HSSC TGT Math Mock Test - 2 Free Online Test 2026

Explanation:

Air pollution control Act:

• The Air (Prevention and Control of Pollution) Act 1981 was a law passed by the Parliament of India to prevent and control the harmful effects of air pollution in India.
• This act is seen as the first concrete step taken by the Government of India to combat air pollution. 
• Act to provide for the prevention, control, and abatement of air pollution, for the establishment, with a view to carrying out the aforesaid purposes, of Boards, for conferring on and assigning to such Boards powers and functions relating thereto. And whereas it is considered necessary to implement the decisions aforesaid in so far as they relate to the preservation of the quality of air and control of air pollution.

Water pollution control Act:

• The Water (Prevention and Control of Pollution) Act was enacted in 1974 to provide for the prevention and control of water pollution, and for the maintaining or restoring of the wholesomeness of water in the country. The Act was amended in 1988.

Noise Pollution Act:

• Noise Pollution (Control and Regulation) Rules 1999 was published under the notification number S.O. 528 (E), dated the 28th June 1999, objections and suggestions are invited from all persons likely to be affected, before the expiry of a period of sixty days from the date on which copies of the Gazette containing the said notification. made available to the heinous.

Biodiversity Act:

• The Biological Diversity Act 2002 is an Act enacted by the Parliament of India to protect or preservation of biological diversity in India and provides a mechanism for equitable sharing of benefits arising out of the use of traditional biological resources and knowledge.
• Act to provide for the conservation of biological diversity, sustainable use of its components, and fair and equitable sharing of the benefits arising out of the use of biological resources, knowledge, and matters connected therewith or incidental thereto.

The correct answer is All of the above.

• A UN Conference on Climate Change, held in Kyoto, Japan, in 1997, resulted in an international agreement to fight global warming which called for reductions in emissions of greenhouse gases by industrialized nations.
• The Kyoto Protocol is an international agreement linked to the United Nations Framework Convention on Climate Change, which commits its Parties by setting internationally binding emission reduction targets.
• It is effective since February 16, 2005. Its first commitment period started in 2008 and ended in 2012.
• The Montreal Protocol, finalized in 1987, is a global agreement to protect the stratospheric ozone layer by phasing out the production and consumption of ozone-depleting substances (ODS).
• The Brundtland Commission emphasizes protecting the future generation. It focused on Sustainable Development (we have a moral obligation to hand over the planet earth in good order to the future generation; that is, the present generation should bequeath a better environment to the future generation.).

Additional Information

• The present generation should promote development that enhances the natural and built environment in ways that are compatible with
  • conservation of natural assets.
  • preservation of the regenerative capacity of the world’s natural ecological system.
  • avoiding the imposition of added costs or risks on future generations.

Explanation:

(i) The COD (Chemical oxygen demand) test is used to measure the content of organic matter of waste water, both biodegradable and non-biodegradble.

(ii) The COD test uses potassium dichromate (K2Cr2O7) in presence of concentrated sulfuric acid (H2SO4) solution that oxidizes both organic (predominate) and inorganic substances in a waste water sample.

(iii) The reagents for COD test are followings:

• Standard potassium dichromate solution (0.25N)
• Concentrated sulfuric acid
• Standard ferrous ammonium sulphate titrant (0.1N)
• Ferroin indicator solution.

Concept:

• The vibrations of an object produce sound.
• Our ears perceive sound.
• Unwanted sound, which affects the well-being of individuals/society, is termed noise.
• The level of sound is measured in Decibel (dB).
• It starts from 0.
• Sound up to 25 dB is called silence, as the human ear can’t perceive it.
• 26-65 dB is called quiet.
• Above 66 dB is noise
• Above 75 dB is excessive noise.
• Human health suffers up to 80 dB.
• Above 90 dB is dangerous.

Explanation:

Military Rifle

• The amount of fuel in the cartridge determines how much noise is created when the weapon is fired.
• When the weapon is fired, the exploding propellant creates a pressure spike.
• This travels down the barrel of the gun.
• This changes into a spherically expanding shock wave as it leaves the barrel.
• This supersonic shock wave is the muzzle blast creating noise.
• The sound ranges from 150-175 dB.

