AWES PGT Math Mock Test - 7 - AWES TGT/PGT MCQ

Food and Agriculture Organization (FAO) released its flagship report, the State of Food and Agriculture (SOFA). Although current agrifood systems provide nourishment and sustain economies, they also impose huge hidden costs on health and the environment – the equivalent of at least $10 trillion annually.
The figure represents nearly 10 per cent of global Gross Domestic Product (GDP), according to the 2023 edition of the report which covers 154 countries.

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 :

The correct answer is d)

A={2,3,4,8,10},B={3,4,5,10,12},C={4,5,6,12,14}

To find : (A∩B) ∪(A∩C)
A∩B = elements common in sets A and B ⟹A∩B={3,4,10} 
A∩C = elements common in sets A and C ⟹A∩C={4}
Now, 
(A∩B)∪(A∩C)=elements in (A∩B) and (A∩C)
(A∩B)∪(A∩C)={3,4,10}∪{4}
(A∩B)∪(A∩C)={3,4,10}.

n(P ∪ Q) = n(P)  +  n(Q) - n(P ∩ Q) 
140 = 120 + 50 - x
140 = 170 -x
x = 30

We have, zk = ωk where ω  



(by De Movire's theorem)
= cos π + i sin π = -1

General term T_r+1 of (x+y)ⁿ is given by 
T_r+1 = ⁿC_r x^n-r y^r
T₂ = ⁿC₂ x^n-2 y = 240
T₃ = ⁿC₃ x^n-3 y² = 720
T₄ = ⁿC₄ x^n-4 y³ = 1080
T₃/T₂ = [(n-1)/2] * [y/x] = 3......(1)
T₄/T₂ = {[(n-1)(n-2)]/(3*2)} * x²/y² = 9/2
T₄/T₃ = [(n-2)/3] * [y/x] = 3/2...(2)
Dividing 1 by 2
[(n-1)/2] * [3/(n-2)] = 2
⇒ 3n−3 = 4n−8
⇒ 5 = n

D = 0
{(-2,1,1) (1,-2,1) ( 1,1, λ) = 0
= (4λ +1 +1) - (-2 - 2 + λ) = 0
4λ + 2 + 4 - λ = 0
3λ + 6 = 0
λ = -2

By definition , The angle θ between the planes A₁x + B₁y + C₁z + D₁ = 0 and A₂ x + B₂ y + C₂ z + D₂ = 0 is given by :

We have :

(x – 1, y + 1) = (5, 6)
x – 1 = 5
x = 6
y + 1 = 6
y = 5

Obviously, every differentiable function is continuous but every continuous function isn't differentiable.

Out of integers from 1 to 11, there are 5 even and 6 odd integers.
Let A – both the numbers chosen are odd
B –sum of the numbers chosen is even. 

Determinant = -2(-12 + 12) -2(-6 - 2) +1(-12 - 4)
= - 2(0) - 2(-8) + 1(16)
= 0 + 16 + 16
= 32

 y = (x² - 3x + 2)/(x² + x -6)
= [(x-2)(x-1)]/[(x-2)(x+3)]
= (x-1)/(x+3)
= 1 - 4/(x+3)
x is not equal to 2 and -3
For x = 2, y = 1/5
for x = -3, y → 1
Range (y): R - {1, 1/5}

Give lines are :
 and 
The D.R's of the lines are -3, 2p/7, 2 and -3p/7, 1, -5

Length of tangents from origin

=1(-5) -2(10) + 3(11)
=-5-20+33 = 8

=1(-30) - 6(20) + 3(66)

= -30-120+198= 48

D = 8 ⇒ 6D = 48

• An intersection is the collection of all the elements that are common to all the sets under consideration.
• Here element 6 & 9 are common in both the sets. So option C is correct. 

In vector form:
Vector equation of a plane that passes through the intersection of planes
 expressed in terms of a non – zero constant λ is given by :

a_n = 57, a = 2, n = 12
a_n = a + (n-1)d
=> 57 = 2 + (12 - 1)d
=> 55 = 11d
d = 5
T10 = a + 10d
=> 2 + 10(5) 
= 52

Since, 1, ω, ω² ..... ω^n-1 are the nth roots of unity, therefore
xⁿ - 1 = (x -1)(x - ω)(x - ω2⁾...(x - ω^n-1)

Putting x = 1 in above equation, we have