SSC CHSL Tier-1 2022: Official Paper (Held On: 17 March, 2023 Shift 2) (Previous Year Paper)

The logic followed here is:

Logic: 1^st number × (1^st number - 1) = 2^nd number.

For, 15 ∶ 210

→ 15 × (15 - 1) 

→ 15 × 14 = 210.

Now, checking the options,

Option 1) 16 ∶ 224

→ 16 × (16 - 1) 

→ 16 × 15 = 240 ≠ 224.

Option 2) 14 ∶ 196

→ 14 × (14 - 1) 

→ 14 × 13 = 182 ≠ 196.

Option 3) 22 ∶ 462

→ 22 × (22 - 1) 

→ 22 × 21 = 462.

Option 4) 13 ∶ 239

→ 13 × (13 - 1) 

→ 13 × 12 = 156 ≠ 239.

Hence, the correct answer is "Option 3".

The logic followed here is:

Logic: (Sum of first two digit's place value) - (Sum of last two digit's place value).

Now,

‘SAGE’ is coded as ‘-8’

⇒ [S(19) + A(1)] - [G(7) + E(5)]

⇒ 20 - 12 = 8.

And, '8 is written as -8'.

For, ‘TABS’ is coded as ‘0’

⇒ [T(20) + A(1)] - [B(2) + S(19)]

⇒ 21 - 21 = 0.

And, '0 is written as 0'.

Similarly, for ‘VERB’

⇒ [V(22) + E(5)] - [R(18) + B(2)]

⇒ 27 - 20 = 7.

And, '7 is written as -7'.

So, 'VERB' will be coded as '-7'.

Hence, the correct answer is "-7".

The correct order as per the dictionary is as follows:

1. Special

2. Species

2) Speck

4. Speckle

5. Spectacle

Here, we can see that Speck is at the third position.

Hence, the correct answer is "Speck".

The logic followed here is:

So, '256' will complete the series.

Hence, the correct answer is "256".

Given Statements:

I. No F is N.

II. All N are L.

The least possible Venn diagram for the given statement is:

Conclusions:

I. All F are L - False (Because, All N are L and no F is N, so those part of N that is L will be definitely not F).

II. All N are F - False (Because, No F is N).

III. Some L are N - True (Because, All N are L so, some L are N is definitely true).

So, Only conclusion III follows.

Hence, the correct answer is "Option 2".

The logic followed here is:

Logic: Consider @ as 'times or power'.

Now,

For, 36 @ 2 = 1296

⇒ 36 × 36 = 1296.

For, 4 @ 4 = 256, 

⇒ 4 × 4 × 4 × 4 = 256.

Similarly, for 9 @ 3 = ?

⇒ 9 × 9 × 9 = 729.

Hence, the correct answer is "729".

The logic followed here is:

For, ‘AWAKED’ is coded as ‘FPFDJW’,

Similarly, for 'FACEUP'

So, 'FACEUP' is coded as 'KTHXZI'.

Hence, the correct answer is "Option 2".

The logic followed here is:

Step I: The 'Shaded Circle' is getting rotated in anti-clockwise direction and shifting its place by +1, +2,+3,+4,+5 places.

Step II: The 'Letter A' is getting rotated in anti-clockwise direction and shifting its place by +1, +2,+3,+4,+5 places.

So, the complete series will be:

Hence, the correct answer is "Option 4".

The logic followed here is:

Logic: 3 has been added in each letter's positional value to get the corresponding letters.

LY ∶ OB

Similarly,

MZ ∶?

Hence, the correct answer is "PC".

The mirror image of the given figure is:

Hence, the correct answer is "Option 4".

The logic followed here is:

Logic: (1^st number - 2^nd number) × 4 + 2 = 3^rd number.

Now, for (40, 20, 82)

⇒ (40 - 20) × 4 + 2

⇒ 20 × 4 + 2 = 82.

For, (36, 18, 74)

⇒ (36 - 18) × 4 + 2

⇒ 18 × 4 + 2 = 74.