Thus, the loudest sound of noise comes from military rifles.

Additional Information

Air raid siren

• The air raid siren produces sound by drawing in the air as it rotates.
• This is then fragmented and thrown out of the horn.
• The faster the rotation louder is the sound
• The contemporary sirens can create sound up to 135 dB at 100 feet.

Loudspeakers

•  Sound is produced by the vibration of the thin diaphragm .
• This disrupts the air pressure around it.
• It is disrupted in the form of the original sound wave.
• An amplified audio signal causes the diaphragm to vibrate.
• The audio signal has the same waveform as the sound wave.
• 75 dB is the maximum permissible loudspeaker decibel limit in India.

Rock music

• The decibel range is 90-120 dB.

In general, the term "socialization" refers to the process of social influence by which a person adopts the culture or subculture of their group and, in the process, shapes their sense of self and personality.

Key Points

• Macro-level sociology examines broad-scale social phenomena like societal change and stability.
• Micro-level sociology examines small human interactions like speech or group dynamics.
• The micro level entails small group interaction. This level is vital because face-to-face, intense, and intimate interaction forms the basic formulation.
• Meso-level socialization units are intermediate size social units smaller than the ones at the macro level but larger than the micro-units like the family or the local community. 
• Microsociology enables this on-the-ground examination but sometimes overlooks the more powerful factors that affect people's behavior.

Hence, it is concluded that Both A and B are true.

The correct answer is Hisar.Key Points

• Pt. Jasraj, the classical musician, was born in Hisar.

Pandit Jasraj:

• Pandit Jasraj was an Indian classical vocalist, belonging to the Mewati Gharana.
• He was born on 28 January 1930 in Pili Mandori, a village in the Hisar district of Haryana.
• He was a recipient of various prestigious awards and honours including Padma Shri (1975), Padma Bhushan (1990), and Padma Vibhushan (2000).
• He passed away in 2020 at the age of 90.
• He was a Mewati gharana-affiliated classical performer from India.
• Jasraj was a groundbreaking artist whose egalitarian outlook made him famous.
• People adored his devotional music and he retained popular appeal in a manner where bhava (passion) and devotion were key.
• He blended Indian devotional music such as haveli sangeet and bhajans (devotional songs/hymns) into a classical environment, making them into serious compositions.
• Mewati Gharana was founded by brothers Utd. Ghagge Nazir Khan and Utd. Wahid Khan of Indore.

The correct answer is Bhiwani district.Key Points

• Mitathal is a village and Indus Valley civilization (IVC) Archaeological site in the Bhiwani tehsil of the Bhiwani district in the Indian state of Haryana.
• Part of Hisar division, it lies 12 kilometers north of the district headquarters Bhiwani and 249 kilometers from the state capital Chandigarh.
• As of the 2011 Census of India, the village had 1,448 households with a total population of 7,434 of which 4,002 were male and 3,432 female.

Additional Information Rakhigarhi

• Rakhigarhi or Rakhi Garhi is a village and an archaeological site belonging to the Indus Valley civilization in the Hisar District of the northern Indian state of Haryana, situated about 150 km northwest of Delhi. It was part of the mature phase of the Indus Valley Civilisation, dating to 2600-1900 BCE.

Banawali

• Banawali, formerly known as Vanavali, is a hamlet and archaeological site located around 15 kilometers from Fatehabad district in Haryana, India. It was settled on the left bank of the dry river Saraswati during the Indus Valley Civilization period.

The correct Answer option is 1 i.e. 8

• The 8-digit 'Parivar Pehchan Patra' (PPP) is launched by Haryana Government.
• It is meant for each family across the state to enable smooth and automatic delivery of several citizen-centric services launched by the state government from time to time.
• By using this document (Patra) the state government aims to monitor each of the approximately 54 lakhs families living across the state.
• Under this, each family will be considered a single unit and allotted an 8-digit unique identification number.
• The document is mandatory to get the social security schemes of the state. The document is mandatory to all government employees of the state.
• The PPP will have the name of the head of the family, besides the names, age, income, mobile number of each and every member of the family.

