NVS PGT Mathematics Mock Test - 5 - NVS TGT/PGT MCQ

Explanation:

• Evolutionary biology: It is a field of science that deals with the study of evolutionary processes like natural selection, speciation & common descent that has led to the diversification of life on earth.
• Charles Darwin is known as the father of ''Evolutionary Biology''.
• Darwin proposed a theory of evolution called natural selection in the year 1859. According to it those populations which are a better fit (reproductively fit) in an environment will be selected by nature and will survive more.
• Charles Darwin wrote a book named ''The origin of species'' which is considered to be the foundation of evolutionary biology.

Additional Information 

• Herbert Spencer- He Was best known for the introduction and application of evolutionary theory to philosophy, psychology, and social sciences
• The famous phrase 'Survival of the fittest' to mean Natural Selection was coined by Herbert Spencer. He originated this phrase after the publication of famous biologist Charles Darwin’s book ‘Origin of Species’ which talked about ‘Natural Selection’.
• Julian Huxley was an English biologist, philosopher, educator, and author who greatly influenced the modern development of embryology, systematics, and studies of behaviour and evolution.
• Stanley Miller along with H.C. Urey provided experimental evidence of ''chemical evolution''

Concept:

• Plants have different types of roots.
• Some store food, some breathe some hang from the branches.

Explanation:

• Roots are the underground structures that help in the absorption of water and minerals provide a proper anchorage to the plant parts, storage of reserve food material (Carrot, Radish), and synthesis of PGR (plant growth regulators).
• Sometimes roots get modified to perform different functions like storage of food, respiration, climbing, etc.
• These types of roots are called modified roots.
• Examples - prop root of the Banyan tree for providing support, Pneumatophores of Rhizophora, and Mangrove plants for respiration.

So, these statements are correct.

• To give support to the plant.
• To store food.
• To absorb water and minerals.

Thus, roots do not function to provide humus.

Given figure are -

From option 1 - Doctor, Man, Student

Some doctor are man, some man are student, some doctor are student.

So It is the best representation of the venn diagram.

Let A  = Doctor, B = Man, C = Student

From option 2 - table, Chair, Furniture

No table is chair, some furniture are table as well as chair. It is not correct representation of the venn diagram.

From option 3 - Gold, silver, ornaments

It is not correct representation of the venn diagram.

From option 4 - Family, Parents, Children

 It is not correct representation of the venn diagram.

Hence, "option 1" is the correct answer.

Four friends W, X, Y and Z are students of Class 10th.

i) W and X are good in Hindi but poor in English.

ii) W and Y are good in Science but poor in Mathematics.

iii) Y and Z are good in English but poor in Social Studies.

iv) Z and X are good in Mathematics as well as in Science.

Thus we can see Y and Z pairs of friends are good, both in English and Science

Hence, the correct answer is "Y and Z".

Subtract 2 from odd digits in given number and add 3 in even digits.

So, in new number there are two digits of five and two digits of seven.

The academic performance of students can be improved if parents are encouraged to supervise the work of their wards. Parents should choose to become involved in homework. They should be involved, believe their involvement will make a positive difference in their children's learning, and perceive that their involvement is invited, expected, and valued by school personnel. The parents need to be engaged in a wide range of activities in this effort, from establishment of basic structures for homework performance to more complex efforts focused on teaching for understanding and helping students develop effective learning strategies.

All the statements are correct. Black board is a primary teaching aid in a classroom. It makes the subject interesting for pupils. It also simplifies the tough topics and keeps the pace of the lecture moderate as it encourages writing while talking and hence making teaching effective.

Let P(x₁,y₁) be a point on the line 3x + 4y = 12
Equation of variable chord of contact of P(x₁,y1₎ w.r.t circle x2 + y2 = 4 
xx₁ + yy₁ − 4 = 0   ...(1)
Also 3x₁ + 4y1 − 12 = 0
⇒ x₁ + 4/3y₁ − 4 = 0   ...(2)
Comparing (1) and (2), we get
x = 1; y = 4/3
∴ Variable chord of contact always passes through (1, 4/3)

The given system of equations does not has a solution if : 


 

0 ⇒ 1(10 -9) - 1(5-3) + 1(3-2)

= 0 ⇒ 1-2 + 1 = 0

Since a, b, c are in H.P.