Similarly, for (212, 106, 426)

⇒ (212 - 106) × 4 + 2

⇒ 106 × 4 + 2 = 426.

Hence, the correct answer is "Option 3".

Given equation: 5 - 6 ÷ 3 × 9 + 1 = 0.

BODMAS Table: 

Let's check each option one by one.

Option 1) 1 and 0

Given: 5 - 6 ÷ 3 × 9 + 1 = 0

After interchanging the numbers we get;

⇒ 5 - 6 ÷ 3 × 9 + 0 = 1

⇒ 5 - 2 × 9 + 0 = 1

⇒ 5 - 18 + 0 = 1

⇒ 5 - 18 = 1

⇒ - 13 ≠ 1

⇒ LHS ≠ RHS

Option 2) 6 and 9

Given: 5 - 6 ÷ 3 × 9 + 1 = 0

After interchanging the numbers we get;

⇒ 5 - 9 ÷ 3 × 6 + 1 = 0

⇒ 5 - 3 × 6 + 1 = 0

⇒ 5 - 18 + 1 = 0

⇒ 6 - 18 = 0

⇒ - 12 ≠ 0

⇒ LHS ≠ RHS

Option 3) 5 and 9

Given: 5 - 6 ÷ 3 × 9 + 1 = 0

After interchanging the numbers we get;

⇒ 9 - 6 ÷ 3 × 5 + 1 = 0

⇒ 9 - 2 × 5 + 1 = 0

⇒ 9 - 10 + 1 = 0

⇒ 10 - 10 = 0

⇒ 0 = 0

⇒ LHS = RHS

Option 4) 6 and 3

Given: 5 - 6 ÷ 3 × 9 + 1 = 0

After interchanging the numbers we get;

⇒ 5 - 3 ÷ 6 × 9 + 1 = 0

⇒ 5 - 0.5 × 9 + 1 = 0

⇒ 5 - 4.5 + 1 = 0

⇒ 6 - 4.5 = 0

⇒ 1.5 ≠ 0

⇒ LHS ≠ RHS

Hence, the correct answer is "Option 3".

The logic followed here is:

Option 1) UVSX

Option 2) OPMR

Option 3) ABZD

Option 4) GHEJ

Here, 'ABZD' is odd among the given options.

Hence, the correct answer is "Option 3".

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

Hence, the correct answer is "Option 2".

The logic followed here is:

So, 'NQOO' will replace the question mark in the given series.

Hence, the correct answer is "NQOO".

According to the given Venn diagram:

The shaded area shows the "total number of students play only one game".

So, the total number of 'students play only one game' = 19 + 21 + 13 = 53.

Hence, the correct answer is "53".

The logic followed here is:

Logic:- Second Number = First Number ÷ 2

And, Third Number = First Number + Second Number.

(34, 17, 51):

→ 17 = 34 ÷ 2

→ 51 = 34 + 17

(46, 23, 69):

→ 23 = 46 ÷ 2

→ 69 = 46 + 23

Let's check each option as per the logic:

1. (68, 34, 204):

→ 34 = 68 ÷ 2

→ 204 ≠ 68 + 34 ⇒ Doesn't satisfy the logic.

1. (54, 27, 108):

→ 27 = 54 ÷ 2

→ 108 ≠ 54 + 27 ⇒ Doesn't satisfy the logic.

1. (72, 36, 108):

→ 36 = 72 ÷ 2

→ 108 = 72 + 36 ⇒ Satisfies the logic.

1. (44, 22, 88):

→ 22 = 44 ÷ 2

→ 88 ≠ 44 + 22 ⇒ Doesn't satisfy the logic.

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

Hence, the correct answer is "Option 3".

The triangles are:

So, there are '10' triangles in the given figure.

Hence, the correct answer is "10".

The logic followed here is:

Logic: (1^st number ÷ 12) + 3^rd number = 2^nd number.