Why PPP when we already have Aadhar?

• Aadhaar represents an individual as a unit, whereas PPP represents a family as a unit.
• Most of the state government schemes are structured around the family.
• At the same time, the sharing of Aadhar information is not allowed, so it becomes difficult to keep track of beneficiaries of schemes via Aadhar.

Features of PPP:

• PPP is linked with social security schemes.
• For example, when a family member turns 60, they will automatically get a message through the software and will automatically start getting benefits of the old-age pension if they meet the required criteria.
• Similarly, the teenagers will get messages on turning 18 years old and shall become eligible for various government schemes that will be notified to them through the software.

Notes:

Chief Minister of Haryana: Manohar Lal Khattar.

Governor of Haryana: Bandaru Dattatreya.

The correct answer is None of the above.

Key Points

• Bhopal Singh Khadri is the Chairman of the Haryana Staff Selection Commission.
• Khadri is a village in Haryana.
  • Block / Tehsil- Chhachhrauli
  • District- Yamunanagar
• As per 2011 Census
  • Total Population- 4051
  • Female Population%- 47.4 % (1921)
  • Total Literacy rate%- 64.8 % (2627)
• Haryana Staff Selection Commission (earlier Subordinate Services Selection Board) is constituted as per the proviso of Article 309 of the constitution of India.
  • The Commission conducts examinations/interviews for appointments to Group ‘C’ services and may be called up on to conduct examination/interview for appointment to Group ‘B’ and ‘D’ services if required by the State Government.
  • It consists of seven Members including the Chairman appointed by the Haryana Govt. on the recommendation of the collegiums consisting of a Minister of Cabinet Rank, Chief Secretary to Govt. Haryana, Legal Remembrance and Secretary to Govt. Haryana, Law and Legislative Department.
  • The Chairman/Member shall cease to be a Chairman or Member of the Commission on attaining the age of 68 & 65 years respectively.

The correct answer is Mahendragarh.

• In the census of 2001, the sex ratio of Mahendragarh district was 918, which was reduced to 895 in 2011 census.
• About Mahendragarh district -
  • It was formerly known as Kanoud because of Kanauadia populated by Brahmins.
  • In the seventeenth century, Maratha ruler Tanti Tope built a fort here.
  • In 1861, ruler Maharaja Narendra Singh of Patiala principality had named this fort in Mahendergarh in honour of his son Mohinder Singh.
  • Because of the name of the fort, this town came to be known as Mahendragarh.
  • According to the 2011 census -
    • Total Population: 9,22,088
    • Literacy Rate: 77.72%
    • Density: 486

The correct answer is Haryana Civil Service Officer Association.

Key Points

• Varsha Khangwal, a senior HCS officer of the 2004 batch, was unanimously elected president of the Haryana Civil Service Officer Association.
  • Varsha Khangwal, presently posted as Additional Director in Information and Public Relations Department, Varsha Khangwal is also senior.
  • The HCS officer of the 2004 batch was unanimously elected as the President of the Association.
  • Varsha Khangwal, currently posted as Additional Director in Information and Public Relations Department, is also a 2004 batch topper.

Additional Information

• ​Former Haryana Chief Secretary and retired IAS Vijay Vardhan have become the new Chief Information Commissioner.
  • Retired IAS SS Phulia took oath as Information Commissioner.
• Haryana Wrestling Association -
  • Its general secretary has been made Rakesh Singh.
• Renu Bhatia, a resident of Faridabad, has been made the chairperson of the Haryana State Women's Commission.
  • They have been appointed for 3 years.

The correct answer is Fatehabad.

Key Points

• Making of Parivar Pehchan Patra (PPP) or family ID is topped by Fatehabad.
• In Fatehabad mora than 85% of the population already registered in PPP.
• Panchkula and Faridabad are the two bottommost districts in making the PPP.
• In Panchkula only 56% population have PPP and in Faridabad 58% of the population has PPP.

