HPSC PGT Mathematics Mock Test - 2 - HPSC TGT/PGT MCQ

The correct answer is The Supreme Court.

Key Points 

• The Supreme Court of India is called the custodian of the Constitution in India.
• The highest court in India, the Supreme Court is considered as the guardian of the Constitution.
• The conflicts or quarrels of jurisdiction between the central government and the state governments or between the legislature and the executive are decided by the court.
• It upholds and uplifts the rule of law and also ensures and protects citizens’ rights and liberties as given in the Constitution.
• Therefore, the Supreme Court is also known as the Guardian of the Constitution.​

Additional Information 

• The Indian constitution provides for a provision of the Supreme Court under Part V (The Union) and Chapter 6 (The Union Judiciary).
• The Supreme Court of India is the highest judicial court and the final court of appeal under the Constitution of India, the highest constitutional court, with the power of judicial review.
• India is a federal state and has a single and unified judicial system with a three-tier structure, i.e. Supreme Court, High Courts, and Subordinate Courts.

Manganese is one of the important raw materials used for smelting iron ore.

Important Points

• Manganese is used for making alloys.
• It is used in manufacturing of enamel, dry cell batteries, plastics, chemicals and glasses.
• It requires almost 10 kg of manganese to manufacture one tonne of steel.
• Odisha is the largest producer of manganese in India with multiple mines located over the iron ore belt of India.
• Some of the major mines are Bonai, Kendujhar, Sundergarh, Gangpur, Koraput, Kalahandi, and Bolanger.
• After Odisha, Karnataka, Maharashtra, Telangana, Goa, and Jharkhand lies in the list of manganese producer in India.
• In 2000-2001, Odisha produced one-third of the country's total production.

Thus, we can conclude that Odisha is the largest producer of manganese.

The correct answer is Prevent stubble burning.

Key Points

• The Supreme Court had appointed Justice Madan B. Lokur committee in October 2020, to prevent stubble burning in the states of Punjab, Haryana and Uttar Pradesh, amid rising levels of pollution in the national capital and adjoining regions.
  • ​Hence, option 2 is correct.
• He is a former judge of the Supreme court. 
• The Supreme Court also directed the appointment of the Environment Pollution Control Authority (EPCA).
• Chief secretaries of Haryana, Punjab and Uttar Pradesh were advised to help the Lokur panel with physical surveillance of fields to check instances of stubble burning and other related matters.
• It will get assistance from National Cadet Corps (NCC), National Service Scheme and Bharat Scouts.

NEP 2020 recommends the use of the mother tongue or local language as the medium of instruction for foundational education.

Socialization is an important process for the functioning and continuation of society. It is a process of learning the rules, habits, and values of a group to which a person belongs whether it is family, friends, colleagues, or any other group.

National Education Policy (July 29, 2020) was finalized after reviewing the suggestions Kasturirangan committee, its vision is to develop a Bharat-centric knowledge society. A society that has its roots in eternal Bhartiya Sanskriti and looking forward to moving with the world. 

Key Points The NEP 2020 stipulated that the three-language formula would be maintained while keeping in mind the Constitution, the aspirations of the people, regions, and the Union, and the necessity to encourage multilingualism as well as national unity.

• It stipulates that the three-language formula would be more flexible, that no language will be imposed on any state, and that one of its key priorities will be the promotion of regional languages.
• In light of the foregoing, the Rajasthan State Council of Educational Research and Training (RSCERT) developed a new curriculum that includes three languages: Hindi, English, and the local dialect/ languages.
• The central government recognizes 18 dialects from the state of Rajasthan, hence the state government has the authority to choose any of these 18 dialects in different regions.

Thus, it can be inferred that as per the NEP 2020, the Rajasthan government has decided to come up with a new syllabus that includes 3 languages, which are Hindi, English, and local languages.

An n×n homogeneous system of linear equations has a unique solution (the trivial solution) if and only if its determinant is non-zero. If this determinant is zero, then the system has an infinite number of solutions. i.e. For a non-trivial solution ∣A∣=0.

If l, m and n are the direction cosines of a line, Direction ratios of the line are the numbers which are Proportional to the direction cosines of the line.

