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B. chemicals within

The Correct option is C. 3.0 A

D. recalibrating the instrument

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GIVEN:

2x³ – 3x² – 17x – 12

CALCULATION:

2x³ – 3x² – 17x – 12

Put x = 1

2 × (1)³ – 3 × (1)² – 17 × 1 – 12

= 2 – 3 – 17 – 12

= 30 [(x – 1) is not a factor of expression.]

Put x = -1

2 × (-1)³ – 3 × (-1)² – 17 × (-1) – 12

= – 2 – 3 + 17 – 12

= 0 [(x + 1) is a factor of expression.]

Now,

2x³ – 3x² – 17x – 12 = (x + 1) (2x² – 5x – 12)

(x + 1) (2x + 3) (x – 4)

Hence, (x + 1), (2x + 3) and (x – 4) are factors of expression. 

Given:

p(x) = 2x³ – 3x² – 2x + 3 and q(x) = 3x² + 8x + 5

Concept:

H.C.F. of two or more equations is the greatest factor that divides each of them exactly.

Calculation:

The factors of p(x) = 2x³ – 3x² – 2x + 3

⇒ x² × (2x – 3) – 1 × (2x – 3)

⇒ (x² – 1) × (2x – 3)

⇒ (x – 1) × (x + 1) × (2x – 3)

And, the factors of q(x) = 3x² + 8x + 5

⇒ 3x² + 5x + 3x + 5

⇒ x × (3x + 5) + 1 × (3x + 5)

⇒ (3x + 5) × (x + 1)

P(x) = 3x² + x+  7

P(-2) = 3(-2)² - 2 + 7

= 3 x 4 + 5

= 12 + 5  = 17.

• First option:
  • It is given that Ali does not play Cricket. 
  • Hence, the first option is incorrect.
• Second, Third and Fourth options:
  • It is given that Benu does not play Kabaddi or Hockey.
  • Hence, Benu must be playing Hockey, Basketball or Cricket.
  • It is given that Cutty plays Hockey.
  • Hence, Benu must be playing Basketball or Cricket.
  • It is given that Dolly plays either Basketball or Hockey and Cutty plays Hockey.
  • Thus, Dolly plays Basketball.
  • Hence, Benu plays Cricket.
  • Hence, the second option is correct and the third and the fourth options are incorrect.

Given:

⇒ Speed of cyclist A = 9kmph = 9 × 5/18 = 5/2 m/s

⇒ Speed of cyclist B = 12kmph = 12 × 5/18 = 10/3 m/s

Let speed of train be a m/s.

Calculation:

Relative speed of train and cyclist A = a - 5/2

⇒ 120/(a - 5/2) = 16

⇒ 7.5 = a - 2.5

⇒ a = 10 m/s

Relative speed of train and cyclist B = 10 - 10/3 = 20/3 m/s

∴ Time in which train crosses cyclist B = 120/(20/3) = 18 seconds

Correct option is C) are skating

Correct option is C) knew / had broken / offered

Correct option is C) skating

C) What is your favorite sport?

D) What was the famous engineer's invention?

On the basis of sources of raw material used, industries are classified into: 

• Agro based industries: These are dependent on raw material produced in the agricultural sector. These industries are labour intensive. 
• Mineral based: These industries produce goods which are used in other industries. These industries are capital intensive.

On the basis of bulk and weight of raw materials and finished goods, industries can be classified into: 

• Heavy industry such as iron and steel. 

Light industries that use light raw-materials and produce light goods such as electrical industries​​​​​​

The two features of heavy industries are: 

• They produce those goods which are used by other industries. 
• They satisfy our wants indirectly.

The two features of light industries are: 

• They produce consumer goods like electrical bulbs, sewings machines etc. 
• They produce goods which satisfy our wants indirectly, e.g. fuse wires. 

B) How long has his father been bowling?

Given:

The speeds of the fast bowler 140, 145, 119, 90, and 95 km/h

Calculation:

Let be assume average speed of the fast bowler is p

⇒ p = (140 + 145 + 119 + 90 + 95)/5 = 589/5 = 117.8

∴ The required result will be 117.8.

Manufacturing sector refers to the secondary sector of the economy which deals with production of goods in large quantities with the help of machines, where raw materials are transformed into more valuable products. Manufacturing is considered as the backbone of economic development because: 

• Manufacturing has contributed to modernisation of agriculture and reduced the dependency on agriculture by providing jobs in secondary and tertiary sectors. 
• It has helped in reducing the poverty and unemployment and aimed at reducing the regional disparities by setting up of industries in rural, backward and tribal areas. 
• Export of industrial goods contributed to valuable foreign exchange earnings. 
• It has added value to raw materials by converting them into finished goods. 
• The prosperity of a nation depends upon the development and diversification of manufacturing. Thus, it has not only made India self-sufficient but more competitive in terms of international market. 
• It brings down regional disparities by establishing industries in tribal and backward areas. 
• Industry sector contributes substantially to GDP.