Important Points

• The 8-digit Parivar Pehchan Patra (PPP) is meant for each family across the state to enable smooth and automatic delivery of several citizen-centric services.
• The state government aims to monitor each of the approximately 54 lakh families living across the state.
• Telangana, Karnataka, and Andhra Pradesh are also exploring the possibility of implementing a similar PPP project.

The correct answer is Option 4.

Key Points

• The National Highways Authority of India Act, 1988 extends to the whole of India.
• It shall come into force on such date as the Central Government may, by notification in the Official Gazette, appoint.
• “National Highway” means any highway for the time being declared as a national highway under section 2 of the National Highways Act, 1956 (48 of 1956);

Additional Information 

• “Authority” means the National Highways Authority of India constituted under section 3;
• “Chairman” means the Chairman of the Authority;
• “Employee” means a person in the full-time service of the Authority;
• “Member” means a member of the Authority appointed under section 3 and includes the Chairman;

Development refers to the qualitative changes in the organism as a whole. Development is a continuous process through which physical, emotional, and intellectual changes occur. It is a wider and more comprehensive term than growth. It is also possible without growth.

Key Points Factors affecting human development

​External factors:

• The factors lying outside the individual in his/her environment are said to be the external factors influencing his/her growth and development. These factors begin their role of influencing the growth and development just immediately after a baby is conceived. These may include the following-
  • The environment in the womb of the mother: What is available to the child for his/her nourishment in the mother’s womb from the time of conception till his/her birth is quite important from the angle of his development.
  • The environment available after birth: Whatever a child gets from different conditions and forces of his/her environment after his/her birth influences his/her growth and development in many ways.
  • Environmental influences are important both at the prenatal and postnatal stages of human development. At the prenatal stage, when a fetus is in the mother’s womb, internal or external harmful agents, such as certain legal or illegal drugs, alcohol, lead, and pollutants can harm the unborn baby’s development. The mother’s nutrition, diseases, and emotional stress can also affect the development of the fetus.
  • These may be described as follows :
    • Accidents and incidents in life: The growth and development of an individual are greatly influenced by the good and bad incidents and accidents which s/he happens to meet in his lifetime. Sometimes, a small injury or an incident may change the entire development course of his life. For example, if a child’s nervous system is damaged in an accident, it will hamper his/her mental development and in turn, it will affect his/her development in other spheres – social, emotional, moral, and physical.
    • The quality of the physical environment, medical care, and nourishment. A child’s growth and development is greatly influenced by the quality of his/her physical environment and medical care and nourishment available to him/her for his living and work. These include open space, a balanced diet, good living and working conditions, and proper medical care. He/she will achieve the heights of his/her growth and development based on the proper availability of these things.
    • What a child gets from this social and cultural environment for the growth and development of his potentials, influences the entire course of his/her development of his/her sense, he develops and becomes what s/he is permitted to and desired by these social and cultural forces.

Additional Information

Internal factors affecting Growth.

• Heredity factors
• Biological and constitutional factors:
• Intelligence
• Emotional factors
• Social nature

Hence, we can conclude that Political Environment is not among the three types of environment which affect human development as external forces.

Santosh Yadav

• Santosh Yadav is a female mountaineer from India
• She was born in Rewari district of Haryana in 1967
• She was the first Indian woman to climb Everest twice.
• She climbed the peak first in May 1992 and then again in May 1993 with an Indo-Nepalese Team.
• She has been awarded the Padma Shree by the government of India in 2000
• She has also been awarded the Tenzing Norgay National Adventure award in 1994

Additional Information

• Padma Shree is the fourth highest civilian award in India
• The first three are Bharat Ratna, Padma Vibhushan and Padma Bhushan
• It is awarded to citizens as well as non-citizens of India
• The Tenzing Norgay National Adventure Award is the highest adventure sports honour in India
• It was formerly known as the National Adventure Awards
• Tenzing Norgay along with Edmund Hillary was the first person to climb Everest
• Bacchendri Pal is the first Indian woman to climb Everest

