HP Forest Guard Exam 2021 Solved Paper with Explanation


HP Forest Guard Exam 2021 Solved Paper

The HP Forest Guard Exam 2021 Solved Paper is an invaluable resource for candidates aspiring to join the Himachal Pradesh Forest Department. This solved paper includes detailed answers to the questions from the 2021 exam, allowing candidates to familiarize themselves with the exam format and question styles. By studying this solved paper, aspirants can identify key topics, understand the reasoning behind each answer, and enhance their overall preparation strategy for the Forest Guard examination.

HP Forest Guard Exam 2021

For those preparing for the HP Forest Guard Exam 2021, this solved paper serves as a crucial study aid. The structured answers and clear explanations not only clarify complex concepts but also help candidates develop effective problem-solving skills. This resource is ideal for thorough study sessions as well as quick revisions, empowering candidates to approach the exam with confidence and a solid understanding of the material.

HP Forest Guard Exam 2021 Solved Paper

➤ In Una and Hamirpur district of Himachal Pradesh which of following hills are found:

  • Aravalli
  • Pir Panjal
  • Shivalik hills
  • Zaskar

The Shivalik hills, also known as the Outer Himalayas, are the foothills of the Himalayas and extend across Una and Hamirpur districts in Himachal Pradesh.

➤ Which of the following is the state animal of Himachal Pradesh?

  • Brown Bear
  • Tiger
  • Cheetah
  • Snow Leopard

The Snow Leopard is the state animal of Himachal Pradesh, symbolizing the region’s rich biodiversity and efforts in wildlife conservation.

➤  Simbalbara National Park is situated in which of the following districts?

  • Sirmour
  • Kullu
  • Lahual & Spiti
  • Shimla

Simbalbara National Park is located in the Sirmour district of Himachal Pradesh and is known for its diverse flora and fauna.

➤  In which of the following places the factories for the extraction of turpentine oil from the resin of pine trees are situated:

  • Bilaspur & Hamirpur
  • Bilaspur & Nahan
  • Bilaspur & Jahu
  • Bilaspur & Rajgrah

Bilaspur and Nahan are known for their turpentine oil extraction factories, which process the resin from pine trees.

➤  Giri and Pubbar are the tributaries of one of the following rivers:

  • Ravi
  • Yamuna
  • Satluj
  • Beas

The Giri and Pubbar rivers are tributaries of the Yamuna river, contributing to its flow from the Himachal region.

➤  In which of the following districts the Chandra Tal lake is situated?

  • Lahul & Spiti
  • Kinnaur
  • Mandi
  • Chamba

Chandra Tal, also known as the Moon Lake, is located in the Lahul & Spiti district, famous for its scenic beauty and trekking routes.

➤ In which of the following places the veterinary college of Himachal Pradesh is situated?

  • Solan
  • Palampur
  • Shimla
  • Bilaspur

The veterinary college of Himachal Pradesh is situated in Palampur, offering various courses in veterinary sciences and animal husbandry.

➤ Which of the following is an artificial man-made lake in Himachal Pradesh?

  • Nako
  • Govind Sagar
  • Prashar Lake
  • Chandra Tal

Govind Sagar is an artificial lake created by the Bhakra Dam on the Sutlej River, providing irrigation and hydroelectric power.

➤ Find out the mismatch between the following match pairs:

  • All India Institute of Medical Science in Himachal Pradesh-Bilaspur
  • World famous handkerchief (Rumal)- Chamba
  • Choti Kashi- Mandi
  • Alpine pastures-Una

Una does not have Alpine pastures, which are typically found in higher altitude regions like Kullu, Shimla, and Chamba.

➤ Who is the present Governor of Himachal Pradesh?

  • Sh. Bandaru Dattatreya
  • Acharya Devvrat
  • Rajinder Vishwanath Arlekar
  • Mrs. Kiran Bedi

Rajinder Vishwanath Arlekar is the current Governor of Himachal Pradesh, appointed in July 2021.

➤ In Himachal Pradesh maximum rainfall is received due to …………

  • South-West Monsoon
  • Western Disturbances
  • North-East Monsoon
  • Winter Monsoon

The South-West Monsoon is the primary source of rainfall in Himachal Pradesh, occurring from June to September.

➤  In Himachal Pradesh monsoon rains are received during ………. Months:

  • June-September
  • April-July
  • July-October
  • October-February

Monsoon rains in Himachal Pradesh occur mainly from June to September, bringing significant precipitation to the region.

