AWES PGT Math Mock Test - 9 - AWES TGT/PGT MCQ

India is ranked 64th out of 108 countries in the GRWI, reflecting a significant decline of 15 places from the previous year. Meanwhile, The top 5 countries which scored the highest on the Global Remote Work Index (GRWI) are Denmark, Netherlands, Germany, Spain and Sweden.

The correct answer is Akbar.

Key Points

•  Akbar(1556-1605):
  • Akbar was born on 15th October 1542. His full name was Abu'l-Fath Jalal ud-din Muhammad Akbar.
  • Akbar succeeded his father Humayun at the age of thirteen on 14th February 1556 as the third Mughal Emperor of India.
  • Akbar made major reforms in the war techniques especially in the use of firearms.
  • He reigned from 1556 to 1605 and extended Mughal power over most of the Indian subcontinent.
  • To preserve the unity of his empire, Akbar adopted programs that won the loyalty of the non-Muslim populations of his realm.

Additional Information

• Jahangir:
  • The fourth Mughal ruler, Jahangir, was succeeded by the famous Akbar the Great.
  • Jahangir was known for his ambivalent stance on religion and his love for art.
  • Like most Mughal rulers, Jahangir has given India a few of the most iconic structures that have lasted the centuries without losing their glory.
• Shahjahan:
  • Shah Jahan was an able military commander.
  • While still a prince, he was able to obtain the submission of the Rajput state of Mewar which Akbar had not been able to defeat.
  • Mewar then became a vassal of the Mughal Empire.
  • On becoming the emperor, Shah Jahan executed many of his former rivals including his own brother Shahryar, imprisoned many more, and consolidated his power.
  • The Mughal rules of succession do not follow primogeniture, i.e., the eldest son succeeding the father; there is always a fight for power by brothers in the Mughal courts upon the death of a ruler.
• Babur:
  • Babur was the founder of the Mughal empire in the Indian subcontinent
  • He ruled the Mughal dynasty from 1526 to 1530.
  • Babur came to India from Ferghana.
  • Babur succeeded to the throne of Ferghana in 1494 when he was only 12 years old.
  • He was forced to leave his ancestral throne due to the invasion of the Uzbeks(Mongol group).
  • He was a descendant of Timur from his father's side and a descendant of Chengiz Khan from his mother's side.
  • He defeated Ibrahim Lodi at Panipat and captured Delhi and Agra in 1526.
  • He defeated Rana Sanga of Mewar at Khanwa in 1527
  • He defeated the Rajputs at Chanderi in 1528.
  • Baburnama or Tuzuk-e-Baburi is the autobiography of Babur.
  • He died at Agra in 1530.

The Buzi Bridge was inaugurated by Union External Affairs Minister Dr S Jaishankar. The Minister also had a meeting with President of Assembly Esperança Bias.
It was built as part of 132 km Tica-Buzi-Nova-Sofala Road project by India in Mozambique.

Anurag Kumar (IPS), a 1994-batch Indian Police Service officer, has been appointed as the Joint Director of the Central Bureau of Investigation (CBI) by the Appointments Committee of the Cabinet (ACC). This appointment is significant in the context of government appointments.

The International Day of Non-Violence is celebrated on October 2nd each year, the birthday of Mahatma Gandhi. This day is an occasion to disseminate the message of non-violence, including through education and public awareness, and reaffirm the desire for a culture of peace, tolerance, understanding and non-violence. Unlike some other observances, the International Day of Non-Violence does not have a specific theme for 2023.

Reliance Industries (RIL) has announced a merger deal with Viacom18 Media and The Walt Disney Company to establish a joint venture (JV) integrating Viacom18 and Star India operations. With RIL committing a significant investment of Rs 11,500 crore (approximately US$ 1.4 billion) into the JV, this strategic move aims to reshape the Indian entertainment and sports industry landscape.

New education Policy 2020 lays particular emphasis on the development of the creative potential of each individual.

• It is based on the principle that education must develop not only cognitive capacities - both the ‘foundational capacities ’of literacy and numeracy and ‘higher-order’ cognitive capacities, such as critical thinking and problem-solving – but also social, ethical, and emotional capacities and dispositions. 
• Experiential learning is synchronous with critical thinking. Critical thinking is the intellectual process of conceptualizing, applying, analyzing, synthesizing, and/or evaluating information. 
• National Education Policy 2020 proposes that experiential learning should be encouraged to promote critical thinking. 

