HSSC TGT Math Mock Test - 7 Free Online Test 2026

Energy Conservation:

• Energy conservation is not about making limited resources last as long as they can, that would mean that you are doing nothing more than prolong a crisis until you finally run out of energy resources altogether.
• Conservation is the process of reducing demand on a limited supply and enabling that supply to begin to rebuild itself. Many times the best way of doing this is to replace the energy used with an alternate source.
• The goal with energy conservation techniques is to

1. Reduce demand
2. Protect and replenish supplies
3. Develop and use alternative energy sources
4. To clean up the damage from the prior energy processes.
5. To reduce energy losses.

Methods of Energy Conservation:

• Install CFL Lights
• Lower the Room Temperature 
• Use Maximum Daylight
• Get Energy Audit Done
• Use Energy Efficient Appliances
• Drive Less, Walk More and Carpooling
• Switch Off Appliances When Not in Use
• Alternative Power (Switching to Solar Energy)  
• Zero Energy Balance

Note:

Energy conservation and efficiency may be related, but they have distinct definitions in the energy world.

Energy conservation involves using less energy by adjusting your behaviors and habits.

Energy efficiency, on the other hand, involves using technology that requires less energy to perform the same function.

Energy-saving light bulbs, large household appliances, smart thermostats, and smart home hubs like Constellation Connect are all examples of technology that can be energy efficient.

 Passion has a motivating factor; therefore, it is a significant need for high-quality learning and teaching.

Important Points

• Passion is seeking for the new and experiencing new ideas.
• Passion is on the basis of effective teaching.
• The passion which is indispensable for learning and teaching facilitates learning through the desire and enthusiasm it creates.
• Passionate teachers by creating effective learning environments endeavor to increase the learning potentials of their students.

Example: Every week a teacher who has a personal interest in music shares with the class current news about musicians and music events and then displays the articles on a bulletin board. The teacher then encourages students to share current events of their own choosing with the class because the teacher is showing enthusiasm for a topic and therefore engaging students in the learning process.

Additional Information

• Only modeling any specific reading strategies or modeling making text-to-text connections by sharing the articles will not be able to keep students' motivation level high or encourage them to follow their passion. We learn by doing not only by reading or writing.

Hence we can conclude that the right answer to this question is promoting a passion for learning.

The correct answer is 8th position.

Key Points

• Sirsa district occupies 8th position in population size during the 2011 census.

• In terms of density, Sirsa ranks at last position in the entire Haryana with a density of 303 as per sq km.
• The sex ratio of Sirsa district is 897 females per 1000 males.
• The district stands at 4th place amongst the 22 districts of the State. The Sex Ratio in rural is 898 and it is better than the urban Sex Ratio which is 896 during the 2011 Census.

The correct answer is Rs. 250.

• Haryana Government has decided to increase the old-age pension amount by Rs. 250 every year.
• It was earlier Rs. 2250 every year but now after Rs. 250 increment it is Rs. 2500.
• The increase would be effective from April 1, 2021.
• Besides old-age pension, benefits have also been hiked under various other social security schemes, including Widows and Destitute Women Scheme, etc.

Additional Information

About Haryana:

• Chief Minister - Manohar Lal Khattar.
• Capital - Chandigarh.
• Districts - 22.
• State Animal - Blackbuck.
• Major Rivers - Yamuna, Ghaggar, Markanda, etc

The correct answer is Rakesh Singh.

Key Points

• Rakesh Koch -
  • He is a resident of Bahadurgarh, Haryana
  • He has been elected General Secretary of the Wrestling Association of Haryana.
  • He has been associated with sports for a long time and is also the director of the Model School located in Bahadurgarh.

Additional Information

• ​Santosh Sharma -
  • This is the head constable of Panipat Police.
  • He has recently brought laurels to the state of Haryana by winning the gold medal in the World Police Sports Competition.
• Preetpal Sangwan -
  • ​He is the Haryana police officer who has been awarded the Police Medal.