Now log (a + c) + log (a – 2b + c)
= log [(a + c){(a + c) – 2b}]
= log [(a + c)² – 2b (a + c)]
= log [(a + c)² – 2 × 2ac]
= log (a – c)² or log (c – a)²
= 2 log (a – c) or 2 log (c – a)
∴ log (a + c) + log (a – 2b + c) = 2 log (c – a)

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

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.

Centre (0, 4) and r = 1

Apply , C1→C1 - C3, C₂→C₂-C₃

= 10 - 12 = -2

(1 + x)ⁿ  = 1 + ⁿC₁x¹  + ⁿC₂x²+..............................+ⁿCnxⁿ
Three consecutive terms coefficients
ⁿCₐ  : ⁿCₐ₊₁  :  ⁿCₐ₊₂  :::  6 : 33 :  110
⇒  ⁿCₐ  = 6K  =>  n!/(a!)(n-a)!  = 6K  => n! = 6K (a!)(n-a)!
ⁿCₐ₊₁   = 33K   => n!/(a+1)!(n-a-1)! = 33K  => n!  = 33K (a+1)!(n-a-1)!
ⁿCₐ₊₂ = 110K  => n!/(a + 2)!(n-a-2)! = 110K  => n! = 110K (a + 2)!(n-a-2)!
6K (a!)(n-a)!  = 33K (a+1)!(n-a-1)!
⇒ 2  (a!)(n-a)(n-a - 1)! = 11 (a + 1)a! (n-a-1)!
⇒ 2(n-a) = 11(a + 1)
⇒ 2n - 2a = 11a + 11
⇒ 2n = 13a + 11
⇒ 13a = 2n - 11
33K (a+1)!(n-a-1)!  = 110K (a + 2)!(n-a-2)!
⇒ 3 (a+1)!(n-a-1)(n-a-2)!  = 10 (a + 2)(a + 1)!(n-a-2)!
⇒ 3 (n - a - 1) = 10(a + 2)
⇒ 3n - 3a - 3 = 10a + 20
⇒  3n = 13a + 23
⇒ 13a = 3n - 23
2n - 11 = 3n - 23
⇒ n = 12

Let y= sin x + cos x

dy/dx=cos x- sin x

For maximum or minimum dy/dx=0

Setting cosx- sin x=0

We get cos x = sin x

x= π/4, 5π/4———-

Whether these correspond to maximum or minimum, can be found from the sign of second derivative.

d^2y/dx^2=-sin x - cos x=-1/√2–1/√2 (for x=π/4) which is negative. Hence x=π/4 corresponds to maximum.For x=5π/4

d^2y/dx^2=-(-1/√2)-(-1/√2)=2/√2 a positive quantity. Hence 5π/4 corresponds to minimum

Maximum value of the function

y= sin π/4 + cos π/4= 2/√2=√2

Minimum value is

Sin(5π/4)+cos (5π/4)=-2/√2=-√2

A and B are disjoint set so their is no common element between A and B.
n(AuBuC) = n(A)+n(B)+ n(C)-n(AnB)-n(Anc)-n(BnC)+n(AnBnC)
As we know n(AuB)=n(A)+ n(B)-n(AnB)
Here when we add A and B we are adding (AnB) two times , as it is present in both A and B. So we subtract (AnB) one time from A and B.
Which means we need to take the area of A and B set but no area should repeat.
When we take three sets A,B and C
We take area of A+ Area of B + area of C ————eq
But they are intersecting so the area we are taking is greater than actual area. We have again added (AnB), (AnC) and (BnC) twice. Therefore we subtract the intersecting area from eq one time as done above
A+B+C-(AnB)-(AnC)-(BnC)
 
The intersection of the sets a and b is the set of all the elements which belong to both A and B. It is denoted by A ∩ B (“A intersection B”).
• If A and B do not have any element in common then A ∩ B= a null set = Ø.

(aⁿ⁺¹ + bⁿ⁺¹)/(aⁿ + bⁿ) is mean between a & b
Mean of a & b =  ( a + b)/2
=> (aⁿ⁺¹ + bⁿ⁺¹)/(aⁿ + bⁿ) = ( a + b)/2
=> 2aⁿ⁺¹ + 2bⁿ⁺¹  = aⁿ⁺¹  + bⁿ⁺¹  + baⁿ + bⁿa
=> aⁿ⁺¹ + bⁿ⁺¹ = baⁿ + bⁿa
=> aⁿ(a - b) = bⁿ(a - b)
=> aⁿ = bⁿ
=> (a/b)ⁿ = 1
=> n = 0    or a  = b

Laws are trigonometry can be applied to all type of triangles. These rules are generalised.

