SSC CHSL Tier-1 2022: Official Paper (Held On: 17 March, 2023 Shift 3) (Previous Year Paper)

The logic followed here is:

Logic: (First number)² - (Second number)² = Third number

• (15, 13, 56) → 15² - 13² = 225 - 169 = 56
• (17, 11, 168) → 172 - 112 = 289 - 121 = 168

Similarly,

• (20, 14, 204) → 202 - 142 = 400 - 196 = 204

Hence, '(20, 14, 204)' is the correct answer.

The logic followed here is:

• 132 F 624 = 657 → 132 + 624 = 756
• 756 when written from right to left, gives the number 657
• 84 F 321 = 504 → 84 + 321 = 405​
• 405 when written from right to left, gives the number 504

Similarly,

• 168 F 27 = ? → 168 + 27 = 195
• ​195 when written from right to left, gives the number 591

Hence, '591' is the correct answer.

The logic followed here is:

Logic: 1 has been added in the first letter's positional value to get the corresponding first letter.

3 has been added in the second letter's positional value to get the corresponding second letter.

OQ: PT

 

Similarly,

WZ:?

Hence, the correct answer is "XC".

The logic followed here is:

 

Similarly,

Hence, 'AVGGBT' is the correct answer.

I. 7 × 9 + 5 – 8 ÷ 4 = 42

After interchanging 5 and 9, we get:

7 × 5 + 9 – 8 ÷ 4 = 42

⇒ 35 + 9 - 2 = 42

⇒ 44 - 2 = 42

⇒ 42 = 42

II. 9 × 3 + 5 ÷ 1 – 4 = 20

After interchanging 5 and 9, we get:

5 × 3 + 9 ÷ 1 – 4 = 20

⇒ 15 + 9 - 4 = 20

⇒ 24 - 4 = 20

⇒ 20 = 20

Hence, ‘Both I and II’ is the correct answer.

The logic followed here is:

Logic: First number × 3 = Second number

1. 2278 – 6834 → 2278 × 3 = 6834 2. 3072 – 9216 → 3072 × 3 = 9216 3. 1008 – 3024 → 1008 × 3 = 3024 4. 3744 – 11322 → 3744 × 3 = 11232 ≠ 11322

Hence, '3744 – 11322' is the correct answer.

The logic used here is:

Logic: The first word is a venue or location, and the second word is an activity or sports typically associated with that location.

Let's check each option as per the logic,

1) Court – Tennis:

→ Tennis is played in the court.

2) Gymnasium – Exercise:

→ Exercise is done in the Gymnasium.

3) Wrestling – Arena:

→ Wrestling is done in the Arena. But the order of the words is incorrect. ⇒ Doesn't follow the logic.

4) Pitch – Cricket:

→ Cricket is played on the pitch.

Here, we can see that only Option 3 doesn't follow the logic.

Hence, the correct answer is "Wrestling – Arena".

When the paper is unfolded, the image we get is shown below:

Hence, the correct answer is "Option 1".

The least possible Venn diagram is shown below:

Conclusions:

I. No T is R. → Follows (As, No R is T)

II. No S is T. → Follows (As, All S are R and No R is T)

III. No R is S. → Does not follow (As, All S are R)

Hence, 'both conclusions I and II follows' is the correct answer.

The image embedded in given figure is as shown below:

Hence, 'option 2' is the correct answer.

When the paper is unfolded, the image we get is shown below,

Hence, the correct answer is "Option 3".

The number of quadrilaterals in the given figure is shown below:

Hence, ‘25' is the correct answer.

The logic followed here is:

Logic: Second Number = (First Number)2

Third Number = (Second Number × 3) 64

(6, 36, 108):

→ 36 = (6)2

→ 108 = 36 × 3

(7, 49, 147):

→ 49 = (7)²

→ 147 = 49 × 3

Let's check each option as per the logic,

1) (8, 64, 96):

→ 64 = (8)²

→ 96 ≠ 64 × 3

2) (8, 32, 64):

→ 32 ≠ (8)²

3) (4, 16, 48):

→ 16 = (4)²

→ 48 = 16 × 3 ⇒ Follow the logic.

4) (4, 16, 64):

→ 16 = (4)²

→ 64 ≠ 16 × 3

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

Hence, the correct answer is "(4, 16, 48)".

The logic followed here is:

Logic: The pair "Arena : Wrestling" represents a place where an activity is performed, namely, wrestling is done in an arena.

Let's check each option as per the logic,

1) Pitch : Exercise

→ Pitch is associated with cricket, not specifically exercise.

2) Athletics : Stadium

→ The order is reversed, so this doesn't match.

3) Tennis : Court

→ The order is reversed, so this doesn't match.

4) Rink : Skating

→ Skating is done in a rink, so this matches the logic.

Here, we can see that only Option 4 follow the logic.

Hence, the correct answer is "Rink : Skating".

The logic followed here is:

Logic: The terms are the cubes of the consecutive numbers starting from 9 in the reversed order.

Hence, the correct answer is "125".

The logic followed here is:

1. IHEW → I - 1 = H; H - 3 = E; E ⇔ V ≠ W 2. ONKP → O - 1 = N; N - 3 = K; K ⇔ P  3. EDAZ → E - 1 = D; D - 3 = A; A ⇔ Z  4. YXUF → Y - 1 = X; X - 3 = U; U ⇔ F

Hence, 'IHEW' is the correct answer.

The code for each letter is shown below:

Code for:

O is 9

S and N is 0 or 6

Clearly, the code for SON is 906.

Hence, ‘906’ is the correct answer.

The logic followed here is:

Logic: The line with square box attached is rotating 135º in clockwise direction.

→ The figure attached with the other line is changing after two terms and rotating 45º in anti - clockwise direction.

The next term of the series:

Hence, the correct answer is "Option 4".

The logic followed here is:

Logic: First number + 235 = Second number

• 391 : 626 → 391 + 235 = 626
• 173 : 408 → 173 + 235 = 408

Similarly,

• 426 : ? → 426 + 235 = 661

Hence, '661' is the correct answer.

Given sequence: p _ nj _ c _ r _ jlcp _ njl _ pr _ _ lc

1. rlpnrcnj → p r nj l c / p r n jlc / p r njl c / pr n j lc 2. rppnrcnj → p r nj p c / p r n jlc / p r njl c / pr n j lc 3. rllnrcnj → p r nj l c / l r n jlc / p r njl c / pr n j lc 4. rlprncnj → p r nj l c / p r r jlc / p n njl c / pr n j lc

• In option 1, 'prnjlc' is repeated.

Hence, ‘rlpnrcnj’ is the correct answer.

The image embedded in given figure is as shown below:

Hence, 'option 1' is the correct answer.

By using the symbols in the table given below, we can draw the following family tree:

Pointing towards a man, Parkhi said, “He is the brother of my son’s mother” → My son's mother is Parkhi herself.

brother of my son’s mother → The man is brother of Parkhi.

Clearly, Husband of Parkhi is brother-in-law of the man.

Hence, ‘Brother in law’ is the correct answer.

The correct order as per the dictionary is:

2. Superintend

3. Superpose

4. Superstition

5. Supervene

4) Supervise

Here, we can see that the word at the fifth position is Supervise.

Hence, the correct answer is "Supervise".

The logic followed here is:

Logic: The first word is the capital city of the second word which is a country.

Tokyo : Japan

→ Tokyo is the capital city of Japan.

Similarly,

Paris : ?

→ Paris is the capital city of France.

Hence, the correct answer is "France".