Here, 0 ≤ x- 3 ≤ 7 - x  
⇒0 ≤ x - 3 and x - 3 ≤ 7 - x
By solvation, we will get 3 ≤ x ≤ 5
So x = 3,4,5 find the values of ^7-x P_{x - 3} by substituting the values of x
at x = 3 ⁴P₀ = 1
at x = 4 ³P₁ = 3 
at x = 5 ²P₂ = 2

Option C is not a trigonometric identity.

Angle between skew lines is the angle between two intersecting lines drawn from any point 

An identity function, also called an identity relation or identity map or identity transformation, is a function that always returns the same value that was used as its argument. That is, for f being identity, the equality f(x) = x holds for all x.

Clearly, range of f (x) 

For f to be onto, codomain = range
∴ Co-domain of function 

This occurs in either the I or the III quadrant. The only way for tan θ positive and sin θ negative is the III quadrant.

Independent event but not equally likely

If a, b, c are in A.P., then b is the arithmetic mean of a and c.
a b and c are in AP.
∴ b - a = c - b
⇒ 2b = a + c          ........ (1)
The arithmetic mean of a and c
= (a+c)/2 
Using equation (1), we get
= 2b/2
= b 
∴ The arithmetic mean of a and c = b
Thus, the arithmetic mean of a and c is b.

Let the d.r’s of a required line be a, b and c. Since, the normal to the given planes x + 2y + z = 3 and 6x + 8y + 3z = 13 are perpendicular to the line.
∴ a +2b+c = 0 and 6a + 8b + 3c = 0
⇒ 
⇒ 
or 
Also, line passes through (2, -1, 3).

Out of 30 Boys,
No. of ways to select 1 boy = ³⁰C₁ = 30
Out of 18 Girls,
No. of ways to select 1 boy = ¹⁸C₁ = 18
No. of ways of selecting 1 boy and 1 girl =
30*18 = 540

Selecting 3 consonants out of 7,
No. of ways = ⁷C₃ 
Selecting 2 vowels out of 4,
No. of ways = ⁴C₂ 
No. of ways of forming the words
= ⁷C₃* ⁴C₂* 5! (for arrangement of the letters)
= 35 * 6 * 120
= 25200 

= cos (log x) cos (cos y)   [cos(log(x/y))+cos(log(xy))] 
= cos (log x) cos (log y)  [cos(log x - log y)+cos(log x +log y)]
= cos (log x) cos (log y) [2 cos(log  x)cos(log y)] = 0

Domain of sin ^-1x is [-1,1]

a + 3 + 5 = 0, replace a value find roots

Let A (a, b) and G (x. y) Now A, G, O are collinear
⇒ x = (2*0 + a)/3
⇒ a = 3x
and similarly b = 3y
Now (a,b) lies on the circle = 9x² + 9y² = 9
=> x² + y² = 1

By definition : The Skew lines are lines in different planes which are neither parallel nor intersecting .

log₁₀ (x³ - x)is defmed ⇒ x³ - x > 0 ⇒ x(x² - 1) > 0 ⇒ (x +1)x(x - 1) > 0
x < -1 ⇒ (x+1)x(x-1) < 0; -1 < x < 0 ⇒ (x+1)x(x-1) > 0
0 < x < 1 ⇒ (x+1)x(x-1) < 0; x > 1 ⇒ (x+1)x(x-1) > 0.
∴ Domain = (-1,0)∪(1, ∞)

S=1²−2²+3²−4²+......−2002²+2003²

Put θ = A, 2θ = B, 4θ = c
∴ A + B + C = 7θ = 2π

But cos (A + B + C)
= cos A cos B cos C - ∑ sin A sin B cosC
∴ sin A sin Bsin C = cos A cos Bcos C - cos 2π

Let us say that the two particular friends are A and B.
If A is invited among six guests and B is not, then:  number of  combinations to select 5 more guests from the remaining 8 friends:
          C(8, 5) =  8 ! / (5! 3!)  = 56
If B is invited among the six guests and A is not , then the number of ways of selecting the remaining 5 guests =  C(8, 5) =  56
Suppose both A and B are not included in the six guests list : then the number of such combinations =  C(8, 6) = 7 * 8 /2 = 28
So the total number of sets of guests that can be selected =  140.

so that the equation becomes 1/z = 1z²

where ω (≠1) is a cube root of unity.