➤ Which one of the following is considered as the best fodder tree?

  • Biul
  • Teak
  • Tooni
  • Semal

Biul (Grewia oppositifolia) is considered the best fodder tree in Himachal Pradesh, providing nutritious feed for livestock.

➤ Which of the following is a greenhouse gas?

  • CO2
  • CH4
  • CFC
  • All of the above

All of these gases—carbon dioxide (CO2), methane (CH4), and chlorofluorocarbons (CFCs)—are greenhouse gases that contribute to global warming.

➤  Increase in concentration of harmful gases in atmosphere which cause ailments to living organisms is called ………………….

  • Air Pollution
  • Climate change
  • Global warming
  • Ozone layer depletion

Air pollution refers to the presence of harmful substances in the atmosphere, which can cause health problems and environmental damage.

➤ Which of the following is the state tree of Himachal Pradesh?

  • Chilgoza Pine
  • Toona
  • Deodar
  • Chirpine

The Deodar cedar (Cedrus deodara) is the state tree of Himachal Pradesh, revered for its cultural and economic significance.

➤ Either of these paths …………………… to the temple.

  • lead
  • leads
  • leading
  • have led

Either of these paths leads to the temple is correct because “either” is singular and requires a singular verb.

➤  They ………………… her since she was a child.

  • have known
  • were knowing
  • know
  • are knowing

The correct answer should be “have known,” but the selected answer “were knowing” is incorrect as it does not fit standard English usage.

➤  Don’t dwell …………………… what has passed away!

  • on
  • into
  • cat
  • for

Don’t dwell on what has passed away means not to focus or linger on past events.

➤  The collective noun for owls is …………………….

  • pack
  • school
  • swarm
  • parliament

A group of owls is called a parliament, reflecting their association with wisdom and knowledge.

➤ Walk fast lest you ………………………….. miss the train.

  • would
  • should
  • could
  • can

“Lest” is always followed by “should” to indicate a warning or precaution.

➤ We ……………………. To help the poor.

  • need
  • dare
  • ought
  • shall

“Ought” is used to indicate duty or correctness.

➤ Complete the sentence:

A burnt child ……………………………………….

  • dreads the burns
  • dreads the fire
  • dares the fire
  • scares the fire

“A burnt child dreads the fire” is a proverb meaning that someone who has had a bad experience will be cautious in the future.

➤ Change the narration: She said to me, “The earth is round”.

  • She asked me that the earth was round
  • She said that the earth is round
  • She tells me that the earth is round
  • She told me that the earth is round

In reported speech, the sentence changes to “She told me that the earth is round.”

➤ Change the voice: “Let a lie never be told”

  • One should never tell a lie
  • None should tell a lie
  • Don’t tell a lie
  • Never tell a lie

“Never tell a lie” is the active voice form of “Let a lie never be told.”

➤ The young one of “Cat” is called?

  • Baby cat
  • Pup
  • Kitten
  • None of these

A young cat is called a kitten.

➤ In the sentence, ‘I have lost my book’. The word ‘have’ is …………….

  • Principal verb
  • Auxiliary verb
  • Transitive verb
  • None of these

“Have” is used as an auxiliary verb in the sentence “I have lost my book.”

➤ The correct saying is:

  • Greed is a curse
  • A greed is a curse
  • The greed is a curse
  • None of these

“Greed is a curse” is a well-known proverb emphasizing that greed leads to negative consequences.

➤ Re-arrange the following jumbled words and choose the correct one: age/an/this/ mobile/of/phones/is

  • An age of mobile phone is this
  • This is an age of mobile phones
  • This an age if of mobile phones
  • Mobile phone is an age of this

The correct arrangement of the words is “This is an age of mobile phones.”

➤ Which one is not correct ?

  • My friends do not smoke
  • He is reading a book
  • Ram has gone to Shimla
  • A lot of money are wasted on the project

The correct sentence should be “A lot of money is wasted on the project.”

➤ What is the comparative degree of “Busy”?

  • Busiest
  • Busier
  • More busy
  • Most busy

The comparative degree of “Busy” is “Busier.”

➤ ‘देवालय ‘ शब्द में कौन से संधि है?

  • गुण संधि
  • याणं संधि
  • दीर्ध संधि
  • उपरोक्त में से कोई नहीं

‘देवालय’ शब्द में दीर्ध संधि है।

➤ अकर्मक और सकर्मक किसके भेद हैं ?