Additional Information Capital of other Countries mentioned are as follows:

• Ireland - Dublin
• Italy - Rome
• Switzerland - Bern

Number of tablets that are only car is shown below:

Hence, ‘8’ is the correct answer.

The correct answer is Southern and southeastern states are important for the production of wheat and other rabi crops.

Key Points

• Punjab, Haryana, Uttar Pradesh, and Madhya Pradesh, are major contributors to the production of wheat, barley, and other rabi crops. Hence Option 1 is incorrect.
• These regions have favorable climatic conditions and fertile soil, making them suitable for the cultivation of rabi crops.
• Wheat is one of the most important rabi crops grown in these states, and they significantly contribute to the overall wheat production in the country.
• Other rabi crops like barley, peas, gram, and mustard are also cultivated in these regions.

Additional Information

• Kharif crops
• Kharif Crops are planted at the onset of the South-West monsoon, primarily in India, Pakistan, and Bangladesh, during the rainy season.
• The sowing of these crops takes place between the months of June and July.
• Upon reaching maturity, typically in October, these crops are harvested in the Autumn season.
• Examples of Kharif crops include rice, cotton, corn, sugarcane, turmeric, pigeon pea, and more.
• Zaid crops
• Zaid Crops are grown during the summer season in regions with a tropical climate.
• These crops are typically cultivated between the months of March and June.
• Zaid crops are known for their quick growth and shorter duration compared to Kharif and Rabi crops.
• Examples of Zaid crops include cucumber, watermelon, bitter gourd and cowpea.
• These crops are often irrigated using modern techniques and are harvested before the onset of the monsoon season.

The correct answer is Both I and II.

Key Points

• "Sawar" refers to a cavalry soldier mounted on a horse.
• The East India Company army did have cavalry units composed of soldiers on horseback. Hence Statement I is correct.
• The musket was a widely used firearm during the time of the East India Company.
• It was a heavy gun typically carried and operated by infantry soldiers. ***Hence Statement II is also correct.*​

Additional Information

• The East India Company was an English, and later British, joint-stock company founded in 1600.
• It was formed to trade in the Indian Ocean region, initially with the East Indies, and later with East Asia.
• In 1600, a group of English businessmen asked Elizabeth I for a royal charter that would let their voyage to the East Indies on behalf of the crown in exchange for a monopoly on trade.
• The merchants put up nearly 70,000 pounds of their own money to finance the venture, and the East India Company was born.

The correct answer is Factories.

Key Points

• The seventh schedule of the Indian constitution deals with the division of powers between the central government and the state governments through three lists: the Union List, the State List, and the Concurrent List.
• The Concurrent List consists of subjects on which both the central government and state governments have the power to legislate, such as criminal law, marriage and divorce, bankruptcy and insolvency, factories, education, forests, and more. Hence option c is correct.
• Both the central and state governments can make laws, regulate, and govern the subjects mentioned in the Concurrent List simultaneously, subject to certain limitations and guidelines.
• In case of a conflict between central and state laws on Concurrent List subjects, the law made by the central government prevails, provided it receives the President's assent.
• Any amendment to the Concurrent List requires the approval of the Parliament, and state legislatures can also make laws on these subjects unless they conflict with existing central laws.

Additional Information

• Union List:
• The Union List consists of around 100 items over which the central government has exclusive legislative authority, including defence, foreign affairs, atomic energy, banking, and telecommunications.
• The central government has the power to make laws, regulate, and govern the subjects mentioned in the Union List uniformly across all states and union territories in India.
• Items in the Union List ensure the central government's authority in critical areas such as national security, inter-state trade and commerce, currency, copyright, air and water pollution, and more.
• Any amendment to the Union List requires the approval of the Parliament through a prescribed legislative process, ensuring that changes to these subjects are made at the national level.
• State List:
• The State List consists of subjects over which state governments have exclusive legislative authority, including public order, police, public health, local government, agriculture, state taxation, and more.
• State governments exercise their legislative and executive powers to make laws, regulate, and govern the subjects mentioned in the State List within their respective states.
• Subjects in the State List allow state governments to address regional and local concerns, implement policies specific to their states, and ensure effective governance at the state level.
• Any amendment to the State List requires the approval of the state legislature concerned and does not require the consent of the Parliament, providing states with autonomy in making changes to these subjects.

The correct answer is M.S. Sahoo.

Key Points

• As on 1^st November 2022, the chairperson of SEBI’s Market Data Advisory Committee (MDAC) was M S Sahoo,
• He is the professor at National Law University, Delhi and former chairperson of Insolvency and Bankruptcy Board of India (IBBI).
• MDAC stands for Market Data Advisory Committee.
• It is a standing committee constituted by SEBI to recommend appropriate policy for access to securities market data, identify segment-wise data perimeters, data needs and gaps, and recommend data privacy and data access regulations applicable to market data.

Additional InformationSEBI

• SEBI stands for Securities and Exchange Board of India.
• The headquarters of SEBI is situated in Mumbai. The regional offices of SEBI are located in Ahmedabad, Kolkata, Chennai, and Delhi.
• It is a statutory regulatory body established by the Government of India in 1992 to protect the interests of investors investing in securities and to regulate the securities market.
• SEBI also regulates how the stock market and mutual funds function.

The correct answer is Cobalt.

Key Points

• Cobalt-60, an isotope of cobalt, is commonly used in the treatment of cancer.
• It emits high-energy gamma rays, which can penetrate tissues and destroy cancer cells.
• Cobalt-60 has a relatively long half-life of 5.27 years, which means it remains radioactive for a significant period.
• This makes it suitable for long-term treatment and allows for the production and distribution of radioactive sources to medical facilities.

Additional Information

• Aluminum
• Aluminum compounds are sometimes used in antacids to help neutralize stomach acid and provide relief from heartburn or indigestion.
• Additionally, aluminum-based adjuvants are commonly used in vaccines to enhance the body's immune response to the vaccine.
• Nickel
• It is sometimes used in medical implants and devices, such as orthopedic implants or dental materials.
• However, it's important to note that some individuals may have an allergic reaction to nickel, so its use in medical devices is carefully considered.
• Iron
• It is an essential mineral for the human body and is involved in various physiological processes.
• Iron supplements are commonly prescribed to individuals with iron deficiency or anemia.
• Iron is necessary for the production of red blood cells, and supplements can help restore iron levels in the body.

The correct answer is 200.

Key Points

• India has 13 major ports and more than 200 notified minor and intermediate ports.
• Minor ports are managed by the state government whereas Major ports are managed by the central government.
• Minor ports Handle coastal and fishing trade.

 Additional Information

• 13 Major Ports of India-
• There are 12 government ports and 1 corporate port.

The correct answer is Kriti Sanon.

Key Points

• IIFA Awards:
• The NEXA IIFA Awards, also known as the International Indian Film Academy Awards, is an annual event that celebrates the achievements and excellence in Indian cinema.
• The awards were initiated by the International Indian Film Academy (IIFA) in the year 2000.
• The first NEXA IIFA Awards ceremony took place in London, United Kingdom, and was aimed at promoting Indian films internationally.
• The main award categories, the NEXA IIFA Awards also include special awards and recognition for various aspects of filmmaking, such as Best Director, Best Actor, Best Actress, Best Music Director, and many more.
• The NEXA IIFA Awards continue to evolve each year, with new themes, concepts, and innovations, contributing to the promotion and growth of Indian cinema worldwide.

