AWES TGT Maths Mock Test - 5 - AWES TGT/PGT MCQ

Madhya Pradesh is leading in implementing the Green Credit Programme, with 500+ approved land parcels for tree plantation across 10 states in two months. 10,000 hectares of land are earmarked. MP has the highest approved degraded forest land (954 hectares), followed by Telangana, Chhattisgarh, Gujarat, and Assam. Public sector undertakings will carry out plantations to earn green credits. The program focuses on ecosystem services, promoting non-carbon environmental actions, benefiting local soil, water, and ecosystems.

Fitch Ratings has reaffirmed the long-term issuer default rating (IDR) of "BBB-" for both State Bank of India (SBI) and Canara Bank, with a stable outlook. This rating reflects their adequate capacity to meet financial commitments, despite variations in risk appetite and loan growth patterns observed by Fitch.

All 6,650 villages in Jammu and Kashmir have achieved Open Defecation Free Plus Model status, making it the first union territory in India to do so. This is a significant achievement, as it means that all villagers now have access to safe and sanitary toilets and that greywater and solid waste are being managed effectively.

Mr. Vikas Sheel, a seasoned bureaucrat, has been appointed as the Executive Director of the Asian Development Bank (ADB) in Manila, reflecting India's commitment to international development.

Change in behaviour is the common sign of a child in stress. A child in stress shows aggressive behaviour and acts irritably.

NEP 2020 emphasizes the role of teachers in promoting critical thinking, creativity, and holistic development of students.

Extra classes could be arranged for such students so as to  bridge the gap in studies (concepts).

National Education Policy 2020 is the first education policy of the 21st century and aims to address the many growing developmental imperatives of our country. This Policy proposes the revision and revamping of all aspects of the educational structure, including its regulation and governance, to create a new system that is aligned with the aspirational goals of 21st-century education.

Key PointsFeatures of NEP 2020:

• Teachers will be encouraged to use a bilingual approach, including bilingual teaching-learning materials, with those students whose home language may be different from the medium of instruction. 
• Children will be exposed to different languages early on (but with a particular emphasis on the mother tongue), starting from the Foundational Stage onwards as multilingualism has great cognitive benefits for young students.
• Multilingualism aims at using languages of all children for teaching-learning and increasing the better innate understanding of how language works. It enhances creativity, divergent thinking, and appreciation of local languages.
• As per the new National Education Policy (NEP), the medium of instruction until at least Grade 5, but preferably till Grade 8 and beyond, will be the home language/mother-tongue/local language/regional language.
• The three-language formula will continue to be implemented while keeping in mind the Constitutional provisions, aspirations of the people, regions, and the Union, and the need to promote multilingualism as well as promote national unity.

Thus,it is concluded that 'multilingualism has great cognitive benefits for young students' statement is proposed in National Education Policy 2020.

⁹⁵C₄ + ⁹⁵C₃ + ⁹⁶C₃ + ⁹⁷C₃ + ⁹⁸C₃ + ⁹⁸C₄ + ⁹⁹C₃ 
= ⁹⁶C₄ + ⁹⁶C₃ + ⁹⁷C₃ + ⁹⁸C₃ + ⁹⁹C₃
= ⁹⁷C₄ + ⁹⁷C₃ + ⁹⁸C₃ + ⁹⁹C₃ 
= ⁹⁸C₄ + ⁹⁸C₃ + ⁹⁹C₃ =  ⁹⁹C₄ + ⁹⁹C₃ = ¹⁰⁰C₄ 

lim(x → 1) (log2 2x)1/^log₂^x
= lim(x →1) (log22 + log2x)1/^log₂^x
As we know that {log ab = log a + log b}
lim(x → 1) {1 + log₂x}1/^log₂^x
log₂x → 0
Put t = log₂x
lim(t → 0) {1 + t}¹/t
= e

On rationalizing,
 Lt x-->0 (1-Cosx)/[√(1+x) +1]
= lt x-->0 2sin²(x/2)[√(1+x)+1] /x
= lt x-->0 [2sin(x/2)/x].sinx/2 [√(1+x) +1 ]
= 2.1/2 .0[1+1]=0

Correct Answer :- d

Explanation : x+2y+3z=4

x+py+2z=3

x+4y+z=3

x = Δx/Δ, y = Δy/Δ, z = Δz/Δ

Δ = 0, Δx = Δy = Δz = 0

As we know that Δy = 0

A = {(1,4,3) (1,3,2) (1,3,μ)} = 0

3μ + 9 + 8 - 9 - 6 - 4μ = 0

=> μ = 2

As Δz = 0

= {(1,2,4) (1,p,3) (1,4,3)} = 0

=> 3p + 16 - 6 - 4p - 12 -6 = 0

=> p = 4

There are 3 girls and 5 boys
∴ Total number of boys and girls = 8
n(s) = Total number of ways of choosing 3 persons

Let E be the event that there are more girls than boys.
⇒ (2 girls & 1 boy) or (3 girls & 0 boy)

 Let P(n) be a given statement involving the natural number n such that
(i) The statement is true for n = 1, i.e., P(1) is true (or true for any fixed natural
number) and
(ii) If the statement is true for n = k (where k is a particular but arbitrary natural
number), then the statement is also true for n = k + 1, i.e, truth of P(k) implies
the truth of P(k + 1). Then P(n) is true for all natural numbers n.

2ⁿ = 128 ⇒ n = 7

Let α, α² be the roots of 3x² + px + 3 = 0. Then 

As α³ = 1 ⇒ α = 1, ω, ω²
We take α = ω so that α² = ω²
Thus - 1 = ω + ω² = α + α² 

(x-x1)/(x1+g) = (y-y1)/(y1+g)
[x-1/(2)^½]/(1/(2)^½) = [y-1/(2)^½]/(1/(2)^½)
[(2x)^½ -1 *(2)^½]/(2)^½ = [(2x)^½ -1 *(2)^½]/(2)^½
(2x)^½ -1 = (2y)^½ -1
= x-y = 0

All possible three number multiplications originate from the following triads:
1,1,30
1,2,15
1,3,10
1,5,6
2,3,5
First one can have 3!/2! = 3 ways and the remaining four triads can have 3! combinations
total combinations = 3 + 4*3! = 27

Length of tangents from origin

Let the first prize be a.
The seven prizes form an AP with first term a and common difference d = −20
Now the sum of all seven prizes = Rs. 700