The equation of the common chord of the circles x²+y²-4x-4y = 0 and x²+y² = 16 is x + y = 4 which meets the circle x2+y2 = 16 at points A(4,0) and B(0,4). Obviously OA ⊥ OB. Hence the common chord AB makes a right angle at the centre of the circle x²+y² = 16.
Hence (d) is the correct answer.

One digit positive integers are 0,1,2,3,4 =5 positive integers
Number of one digit no. can be formed = 4
Number of two digit no. can be formed = 4*4 = 16
Number of three digit no. can be formed = 4*4*3 = 48
Number of  four digit no. can be formed = 4*4*3*2 = 96
Number of five digit no. can be formed = 4*4*3*2*1 = 96
Total = 4+ 16+ 48+ 96+ 96 = 260

Upper Triangular matrix is given by  :
.
 Here, a_ij=0 , if i is greater than j.and a_ij ≠ 0, if I is less than j.

National education policy 2020:

• The Union Cabinet has approved the new National Education Policy (NEP), 2020 with an aim to introduce several changes in the Indian education system.
• The main goal of the school education regulatory system is to improve educational outcomes so that children can learn to implement the acquired knowledge and skills in their practical life.

Key Points

Experiential learning:

• Experiential learning refers to the learning by gaining experience through active involvement. 
• In all stages, experiential learning will be adopted, including  arts-integrated and sports-integrated education, story-telling-based pedagogy, etc.
• Pedagogical approaches proposed in experimental learning under NEP-2020 includes:
  • Art-integrated education:
    •    It is a cross-curricular pedagogical approach that utilizes various aspects and forms of art and culture as the basis for learning of concepts across subjects.
    • It will be embedded in classroom transactions not only for creating joyful classrooms, but also for imbibing the Indian ethos through integration of Indian art and culture in the teaching and learning process at every level. 
  • Sports-integrated education:
    • It is another cross-curricular pedagogical approach that utilizes physical activities including indigenous sports, in pedagogical practices to help in developing skills such as collaboration, self-initiative, self-direction, self-discipline, teamwork, responsibility, citizenship, etc.
    • Sports-integrated learning will be undertaken in classroom transactions to help students adopt fitness as a lifelong attitude and to achieve the related life skills.
  • Story-telling-based pedagogy:
    • It refers to the art of narrating a story more interactively to people who are willing to listen. It is used as a strategy in teaching which broadens learner's reading choices.
      In a storytelling based pedagogy, the story chosen by the teacher to narrate is directly or indirectly related to the lesson to develop their fullest potential, both educationally and morally.

   ​Hence, it could be concluded that all of the above are the pedagogical approach proposed in experimental learning under NEP-2020.

n(S) = Total number of ways of pulling out socks

Let E be the event that they are of the same colour i.e. either both brown or both white.

Example- If the world had a lot of mavericks, the problem of religious violence wouldn't be there.

"Renaissance" is the correct word and it means the revival of something in a modified form.
Example- The renaissance was a period where great pieces of art were created.

• ‘ढूँढ-ढाँढ’ समोच्चरित भिन्नार्थक शब्द-युग्म नहीं है।
• ढूँढ का अर्थ : खोज, तलाश।
• अन्य सभी समोच्चरित भिन्नार्थक शब्द हैं।

Key Pointsअन्य विकल्प :

• कटिबद्ध- तैयार या तत्पर।
• कटिबंध- कमरबंद, कमर पर बाँधा जाने वाला आभूषण।
• करकट- कूड़ा कचरा।
• कर्कट- केकड़ा।
• क्रांति- विद्रोह।
• क्लांति- थकावट।

Additional Information

• समोच्चरित भिन्नार्थक शब्द - वे बोलचाल में लगभग एक जैसे लगते हैं, परन्तु उनके अर्थ में भिन्नता होती है। ऐसे शब्द ‘समोच्चरित भिन्नार्थक शब्द’ कहलाते हैं।
  जैसे- घन और धन दोनों के उच्चारण में कोई खास अन्तर महसूस नहीं होता परन्तु अर्थ में भिन्नता है।

अन्य उदाहरण :

• अवधि - अवधी
• ग्रह - गृह
• जलद - जलज
• निश्छल - निश्चल