AWES TGT Maths Mock Test - 6 - AWES TGT/PGT MCQ

Prime Minister Modi announced India's plan to open an embassy in Timor-Leste during the ASEAN-India summit in Jakarta, Indonesia, emphasizing India's commitment to stronger ties with Timor-Leste and the ASEAN region.

Reliance Industries (RIL) has announced a merger deal with Viacom18 Media and The Walt Disney Company to establish a joint venture (JV) integrating Viacom18 and Star India operations. With RIL committing a significant investment of Rs 11,500 crore (approximately US$ 1.4 billion) into the JV, this strategic move aims to reshape the Indian entertainment and sports industry landscape.

The US Chamber of Commerce released the 12th edition of the International Intellectual Property (IP) Index, ranking 55 economies on their IP frameworks. India secured the 42nd position with a 38.64% overall score. The United States, the United Kingdom, and France topped the list, emphasizing the pivotal role of strong IP systems in economic development. The index evaluates the effectiveness of IP landscapes in fostering innovation and creative industries globally.

The Education of children with special needs should be provided along with children with non-special needs. To promote the education of special needs children along with non-special needs children concept of inclusive education was proposed. In Inclusive Education, all students are welcomed, they have been given equal opportunity irrespective of caste, creed, religion, special-needs, non-special needs.
Hence, the correct answer is, 'Along with other normal children.'

Affective motives deal with the need to reach satisfying feeling states and obtain personal goals. Maslow's theory deals with all types of needs. His Hierarchy of Needs Theory includes Psychological needs (food, air, water.) Safety needs (personal security, health.) Love and Belonging need (friendship, intimacy.) Esteem needs (respect, status.
Hence, this is the correct answer.

Let S = {Persons who drive scooter}
C = {Persons who drive car}
Given, n(S ∪ C) = 80, n(S) = 35, n(C) = 60
Therefore, n(S ∪ C) = n(S) + n(C) - n(S ∩ C)
80 = 35 + 60 - n(S ∩ C)
80 = 95 - n(S ∩ C)
Therefore, n(S ∩ C) = 95 – 80 = 15
Therefore, 15 persons drive both
scooter and car.
Therefore, the number of persons who
drive a scooter only = n(S) - n(S ∩ C)
= 35 – 15
= 20
Also, the number of persons who drive car only = n(C) - n(S ∩ C)
= 60 - 15
= 45

There are 8 letters in the word TRIANGLE.
2 alphabets are fixed, remaining are 6 alphabets
So, number of arrangements = ⁶P₆
= 6!
= 720

⇒ αS = α + 2α² + 3α³ + ...+(n -1)α^n-1 +nαⁿ

On subtracting, we get

Since, α is nth root of unity, therfore
αⁿ = 1 

z =| z | -3+ 2i ⇒ | z |²= (| z | -3)² + 4 = | z |² -6 | z | +9 + 4Þ | z | 13/6
=
Thus,  z = - 5/6 + 2i

Substitute ‘n’ and verify the options.

d = 100
S_n = 21700
n = 14
S_n = n/2[2a + (n-1)d]
21700 = 14/2[2a + (14-1)100]
= 21700 = 7[2a + 1300]
= 3100 = 2a + 1300
⇒ 3100 - 1300 = 2a
⇒ 1800 = 2a
⇒ a = 900

Roots of (x - α) (x - β) = λ are γ and δ, 
i.e., (x - α) (x - β) - λ = (x - γ) (x - δ)
So, (x - γ) (x - β) + λ = (x - α) (x - β)

9(2x+5) - 3(5x+2) = 0
18x+45-15x-6 = 0
3x = -39
x = -13

For internal point p(2, 8),  4 + 64 – 4 + 32 – p < 0 ⇒ p > 96 
and x intercept = therefore 1 + p < 0
⇒ p < -1 and  y intercept = ⇒ p < -4
Hence (D) is the correct answer.

We know that in a circle of radius r units, if an arc of length l units subtends an angle theta radian at the centre, then θ = l/ r.
Here, r = 7 m (length of rope will be equal to radius) and l = 210 m (length of arc will be the length which the cow grazed)
Thus, θ = 210^o/ 7 
= 30^o

Given 

Required area :
= (1/4) area of ellipse – area of right angled triangle AOB.   (π - 2)

a+2d=600
a+6d=700
4d=100
d=25
so a+2x25=600
a+50=600
a=550

First Term =  a+b
Second Term =  a-b
Common Difference is a-b-a-b = -2b.

Summation of 22 terms of an A.P. is     
n/2 [ 2a + (n-1)d ]
22/2 [2 ( a+b) + (22-1)-2b ]
11  [ 2a+2a-b + (21)-2b  ]
11  [  2a+2b - 42b ]
11  [ 2a - 40b ]
22a - 40b.

So, the summation of given A.P. for 22 terms is 22a - 40b 

Sum of two solutions is zero ,so both are inverse of each other. So we have the solutions as a,-a,b.
(x-a)(x+a)(x+b)=(x²-a²)(x+b)=x³+bx²-a2x-a2b
pq=-a²b=r

b-ax=0

b=ax

b/a=x

i.e. remainder is p(b/a)