AWES TGT Maths Mock Test - 9 - AWES TGT/PGT MCQ

India signed a Memorandum of Understanding (MoU) on Digital Cooperation with Colombia. This MoU aims to facilitate the sharing of India's open-sourced Digital Public Infrastructures (DPIs) with a focus on India Stack Solutions, contributing to digital transformation efforts in Colombia.

The Indian Coast Guard ship 'Varaha' made a port call in Mozambique, specifically in Maputo. This visit highlights India's strategic deployment in East Africa and emphasizes professional engagements in areas such as Marine Pollution Response and maritime Search and Rescue.

Amazon Pay, the fintech arm of Amazon India, has secured a payment aggregator license from the Reserve Bank of India (RBI), enabling strengthened distribution channels and innovative payment solutions. This approval signifies Amazon Pay's commitment to providing secure and convenient digital payment experiences, aligning with its mission to serve merchants and customers effectively in India's growing fintech ecosystem.

The teacher's role is to empower every student irrespective of their diversity is important. Diversity among learners could be with reference to their learning abilities, socio-economic backgrounds, cultural variations or even emotional behavioural characteristics.

Key Points

• The system of education calls for providing equal opportunity to every child for optimal development. “Inclusive Education” has emerged as a guiding principle to envisage this vision.
• Inclusive Education is an approach to educating all children who are at risk for neglect in the education system. It expects that all learners learn together through access to common educational provisions.
• In our democratic country, equality of opportunity is guaranteed to the citizens. In spite of this constitutional right bestowed upon us, informal discrimination is commonly observed in our society. Restrictions are imposed upon individuals based on their deviation in social, economical, cultural, physical, intellectual and behavioural attributes. 
• Inclusive education helps the development of children in different ways. Students with specific challenges make gains in physical, cognitive and social development and motor skills. They do well when the general environment is adjusted to meet their needs.
• The practice can help overcome discrimination which is widespread in every sphere of society.
• Inclusive education can help break the cycle of poverty and exclusion.
• This practice can help to develop a learning and effective environment with the physical facilities and the support of trained teachers.

Hence, it can be concluded that "Educational policies" is not the barriers to Inclusive Education.

Making the mentally retarded students learn through concrete experiences and making them apply the learned skills will surely work for mentally retarded children. Therefore, it becomes important for the teacher to plan out instructions for clear understanding of the concepts. 

Non-discursive communication refers to any form of communication that does not involve the use of words or language.

• Speaking involves the use of words or language to communicate, which is the opposite of non-discursive communication.
• Non-discursive communication includes forms of communication that do not involve the use of words, such as facial expressions, body language, gestures, and silence.
• It is an important aspect of human communication and can play a significant role in how we interact with others and convey meaning and emotion.

Thus, it is concluded that Speaking is NOT a form of non-discursive communication.

Learning disabilities are neurologically-based processing problems. These processing problems can interfere with learning basic skills such as reading, writing and/or math. They can also interfere with higher level skills such as organisation, time planning, abstract reasoning, long or short term memory and attention. They are not caused due to the method of teaching used by the teacher. They may be present due to improper brain development, or infection in brain, etc. Constant fights amongst parents also lead to mental strain and anxiety in students, which may lead to learning disabilities.

Learning disability is a neurological disorder that impairs the ability to receive and process information. Today, more than ever, the need for instructors who are both capable and knowledgeable about teaching children with disabilities is critical.

If A and B are symmetric matrices of the same order, then , AB + BA is always a symmetric matrix.

U = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11}
A = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
B = {1, 3, 5, 7, 9}
A ∩ B = {1, 3, 5, 7, 9}
(A ∩ B)’ = U - (A ∩ B)
(A ∩ B)’ = {0, 2, 4, 6, 8, 10, 11}

At least one yellow chair means “total way no yellow chair”
Total ways to select 3 chair form the total (2+3+4) = ⁹C₃

Now, we dont want even one yellow chair.
So we should select 3 chairs from 6 chairs (2 green & 4 blue) = ⁶C₃

Hence, ways to select at least one yellow chair = 84 - 20 = 64 ways.

(cot α₁) (cot α₂)........... cot α_n =1
(cos α₁) (cos α₂) .......... cos α_n = (sin α₁) (sin α₂) .......... sin α_n
Let y = (cos α₁) (cos α₂) ................ (cos α_n) (to be maximum)
Squaring y² = (cos² α₁) (cos² α₂) ................ (cos² α_n)
= (cos α₁ sin α₁) (cos α₂ sin α₂) ................ (cos α_n sin α_n)    using equation 1

[sin 2α₁. sin2α₂ .........sin 2α_n]
0 < sin2α₁. sin2α₂ .........sin 2α_n < 1

n(A) = 3
n(B) = 2
(x, 4), (y, 5), (z, 4) are three distinct elements of A x B
So, x, y, z ϵ A
4, 5 ϵ B
A = {x, y, z}
B = {4, 5}

We have : 

D is not a trigonometric identity.

R is symmetric and transitive but not reflexive 

Fact

Remember, if the total number of tickets is (2n + 1) and three (3) tickets are drawn at random; then the number of ways that numbers on the drawn tickets are in AP is n².
Here 2n + 1 = 15
⇒ 2n = 14
⇒ n = 7

We have, f(x) = |x−1|, which always gives non-negative values of f(x) for all x ∈ R.Therefore range of the given function is all non-negative real numbers i.e. [0,∞).

The Magnitude of y = 3sinx is 3.
graph{y=-3*sinx [-10, 10, -5, 5]}
Amplitude is the height of a periodic function, aka the distance from the center of the wave to it's highest point (or lowest point). You can also take the distance from the highest point to the lowest point of the graph and divide it by two.

n. n! = [(n + 1) – 1]n! = (n + 1)! – n!
∴ 1 + 2! – 1! + … + (n + 1)! – n! = (n + 1)!

Concept:

The null set is a subset of every set. (ϕ ⊆ A)

Every set is a subset of itself. (A ⊆ A)

The number of subsets of a set with n elements is 2ⁿ.

The number of proper subsets of a given set is 2ⁿ - 1

Calculation:

Statement I: If A = {x: x is an even natural number} and B = {y: y is a natural number}, A subset B.

A = {2, 4, 6, 8, 10, 12, ...} and B = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, ...}.

It is clear that all the elements of set A are included in set B.

So, set A is the subset of set B.

Statement I is correct.

Statement II:  Number of subsets for the given set A = {5, 6, 7, 8} is 16.

Given: A = {5, 6, 7, 8}

The number of elements in the set is 4

We know that,

The formula to calculate the number of subsets of a given set is 2ⁿ

 = 2⁴ = 16

Number of subsets is 16

Statement II is incorrect.

Statement III: Number of proper subsets for the given set A = {5, 6, 7, 8} is 15.

The formula to calculate the number of proper subsets of a given set is 2ⁿ - 1

 = 2⁴ - 1

 = 16 - 1 = 15

The number of proper subsets is 15.

Statement III is correct.

∴ Statements I and III are correct.

P(x₀ , y₀) : pt on curve nearest to line.
Normal at P is perpendicular to the line Normal at P has slope 
∴ y₀ = 2 and x₀ = 11; P(11, -2)

Length of transverse common tangent = [d² - (r1+r2)²]^1/2
Given d=25 and r1=4 & r2=3
∴ L= [(25)² - (7)²]^1/2
L=24

f (x) is continuous at x = π, - π