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

• The Constituent Assembly met for the first time in New Delhi on 9 December, 1946 in the Constitution Hall which is now known as the Central Hall of Parliament House.
• The Constituent Assembly took almost three years (two years, eleven months and seventeen days to be precise) to complete its historic task of drafting the Constitution for Independent India.
• The Assembly met once again on 24 January, 1950, when the members appended their signatures to the Constitution of India.

Key-Points​

• The Constituent Assembly held its first meeting on December 9, 1946.
• The Muslim League boycotted the meeting and insisted on a separate state of Pakistan.
• The meeting was thus attended by only 211 members.
• Dr Sachchidanand Sinha, the oldest member, was elected as the temporary President of the Assembly, following the French practice.
• Later, Dr Rajendra Prasad was elected as the President of the Assembly

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.

• Neeraj Chopra is an Indian athlete who competes in the javelin throw.
• He won a gold medal at the 2018 Asian Games and set a national record of 88.06 m.
• He also clinched a gold medal at the 2018 Commonwealth Games.
• He was also the champion of the 2016 IAAF World U20 Championship and set a world junior record of 86.48 m. 

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.

The correct answer is Sarvan Kumar Garg.

Key Points

• Haryana Gau Seva Aayog was established under Section 3 of The Haryana Gau Seva Aayog Act, 2010 enacted by the legislature of the State of Haryana for the preservation and welfare of cows in the State.
  • The main objective is to work for the proper implementation of laws with respect to the prohibition of slaughter and/or cruelty to cows.
  • It also regulates and preserves the functionality of bills associated with cow protection law i.e. Gauvansh Sanrakshan and Gausamvardhan Bill under the Haryana Government.
• It has established Haryana Gauvansh Anusandhan Kendra at Kamdhenu Gaushala Seva Sadan, Pinjore
• Chairman- Sh. Sarvan Kumar Garg
• Vice-Chairman- Sh. Vidya Sagar Baghla

Animals solve problems by understanding – like human beings, instead of going through either the trial and error process or stimulus response association. In this case, learning took place by insight. Learning by insight involves finding a solution to the problem by thinking over the problem and understanding the various aspects of the problematic situation.
Insight learning refers to the sudden realisation of the solution of any problem without repeated trials or continuous practices. To further elaborate on its definition, insight learning is the type of learning in which one draws on previous experience and also seems to involve a new way of perceiving logical and cause-and-effect relationship.

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.

Equation of normal at any point (x₁, y₁) is  it passes through 
P (h, k) then  thus (x₁, y₁) lie on the conic 

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.

The geometric mean of two numbers, say x, and y is the square root of their product x * y.
 Mean = [x * y]^1/2
= [5 * 8]^1/2
= [40]^1/2
= 2(10)^1/2

The two curves y² = 4x and y = x meet where x² = 4x i.e ..where x = 0 or x = 4 . Moreover , the parabola lies above the line y = x between x = 0 and x = 4 . Hence , the required are is :

If you interchange (switch) two rows (or columns) of a matrix A to get B, then det(B) = –det(A). Hence, the determinant is -(-7)

= 7

No of word formed taking E at first place = 3! 
Taking F at first place = 3! 
Taking I in the first place = 3!
W in first and E in second = 2!
W in first F in second and E in third = 1! 
W in first I in second and E in third = 1 
W in first I in second and F in third = 1 
W in first I in second and F in third and E in fourth = 1 
Total =24

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.

f (x) = 2 – 3x ⇒ f ‘ (x) = - 3 < 0 for all x ∈ R . so, f is strictly decreasing function.

Det.A = 0.

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

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

given that harmonic mean between the roots of the 
given equation is 4.

Since AB is the diameter of the circle. 
From figure, 
Also equation of the circle is 

equation of tangent to this circle at (0, 0) is ax + by = 0 ……(1)
∴ m = length of perpendicular from


and n = length of perpendicular from 


Hence (D) is the correct answer.

S=1²−2²+3²−4²+......−2002²+2003²

Let the other nos. be a and b
then (x+y+1+2+6)/5 = 4.4
x + y = 13 ---------------------(1)
Variance = 8.24


41.2 = 19.88 + (x2 + 19.36 – 8.8x) + (y2 + 19.36 – 8.8y) 
21.32 = x2 + y2 + 38.72 – 8.8(x + y) 
x2 + y2 + 38.72 – 8.8(13) – 21.32 = 0 
(using equation (1)) 
x2 + y2 – 97 = 0 …(2) 
Squaring equation (1) both the sides, 
we get (x + y)2 = (13)^2 
x2 + y2 + 2xy = 169 
97 + 2xy = 169 
(using equation (2)) 
xy = 36 or x = 36/y (1)
⇒ 36/y + y = 13 
y2 + 36 = 13y 
y2 – 13y + 36 = 0 
(y – 4)(y – 9) = 0 
Either (y – 4) = 0 or (y – 9) = 0 
⇒ y = 4 or y = 9 
For y = 4 x = 36/y 
= 36/4 = 12 
For y = 9 
x = 36/9 
x = 4 
Thus, remaining two observations are 4 and 9.

f(0) = lim(x→0) x sin (1/x)
​We know ∀ x ∈ R,sin (1/x) ∈ [−1,1]
Hence, f(0) = lim(x→0) xsin(1/x) 
= 0