NVS PGT Mathematics Mock Test - 3 - NVS TGT/PGT MCQ

The correct answer is No weight.

Gravity is a force that attracts a body toward the centre of the earth or any other mass-bearing physical body.

F = mg
where F is force, 
m is mass, and 
g is acceleration due to gravity.

The weight of an object is the force that attracts it to the earth.

A body that is free to fall under the influence of gravity is acted upon by the force of gravity.

However, the object is not exerting any force on any surface. As a result, the weight of object is no weight (zero).

Given number: 

5934162

New number after digits are arranged in descending order:

9654321

Thus we can see only position of one digit is remain unchanged.

Hence, the correct answer is "One".

There are 8 triangles in the figure. By counting the individual triangles, we can see that there are 2 large triangles, 4 medium triangles, and 2 small triangles, making a total of 8 triangles.

The above information can be summarized below diagram,

Therefore, the code for “was” will be “3”. 

Hence, option 4 is the correct answer.

Successful teachers are those who have the ability to maximise the learning potential of all students in their class. Developing positive relationships between a teacher and student is a fundamental aspect of quality teaching and student learning. In order to develop rapport with pupils, a teacher should behave with them in a democratic way, guide them, and he should have communicative ability.
Gillespie recognised that the inherent qualities of a student-teacher relationship (caring, knowing, trust and mutual respect) and a teacher's rapport with students results in a classroom environment where students are affirmed and supported to achieve their best.

The given system of equation has a unique solution if : 

[log₁₀ x] = 0, for any value of x ∈ {1, 2, ......9), ...(1)
Similarly [log₁₀ x] = 1, for x ∈ {10, 11, 12 ... 99}...(2)
and [log₁₀x] = 2, for
x ∈ {100, 101, 102, ... 999} ...(3)
Now consider, 1 ≤ n ≤ 9, then
[log₁₀1] + [log₁₀2] + [log₁₀3] ... [log₁₀ n] = 0 (i.e., ≠ n)
Hence the expression given in the question cannot be satisfied.
Now consider, 10 ≤ n ≤ 99, then [log₁₀1] + [log₁₀2] ... [log₁₀n]
From (1) and (2), the above expression becomes (0 + 0 ... 9 times) + (1 + 1 + ... (n – 9) times) = n – 9
Using the same approach, for
100 ≤  n ≤ 999, [log ₁₀1] + [log₁₀2] ... [log ₁₀n] = 90 + 2(n – 99)
If can be seen that, only for the third case i.e., 100 ≤  n ≤  999, can the expression given in the question be satisfied.
Hence 90 + 2(n – 99) =  n
⇒ n = 198 – 90 = 108
∴ 107 ≤ n < 111.

A relation R on a non empty set A is said to be symmetric if fx Ry ⇔ yRx, for all x , y ∈ R .

       ............. (i)
        ............. (ii)
On multiplying Equation (i) by i and adding it Eq. (i), we get

Again multiplying Eq. (ii) by i and subtracting it from Eq (i) we get
  ............. (iv)

On multiplying Eqs (iii) and (iv) we get

Let z = 0 + ib, where b < 0. Then z is represented by a point on the negative direction of y-axis. 

Total no of players = 14 out of which 5 are fixed.
So, 11-5 = 6
Remaining players = 14 - 6
= 9 players
9C6 = 9!/(3!*6!)
= 84 

We know that a number between 100 and 1000 has three digits. 
So we have to find all the three digit numbers with distinct digits.

We cannot have 0 at the hundred’s place for 3-digit number.  So the hundred’s place can be filled with any of the 9 digits.  1,2,3,…..9.  So, there are 9 ways of filling the hundred’s place.

Now, 9 digits are left including 0.  So ten’s place can be filled with any of the remaining 9 digits in 9 was.  Now the unit’s place can be filled with any of the remaining 8 digits.  So, there are 8 ways of filling the unit’s place.

Hence, the total number of required numbers = 9 x 9 x 8= 648.

As the value of ‘n’ increases, it becomes difficult and tedious to calculate the value of ⁿC_x.

Cosines of the angles α,β,γ are called direction cosines.

