AWES TGT Maths Mock Test - 8 - AWES TGT/PGT MCQ

Bengaluru, known as the ‘garden city,’ faces its worst domestic water crisis. Over 30 localities receive water on a rotational basis every alternate day, with supply lasting only 30-45 minutes. The city, once abundant with 262 lakes, now has only 81 due to real estate development. The remaining lakes are at risk, impacting the city’s water supply. The reliance on the Krishna Raja Sagara reservoir is strained by a weak monsoon, leading to water shortages and skyrocketing tanker prices. Community involvement is crucial for lake preservation.

The Goa state government will set up a blended finance facility in partnership with the World Bank. This is the first of its kind, climate-focused, multi-sectoral initiative at the sub-national level. This will provide financial support to low-carbon climate friendly initiatives in Goa. The World Bank was established in the year 1944. Its headquarters is in Washington, D.C. Is in.

The US House of Representatives has bolstered the Quadrilateral Security Dialogue (Quad) by passing legislation to strengthen ties among the member nations – USA, Australia, India, and Japan. The bill mandates the creation of an Intra-Parliamentary Working Group for regular discussions among lawmakers, fostering political exchanges. It also instructs the Biden Administration to submit a report for enhanced governmental coordination within 180 days, urging talks with partner countries within 60 days to establish a parliamentary group.

NASA and Japan’s space agency, JAXA, are planning to launch the world’s first wooden satellite, LignoSat, in 2024. The satellite is designed to reduce space debris and is made of biodegradable magnolia wood, known as Hoonoki in Japanese. The satellite is being developed by scientists at Kyoto University. First tests have been performed in space-simulating laboratories, and wood samples found no signs of damage, decomposition, or mass changes. The initiative aims to make spaceflight operations more sustainable and pave the way for a more sustainable future in orbit.

Learning takes place by comparing previous knowledge and experience with the present learning experience through thinking and activities. Learning is a universal skill seen in all species. Thinking and Learning are two interwoven activities that help to develop knowledge, critical thinking, and creative thinking.

Key Points

•  Despite the addition of more specialized disciplines and subject instructors, experiential learning within each subject and investigations of relationships among different subjects will be encouraged and highlighted.
• Experiential learning will be implemented at all levels, with investigations of the connections between various disciplines as well as hands-on learning, education that incorporates the arts and sports, and pedagogy centered on telling stories, among others, as normal practices within each subject.
• Classroom activities will change to competency-based learning and teaching to address the achievement gap in learning outcomes. Additionally, the assessment instruments—including assessment "as," "of," and "for" learning—will be in line with the learning objectives, skills, and attitudes that are listed for each subject in a given class.
• Each subject's curriculum will be edited down to the fundamentals in order to allow room for critical thinking and more all-encompassing, inquiry-based, discovery-based, discussion-based, and analysis-based learning.

Hence, National Education Policy 2020 proposes that experiential learning should be encouraged to promote critical thinking. 

The Assessment process should not be boring, or it should be on the basis of only one aspect. The teacher should be careful about using a variety of ways to collect information, about the students learning across scholastic and co-scholastic boundaries. Only scholastic areas should not be focused on assessment. It should also include co-scholastic areas.
Hence, the correct answer is, 'Using a variety of ways to collect information about the students learning across scholastic and co-scholastic boundaries.'

Brainstorming is a creative group work in which group members produce large number of ideas quickly on a given topic or problems for subsequent evaluation. In this method, anyone can exchange remarks with anyone except that the participants are not allowed to criticize the ideas. Sometimes, quantity of ideas is more important than quality. Spontaneity is the hallmark of brainstorming sessions. On the spot ideas are expected.

Inclusion as a philosophy or practice cannot be discussed meaningfully unless it is situated in the context of diversity across the members of the group, especially in the framework of inclusive education. 

