AWES PGT Math Mock Test - 4 - 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.

SpaceX successfully deployed the TSAT-1A satellite developed by Tata Advanced Systems Limited in partnership with Satellogic Inc. The launch took place from SpaceX’s Falcon 9 rocket from Kennedy Space Center, Florida. The TSAT-1A satellite was assembled at TASL’s Assembly plant in Vemagal, Karnataka, and is designed to deliver high-resolution optical satellite images.

The correct answer is Dynasty.

Key Points

• When members of the same family become rulers one after the other, the family is called a dynasty.
• An example of a dynasty is the Mauryan Dynasty.
• Wherein, there were three important rulers- Chandragupta, his son Bindusara, and Bindusara's son Ashoka.
• Alternative terms for dynasty are 'family', 'clan' etc.

 Thus, we can say that Dynasty is when members of the same family become rulers one after the other.

Additional Information

•  Empire is a political construct in which one state dominates over another state or a series of states.

The correct answer is 2 i.e. Bolsheviks.

Some facts about the Russian Socialist Democratic party(RSDP):

• The formation was the party that happened in 1898.
• The party followed Marxist ideas, believing the industrial working class, not peasants, would bring about revolution.
• The party ideas were based on the philosophies of Karl Marx and Friedrich Engels, namely that despite Russia's agrarian life, the real radical potential extended with the industrial working class.
• They played an important role in the politics of Russia at that time and they also won few seats in the elections.
• It was mainly divided into two groups - Bolsheviks and Mensheviks.
• The following table will help you to understand them better:

World Oral Health Day is celebrated annually on March 20 to raise awareness about oral health and its connection to overall well-being. It was first observed on September 12, 2007, which marked the birthday of Dr. Charles Godon, the founder of FDI World Dental Federation. The day aims to highlight the importance of oral hygiene and preventive measures against common oral diseases like cavities, which affect a significant portion of the global population.

Useful strategies for teaching students with mental retardation include the following:

• Teach one concept or activity component at a time
• Teach one step at a time to help support memorisation and sequencing
• Teach students in small groups, or one-on-one if possible
• Always provide multiple opportunities to practice skills in a number of different settings
• Use physical and verbal prompting to guide correct responses, and provide specific verbal praise to reinforce these responses

Mastery over the subject matter is one of the very essential factors of a teacher that affect the process of learning. 

Informal education is a form of education that is learnt by the student outside the school. Family plays a major role in the informal education of a child. 

Let, sin^-1(0.6) = A…………(1)
  ( Since, sin² A + cos² A = 1 ⇒ sin² A = 1 - cos² A ⇒ sin A = √(1-cos² A) )

cosec A (sin B cos C + cos B sin C) = cosec A × sin(B+C)
= cosec A × sin(180 – A)
= cosec A × sin A
= cosec A × 1/cosec A
= 1

A³ = I ⇒  Pre - multiplying both sides by A⁻¹,A⁻¹, A³ = A⁻¹ I ⇒ A² = A⁻¹

It is asked to find out the number of ways in which 8 different flowers can be seated to form a garland so that 4 particular flowers are never separated.

According to the question, there are 8 flowers, but it is given that four particular flowers are never separated. So four particular flowers will always remain adjacent to each other.

To solve this problem we should know the following cases of circular permutations:

• If clockwise and anti-clockwise orders are different, the total number of circular permutations is: (n-1)!.
• If anti-clockwise and clockwise orders are taken as the same, then the total number of circular permutations is given by (n-1)!/2!

It is important to know which formula is applicable in this case.

When we turn a garland it forms a different arrangement. But it still is the same garland.
For example, consider a set of numbers like ‘1234’. When turned around it looks like ‘4321’ but it still is the same permutation of numbers.
In a similar way, the garland when turned might have a different permutation but it still is the same garland.
Therefore we’ll use the 2nd formula.
For n distinct objects in which clockwise and anticlockwise orders are taken as the same, the total number of circular permutations is: (n-1)!/2
Here in this case, given that four flowers must be together in all cases.
So we’ll club together all four particular flowers and consider this as one object.
Now we have 5 different objects - four flowers and four particular flowers clubbed as one object. Now we have to arrange these five objects in five circular seats.
In that case, the number of permutations is (5-1)!
And in every permutation, the clubbed flowers can be arranged in 4! ways.
So there are a total of (5-1)! * 4! Permutations.
But we have seen that the garland is the same in anticlockwise and clockwise order.
Therefore for every permutation, we have included its rotated permutation.
So the total number of circular permutations of garlands is : (5-1)!*4! /2

(5-1)! * 4! /2 = (4*3*2*1)*(4*3*2*1)/2
= 24 * 12 = 288

Thus the total number of ways in which 8 different flowers can be seated to form a garland so that four particular flowers are never separated is 288.