(i) The graph of the function y = cos x is continuous and extends on either side in symmetrical wave form.
(ii) Since the graph of y = cos x intersects the x-axis at the origin and at points where x is an odd multiple of 90°, hence cos x is zero at x = (2n + 1)/π² where n = 0, ±1, ±2, ±3, ±4, ……………... .

α = cisx, β = cisy, γ = cisz
Given α + 2β + 3γ = 0 ⇒ α³ + 8β³ + 27 γ³ = 18αβγ
⇒ sin 3x + 8sin 3y + 27 sin 3z = 18sin(x + y + z)

a = 4, l = 31, n = 8
(l-a)/(n+1) = (31-4)/(8+1)
= 27/9 
= 3

A+2B=7------(1)
3A+2B=9------(2)
Subtracting (2) from (1)
we get, 2A=2
A=1
Subsitute A=1 in (1)
1+2B=7
2B=6
B=3
therefore A = 1, B = 3
 

P (A will die within a year) = x
P (B will die within a year) = y
∴ P (Exactly one of them will be alive at the end of the year)
= P (A is alive & B is dead)+ P (A dies B is alive)

(As these are independent events)

nth G.M. between a and b is
G_n = arⁿ
Where common ratio is r = (b/a)^(1/(n+1))
​So, to insert 3 geometric means between 1 and 256
 r = (b/a)^(1/(n+1))
r = (256/(1)^(1/(3+1))
r = (256)^1/4
r  = (4)^(4)1/4
r = 4
G_n = 1 * (4)ⁿ
G₁ = 1 * (4)¹ = 4
G₂ = 1 * (4)² = 16
G₃ = 1 * (4)³ = 64
The terms are  4, 16, 64

Children think that everything around them, including toys, is alive. This example points to a prominent characteristic of the preoperational stage called ‘animism’ by Piaget. It is a result of egocentric thinking and refers to the tendency of children to assign humanistic qualities to inanimate things.

• They believe that non-living things have desires and think, feel, and act like them.
• A logical consequence of animistic thinking is the strong emotional response towards non-living objects―talking to their toys, taking care of them, and expressing their feelings towards them. 

National Education Policy 2020-

According to NEP 2020, A good educational institution is one in which every student feels welcomed and cared for, where a safe and stimulating learning environment exists, where a wide range of learning experiences are offered, and where good physical infrastructure and appropriate resources conducive to learning are available to all students.

Key PointsSome important fundamental principles of the NEP 2020 are- 

• It will include Progress of the Child in Inquiry-Based Learning, Quiz, Projects Roleplay, Group Work, Portfolios, etc, as part of the assessment of the students.
• It includes the overall development of the leader, it covers all three aspects as Cognitive domain, affective domain, and psychomotor domain.
• Making board examination low stake and less stressful by focusing on Logic and Core Competencies
• It emphasizes group work as well as individual work, NEP 2020 links the study to the curriculum.

Hence, we can conclude that in the context of progress of the child, National Education Policy 2020 proposes inquiry-based learning.

The relation { } ⊂ A x A on a is surely not reflexive. However, neither symmetry nor transitivity is contradicted. So { } is a transitive and symmetry relation on A.

In the sentence, we are being told that Sir Surendranath is the greatest Indian orator. The given sentence expresses this in comparative degree. Therefore, the correct answer is 'greater'. 

The sentence is grammatically correct.
Hence, there is no error in the given sentence.

सही उत्तर 'लोक + एषण = लोकएषणा' है।

• दिए गए विकल्पों में असुमेलित 'लोक + एषण = लोकएषणा' है।
• 'लोक + एषणा' का सही सुमेल 'लोकैषणा (अ + ए = ऐ)' होता है।
• यह 'वृद्धि स्वर संधि' का उदाहरण है।
• इसमें अ या आ के बाद ए या ऐ आए तो ‘ऐ’ और ओ और औ आए तो औ हो जाता हो।

अन्य विकल्प-

• मातृ + इच्छा = मात्रिच्छा - यण स्वर संधि
• लघु + उत्तर = लघूत्तर - दीर्घ स्वर संधि
• सु + समा = सुषमा - व्यंजन स्वर संधि

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