Important Points

• NEXA International Indian Film Academy Awards 2022:
• Best Actor (Male): Vicky Kaushal (Sardar Udham)
• Best Actor (Female): Kriti Sanon (Mimi)
• Best Director: Vishnuvaradhan  (Shershaah)
• Best Film:  Shershaah
• Best Playback Singer Female: Asees Kaur for ‘Raataan Lambiyan’, (Shershaah)
• Best Playback Singer Male: Jubin Nautiyal for song ‘Raataan Lambiyan’, (Shershaah)
• Best Lyrics: Kausar Munir for ‘Lehra Do’, 83
• Best Music Direction: A R Rahman for Atrangi Re and Jasleen Royal, Javed-Mohsin, Vikram Montrose, B Praak, Jaani for Shershaah
• Best Male Debut: Ahan Shetty  (Tadap)
• Best Female Debut: Sharvari Wagh (Bunty Aur Babli 2)
• Best Story Adapted: Kabir Khan, Sanjay Puran Singh Chauhan for 83
• Best Original Story: Ludo by Anurag Basu
• Best Supporting Actor Female: Sai Tamhankar (Mimi)
• Best Supporting Actor Male: Pankaj Tripathi (Ludo)

The correct answer is Abhilasha Barak.

Key Points

• Captain Abhilasha Barak has created history by becoming the first woman officer to join the Army Aviation Corps as Combat Aviator.
• Captain Barak's achievement has been described as a "Golden Letter Day" in the history of Indian Army Aviation.
• She was awarded the coveted wings along with 36 other army pilots during a ceremony held at the Combat Army Aviation Training School in Nashik.
• Abhilasha Barak hails from Haryana, India.

Important Points

• India's 1^st woman Rafale fighter jet pilot Shivangi Singh was part of the Indian Air Force tableau at the Republic Day Parade 2022.
• She is only the 2^nd woman fighter jet pilot to be part of the IAF tableau.
• In 2021, Flight Lieutenant Bhawna Kanth became the first female fighter jet pilot to be part of the IAF tableau.
• The IAF tableau's theme- 'Indian Air Force transforming for the future'.
• Avani Chaturvedi is one of the three first three Indian female fighter pilots who received the 'Nari Shakti Puraskar 2019'  on 8^th March 2020.
• The President of India presented the prize to Avani Chaturvedi along with Mohana Jitarwa and Bhawna Kanth.
• The trio was inducted into the IAF's fighter squadron after the Government of India decided to open a fighter stream in the force for women on an experimental basis.
• The three were the first to be inducted into the squadron and conduct a solo flight in MIG-21 in 2018.

The correct answer is three.

Key Points

• Raja Parba (Mithuna Sankranti)-
• Raja Parba, also known as Mithuna Sankranti, is a cultural festival celebrated in the Indian state of Odisha.
• It marks the onset of the agricultural season and is observed during the mid-June period, coinciding with the solar transition of the zodiac sign Gemini (Mithuna).
• It is a three-day-long festival celebrating womanhood.
• 2^nd day of the festival marks the beginning of the solar month of Mithuna, on which the season of rains starts.
• It is believed that Mother Goddess Earth undergoes menstruation during the first three days.
• 4^th day is called Vasumati Snana.
• Folk songs and dance performances, especially the "Dalkhai" dance, are an integral part of the Raja Parba celebrations.
• The festival signifies the importance of nature, agriculture, and the vitality of women in Odisha's culture and tradition

Additional Information

• Other Important festivals of Odisha:

The correct answer is Both I and II 

Key Points

• Newton's first law of motion 
• States that "An object at rest stays at rest and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force."
• Objects tend to "keep on doing what they're doing."
• In fact, it is the natural tendency of objects to resist changes in their state of motion.
• This tendency to resist changes in their state of motion is described as inertia.

​(Hence statement I is correct)

• Inertia:
• The resistance an object has to a change in its state of motion.
• All objects resist changes in their state of motion. All objects have this tendency - they have inertia.
• The tendency of an object to resist changes in its state of motion varies with mass.

​((Hence statement II is correct))

• Mass is that quantity that is solely dependent upon the inertia of an object.
• The more inertia that an object has, the more mass that it has.
• A more massive object has a greater tendency to resist changes in its state of motion.

Additional Information

• Laws of motion:

The correct answer is 45.

Key Points

• About Khelo India Programme:
• Khelo India was formed by merging three schemes: Rajiv Gandhi Khel Abhiyan, Urban Sports Infrastructure Scheme, and National Sports Talent Search Scheme.
• It works to promote "Sports for All" and "Sports for Excellence".
• Its aim is the mass participation of youth in annual sports competitions through a structured competition.
• Khelo India Youth Games 2021:-
• The 4^th edition of the Khelo India Youth Games was held in Haryana.
• The Games were held in Panchkula.
• Gatka, Kalaripayattu, Thang-Ta, and Mallakhamba, four indigenous games were added in December 2020.
• This was announced by Sports Minister Kiren Rijiju and Haryana Chief Minister Manohar Lal Khattar.
• Usually, the Khelo India Youth Games take place in January every year.
• Haryana came second in both Khelo India Youth Games 2019 and 2020 editions (200 medals in 2020 and 159 medals in 2019).
• The Haryana government decided to organize the Khelo India Youth Games in February 2022, in view of the possible third wave of the Covid-19 pandemic.

Additional Information Fifth Edition of Khelo India Youth Games:-

• Khelo India Youth Games 2022 was organized in 8 cities of Madhya Pradesh from 31 January to 11 February 2023.
• These were organized in Madhya Pradesh's Bhopal, Balaghat, Mandla, Maheshwar, Jabalpur, Ujjain, Gwalior and ,Indore.
• There were a total of 28 sports in this game.
• This time, break dance and Malkhamb was also been included in the games.
• The Khelo India Youth Games were started on 31 January 2018 at the Indira Gandhi Indoor Stadium in New Delhi.

5^th Khelo India games medal tally-

The correct answer is Coromandel Coast.

Key Points

• The Coromandel Coast is located on the eastern coast of India.
• It is the coastal plain in eastern Tamil Nadu state.
• It is bounded by the Utkal Plains to the north, the Bay of Bengal to the east, the Kaveri Delta to the south, and the Eastern Ghats to the west.
• Extending over an area of about 22,800 square kilometres.

 Important Points

• Eastern Coastal Plains of India-
• The eastern coastal plains stretch from West Bengal in the north to Tamil Nadu in the south and pass through Andhra Pradesh and Odisha.
• The Eastern coast is again divided into three categories:
• Utkal coast- Extending between the Chilika Lake and Kolleru Lake, they are much wider than the western coastal plains and undergo immense rainfall.
• Andhra coast- Extending between the Kolleru Lake and Pulicat Lake, the Andra coast forms a basin area for the Krishna and the Godavari rivers.
• Coromandel coast- The Coromandel coast extends between Pulicat Lake and Kanyakumari in Tamil Nadu.
• This Indian coastline remains dry in summer and receives rainfall during the winters due to the northeast monsoons.
• Western Coastal Plains of India-
• Western Coastal Plains stretches from Kerala in the south to Gujarat in the north passing through Karnataka, Goa and Maharashtra.
• The western coast is further divided into four categories:
• Kachchh and Kathiawar coast- Kachchh, formerly a gulf is formed by the deposition of silt by the Indus. Kathiawar is situated to the south of Kachchh.
• Konkan coast-  It extends between Daman in the north to Goa in the south.
• Rice and cashew are the two important crops of this region.
• Kannada coast- It extends between Marmagaon and Mangalore and is rich in iron deposits.
• Malabar coast- Extending between Mangalore to Kanyakumari, the Malabar coast is relatively broad.
• This region also consists of lagoons running parallel to the coast in southern Kerala.

The correct answer is the Output unit.

