AWES PGT Math Mock Test - 2 - AWES TGT/PGT MCQ

Traditional products from Tripura, Matabari Pera Prasad and Rignai Pachara textiles, have recently earned Geographical Indication (GI) tags, bringing the state’s total to 4 GI protected products. Matabari Pera Prasad, a sweet from Tripureswari temple, is made from milk and sugar. Rignai Pachara textiles, traditional hand-woven attire, symbolize Tripura’s cultural heritage. These products’ GI recognition highlights their significance and authenticity, attracting global attention and marketing opportunities.

Antonie Van Leeuwenhoek was a Dutch scientist who is credited with being the first person to observe and describe microorganisms using a microscope. He made his microscopes, which were far more powerful than any that had been made before. Van Leeuwenhoek's discoveries revolutionized our understanding of the microscopic world and laid the foundation for the field of microbiology.

Microsoft and OpenAI are jointly embarking on a $100 billion project to create “Stargate,” an AI supercomputer. Scheduled for launch in 2028, it follows OpenAI’s AI upgrade in 2022. The project aims to surpass existing data centers’ capabilities by 100 times. Divided into five phases, with Stargate as the fifth, a smaller fourth-phase supercomputer is slated for release in 2026. Significant costs will be allocated to acquiring essential AI chips.

The correct answer is ​Prohibition of employment of children in factories and mines.

Key Points

• RIGHT AGAINST EXPLOITATION : (Asked in UPSC Prelims 2017)
  • Prohibition of Traffic in Human Beings and Forced Labour
    • Article 23 prohibits traffic in human beings, begar (forced labour), and other similar forms of forced labour.
    • Any contravention of this provision shall be an offence punishable in accordance with the law.
    • This right is available to both citizens and non-citizens.
    • It protects the individual not only against the State but also against private persons.
    • The expression ‘traffic in human beings’ include
      • Selling and buying of men, women, and children like goods
      • Immoral traffic in women and children, including prostitution 
      • Devadasis
      • Slavery.
    • To punish these acts, the Parliament has made the Immoral Traffic (Prevention) Act, 1956.
    • The term ‘begar’ means compulsory work without remuneration.
    • It was a peculiar Indian system under which the local zamindars sometimes used to force their tenants to render services without any payment.
    • In addition to begar, Article 23 prohibits other ‘similar forms of forced labor’ like ‘bonded labor’.
      • The term ‘forced labor’ means compelling a person to work against his will.
  • Prohibition of Employment of Children in Factories 
    • Article 24 prohibits the employment of children below the age of 14 years in any factory, mine, or other hazardous activities like construction work or railway.
      • But it does not prohibit their employment in any harmless or innocent work.

Delhi was labeled as the world’s most polluted capital city in the 2023 World Air Quality Report by Swiss Organization IQAir. India ranked third in air quality with an average annual PM2.5 concentration of 54.4 µg/m³. Bangladesh and Pakistan were worse off, while Bihar’s Begusarai was named the most polluted metropolitan area. Ten of the top 11 polluted cities were Indian, with Lahore being the only exception. 96% of India’s population faces PM2.5 levels exceeding WHO guidelines.

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- 

• It will include Progress of the Child in Inquiry-Based Learning, Quiz, Projects Roleplay, Group Work, Portfolios, etc, as part of the assessment of the students.
• It includes the overall development of the leader, it covers all three aspects as Cognitive domain, affective domain, and psychomotor domain.
• Making board examination low stake and less stressful by focusing on Logic and Core Competencies
• It emphasizes group work as well as individual work, NEP 2020 links the study to the curriculum.

Hence, we can conclude that in the context of progress of the child, National Education Policy 2020 proposes inquiry-based learning.

An n×n homogeneous system of linear equations has a unique solution (the trivial solution) if and only if its determinant is non-zero. If this determinant is zero, then the system has an infinite number of solutions. i.e. For a non-trivial solution ∣A∣=0.