Now,

For (36, 48, 45)

⇒ (36 ÷ 12) + 45

⇒ 3 + 45 = 48.

For (72, 96, 90)

⇒ (72 ÷ 12) + 90

⇒ 6 + 90 = 96.

Similarly, for (60, 80, 75)

⇒ (60 ÷ 12) + 75

⇒ 5 + 75 = 80.

Hence, the correct answer is "Option 4".

For find the opposite surface of 'A', we need to compare the common surface in the given dices,

So, From Dice 1 and Dice 2,

 

→ Letter C and B is the common surface,

So, the remaining 'Z' will be the opposite face of 'A'.

Hence, the correct answer is "Option 4".

When the paper is unfolded, the image we get is as follows:

Hence, the correct answer is "Option 4".

Family Chart:

Given: Pointing towards a photo of a man, Shivang said, “He is the father of my mother’s brother”.

So, the man is Maternal Grandfather of Shivang.

Hence, the correct answer is "Option 2".

The logic followed here is:

Logic: The first word is used to make the second word.

Let's check each option as per the logic,

1) Brick – Wall:

→ Brick is used to make wall.

2) Pulp – Paper:

→ Pulp is used to make Paper.

3) Wood – Furniture:

→ Wood is used to make Furniture.

4) Metal – Ore:

→ Metal is not used to make ore. Here, the order is wrong.

Here, we can see that only Option 4 doesn't follow the logic.

Hence, the correct answer is "Metal – Ore".

The logic followed here is:

Logic: The first word is used by the second word.

Pen ∶ Author

→ Pen is used by the author.

Similarly,

Gun ∶?

→ Gun is used by the soldier.

Hence, the correct answer is "Soldier".

The logic followed here is:

Logic: The word on the right side is the sound made by the word on the left side.

Rain ∶ Patter

→ Patter is the sound of the rain.

Similarly,

Goat ∶?

→ Bleat is the sound made by the Goat.

Hence, the correct answer is "Bleat".

The correct answer is Rest of India.

Key Points

• The Irani Trophy:-
• It is a domestic first-class cricket tournament in India.
• It is played annually between the Rest of India team, consisting of top domestic players from various states, and the Ranji Trophy champions, the winner of the premier domestic cricket competition in India.
• The Rest of India team:-
• It is also known as ROI, is a domestic cricket team in India that participates in the Irani Trophy.
• The Rest of India team is composed of top-performing players from various states who are not part of the Ranji Trophy-winning team.
• They won the Irani Trophy 2022

Additional Information

• Mumbai:-
• It is one of the most successful cricket teams in Indian domestic cricket.
• The Mumbai cricket team represents the Mumbai Cricket Association (MCA) and competes in various domestic tournaments, including the Ranji Trophy.
• India Blue:-
• It represents one of the cricketing regions in India and is made up of top domestic players.
• The team consists of players who have performed well in the domestic cricket season and are selected to represent the India Blue team.
• Saurashtra:-
• It is a cricket team that represents the Saurashtra Cricket Association (SCA) in Indian domestic cricket.
• Saurashtra is a region located in the western part of the Indian state of Gujarat.

The correct answer is Haryana - Rajasthan Belt.

Key Points

• Iron ore belt in India:-
• The iron ore belt in India refers to the region that contains high-quality iron ore deposits.
• It is located in the central and southern parts of the country.
• The iron ore belt stretches from the state of Odisha in the east to Jharkhand, Chhattisgarh, and Andhra Pradesh in the central and southern regions.
• Haryana - Rajasthan Belt is not an iron ore belt. (Hence option 2 is correct)

Additional Information

• The Maharashtra-Goa belt:-
• It is a significant iron ore-producing region in western India.
• It is located along the western coast, spanning parts of Maharashtra and Goa states.
• This belt is known for its iron ore deposits, particularly the high-quality hematite ores.
• The Odisha-Jharkhand belt:-
• It is a major iron ore-producing region in eastern India.
• It encompasses parts of the states of Odisha and Jharkhand and is one of the richest mineral belts in the country.
• Durg-Bastar-Chandrapur belt:-
• It is not primarily known as an iron ore-producing region.
• Instead, it is a significant geological belt in central India that is rich in mineral resources, including coal and other minerals like limestone, bauxite, and manganese.