Key Points

• The central processing unit (CPU) is the core of a computer system and consists of the arithmetic logic unit (ALU) and the control unit and registers.
• The output unit is not a part of the CPU.

(Therefore option 4 -Output unit is the correct answer)**

• A central processing unit (CPU), is also called a central processor, main processor, or just processor.
• It is the electronic circuitry that executes instructions comprising a computer program.
• The CPU performs basic arithmetic, logic, controlling, and input/output (I/O) operations specified by the instructions in the program.
• This contrasts with external components such as main memory and I/O circuitry, and specialized processors such as graphics processing units.

Additional InformationThe principal components of a CPU include:

• Control Unit:
• A control unit that orchestrates the fetching (from memory) and execution of instructions by directing the coordinated operations of the ALU, registers and other components.
• The control unit (CU) is a component of a computer's central processing unit (CPU) that directs the operation of the processor.
• It tells the computer's memory, arithmetic logic unit and input and output devices how to respond to the instructions that have been sent to the processor.
• ALU (arithmetic logic unit)-
• The arithmetic logic unit (ALU) performs arithmetic and logic operations.
• In computing, an arithmetic logic unit is a combination digital circuit that performs arithmetic and bitwise operations on integer binary numbers.
• This is in contrast to a floating-point unit, which operates on floating-point numbers.
• Registers:
• Processor registers that supply operands to the ALU and store the results of ALU operations.
• A processor register is a quickly accessible location available to a computer's processor.
• Registers usually consist of a small amount of fast storage, although some registers have specific hardware functions, and may be read-only or write-only.

The correct answer is Acute.

Key Points

• Acute diseases
• Some diseases last for only very short periods of time, and these are called acute diseases.
• These diseases occur suddenly and last for a shorter time period.
• Acute disease causes sudden damage to the body.
• Examples of some Acute diseases are Typhoid, bone fracture, heart attack, cholera, common cold, jaundice, malaria, etc.

Important Points

• Diseases are mainly two types based on the duration of time which are Acute and chronic diseases.
• Chronic diseases
• The diseases that occur over a period of time and last a longer duration of time, or even for a lifetime are called chronic diseases.
• These diseases progress gradually and usually end up causing long-term damage to organs and internal systems. sometimes chronic diseases become fatal and cause loss of life.
• Examples of Chronic diseases are Diabetes, cancer, tuberculosis, arthritis, etc.

Additional Information

• Genetic or hereditary diseases
• A hereditary disease is often described as something that “runs in the family.”
• It is passed down from one or both parents to a child, who may then pass it to his or her children.
• Examples of hereditary disorders are: Thalassemia, Haemophilia, Sickle-cell anaemia

The correct answer is 1999

Key Points

• ​The Insurance Regulatory and Development Authority of India (IRDAI), is a statutory body formed under an Act of Parliament, i.e., the Insurance Regulatory and Development Authority Act, 1999 (IRDAI Act 1999)
• It was founded in 1999.
• It is founded for the overall supervision and development of the Insurance sector in India.
• The body was created on the recommendations of the Malhotra Committee Report.
• Its headquarter is located in Hyderabad.
• It regulates under the Ministry Of Finance.
• Debasish Panda is the chairperson of IRDAI.

Important Points

• Organisational Setup:
• A Chairman
• Five whole-time members
• Four part-time members
• All the members of the Insurance Regulatory and Development Authority of India are appointed by the Government of India.

The correct answer is Wular.

Key Points 

• Wular Lake is the largest freshwater lake in India and lies in the Kashmir Valley.
• Wular Lake is also one of the largest freshwater lakes in Asia.
• It is sited in the Bandipora district in Jammu and Kashmir, India.
• The lake basin was formed as a result of tectonic activity and is fed by the Jhelum River.
• The lake's size varies seasonally from 12 to 100 square miles.
• Wular Lake is important to fish habitat, the main species being the common carp, rosy barb, mosquitofish, Nemacheilus species, etc.

Additional InformationLoktak Lake-

• Loktak Lake is the largest freshwater lake in North East India and is famous for the phumdis (heterogeneous mass of vegetation, soil and organic matter at various stages of decomposition) floating over it.
• The lake is located at Moirang in Manipur state, India.
• Loktak Day is observed every year on the 15^th of October at the periphery of the Loktak lake.
• This ancient lake plays an important role in the economy of Manipur. It serves as a source of water for hydropower generation, irrigation and drinking water supply.
• The lake is also a source of livelihood for the rural fishermen who live in the surrounding areas and on phumdis, also known as phumshongs.

Bhimtal Lake-

• One of the well-known lake cities in the Kumaon region (Uttarakhand) is Bhimtal.
• In honor of the well-known Mahabharata character Bheem, Bhimtal was formerly called "Bheemsarovar Lake."
• According to mythology, the Pandavas used to travel back to Bhimtal during their exile to visit their home.
• As a result, the Bhimeshwar Mahadev temple was built here in honor of Bheema.

Barapani Lake-

• Barapani Lake is situated in  Meghalaya.
• Barapani Lake is also known as Umiam Lake.
• It is an artificial water reservoir created by damming the Umiam river.

The correct answer is 4G.

Key Points

• In Telecommunications, LTE Technology stands for Long-Term Evolution.
• LTE is a standard for wireless broadband communication and is the primary technology used in 4G networks.
• It provides faster data transfer rates, lower latency, and improved spectral efficiency compared to previous generations.
• It allows us to download many things such as music, videos, websites etc.
• It is known for being developed by the 3GPP.
• 4G has the more stability and faster speed when compares to the LTE.
• It is because LTE is a half point between 3G and 4G.
• Its capability is 3.95G which has been marketed as 4G LTE.

Additional Information3G (Third Generation):

• 3G refers to the third generation of wireless technology.
• Common 3G technologies include UMTS (Universal Mobile Telecommunications System) and CDMA2000 (Code Division Multiple Access 2000).
• 3G networks provided faster data speeds compared to 2G but were slower than 4G.

2G (Second Generation):

• 2G refers to the second generation of wireless technology.
• Common 2G technologies include GSM (Global System for Mobile Communications) and CDMA (Code Division Multiple Access).
• 2G networks primarily focused on voice calls and provided limited data capabilities.

1G (First Generation):

• 1G refers to the first generation of wireless technology.
• 1G networks were analog-based and primarily supported voice calls.
• 1G networks had limited data capabilities and slower transmission speeds compared to subsequent generations.

The correct answer is Both I and II.

Key Points

• Macroeconomics is a branch of economics that deals with the structure, performance, and behaviour of the overall economy.
• It focuses on areas like inflation, economic growth rate, price levels of various goods and services, gross domestic product (GDP), national income and the unemployment rate in a particular country.
• The study of macroeconomics is essential to understand the economic performance of a nation and the factors that affect it.

Important Points

• Macroeconomics deals with the following studies:
• Reasons behind the unemployment of resources: 
• Macroeconomics focuses on understanding and analyzing the factors that contribute to unemployment on a broader scale.
• It examines the causes and consequences of unemployment, such as changes in aggregate demand, labour market conditions, technological advancements, and government policies that affect employment levels.
• Determination of total output: 
• Macroeconomics is concerned with studying and explaining the determinants of a country's total output or national income.
• It analyzes the factors that influence aggregate production and economic growth, including consumption, investment, government spending, and net exports.
• Macroeconomists investigate the relationship between these variables and their impact on overall economic performance.

