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

The Haryana Assembly passed a bill aimed at curbing illegal immigration, addressing concerns regarding the activities of unregistered travel agents. This legislative action reflects the state's efforts to tackle issues related to immigration and safeguard the interests of its residents.

Lebanese Judge Nawaf Salam was elected as the new president of the International Court of Justice (ICJ) for a three-year term, succeeding US Judge Joan Donoghue. This appointment highlights Salam's distinguished career path and his significant role within the field of international law.

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.

Key Points  
Some important fundamental principles of the NEP 2020 are:

• Full equity and inclusion as the cornerstone of all educational decisions to ensure that all students are able to thrive in the education system.
• It includes the overall development of the leader, it covers all three aspects as Cognitive domain, affective domain, and psychomotor domain.
• Emphasis on conceptual understanding rather than rote learning and learning-for-exams.
• Assessment of the students should be done by using different methods, by different activities including role play, portfolios, etc.
• The curriculum/instruction is in the native language or in the mother tongue of the primary students so that they can understand and imply it perfectly.
• Promoting self-assessment and the peer assessment done by the student in the classroom.
• Respect for diversity and respect for the local context in all curriculum, pedagogy, and policy, always keeping in mind that education is a concurrent subject.
• Establishment of the linkage of the concepts with the environment or we can say that the linkage of the school with the home.
• The teacher should promote or encourage the abilities of the learners, they should reflect on the unique abilities of the learners on their report card so that learner improves their unique abilities much better than now.
• Promoting multilingualism and the power of language in teaching and learning.
• Creativity and critical thinking encourage logical decision-making and innovation.
• It emphasizes group work as well as individual work, NEP 2020 links the study to the curriculum.

Thus by all these references, we can conclude that According to National Education Policy 2020, the progress card of the students communicated to the parents would be a reflection of the progress as well as the uniqueness of the student.

Pressure from parents, Fear of failure, and Competition with peers affects negatively. Only meaningful association is a factor that affects positively. Meaningful associations can be an association between teacher and student, As teachers may influence their student's learning. Forming an association with any such person to whom the students get knowledge and motivation whether it is peer association, Teacher-students association, etc.
Hence, the correct answer is, 'Meaningful association.'

Equilibration takes place when a child strikes balance between the two processes while trying to internalise the perceived object.

Equilibration: The process of striking a balance between accommodation and assimilation. On the other hand, When the child strikes a balance between the two processes while trying to internalize the perceived object, adaptation (a relatively stable structure) takes place.

T_r+1 = ²ⁿCr(x)^r (1)^2n-r
T_r+3 = ²ⁿC_r+2 (x)^r+2 (1)^2n-r-2
T_r+1 : T_r+3 
= ²ⁿC_r = ²ⁿC_r+2
=> 2n!/(2n-r)!r! = 2n!/(r+2)!(2n-r-2)!
=> 1/(2n-r)(2n-r-1) = 1/(r+2)(r+1)
=> (r+2)(r+1) = (2n-r)(2n-r-1)
=> r2 + 3r + 2 = 4n2 - 2nr - 2n - 2nr + r^2 + r
=> 0 = 4n2 - 4nr - 2n + r - 3r - 2
=> 0 = 4n2 - 4nr - 2n + r - 3r - 2 - 2 + 2
=> 0 = 4n2 - 4nr - 4 - [2n + 2r - 2]
=> 4n(n-r-1) -2(n-r-1)
Therefore n - r - 1 = 0
=> n = r+1

lim x → 2 [(2^x - 4) (2^x - 2) ((√2^x) + 2)]/[(√2^x - 2) (√2x - 2)]
= lim x → 2 [(2x - 4) (2 *4)]/(√2x - 2)
= 2 lim(x → 2) [(√2x)2 - (2)2]/(√2x - 2)
= 2 lim(x → 2) [(√2x)2 + 2) (√2x)2 - 2)]/(√2x - 2)
= 8

