HSSC TGT Math Mock Test - 5 Free Online Test 2026

The process flow in an integrated solid waste management system is:

Generation-Source Separation-Collection-Facility Separation-Transfer and Transport-Landfill

The correct answer is Shekh Farid (Farid-ud-din-Shakarganj).

• The Chisti sect was established in Haryana by Shekh Farid (Farid-ud-din-Shakarganj).

Key Points

• Fariduddin Ganjshakar
  • He was a 13th-century Punjabi Sunni Muslim preacher.
  • He was one of the most revered and distinguished Muslim mystics of the medieval period.
  • He is also known as Baba Farid.
  • He was one of the founding fathers of the Chishti Sufi order.
  • He received his early education at Multan and there he met his teacher Qutbuddin Bakhtiar Kaki.
  • He moved to Delhi after completing his education.
  • When Quṭbuddīn Bakhtiyār Kākī died in 1235, Farīd became his spiritual successor and got settled in Ajodhan.
  • His shrine darbār is located in Pakpattan, Punjab, Pakistan.
• The Chishtī Order is a tariqa, an order or school within the mystic Sufi tradition of Sunni Islam.
  • The Chishti Order is known for its emphasis on love, tolerance, and openness.
  • It was the first of the four main Sufi orders (Chishti, Qadiri, Suhrawardi and Naqshbandi).

The correct answer is Shannan Dhaka.

• Haryana resident Shanan Dhaka has topped the first women’s batch of the National Defence Academy exam. Until last year, women were not permitted to sit for the exam.

Additional Information

• National Defence Academy:
  • National Defense Academy (NDA) is the combined Defense Services Training Institute of the Indian Armed Forces, where cadets of the three services i.e. Indian Army, Indian Navy, and Indian Air Force train together before joining their respective services.
  • The NDA is located in Khadakwasla, Pune, Maharashtra.
  • It is the first tri-service academy in the world.

The correct answer is Karnal.

• It is believed that the name of the city of Karnal is derived from Karna-Tal, which translates into Karna Lake.
  • This can also be the reason for calling Karnal the city of Karna in the local language.
  • Karna Lake is maintained by Haryana Tourism Corporation.

Additional Information

• The city of Karnal, said to have been founded by King Karna of Mahabharata fame, rose to prominence in 1739 when Nadir Shah defeated Muhammad Shah at Karnal.
  • Raja Gopal Singh of Jind captured Karnal in 1863, and the Marathas established themselves in Karnal in 1785.
  • However, there were clashes between the Marathas and the Sikhs.
  • In 1795 the Marathas finally snatched it from Raja Bhag Singh of Jind and handed it over to George Thomas, who took part in the fighting.

The correct answer is Statement (i) and (iii).

• The rainfall in Haryana occurs during the months of July–September with occasional showers during December–January.
• The range of rainfall in this region varied between 160-751 mm.
• Western disturbances are responsible for the showers during Dec-Jan.
  • Hence Statement (ii) is incorrect.
• The summers are generally quite hot and winters are fairly cool.
• The State has three distinct seasons, viz. winter (November–March), summer (April–June), and Rainy season (July–October).
• Haryana falls in the Agro Climatic Zone-VI, which is called Trans-Gangetic Plains Region.
• Haryana falls in the Seismic Zones II, III & IV creating low to moderate damage risk from Earthquakes.

Notes:

• Western Disturbances:
  • The western disturbances originate in the Mid-latitude region near the Europe and Atlantic ocean.
  • The low pressure forms over the Mediterranean Sea and travels over Iraq, Afghanistan, and Pakistan before entering India and it has a sufficient amount of moisture.
  • It influences the weather of the north and north-western regions in India.
  • It damages the crops in the North Indian states like Haryana, Punjab, Madhya Pradesh, and Rajasthan, because they are non-seasonal rains.

The correct answer is Parking allowed.

Key Points 

• Parking allowed:

• Entry prohibited:

• Crossroad ahead:

Important Points 

There are three kinds of road signs in India:

Mandatory Signs:

• These are the road signs that need to be followed compulsorily.
• These signs are used to make sure the free movement of traffic.
• By these signs, the road users are made aware of the specific laws, such as those of speed limits and no parking zones, etc.