Important Points

• NEP 2020 is the 21st Century’s first education policy in India. The development of the creative potential of each student is emphasized in the National Education Policy 2020. 
• New Policy aims for Universalization of Education from pre-school to secondary level with 100 % GER in school education by 2030.
• NEP 2020 will bring 2 crores, out-of-school children, back into the mainstream. New 5+3+3+4 school curriculum with 12 years of schooling and 3 years of Anganwadi/ Pre-schooling.

Additional Information

• NEP 2020 does not focus on rote memorization or recall. 

Hence, we can conclude that the right answer to this question is experiential learning; critical thinking.  

Education Policy lays particular emphasis on the development of the creative potential of each individual. It is based on the principle that education must develop not only cognitive capacities - both the ‘foundational capacities ’of literacy and numeracy and ‘higher-order’ cognitive capacities, such as critical thinking and problem solving – but also social, ethical, and emotional capacities and dispositions.

National Education Policy 2020-

According to NEP 2020, A good educational institution is one in which every student feels welcomed and cared for, where a safe and stimulating learning environment exists, where a wide range of learning experiences are offered, and where good physical infrastructure and appropriate resources conducive to learning are available to all students.

Key PointsSome important fundamental principles of the NEP 2020 are- 

• Full equity and inclusion as the cornerstone of all educational decisions to ensure that all students are able to thrive in the education system.
• It includes the overall development of the leader, it covers all three aspects as Cognitive domain, affective domain, and psychomotor domain.
• Promoting self-assessment and the peer assessment done by the student in the classroom.
• Focus on regular formative assessment for learning rather than the summative assessment that encourages today’s ‘coaching culture. It promotes 360- degree multidimensional progress report cards on the basis of different methods of assessments.
• Respect for diversity and respect for the local context in all curriculum, pedagogy, and policy, always keeping in mind that education is a concurrent subject.
• Emphasis on conceptual understanding rather than rote learning and learning-for-exams.
• Creativity and critical thinking encourage logical decision-making and innovation.
• Establishment of the linkage of the concepts with the environment or we can say that the linkage of the school with the home.
• Promoting multilingualism and the power of language in teaching and learning.
• It emphasizes group work as well as individual work, NEP 2020 links the study to the curriculum.

So that we can conclude that 360- degree multidimensional progress report cards follow National Education Policy 2020 proposes in the content of the assessment.

The teacher can deal with the individual differences of the students if she is aware of the abilities, interest and aptitudes of each student. She can then concentrate on each student and help them overcome the difficulties that they have.

 National Education Policy is the first education policy of the 21st century and aims to address the many growing developmental imperatives of this country. This Policy proposes the revision and revamping of all aspects of the education structure, including its regulation and governance, to create a new system that is aligned with the aspirational goals of 21st-century education, while remaining consistent with India’s traditions and value systems.

• The National Education Policy emphasizes the development of each individual's creative potential, in all its richness and complexity.

Key Points

The National Education Policy 2020 has set an ambitious goal of achieving universal foundational literacy and numeracy for primary school children by 2025. This means that by the time children reach grade 3, they will be able to read a grade 3 language textbook and attain essential addition and subtraction skills.

• Attaining foundational literacy and numeracy for all children must receive urgent national attention, with immediate measures to be taken on many fronts and with clear goals that will be attained in the short term (including that every student must achieve foundational literacy and numeracy by Grade 3).
• The very highest priority of the education system will be to achieve universal foundational literacy and numeracy in primary school and beyond by 2025.
• If we specifically talk about  Universal foundation numeracy then the first objective of NEP 2020 to achieve Universal foundation numeracy by 2025 is to achieve build the Number sense in children.
• The rest of this Policy will be largely irrelevant for such a large portion of our students if this most basic learning requirement (i.e., reading, writing, and arithmetic at the foundational level) is not first achieved.
• To this end, all State/UT governments will immediately prepare an implementation plan for attaining universal foundational literacy and numeracy in all primary and middle schools, identifying stage-wise targets and goals to be achieved by 2025, and closely tracking and monitoring the progress of the same.

Thus, it is concluded that the first objective of NEP 2020 to achieve Universal foundation numeracy by 2025 is number sense.    