  • संज्ञा
  • क्रिया
  • सर्वनाम
  • विश्लेष्ण

अकर्मक और सकर्मक क्रिया के भेद हैं।

➤ फल के रूप में ‘आम’ शब्द किस प्रकार का शब्द हैं ?

  • तत्सम
  • तदभव
  • देशज
  • विदेशी

फल के रूप में ‘आम’ तदभव शब्द है।

➤ जिस वाक्य में दो या अधिक मुख्य या स्वतंत्र उपवाक्य हों, उसे क्या कहते हैं ?

  • सयुंक्त वाक्य
  • सरल वाक्य
  • मिश्र वाक्य
  • उपरोक्त में से कोई नहीं

जिस वाक्य में दो या अधिक मुख्य या स्वतंत्र उपवाक्य हों, उसे सयुंक्त वाक्य कहते हैं।

➤ ‘अनुराग’ शब्द का विलोम क्या है ?

  • प्रेम
  • विराग
  • पराग
  • उपरोक्त में से कोई नहीं

‘अनुराग’ शब्द का विलोम ‘विराग’ है।

➤ निम्नलिखित में से शुद्ध रूप कौन सा है ?

  • अनुग्रहीत
  • अनुगृहीत
  • अनुगहित
  • उपरोक्त में से कोई नहीं

‘अनुगृहीत’ शब्द शुद्ध रूप है।

➤ लिखने की रीति को क्या कहते हैं ?

  • लिखावट
  • सुलेख
  • श्रुतिलेख
  • वर्तनी

लिखने की रीति को वर्तनी कहते हैं।

➤ ‘हर पंद्रह दिन बाद होने वाला’ वाक्यांश के लिए सही शब्द कौन सा है ?

  • साप्तहिक
  • वार्षिक
  • मासिक
  • पाक्षिक

‘हर पंद्रह दिन बाद होने वाला’ वाक्यांश के लिए सही शब्द ‘पाक्षिक’ है।

➤ ‘आचार्य’ शब्द का स्त्रीलिंग क्या होगा ?

  • आचार्याणी
  • आचार्या
  • आचार्यी
  • आचार्यांनी

‘आचार्य’ शब्द का स्त्रीलिंग ‘आचार्या’ होगा।

➤ हिंदी वर्णमाला में स्वरों की कुल संख्या कितनी है ?

  • 33
  • 13
  • 44
  • 11

हिंदी वर्णमाला में 11 स्वर होते हैं। ये स्वर हैं अ, आ, इ, ई, उ, ऊ, ऋ, ए, ऐ, ओ, और औ। इन स्वरों का उपयोग शब्दों और वाक्यों में ध्वनि को स्पष्ट करने के लिए किया जाता है।

➤ ‘बादल’ शब्द का पर्यायवाची है ?

  • जलज
  • नीरज
  • जलद
  • पुष्कर

‘बादल’ का पर्यायवाची शब्द ‘जलद’ है। ‘जलद’ का अर्थ भी बादल होता है और इसका प्रयोग अधिकतर साहित्यिक या काव्यात्मक भाषा में किया जाता है।

➤ ‘व्’ का उच्चारण स्थान क्या है ?

  • कण्ठ
  • ओष्ठ
  • दन्तोष्ठ
  • मूर्धा

‘व्’ का उच्चारण दन्तोष्ठ स्थान पर होता है, जिसका अर्थ है कि इसे दांतों और होंठों के बीच से उच्चारित किया जाता है। इस उच्चारण की विशेषता यह है कि इसे बोलते समय दांत और होंठ हल्के से मिलते हैं।

➤ हिंदी भाषा किस लिपि में लिखी जाती है ?

  • ब्राम्हीं
  • संस्कृत
  • देवनागरी
  • भारती

हिंदी भाषा देवनागरी लिपि में लिखी जाती है, जो एक वर्णमाला आधारित लिपि है। इसमें प्रत्येक अक्षर का अपना एक विशिष्ट ध्वनि और प्रतीक होता है, जिससे हिंदी लिखना और पढ़ना संभव होता है।

➤ रामचरितमानस की भाषा कौन से है ?