Cautionary Signs:

• These traffic signs are required to make the road users realize potential dangers or safety hazards on the road.

Informatory Signs:

• These traffic signs are used to tell information like distances, fuel stations, nearby medical centers, public convenience, etc.

Work education is considered purposeful and meaningful physical labor, which is organized as the inherent part of the educational process.

Key Points

Characteristics of work education:

• Work education helps in initiating feelings of leadership and leadership skills.
• Work education benefits coordination in hand and brain.
• Work education helps in developing socially desirable values.
• Work education is an essential and significant factor in the learning process.
• Work education develops regular habits and a positive attitude to fulfill the basic needs of their body.
• Work education helps in the development of personality.
• Work education provides opportunities for experiencing conditions related to community services.

​​Hence, we can conclude that work education benefits co-ordination in hand and brain and work education is an essential and significant factor in the learning process both statements are correct.

A Student Council is a group of elected and volunteer students who work with an adult advisor within the framework of a constitution or bylaws to provide a means for student expression and assistance in school affairs and activities, provide opportunities for student leadership experience, and promote student, faculty, and community relations. Student councils seek to achieve the following goals through projects and activities:

• Strive to promote citizenship
• Scholarship must be promoted
• Promote leadership opportunities
• Providing an opportunity for social growth
• Promote human relations
• Promote cultural values

Key Points 

Objectives of Studnet Council are:

• To develop, plan, and complete initiatives and activities that will benefit the school, students, faculty, administration, Board of Trustees, and community.
• Develop and deliver leadership and service opportunities in the local school and community.
• Elections, participation in a constitutional representative parliament, and other activities will be used to create a living workshop of democratic processes.
• Contribute to students' educational experiences by increasing their positive involvement in school, expanding their areas of responsibility, and allowing them more direct involvement in planning and implementing programmes.

Thus from the above-mentioned points, it is clear that the primary purpose of the student council is that of providing students with opportunities for social growth.

Jean Piaget, a Swiss psychologist, has made a systematic study of cognitive development in his theory that is categorized in four stages. 

According to Piaget’s Cognitive Development Theory:

• Cognitive development takes place at different rates at different stages of development.
• Cognition develops through the interaction between the child and the environment.
• Piaget’s theory focuses not only on understanding how children acquire knowledge but also on understanding the nature of the child’s intelligence.

Important Points

Piaget’s Four Stages of Cognitive Development:

Hence, from the above explanation, it can be concluded that to understand the family tree, children need to use mental reversibility skills.

Concept:

​Noise pollution:

Noise pollution is generally defined as regular exposure to elevated sound levels that may lead to adverse effects in humans or other living organisms. According to the World Health Organization, sound levels less than 70 dB are not damaging to living organisms. Exposure for more than 8 hours to constant noise beyond 85 dB may be hazardous.

Sources of Noise Pollution:

1). Agricultural machine pollution:

Tractors, thrashers, harvesters, tube wells, powered tillers, etc. have all made agriculture highly mechanical but at the same time highly noisy. Noise level 90 dB to 98 dB due to the running of farm machines have been recorded in the state of Punjab.

2). Household pollution:

The household is an industry in itself and is a source of many indoor noises such as the banging of doors, noise of playing children, crying of infants, moving of furniture, the loud conversation of the inhabitants, etc. Besides these are the entertainment equipment in the house, namely the radio, record-players, and television sets. 

3). Transport pollution:

The automobile revolution in urban centers has proved to be a big source of noise pollution. Increasing traffic has given rise to traffic jams in congested areas where the repeated hooting of horns by impatient drivers pierce the ears of all road users. Heavy trucks, buses, trains, jet-planes, motor-cycles, scooters, mopeds, jeeps noise pollution, etc. are the cause of transport pollution.

4). Defense equipment pollution:

A lot of noise pollution is added to the atmosphere by artillery, tanks, launching of rockets, explosions, exercising of military airplanes, and shooting practices. Screams of jet engines and sonic booms have a deafening impact on the ears.