• The Kabuli Bagh Mosque is a mosque in Panipat.
• Built-in1527 by the emperor Babur to mark his victory over Sultan Ibrahim Lodhi at the first Battle of Panipat in 1526.
• The mosque is named after Kabuli Begum, Babur's wife.
• When Babur's son Humayun defeated Sher Shah Suri's descendants near Panipat.

Mostly composed of methane, the Compressed Natural Gas (CNG) is the cleanest of all the fossil fuels. It is called the cleanest fuel because when burnt, it produces only carbon dioxide and water vapor. Its key points are:

• It is used as an alternative to petrol and diesels because it is cheaper, greener and more efficient.
• It is compressed to increase the storage capacity of vehicles.
• It is environmentally friendly.
• It is safer than petrol and diesel.

Hence, the full form of CNG is Compressed Natural Gas.

• Haryana does not have any perennial river of its own. The important rivers flowing through the state are the Yamuna, Saraswati, and Ghaggar. These rivers are one of the sources of irrigation in Haryana. Following are the major rivers of Haryana state-
  • Yamuna River
  • Ghaggar River
  • Saraswati River
  • Dohan River
  • Tangri River
  • Krishnavati River
  • Sahibi River
  • Markanda River
  • Chetang River
  • Rakshi River
  • Indori River

Saraswati River:

• Origin - Har-ki-Doon Glacier from Garhwal (Uttaranchal) (approximate).
• Admission in Haryana- Ambala.
• Passes through districts- Ambala, Kurukshetra.
• Tributaries- Tangri, Markanda, Chutang.
• Merger or Termination- Joins the Ghaggar river in Sangrur (Punjab).

Additional InformationDohan River:

• Origin - It originates from Mandholi village near Neem Ka Thana in the Sikar district of Rajasthan.
• Entry in Haryana- Rewari.
• It passes through the districts- of Rewari and Mahendragarh.
• Merging or ending - merges into the Yamuna at Mahendragarh.
• Dohan River is a rainy river that originates in Mandoli village near Neem Ka Thana in the Sikar district of Rajasthan. It is a tributary of the Sahibi River, which later joins the Yamuna.

Ghaggar River:

• Origin: It originates from a place called Dagshai (Shimla) in the Shivalik hills of Himachal Pradesh.
• Entry in Haryana- Pinjore (Panchkula).
• It passes through the districts- of Panchkula, Ambala, Kaithal, Fatehabad, and Sirsa.
• Tributaries- Kaushalya River, Markanda, Saraswati, Tangri and Chautang.
• Merger or Termination- After Sirsa, it enters Rajasthan and becomes extinct.
• Dam and Kund- Kaushalya Dam (Panchkula), Chamala Dam, Dangarna Dam

Growth leads to the development of personality and behavioral traits, which is called maturation. In general, as organisms grow inside the structure, it is less quantitative and more emotional and cerebral. An illustration would be brain growth which makes it possible to manage activities that are more complicated.

Key Points

• The maturation stage marks the end of growth and the consolidation of acquired mental, social, and emotional development. In essence, maturation is a process of internal improvement, alteration, and development of an organism's potential. Being mature is a necessary prerequisite for learning. So, Maturation is a developmental process.
• Learning is the development that results from effort and repetition. We are aware that learning and maturation interact to influence development. The constraints of maturation are imposed on growth. It suggests that even when learning is fostered, growth cannot advance past a certain point due to limitations in hereditary endowment. So, Maturation and learning work together to promote the development of an individual.
• For example, bicycle riding will be learnt only as a result of effort, practice and training.

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

The correct answer is Kheri Gujjar.Key Points

• By excavations done in Kheri Gujjar of Sonepat district, earthen utensils belonging to Mahabharata period have been found.
• Kheri Gujjar is a Village in Ganaur Tehsil in Sonipat District of Haryana State, India.
• It belongs to Rohtak Division .
• It is located 23 KM towards North from District head quarters Sonipat. 7 KM from Ganaur. 205 KM from State capital Chandigarh.

