AWES PGT Math Mock Test - 10 - AWES TGT/PGT MCQ

World Down Syndrome Day is observed annually on March 21st, chosen to symbolize the 21st chromosome that causes Down Syndrome. This day raises awareness about the condition and supports individuals with Down Syndrome through various treatments and educational initiatives.

The Bombay Stock Exchange (BSE) as its combined market capitalization reached ₹400-lakh crore for the first time. This reflects the growing valuation and strength of the BSE in the financial market, showcasing a substantial increase from previous milestones like ₹200-lakh crore.

• Kesavananda Bharati Case is a landmark case where the Supreme Court defined the basic structure of the Indian Constitution. The judgement for this case was delivered on April 24, 1973.
• The case is also known as the Fundamental Rights Case. The Supreme Court asserted its right to strike down amendments to the constitution that were in violation of the fundamental architecture of the constitution.

The Union Ministry of road transport and highways is planning to extend its Incident Management Services (IMS) to all national highways.
The purpose of this step is to minimize road fatalities and improve safety for road users. Incident Management Services (IMS) on national roads will be provided, run, and maintained by businesses.

India is set to chair the International Sugar Organisation (ISO) in 2024, underlining its prominent position as the world's largest consumer and second-largest producer of sugar.

Adani Total Energies Biomass Limited (ATBL), a subsidiary of Adani Total Gas Limited (ATGL), has commissioned the first phase of Barsana BioGas plant in Mathura, Uttar Pradesh. The project, developed in three phases, will have a total capacity of 600 tonnes per day, producing 42 tonnes per day of Compressed Biogas (CBG) and 217 tonnes per day of organic fertilizer. It’s set to be India’s largest agri-waste-based bio-CNG plant, costing over ₹200 crore, utilizing advanced anaerobic digestion technology for sustainability and reducing greenhouse gas emissions.

The correct answer is ​Nilgiri.

Key Points

• Nilgiri Biosphere Reserve
  • The name ’Nilgiris’ with literary meaning ‘blue mountains’ has originated from the blue flower-clad mountains of the Nilgiris plateau within the State of Tamil Nadu.
  • It was the first biosphere reserve in India established in the year 1986. Hence, Option 2 is correct.
  • The total area of the Nilgiri Biosphere Reserve is 5,520 sq. km.
  • It is located in the Western Ghats and encompasses parts of Tamil Nadu, Kerala, and Karnataka.
  • The confluence of Biotic zones: It exemplifies the tropical forest biome which portrays the confluence of Afro-tropical and Indo-Malayan biotic zones of the world.
  • Many of the major tributaries of the river Cauvery like the Bhavani, Moyar, Kabini, and other rivers like Chaliyar, Punampuzha, etc., have their source and catchment areas within the reserve boundary.
  • Tribal groups like the Todas, Kotas, Irullas, Kurumbas, Paniyas, Adiyans, Edanadan Chettis, Cholanaickens, Allar, Malayan, etc., are native to the reserve.
  • The Mudumalai Wildlife Sanctuary, Wayanad Wildlife Sanctuary, Bandipur National Park, Nagarhole National Park, Mukurthi National Park, and Silent Valley are the protected areas present within this reserve.

Additional Information

• Sundarbans
  • It is a mangrove area in the delta formed by the confluence of the Ganges, Brahmaputra, and Meghna Rivers in the Bay of Bengal.
  • It spans from the Hooghly River in India's state of West Bengal to the Baleswar River in Bangladesh's division of Khulna.
• The Nanda Devi National Park or Nanda Devi Biosphere Reserve
  • It was established in 1982.
  • In the year 1988, Nanda Devi National Park and its surrounding area were declared as Biosphere Reserve under the MAB programme of UNESCO.
  • It is a national park situated around the peak of Nanda Devi in Chamoli Garhwal district of Uttarakhand, in northern India.
  • The entire park lies at an elevation of more than 3,500 m above mean sea level.
• The Pachmarhi Biosphere Reserve
  • It is a non-use conservation area and biosphere reserve in the Satpura Range of Madhya Pradesh state in central India.
  • The conservation area was created in 1999 by the Indian government. It also contains animals from the Himalayan peaks and the lower western ghats.

DBS Bank India pledged USD 250 million to support new-age start-ups and 'new economy' companies, demonstrating its commitment to fostering innovation and entrepreneurship in India's start-up ecosystem amid challenges related to capital accessibility.

Encouraging maximum participation of students in the classroom. Help students set goals based on their interest. Giving freedom to students for expressing their ideas

All India Council of Elementary Education was established by the government of India and was responsible for looking after the development and working of elementary education. In order to accelerate the pace of expansion of elementary education and to fulfill the directive of Article 45 of the Constitution, the Government of India decided that an All-India Council of Elementary Education should be established with effect from July 1, 1957.

