SSC CHSL Tier-1 2022: Official Paper (Held On: 14 March, 2023 Shift 2) (Previous Year Paper)

The triangles are:

So, there are '29' triangles in the given figure.

Hence, the correct answer is "29".

The image embedded in given figure is as shown below:

 

Hence, "Option 1" is the correct answer.

The logic followed here is:

→ Second Number = (First Number × 6) + 1

Let's check as per the logic used,

14 ∶ 85

→ 85 = (14 × 6) + 1

→ 85 = 84 + 1

→ 85 = 85.

20 ∶ 121

→ 121 = (20 × 6) + 1

→ 121 = 120 + 1

→ 121 = 121.

Similarly,

11 ∶?

→ ? = (11 × 6) + 1

→ ? = 66 + 1

→ ? = 67

Hence, the correct answer is " 67 ".

The logic followed here is:

→ Each letter in the second set is obtained by moving one position forward in the English alphabet from its corresponding letter in the first set.

Let's check as per the logic:

LREA ∶ MSFB

Similarly,

BSFX ∶ ?

Hence, the correct answer is " CTGY ".

The logic followed here is:

Logic: (First Number ÷ 2) × (Second Number ÷ 2) = Third Number.

Let's check as per the logic,

(48, 16, 192):

→ (48 ÷ 2) × (16 ÷ 2) = 192

→ 24 × 8 = 192

→ 192 = 192 → LHS = RHS.

(22, 62, 341):

→ (22 ÷ 2) × (62 ÷ 2) = 341

→ 11 × 31 = 341 → LHS = RHS.

Let's check each option as per the logic,

1) (32, 24, 222):

→ (32 ÷ 2) × (24 ÷ 2) = 222

→ 16 × 12 = 222

→ 192 ≠ 222 → LHS ≠ RHS.

2) (74, 38, 713):

→ (74 ÷ 2) × (38 ÷ 2) = 713

→ 37 × 19 = 713

→ 703 ≠ 713 → LHS ≠ RHS.

3) (84, 78, 1638):

→ (84 ÷ 2) × (78 ÷ 2) = 1638

→ 42 × 39 = 1638

→ 1638 = 1638→ LHS = RHS.

4) (92, 46, 1068):

→ (92 ÷ 2) × (46 ÷ 2) = 1068

→ 46 × 23 = 1068

→ 1058 ≠ 1068 → LHS ≠ RHS.

Here, we can see that only Option 3 follow the logic.

Hence, the correct answer is "(84, 78, 1638)".

The paper after unfolded will be:

Hence, the correct answer is "Option 4".

The logic followed here is:

Logic: Digit sum of the Sum of the place value of the given word.

Now,

‘ROUTE’ is coded as ‘7’

⇒ R(18) + O(15) + U(21) + T(20) + E(5)

⇒ 79 → 7 + 9 = 16

⇒ 16 → 1 + 6 = 7.

For, ‘SHARE’ is coded as ‘6’

⇒ S(19) + H(8) + A(1) + R(18) + E(5)

⇒ 51 → 5 + 1 = 6.

Similarly, for ‘TABLE’

⇒ T(20) + A(1) + B(2) + L(12) + E(5)

⇒ 40 → 4 + 0 = 4.

So, 'TABLE' will be coded as '4'.

Hence, the correct answer is "4".

The logic followed here is:

Given Sequence: A A_AB_ABC_A_C_E

Now, putting the letters in the blank spaces given in the option one by one:

Option 1) pslilsprr → p I f i r s / p l f i r s / p l f i r s / p I f i r r

Option 2) pslilspsr → p I f i r s / p l f i r s / p l f i r s / p I f i s r

Option 3) prlilsprs → p I f i r r / p l f i r s / p l f i r s / p I f i r s

Option 4) pslilsprs → p I f i r s / p l f i r s / p l f i r s / p I f i r s

Here, 'Option 4' followed a pattern.

Hence, the correct answer is "Option 4".

The logic followed here is:

→ The first word is used to manufacture the Second word.

Let's check using the logic,

 

⇒ In the pair "Sugarcane - Jaggery," jaggery is a product or derivative of sugarcane.

It is not directly related to the other word pairs where the second word is a material or substance used in the construction or manufacturing process.

Hence, the correct answer is " Sugarcane - Jaggery ".

The logic followed here is:

Logic: (2^nd number + 3^rd number) ÷ 2 - 101 = 1^st number.

Now,

For (812, 879, 947)

→ (879 + 947) ÷ 2 - 101

→ 1826 ÷ 2 - 101 

→ 913 - 101 = 812.

For (648, 715, 783)

→ (715 + 783) ÷ 2 - 101

→ 1498 ÷ 2 - 101 

→ 749 - 101 = 648.

Similarly, for (612, 679, 747)

→ (679 + 747) ÷ 2 - 101

→ 1426 ÷ 2 - 101 

→ 713 - 101 = 612.

Hence, the correct answer is "Option 3".

Alternate MethodLogic: 1^st number + 67 = 2^nd number;

2^nd number + 68 = 3^rd number.

For (812, 879, 947)

→ 812 + 67 = 879

→ 879 + 68 = 947.

For (648, 715, 783)

→ 648 + 67 = 715

→ 715 + 68 = 783.

Similarly, for (612, 679, 747)

→ 612 + 67 = 679

→ 679 + 68 = 747.

Hence, the correct answer is "Option 3".

The logic followed here is:

⇒ The relationship between the words is that they are antonyms, representing opposite conditions or states.

Dry ∶ Wet

→ Wet is the antonym of Dry.

Let's check each option as per the logic:

1) Tall ∶ Large:

→ These words do not represent opposite conditions or states. They are not antonyms.

2) Healthy ∶ Sick:

→ These words represent opposite conditions, similar to "Dry ∶ Wet." They are antonyms.

3) Good ∶ Best:

→ These words represent different degrees or levels of quality, not opposite conditions. They are not antonyms.

4) Short ∶ Tiny:

→ These words represent different sizes but not opposite conditions. They are not antonyms.

⇒ Based on the logic that the word pairs represent antonyms, the pair that follows the same logic is option 2.

Hence, the correct answer is " Healthy ∶ Sick ".

Family Chart:

Given: 

E is the brother of F.

D is the wife of E.

G is the father of H.

F is the sister of G.

So, E is Brother of G.

Hence, the correct answer is "Option 1".

The logic followed here is:

⇒ © denotes addition.

⇒ (Sum of the numbers) × 3 = Final result.

Let's check as per the logic,

13 © 62 = 225

→ (13 + 62) × 3 = 225

→ (75) × 3 = 225

→ 225 = 225.

4 © 38 = 126

→ (4 + 38) × 3 = 126

→ (42) × 3 = 126

→ 126 = 126.

Similarly,

29 © 17 =?

→ (29 + 17) × 3

→ (46) × 3 = 138.

Hence, the correct answer is " 138 ".

The correct logical order is:

5. World

6. Asia

7. India

8. Uttar Pradesh

9. Taj Mahal

⇒ The world consists of various countries and continents, including Asia.

 India is a country located in Asia.

Uttar Pradesh is a state in India.

The Taj Mahal is a famous monument located in Uttar Pradesh.

Hence, the correct answer is " 5, 2, 1, 3, 4 ".

The image embedded in given figure is as shown below:

Hence, "Option 2" is the correct answer.

The logic followed here is:

→ 4 has been added in each letter's positional value to get the next term.

Let's check as per the logic,

1) SWA:

2) UYC:

3) VZC:

4) CGK:

Here, the correct answer is " VZC ".

Given Statements:

I. All G are N.

II. No A is N.

The least possible Venn diagram for the given statement is:

Conclusions:

I. Some G are A - False (Because, all G are N, and no N is A, it implies that no G is A).

II. Some N are G - True (All G are N implies that Some N are G).

III. All A are G - False (Because, all G are N, and no N is A, it implies that no G is A).

So, Only conclusion II follows.

Hence, the correct answer is "Option 4".

The logic followed here is:

Logic: The first word is a place, and the second word is a professional who works in that place.

Here,

School : Teacher → A teacher works in a school.

Similarly,

Laboratory : ? → A scientist works in a laboratory.

Hence, the correct answer is "Scientist".

The Venn diagram which correctly represents the relationship between Indians, Brain Specialist and Surgeon is shown below:

Hence, the correct answer is " Option 3 ".

The image embedded in given figure is as shown below:

 

Hence, "Option 4" is the correct answer.

The logic followed here is:

So, '325' will complete the series.

Hence, the correct answer is "325".

Equation I: 24 ÷ 8 × 2 + 7 - 6

After interchanging × and -, we get the equations:

→ 24 ÷ 8 - 2 + 7 × 6

→ 3 - 2 + 7 × 6 =?

→ 3 - 2 + 42 =?

→ 45 - 2 = 43.

Equation II. 8 × 6 - 9 ÷ 3 + 10

After interchanging × and -, we get the equations:

→ 8 - 6 × 9 ÷ 3 + 10

→ 8 - 6 × 3 + 10 =?

→ 8 - 18 + 10 =?

→ 18 - 18 = 0.

Hence, the correct answer is " 43 and 0 ".

The logic followed here is:

⇒ First Number × (First Number)² + 2 = Second Number.

Let's check as per the logic,

1) 14 - 2762

→ 14 × (14)² + 2 = 2762

→ 14 × 196 + 2 = 2762

→ 2744 + 2 = 2762

→ 2746 ≠ 2762

→ LHS ≠ RHS.