The correct answer is Both I and II

Key Points

• Marginal utility:-
• It refers to the additional satisfaction or benefit a consumer derives from consuming one additional unit of a commodity or product.
• It is a concept used in economics to analyze consumer behaviour and the relationship between the quantity consumed and the utility or satisfaction obtained from it.
• Both statements I and II are correct regarding the marginal utility of a commodity.
• Statement I: The marginal utility refers to the additional utility or satisfaction gained from consuming one more unit of a commodity.
• It represents the change in total utility resulting from the consumption of an additional unit of the commodity.
• Therefore, a statement I is accurate.
• Statement II: The law of diminishing marginal utility states that as the consumption of a commodity increase, the marginal utility derived from each additional unit of the commodity diminishes.
• In other words, as you consume more of a commodity, the satisfaction or utility gained from each additional unit decreases.
• Hence, statement II is also correct.

​The correct answer is Gujrat.

Key Points

• The first compressed natural gas (CNG) Terminal in the world will be built near Gujarat's Bhavnagar port for an estimated cost of Rs 4,000 crore by a consortium of the Mumbai-based Padmanabhan Mafatlal Group and the UK's Foresight Group.
• On September 29, Prime Minister Narendra Modi will lay the foundation for the project.
• The massive CNG Terminal project has a cargo handling capacity of 1.5 million metric tonnes per annum (MMTPA).
• The Gujarat Maritime Board (GMB), which is currently managing the Bhavnagar Port will also support the project as it would be developed using a public-private partnership (PPP) approach.
• The upcoming CNG Terminal will have the fourth largest lock gate system in the world in addition to an ultra-modern container terminal, a multipurpose terminal, a Ro-Ro terminal, and a liquid terminal.
• The future brownfield project will also have direct door-step connectivity to the existing roadway and railway network connecting to the largest industrial zones, the Dedicated Freight Corridor, and the northern hinterland of India.
• The construction of the port is expected to commence in the first half of 2023 and the port will be operational in 2026.

Additional Information

• Maharashtra:-
• It is a state located in the western region of India. It is the third-largest state by area and the second-most populous state in the country.
• The capital city of Maharashtra is Mumbai, which is also the financial and entertainment capital of India.
• The state is known for its rich cultural heritage, historical landmarks, and diverse cuisine.
• Bihar:
• It is the third-most populous state in the country.
• The capital city of Bihar is Patna.
• The state has a deep-rooted historical significance and is associated with the ancient kingdoms of Magadha and Maurya.
• Bihar is known for its cultural and religious heritage, with important pilgrimage sites like Bodh Gaya, where Gautama Buddha attained enlightenment.
• Madhya Pradesh:
• Madhya Pradesh is a state located in central India.
• It is the second-largest state by area and the sixth-most populous state in the country.
• The capital city of Madhya Pradesh is Bhopal.
• The state is known for its rich history and architectural marvels, with landmarks such as the Khajuraho Group of Monuments, Sanchi Stupa, and the Gwalior Fort.

The correct answer is 20^th June.

Key Points

• World Refugee Day:-
• It is an international observance held annually on June 20^th.
• It is a day designated by the United Nations to honor the courage, resilience, and strength of millions of refugees worldwide who have been forced to flee their homes due to conflict, persecution, or other forms of violence.
• The main purpose of World Refugee Day is to raise awareness about the plight of refugees and to mobilize support for their protection and well-being.
• It serves as a reminder that refugees are ordinary people who have been through extraordinary circumstances and deserve compassion, empathy, and assistance.
• The theme for World Refugee Day may vary each year, focusing on different aspects of the refugee crisis. It serves as a platform to shed light.