  • अवधी
  • ब्रज भाषा
  • खड़ी बोली
  • संस्कृत

रामचरितमानस की भाषा अवधी है, जो कि एक प्रकार की हिंदी भाषा है। अवधी का प्रयोग विशेष रूप से उत्तर भारत में होता है और यह हिंदी की प्राचीन बोलियों में से एक मानी जाती है।

➤ ‘तूती बोलना’ मुहावरे का सही अर्थ बताएं

  • बाजा बजना
  • प्रभाव होना
  • बेकार होना
  • डर जाना

‘तूती बोलना’ मुहावरे का अर्थ होता है प्रभाव होना। इसका प्रयोग तब किया जाता है जब किसी व्यक्ति का प्रभाव अत्यधिक होता है या किसी स्थिति पर गहरा असर होता है।

➤ What is the chemical name of dry ice?

  • Duralium
  • Calcium Sulphate
  • Solid carbon dioxide
  • Silver nitrate

Dry ice is chemically known as solid carbon dioxide. It sublimates directly from a solid to a gas at room temperature, making it useful for various cooling applications without leaving any residue.

➤ Name the pandemic which has affected people all over the world during 2020-2021

  • SARS
  • Delta
  • COVID-19
  • Wuhan

The COVID-19 pandemic, caused by the novel coronavirus SARS-CoV-2, significantly impacted global health, economies, and daily life from 2020 to 2021. It led to widespread illness, death, and disruptions across various sectors.

➤ Which of the following acid is present in the gastric juice human body?

  • Acetic acid
  • Nitric acid
  • Hydrochloric acid
  • Sulphuric acid

Hydrochloric acid is present in gastric juice in the human body. It plays a crucial role in digestion by breaking down food and killing harmful bacteria that enter the stomach.

➤ Some of the organisms are sensitive to different levels of air pollution and are used as pollution indicators. Select which among the following fits into this category?

  • Fungi
  • Freshwater algae
  • Bacteria
  • Lichens

Lichens are highly sensitive to air pollution, making them excellent indicators of air quality. They can reflect changes in air pollution levels over time, helping in environmental monitoring.

➤ What does our body produce to fight the invader when disease-carrying microbes enter the body?

  • Antibiotics
  • Antigens
  • Pathogen
  • Antibodies

When disease-carrying microbes invade the body, it produces antibodies. These proteins are specifically designed to identify and neutralize pathogens, thereby helping the immune system to fight infections effectively.

➤ Which of the following is responsible for marble cancer?

  • Acid rain
  • CFC
  • Ozone
  • Oxygen

Acid rain is responsible for marble cancer. It causes the deterioration of marble structures by reacting with calcium carbonate in the marble, leading to surface damage and loss of quality.

➤ Lightning conductor is a device used to protect?

  • Building from the effect of lightning
  • Building from the effect of earthquake
  • Building from heavy rain
  • Structures from heavy wind

A lightning conductor is designed to protect buildings from the effects of lightning. It provides a path for the electrical discharge to safely reach the ground, thereby preventing damage to the structure.

➤ In human body the blood glucose level is controlled by ……… harmone

  • Glucogen
  • Insulin
  • Adrenalin
  • Thyroxin

Insulin is the hormone responsible for regulating blood glucose levels in the human body. It helps cells absorb glucose from the bloodstream, maintaining energy balance and metabolic function.

➤ Rhizobium bacteria found in root nodules of leguminous plants is an ……………..

  • Atmospheric carbon fixer
  • Atmospheric oxygen fixer
  • Atmospheric nitrogen fixer
  • All of these

Rhizobium bacteria are known as atmospheric nitrogen fixers. They convert atmospheric nitrogen into a form that plants can use for growth, which is vital for soil fertility and plant health.

➤ Which of the following non-metal is a good conductor of electricity?

  • Coal
  • Graphite
  • Sulphur
  • Phosphorus

Graphite is a non-metal that is an excellent conductor of electricity due to its structure, which allows electrons to move freely within its layers.

➤ In which of the following categories Adma’s Apple is more prominent?

  • Boys of any age
  • Adolescent girls
  • Girls of any age
  • Adolescent boys

Adma’s Apple, or the prominence of the laryngeal prominence, is more pronounced in adolescent boys due to hormonal changes during puberty, which cause the voice box to grow.

➤ Which of the following metal is stored in kerosene oil due to its high reactivity with air and water?

  • Sodium
  • Zinc
  • Calcium
  • Magnesium

Sodium is stored in kerosene oil because it reacts vigorously with both air and water. The kerosene oil prevents these reactions by providing a barrier from moisture and oxygen.

➤ In which of the following are the role of bacteria is not present?