2) 16 - 4098

→ 16 × (16)2 + 2 = 4098

→ 16 × 256 + 2 = 4098

→ 4096 + 2 = 4098

→ 4098 = 4098

→ LHS = RHS.

3) 11 - 1333

→ 11 × (11)2 + 2 = 1333

→ 11 × 121 + 2 = 1333

→ 1331 + 2 = 1333 

→ 1333 = 1333

→ LHS = RHS.

4) 13 - 2199

→ 13 × (13)2 + 2 = 2199

→ 13 × 169 + 2 = 2199

→ 2197 + 2 = 2199

→ 2199 = 2199

→ LHS = RHS.

Here, we can see that only Option 1 doesn't follow the logic.

Hence, the correct answer is " 14 - 2762 ".

The logic followed here is:

Step I: The arrow and rhombus are getting exchanged and flipped in all alternate images.

Step II: The arrow and rhombus are getting exchanged with it's place in all alternate images.

Hence, the correct answer is "Option 2".

The logic followed here is:

'GRMTS' is coded as 'OPINC',

Similarly, for 'BATCH'

So, 'BATCH' is coded as 'DYPWX'.

Hence, the correct answer is "Option 2".

The correct answer is Ctrl + Y.

Key Points

• Ctrl + Y is used to redo the last action in MS- Excel.​

Additional Information

The correct answer is Parwez Shah.

Key Points

• Pathar Ki Masjid, also known as Saif Khan's Mosque, Chimni Ghat mosque, and Sangi Masjid, is a mosque in Patna, Bihar, India.
• It was built in 1621 by Parvez Shah, the son of Mughal emperor Jahangir.
• The mosque is built of stone, hence the name "Pathar ki Masjid".
• It is located on Ashok Rajpath between Sultanganj and Alamganj.
• The mosque is a single-domed structure with four minarets.
• The central dome is supported by four arches.
• The mosque is a fine example of Mughal architecture.
• Pathar Ki Masjid is a beautiful and historic mosque that is an important part of the cultural heritage of Patna.
• It is a popular tourist destination and a place of worship for the Muslim community.

The correct answer is Inelastic.

Key Points

• Demand - 
• ​Demand means quantity demanded by customers at different prices during a given time period.
• Inelastic Demand:
• When due to change in price (whether increase or decrease), quantity demanded remains same, it is known as inelastic Demand.
• In case of inelastic Demand, when the price is increased, it will cause the total expenditure of the consumer to increase because total expenditure = quantity demanded × price.
• The demand will not change but the change in price cause consumer's total expenditure to increase.​

Additional Information

• Perfectly inelastic
• A perfectly inelastic demand has an elasticity of 0.
• A perfectly inelastic demand is one when there is no change in the demand for a product with a change in its price.
• For a perfectly inelastic demand, the demand curve is represented as a straight vertical line.
• Perfectly elastic
• When a small change in the price of a product causes a major change in its demand, it is said to be perfectly elastic demand.
• In perfectly elastic demand, a small rise in price results in a fall in demand to zero, while a small fall in price causes an increase in demand to infinity.
• In such a case, the demand is perfectly elastic or e = ∞.
• Unitary elastic
• The demand curve for unitary elastic demand is a rectangular hyperbola.
• When the proportionate change in demand produces the same change in the price of the product the demand is referred to as unitary elastic demand.
• The elasticity of a unitary elastic demand is 1.

The correct answer is Keyboard.

Key Points

• An input device is a peripheral (piece of computer hardware equipment) used to provide data and control signals to an information processing system such as a computer or other information appliance.
• The Central Processing Unit (CPU) of a computer receives the input and processes it to produce the output.
• Examples of input devices include
• Keyboards, mouse, scanners, digital cameras, joysticks, Microphone, TouchPad, Webcam, remote, biometric devices, etc.
• Keyboard is a basic input device that is used to enter data into a computer or any other electronic device by pressing keys.
• Mouse is a hand-held input device that is used to move cursor or pointer across the screen.
• Scanner uses the pictures and pages of text as input.

Te correct answer is Both I and II.

Key Points The Industrial Policy Resolution (IPR) 1956

• Adopted to achieve the aim of a socialist state with the government controlling the major strategic industries of the economy.
• According to this resolution, industries were classified into the following three categories:
• Category 1: Those industries that were established and owned exclusively by the public sector.
• Category 2: Those industries in which the public sector would perform the primary role while the private sector would play the secondary role i.e., the private sector supplements the public sector In these industries and new units could be set up only by the public sector.
• Category 3: Those industries that are not included in Category 1 and Category 2 were left to the private sector.
• The government kept indirect control of the industries in the private sector through the policy of industrial licensing.​

Additional Information

• Highlights of IPR 1956:
• In order to initiate a new industry or expand existing capacity, private entrepreneurs were supposed to obtain licenses from the government.
• Licensing, imposition of the tax, tax exemptions, and subsidies were used by the government:
• to regulate private industries.
• bring about a reduction in regional disparities in industrial development.
• to keep a check on the production of goods that are socially undesirable.
• Hence, the government fully controlled the private sector either directly or Indirectly through the IPR 1956.

Correct Answer Retreating Monsoon

**Key Points:**Retreating monsoons:

• During October-November, with the apparent movement of the sun towards the south, the monsoon trough or the low-pressure trough over the northern plains becomes weaker.
• This is gradually replaced by a high-pressure system.
• The south-west monsoon winds weaken and start withdrawing gradually.
• By the beginning of October, the monsoon withdraws from the Northern Plains.
• The months of October-November form a period of transition from hot rainy season to dry winter conditions.
• The retreat of the monsoon is marked by clear skies and a rise in temperature.
• While day temperatures are high, nights are cool and pleasant.

Thus, October-November months are associated with retreating monsoons/the transition season.

Additional InformationSouthwest monsoon season:

• The period June to September is referred to as the 'Southwest Monsoon' period.
• The Southwest Monsoon period is the principal rainy season for the Indian subcontinent.
• This is the summer monsoon period where the southwest monsoon holds away over the country.
• The whole country receives nearly 75% of its rainfall during this period.

Monsoon: 

• Monsoon, a major wind system that seasonally reverses its direction, such as one that blows for approximately six months from the northeast and six months from the southwest.
• The primary cause of monsoons lies in different warming trends over land and sea, though other factors may be involved.
• There are two monsoons (or rainy seasons) in India.
• The summer monsoon season in India, otherwise known as the southwest monsoon, lasts from June to September and affects the whole of India.
• Then the northeast or winter monsoon brings seasonal rainfall to Southeast India from October to December.

Correct Answer Andimuthu Raja

Key Points

• The 2G Saga refers to a major corruption scandal that unfolded in India in 2008, involving the allocation of 2G (second-generation) telecom spectrum licenses.
• It was one of the biggest corruption scandals in Indian history and had far-reaching consequences.
• Andimuthu Raja is an Indian politician who was a central figure in the 2G spectrum allocation scandal.
• He was the Minister of Communications and Information Technology in the Government of India from 2007 to 2010.
• Raja, a member of the Dravida Munnetra Kazhagam (DMK) political party, played a key role in the allocation of 2G spectrum licenses at significantly undervalued prices, leading to allegations of corruption and irregularities.

The correct answer is an aquifer

Key Points:

• An aquifer is an underground layer of porous rocks or permeable rocks that store and retain groundwater levels in the soil.
• The underground aquifer is built with all types of porous or permeable rock materials, such as sand, gravel, or silt, making it a suitable water absorber.
• The rainwater enters the aquifer through the soil and becomes a part of the groundwater.
• The groundwater from the aquifers then resurfaces from springs and wells.
• We can also extract the aquifer water with the help of a water well.
• The study of groundwater, aquifer, and their property is known as hydrogeology.

**Additional Information:**Pond:

• A pond is an area filled with water, either natural or artificial, that's lower than a lake.
• Defining them to be lower than 5 hectares (12 acres) in area, lower than 5 measures (16 ft) deep, and with lower than 30 emergent foliage helps in distinguishing their ecology from that of lakes and washes.

Lake:

• A lake is an area filled with water, localized in a basin, surrounded by land, and distinct from any river or other outlet that serves to feed or drain the lake.

Well:

• A well is an excavation or structure created in the ground by digging, driving, or drilling to access liquid resources, usually water.

The correct answer is Buccal cavity

**Key Points:**The human digestive system consists of two parts, the alimentary canal, and the associated glands.

• The mouth leads the food to be digested to the buccal cavity.
• The buccal cavity has a number of teeth and a muscular tongue.
• The uppermost part of the buccal cavity is called the palate.
• The digestion of carbohydrates begins in the buccal cavity.
• From the mouth, food reaches into the stomach through a food pipe called the esophagus.
• There is no digestion inside the food pipe.
• The digestion of fat begins in the stomach.
• Lipase is the digestive enzyme of fat.
• The digestion of protein occurs in the stomach and duodenum.
• Pepsin is the digestive enzyme of protein.

