श्र = श् + र

Important Pointsवर्ण के दो भेद होते हैं।

1. स्वर वर्ण
2. व्यंजन वर्ण

अघोष व सघोष व्यंजन -

अघोष

• जिन वर्णों के उच्चारण में स्वर तंत्रियों में कंपन नहीं होता है और वर्णों का उच्‍चारण करते समय केवल श्‍वास का प्रयोग किया जाता है, उन्हें अघोष वर्ण कहते हैं।
• क-वर्ग, च-वर्ग, ट-वर्ग, त-वर्ग, प-वर्ग के प्रथम और द्वितीय वर्ण अघोष वर्ण होते हैं।
• अघोष ऊष्म वर्ण - श, ष, स

सघोष

• जिन वर्णों के उच्चारण में स्वर तंत्रियों में कंपन होता है उन्हें सघोष वर्ण कहते हैं।
• क-वर्ग, च-वर्ग, ट-वर्ग, त-वर्ग, प-वर्ग के तृतीय, चतुर्थ व पंचम वर्ण सघोष वर्ण होते हैं।
• सघोष अंतःस्थ वर्ण - य, र, ल, व
• सघोष ऊष्म वर्ण- ह

अल्‍पप्राण व महाप्राण व्यंजन -

अल्‍पप्राण

• जिन वर्णों के उच्चारण में श्वास या प्राण वायु की मात्रा अल्प(कम) होती है, उन्हें अल्पप्राण वर्ण कहते हैं।
• क-वर्ग, च-वर्ग, ट-वर्ग, त-वर्ग, प-वर्ग के प्रथम, तृतीय व पंचम वर्ण अल्पप्राण वर्ण होते हैं।
• अल्‍पप्राण अंतःस्थ वर्ण - य, र, ल, व

महाप्राण

• जिन वर्गों के उच्चारण में श्वास या प्राण वायु की मात्रा अधिक होती है, उन्हें महाप्राण वर्ण कहते हैं।
• क-वर्ग, च-वर्ग, ट-वर्ग, त-वर्ग, प-वर्ग के द्वितीय व चतुर्थ वर्ण महाप्राण वर्ण होते हैं।
• महाप्राण ऊष्म वर्ण- श, ष, स, ह