Additional Information

• Other Important days in June:-
• June 1:-  Global Day of Parents
• June 5:-  World Environment Day
• June 8:-  World Oceans Day
• June 14:-  World Blood Donor Day
• June 17:-  World Day to Combat Desertification and Drought
• June 19:-  Juneteenth
• June 20:-  World Refugee Day
• June 21:-  International Day of Yoga
• June 23:-  United Nations Public Service Day
• June 26:-  International Day against Drug Abuse and Illicit Trafficking
• June 30:-  International Asteroid Day

The correct answer is Fifth.

Key Points

• PARAM:-
• It is a series of supercomputers developed by the Centre for Development of Advanced Computing (C-DAC) in India.
• It stands for "Parallel Machine." PARAM was one of the earliest supercomputing initiatives in India and has evolved over time to encompass various generations and models.
• The PARAM series started with PARAM 8000, which was commissioned in 1991 and was India's first indigenous supercomputer. Since then, several iterations of the PARAM supercomputers have been developed, each offering increased computing power and performance.
• Some notable PARAM supercomputers include:
• PARAM 8000: India's first supercomputer, introduced in 1991.
• PARAM 8000 Plus: An upgraded version of PARAM 8000, released in 1994.
• PARAM 8600: A supercomputer launched in 1998, which utilized a distributed memory architecture.
• PARAM 10000: Introduced in 1998, PARAM 10000 was designed for weather forecasting and other scientific applications.
• PARAM Padma: A supercomputer launched in 2002, featuring high computational power and network bandwidth.
• PARAM Yuva: A supercomputer unveiled in 2009, offering significant computing capabilities for research and development.
• PARAM Shakti: A series of indigenous supercomputers based on RISC-V architecture, developed by C-DAC and announced in 2018. This series aims to promote the development and adoption of the indigenous processor architecture in India.
• PARAM Siddhi-AI: An artificial intelligence-focused supercomputer unveiled in 2020, designed to accelerate research in AI and machine learning applications.

The correct answer is Odisha.

Key Points

• Tropic of Cancer:-
• The Tropic of Cancer is an imaginary line of latitude located at approximately 23.5 degrees north of the equator.
• It is one of the five major lines of latitude that mark the Earth's surface and plays a significant role in defining the Earth's climate zones.
• The Tropic of Cancer is specifically the northernmost point where the Sun appears directly overhead at noon during the June solstice.
• This event marks the beginning of summer in the Northern Hemisphere. It also signifies the boundary of the tropical region and separates it from the subtropical and temperate zones.
• The Tropic of Cancer passes through several countries, including India, Mexico, Egypt, Saudi Arabia, and China, among others.
• It does not pass through Odisha.
• It passes through:-
• Gujrat
• Rajasthan
• Chhattisgarh
• Madhya Pradesh
• Jharkhand
• West Bengal
• Tripura
• Mizoram

The correct answer is  Neeraj Chopra.

Key Points

• The Diamond League:-
• It is an annual series of elite track and field athletic events that bring together the best athletes from around the world.
• It is organized by World Athletics (formerly known as the International Association of Athletics Federations or IAAF) and consists of a collection of prestigious meets held in various cities across the globe.
• Neeraj Chopra:-
• Neeraj Chopra is an Indian athlete and javelin thrower.
• He was born on December 24, 1997, in Khandra village in the Panipat district of Haryana, India.
• Chopra's biggest achievement came at the 2020 Tokyo Olympics, which were held in 2021 due to the COVID-19 pandemic.
• He won the gold medal in the men's javelin throw event, becoming the first Indian athlete to win a track and field gold medal at the Olympics.
• Neeraj Chopra's winning throw of 87.58 meters not only secured him the gold but also set a new national record.
• He became the first Indian to win Diamond League Finals title for javelin throw in 2022. . (Hence option I is correct)