Additional Information Digestive system:

• It consists of the long alimentary canal and associated glands.
• The alimentary canal includes
• Mouth (buccal cavity)
• Oesophagus (food pipe)
• Stomach
• Small intestine
• Large intestine

The glands associated with the digestive system are as follows: 

• Liver
• Pancreas
• Intestinal glands

The correct answer is Indravati

Key Points:

• The Godavari river is the largest river system in Peninsular India.
• The Godavari basin extends over the States of Maharashtra, Andhra Pradesh, Chhattisgarh, and Odisha in addition to smaller parts in Madhya Pradesh, Karnataka, and Puducherry (Yanam).
• The other names for the Godavari River are The Vriddh (Old) Ganga or the Dakshin (South) Ganga.
• Godavari river drains into the Bay of Bengal.
• Godavari river originates from Bramhagiri mountains at Trimbakeshwar.
• Tributaries: Pravara, Purna, Manjira, Penganga, Wardha, Wainganga, Pranhita (combined flow of Wainganga, Penganga, Wardha), Indravati, Maner, and the Sabri.
• The longest tributary- The Manjira
• The largest tributary- The Pranhita

Additional Information Chambal:

• The Chambal river originates in Manpura near Indore in Madhya Pradesh.
• The length of the river is 900 km and it is a tributary of the Yamuna river.
• The Chambal River remains one of North India’s unpolluted rivers, home to a rich diversity of flora and fauna.
• The National Chambal Gharial Wildlife Sanctuary is famous for the rare Ganges river dolphin.
• Apart from the Ganges river dolphin, the other inhabitants of the sanctuary include magar (crocodile) and gharial (alligator). Migratory birds from Siberia form part of its rich avian fauna.

Banas:

• Banas river originates from Khamnor Hills of the Aravalli Range, near Kumbhalgarh in Rajsamand, Rajasthan.  '
• Banas river is a tributary of the Chambal River and ii is approximately 512 kilometers in length.
• This river is also called ‘Van Ki Asha‘.
• There is another river in Rajasthan with name of Banas.
• The Banas river entirely flows within the Rajasthan in:-
• Ajmer, Bhilwara, Bundi, Chittorgarh, Dausa, Jaipur, Pali, Rajsamand, Sawai Madhopur, Sirohi, Tonk, and Udaipur districts of Rajasthan.
• It flows northeast through the Mewar region of Rajasthan and meets the Chambal near the village of Rameshwar in Sawai Madhopur district.

Tawa:

• Tawa River is the tributary of the Narmada River.
• It is the longest tributary of the Narmada River.
• Its origin is in the Satpura range.
• It meets the Narmada at Hoshangabad district.
• Its length is 172 km.

Correct Answer Andaman and Nicobar Islands

The elongated chain of islands located in the Bay of Bengal extending from north to south is called Andaman and Nicobar islands. 

**Key Points:**Andaman and Nicobar islands:

• Andaman and Nicobar Islands situated in the Bay of Bengal, run like a narrow chain in the north-south direction extending between 6° 45′ N to 13° 45′ N.
• This archipelago is composed of around 265 big and small islands (203 Andaman islands + 62 Nicobar Islands)
• The Andaman and Nicobar Islands extend from 6° 45′ N to 13° 45′ N and from 92° 10′ E to 94° 15′ E for a distance of about 590 km.
• The total area of this elongated island is 8,249 sq. km.
• The Andaman islands are divided into three main islands i.e. North, Middle, and South.
• Duncan's passage separates Little Andaman from South Andaman.
• The Great Andaman group of islands in the north is separated by the Ten Degree Channel from the Nicobar group in the south.
• The Grand Channel is between the Great Nicobar islands and the Sumatra islands of Indonesia.
• The Coco Strait is between the North Andaman islands and the Coco Islands of Myanmar.
• Port Blair, the capital of Andaman Nicobar Islands lies in the South Andaman.
• Among the Nicobar islands, the Great Nicobar is the largest.
• It is the southernmost island and is very close to Sumatra island of Indonesia.
• The Car Nicobar is the northernmost.
• Most of these islands are made of tertiary sandstone, limestone, and shale resting on basic and ultrabasic volcanoes.
• The Barren and Narcodam Islands, north of Port Blair, are volcanic islands

Additional Information Puducherry:

• There are total 4 Districts in Puducherry.
• The city is surrounded by Tamil Nadu state, on the Coromandel Coast of the Bay of Bengal, 105 miles (170 km) south of Chennai (Madras).
• The Union Territory of Puducherry has been formed consolidating four erstwhile French establishments viz Puducherry, Karaikal, Mahe and Yanam.
• Karaikal District is in the state of Tamil Nadu and is next to Puducherry in area and population.
• Mahe is surrounded by the State of Kerala and Yanam by the state of Andra Pradesh.
• Yanam is one of the regions in the Union Territory of Puducherry which is 870 km away from it.
• The town of Yanam lies on the mouth of the Godavari River where it flows into the Bay of Bengal.

'Daman' is the capital of the Union Territory of Daman and Dadra and Nagar Haveli.

Dadra and Nagar Haveli and Daman and Diu are part of the union territory.

The correct answer is 'Baba Dayal Das'.

Key Points:

• Nirankari is a religious reform movement within Sikhism.
• The Nirankari movement was founded by Baba Dayal Das in 1851.
• He believed that God is formless, or nirankar (hence the name Nirankari).
• The movement expanded in northwest Punjab.

Additional Information Baba Ram Singh:

• Baba Ram Singh was born in the year 1815.
• He was a son of a poor carpenter, in a small village of Bhaini.
• Which was around 7 kilometers away from Ludhiana.
• In the early 1840s, he served as a soldier in the Sikh Army of Prince Naunihal Singh.
• He left the army after the overthrow of the Sikh rule.
• In the year 1838, he came in contact with Baba Balak Singh, and he also remained in touch with Bhagat Jawar mal as well.

 Guru Gobind Singh

Birth:

• He was born on December 22 in Patna in the year 1666.
• His birth anniversary is observed as Guru Gobind Singh Jayanti every year in accordance with the lunar calendar.
• He was a poet, spiritual leader, philosopher, warrior and writer.
• 10^th Guru:
• He was the tenth Guru of the Sikhs.

Khalsa Panth:

• He was the founder of the Khalsa Panth. 
• He also founded the Sikh warrior community called Khalsa in 1699.
• He became a Sikh guru at the age of nine, after the death of his father Guru Tegh Bahadur.
• His father was executed by Aurangzeb.

Five K's

• He introduced the five K's for the Sikhs including:
• Kesh: uncut hair
• Kangha: a wooden comb
• Kara: an iron or steel bracelet worn on the wrist
• Kirpan: a sword
• Kacchera: short breeches.

The correct answer is Neither I nor II.

Key Points

• Both pairs are correctly associated. Batting is a term used in cricket, and a goal is a term used in netball.
• Here are tables of important terms related to cricket and netball:

Additional Information

• Terms related to cricket.

• Terms related to Netball.

The correct answer is Taxes on lands and buildings

Key PointsUnion List Subjects:

• It originally had 97 subjects but now it has 100 subjects.
• ​Defence
• Army
• International Relations
• Ports
• Railways
• Highways
• Communication
• Economy

State List Subjects:

• It originally had 66 subjects but now it has 61 subjects
• Public order
• Police
• Public health and sanitation
• Hospitals and dispensaries
• Betting and gambling
• Taxes on Buildings and Lands.

Concurrent List Subjects:

It has 52 subjects.

• Education
• Forest
• Trade unions
• Marriage
• Adoption
• Succession
• Industrial and labour disputes
• ​Economic and social planning

The correct answer is Hyderabad.

Key Points:

• India will host the second United Nations World Geospatial Information Congress (UNWGIC) in October 2022, at Hyderabad.
• The theme would be ”Towards Geo-enabling the Global Village.”
• Every four years, the United Nations Committee of Experts on Global Geospatial Information Management (UN-GGIM) hosts UNWGIC.
• China in 2018 hosted the UNWGIC for the first time in October.
• UNWGIC is organized with the objective of enhancing international collaboration among the Member States and relevant stakeholders in Geospatial information management and capacities.
• Prime Minister Narendra Modi inaugurated the function.

The correct answer is Central Vigilance Commission.

Key Points

• Vigilance Commissioner Suresh N. Patel was sworn in as the Central Vigilance Commissioner (CVC) by President Droupadi Murmu on 3 August 2022.
• Mr Patel also administered the oath of office to former Intelligence Bureau (IB) chief Arvind Kumar and ex-IAS officer Praveen Kumar Srivastava as the vigilance commissioners.

Additional Information 

• The Indian government's highest authority, the Central Vigilance Commission (CVC), combats official corruption.
• The Commission consists of:
• A Central Vigilance Commissioner – Chairperson;
• Not more than two Vigilance Commissioners – Members.

Important Points 

• Vigilance Commissioner Praveen Kumar Srivastava has been appointed as the acting Central Vigilance Commissioner (CVC) on 28 Dec 2022.

The correct answer is access to its Wi-Fi at 100 railway stations.

Key Points

• RailTel, a Mini Ratna PSU, has launched Prime Minister Wi-Fi Access Network Interface (PM-WANI) scheme based on access to its Public Wi-Fi services across 100 railway stations across the country.
• This public-friendly service was virtually launched by RailTel chairman and managing director Puneet Chawla.
• To access this Wi-Fi network, android users can download the mobile app ‘Wi-DOT’ available on Google Play Store.
• This app has been developed in close coordination with C-DOT.
• This method of accessing Wi-Fi through the ‘mobile app’ will be in addition to the existing method of accessing Wi-Fi at these stations through the conventional method of selecting Rail Wire Service Set Identifier (SSID).
• PM-WANI is an ambitious program of the Department of Telecom (DoT) to connect all silo Wi-Fi networks for ease of use and to proliferate broadband usage for the masses.
• The government had further plans to extend the PM-WANI-based access of Rail-Tel’s public Wi-Fi services to all 6,102 railway stations in a phased manner.