Additional Information

• Sonipat
  • The name Sonepat is derived from the word Sonpat which means in Sanskrit language the suvarna prastha (gold place).
  • The Sonipat region has yielded pottery of pre-Harappan, late-Harappan, Painted Grey Ware, early historical, Northern Black Polished Ware and early medieval time.
  • One popular tradition avers that it is one of the five patas or prasthas (Indraprastha, Panipat, Talpat, Bhaghpat and Sonipat) mentioned in the Mahabharata.
  • On 22 December 1972, Sonipat was given status of a full-fledged district.
  • Khwaja Khizr Tomb is a famous maqbara located at Jatwara, Sonipat built by Ibrahim Lodi in the memory of Khwaja Khizr.

Charles H. Cooley was an American Sociologist he was best known for his concept of the looking-glass self.

Key Points

• Cooley is most famous for his theory of the looking-glass self.
• According to this concept, the child self grows out of society's interpersonal interactions and the perceptions of others.
• He describes how we each create our own self-image.
• The looking-glass self is the process by which people evaluate themselves based on how others see them. People first imagine how they appear to others.
• Second, they imagine how others judge them based on their appearance.
• Third, people have an emotional reaction to that imagined reaction such as pride or embarrassment. It is the process by which people evaluate themselves based on how other see them.

Important Points

• George Herbert Mead developed a theory of social behaviorism to explain how social experience develops an individual’s personality. Mead’s central concept is the self: the part of an individual’s personality composed of self-awareness and self-image. Mead claimed that the self is not there at birth, rather, it is developed with social experience.
• Vygotsky focused on the connection between people and the sociocultural context in which they act and interact in shared experiences.

​Hence, it can be concluded that this statement was given by Charles H. Cooley.

Any object or material that is used to facilitate learning and teaching can be considered as teaching-learning material (TLM). In other words, any material suitable for use in teaching is invariably a learning material.

Key Points

• We are familiar with materials specifically prepared for teaching and learning particular subjects or topics. Maps, charts, pictures, models, toys, marbles, coloured sticks, flashcards, number and alphabet cards are examples of some of the most common prepared TLMs known and used by teachers. Standard items like maps, globes, charts, scales, measuring tapes are usually purchased from the market.
• TLMs is based on the audio and visual effects produced by the materials. Accordingly, there are three types of TLMs: Audio, Visual and Audio-Visual.
  • Audio aids The materials or devices which call upon the auditory senses and thus help the individuals to learn through listening e.g. Radio broadcasts, Cassette and CD player.
  • Visual aids: The aids which call upon the visual senses and thus help the learners to learn through viewing. The important and under this head are Blackboard, Charts, Pictures, Graphs, Models, Film strips, Slides etc.
  • Audio-Visual Aids: The devices which require the auditory as well as visual senses and help the students to learn through listening as well as viewing. Examples of such aids are television, films and computer-assisted instruction.
• Still another way of categorizing TLMs is based on projected, non- projected or experiential.
  • Projected aids: Movies, epidiascope, the magic lantern, micro-projectors and projection with the overhead projectors, LCD projector are examples of projected aids.
  • Non-Projected aids: Chalkboard, felt board, bulletin board, photographs, posters, maps, charts, globes, specimens, and textbook illustrations, come under non-projected aids.
  • Experiential Aids: Field trips, educational tours, visiting important institutions and industries, observing experiments, demonstrations and natural phenomena are a few examples of experiential aids

Thus, it can be concluded that micro-projectors - non-projected aids is not teaching-learning material - category of teaching-learning material.

Probability of an egg being defective =10/100=110
So, probability of an egg being non-defective=1−0.1=0.9
10 eggs are drawn successively with replacement.
So, the probability of getting no defective egg =(0.9)¹⁰
Hence, the probability that there is at least one defective egg = 1−(0.9)¹⁰

A proper subset of a set is any subset that is not the entire set itself.