The five factors responsible for the location of jute mills along the Hugli basin are: 

• Proximity or nearness to the jute producing areas. 
• Inexpensive water transport. 
• Good network of roadways, railways and waterways which helps in the movement of raw material to the mills. 
• Availability of abundant water for processing of raw jute. 
• Cheap labour from West Bengal, Bihar, Odisha and Uttar Pradesh.
• Kolkata being a large urban centre provides banking, insurance and port facilities for export of jute goods.

The following factors affect the location of an industry: 

• Availability of raw materials: Close proximity to raw material, regular supply at cheap cost are of utmost significance, e.g., concentration of heavy industries in Chattisgarh. 
• Labour: Modern industry requires both skilled and unskilled labour at low cost. It also determines the location of industry, e.g., cotton textile industry in Maharashtra. 
• Capital: Industries are capital intensive. Banks and other financial institutions, insurance etc. play an important role in setting up production units. 
• Power: All production units depend on one or other sources of power like coal, oil, gas etc. Regular and cheap supply of power is required to keep industries operational, e.g., iron and steel industries near Raniganj and Jharia coal fields. 
• Market: Goods manufactured need to be sold in the market to maintain the demand and supply. 

i. The first fertilizer plant in India was setup at Ranipat in Tamil Nadu in 1906. The real growth of the industry began with the establishment of a plant at sindri by the Fertilizer d Corporation of India in 1951. 

ii. The increased demand of fertilizer as a result of Green REvoluiton led to the spread of this industry in several parts of india.  

Distribution:

i. Gujarat, Tamil Nadu, Uttar Pradesh, Punjab and Kerala produce more than half of the total fertilizer production in India. 

ii. Andra Pradesh and Karnataka are other important producers. 

iii. Because of the easy availability of natural gas the fertilizer industry is widely spread in the country. 

Production: 

India produces about 1 million tones of nitrogenous, 4 million tones of phosphatic and 1.7 million tones of potassic fertilizers. The country is required to import potassium from abroad. 

anhydrous AlCl₃.

Correct answer is  (d) S_N²

(a) Polyphenol oxidase

(b) The staggered conformation of ethane is more stable than eclipsed conformation, because staggered conformation has no torsional strain.

A) Can / play 

Correct answer is Kabaddi

Correct option is D) cards

• Some of the earliest bhakti movements were led by the

1. Alvars (literally, those who are -immersed in devotion to Vishnu)  
2. Nayanars (literally, leaders who were devotees of Shiva).

• They travelled from place to place singing hymns in Tamil in praise of their gods. Hence statement 1 is Correct.
• During their travels, the Alvars and Nayanars identified certain shrines as abodes of their chosen deities. Very often large temples were later built at these sacred places.
• Both sects did not believe in Caste-based discrimination and people from various backgrounds joined the sect. Hence statement 2 is Correct.
• These developed as centres of pilgrimage. Singing compositions of these poet-saints became part of temple rituals in these shrines, as did worship of the saints‘ images. 
• The most striking features of these traditions were the presence of women like Andal was a women Alvar and Karaikkkal Ammaiyar( Nayanar), a devotee of Shiva, adopted the path of extreme asceticism in order to attain her goal.
• These women renounced their social obligations but did not join an alternative order or become nuns. Hence, statement 3 is Incorrect.

The correct answer is Rajgarh.

• The Narsinghgarh fort is known as the "Kashmir-e-Malwa" region. It is located in the Rajgarh district of Madhya Pradesh state.
• This fort is built by Dewan Parasram in 1681, this town named Bhagwan Shri Narsingh (incarnation of god Vishnu).
• The State of Narsinghgarh was carved out by Paras Ramji, after his death the younger brother of him, Rawat Mohan Singhji ruled Rajgarh in 1681 A.D.

The correct answer is Panna.

• The Ajaygarh Fort was built by King Ajaypal. It is located in the Panna district of Madhya Pradesh.
• The state was founded in 1785  and Ajaigarh was one of the princely states of India during the British Raj period.
• The fort is bordered by beautiful Vindhya Hills and provides architectural beauty and historical past, which speaks about the Chandela dynasty, From the top of the fort you can feel the beauty of the Ken river.
• Panna is one of the major cities of Madhya Pradesh state. It is famous for diamond mines in India.
• It is famous for the tiger reserve namely Panna national park. This district was the famous capital of Chhatra Sal (The Bundela Rajput who fought against the Mughal Empire).