Additional Information

• Shivpal Singh:-
• ​Shivpal Singh is an Indian javelin thrower.
• He was born on June 6, 1995, in the Varanasi district of Uttar Pradesh, India.
• Shivpal Singh comes from an athletic background, with his father being a former national-level javelin thrower.
• Davinder Singh Kang:-
• ​Davinder Singh Kang is an Indian javelin thrower.
• He was born on 20 June 1988 in the Jalandhar district of Punjab, India.
• Kang is known for being the first Indian javelin thrower to qualify for the finals of the World Championships.
• Annu Rani:-
• ​Annu Rani is an Indian javelin thrower.
• She was born on 28 August 1992 in the Meerut district of Uttar Pradesh, India.
• Rani is known for her accomplishments in the javelin throw event and has represented India in various international competitions.

The correct answer is Satyajit Ray.

Key Points

• Satyajit Ray:-
• Satyajit Ray (1921-1992) was a renowned Indian filmmaker, screenwriter, author, and composer.
• He is considered one of the greatest filmmakers in the history of cinema and is often credited with bringing Indian cinema to the global stage.
• Ray is particularly known for his realistic and artistic approach to filmmaking, focusing on human relationships and social issues.
• Ray's directorial debut came with the film "Pather Panchali" (1955), the first installment of his critically acclaimed Apu Trilogy.
• The trilogy, which also includes "Aparajito" (1956) and "Apur Sansar" (1959), follows the life of a young boy named Apu and is considered a masterpiece of world cinema.
• Satyajit Ray received numerous awards and accolades throughout his career:-
• He was honored with the prestigious Legion of Honour by the French government, and in 1992.
• He was posthumously awarded the Academy Award for Lifetime Achievement.
• The Academy Awards:-
• They are also known as the Oscars, are an annual set of awards honoring artistic and technical excellence in the film industry.
• The awards are presented by the Academy of Motion Picture Arts and Sciences (AMPAS), and they recognize outstanding achievements in various categories, including acting, directing, writing, and film production.

Additional Information

• Tarun Majumdar:-
• Tarun Majumdar is an Indian film director and screenwriter known for his work in Bengali cinema.
• He was born on February 22, 1931, in Comilla, British India (now Bangladesh).
• Majumdar is considered one of the pioneers of the parallel cinema movement in Bengal and is often associated with the "middle cinema" genre.
• K Viswanath:-
• ​Kasinathuni Viswanath, popularly known as K. Viswanath, is an eminent Indian film director, screenwriter, and actor, primarily associated with Telugu cinema.
• He was born on February 19, 1930, in Repalle, Andhra Pradesh, India.
• Viswanath is known for his artistic and socially relevant films, which have garnered critical acclaim and widespread recognition.
• T. Rama Rao:-
• Nandamuri Taraka Rama Rao (NTR), was a prominent Indian actor, filmmaker, and politician.
• He was born on May 28, 1923, in Nimmakuru, Andhra Pradesh, India, and passed away on January 18, 1996.
• NTR had a remarkable career in the Telugu film industry, where he acted in over 300 films and gained immense popularity.
• He made his acting debut in 1949 with the film "Mana Desam" and went on to portray a wide range of roles, including mythological, historical, and social dramas

The correct answer is Change of inventories of a firm during a year (value added + intermediate goods used by the firm – sale of the firm during a year).

Key Point

• The correct way to express the change of inventories of a firm during a year is by calculating the inventory turnover or by using the formula for the change in inventories.
• Inventory Turnover:
• Inventory turnover is a financial ratio that measures the number of times a company's inventory is sold and replaced during a given period.
• It is calculated by dividing the cost of goods sold (COGS) by the average inventory value.
• The formula for inventory turnover is:
• Inventory Turnover = Cost of Goods Sold / Average Inventory
• Change in Inventories::-
• The change in inventories can be calculated by subtracting the ending inventory value from the beginning inventory value.
• The formula for the change in inventories is:
• Change in Inventories = Ending Inventory - Beginning Inventory
• This measure represents the net increase or decrease in inventory over a specific period, such as a year. A positive value indicates an increase in inventory, while a negative value suggests a decrease.