For the set {1, 2, 3}:

1. The total number of subsets is 2^3 = 8.
   (Each of the 3 elements can either be in or out of a subset.)

2. Since only one of these subsets is the entire set itself, the number of proper subsets is 8 – 1 = 7

Let point A be (a, b) and point B is (-a, b)

∴ distance between A and B
 

A function is a relation in which no two ordered pairs have the same first element. A function associates each element in its domain with one and only one element in its range. R={(1,2), (1,4)(3,1),(5,1)} is not  a function because all the first elements are not different.

Total number of outcomes=90-1=89
No. of favourable outcomes = Total outcomes - One digit number =89-8=81
Probability of having a two digit number=Total number of outcomes/No. of favourable outcomes=81/89

Given: P(win) = 0.3.

Assuming the only possible outcomes are win or lose, these are complementary events and their probabilities sum to 1.

Therefore, P(lose) = 1 − P(win) = 1 − 0.3 = 0.7.

Hence the probability of losing is 0.7, so option B is correct.

According to question, Diameter (BD) = 2 x radius = 2 x 12 = 24 cm
∴ Area of square

The orthogonal projection on x- axis is given by : 

f(x)= {−(x−1)/x²   x<1,   x(x−1)/x²  x≥1}
​f'(x)= {(x−2)/x³   x<1,      −(x−2)/x³   x≥1}
​x<1, if f′(x)<0 (for f(x) to be monotonically decreasing
⇒ (x−2)/x³<0
⇒x∈(0,2)
But x<1 ⇒ x∈(0,1)
For x≥1, if f′(x)<0
⇒ −(x−2)]/x³<0
⇒(x−2)/x³ > 0
⇒x∈(−∞,0)∪(2,∞)
But, x≥1   ⇒x∈(2,∞)
Hence, x∈(0,1)∪(2,∞)

We know that the midpoint of two points (x1, y1) and (x2, y2) is given by:
((x1 + x2) / 2, (y1 + y2) / 2)

Given midpoint is (2, 2p + 2).

So,
(3p + (-2)) / 2 = 2 --> (3p - 2) / 2 = 2
Multiply both sides by 2:
3p - 2 = 4
3p = 6
p = 2

Now, substitute p = 2 in the second part:
(4 + 2q) / 2 = 2p + 2
(4 + 2q) / 2 = 4 + 2
(4 + 2q) / 2 = 6
Multiply both sides by 2:
4 + 2q = 12
2q = 8
q = 4

So, p = 2 and q = 4.

Answer:
c) 2, 4

If A = [a_ij]_2x2 where a_ij = i + j, then, 

According to definition of parabola , is is the locks of the points in that planes that are equidistant from both focus and directrix.

Given, focus : (-3,0)
directrix : x + 5 = 0
Let (x ,y) is the point on the parabola .
∴ distance of point from focus = distance of point from directrix
⇒ √{(x + 3)² + y²} = |x + 5|/√(1² + 0²)
⇒ √{(x + 3)² + y² } = |x + 5|
squaring both sides,
(x + 3)² + y² = (x + 5)²
⇒y² = (x + 5)² - (x + 3)²
⇒y²= (x + 5 - x - 3)(x + 5 + x + 3)
⇒y² = 2(2x + 8) = 4(x + 4)

Hence, equation of parabola is y² = 4(x + 4)

It is given that :  are unit vectors such that 
then :

Here, Area of circle (A) = πr² and Circumference of circle (C) = 2πr
 
Putting value of C in A = πr², we get

Let middle point of chord is P(h,k)
Thus equation of chord with mid point P is,  kx+hy=2hk
Given slope of this chord is m
⇒ −k/h = m
⇒k+mh=0
Thus locus of P(h,k) is, y+mx=0