Additional Information

• John Maynard Keynes is known as the founding father of Macroeconomics as a separate discipline.
• He was born on June 5, 1883, in Cambridge.
• He completed his degree in Mathematics and also joined Civil Services in Britain.
• He represented the British Treasury at the Conference of Versailles.
• He expressed his concerns about the fine imposed on Germany in his book 'The Economic Consequences of Peace'.

The correct answer is New Zealand.

Key Points

• The final of the ICC World Test Championship between India and New Zealand will be played in a bio-secure bubble at the Hampshire Bowl in Southampton, England.
• It started on 1 August 2019 with the first Test of the 2019 Ashes series and finished with the Final at the Rose Bowl, Southampton in June 2021.
• New Zealand won the ICC Test Championship mace for the first time and was also awarded the cash prize of US$1.6 million, while India won US$800,0.
• The Captain of New Zealand is Kane Williamson. (As of 2023)
• The ICC World Test Championship is an international cricket competition organized by the International Cricket Council (ICC) for the ten test cricket-playing nations.

Important Points

• International Cricket Council
• It is the world governing body of cricket.
• It was founded as the Imperial Cricket Conference in 1909.
• It was founded by representatives from Australia, England, and South Africa.
• It was renamed the International Cricket Conference in 1965.
• It took its current name in 1987.
• Headquarters of ICC: Dubai, UAE.

The correct answer is VVS Laxman.

Key Points

• A stylish batsman who could score against any kind of bowling, VVS Laxman played over a hundred Tests to aggregate more than 8,000 runs.
• Cricket fans still remember with awe his game-changing knock of 281 against Australia in 2001 at Eden Gardens.
• Vangipurapu Venkata Sai Laxman is a former Indian international cricketer and a former cricket commentator and pundit.
• A right-hand batsman known for his elegant stroke play, Laxman played as a middle-order batsman in Test cricket.
• He was born on 1 November 1974.
• Book: 281 AND BEYOND Author: VVS Laxman with R Kaushik Publisher: Westland Sport.

Additional Information

• The Test of My Life is the biography of Yuvraj Singh.
• Playing It My Way is the autobiography of Sachin Tendulkar.
• Muhammad Ali is a boxer. His book's name is ''His Life and Times".
• **Suresh Raina'**s autobiography, titled "Believe – What Life and Cricket Taught Me"
• Virat Kohli : Driven: The Virat Kohli Story

The correct answer is Option 2. 

Key Points

• The Citizenship Act was first passed in India in the year 1955.
• The original Citizenship Act of 1955 laid down the framework for Indian citizenship and defined the various ways in which a person could acquire or lose citizenship in India.
• Since its enactment, the act has undergone several amendments to accommodate changes and evolving perspectives on citizenship.

Additional Information

• There are four main ways through which an individual can acquire Indian citizenship:
• By Birth: A person born in India on or after January 26, 1950, is considered an Indian citizen by birth, with a few exceptions.
• By Descent: Individuals born outside India on or after January 26, 1950, but have at least one Indian parent, are eligible for Indian citizenship by descent.
• By Registration: Certain categories of people, such as individuals of Indian origin residing outside India, can acquire Indian citizenship through registration by fulfilling specific criteria.
• By Naturalization: Foreigners who have resided in India for a specified period of time and meet other qualifications can apply for Indian citizenship through naturalization.

The correct answer is Option 2. 

Key Points

• The Indian Independence Act of 1947 partitioned British India into two separate dominions, India and Pakistan, based on religious lines.
• The act facilitated the transfer of power from British colonial rule to the newly formed governments of India and Pakistan.
• It granted full legislative authority to India and Pakistan, establishing them as independent and sovereign nations.
• The partition resulted in widespread communal violence and riots between religious communities, leading to a significant loss of life and displacement of people.
• The act allowed princely states to choose between joining India, joining Pakistan, or remaining independent, leaving the decision to the rulers of these states.

Additional Information

• The Rowlatt Act, also known as the Anarchical and Revolutionary Crimes Act of 1919, was a legislative act passed by the British colonial government in India during the period of British rule.
• It was named after its sponsor, Sir Sidney Rowlatt, who was a British judge.
• The Government of India Act refers to several legislative acts passed by the British Parliament during the period of British rule in India.
• These acts were intended to regulate and govern the administration of British India.
• ​Pitt's India Act, officially known as the East India Company Act 1784, was an important piece of legislation passed by the British Parliament under the leadership of Prime Minister William Pitt the Younger.
• The act was designed to bring about significant reforms in the governance and administration of the British East India Company's territories in India.

The correct answer is Option 1. 

Key Points

• Australian tennis player Ashleigh Barty defeated American Danielle Collins to win the Australian Open women's title on 29 January 2022.
• Barty is the first Australian player to win the Australian Open singles championship since 1978.
• She won the French Open in 2019 and Wimbledon in 2021 and has been the no.1 ranked female player in the world for over 100 weeks.

Additional Information

• Spain's Rafael Nadal won the Australian Open Men's Singles final on 30 January 2022.
• With this victory, Rafael has become the first man to win 21 Grand Slam titles.
• He overtook Roger Federer and Novak Djokovic by winning this title.
• In tennis, Aslan Karatsev won the men’s singles title at the Sydney Tennis Classic final, to claim his third ATP Tour title.
• World number six Rafael Nadal won the men’s singles tennis title at the 2022 Melbourne Summer Set 1.
• French tennis player Gael Monfils has won the men’s singles event of the 2022 Adelaide International 1 to claim the 11^th ATP title of his career.
• The Davis Cup 2021 was won by the Russian Tennis Federation with a 2-0 lead over Croatia in the Davis Cup final in Madrid.
• Alexander “Sascha” Zverev has won the fifth ATP title of the season (2021) and 18^th overall at the Vienna Open 2021.

The correct answer is Option 3. 

Key Points

• Birju Maharaj was a noted dancer of Kathak.
• Kathak is one of the major classical dance forms of India and is characterized by intricate footwork, graceful movements, storytelling, and expressive facial expressions.
• Birju Maharaj, whose full name is Pandit Birju Maharaj, is a highly acclaimed Kathak dancer, choreographer, and guru (teacher) who has made significant contributions to the art form.
• He comes from a long lineage of Kathak dancers and has achieved international recognition for his mastery and innovative approach to Kathak dance.

Additional Information

• Bharatanatyam is a classical Indian dance form that originated in the state of Tamil Nadu, characterized by intricate footwork, expressive gestures, rhythmic movements, and storytelling.
• Manipuri is a classical Indian dance form from the northeastern state of Manipur, known for its graceful movements, fluid body postures, use of intricate hand gestures, and vibrant costumes.
• Sattriya is a classical Indian dance form from the state of Assam, characterized by its devotional themes, rhythmic footwork, graceful movements, and rich cultural heritage.

The correct answer is Option 1. 

Key Points

• Amir Khusro was a prominent poet, musician, and scholar who lived in the 13^th century.
• He is often referred to as "Tuti-e-Hind" or "The parrot of India" due to his exceptional talent and mastery in various fields, including poetry, music, and language.

Additional Information

• Lata Mangeshkar was a renowned Indian playback singer known for her melodious voice and contributions to the Hindi film industry.
• Pandit Ravi Shankar was a virtuoso sitar player and composer who popularized Indian classical music worldwide.
• Kalidas was a famous classical Sanskrit poet and playwright in ancient India.

Given:

Rajiv sells a pen at a profit of 5 percent.

He sells the pen for Rs. 36 more, then he earns a profit of 14 percent.

Concept Used:

Cost Price = Selling Price × 100/(100 + Profit%)

Calculation:

Let the CP of a pen = Rs. x

Profit = 5%

SP = Rs. 1.05x

According to question

1.05x + 36 = 1.14x

1.14x - 1.05x = 36

.09x = 36

x = Rs. 400

∴ CP of a pen = Rs. 400

∴ Option 4 is the correct answer.