  • Leather industry
  • Apiculture industry
  • Alcohol and vinegar industry
  • Tobacco & Tea industry

Bacteria play a role in the leather, alcohol, vinegar, and tobacco industries, but not in the apiculture (beekeeping) industry. In apiculture, bees are primarily responsible for honey production, not bacteria.

➤ An electric heater has a wattage of 1,500 W. How much electric energy does it consume in 10 hours?

  • 15 kWh
  • 150 W
  • 15000 W
  • Data is insufficient

An electric heater with a wattage of 1,500 W consumes 15 kWh of energy in 10 hours. This is calculated by multiplying the power (1,500 W) by the time (10 hours) and converting watts to kilowatts (1,500 W = 1.5 kW).

➤ If a person is not able to see far off objects, then from which of the following he or she is suffering?

  • Presbyopia
  • Hypermetropia
  • Myopia
  • Astigmatism

Myopia, or nearsightedness, is the condition where a person can see close objects clearly but struggles with distant vision. This happens because the light entering the eye focuses in front of the retina.

➤ Which one of the following is laughing gas?

  • NO2+CO2
  • N2 O5
  • N2 O
  • NO2

Nitrous oxide (N2O) is commonly known as laughing gas. It is used in medical anesthesia and can produce a feeling of euphoria and laughter when inhaled.

➤ ‘Widal Test’ is used to diagnose which disease?

  • Typhoid
  • Malaria
  • AIDS
  • Cancer

The Widal test is used to diagnose typhoid fever. It detects the presence of antibodies against Salmonella typhi bacteria, which cause the disease.

➤ On what principle does a stethoscope work?

  • Refraction of sound
  • Reflection of sound
  • Speed of Sound
  • Intensity of sound

A stethoscope works on the principle of sound reflection. It amplifies the sounds produced by the body, such as heartbeats and lung sounds, by reflecting them through its tubes to the listener’s ears.

➤ Which colour of light deviates least while passing through a glass prism?

  • Red
  • Blue
  • Green
  • Violet

Red light deviates the least when passing through a glass prism because it has the longest wavelength and is refracted less compared to colors like violet or blue.

➤ Which of the following is included in an ecosystem?

  • All living organisms
  • Non-living objects
  • Some times living and some times non-living object
  • Both

An ecosystem includes both living organisms (biotic components) and non-living objects (abiotic components). The interaction between these components creates a functional system that supports life.

➤ A man walks 1 km to east and then he turns to south and walks 5 km. After that he turns to East and walks 2 km. After this he turns to north and walk 9 km. What is the distance from his starting point?

  • 3 km
  • 5 km
  • 4 km
  • 7 km

To solve this, we need to plot the path on a coordinate plane. Starting from the origin (0,0), he walks 1 km east to (1,0), then 5 km south to (1,-5), then 2 km east to (3,-5), and finally 9 km north to (3,4). The distance from (3,4) to the origin (0,0) is found using the distance formula: sqrt((3-0)² + (4-0)²) = sqrt(9 + 16) = sqrt(25) = 5 km.

➤ The total of the ages of Raju, Amar and Satish is 80 years. What was the total of their ages 3 years ago?

  • 71 years
  • 72 years
  • 74 years
  • 77 years

Three years ago, each of the three individuals was 3 years younger, so the total age three years ago would be 80 – 3*3 = 80 – 9 = 71 years.

➤ A person crosses a 200 m long road in 2 minutes. What is his speed in km per hour?

  • 3
  • 6
  • 9
  • 12

To find the speed, first convert 200 meters to kilometers (0.2 km). The time is 2 minutes, which is 2/60 hours = 1/30 hours. Speed = distance/time = 0.2 km / (1/30) hours = 0.2 * 30 = 6 km/h.

➤ In a mixture of 60 litres the ratio of milk and water is 2:1. If the ratio of the mixture of milk and water is to be made 1:2, then find out the quantity of water to be further added?

  • 20 litres
  • 30 litres
  • 40 litres
  • 60 litres

Currently, the mixture has 40 liters of milk and 20 liters of water (2:1 ratio). To achieve a 1:2 ratio, the total quantity of the mixture needs to be doubled to 120 liters (40 liters milk + 80 liters water). Thus, 60 liters of additional water must be added.

➤ What is the probability of an impossible event?

  • 1
  • 0
  • -1
  • -2

An impossible event has zero probability of occurring because it cannot happen under any circumstances. Therefore, its probability is 0.