Dyslexia is a type of learning disorder that involves difficulty in reading or recalling a sequence of letters in words (decoding) due to problems like speech sounds. It has an impact on areas of the brain that process language. It is also known as a reading disability.
Hence, this is the correct answer.

a ⊥ a is not true. So, R is not reflexive
a ⊥ b and b ⊥ c does not imply a ⊥ c. So, R is not transitive
But, a ⊥ b ⇒ b ⊥ a is always true. 

tan^-1 (tan 3π/5)
This can be written as:
tan^-1 (tan 3π/5) = tan^-1 (tan[π – 2π/5])
= tan^-1 (- tan 2π/5) {since tan(π – x) = -tan x}
= –tan^-1 (tan 2π/2)
= –2π/5

x² = 16 ⇒ x = ±4 and 2x = 6 ⇒x = 3

There is no value of x which satisfies both the above equations. Thus, A = φ

No. of diagonals in a n-sided polygon = n *(n – 3)/2      
No. of diagonals in a hexagon = 6 *(6 – 3)/2 = 9

For sin²(X), we will use the cos double angle formula:
cos(2X) = 1 - 2sin²(X)
The above formula can be rearranged to make sin²(X) the subject:
sin²(X) = 1/2(1 - cos(2X))
You can now rewrite the integration: 
∫sin²(X)dX = ∫1/2(1 - cos(2X))dX
Because 1/2 is a constant, we can remove it from the integration to make the calculation simpler. We are now integrating:
1/2 x ∫(1 - cos(2X)) dX 
= 1/2 x (X - 1/2sin(2X)) + C]-pi/4 to pi/4
∫sin2(X) dX = [1/2X - 1/4sin(2X)]-pi/4 to pi/4 + C
½[-pi/2] - 1/4sin(2(-pi/4)] - ½[pi/2] - 1/4sin(2(pi/4)] 
= π/2

As (1 – p) is root of the equation: x² + px + (1 – p) = 0

(1 – p)² + p(1 – p) + (1 – p) = 0

(1 – p)[1 – p + p + 1] = 0

(1 – p) = 0

p = 1

Therefore, given equation now becomes

x² + x = 0

x(x + 1) = 0

x = 0, -1

The product of two consecutive natural number is natural.
And all even number be natural number.
So, P(n), n ∈ N

∴ 

= sin θ + sin 3θ + sin 5θ + .....+ sin 29θ

an = ar^(n-1)
 Given, a = √3, r = 3/√3
​r = √3
a₅₀ = ar^(n-1)
= (√3)(√3)^(50-1)
= (√3)(√3)⁴⁹
= (√3)⁵⁰

• We have, A^c in X = The set of elements in X which are not in A = 0,1
• {0} ∈ A^c w.r.t. X is false, because {0} is not an element of A^c in X.
• ϕ ∈ A^c in X is false because ϕ is not an element of A^c in X.
• {0} ⊂ A^c in X is correct because the only element of {0} namely 0 also belong to A^c in X.
• 0 ⊂ A^c in X is false because 0 is not a set.

sin x + sin y = sin (x + y)




The possibilities are x = 0 or, y = 0 or, x + y = 0
When x = 0 , y = ±1
When y = 0 , x = ±1

Clearly, there are 6 pairs.

(3-4i) / (2-3i)*(2+3i) / (2+3i) = (6+9i-8i+12) / 13=(18/13)+(i/13)

As the denominator of the function  is a modulus function i.e.

Correct Answer :- b

Explanation : Let P(n) be the given statement, i.e., P(n) : (2n + 1) < 2n

for all natural

numbers, n ≥ 3. We observe that P(3) is true, since

2.3 + 1 = 7 < 8 = 23

Assume that P(n) is true for some natural number k, i.e., 2k + 1 < 2k

To prove P(k + 1) is true, we have to show that 2(k + 1) + 1 < 2k+1. Now, we have

2(k + 1) + 1 = 2 k + 3

= 2k + 1 + 2 < 2k + 2 < 2k

. 2 = 2k + 1

Thus P(k + 1) is true, whenever P(k) is true.

Hence, by the Principle of Mathematical Induction P(n) is true for all natural numbers, n ≥ 3

cos(2π - θ) = cosq ⇒ f is many-one.
Range (f) = [-1,1] ⊂ R ⇒ f is in to.

, then , its Cartesian equation is given by :

Base of the logarithmic function 5 – |x| > 0 and 5 – |x| ≠ 1
So, x ∈ (–5, –4) ∪ (–4, 4) ∪ (4, 5) ...(i)
Also, (x–1) (x–2) (x–4) must be greater than zero as well
So, x ∈ (1, 2) ∪ (4, ∞) ...(ii)
Combining (i) and (ii) : x ∈ (1, 2) ∪ (4, 5)