Additional Information

• Indian railway:
• The first railway on the Indian sub-continent ran over a stretch of 21 miles from Bombay to Thane.
• The governor-general at that time was Lord Dahousie
• The idea of a railway to connect Bombay with Thane, Kalyan, and with the Thal and Bhore Ghats inclines first occurred to Mr. George Clark, the Chief Engineer of the Bombay Government, during a visit to Bhandup in 1843.
• The formal inauguration ceremony was performed on 16^th April 1853.
• The first train had 14 railway carriages and carried about 400 guests.
• It was operated by three locomotives, named Sahib, Sultan, and Sindh.

The correct answer is High land revenue.

Key Points

• The Patidar peasants in Kheda, Gujarat, organized non-violent campaigns against the British primarily due to their demand for high land revenue.
• This was one of the key issues that led to the Kheda Satyagraha of 1918, a significant event in the Indian independence movement, which was led by figures like Mohandas Karamchand Gandhi, Vallabhbhai Patel, and others.

Additional Information

• Kheda Satyagraha
• In the middle of the Kheda Satyagraha (1918), Gandhi also got involved in the Ahmedabad textile mill strike.
• Here his adversaries were the Gujarati millowners.
• The immediate reason for the industrial conflict was the withdrawal of plague bonus, which was being given to dissuade workers from leaving the city in the face of mounting plague-related deaths.
• Also, it was during Ahmedabad textile mill strike that Gandhiji for the first time during the Indian National Movement took fast unto death( to strengthen the workers‘ resolve).
• Hence his first hunger strike was during Ahmedabad Strike and not at Kheda.
• The cause for Kheda Satyagraha was that the peasants of Kheda district were in extreme distress due to a failure of crops and that their appeals for the remission of land revenue were being ignored by the Government.
• Discontinuation of the Plague bonus was the immediate cause for Ahmedabad textile mill strike.

The correct answer is 80.

Key Points

• The Rajya Sabha or Council of States is the upper house of the Parliament of India.
• Composition/Strength of Rajya Sabha:
• Article 80 of the Constitution lays down the maximum strength of Rajya Sabha as 250.
• Out of 250 seats of Rajya Sabha, 12 members are nominated by the President and 238 are representatives of the States and of the two Union Territories.
• The present strength of Rajya Sabha is 245, out of which 233 are representatives of the States and Union territories of Delhi and Puducherry and 12 are nominated by the President.
• The members nominated by the President are persons having special knowledge or practical experience in respect of such matters as literature, science, art and social service.

Important Points

• Rajya Sabha (Council of States):
• The Government of India Act, 1919 provided for the creation of a ‘Council of State’ as a second chamber of the then legislature.
• Rajya Sabha is the Upper house of the bicameral Parliament of India.
• Allocation of Seats:
• The Fourth Schedule of the Constitution provides for the allocation of seats to the States and Union Territories in Rajya Sabha.
• The allocation of seats is made on the basis of the population of each State.

Additional Information

• Lok Sabha:
• Lok Sabha is composed of representatives of the people chosen by direct election on the basis of adult suffrage.
• Article 81 of the Constitution defines the composition of the House of the People or Lok Sabha.
• The maximum strength of the House envisaged by the Constitution is 550.
• Out of 550 seats of Lok Sabha:
• Up to 530 members represent the States
• Up to 20 members represent the Union Territories
• The house currently has 543 seats, which are filled by the election of up to 543 elected members.

The correct answer is Brisbane.

Key Points

• American executive Cindy Hook has been appointed as the inaugural CEO of the organising committee for the 2032 Olympic and Paralympic Games in Brisbane.
• The organising committee announced the appointment on December 13 after engaging with 50 candidates over six months.
• Hook was based in Singapore as CEO of Deloitte Asia Pacific until June and had previously worked for the international professional services network in the US and in Australia, moving to Sydney in 2009 to lead the auditing practice for six years and later becoming CEO of the Australian operation in 2015.
• The International Olympic Committee awarded the 2032 Games to Brisbane in July of last year, under a revamped procedure for choosing host cities that saw a small group of IOC members identify and propose host cities to the board.
• Australia has twice previously hosted the Summer Olympics, at Melbourne in 1956 and Sydney in 2000.
• The 2032 organizing committee held its first board meeting in April and, on July 23, started the decade-long countdown.

Additional Information

• The 2032 Summer Olympics, officially known as the Games of the XXXV Olympiad and also known as Brisbane 2032, will be an international multi-sport event scheduled to take place from 23 July to 8 August 2032, in Brisbane, Queensland, Australia.
• Following changes in the bidding rules, the International Olympic Committee selected and announced Brisbane as the winning bid on 21 July 2021, two days before the start of the 2020 Summer Olympics.

The correct answer is Bharat Muni.

Key Points

• The Natya Shastra, an ancient Indian treatise on the performing arts, encompassing theatre, dance and music, is traditionally attributed to Bharata Muni.
• It provides information about musical instruments, as well as a wide range of other subjects related to the performing arts.

Additional Information

• Amir Khusrau:
• A legendary figure in Indian music and culture, Amir Khusrau was a 13^th-century Sufi musician, poet, and scholar from India.
• He has been credited with introducing several musical styles and instruments to Indian music, such as the qawwali and the sitar.
• Khusrau served in the court of several Delhi sultans and is known for his contributions to Hindustani classical music.
• Tansen:
• Tansen, originally named Ramtanu, was a prominent figure of Hindustani classical music in the medieval period.
• He was a court musician in the darbar (court) of the Mughal Emperor Akbar.
• His contributions to Indian music include compositions in Dhrupad, one of the oldest genres of Hindustani classical music.
• Many legends are associated with his musical prowess.
• Kalidas:
• Kalidas was a classical Sanskrit writer and is often considered ancient India's greatest playwright and poet.
• His notable works include plays like Abhijnana Shakuntalam (The Recognition of Shakuntala) and epic poems like Raghuvamsha (The Dynasty of Raghu).
• However, he is not directly associated with musical instruments or treatises on music.

The correct answer is Brazil.

Key Points

• Brazil beat Morocco 1-0 in the opening match of the 2022 FIFA U-17 World Cup at the Kalinga Stadium in Bhubaneswar.
• The national football federation has never provided an explanation for the choice, however, there are many theories.
• Some stated the All-India Football Federation (AIFF) could not afford to send the players to Brazil at the time, while some claimed it was because the team intended to play barefoot.
• The 32 football games of the FIFA U-17 Women's World Cup 2022 were played at three locations.
• The DY Patil Stadium in Navi Mumbai, Maharashtra; the Pandit Jawaharlal Nehru Stadium in Margao, Odisha.
• It took place at Navi Mumbai.
• At the Kalinga Stadium in Bhubaneswar, the seventh FIFA U17 Women's World Cup got underway on October 11, 2022.
• On October 30, the championship game was placed at the DY Patil Stadium.
• Spain, defending champions won the FIFA U-17 Women's World Cup against the first-time finalists Colombia. FIFA U-17 Women's World Cup was played between Spain and Colombia in the Patil Sports Stadium.
• India hosted the competition for the first time this year and made their debut.

Additional Information 

• The FIFA Under 17 Women's World Cup took place in India in 2022.
• It was the first time the nation has hosted a competition from the women's world football governing body.
• This is the third-most significant Women's Competitions event on the FIFA calendar, featuring 36 games between 16 nations at 5 locations in India.
• One of the most significant tournaments ever to be organised in Indian football history, the FIFA Under 17 Women's World Cup has served as a crucial starting stone in the careers of several international football heroes.
• The FIFA Under 17 Women's World Cup had a long-lasting impact on Indian football, modernising the facilities, establishing suitable operational guidelines, and raising the level of play in general.
• Unquestionably, the FIFA Under-17 Women's World Cup in India in 2022 has the potential to revolutionise Indian football.
• With an expected global audience of around 200 million people from almost 200 different nations, the tournament has a significant impact on the entire world.
• This presents India with a fantastic opportunity to showcase its cities, culture, and capacity to host events of the greatest calibre.

The correct answer is Peace.

Important Points 

• Kailash Satyarthi 
• Kailash Satyarthi is an Indian social activist who works and campaigned against child labour in India and elsewhere and advocated the right to education.
• In 2014 he was the recipient of the Nobel Peace Prize, along with Pakistan Malala Yousafzai, “for their struggle against the suppression of children and young people and for the right of all children to education”.
• Kailash Satyarthi founded the movement called Bachapan Bachao Andolan in India. Hence statement B is correct.
• Kailash Satyarthi is the fifth Indian Nobel prize winner.
• Other Noble Prize winners from India:
• Rabindranath Tagore
• Chandrashekhar Venkataraman
• Mother Teresa
• Amartya Sen

Key Points 

• The 2025 Nobel Prizes were awarded across five categories, highlighting achievements in quantum physics, materials science, immunology, literature, and peace.
• Physics Prize:
• Awarded to John Clarke, Michel H. Devoret, and John M. Martinis for their work in macroscopic quantum mechanical tunneling and energy quantization in electric circuits, showcasing quantum mechanics at a macroscopic scale.
• Their work enabled advances in quantum computing, cryptography, and quantum sensors.
• Chemistry Prize:
• Awarded to Susumu Kitagawa, Richard Robson, and Omar M. Yaghi for their development of metal-organic frameworks (MOFs), materials with vast internal surface areas for various applications such as water harvesting, carbon capture, and toxic gas storage.
• Medicine Prize:
• Awarded to Mary E. Brunkow, Fred Ramsdell, and Shimon Sakaguchi for discovering regulatory T cells (Tregs) that prevent autoimmune diseases and play a role in cancer therapy.
• Their work has revolutionized the understanding of autoimmune diseases and immunotherapy.
• Literature Prize:
• Awarded to László Krasznahorkai for his visionary works, including "Satantango", which explore themes of apocalyptic terror, chaos, and human isolation.
• Known for long, complex sentences and dark, philosophical narratives.
• Peace Prize:
• Awarded to Maria Corina Machado, a Venezuelan leader and symbol of democratic resistance against authoritarianism in Venezuela, emphasizing "ballots over bullets" and leading the opposition.
• Praised for her courage despite life-threatening risks and for unifying the opposition around democratic principles.