= [(5/4) + (3/4)] / [(5/4) - (3/4)]
=(8/4) / (2/4)
=4

 tan(45°) = tan(45°/2 + 45°/2)
= 2tan(45°/2)/(1 - tan²(45°/2))
(Using expansion for tan(2x))
This implies, 1 = 2tan(45°/2)/(1 - tan²(45°/2))
Rearranging terms, tan²(45°/2) + 2tan(45°/2) - 1 = 0
Solving the quadratic equation x² + 2x - 1 = 0 gives
x = (√2 - 1) or (-√2 - 1)
But tan(45°/2) lies in the first quadrant, therefore it should be positive.
tan(45°/2) = (√2 - 1)

We can expand (1+x)(1−x)ⁿ as 
= (1+x)(ⁿC₀​− ⁿC₁​.x + ⁿC₂​.x² + ........ +(−1)^n nC_n​xⁿ)

Coefficient of xⁿ is 
(−1)^n nC_n ​+ (−1)^n−1 nC_n−1
​=(−1)ⁿ(1−n)

a,b,c are in H.P
∴1/a , 1/b , 1/care in A.P
∴2/b= 1/a+1/c_______ (1)
∴ x/a+y/b+1/c=0 ________ (2)
∴ From (1)
1/a+1/c−2/b=0 ______ (3)
∴ From (2) & (3)
We infer that,
(x=1,y=−2)
∴ Point is (1,−2)

If l₁, m₁, n₁ and l₂, m₂, n₂ are the direction cosines of two lines; and θ is the acute angle between the two lines; then the cosine of the angle between these two lines is given by : 

Expand (x + ai)ⁿ and (x – ai)ⁿ then multiply.

Use Baye’s Theorem formula


A : Red ball is drawn






= 14/39

Out of 20 professors, excluding the principal and vice-principal, 18 professors are left.
No. of ways of selecting 5 professors out of 18 = ¹⁸C₅

Let the equation of the required circle be (x – h)² + (y – k)² = r².
Since the centre of the circle passes through (0, 0),
(0 – h)² + (0 – k)² = r²
⇒ h² + k² = r²
The equation of the circle now becomes (x – h)² + (y – k)² = h² + k².
It is given that the circle makes intercepts a and b on the coordinate axes. This means that the circle passes through points (a, 0) and (0, b). Therefore,
(a – h)² + (0 – k)² = h² + k² …………… (1)
(0 – h)² + (b – k)² = h² + k² ………… (2)
From equation (1), we obtain a² – 2ah + h² + k² = h² + k²
⇒ a² – 2ah = 0
⇒ a(a – 2h) = 0
⇒ a = 0 or (a – 2h) = 0
However, a ≠ 0; hence, (a – 2h) = 0 ⇒ h =a/2.
From equation (2), we obtain h² + b² – 2bk + k² = h² + k²
⇒ b² – 2bk = 0
⇒ b(b – 2k) = 0
⇒ b = 0 or(b – 2k) = 0
However, b ≠ 0; hence, (b – 2k) = 0 ⇒ k =b/2. Thus, the equation of the required circle is

Commutative law, in mathematics, either of two laws relating to number operations of addition and multiplication, stated symbolically: a + b = b + a and ab = ba

Therefore , the answer is -cos(x³) + c

The domain in ordered pair (x,y) is represented by x-coordinate. Therefore, the domain of the given function is given by : {1, 3, 2}.

The function is defined as:

f(x) = { 2x - 3, for x ≥ 2
          x, for x < 2

Calculate f(2):

Since 2 ≥ 2, use the first part:

f(2) = 2(2) - 3 = 4 - 3 = 1

Calculate f(1):

Since 1 < 2, use the second part:

f(1) = 1

Therefore, f(1) = f(2) = 1.

Eliminating y, we get :

Required area:

∵ In ∆ABC,
AB = AC
∴ ∠B = ∠C    ...(1)
| Angles opposite to equal sides of a triangle are equal
In ∆ABC,
∠A + ∠B + ∠C = 180°
| Sum of all the angles of a triangle is 180°
⇒ 90° + ∠B + ∠C = 180°
| ∵ ∠A = 90° (given)
⇒    ∠B + ∠C = 90°    ...(2)
From (1) and (2), we get
∠B = ∠C = 45°.