Given

tan 10° tan 25° tan 45° tan 65° tan 80° 

Concept used

Tan (90 - θ) = cotθ 

Calculation

⇒ tan (90 - 10) × tan (90 - 65) × tan 45° × tan 65° × tan 80° 

⇒ cot 80° × cot 65° × 1 × tan 65° × tan 80° 

∴ Ans = 1

Given:

x4 + 1/x4 = 16

Formula:

(a2 + b2) = (a + b)2 - 2ab

Calculation:

(x² + 1/x²)² = x4 + 1/x4 + 2 × x² × 1/x²

⇒ (x2 + 1/x2)2 = 16 + 2

⇒ (x2 + 1/x2)2 = 18

⇒ (x2 + 1/x2) = √18 = 3√2

∴ The correct answer is option (2).

Calculation:

J1 = The value of average cost price of A, B, C and D = (300 + 250 + 150 + 200)/4

900/4 = 225

J2 = The total profit of all articles = 50 + 25 + 100 + 150 + 75 + 125 = 525

The value of (J1 ∶ J2) = 225 : 525

3 : 7

∴ Option 4 is the correct answer.

Given:

Piyush marks the price more than the cost price by = 30%

Discount = 20%

Selling price of the article = Rs. 5720

Formula:

SP = MP × [(100 – Discount%)/100]

Calculation:

MP of the article = 5720 × 100/80

∴ Cost price of the article = 5720 × 100/80 × 100/130 = Rs. 5500

∴ Option 4 is the correct answer.

Shortcut Trick

Direct formula for the height (distance) of a trapezium:

Height = (2 × Area) ÷ (Sum of parallel sides)

Height = (2 × 875) ÷ (21 + 14)

Height = 1750 ÷ 35 = 50 cm

∴ The correct answer is 50 cm.

Alternate Method

Given:

Parallel side 1 (a) = 21 cm

Parallel side 2 (b) = 14 cm

Area of trapezium = 875 cm²

Formula Used:

Area of Trapezium = 1/2 × (Sum of parallel sides) × Height

Calculations:

⇒ 875 = 1/2 × (21 + 14) × h

⇒ 875 = 1/2 × 35 × h

⇒ 875 = 17.5 × h

⇒ h = 875 ÷ 17.5

⇒ h = 50 cm

∴ The correct answer is 50 cm.

Additional Information

Properties of a Trapezium

A trapezium is a quadrilateral with at least one pair of parallel sides. The height is the perpendicular distance between these parallel lines.

Median of a Trapezium

The length of the median (the segment connecting the midpoints of the non-parallel sides) is the average of the two bases: Median = (a + b) ÷ 2.

Isosceles Trapezium

In an isosceles trapezium, the non-parallel sides are equal in length, and the base angles are equal.

Calculation:

We need to find the value of (J1 ∶ J2), where:

J1 is the total number of male and female teachers in school P.

J2 is the difference between the total number of male and the total number of female teachers in all 5 schools.

J1 = Total number of male and female teachers in school P

J1 = Sum of Male + Sum of Female

J1 = 80 + 60 = 140

J1 = 140

J2 = Difference between the total number of male and the total number of female teachers in all the 5 schools

J2 = Sum of Male - Sum of Female

J2 =(60 + 80 + 70 + 50 + 30) -  (80 + 70 + 20 + 10 + 30)

J2 = 290 - 210

J2 =  80

140 ∶ 80.

7 : 4

Therefore, the value of (J1 ∶ J2) is ​7 : 4

Given:

$\rm \frac{7\ of\ 14\div 4}{5\times4\div 2}+\frac{6\div12\times 3}{5\div25\times 2}+\frac{15\div5\times6}{5\times 15\div6}?$

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

$\rm \frac{7\ of\ 14\div 4}{5\times4\div 2}+\frac{6\div12\times 3}{5\div25\times 2}+\frac{15\div5\times6}{5\times 15\div6}$

$\rm \frac{24.5}{10}+\frac{1.5}{0.4}+\frac{18}{12.5}$

2.45 + 3.75 + 1.44

7.64

∴ Option 1 is the correct answer.

Given:

The ratio of the present age of two girls is 3 ∶ 4.

After two year the ratio will be 7 ∶ 9.

Calculation:

Let the present age of two girls be 3x and 4x.

Acc to question,

(3x + 2)/(4x + 2) = 7/9

27x + 18 = 28x + 14

x = 4

Present ages of girls = 12 and 16

I. After 10 years their ages will be 22 and 26.

Ratio = 11 : 13

Statement is wrong

II. After 12 years their ages will be 24 and 28

Ratio = 6 : 7

Statement II is correct.

∴ Option 1 is the correct answer.

Given:

ABCD is a cyclic quadrilateral.

∠B is opposite to ∠D.

∠B and ∠D are x + 10 and 2x + 35 respectively.

Concept Used:

In a cyclic quadrilateral, the sum of a pair of opposite angles is 180 degrees.

Calculation:

Since angle B and angle D are opposite to each other, we have:

∠B + ∠D = 180°

x + 10 + 2x + 35 = 180

Solving for x:

⇒ 3x + 45 = 180

⇒ 3x = 135

⇒ x = 45

So, the value of x is 45°.

∴ Option 4 is the correct answer.

Shortcut Trick

Let Q's expenditure be 100.

P's income = 400% of 100 = 400.

Q's income = 400 ÷ 2.5 = 160.

P's expenditure = 180% of 100 = 180.

P's savings = 400 − 180 = 220, and Q's savings = 160 − 100 = 60.

∴ The correct answer is 11 : 3.

Alternate Method

Given:

⇒ P's income (I_p) = 2.5 × Q's income (I_q)

⇒ P's expenditure (E_p) = 1.8 × Q's expenditure (E_q)

⇒ P's income (I_p) = 4 × Q's expenditure (E_q)

P

Exp: 180

Sav: 220

Income: 400

Q

Exp: 100

Sav: 60

Income: 160

Calculations:

⇒ From the first and third conditions, we equate I_p:

⇒ 2.5 × I_q = 4 × E_q

⇒ I_q = 4 ÷ 2.5 × E_q = 1.6 × E_q

⇒ Savings = Income − Expenditure

⇒ P's Savings (S_p) = I_p − E_p = 4 × E_q − 1.8 × E_q = 2.2 × E_q

⇒ Q's Savings (S_q) = I_q − E_q = 1.6 × E_q − E_q = 0.6 × E_q

⇒ Ratio of S_p to S_q = 2.2 × E_q : 0.6 × E_q

⇒ Ratio = 22 : 6 = 11 : 3

∴ The correct answer is 11 : 3.

Additional Information

Income, Expenditure & Savings

Income = Expenditure + Savings. Any increase in Income will be reflected as an increase in either Expenditure or Savings or both.

Base Value in Percentages

When comparing two quantities, always check the base of the percentage. For instance, '250% of Q's income' designates Q's income as the base (100%).

Simplifying Ratios

To find the ratio of two dependent quantities, express them in terms of a single common variable to easily eliminate it during division.

Given:

$\rm \sin θ=\frac{5}{13}$

Concept Used:

cos θ = √(1 - sin² θ)

Calculation:

sin θ = 5/13

⇒ cos θ = √(1 - (5/13)²)

⇒ cos θ = √(169 - 25)/169

⇒ cos θ = √(144/169)

⇒ cos θ = 12/13

Put the values in $\rm \frac{\cos^2 \theta-\sin^2 \theta}{2\cos \theta.\sin \theta}$

⇒ $\rm \frac{(12/13)^2 -(5/13)^2}{2\times 12/13 \times 5/13}$

⇒ $\rm \frac{119/169}{120/169}$

⇒ 119/120

∴ Option 4 is the correct answer.