Key Points

• Inclusive education means creating effective classrooms where the educational needs of all children are addressed irrespective of ability or disability.
• It implies all learners, young people - with or without disabilities being able to learn together through access to common pre-school provisions, schools, and community educational settings with an appropriate network of support services.
• Social inclusion refers to a process by which efforts are made to ensure equal opportunities for all, regardless of their background, be it money, class, ethnicity, gender, race, or whatever the index of diversity be, to enable full and active participation in all aspects of life, including civic, social, economic, and political activities, as well as participation in decision-making processes.
• Social inclusion can be approached as a goal, an objective, and a process. Its process affects almost all societal activities, and should therefore be approached from various dimensions.
• Hence, the effort for quality-based inclusive education for all should be a Child-centered, relevant, and justified process of learning in a social context so that is not affected by social barriers and get an equal opportunity to learn and develop in life.

​Thus, it is concluded that a Child-centered, relevant, and justified process of learning in a social context will be the effort for quality-based inclusive education for all.

Hint

• Sensitivity towards all the needs of the children comes under child-centered education. The teacher must take care and be sensitive towards the children.
• Improvement in self qualification and teaching methodology: Teacher will improve themselves and their methodologies to impart quality education to children. This is also a part of child-centered education.
• School should be complete with all the high technology instruments to impart quality, relevant and justified education to children.

One of the goals of education is to develop independent learning in students. However, at times, students might need a little push from the teacher in order to achieve that independence. Scaffolding is a technique that helps during such a scenario.

⇒ z is purely real.
∴ Im (z) = 0

Centre is (1, 3) and radius = 2
If r = radius of second circle then r² = 2² + (3 - 1)² + (2 - 1)²
⇒ r = 3.
Hence (C) is the correct answer.

Let √(5 – 12i) = x + iy
Squaring both sides, we get
5 – 12i = x² + 2ixy +(iy)² = x² – y² + 2xyi.
Comparing real and imaginary parts , we get
5 = x² – y² ———– (1) and xy = – 6 ———— (2)
Squaring (1), we get
25 = (x² – y²)2 = (x² + y²)² – 4x²y²
⇒ 25 = (x² + y²)² – 4(– 6)²
⇒ (x² + y²)² = 169
⇒ x² + y² = 13 ———- (3)
Adding (1) and (3) we get
2x² = 18
⇒ x = ± 3.
Subtracting (1) from (3) we get
2y² = 8
⇒ y = ± 2.
Hence, square root of √(5 – 12i) is (3 – 2i)
Similarly, √(5 + 12i) is (3 + 2i)
√(5 + 12i) + √(5 – 12i)
⇒ (3 + 2i) + (3 - 2i)
⇒ 6

Correct option is D.
To find A×B we take one element from set A and one from set B. 

Given that 99 elements are common to both set A and set B.

Suppose these common elements are N_1​,N₂​,N₃​,...N₉₉​. 

Select an ordered pair for A×B such that both are selected out of these common elements. Examples: (N₁​,N_2​),(N₃​,N_5​)
All these will also be elements of B×A. Hence number of elements common to A×B and B×A is 99×99=99² ( first element in ordered pair can be selected in 99 ways; second element can also be selected in 99 ways)

n[(A×B)∩(B×A)]=n[(A∩B)∩(B∩A)]=(99)(99)=99²

= 6.280 cm

y=sin4x,  and z=cos4x
So by using chain rule
df(x)/dx = dsin⁴x/dx + dcos⁴x/dx
=dy⁴/dy * dy/dx + dz⁴/dz * dzdx
=dy⁴/dy * dsinxdx + dz⁴/dz * dcosx/dx
=4y⁽⁴⁻¹⁾⋅cosx+4z(4−1)⋅(−sinx)
=4sin³xcosx − 4cos³xsinx
=4sinxcosx(sin²x − cos²x)
=2sin2x(−cos2x)
=−2sin2xcos2x
=−sin4x

Any square matrix when multiplied with its inverse gives the identity matrix. Note that non square matrices are not invertible.