LHD = limh→0 ((−h)² sin(−1/h) − 0)/−h
limh→0 −h² sin(1/h)/−h
= limh→0 h × sin(1/h)
= 0
RHD = limh→0 (h² sin(1/h) − 0)/h
= limh→0 h × sin(1/h)
= 0
RHD=LHD
∴ f(x) is differentiable at x= 0

Number of words beginning with A = 4! = 4 × 3 × 2 = 24
Number of words beginning with N = 4! = 4 × 3 × 2 = 24
Number of words beginning with R = 4! = 4 × 3 × 2 = 24
Number of words beginning with U = 4! = 4 × 3 × 2 = 24
So, in total 96 words will be formed while beginning with letter A, N, R and U.
Now, 97th word according to dictionary order will be VANRU
Now, 98th word according to dictionary order will be VANUR
Now, 99th word according to dictionary order will be VARNU
Finally, 100th word according to dictionary order will be VARUN.
Hence, option (c) is the correct answer.

    (Triangle Inequality)
 ....(i)

       ....(ii)

Adding (i), (ii),(iii), we have 

Apply , C1→C1 - C3, C₂→C₂-C₃

= 10 - 12 = -2

Probability of getting head = 1/2 and probability of throwing 5 or 6 with a dice = 2/6 1/3 . He starts with a coin and alternately tosses the coin and throws the dice and he will if he get a head before he get 5 or 6.

n³ + (n+1)³ + (n−1)³
=3(n)³ + 6n
=3n(n² + 2)
=3n(n² − 1 + 3)
=3(n(n−1)(n+1)+3n)
n(n−1)(n+1) and 3n are both divisible by 3. Hence their sum is also divisible by 3. 
Therefore the whole number is divisible by 9.

We have , 

Therefore, range of f(x) is {-1}.

⁸C_r = ⁸C_p = ⁸C^8-p     
So, either r = p or r = 8 – p
i.e. r = p or r + p = 8

The expression depicts the ratio of two numbers, if the ratio between the numbers is constant, then it will definately form a GP.

A = {(5x+2, 2x, 2x) (5x+2, x+2, 2x) (5x+2, 2x, x+2)}
= (5x+2) {(1, 2x, 2x) (1, x+2, 2x) (1, 2x, x+2)}
= (5x+2) [(1(x+2)^2 - 4x^2) - 2x(x+2 - 2x) + 2x(2x - x - 2)]
= (5x+2) [(x+2 - 2x)(x+2+2x)-2x(2 - x) + 2x(x-2)]
= (5x+2) [(2-x)(3x+2) -2x(2-x) -2x(2-x)]
= (5x+2) (2-x)[3x+2-2x-2x]
= (5x+2) (2-x)²

As value of both determinants are equal
∴ (1×1) - (1×1) = 4x - 2
0 = 4x-2.
4x = 2.
x = 2/4 = 1/2

A = {(a, b) ∈ R × R : |a − 5| < 1 and |b − 5| < 1}

⇒ a ∈ (4, 6) and b ∈ (4, 6)

Therefore, A = {(a, b): a ∈ (4, 6) and b ∈ (4, 6)}

Now, B = {a, b) ∈ R × R : 4 (a − 6) ² + 9(b−5) ² ≤ 36}

From the conditions above for set A, the maximum value of B is:

4 (a − 6) ² + 9(b−5) ² = 4 (4 − 6)² + 9(6−5)² = 25 ≤ 36

We can check for other values as well.

Elements of set A satisfy the conditions in Set B.

Hence, A is a subset of B.

Correct answer is D.