Given:

The perimeter of an isosceles triangle = 91 cm.

One of the equal sides measures 28 cm.

Concept used:

An isosceles triangle two angles will also be the same in front of the equal sides.

Formula used:

P = (2a + b)

Where, p = perimeter

a = side and b = another side

Calculation:

Let the length of the equal sides be x

P = (2a + b)

⇒ 91 = 2 × 28 + b

⇒ (91 – 56) = b

⇒ 35 = b

∴ The length of the non-equal side is 35 cm.

∴ Option 4 is the correct answer.

Given:

There are five prime numbers between 30 and 50

Concept Used:

Average = (Sum of the observation)/Number of observation

Calculation:

Prime numbers between 30 and 50 are 31, 37, 41, 43, and 47

⇒ Average = (Sum of the observation)/Number of observation

⇒ Average = (31 + 37 + 41 + 43 + 47)/5

⇒ 199/5

⇒ 39.8

∴ Average of all prime numbers b/w 30 and 50 is 39.8

∴ Option 2 is the correct answer.

Given:

In ΔXYZ, I is the incentre.

∠XYZ = 40

Concepts used: 

Angle formed at incentre opposite to given side = 90° +( ½ × angle opposite to given side)

Calculation:

In ΔXYZ, I is the incentre

∠XIZ = 90° + ( ½ × ∠XYZ)

⇒ ∠XIZ = 90° + ( ½ × 40)

⇒ ∠XIZ = 90° + 20°

⇒ ∠XIZ = 110° 

∴ Measure of ∠XIZ is equal to 110°.

∴ Option 2 is the correct answer.

Given:

The three sides of the triangle are 9 cm, 6 cm, and 5 cm respectively.

Formula Used:

R = abc/4A

Calculation:

Let be assume a, b, and c is the sides of the triangle.

⇒ Area of triangle = √{s(s - a) (s - b) (s - c)}

⇒ s = (a + b + c)/2 = 20/2 = 10 cm

⇒ √{10 × (10 - 9) × (10 - 6) × (10 - 5)}

A = √(200)

A = 10√2

R = (abc) / (4A)

R = (9 × 6 × 5) / (4 × 10√2)

R = (270) / (40√2)

R = (27√2/8)

Therefore, the value of the circumradius of the triangle with sides 9 cm, 6 cm, and 5 cm is (27√2/8).

Shortcut Trick

Ratio of efficiency (Work/Time) of S to T = (1/2 ÷ 1/8) : 1 = 4 : 1.

Combined efficiency = 4 + 1 = 5 units/day.

Total work = Combined efficiency × Time = 5 × 60 = 300 units.

Time taken by S alone = Total work ÷ S's efficiency = 300 ÷ 4 = 75 days.

∴ The correct answer is 75 days.

Alternate Method

Given:

Work done by S = 1/2 × Work done by T

Time taken by S = 1/8 × Time taken by T

Combined time for (S + T) = 60 days

Formula Used:

Efficiency = Work ÷ Time | Total Work = Efficiency × Time

Calculations:

⇒ Let efficiency of T = 1 unit/day.

⇒ Efficiency of S = (Work of S ÷ Time of S) = (1/2 ÷ 1/8) × Efficiency of T

⇒ Efficiency of S = (1/2 × 8) × 1 = 4 units/day.

⇒ Total efficiency of (S + T) = 4 + 1 = 5 units/day.

⇒ Total Work = Combined efficiency × Total time = 5 × 60 = 300 units.

⇒ Days taken by S alone = Total Work ÷ Efficiency of S = 300 ÷ 4 = 75 days.

∴ The correct answer is 75 days.

Additional Information

Efficiency and Time Relationship

Efficiency is inversely proportional to the time taken to complete a task. If efficiency ratio is a : b, then time ratio is b : a.

Work and Days Formula

The fundamental relation is M₁D₁E₁/W₁ = M₂D₂E₂/W₂, where M is persons, D is days, E is efficiency, and W is work.

Combined Work Rate

If A takes 'x' days and B takes 'y' days, they together take (x × y) ÷ (x + y) days to complete the work.

Shortcut Trick Given, sin α = 1/2 and sin β = 1/2. Since 0° < α, β < 90°, we know that sin 30° = 1/2. ⇒ α = 30° and β = 30° ⇒ We need to find cos (α + β) ⇒ cos (30° + 30°) = cos 60° = 1/2 ∴ The correct answer is 1/2.

Alternate Method Given: sin α = 1/2, (0° < α < 90°) sin β = 1/2, (0° < β < 90°) Formula Used: cos (α + β) = cos α × cos β − sin α × sin β sin2 θ + cos2 θ = 1

Calculations: ⇒ cos2 α = 1 − sin2 α = 1 − (1/2)2 ⇒ cos2 α = 1 − 1/4 = 3/4 ⇒ cos α = √3/2 (Since α is in the first quadrant, cos α is positive) ⇒ Similarly, cos β = √3/2 ⇒ cos (α + β) = cos α × cos β − sin α × sin β ⇒ cos (α + β) = (√3/2) × (√3/2) − (1/2) × (1/2) ⇒ cos (α + β) = 3/4 − 1/4 = 2/4 ⇒ cos (α + β) = 1/2 ∴ The correct answer is 1/2.

Additional Information Trigonometric Identities Fundamental identities are: sin2 θ + cos2 θ = 1, 1 + tan2 θ = sec2 θ, and 1 + cot2 θ = cosec2 θ. Compound Angle Formulas Addition formulas: sin (α + β) = sin α × cos β + cos α × sin β, and cos (α + β) = cos α × cos β − sin α × sin β. Trigonometric Quadrants In the first quadrant (0° to 90°), all trigonometric functions are positive. In the second quadrant, only sin and cosec are positive.

Shortcut Trick

Use the direct algebraic identity: a³ + b³ + c³ = (a + b + c)[(a + b + c)² − 3(ab + bc + ca)] + 3abc

Substitute the given values: (a + b + c) = 1, (ab + bc + ca) = −1, and abc = −1

Value = 1 × [1² − 3(−1)] + 3(−1)

Value = 1 × [1 + 3] − 3 = 4 − 3 = 1

∴ The correct answer is 1.

Alternate Method

Given: a + b + c = 1, ab + bc + ca = −1, abc = −1

Formula Used: a³ + b³ + c³ − 3abc = (a + b + c)(a² + b² + c² − (ab + bc + ca))

Finding the sum of squares:

⇒ (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)

⇒ (1)² = a² + b² + c² + 2(−1)

⇒ 1 = a² + b² + c² − 2

⇒ a² + b² + c² = 1 + 2 = 3

Substituting into the sum of cubes formula:

⇒ a³ + b³ + c³ − 3(−1) = 1 × [3 − (−1)]

⇒ a³ + b³ + c³ + 3 = 1 × (3 + 1)

⇒ a³ + b³ + c³ + 3 = 4

⇒ a³ + b³ + c³ = 4 − 3 = 1

∴ The correct answer is 1.

Additional Information

Algebraic Identity Variant

The expression a² + b² + c² − ab − bc − ca can also be expressed as ½[(a − b)² + (b − c)² + (c − a)²].

Conditional Cube Rule

If a + b + c = 0, then the identity simplifies to a³ + b³ + c³ = 3abc.