⇒ Santosh Yadav belongs to Haryana

There’s a result in mathematics used for this. It says that a power set B of any set A is a set of all the subsets of A and the number of elements of B will be 2^n where n is the number of elements of A.
So taking your question as an example;
A = {1,2,3}
B : set of all subsets of A
List out all the subsets of A - {1},{2},{3},{1,2},{2,3},{1,3},{1,2,3},{empty set}
Number of elements in A (n) = 3 
so 23 = 8
So, B = {{1},{2},{3},{1,2},{2,3},{1,3},{1,2,3},{empty set}} 
and the number of elements are 8.

ax²+by²+2hxy+2gx+2fy+c = 0
In the circle equation,
Coefficients of x² & y² are the same and non-zero.
Therefore, a = b ≠ 0
There is no term for xy. Therefore, h = 0.
Radius of the circle: r² = g² + f² – c,
So, g² + f² – c > 0

As AB = AC so angle ACB = angle(ABC) as angles opposite to equal sides r equal.

In triangle PBC and Triangle QCB we see that:
i) PB = QC (given)
ii) angle(PBC) = (angle)QCB (proved earliar)
iii) BC = BC (common)

So, triangle PBC is congruent to triangle QCB by SAS axiom of congruency.

LHD = limh→0 ((−h)² sin(−1/h) − 0)/−h
limh→0 −h² sin(1/h)/−h
= limh→0 h × sin(1/h)
= 0
RHD = limh→0 (h² sin(1/h) − 0)/h
= limh→0 h × sin(1/h)
= 0
RHD=LHD
∴ f(x) is differentiable at x= 0

Let I = ∫(0 to pi/2)x³ sin(tan−1x⁴)/(1+x⁸)dx
Put tan−1 x⁴ = t
4x³/(1+x⁸)dx = dt
⇒x³dx/(1+x⁸) = dt/4
Now, I = 1/4∫sin t dt
=−[1/4 cos t]0 to pi/2 + c
= -1/4[cos(0) - cos(pi/2)] +c
= 1/4[-cos(pi/2) + cos(0)] +c
= ¼[-0+1]
= 1/4 

The correct answer is:

2. a = bq + r, 0 ≤ r < b.

Explanation:

This is the division algorithm, a fundamental concept in number theory.

The division algorithm states that for any two positive integers aaa (the dividend) and b (the divisor), there exist unique whole numbers q (the quotient) and r (the remainder) such that:

a=bq+r

Where:

• q is the quotient (how many times b fits into a),
• r is the remainder (what is left over after dividing),
• 0≤r<b, meaning the remainder is always less than the divisor b but greater than or equal to zero.

Example:

Suppose a=23 and b=5. When you divide 23 by 5:

• The quotient q=4 (because 5 fits into 23 four times),
• The remainder r=3 (because 23−(5×4)=3).

So, the equation becomes:

23=5×4+3

Where a=23, b=5, q=4, and r=3, which fits the form of the division algorithm.

Thus, option 2 is the correct answer because it accurately represents the division algorithm.

The relationship between the mean, quartile and the standard deviation are as follows:
Mean Deviation is the mean of all the absolute deviations of a set of data.
Quartile deviation is the difference between “first and third quartiles” in any distribution.
Standard deviation measures the “dispersion of the data set” that is relative to its mean.
Mean Deviation = 4/5 × Quartile deviation
Standard Deviation = 3/2 × Quartile deviation

The assertion is false because the degree of the polynomial is determined by the highest power of x, which is 4 in this case, making it a polynomial of degree 4. The reason is true because the highest power of x indeed determines the degree of a polynomial, but it incorrectly describes the polynomial in the assertion.

Factors are following:
5 = 5 x 1
15 = 5 x 3
20 = 2 x 2 x 5

LCM = 5 x 3 x 2 x 2 = 60
HCF = 5
Ratio = LCM/HCF = 60/5 = 12/1 = 12:1