C₁, O, C₂ are collinear

The two curves y² = 4x and y = x meet where x² = 4x i.e ..where x = 0 or x = 4 . Moreover , the parabola lies above the line y = x between x = 0 and x = 4 . Hence , the required are is :

An identity function, also called an identity relation or identity map or identity transformation, is a function that always returns the same value that was used as its argument. That is, for f being identity, the equality f(x) = x holds for all x.

Let S be success &F be failure and let p = probability of getting head = 1/2
q = 1/2
A starts the game then
P (A wins) = P (A wins in first throw) + P (A wins in third throw) + P (A wins in fifth throw) +......... ∞
= P(S) + P(FFS) + P(FFFFS) +......... ∞
= p + q.q.p + q.q.q.q.p +.........


This is an infinite GP and hence its sum is

e² = (a² / b²) + 1
3 = (a² / b²) + 1
a²/b² = 2
a² = 2b²
Product of perpendicular distance of any point on hyperbola = (a²b²)/a² + b²
= [2(b²).b²]/(2b² + b²)
= [2b²]/3 = 6
= 2b² = 18
=> b² = 9
=> b = 3
Length (2b) = 2(3) 
= 6

The distance of a point whose position vector is  from the plane  given by :

Independent event but not equally likely

 lim(x → π) sinx/x-π
lim(h → 0) sin(π-h)/π-h-π
lim(h → 0) -sinh/h
⇒ -1

Out of 30 Boys,
No. of ways to select 1 boy = ³⁰C₁ = 30
Out of 18 Girls,
No. of ways to select 1 boy = ¹⁸C₁ = 18
No. of ways of selecting 1 boy and 1 girl =
30*18 = 540

Required area :

Let A (a, b) and G (x. y) Now A, G, O are collinear
⇒ x = (2*0 + a)/3
⇒ a = 3x
and similarly b = 3y
Now (a,b) lies on the circle = 9x² + 9y² = 9
=> x² + y² = 1

log₁₀ (x³ - x)is defmed ⇒ x³ - x > 0 ⇒ x(x² - 1) > 0 ⇒ (x +1)x(x - 1) > 0
x < -1 ⇒ (x+1)x(x-1) < 0; -1 < x < 0 ⇒ (x+1)x(x-1) > 0
0 < x < 1 ⇒ (x+1)x(x-1) < 0; x > 1 ⇒ (x+1)x(x-1) > 0.
∴ Domain = (-1,0)∪(1, ∞)

Each of the answer choices in the form of the product of two factors on the left and a “≥ 0” or “ ≤ 0” on the right.
The product will be negative when the two factors have opposite signs, and it will be positive when the factors have the same sign. Choice (a), for example, has a “≥0”, so you’ll be looking for other factors to have the same sign.


The graph of x ≤ 0 and y ≤ 2x looks like this.

Together, they make the graph in the figure.

P(n)  b e a statement 2ⁿ < n!
for(n=1) 2¹ < 1!
=> 2 < 1(false)
for(n=2) 2² < 2!
=> 4 < 2 (false)
for(n=3) 2³ < 3!
=> 8 < 6(false)
for(n=4) 2⁴ < 4!
=> 16 < 2⁴ (true)
for(n=5) 2⁵ < 5!
=> 32 < 120 (true)
Therefore 2n < n! is greater for all n>3

y = V^3/3
V = x² - 2x + 3
y = 1/3*v³
dy/dx = d/dx{1/3*(x²-2x+3)³} 
= 1/3*3*(x²-2x+3)²*(2x-2) 
{d/dx(xⁿ)=nx^n-1*dx/dx} 
= 2(x-1)*(x²-2x+3)²

√(-1)² + (√3)² 

= 2

If set A is equal to set B then every element of set A is in set B i.e. A ⊂ B and every element of set B is in set A i.e. B ⊂ A. Hence A ⊂ B and B ⊂ A.

Due to the rule if a square matrix is of order n x n then, |kA| = kⁿ |A|.

The given system of equations does not have solution if : 

- 0 ⇒ 1(-14) - 4(-7) -2(7) = 0