Additional Information

• Geographical Distribution:
• United States leads with six laureates.
• Other countries: Japan (2 laureates), Australia, Hungary, and Venezuela (1 laureate each).
• Ceremony: 
• The award ceremony will take place on December 10, 2025, in Stockholm (Peace Prize in Oslo).
• Each prize includes 11 million Swedish kronor, a gold medal, and a diploma.

The correct answer is Membrane-bound cell organelles are present.

Key Points

• Statement 2 is incorrect because one of the primary distinguishing characteristics of prokaryotic cells is the absence of membrane-bound organelles.
• Unlike eukaryotic cells, prokaryotic cells do not contain a nucleus or other organelles (like mitochondria, endoplasmic reticulum, or Golgi apparatus) that are enclosed within membranes.
• Instead, the genetic material in prokaryotic cells**, typically a circular strand of DNA, is found in a part of the cell called the nucleoid, which is not a membrane-bound structure.**
• The other metabolic activities in the cell occur in the cytoplasm or across the cell membrane, not within specialized organelles.
• In contrast, eukaryotic cells, which include animal and plant cells, do contain a variety of membrane-bound organelles, each with specific functions.
• For example, the nucleus contains the cell's genetic material, while mitochondria generate most of the cell's supply of adenosine triphosphate (ATP), used as a source of chemical energy.

Additional Information

• Other Statements:
• They have only very small ribosomes as organelles:
• Prokaryotic cells, such as bacteria, do contain ribosomes, which are small structures that participate in protein synthesis.
• Unlike eukaryotic cells, the ribosomes in prokaryotes are smaller (70S as opposed to the 80S ribosomes in eukaryotes), and they are not membrane-bound.
• Their chromosomes are composed of only nucleic acid:
• The chromosome of a prokaryotic cell is typically a single, circular DNA molecule that's located in the nucleoid region.
• Unlike eukaryotic chromosomes, prokaryotic chromosomes are not associated with histone proteins.
• The DNA is more or less "naked," and directly interacts with the cytoplasm.
• Their size is generally in the range of 1-10 μm:
• Prokaryotic cells are generally smaller than eukaryotic cells.
• They typically range in size from 1-10 micrometres (μm), which is significantly smaller than most eukaryotic cells.
• This smaller size allows for a larger surface area to volume ratio, which helps nutrients and waste to quickly enter and exit the cell.

The correct answer is Option 4.

Key Points

• Metallurgical coal is high-grade lignite coal which has a special value for smelting iron in blast furnaces, this statement is NOT correct.
• Metallurgical coal**, also known as coking coal, is a high-quality hard coal (not lignite) used to produce coke, which is necessary for iron smelting in blast furnaces.**
• Metallurgical coal needs to have low sulfur and phosphorus contents, making it much rarer and more valuable than thermal coal, which is used to produce heat and electricity.
• Typically, bituminous coal or anthracite is used for this purpose, not lignite, which is lower-grade coal.

Additional Information

• Anthracite is the highest quality hard coal:
• Anthracite is indeed the highest grade of coal.
• It's the oldest type of coal, having spent the most time underground exposed to pressure and heat.
• It's very hard and shiny (hence "hard coal") and burns cleanly with little soot, making it much cleaner than other types of coal.
• It's less common than other forms, which makes it more expensive.
• Coal that has been buried deep and subjected to increased temperatures is bituminous coal:
• Bituminous coal is a medium-rank coal between sub-bituminous coal and anthracite.
• It has been subjected to higher pressures and temperatures than lignite and sub-bituminous coal, but not as much as anthracite.
• Bituminous coal is commonly used for generating electricity and heating in industrial processes.
• Lignite is a low-grade brown coal, which is soft with high moisture content:
• Lignite, often referred to as brown coal, is indeed a low-grade coal.
• It's softer than bituminous coal or anthracite, and it has a high moisture content.
• This makes it less energy-dense and more polluting than higher-grade coals.
• Lignite is often used in electricity production in power plants located near mining sites.

Given:

The length of chord AB is equal to the radius of the circle

Formula used:

The subtended angle θ in a circle can be found using the formula θ = 2 arcsin(d/2r), where d is the length of the chord and r is the radius of the circle.

Calculation:

Given that the length of the chord AB (d) is equal to the radius (r), we can substitute r for d in the formula:

θ = 2 arcsin(r/2r)

This simplifies to:

θ = 2 arcsin(1/2)

Using the arcsine values we know that arcsin(1/2) is equal to 30 degrees. So:

θ = 2 × 30

θ = 60 degrees

∴ The angle subtended by the chord at the centre of the circle is 60 degrees.

Shortcut Trick

In a circle, a chord of the same length as the radius subtends an angle of 60 degrees at the center. This is a property of circles, and it can be proved using elementary geometry and trigonometry. You don't need to do the full calculation if you remember this fact.

Given:

$\frac{x^2-1}{x}=8$

Formula used:

If (x - $\frac{1}{x}$) = k, then (x³ - $\frac{1}{x^3}$) = k³ + 3k

Calculation:

⇒ $\frac{x^2}{x} - \frac{1}{x} = 8$

⇒ x - $\frac{1}{x}$ = 8

⇒ $\frac{x^6-1}{x^3} = x^3 - \frac{1}{x^3}$

⇒ x³ - $\frac{1}{x^3}$ = 8³ + 3 × 8

⇒ 512 + 24

⇒ 536

∴ The correct answer is option (2).

Given:

The radius of a circle is 10 cm.

A chord of length 20 cm is drawn.

Concept used:

The diameter of a circle subtends an angle of 90° at the circumference of the circle.

The diameter is the largest chord of a circle.

The length of the diameter = 2 × Radius

Calculation:

Let the radius of the circle be R cm.

According to the concept,

R = 10 cm

So, Diameter = 2 × R = 2 × 10 = 20 cm

According to the question,

The chord has a length of 20 cm.

A diameter divides the circle into two semi-circles, each having an angle of 90 degrees at the circumference of the circle.

So, the angle made by the chord (diameter in this case) at the circumference of the circle is 90 degrees.

Therefore, the correct answer is 1) 90 degrees.

Given:

12 men can do a work in 8 days while 4 boys can do it in 40 days.

Concept Used:

M₁D₁ = M₂D₂

Calculation:

⇒ 12M × 8 = 4B × 40

⇒ 3M = 5B

⇒ M : B = 5 : 3

Total work = 12 × 5 × 8 = 480

9 boys and 3 men together will complete the same work in = 480/(9 × 3 + 3 × 5)

⇒ 480/42

⇒ 80/7 days

∴ Option 3 is the correct answer.

Shortcut Trick

Given that 6 cot θ = 5, we can simplify the required expression.

Divide both the numerator and the denominator by sin θ to convert the terms into cot θ.

Expression = (6 cot θ + 1) / (6 cot θ − 4)

Substitute 6 cot θ = 5 directly: (5 + 1) / (5 − 4) = 6 / 1 = 6.

∴ The correct answer is 6.

Alternate Method

Given: 6 cot θ = 5

Formula Used: cot θ = Base / Perpendicular = cos θ / sin θ

⇒ 6 cot θ = 5 ⇒ cot θ = 5/6

⇒ Since cot θ = cos θ / sin θ, we can assume cos θ = 5k and sin θ = 6k.

⇒ Required value = (6 cos θ + sin θ) / (6 cos θ − 4 sin θ)

⇒ Substituting the values: [6(5k) + 6k] / [6(5k) − 4(6k)]

⇒ Value = (30k + 6k) / (30k − 24k)

⇒ Value = 36k / 6k = 6

The calculated result 6 matches Option 3.

∴ The correct answer is 6.

Additional Information

Trigonometric Ratio Identities

The fundamental quotient identity for cotangent is cot θ = cos θ / sin θ and for tangent is tan θ = sin θ / cos θ.

Reciprocal Relationships

The cotangent function is the reciprocal of the tangent function: cot θ = 1 / tan θ.

Pythagorean Identity

Another important identity involving cotangent is 1 + cot² θ = cosec² θ.

Calculation:

Statement I:

The expenditure of R in year Y1 and Y2 together = 600 + 500 = 1100

The expenditure of S in year Y3 and Y4 together = 700 + 500 = 1200

Percentage of the expenditure of R in year Y1 and Y2 together to the expenditure of S in year Y3 and Y4 together = 1100/1200 × 100 = 91.66%

Statement I is not correct.

Statement II:

Total expenditure of company S = 1200 + 900 + 700 + 500 + 400 = 3700

Total expenditure of company R = 600 + 500 + 800 + 400 + 1000 = 3300

Percentage of the total expenditure of company S to the total expenditure of company R = 3700/3300 × 100 = 112.12%

Statement II is correct.

