HPSC PGT Mathematics Mock Test - 9 - HPSC TGT/PGT MCQ

Concept:

• Food comprises constituents like proteins, carbohydrates, fats and supplementary substances such as minerals, vitamins and water that are vital for life.
• These constituents are known as nutrients. For proper functioning of our body, we need to consume bodybuilding foods (e.g. milk, meat, poultry, fish, eggs, pulses, groundnuts); energy-giving foods (e.g. cereals, sugar, roots, fats and oils); and protective foods (e.g. vegetables, fruits).

Explanation:

• Carbohydrates are the main source of energy for our body.
• Carbohydrates are of two types – simple and complex.
• Simple carbohydrates - These are quick-energy foods, e.g. sugar. Sources of simple carbohydrates are natural fruits, milk and milk products, and vegetables including potatoes and carrots.
• Complex carbohydrates - These are better sources of energy than sugar since they are released slowly. Sources of complex carbohydrates are bread, cereals (rice, wheat, bajra, corn, barley, ragi, sorghum, millets etc.),

Gram is not a source of carbohydrate, it is a source of protein.

Additional Information

Proteins:

• proteins are obtained from the animal as well as vegetable sources. Proteins of animal origin are found in milk, eggs, cheese, fish and meat.
• Proteins from these sources contain all the essential amino acids (EAA) in adequate amounts.
• Vegetable proteins are found in pulses (legumes), cereals, beans, nuts, oilseeds, etc

Given:

The ratio of the present age of Annu and Raj = 4 : 5

Then after 8 years ratio of their age = 5 : 6

Calculation:

Let be assume the present age of Annu and Raj is 4x and 5x respectively

⇒ (4x + 8)/(5x + 8) = 5/6

⇒ 24x + 48 = 25x + 40

⇒ x = 8

⇒ The age of Annu = 4x = 4 × 8 = 32

⇒ The age of Raj = 5x = 5 × 8 = 40

∴ The required result will be 32 years, and 40 years respectively.

Hence, "Printer" is the correct answer.

Important PointsInput Device: A piece of equipment/hardware that helps us enter data into a computer is called an input device. For example keyboard, mouse, etc. 

1. Keyboard:

• A simple device comprising keys and each key denotes either an alphabet, number, or number commands which can be given to a computer for various actions to be performed
• It has a modified version of typewriter keys
• The keyboard is an essential input device and computers and laptops both use keyboards to give commands to the computer

2. Joy Stick:

• It is a device that comprises a stick that is attached at an angle to the base so that it can be moved and controlled
• Mostly used to control the movement in video games
• Apart from a computer system, a joystick is also used in the cockpit of an aeroplane, wheelchairs, cranes, trucks, etc. to operate them well

3. Scanner:

• This device can scan images or text and convert it into a digital signal
• When we place any piece of a document on a scanner, it converts it into a digital signal and displays it on the computer screen

Output Device: A piece of equipment/hardware that gives out the result of the entered input, once it is processed (i.e. converts data from machine language to a human-understandable language), is called an output device. For example printers, monitors, etc. 

Printer:

• A device that makes a copy of the pictorial or textual content, usually over a paper is called a printer
• For example, an author types the entire book on his/her computer and later gets a printout of it, which is in the form of paper and is later published
• Multiple types of printers are also available in the market, which can serve different purposes

Education Policy lays particular emphasis on the development of the creative potential of each individual. It is based on the principle that education must develop not only cognitive capacities - both the ‘foundational capacities ’of literacy and numeracy and ‘higher-order’ cognitive capacities, such as critical thinking and problem solving – but also social, ethical, and emotional capacities and dispositions.

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 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.
• 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.
• Promoting engaging and contextual pedagogy to ensure retention of students from socio-economically disadvantaged groups.
• 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 the NEP 2020 the engaging and contextual pedagogy ensures the retention of students from socio-economically disadvantaged groups.

Hint

• Standard curriculum: Standard curriculum should not be followed in the classroom, Curriculum should be flexible and based on the needs and abilities of the learners.
• Learning of the students should be done in multiple ways, such as observational learning, learning through interaction, etc. it should not be only textbook based.

NEP 2020 aims to provide a holistic and multidisciplinary education that focuses on the overall development of students.

The possible orders in which the matrix with 6 elements can be formed are 2×3, 3×2, 1×6, 6×1.

Therefore, the possible orders pairs are (2,3), (3,2), (1,6), (6,1).

Thus, (3,1) is not possible.

Therefore, the correct answer is D.

 which does not exist at x = 0 ∈ (-2 , 2). So , Rolle’s theorem is not applicable.

At least one yellow chair means “total way no yellow chair”
Total ways to select 3 chair form the total (2+3+4) = ⁹C₃

Now, we dont want even one yellow chair.
So we should select 3 chairs from 6 chairs (2 green & 4 blue) = ⁶C₃

Hence, ways to select at least one yellow chair = 84 - 20 = 64 ways.

Constant Function is defined as the real valued function.
f : R→R, y = f(x) = c for each x∈R and c is a constant.

So, this function basically associate each real number to a constant value.