• Elephanta Caves are a network of sculpted caves located on Elephanta Island, or Gharapuri (literally "the city of caves") in Mumbai Harbour, 10 kilometres to the east of the city of Mumbai in the Indian state of Maharashtra.
• The island, located on an arm of the Arabian Sea, consists of two groups of caves - the first is a large group of five Hindu caves, the second, a smaller group of two Buddhist caves.
• The Elephanta site was first occupied by Hinayana Buddhists, before the arrival of the Brahmans to the island, to raise a large stupa to the Buddha with seven smaller stupas around it, probably around the 2nd century BCE.
• The Hindu caves contain rock cut stone sculptures, representing the Shaiva Hindu sect, dedicated to Lord Shiva. It was designated a UNESCO World Heritage Site in 1987 to preserve the artwork and is currently maintained by the Archaeological Survey of India (ASI).
• Hence, the correct answer is Saiva Images.

Ellora caves-

• The Ellora caves, locally known as 'Verul Leni' is located on the Aurangabad - Chalisgaon road at a distance of 30 km north - northwest of Aurangabad, in the Indian state of Maharashtra.
• Ellora is one of the largest rock-cut monastery - temple caves complexes in the world, and a UNESCO World Heritage Site.
• The cave temples and monasteries at Ellora, excavated out of the vertical face of an escarpment, are 26 km north of Aurangabad.
• Sculptors, inspired by Buddhism, Jainism and Hinduism, created elaborate rock carvings. Extending in a linear arrangement, the 34 caves contain Buddhist Chaityas or halls of worship, Viharas or monasteries and Hindu and Jain temples.
• Spanning a period of about 600 years between the 5th and 11th century A.D., the earliest excavation here is of the Dhumar Lena (Cave 29).
• The Kailasha temple features the largest single monolithic rock excavation in the world.
• During the regime of the Rashtrakuta were the famous Ellora caves of Maharashtra built.

Ajanta Caves-

• The Ajanta Caves are a series of 29 Buddhist cave temples in Ajanta, India, some of which date from the 2nd century BC. Encompassing both Theravada and Mahayana Buddhist traditions, the Ajanta caves preserve some of the best masterpieces of Buddhist art in India.
• Out of 29, 25 caves were used as Viharas or residential caves while 4 were used as Chaitya or prayer hills.
• It is said that Buddhist monks lived, studied and prayed in Ajanta caves for a long time.
• The Ajanta Caves were carved in the 2nd century BC out of a horseshoe-shaped cliff along the Waghora River.
• The caves were designated a UNESCO World Heritage site in 1983.

The correct answer is Shiva.

• Elephanta Caves are a UNESCO World Heritage Site and a collection of cave temples predominantly dedicated to the Hindu god Shiva.
• The 'City of Caves', on an island in the Sea of Oman close to Bombay, contains a collection of rock art linked to the cult of Shiva.
• The Elephanta Caves are located in Western India on Elephanta Island (otherwise known as the Island of Gharapuri), which features two hillocks separated by a narrow valley.
• The Elephanta Caves are considered to be a contribution by the Kalachuris and the latest rules to contribute were the Rashtrakutas.

The correct answer is " Tropical Deciduous Forests".

• Tropical Deciduous Forest is also referred to as " Monsoon Forest".
• Tropical Deciduous forests are found in the belt along the equator between the tropics of Cancer and Capricorn as well as in the humid subtropics
• Tropical Deciduous Forests are home to trees with broad leaves which shed in one season of the year. 
• The range of the rainfall in this forest is 70 - 200cms.
• There are two types of deciduous forest namely -

1. Moist Deciduous Forest
2. Dry Deciduous Forest.

• Some of the major states in which these types of forests are found are -

1. Madhya Pradesh
2. Uttar Pradesh
3. Chattisgarh
4. Odisha
5. Some parts of Maharashtra

The correct answer is Amazon.

• Jeff Bezos is the Founder and CEO of Amazon.com.
• On 22nd July he was named as the third richest man in the world.
• According to Bloomberg, Bezos's total net worth hit $65.05 billion pushing him past Berkshire Hathaway's founder Warren Buffett by $32 million.
• Bezos's rise is largely due to his stock ownership in Amazon.