Trinomial Square

The square of a trinomial is given by (a + b + c)² = a² + b² + c² + 2(ab + bc + ca).

Shortcut Trick

A depreciation of 20% means the value becomes 80% or 4/5 of the previous year's value.

Value after 3 years = 20000 × (4/5)³

⇒ 20000 × (64/125)

⇒ 160 × 64 = 10240

∴ The correct answer is Rs. 10240.

Alternate Method

Given:

Initial Value (P) = Rs. 20000

Rate of Depreciation (R) = 20%

Time Period (n) = 3 years

Formula Used:

Value after n years = P × (1 − R/100)ⁿ

Calculations:

⇒ Final Value = 20000 × (1 − 20/100)³

⇒ Final Value = 20000 × (80/100)³

⇒ Final Value = 20000 × (0.8)³

⇒ Final Value = 20000 × 0.512

⇒ Final Value = 10240

∴ The correct answer is Rs. 10240.

Additional Information

Depreciation (Reducing Balance)

When value decreases by a fixed percentage on the current book value, use: V = P(1 − r/100)ⁿ.

Appreciation (Growth)

When the value of an asset or population increases over time, use: V = P(1 + r/100)ⁿ.

Straight Line Depreciation

If depreciation is a fixed amount calculated only on the initial cost: Total Depreciation = (Initial Value × Rate × Time) / 100.

Successive Percentage Change

For two successive changes of x% and y%, the net effective change is [x + y + (xy/100)]%.

Calculation:

To find the value of $(a + b)^3 - a^3 - b^3$, we can expand the cube of a binomial using the formula for $(a - b)^3$:

$(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3$

Substituting this into the expression, we have:

$(a + b)^3 - a^3 - b^3 = (a^3 + 3a^2b + 3ab^2 + b^3) - a^3 - b^3$

Expanding and simplifying, we get:

$(a + b)^3 - a^3 - b^3 = a^3 + 3a^2b + 3ab^2 + b^3 - a^3 - b^3$

The terms $a^3 and \space b^3$ will cancel out, leaving:

$(a + b)^3 - a^3 - b^3 = 3a^2b + 3ab^2$

Therefore, the value of $(a + b)^3 - a^3 - b^3 \space is \space 3ab(a + b)$

∴ Option 3 is the correct answer.

Calculation:

According to the question:

15% : 5%

3 : 1

∴ Option 4 is the correct answer.

Calculation:

According to the question: 

(550 - 330)/330 × 100 = 66.66%

∴ Option 2 is the correct answer.

Formula Used:

Mean = Sum of observation/No. of observation

Calculation:

Using the above formula-

⇒ Sum of observation = 36 × 8 = 288

⇒ Change in sum = 5 × 5 - 4 × 3 = 13

⇒ New mean  = 301/8 = 37.625

∴ The correct answer is 37.625.

∴ Option 4 is the correct answer.

Shortcut Trick

Total Distance = Speed × Time = 36.3 × (75 ÷ 60) = 45.375 km

Convert Distance to cm: 45.375 × 1,00,000 = 4,537,500 cm

Circumference of wheel (πd) = (22 ÷ 7) × 7 = 22 cm

Number of Revolutions = Total Distance ÷ Circumference = 4,537,500 ÷ 22 = 206250

∴ The correct answer is 206250.

Alternate Method

Given:

Diameter of the wheel (d) = 7 cm

Speed of the cyclist = 36.3 km/hr

Time taken = 75 minutes

Formula Used:

Distance = Speed × Time

Circumference = π × Diameter

Number of Revolutions (n) = Total Distance ÷ Circumference

Calculations:

⇒ Time in hours = 75 ÷ 60 = 1.25 hours

⇒ Distance covered = 36.3 × 1.25 = 45.375 km

⇒ Distance in cm = 45.375 × 1000 × 100 = 4,537,500 cm

⇒ Circumference of the wheel = (22 ÷ 7) × 7 = 22 cm

⇒ Number of Revolutions = 4,537,500 ÷ 22

⇒ Number of Revolutions = 206250

∴ The correct answer is 206250.

Additional Information

Distance covered in one revolution

The distance covered by a circular wheel in one complete revolution is equal to its circumference (2πr or πd).

Unit Conversion

1 kilometer = 1,000 meters and 1 meter = 100 centimeters; thus, 1 km = 1,00,000 cm.

Speed-Time Relation

To find Distance, ensure Speed and Time are in compatible units (e.g., km/hr and hours, or m/s and seconds).

The correct answer is 'Option 1'.

Key Points

• The part of the sentence with an error is: 'tools for finding and eat food'
• The correct phrase should be 'tools for finding and eating food'.
• The error is due to incorrect verb tense agreement.
• When listing actions (like "finding" and "eating"), all verbs should be in the same tense and form. In this case, they should both be gerunds (verb + ing) to maintain parallel structure.

The corrected sentence would read: "Our hands have been crucial tools for finding and eating food, and helping us navigate the world."

The correct answer is 'Option 1'.

Key Points

• The phrase "playing 'patriotic tunes'" is grammatically correct and makes sense within the context of the sentence.
• "Patriotic tunes" is a common phrase used to describe music that is related to or supports love for one's country.

Therefore, the given sentence is correct.

The correct answer is 'Option 3'.

Key Points

• The correct passive form of the given sentence is: The letter was lost by the manager.
• The structure of a passive sentence is: subject + auxiliary verb (be) + past participle + (by + agent).
• In this case, "The letter" is the subject, "was" is the auxiliary verb (the past tense of 'be'), "lost" is the past participle of "lose", and "by the manager" is the agent.

Therefore, the correct answer is: 'The letter was lost by the manager.'

Additional InformationOption 1, "The letter was loss by the manager," is incorrect because "loss" is a noun, not a verb.

Option 2, "The letter was loose by the manager," is incorrect because "loose" is an adjective, not the past participle of a verb.

Option 4, "The letter was lose by the manager," is incorrect because "lose" is the base form of the verb, not the past participle.

The correct answer is 'Option 2'.

Key Points

• P. The earliest years of a child’s life are critical.
• This sentence introduces the main topic of the paragraph: the importance of the earliest years in a child's life.
• S. These years determine a child’s survival and thriving in life, and lay the foundations for her/his learning and holistic development.
• This sentence extends the idea introduced in sentence P, explaining what makes these years so crucial.
• R. It is during the early years that children develop the cognitive, physical, social and emotional skills that they need to succeed in life.
• This sentence provides specific details about the importance of these years, expanding on what was mentioned in sentence S.
• Q. This is why an establishment has been created for the protection of children in these crucial years, known as ECCE.
• This sentence concludes the paragraph by giving a reason for the creation of an establishment (ECCE) based on the importance of these early years that was detailed in sentences P, S, and R.

Therefore, the correct answer is: 'PSRQ'.

The correct answer is 'Option 3'.

Key Points

• The segment in the sentence which contains a grammatical error is: 'perhaps aged young as'
• The correct phrase should be "perhaps as young as" instead of "perhaps aged young as".
• This is a common phrase used to estimate someone's age.

Therefore, the corrected sentence would be: "A witness had seen a youth, perhaps as young as ten or eleven, acting suspiciously."

The correct answer is 'Option 2' i.e. 'Finally finished'.

Key Points

• The correct improvement for the underlined part of the sentence, "finally finish," is: finally finished
• The context of the sentence indicates that the speaker has completed their taxes.
• Therefore, the past tense verb "finished" should be used instead of the present tense verb "finish."

Therefore, the correct sentence is: 'I won't bore you with the details, but I finally finished my taxes.'