The correct answer is **Alt + Tab.**​

Key Points

• Microsoft:-
• It is s widely recognized for its operating systems such as Microsoft Windows and software applications like Microsoft Office suite (including Word, Excel, PowerPoint, etc.), Microsoft Edge web browser, and many other tools and services.
• Windows 10:-
• It is a widely used operating system developed by Microsoft.
• It is part of the Windows NT family of operating systems and serves as the successor to Windows 8.1
• Alt + Tab:- It is a shortcut for switching between open applications or windows in most operating systems.

Additional Information

• Here are some common keyboard shortcuts for Windows 10:
• Shift + Tab:- to navigate backward through fields or elements, particularly in forms or dialog boxes.
• Shift + Alt + Tab:- to navigate through open applications or windows in reverse order.
• Alt + Shift:- to switch between keyboard input languages or keyboard layouts in many operating systems

The correct answer is The Rhine Valley

Key Points

• Fold Mountain:-
• Fold mountains are a type of mountain formed by the folding of layers of rock in the Earth's crust.
• They are characterized by long, linear ridges and valleys that often extend for hundreds of kilometers.
• The process of mountain formation through folding is known as orogeny.
• The Rhine Valley:-
• The Rhine Valley refers to the region along the Rhine River, which is one of the major rivers in Europe.
• The Rhine River flows through multiple countries, including Switzerland, Germany, France, and the Netherlands.
• The Rhine Valley encompasses the areas surrounding the river as it meanders through these countries.

Additional Information

• Aravali range:-
• The Aravali Range is a mountain range located in western India, primarily in the states of Rajasthan and Haryana.
• It is one of the oldest mountain ranges in the world, dating back to millions of years.
• The Aravali Range stretches approximately 800 kilometers (500 miles) from Gujarat in the southwest to Delhi in the northeast.
• It is a type of fold mountain.
• Appalachians:-
• The Appalachians, also known as the Appalachian Mountains or Appalachian Range, are a vast mountain system in eastern North America.
• They extend for about 2,400 kilometers (1,500 miles) from Newfoundland and Labrador in Canada, down through the eastern United States, and into northern Alabama in the southeastern part of the country.
• The Appalachian Mountains are one of the oldest mountain ranges in the world.
• It is a type of fold mountain.
• Ural Mountains:-
• ​It is a mountain range that stretches for about 2,500 kilometers (1,550 miles) from north to south, dividing the European and Asian continents.
• The range starts from the Arctic Ocean in the north and extends to the Ural River in the south, which separates Russia into its European and Asian parts.
• It is a type of fold mountain.

Mistake Points

There are two notable individuals named Manpreet Singh from India who excel in different sports. One is a renowned field hockey player, while the other is an amateur boxer. The field hockey player, Manpreet Singh, holds the position of captain in the Indian national team and is widely regarded as one of the world's best in his sport. On the other hand, the amateur boxer, Manpreet Singh, was trained at the Army Sports Institute and competes in the 82 – 91 kg weight category. Notably, he achieved a silver medal in the 2010 Asian Games, which took place in Guangzhou, China.

Solution:

The correct answer is  Both I and II.

Key Points

• Manpreet Singh:-
• Manpreet Singh (born 3 May 1985)is an amateur boxer from India and a product of Army Sports Institute. (Hence option I is correct)
• He competes in 82 – 91 kg category.
• Manpreet won silver medal in 2010 Asian Games held in Guangzhou, China.
• Boxing:-
• Boxing is a combat sport that involves two individuals, typically of similar weight, who engage in a contest of strength, speed, agility, and strategy.
• The objective of boxing is to score points or achieve a knockout by landing punches on the opponent while avoiding being hit.
• Neeraj Chopra:-
• Neeraj Chopra is an Indian athlete and javelin thrower. (Hence option II is correct)
• He was born on December 24, 1997, in Khandra village in the Panipat district of Haryana, India.
• Chopra's biggest achievement came at the 2020 Tokyo Olympics, which were held in 2021 due to the COVID-19 pandemic.
• He won the gold medal in the men's javelin throw event, becoming the first Indian athlete to win a track and field gold medal at the Olympics.
• Neeraj Chopra's winning throw of 87.58 meters not only secured him the gold but also set a new national record.
• Javelin Throw:-
• Javelin throw is a track and field event in which athletes compete to throw a javelin, a spear-like implement, as far as possible.
• It is one of the oldest Olympic events and requires a combination of strength, technique, and speed.