If a₁, b₁, c₁ and a₂, b₂, c₂ are the direction ratios of two lines and θθ is the acute angle between the two lines; then , the cosine of the angle between these two lines is given by :

For ax²+bx+c=0,
if the two roots are of different signs, their product must be –ve => c/a < 0
=> p(p-1)/3 < 0 => p(p-1) < 0 => 0 < p < 1
 = (0,1) 

If a line makes angles 90^∘, 135^∘, 45^∘ with the x, y and z – axes respectively, then the direction cosines of this line is given by :

(cot α₁) (cot α₂)........... cot α_n =1
(cos α₁) (cos α₂) .......... cos α_n = (sin α₁) (sin α₂) .......... sin α_n
Let y = (cos α₁) (cos α₂) ................ (cos α_n) (to be maximum)
Squaring y² = (cos² α₁) (cos² α₂) ................ (cos² α_n)
= (cos α₁ sin α₁) (cos α₂ sin α₂) ................ (cos α_n sin α_n)    using equation 1

[sin 2α₁. sin2α₂ .........sin 2α_n]
0 < sin2α₁. sin2α₂ .........sin 2α_n < 1

a = 4, b = 5
angle c = 60o
cos c = (a² + b² - c²)/2ab
= 1/2 = (16 + 25 - c²)/40
⇒ 20 = 41 - c2
c² = 21
⇒ c = (21)^1/2
⇒ c = 4.58

a₁ + a_2n = a₂ + a_2n-1 = a_n + a_n-1 = K(say)

 lt x1^+   f(x) = log(4x -3) (x²- 2x + 5)
= ln(x² - 2x +5)/ln(4x-3)
lt(h → 0)   ln(1+h)² - 2(1+h) + 5)/ln(4(1+h) - 3)
lt(h → 0)   ln(1+h² + 2h - 2 -2h + 5)/ln(4 + 4h - 3)
ln(h → 0)    ln(4 + h²)/(1+4h)
Divide and multiply the denominator by 4h
ln(h → 0)    ln(4 + h²)/[((1+4h)/4h) * 4h]
As we know that (1+4h)/4h = 1
ln 4/(4*0)   = + ∞ (does not exist)
 lt x→ 1^-   f(x) = log(4x -3) (x²- 2x + 5)
lt(h → 0)   ln(1-h)² - 2(1-h) + 5)/ln(4(1-h) - 3)
lt(h → 0)   ln(1+h² - 2h - 2 + 2h + 5)/ln(4 - 4h - 3)
ln(h → 0)    ln(4 + h²)/(1 - 4h)
Divide and multi[ly the denominator by (-4h)
ln(h → 0)    ln(4 + h²)/[((1+4h)/-4h) * (-4h)
As we know that (1-4h)/(-4h) = 1
ln 1/(-4*0)   = - ∞ (does not exist)

  represents a circle of radius p having centre at (0, 2 √3) and arg z = π/6 is a line making an angle of 300 with OX and lying in 1st quadrant.  
Let CM be perpendicular from C on OA.  Then, 

Now, the two curves will intersect if CM ≤ P  i.e., 3 ≤ P ⇒ P ≥ 3
Hence, the least value of p is 3 

 N!/(n-5)! = 60×(n-1)!/(n-1-3)!
n!/(n-5)! = 60×(n-1)!/(n-4)!
n(n-1)!/(n-5)!=60×(n-1)!/(n-4)×(n-5)!
n=60/(n-4)
n(n-4)=60
n^2-4n-60=0
(n-10)(n+6)=0
n=10 and n is not equal to -6.

i) 6!/(6-3)!=6*5*4=120

.

ii) 2/6 * 120 = 40

.

iii) 2/6 * 120 = 40

.

iv) 1/6 * 120 = 20

, therefore matrix A has 4 elements in each row

f (x) is continuous at x = π, - π

The discriminant D of the quadratic equation is given by
D = 121(a + b + c)² + 24(a – b)2
As a, b, c are real, 121(a + b + c)² > 0
Also, as a ≠ b ,  (a - b)² > 0 ; Thus, D > 0
Therefore, the equation (1) has real and unequal roots. 

If A ∪ B = A ∩ B then A = B.
Example: Let A = {1, 2, 3, 4} & B = {1, 2, 3, 4}
(AUB) = (A⋂B)
⇒{1,2,3,4} = {1,2,3,4}