5). Industrial pollution:

Progress in technology or industrialization has resulted in creating noise pollu­tion. Textile mills, printing presses, engineering establishments, and metal works, etc. contribute heavily towards noise pollution. 

6). Miscellaneous Sources:

The automobile repair shops, construction-works, blasting, bulldozing, stone crushing, etc. are other sources of noise pollution.

A = {x : x = 2ⁿ, n ≤ 6}
For (n = 1,2,3,4,5,6) {2,4,8,16,32,64}
B = {x : x = 4ⁿ, n ≤ 2}
For (n = 1,2) {4,8}
A - B = {2, 8, 32, 64}

Hence equation of tangent to the given curve at (0 , 1) is :

(y−1) = 2(x−0),i.e..y−1 = 2x 

Since y−coordinate is called ordinate. 
Therefore, ordinate is −7.

Probability that Amit will qualify the exam(E) = 0.06
Probability that Priyanka will qualify the exam(F) = 0.12
Probability that both will qualify the exam P(E⋂F) = 0.02
P(EUF) = P(E) + P(F) - P(EUF)
= 0.06 + 0.12 - 0.02   = 0.16
P(E’⋂F’) = 1 - P(EUF)
⇒ 1 - 0.16
= 0.84

 Parabola is x² – 8x + 2y + 7 = 0 
∴   (x – 4)² = – 2y – 7 + 16 
∴   (x – 4)² = – 2[y – (9/2)]
 ∴   x² = – 4ay  
 ⇒ x = x – 4, y = y – (9/2) and 2 = 4a
 i.e. a = (1/2) 
 Its focus is given by x = 0 and y = 0 i.e. x – 4 = 0   and     y – (9/3) = 0 
∴    x = 4    and y = (9/2) 
∴ focus [4, (9/2)].

L.C.M. of 3, 4, 5, 6, 8 = 2 × 2 × 2 × 3 × 5 = 120 
Pair of 2, 3 and 5 is not completed.
To make it a perfect square, the number should be multiplied by 2, 3, 5.

Required number = 120 x 2 x 3 x 5 = 3600.

Total no. of outcomes=52
No. of ace cards=4
No. of non-ace cards=48
Probability of getting a non-ace card = No. of favourable outcomes / total no. of outcomes
=48/52=12/13

Let, PQ be a chord of a circle with centre O and radius 10cm. Draw OR ⊥PQ = .

Now, OP = 10cm and OR = 5cm

In right triangle ORP, we get

OP² = PR² + OR²

PR2 = OP² - OR²

PR² = 10² - 5² = 75

Since, the perpendicular from the centre to a chord bisects the chord.

Therefore, PQ = 2 x PR

= 2 x 8.66 = 17.32 cm

In ∆ BDC and ∆ BAC
Angle BAC = BDC
(angle made on same segment BC)
Since ABC is making right angle (90)
So,
In ∆ABC
ABC +BAC+ACB=180
(angle sum property of triangle)
90+42+ACB=180
ACB=180-132
ACB=48^o

f’(x) > 0 
=> f(x) is increasing
f’’(x) < 0  => f(x) is convex

For every square matrix (A – A’) is always skew – symmetric.

√x / √(16+√x) - 4

= (√x * √(16+√x) + 4) / ( √(16+√x) - 4) * (√(16+√x) + 4)

= (√x * √(16+√x) + 4) / 16+√x - 16

= √(16+√x) + 4

now at lim x->0

= √16 + 4 = 8

Determinant of a skew symmetric even ordered matrix A is a non zero perfect square.

Area of the circle with radius r =πr²
Now, New Radius = r + 100% of r = r + r = 2r
∴ New Area = π(2r)² - 4πr²
∴ Increased Area = 4πr² -  πr² = 3πr²
And Area increased in

A = {(2,1) (1,2)}
A² =  {(2,1) (1,2)} * {(2,1) (1,2)}
A² = {(4 + 1) (2 + 2)} {(2 + 2) (1 + 4)}
A² = {5,4} {4,5}

• Number of proper subsets of a given set = 2^m - 1, where m is the number of elements.
• Here the number of elements is 3. So the number of proper subsets of A = 2³ - 1 = 7.