∴ Option 2 is the correct answer.

Calculation:

Company gain in 2016 = 54 - 51 = 3

Company gain in 2017 = 64 - 60 = 4

Company gain in 2018 = 80 - 75 = 5

Company gain in 2019 = 82 - 80 = 2

Company gain in 2020 = 98 - 87 = 11

Company gain the minimum amount in 2019.

∴ Option 3 is the correct answer.

Given:

Marked price = (M.P) = Rs. 210

Selling price = (S.P) = Rs. 189

Formula used:

If marked price is M.P, selling price is S.P  and discount is D, then

Discount = M.P - S.P

Rate of discount = (100/M.P) × Discount

Calculation:

Discount = 210 - 189 = Rs. 21

So, Rate of discount = (21/210) × 100 = 10 %

∴ The rate of discount is 10 %

Shortcut Trick

Ratio of Volumes (V₁/V₂) = (r₁/r₂)² × (h₁/h₂)

32/9 = (r₁/r₂)² × (8/9) ⇒ (r₁/r₂)² = 4 ⇒ r₁/r₂ = 2/1

Base Area of second cylinder = 616 cm² ⇒ πr₂² = 616 ⇒ r₂ = 14 cm

Radius of first cylinder (r₁) = 2 × r₂ = 2 × 14 = 28 cm

∴ The correct answer is 28 cm.

Alternate Method

Given: Ratio of Volumes = 32 : 9, Ratio of Heights = 8 : 9, Base Area of 2^nd cylinder = 616 cm².

Formula Used: Volume of Cylinder = Base Area × Height

⇒ V₁ / V₂ = (Area₁ × h₁) / (Area₂ × h₂)

⇒ 32 / 9 = (Area₁ / 616) × (8 / 9)

⇒ 32 / 8 = Area₁ / 616

⇒ Area₁ = 4 × 616 = 2464 cm²

⇒ π × r₁² = 2464

⇒ 22/7 × r₁² = 2464

⇒ r₁² = (2464 × 7) / 22 = 112 × 7 = 784

⇒ r₁ = √784 = 28 cm

∴ The correct answer is 28 cm.

Additional Information

Volume of a Cylinder

The volume (V) is calculated as the product of the base area and the height: V = πr²h.

Surface Area of a Cylinder

Curved Surface Area (CSA) = 2πrh and Total Surface Area (TSA) = 2πr(r + h).

Radius and Area Relation

If the base area is A, then the radius r = √(A/π). For A = 616 cm², r = 14 cm.

Shortcut Trick

Ratio of sides EF : FG = 10 : 15 = 2 : 3.

In a right triangle with sides 2 and 3, Hypotenuse (EG) = √(2² + 3²) = √13 units.

For ∠G, Perpendicular = EF = 2 units and Hypotenuse = √13 units.

cosec G = Hypotenuse ÷ Perpendicular = √13 / 2.

∴ The correct answer is √13/2.

Alternate Method

Given: In ΔEFG, ∠F = 90°, EF = 10 cm, FG = 15 cm.

Formula: Pythagoras Theorem: EG² = EF² + FG² | cosec G = Hypotenuse / Opposite side.

⇒ In ΔEFG, by Pythagoras Theorem:

⇒ EG² = 10² + 15²

⇒ EG² = 100 + 225 = 325

⇒ EG = √325 = √(25 × 13) = 5√13 cm

⇒ cosec G = Hypotenuse / Perpendicular (Opposite to G)

⇒ cosec G = EG / EF

⇒ cosec G = (5√13) / 10

⇒ cosec G = √13 / 2

∴ The correct answer is √13/2.

Additional Information

Trigonometric Ratio Definitions

In a right-angled triangle, sin θ = Perpendicular/Hypotenuse, cos θ = Base/Hypotenuse, and tan θ = Perpendicular/Base.

Reciprocal Relations

cosec θ is the reciprocal of sin θ (1/sin θ), sec θ is the reciprocal of cos θ (1/cos θ), and cot θ is the reciprocal of tan θ (1/tan θ).

Pythagoras Theorem

For any right triangle with legs a, b and hypotenuse c, the relationship is always a² + b² = c².

Shortcut Trick

Overall Selling Price = 30 × 1.10 = Rs. 33/kg.

Equating total SP parts: 8x + 45(x − 8) = 33x

53x − 360 = 33x ⇒ 20x = 360 ⇒ x = 18

Quantity sold at Rs. 45/kg = x − 8 = 18 − 8 = 10 kg.

∴ The correct answer is 10 kg.

Alternate Method

Given:

Cost Price (CP) = Rs. 30/kg, Overall profit = 10%

Quantity sold at Rs. x/kg = 8 kg

Quantity sold at Rs. 45/kg = (x − 8) kg

Formula Used:

Mean SP = CP × (100 + Profit%) ÷ 100

Alligation ratio = (SP₂ − Mean SP) / (Mean SP − SP₁)

Calculations:

⇒ Mean Selling Price = 30 × 1.1 = Rs. 33/kg

⇒ Using the Alligation ratio: 8 / (x − 8) = (45 − 33) / (33 − x)

⇒ 8 / (x − 8) = 12 / (33 − x)

⇒ 2 / (x − 8) = 3 / (33 − x)

⇒ 2 × (33 − x) = 3 × (x − 8)

⇒ 66 − 2x = 3x − 24

⇒ 5x = 90

⇒ x = 18

⇒ Quantity sold at Rs. 45/kg = 18 − 8 = 10 kg

∴ The correct answer is 10 kg.

Additional Information

Mixtures & Alligation Rule

It allows finding the ratio in which two ingredients at given prices must be mixed to produce a mixture of a desired price: Quantity 1 / Quantity 2 = (Price 2 − Mean Price) / (Mean Price − Price 1).

Profit and Loss Basics

Selling Price (SP) is calculated as CP × (100 + Profit%) ÷ 100. When multiple parts are sold at different prices, the overall SP is the weighted average of the individual SPs.

Replacement Method

When a quantity 'y' is replaced 'n' times from a total mixture 'x', the remaining quantity of the original substance is given by x × (1 − y/x)ⁿ.

Shortcut Trick

Distance x = Speed after repair × Time = 108 × 3 = 324 km.

New distance to cover = 5x = 5 × 324 = 1620 km.

Time before repair = New Distance ÷ Speed before repair = 1620 ÷ 72.

Time = 22.5 hours = 22 hr 30 min.

∴ The correct answer is 22 hr 30 min.

Alternate Method

Given:

Speed of car after repair = 108 km/hr

Speed of car before repair = 72 km/hr

Time taken to cover distance x (after repair) = 3 hr

Formula Used:

Distance = Speed × Time

Time = Distance ÷ Speed

Calculations:

⇒ First, calculate the distance x using the speed after repair:

⇒ x = 108 km/hr × 3 hr = 324 km

⇒ Now, calculate the new distance to be covered before repairing (5x):

⇒ 5x = 5 × 324 = 1620 km

⇒ Calculate the time taken to cover 1620 km at the speed of 72 km/hr (before repair):

⇒ Time = 1620 ÷ 72

⇒ Time = 22.5 hours

⇒ Since 0.5 hours = 0.5 × 60 minutes = 30 minutes,

⇒ Time = 22 hr 30 min

∴ The correct answer is 22 hr 30 min.

Additional Information

Speed-Time Proportionality

For a constant distance, Speed is inversely proportional to Time (S₁/S₂ = T₂/T₁).

Unit Conversion

To convert speed from km/hr to m/s, multiply the value by 5/18. To convert from m/s to km/hr, multiply by 18/5.

Average Speed Formula

Average Speed = Total Distance ÷ Total Time. If a car covers equal distances at speeds u and v, then Average Speed = 2uv ÷ (u + v).

Given:

The ratio of incomes of P and Q is 1:2

The ratio of income of Q and R is 3:2

One-third of P's income is Rs. 4400 less than half of P's income.

Calculation:

P's income = x

Q's income = 2x (since the ratio of P's income to Q's income is 1:2)

According to the given information:

One-third of P's income is Rs. 4400 less than half of P's income.

(1/3)x = (1/2)× x - 4400

To simplify the equation, we can multiply both sides by 6 to get rid of the fractions:

x/2 - x/3 = 4400

x/6 = 4400

x = 26400

So

Q's income = 2x = 2 × 26400 = 52800

∴ Option 2 is the correct answer.

Calculation:

(22 + 1) (24 + 1) (28 + 1) (216 + 1) ........ (2128 + 1)

Divide by (22 - 1) in numerator and denominator

1/(22 - 1)[(22 - 1)(22 + 1) (24 + 1) (28 + 1) (216 + 1) ........ (2128 + 1)]

1/(22 - 1)[(2⁴ - 1) (24 + 1) (28 + 1) (216 + 1) ........ (2128 + 1)]

1/(22 - 1)[(2⁸ - 1) (28 + 1) (216 + 1) ........ (2128 + 1)]

1/(22 - 1)[(2¹⁶ - 1) (216 + 1) ........ (2128 + 1)]

1/(22 - 1)(2²⁵⁶ - 1)

(2256 - 1)/3

∴ Option 2 is the correct answer.

Shortcut Trick

Student's scored percentage = Passing percentage − Failing gap percentage

Scored percentage = 40% − 20% = 20%

Since 20% of the maximum marks corresponds to the 40 marks obtained:

Maximum marks = (40 ÷ 20) × 100 = 200

∴ The correct answer is 200 marks.

