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.

The Danish World No.1 Viktor Axelsen clinched victory in the Japan Open final after defeating Jonatan Christie of Indonesia.
In women’s singles, world number two An Se-Young of South Korea beat He Bing Jiao of China to clinch the title. She also replaced replacing Japan’s reigning world champion Akane Yamaguchi to bag the World No. 1 spot.

The United Nations Environment Programme’s (UNEP) Production Gap report has been released in anticipation of the COP28 climate conference.
It warns that global fossil fuel production over the next seven years is projected to exceed more than double the levels required to stay within the climate goals outlined in the 2015 Paris climate agreement, including the crucial target of limiting global warming to 1.5 degrees Celsius.

Gifted students have some advanced mental potential as compared with other children. Hence, they should be asked to spend more time on questions dealing with creating so that their extraordinary abilities can be channelled into discovering new ways to solve a problem.
Hence, this is the correct answer.

Some games, like some real situations, are intensely competitive, where an individual or a team has to compete against someone else. In case of a team, cooperation among members is of paramount importance to reach the objective or to deal with any issue effectively, So, both these skills are required to excel in different real life situations. A teacher must know what would bring out the best in the students and ensure the same.

Continuous Comprehensive Evaluation is a school-based evaluation system. It promotes orderly learning and development. It includes regularity in assessment, diagnosis of learning gaps, retesting, etc. So, CCE emphasizes how learning can be observed, recorded, and improved upon. It is a 'continuous' process after each course over the entire session. 'Comprehensive' means the scheme follows both scholastic and co-scholastic aspects of students.
Hence, the correct answer is, 'How learning can be observed, recorded and improved upon.'

Good problem solvers often have creativity, lack of response set, divergent thinking.

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

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.

When P = 1000 and t = 0 ., then ,
c = 1000, therefore, we have :

Given, function f : R→R such that f(x) = x², 
Let A and B be two sets of real numbers.
Let x₁, x₂ ∈ A such that f(x₁) = f(x₂).
⇒1 + (x₁)² = 1 + (x₂)²
​⇒ (x₁)² − (x₂)² = 0
⇒(x₁ − x₂)(x₁ + x₂)=0
⇒ x₁ = ± x₂. 
Thus f(x₁) = f(x₂) does not imply that x₁ = x₂.
For instance, f(1) = f(−1) = 1, i.e. , two elements (1, -1) of A have the same image in B. So, f is many-one function.

 Since a,b,c are in H.P, so b = 2ac/(a+c).
Also, b,c,d are in H.P, so c = 2bd/(b+d).
Therefore, (a+c)(b+d) = 2ac/b × 2bd/c
⇒ab+cb+ad+cd = 4ad
⇒ab+bc+cd = 3ad

Slope of the line segment joining the point of contact P (x , y) to the point (- 4 , - 3) = 

(i) xRx ⇔ 2x² - 3x.x + x²  

∴ R is reflexive
(ii) For x = 1, y= 2; 2x² - 3xy + y² = 0
∴ 1 R 2 but 2.2² - 3.2.1 + 1² = 3 ≠ 0.
So, 2 is not R-related to 1.
∴ R is not symmetric. 

8(1) + 8(11) + 8(111) + 8(1111) +........up to n times
= 8{ 1 + 11 + 111 + 1111 + ....... up to n times}
= 8/9{9 + 99 + 999 + 9999 + ..... up to n times}
= 8/9 {(10-1 )+ (100-1) + (1000-1) + (10000-1) + ........up to n times}
= 8/9 {(10 + 100 + 1000 + 10000 +...... n times) - (n×1)}
= 8/9{( (10×(10ⁿ -1))/(10-1)) -n}
= 80/81(10ⁿ - 1) - n
=  8/81(10ⁿ⁺¹ - 10 -9n)

Equation of tangent at (x1 , y1) to the circle x² + y² =25 is given by,
xx1 + yy1 = 25. Now comparing it with 3x+4y = 25
We get required point of contact (3,4)

Let BC = a, CA = b & AB = c


∴ b + c = 2s – a = 10.
Locus of A is an ellipse with major axis of length 10

∑a(b - c) = 0, then both roots of equation is 1. 
Product of roots 


Hence, roots are in H.P.

We know that the equation
ax² + by² + 2hxy + 2gx + 2fy + c = 0
represent a rectangular hyperbola if Δ ≠ 0, h² > ab and a + b = 0.
∴ The given equation represents a rectangular hyperbola if 4 + k = 0 i.e. k = -4 

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 

The function is clearly differentiable except possible at x = 2, 3

α⋅β = 4
α+β = 2
α²+β² = (α+β)² - 2αβ
= 4−8=−4
(a+b)³ = a³ + b³ + 3ab(a+b)
(α²+β²)³=α⁶ +β⁶+3α²β²(α²+β²)
-64=α6+β6+3*16(-4)
α6+β6=192−64=128

Convert into sine form this is a increasing function

Hence, f(x) lies in the range of (0, ∞)