➤ Which of the following is an irrational number?

  • 3
  • 3/7
  • 1/3
  • 22/7

22/7 is a rational number, not irrational. An irrational number is one that cannot be expressed as a simple fraction, such as the square root of 2 or pi.

➤ Which one of the following is the formula for estimation of volume of a sphere?

  • 2/3 πr3
  • 4/3 πr3
  • 1/3 πr3
  • πr3

The formula for the volume of a sphere is 4/3 πr3, where r is the radius of the sphere.

➤ The two trees standing erect on a plane surface having height of 6 and 11m, respectively. If the distance between the bottoms of both the trees is 12m, then what is the distance between the top tips of the stem of these two trees?

  • 17 m
  • 13 m
  • 6 m
  • 18 m

To find the distance between the tops of the trees, calculate the difference in height (11m – 6m = 5m) and use the Pythagorean theorem to find the distance: sqrt(12² + 5²) = sqrt(144 + 25) = sqrt(169) = 13 m.

➤ A student multiplied a number by 3/5 instead of 5/3. What is the percentage error in the calculation?

  • 4%
  • 8%
  • 16%
  • 64%

The correct multiplication factor is 5/3. The student used 3/5. The error percentage can be calculated as follows: Error = [(5/3) – (3/5)] / (5/3) * 100% = (16/15 – 9/15) / (5/3) * 100% = 7/15 / (5/3) * 100% = 7/15 * 3/5 * 100% = 64%.

➤ What is the decimal expansion of 17/8?

  • Terminating
  • Non-terminating
  • Recurring
  • Non-terminating recurring

17/8 is a terminating decimal, as it can be expressed as 2.125. This decimal has a finite number of digits and does not recur.

➤ An angle which is greater than 180° and less than 360° is ……

  • Complimentary angle
  • Reflex angle
  • Straight angle
  • Supplementary angle

An angle greater than 180° but less than 360° is called a reflex angle.

➤ How many bags of grains can be stored in a cuboid granary of 12 m x 6 m x 5 m, if each bag occupies a space of 0.48 m3?

  • 75
  • 750
  • 1500
  • 375

The volume of the granary is 12 m × 6 m × 5 m = 360 m3. The number of bags that can be stored is the total volume divided by the volume of each bag: 360 / 0.48 = 750 bags.

➤ If two dice are thrown simultaneously, the probability of getting a sum of 9 is:

  • 1/10
  • 3/10
  • 1/9
  • 4/9

There are 36 possible outcomes when rolling two dice. The pairs that sum to 9 are (3,6), (4,5), (5,4), and (6,3). So, there are 4 favorable outcomes. Probability = 4 / 36 = 1/9.

➤ If the mode and mean of a set of numbers are 8 and 9, respectively, then the value of the median will be?

  • 57
  • 67
  • 97
  • 24

In a dataset where the mean is 9 and the mode is 8, the median will be the value that balances the dataset, which is the value between the mean and mode. Thus, the median is 67.

➤ The areas of rhombus having d1 = 16 cm, d2 = 12 cm will be :

    • < li>16*12 cm

2

  • 96 cm2
  • 8*6 cm2
  • 144 cm2

The area of a rhombus is given by (1/2) × d1 × d2. Substituting the given diagonals: (1/2) × 16 cm × 12 cm = 96 cm2.

➤ Select the correct value of (1 + Cos2 θ) out of the following:

  • Sin2 θ
  • cos2 θ
  • Tan2 θ
  • cot2 θ

By using the Pythagorean identity, we know that 1 + cos2 θ = sin2 θ + cos2 θ = 1. Hence, 1 + cos2 θ equals sin2 θ.

➤ What will be the value of P for polynomial x3 + 4 x2 – Px + 8 if (x – 2) exactly divides it:

  • 16
  • 3
  • 5
  • 0

To find P, use the fact that (x – 2) is a factor. Substitute x = 2 into the polynomial: 23 + 4 × 22 – 2P + 8 = 0, solving gives P = 16.

➤ If a wooden cylinder, cone and hemisphere are of the same base and same height then the ratio of their volumes will be?

  • 3:1:2
  • 3:2:1
  • 1:2:3
  • 1:3:2

The volumes of a cylinder, cone, and hemisphere with the same base radius and height are in the ratio of 3:1:2. This is because the volume of a cylinder is πr2h, of a cone is (1/3)πr2h, and of a hemisphere is (2/3)πr3.

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