It is a linear function where f(x₁) = f(x₂) for all x₁,x₂ ∈ R

For f : R→R, y = f(x) = c for each x ∈ R
Domain = R
Range = {c}
The value of c can be any real number.

For ax²+bx+c=0,
if the two roots are of different signs, their product must be –ve => c/a < 0
=> p(p-1)/3 < 0 => p(p-1) < 0 => 0 < p < 1
 = (0,1) 

lim(x → ∞) [(x-2)/(x+3)]^2x
lim(x → ∞) [(x-2)/(x+3)]² * [(x-2)/(x+3)]^x

lim(x → a) [f(x) * g(x)] = lim(x → a) f(x) * lim(x → a) g(x)

lim(x → ∞) [(x-2)/(x+3)]² * lim(x → ∞) [(x-2)/(x+3)]^x
Lets evaluate the limits of both the functions separately,
lim(x → ∞) [(x-2)/(x+3)]²
= lim(x → ∞) [(x(1-2/x)/(1+3/x)]²
lim(x → ∞) [(1-2/x)/(1+3/x)]²
Apply infinity property,
= [(1-0)/(1-0)]²
= 1
Now, lim(x → ∞) [(x-2)/(x+3)]²
= lim(x → ∞) exln[(x-2)/(x+3)]
= lim(x → ∞) ln[(x-2)/(x+3)]/(1/x)
Apply L hospital rule
lim(x → ∞) d/dx[ln(x-2)/(x+3)]/[d/dx(1/x)]
= lim(x → ∞) {1/[(x-2)/(x+3)] * d/dx[(x-2)/(x+3)]}/(-1/x2)
= lim(x → ∞) {(x+3)/(x-2)[(x+3)d/dx(x-2) - (x-2)d/dx(x+3)]/(x+3)²}/(-1/x2)
= lim(x → ∞) {(x+3)/(x-2)[(x+3)-(x-2)]/(x+3)2}/(-1/x2)
= lim(x → ∞) {(x+3)/(x-2)[5/(x+3)²]}/(-1/x2)
= lim(x → ∞) [-5x2/(x+3)(x-2)]
= lim(x → ∞) [-5x2/(x2 + x - 6)]
Again apply L hospital rule,
= lim(x → ∞) [d/dx(-5x2)/(d/dx(x2 + x - 6))]
= lim(x → ∞) [-10x/(2x + 1)]
Again applying L hospital rule,
= lim(x → ∞) [d/dx(-10x)/(d/dx(2x + 1))]
=  lim(x → ∞) [-10/2] 
=  lim(x → ∞) [-5]
= -5
= lim(x → ∞) exln[(x-2)/(x+3)]² = e(-5)2
= 1/e10
= lim(x → ∞) [(x-2)/(x+3)](x+3) = 1/e¹⁰ (1)
= 1/e¹⁰ = e^-10

touches the another circle

Now, Central first circle will be
And its radius will be 3 units.
Also,centre of second circle
And radius,

As both touches each other
So,

As b and c are linear constants ,independent of x and y, then by substituting them in the equation given, we get an equation linear in x and y. Thus, the given equation represents a straight line.

(cot α₁) (cot α₂)........... cot α_n =1
(cos α₁) (cos α₂) .......... cos α_n = (sin α₁) (sin α₂) .......... sin α_n
Let y = (cos α₁) (cos α₂) ................ (cos α_n) (to be maximum)
Squaring y² = (cos² α₁) (cos² α₂) ................ (cos² α_n)
= (cos α₁ sin α₁) (cos α₂ sin α₂) ................ (cos α_n sin α_n)    using equation 1

[sin 2α₁. sin2α₂ .........sin 2α_n]
0 < sin2α₁. sin2α₂ .........sin 2α_n < 1

As the quadrants lies in first and second quadrant
y = -a    Focus(0,a)
x^{2 = 4ay}
 

The Required point is the radical centre of the three given circles. The radical axes of the three circles taken in pairs are 3x - 24 = 0,16y + 120 = 0 and - 3x + 16y + 80 = 0. On solving, the required point is (8, -15/2).

Let
A – The answer is correct
E1 – Student. Knows the answer
E2 – Student Guesses

 We know that he knows and he answers correctly.
= 1.
 We know that he guesses and the answer is correct.
= 1/4
P(E₁) = He knows the answer = 3/4
P(E₂) = He guesses = 1/4
Substituting all these values in (1) we get :

D is not a trigonometric identity.

No of ways to make a necklace out of 11 beads = (11-1)!/2 
= 10!/2
Out of 11 beads there are identical red and black heads.
No. of arrangements = (10)!/[2*(5!6!)]

a = 4, b = 5
angle c = 60o
cos c = (a² + b² - c²)/2ab
= 1/2 = (16 + 25 - c²)/40
⇒ 20 = 41 - c2
c² = 21
⇒ c = (21)^1/2
⇒ c = 4.58

As n(A ∪ B) = n(A) + n(B) - n(A ∩ B)
But in case of disjoint sets, n(A ∩ B) = 0
∴ n(A ∪ B) = n(A) + n(B)

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