• Vijay Shekhar Sharma is an entrepreneur and founder of Paytm.
• Kalyan Krishnamurthy is the CEO of Flipkart.
• Kunal Bahl is the founder of Snapdeal.
• Ananth Narayanan is the founder of Myntra.

The correct answer is The Equator.

• A Great Circle is any circle that circumnavigates the Earth and passes through the center of the Earth.
• A great circle always divides the Earth in half, thus the Equator is a great circle (but no other latitudes) and all lines of longitude are great circles. 
• The Equator:
  • It is an imaginary line on the surface of the Earth at the same distance from the North Pole and the South Pole.
  • It divides the Earth into the Northern and Southern Hemispheres.
  • On the northern side of this line are the Tropic of Cancer at 23½ ° and the Tropic of Capricorn at 23½ ° on the southern side.
  • The equator passes through the land or waters of 14 countries.​

​

• The Tropic of Capricorn:
  • It is an imaginary line drawn from the west to the east, at 23° 23 '22" parallel to the equator in the southern hemisphere.
  • The area to the north of the Tropic of Capricorn and south of the Tropic of Cancer is called the "tropical region".​
• The Tropic of Cancer:
  • It is a latitude line drawn from west to east at 23.5 degrees in the Northern Hemisphere, parallel to the equator on the globe.
  • It is the northernmost latitude line of the Earth, on which the sun shines vertically in the afternoon.
• The Arctic Circle:
  • The position of the Arctic Circle is 66° 33′46.6 ″ north of the equator.
  • Its latitude depends on the axial tilt of the Earth

1.  A × (B ∩ C) ={1, 2} × Φ = Φ

A × B = {(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (2, 4)}

A × C = {(1, 5), (1, 6), (2, 5), (2, 6)}

(A × B) ∩ (A × C) = Φ

Hence; A × (B ∩ C) = (A × B) ∩ (A × C)

2. A × C = {(1, 5), (1, 6), (2, 5), (2, 6)}

B × D = {1, 2, 3, 4} × {5, 6, 7, 8}

= {(1, 5), (1, 6), (1, 7), (1, 8), (2, 5), (2, 6), (2, 7), (2, 8), (3, 5), (3,6), (3, 7), (3, 8), (4, 5), (4, 6), (4, 7), (4, 8)}

Hence A × C is a subset of B × D.

1. Given; f(x) = \(\frac{x^2 + 2x + 1}{x^2 - 8x + 12}\)

The function is not defined at points where the denominator becomes zero.

x² – 8x +12 = 0 ⇒ (x – 6)(x – 2) = 0 ⇒ x = 2, 6

Therefore domain of fis R – {2, 6}.

2. Given; f(x) = \(\frac{x^2 + 3x + 5}{x^2 -5x + 4}\)

The function is not defined at points where the denominator becomes zero.

x² – 5x + 4 = 0 ⇒ (x – 4)(x -1) = 0 ⇒ x = 1, 4

Therefore domain of f is R – {1, 4}.

R – {(9, -3), (9, 3), (4, -2), (4, 2), (25, -5), (25, 5)}

R = {{x, y) : y² = x}

Domain of R = {9, 4, 25}

Range of R = {5, 3, 2, -2, -3, -5

(i) x, 10, y, 24, 2 are in A. P.

Let d be common difference

\(\therefore\) x + d = 10-----(i)

x + 2d = y----(ii)

x + 3d = 24----(iii)

x + 4d = z---(iv)

Now, substract equation (i) from (iii), we get

(x + 3d) - (x + d) = 24 - 10

⇒ 2d = 14 ⇒ d = \(\frac{14}2\) = 7

\(\therefore\) x + 7 = 10 ⇒ x = 10 - 7 = 3 From(i)

\(\therefore\) y = x + 2d = 3 + 2 x 7 = 3 + 14 = 17 From(ii)

\(\therefore\)  z = x + 4d = 3 + 4 x 7 = 3 + 28 = 31 From (iv)

(ii) Given A.P. is 3, 6, 9, 12,.....111.

First term a = 3

\(\therefore\) common difference is d = a₂ - a₁ = 6 - 3 = 3

Let A.P. has n terms.

\(\therefore\) a_n = 111

⇒ a + (n - 1)d = 111 (\(\because\) a_n = a + (n - 1)d)

⇒ 3 + (n - 1)3 = 111

⇒ 3(n - 1) = 111 - 3 = 108

⇒ n - 1 = 108/3 = 36

⇒ n = 36 + 1 = 37

Hence, number of terms in A.P. is 37.

Correct option is E) valuable

Correct option is D) test

Correct option is A) speaking

Correct option is D) qualifications

Correct option is D) personal qualities