Let A1, A2, A3, ........ , A40 be 40 A.M's between two numbers 'a' and 'b'.
Then, 
a, A1, A2, A3, ........ , A40, b is an A.P. with common difference d  = (b - a)/(n + 1) = (b - a)/41
[ where n = 40]
now, A1, A2, A3, ........ , A40  = 40/2( A1 + A40)
A1, A2, A3, ........ , A40 = 40/2(a + b)
[ a, A1, A2, A3, ........ , A40, b is an Ap then ,a + b = A1 + A40]
sum of 40A.M = 120(given)
120= 20(a + b)
=> 6 = a + b ----------(1)
Again, consider B1, B2, ........ , B50  be 50 A.M.'s between two numbers a and b.
Then, a, B1, B2, ........ , B50, b will be in A.P. with common difference = ( b - a)/51
now , similarly,
B1, B2, ........ , B50 = 50/2(B1 + B2)
= 25(6) ----------------from(1)
= 150

cot^-1a - cot^-1b + cot^-1 b - cot^-1 c - cot^-1 a = 0

Let the equation of circle x² + y² + 2gx + 2fy + c = 0..........(1)
Equation of tangent at Origin(0,0)
So, x(0) + y(0) = g(x+0) +f(y+0) + c = 0
or gx + fy + c = 0
But it is given to be axis of x, so y=0
therefore, g = 0, c=0
Equation(1) becomes x² + y² + 2fy = 0..(2)
If it touches the line 3y = 4x + 24
i.e 4x - 3y + 24 = 0
Then the length is perpendicular from centre (0,-f) on the line is numerically = radius f,
[4(0) -3(-f) + 24]/(16 + 4)^1/2 = +-f
=> 3f + 24 = +- 5f
= f = 12, -3
Putting these values of f in (2), we get
x² + y² + 24y = 0, x² + y² - 6y = 0

α + β = (a – 2), αβ = –a –1
α² + β² = (α + β)² - 2αβ = (a - 2)² + 2(a + 1)
α² + β² = α² - 2a + 6
ax² + bx+ c takes least value -D/4a, so, least value at of α² + β² is 5.

The normal line to circle is →y² - 2 y + 4 x -2 xy=0
→ y(y-2) - 2x(y-2)=0
→ (y-2)(y-2x)=0
the two lines are , y=2 and 2 x -y =0
The point of intersection of normals are centre of circle.
→ Put , y=2 in 2 x -y=0, we get
→2 x -2=0
→2 x=2
→ x=1
So, the point of intersection of normals is (1,2) which is the center of circle.
Also, the circle passes through (2,1).
Radius of circle is given by distance formula = [(1-2)² + (2-1)²]^½ 
=(1+1)^½ =(2)^½
The equation of circle having center (1,2) and radius √2 is
= (x-1)²+(y-2)²=[√2]²
→ (x-1)²+(y-2)²= 2
x²+y² -2x-4y+3 = 0

In cartesian co-ordinate system :
Equation of a plane passing through three non collinear

Points (x₁, y₁, z₁) , (x₂, y₂, z₂) and (x₃, y₃, z₃) is given by :



Therefore, the equations of the planes that passes through three points (1,1,0), (1,2,1),  (-2,2,-1) is given by :



⇒ (x-1)(-2) - (y-1) (3) + 3z = 0
⇒ 2x+3y - 3z = 5

Given sequence : 2, 2√2, 4….
First term a₁ = a = 2 and 2nd term a₂ = 2√2, then
Common ratio r = a₂/a = (2√2)/2
Let a_n = 64
∴ ar^(n-1) = 64
⇒ 2.(√2)^(n-1) = 32
⇒ (2)^(n-1)/2 = 32
∴ (2)^(n-1)/2 = (2)⁵
⇒ (n − 1)/2 = 5,
⇒ n = 11

Apply Trig Substitution: x=4sin(u)​

Let equation of tangent with slope =m and point (0,1)
(y−1)=m(x−0)⇒y=mx+1
Intersection point
x²+(mx+1)²−2x+4(mx+1)=0
(1+m²)x²+(−2+6m)x+5=0
For y=mx+1 to be tangent, discriminant =0
(6m−2)²−4×5(1+m²)=0
36m²+4−24m−20m²+20=0
16m²−20m+24=0
⇒ 2m²−3m−2=0
(2m+1)(m−2)=0

Here , D.R’s of normal to the plane are 1, 1 , 1 ,its D.C ‘s are :

On dividing x + y + z = 1 by √3 , we get :
 It is of the form : lx+my+nz = d , therefore , d = 1/√3 .