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

India is poised to restart the manufacturing of Penicillin G in 2024 after a hiatus of three decades. This resurgence is attributed to the government's Production Linked Incentive (PLI) scheme, aiming to revitalize domestic pharmaceutical manufacturing.

India won the Asian Champions Trophy title in 2023, securing their fourth championship in the tournament's history. The Indian hockey team on 12 August defeated Malaysia 4-3 to win for the fourth time at the Asian Champions Trophy 2023 final, at the Mayor Radhakrishnan Stadium in Chennai on Saturday. With four Asian Champions Trophy titles, India is the most successful team in the history of the tournament.

The 7th Indian Ocean Conference took place in Perth, Australia. Organized by India Foundation in collaboration with the Ministry of External Affairs and Department of Foreign Affairs and Trade, the conference aimed to address various issues concerning the Indian Ocean region under the theme "Towards a Stable and Sustainable Indian Ocean".

Moral development is one’s ability to take decision about right and wrong.

Moral development is the process through which children develop proper attitudes and behaviors toward other people in society, based on social and cultural norms, rules, and laws.

Ankit, a 12 years boy, is not enrolled in school due to some circumstances. He has requisite computational skills and intends to enroll in a school to learn. Ankit has an aptitude for learning.

• An aptitude test is designed to assess what a person is capable of doing or to predict what a person is able to learn or do given the right education and instruction.
• It represents a person's level of competency to perform a certain type of task.
• Aptitude can be defined as someone’s natural ability to do something.
• Teaching aptitude, hence, refers to an individual’s innate ability in teaching.
• It can also be defined as the ability of a person to teach, once they are given the necessary training.

Therefore, we can conclude that Ankit, a 12 years boy, is not enrolled in a school due to some circumstances. He has requisite computational skills and intends to enroll in a school to learn. Ankit has an aptitude for learning.

Children with special needs are disabled and any restriction or lack (resulting from an impairment) of ability to perform an activity in a manner or within the range considered normal for a human being. 

Key Points

Education of children with special needs should be provided in an inclusive classroom, along with other normal children as:

• Inclusive classroom values the diversity, each child brings to the classroom and facilitates all with equal opportunities to learn and grow.
• They should be taught in the same schools only with the help of special education experts.
• It provides a provision to include disabled children along with normal children in a regular classroom regardless of their differences and disabilities.
• it will integrate children with disabilities in the general community to prepare them for normal development and will keep them as a part of mainstream education

• If we provide them, education in special schools or in special classes or by special teachers, the inferiority complex will develop in them which could lead to anxiety and frustration.

Hence, we can conclude that children with special needs should be taught in the same schools only with the help of special education experts. 

Let P be the principal at any time t. then,





When P = 100 and t = 0., then, c = 100, therefore, we have:

Now, let t = T, when P = 100., then;

The given inequality is 5x– 3 < 7
=> 5x – 3 + 3 < 7 + 3                             [3 is added both sides]
=> 5x < 10
=> x < 10/5
=> x < 2
When x is a real number, the solutions of the given inequality are given by x < 2, i.e., all real numbers x which are less than 2.

z₁ = |z₁(cosθ₁ + i sinθ₁)
z₂ = |z₂(cosθ₂ + i sinθ₂)|
Given that |z₁| = |z₂|
And arg(z₁) + arg(z₂) = pi
θ₁ + θ₂ = pi
⇒ θ₁ = pi - θ²
Now, z₁ = |z2|[cosθ(pi - θ₂) + i sin(pi - θ₂)]
= z₁ = z₂(-cosθ₂ + i sinθ₂)
= z₁ = - |z₂|(cosθ₂ - i sinθ₂)|
= z₁ = - |z₂|(cosθ₂ - i sinθ₂)
⇒ z₁ = - z₂(bar)

Because, f(- x) = f(x) is the necessary condition for a function to be an even function, which is only satisfied by x²+ sin²x .

2001 = 3 x 23 x 29 and (3+23+29)
= 55 ⇒ a = 3, b = 23, c = 29

6, a bare in H.P 
 are in A.P.

Because , the determinant of a skew symmetric matrix of odd order is always zero and of even order is a non zero perfect square.

Required area :

x-y-3=0

or a symmetric matrix A’ = A . therefore , 

Put   therefore the given expressionis sin2θ = 2sinθcosθ

3^2x2 = 3⁴ = 81

Given lines are x+4y=3   (i) 
& 3x+y=15        (ii)
We first check which of the line (i) & (ii) is line of regression y
on x and x on y. Let line x+4y=3 be the line of regression x on y, then
other be the line of regression y on x.
∴ From (i) i.e. line of regression x on y we have x=−4y+3
∴ b(xy)=regression coefficient x on y=−4 and 3x+y=15
∴ y=−3x+15
∴ b(yx)=regression coefficient y on x=-3
Now count r²=b(yx)b(xy)=(−4)(−3)=12
⇒ ∣r∣=2(3)^1/2
​which is not possible as 0≤r²≤1. So our assumption is wrong
and line x+4y=3 is line of regression y on x & 3x+y=15 is line of
regression x on y.
∴ 3x+y=15
⇒ x=(15−y)/3
⇒ x=(15−3)/3   (By putting y=3)
​= 4

A = {3, 5}
A × A = {(3, 3), (3, 5), (5, 3), (5, 5)}
A × (A × A) = {(3, 3, 3), (3, 3, 5), (3, 5, 3), (3, 5, 5), (5, 3, 3), (5, 3, 5), (5, 5, 3), (5, 5, 5)}

Total number of letters = 4
 Number of ordered pairs of letters that can be formed like (A, M) or (P, O) etc = ⁴P₂ ​= 4!/2!
​= 24/2
​= 12

Step-by-step explanation:

Customers are asked to stand in the lines. If one customer is extra in a line, then there would be two less lines. If one customer is less in line, there would be three more lines.

Let say There are  C customers in a Line  and total L number of lines

Total number of customers = ( customers in a line) * (number of Lines)

=>Total number of customers =  CL

If one customer is extra in a line, then there would be two less lines

=> Total number of customers = (C + 1)(L -2)

(C + 1)(L -2)  = CL

=> CL + L - 2C - 2 = CL

=> L - 2C  = 2   - eq 1

If one customer is less in line, there would be three more lines.

=> Total number of customers = (C - 1)(L +3)

(C - 1)(L +3) = CL

=> CL - L + 3C - 3 = CL

=> - L + 3C = 3    - eq 2

Adding eq 1 & eq 2

=> C = 5

L - 2(5) = 2

=> L = 12

5 customers in a Line

Total Number of customers =  CL = 5*12  = 60