Alternate Method

Given:

Marks obtained by the student = 40 marks

Failing gap = 20% of maximum marks

Passing percentage = 40% of maximum marks

Formula Used:

Passing Marks = Obtained Marks + Shortfall Marks

0% 20% 40% (Pass) 100%

Scored Failed by

40 Marks

20% Gap

Max Marks = 100% = 200 Marks

Calculations:

Let the maximum marks be x.

⇒ Passing marks = 40% of x = 0.4x

⇒ Shortfall (Failed by) marks = 20% of x = 0.2x

⇒ Obtained marks + Shortfall marks = Passing marks

⇒ 40 + 0.2x = 0.4x

⇒ 0.4x − 0.2x = 40

⇒ 0.2x = 40

⇒ x = 40 ÷ 0.2

⇒ x = 200

∴ The correct answer is 200 marks.

Additional Information

Concept of Passing Marks

If a student scores 'M' marks and fails by 'X' marks, then Passing Marks = M + X. If they score 'N' marks and get 'Y' marks above passing, then Passing Marks = N − Y.

Fraction Equivalent Strategy

Converting percentages to fractions speeds up calculations. 20% = 1/5 and 40% = 2/5. Here, (2/5)x − (1/5)x = 40 ⇒ (1/5)x = 40 ⇒ x = 200.

Percentage Base Rule

Whenever a percentage is mentioned (like 20% failed marks), it is always calculated on the Total/Maximum Marks of the exam unless specified otherwise.

Given:

Circum-radius = 14 cm

Formula used:

Circum-radius, r = a/√3

Length of median = Height of equailateral triangle = √3a/2

where, a = side of equailateral triangle

Calculation:

⇒ r = a/√3

⇒ a = 14√3

Now, Length of median = √3a/2

⇒ (√3 × 14√3)/2 = 21 cm

∴ Option 2 is the correct answer.

Calculation:

The given expression alternates between adding and subtracting the numbers 1, 7, 2, 8, 3, 9, 4, 10, and so on.

We can observe that the numbers being added increase by 1 each time, while the numbers being subtracted also increase by 1 each time.

To find the value of the expression to 100 terms, we can group the terms into pairs.

Each pair consists of a positive number and its negative counterpart.

The sum of each pair is always -6 because (-7 + 1 = -6, -8 + 2 = -6, -9 + 3 = -6, and so on).

Since we have 100 terms in total, we can form 50 pairs.

Each pair sums up to -6, so the sum of the 100 terms is:

50 pairs ×  (-6) = -300

Therefore, the value of the expression 1 - 7 + 2 - 8 + 3 - 9 + 4 - 10 + ... to 100 terms is -300.

∴ Option 3 is the correct answer.

Calculation:

-sin θ + cosec θ = 6

⇒ -sin θ + 1/sin θ  = 6

⇒ 1 - sin² θ = 6 sin θ 

⇒ sin2 θ + 6 sin θ - 1 =  0

Apply quadratic roots formula,

x = (-b ± √b² - 4ac)/2a

Here x = sinθ , a = 1, b = 6, c = -1

⇒ sinθ = (-6 ± √6² - 4 × (-1))/2

⇒ sinθ = (-6 ± √40)/2

⇒ sinθ = (-3 ± √10)

⇒ sin θ + cosec θ = sin θ + 6 + sin θ           (cosec θ = 6 + sin θ)

⇒ 2sin θ + 6

⇒ 2(-3 ± √10) + 6

⇒ -6 ± 2√10 + 6

⇒ ± 2√10

⇒ √40

∴ Option 2 is the correct answer.

Calculation:

Let's solve the given equation $a^3 + 3a^2 + 3a = 63$ and find the value of $a^2 + 2a$

We can factor the left side of the equation by recognizing it as a cube of a binomial:

$(a + 1)^3 = a^3 + 3a^2 + 3a + 1$

Comparing this with the given equation, we have:

$(a + 1)^3 = 63 + 1$

Taking the cube root of both sides, we get:

a + 1 = ∛(64)

Simplifying further, we have:

a + 1 = 4

Subtracting 1 from both sides:

a = 4 - 1

a = 3

Now we can find the value of $a^2 + 2a:$

$a^2 + 2a = 3^2 + 2(3) = 9 + 6 = 15$

Therefore, the value of $a^2 + 2a$ is 15.

∴ Option 3 is the correct answer.

Calculation:

Average income of C and D together = (600 + 400)/2 = 500

Saving of C = 600 - 200 = 400

Saving of D = 400 - 100 = 300

Average saving of C and D together = (400 + 300)/2 = 350

The difference between the average income and average savings in year C and D together is = 500 - 350 = 150

∴ Option 3 is the correct answer.

Calculation:

The average number of students studying science in the given years = (78 + 69 + 83 + 55 + 65)/5

⇒ 350/5 = 70

The total strength of students studying in the year 2022 = (76 + 65 + 48 + 31) = 220

Ratio of the average number of students studying science in the given years to the total strength of students studying in the year 2022 = 70 : 220

⇒ 7 : 22

∴ Option 1 is the correct answer.

Shortcut Trick List all odd numbers between 100 and 120: 101, 103, 105, 107, 109, 111, 113, 115, 117, 119. Remove multiples of 3 (sum of digits): 111 (1+1+1=3) and 117 (1+1+7=9). Remove multiples of 5: 105 and 115. Remove multiples of 7: 119 (7 × 17). Remaining prime numbers: 101, 103, 107, 109, 113. ∴ The correct answer is 5.

Alternate Method Given: Range between 100 and 120. Formula: A number is prime if it is not divisible by any prime number less than or equal to its square root (√n). For n < 121, √n < 11. We only need to check divisibility by 2, 3, 5, and 7.

⇒ Divisibility test for 111: 1 + 1 + 1 = 3 (Divisible by 3) ⇒ Divisibility test for 117: 1 + 1 + 7 = 9 (Divisible by 3 and 9) ⇒ Divisibility test for 119: 119 ÷ 7 = 17 (Divisible by 7) ⇒ Count of primes = 101, 103, 107, 109, 113 = 5 prime numbers. ∴ The correct answer is 5.

Additional Information Prime Numbers (1 to 100) There are exactly 25 prime numbers between 1 and 100. The smallest is 2, which is also the only even prime number. Divisibility Rule for 3 A number is divisible by 3 if the sum of its digits is a multiple of 3. Testing for Primality To check if a number n is prime, test divisibility by all primes up to √n. If none divide n, then n is prime.

Shortcut Trick

Original average of 16 numbers = 35

Net deviation of removed numbers (18, 17, 24, 35) = (−17) + (−18) + (−11) + 0 = −46

Removing numbers with a negative net deviation increases the average of the remaining values.

Increase in average = 46 ÷ 12 = 3.83

New average = 35 + 3.83 = 38.83

∴ The correct answer is 38.83.

Alternate Method

Given:

Average of 16 numbers = 35

Removed numbers = 18, 17, 24 and 35

Formula Used:

Average = Sum of numbers ÷ Total numbers

4 removed 12 remaining Sum = 94 Sum = 466 New Avg = 38.83 Total: 16 numbers, Avg = 35, Sum = 560

Calculations:

⇒ Total sum of 16 numbers = 16 × 35 = 560

⇒ Sum of removed numbers = 18 + 17 + 24 + 35 = 94

⇒ Total sum of remaining 12 numbers = 560 − 94 = 466

⇒ New average = 466 ÷ 12

⇒ New average = 233 ÷ 6 = 38.83

∴ The correct answer is 38.83.

Additional Information

Average Basic Concept

The average of a set of numbers is the sum of the values divided by the total count of numbers.

Net Deviation Method

Removing items with a net negative deviation from the overall average increases the average of the remaining items. Similarly, removing positive deviations decreases the average.

Weighted Average

When combining two groups, the combined average is calculated as (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Given:

Annual interest rate = 10%

Compounding frequency = half-yearly

Formula Used:

a + b +ab/100

Calculation:

x% is compounded half-yearly

a + b +ab/100 using this,

x + x + x²/100

2x + x2/100

According to the question:

10 = 2x + x2/100

1000 = x(200 + x)

x = 4.88 percent

Please note that this type of calculation is not possible in the exam, so it is better to use the option method after this.

Just put values from options.

 Please note that here x is the rate of interest for half year, not per annum. Please go through the question carefully.

Shortcut Trick

For a cyclic quadrilateral where sides are produced to meet at point Z, the secant-secant property states: ZK × ZJ = ZL × ZM.

Total length ZJ = ZK + JK = 12 + 10 = 22 cm.

Applying the formula: 12 × 22 = ZL × 33

⇒ 264 = 33 × ZL

⇒ ZL = 264 ÷ 33 = 8 cm.

∴ The correct answer is 8 cm.

Alternate Method

Given:

JK = 10 cm, KZ = 12 cm, MZ = 33 cm

JKLM is a cyclic quadrilateral.

Formula Used:

Intersecting Secant Theorem: When two secant lines intersect at an external point Z, the product of the external segment and the whole secant is equal for both lines: ZK × ZJ = ZL × ZM.

Calculations:

⇒ Total length of secant ZJ = ZK + JK

⇒ ZJ = 12 + 10 = 22 cm

⇒ According to theorem, ZK × ZJ = ZL × ZM

⇒ 12 × 22 = ZL × 33

⇒ 264 = 33 × ZL

⇒ ZL = 264 ÷ 33

⇒ ZL = 8 cm

∴ The correct answer is 8 cm.

Additional Information

Cyclic Quadrilateral Properties

In a cyclic quadrilateral, the sum of opposite angles is 180°. Also, the exterior angle at any vertex is equal to the interior opposite angle.

Power of a Point Theorem

For an external point Z, the product of segments of any secant line is constant (ZK × ZJ = ZL × ZM = Constant), which is also equal to the square of the tangent length from that point.

Similar Triangles

When sides of a cyclic quadrilateral are produced, the triangle formed by the intersection point and the nearer vertices is similar to the triangle formed with the farther vertices (▵ZKL ∼ ▵ZMJ).

Here the correct answer is Option 4.

Key Points

• The error in the sentence lies in the phrase "the universe other objects."
• Here's a breakdown of the sentence:
• "Scientists have a few tricks up" - This fragment is grammatically correct and establishes the subject "Scientists" and their possession of "a few tricks."
• "their sleeves for dealing with" - This fragment is also grammatically correct. It indicates that the tricks are kept "up their sleeves" (a figurative expression meaning to keep something secret or hidden) and are used for "dealing with" various situations.
• "No error" - This option is incorrect because there is indeed an error in the sentence.
• "the universe other objects" - This fragment contains the error. "the universe" should be separated from "other objects" with the conjunction "and" to clearly indicate that the tricks are used for both the universe and other objects.

Corrected sentence: "Scientists have a few tricks up their sleeves for dealing with the universe and other objects."

Here the correct answer is Mollifying. (किसी के क्रोध या परेशानी को कम करना, किसी अशांत व्यक्ति को शांत करना)

Key Points

• The word "Pacific" has several meanings, but in this context, it most likely refers to the adjective form of "peaceful" or "calm." It is derived from the Latin word "pacificus," which means "peaceful" or "mild."
• Example sentence: "The atmosphere in the room was pacific, with everyone engaging in friendly conversation."
• Option 1) Mollifying: This word means to soothe, appease, or calm. It is synonymous with "pacifying" or "making peaceful."
• Example sentence: "The manager mollified the angry customer by offering a refund and a sincere apology."
• Option 2) Bellicose: This word means warlike or inclined to fight. It is the opposite of "Pacific."  (लड़ाकू)
• Example sentence: "His bellicose attitude made it difficult to find a peaceful resolution to the conflict."
• Option 3) Inimical: This word means hostile, unfriendly, or harmful. It is the opposite of "Pacific." (हानिकारक; अस्तित्व को संकट में डालना)
• Example sentence: "The CEO's inimical behavior towards his employees created a tense work environment."
• Option 4) Chafing: This word means to irritate or cause discomfort. It does not have a direct synonym for "Pacific." (पपड़ियाना)
• Example sentence: "The tight shoes were chafing against her heels, causing blisters."
• In this context, "mollifying" best captures the meaning of "Pacific" as it implies the act of soothing or calming, aligning with the sense of peacefulness and calmness associated with the word.

The correct answer is (1) Frightful.

Key Points

• The word "ferocious" is an adjective that describes something or someone extremely fierce, savage, or violent.
• Example sentence: "The tiger's ferocious roar echoed through the jungle, sending shivers down their spines."
• Option 1) Frightful: This word means causing fear or terror, and it is synonymous with "ferocious."
• Example sentence: "The storm brought forth frightful winds and lightning, causing widespread panic."
• Option 2) Mild: This word means gentle or not severe, which is the opposite of "ferocious."
• Example sentence: "The puppy had a mild temperament and showed no signs of being ferocious."
• Option 3) Conscientious: This word means diligent, thorough, or attentive to detail. It does not have a direct synonym for "ferocious."
• Example sentence: "She was a conscientious worker, always completing her tasks with great care."
• Option 4) Tame: This word means (of an animal) not dangerous or frightened of people; domesticated.
• Example sentence: "The fish are so tame you have to push them away."

The correct answer is 4) exile.

Key Points

• In the Hindu epic Mahabharata, the Pandavas were banished from their kingdom of Hastinapur for thirteen years as a result of a gambling match.
• During this period, they had to live in the forest, disguised and in hiding.
• The word "exile" refers to **a state of being barred or forced to leave one's home or country, often as a form of punishment or self-imposed separation.(**निर्वासन)
• In this context, the Pandavas were exiled from their kingdom and had to live in exile for thirteen years.
• Example: After being convicted of treason, the former political leader was sent into exile, forced to live in a remote and unfamiliar country for the remainder of his life.
• In conclusion, the correct answer is 4) exile because it accurately describes the situation of the Pandavas returning to Hastinapur after being banished for thirteen years.

Additional Information

• Now let's explain the other options:
• Acceptance: This word does not fit the context. "Acceptance" refers to the action of accepting or agreeing to something willingly or without resistance.(स्वीकार) It does not relate to the Pandavas' situation of returning to Hastinapur after their exile.
• Example sentence: His acceptance of the job offer brought him joy and relief.
• Entertainment: This word does not fit the context either. "Entertainment" refers to an activity or performance that provides amusement or enjoyment to an audience(मनोरंजन). It does not relate to the Pandavas' return from exile.
• Example sentence: The concert provided great entertainment for the audience.
• Eminence: This word does not fit the context. "Eminence" refers to being distinguished or renowned in a particular field or area(श्रेष्ठता). It does not relate to the Pandavas' situation of returning to Hastinapur after their exile.
• Example sentence: The scientist achieved eminence in the field of physics.

The incorrectly spelled word is: Guilde.

Key Points

• The correct spelling is "Guild."
• A guild is an organization or association of individuals who come together for a common purpose or interest, such as a guild of craftsmen or a guild of gamers.
• Here's an example sentence: "The blacksmith joined the local guild to network with other skilled artisans."
• In summary, the incorrect spelling is "Guilde," and the correct spelling is "Guild."

Additional Information

• Now let's look at the other options:
• Build - This is the correct spelling. "Build" is a verb that means to construct or assemble something.
• For example, "The construction workers will build a new house."
• Shield - This is the correct spelling. A shield is a protective device or barrier used for defense.
• For instance, "The knight raised his shield to block the enemy's attack."
• Field - This is the correct spelling. "Field" has multiple meanings, including an area of land used for a specific purpose, such as a sports field, or a particular branch of study or work, like the field of medicine.
• Here's an example sentence: "The soccer match took place on the field behind the school."

Here the correct answer is Advance.

Key Points

• The most appropriate antonym of the word "INTERFERE" is: ADVANCE.
• "Interfere" means to intrude or intervene in a situation, often causing disruptions or hindrances. It implies getting involved in a way that negatively impacts the progress or normal functioning of something.
• For example, "The loud noise from the construction site interfered with my ability to concentrate."
• The antonym "Advance" means to move forward, make progress, or promote the development of something. It suggests a positive and proactive action that helps in the forward movement or improvement of a situation.
• For instance, "The company implemented new strategies to advance its market position."
• In summary, the most appropriate antonym of "INTERFERE" is "ADVANCE," as it represents the opposite action of moving forward or promoting progress.

Additional Information

• Now let's look at the other options:
• INTERCEDE - This word is not an antonym of "Interfere." "Intercede" means to mediate or intervene on behalf of others in a conflict or dispute, usually with the intention of helping or reconciling. It does involve interference but in a different context and with a different purpose.
• HAMPER - This word is synonymous with "Interfere" and does not serve as an antonym. "Hamper" means to hinder, obstruct, or impede progress or movement. It implies causing obstacles or difficulties.
• JAM - Similar to "Hamper," "Jam" is not an antonym but rather a synonym of "Interfere." It denotes a situation where something becomes stuck or blocked, leading to disruption or interference. For example, "The printer jammed, interfering with the document printing process."

Hinglish

• INTERCEDE - हस्तक्षेप करना
• ADVANCE - आगे बढ़ना
• HAMPER - बाधा डालना
• JAM - जाम

The correct answer is: Decamped with valuables.

Key Points

• The sentence contains a grammatical error in the underlined part.
• The correct verb form to use in this context is "decamped" (past tense), not "decamp" (present tense).
• Additionally, the word "valuables" should be used instead of "valuable" to indicate multiple valuable items.
• Therefore, option 1 is the correct choice as it corrects both the verb form and the noun form.
• The verb "decamp" means to leave quickly or secretly, often with the intention to escape or evade capture. In this context, it indicates that the thieves left the house after entering it.
• Using the past tense form "decamped" is appropriate because it indicates an action that has already happened in the past. The phrase "with valuables" indicates that the thieves took multiple valuable items from the house.
• This sentence uses the correct verb form and plural noun form, making it grammatically accurate and conveying the intended meaning of the thieves leaving the house with multiple valuable items.

Correct Sentence: "The thieves entered a house at night and decamped with valuables worth Rs. 50,000."

The correct answer is: very proud.

Key Points

• The original sentence "His father was few proud of his power over the horse" contains an error.
• The word "few" is incorrect in this context. It should be replaced with the word "very" to convey a strong sense of pride.
• "Very" is an adverb that intensifies the adjective "proud" and emphasizes the degree of pride.
• In this corrected sentence, "very proud" accurately describes the level of pride the father feels towards his power over the horse.
• The adverb "very" modifies the adjective "proud," emphasizing the intensity of the emotion.
• Thus, the correct answer is Option 3.

Correct Sentence: "His father was very proud of his power over the horse."