The correct answer is 7.4

Key Points

• pH:-
• pH scale is used to know if the substance is acidic or basic.
• The scale ranges from 0 to 14.
• 0 is strongly acidic and 14 is strongly basic or alkaline.
• The pH of 7 is considered neutral.
• The p in pH stands for ‘potenz’ in German, meaning power.
• pH of human blood is 7.4. (Hence Option 4 is correct)

Additional Information

• pH values of some common substances:-​

The correct answer is Russia.

Key Points

• International Space Station (ISS):-
• ​The International Space Station (ISS) is a multinational cooperative project involving space agencies from the United States (NASA), Russia (Roscosmos), Europe (ESA), Japan (JAXA), and Canada (CSA).
• It is a habitable space station that orbits the Earth and serves as a research laboratory, observatory, and living space for astronauts from different countries.
• Russia will opting out of it by the 2024.
• Roscosmos:-
• Roscosmos, also known as the Russian Space Agency, is the government corporation responsible for the space activities of Russia.
• It was formed in 1992 following the dissolution of the Soviet Union and the subsequent restructuring of the Russian space industry.
• Roscosmos is tasked with various responsibilities related to space exploration, scientific research, and the development of space technologies.
• Its primary objectives include the launch and operation of manned and unmanned spacecraft, satellite deployment, and the advancement of space science.

Additional Information

• NASA:-
• NASA, short for the National Aeronautics and Space Administration, is an independent agency of the United States federal government responsible for the country's civilian space program and for aeronautics and aerospace research.
• NASA was established on July 29, 1958, replacing its predecessor, the National Advisory Committee for Aeronautics (NACA)
• JAXA:-
• JAXA stands for the Japan Aerospace Exploration Agency. It is the national space agency of Japan and is responsible for the country's space exploration, satellite deployment, and aerospace research.
• JAXA was formed on October 1, 2003, through the merger of three former organizations: the Institute of Space and Astronautical Science (ISAS), the National Aerospace Laboratory of Japan (NAL), and the National Space Development Agency of Japan (NASDA).

The correct answer is Pulicat.

Key Points

• Pulicat Lake (also known as Pulicat Lagoon) lies on the borders of Andhra Pradesh and Tamil Nadu.
• Pulicat Lake is the second-largest brackish water lagoon in India.
• It spans the states of Andhra Pradesh and Tamil Nadu, with the majority of its area falling in Andhra Pradesh.
• The lake is separated from the Bay of Bengal by a barrier island known as Sriharikota.
• Pulicat Lake is home to a rich variety of flora and fauna, including numerous bird species, making it an important bird sanctuary and an ecologically significant area.

Additional Information

• Dal Lake:
• Dal Lake is a popular tourist attraction located in Srinagar, Jammu and Kashmir.
• It is known for its scenic beauty, serene surroundings, and floating gardens called "Rad" and "Sankara."
• The lake is surrounded by snow-capped mountains, Mughal gardens, and charming houseboats.
• Shikaras, traditional wooden boats, are commonly used for transportation and sightseeing on Dal Lake.
• Loktak Lake:
• Loktak Lake is the largest freshwater lake in Northeast India, situated in Manipur.
• It is known for its floating phumdis (heterogeneous mass of vegetation, soil, and organic matter) that can be seen on the lake's surface.
• The lake is home to the Keibul Lamjao National Park, which is the world's only floating national park and a refuge for the endangered Manipur brow-antlered deer.
• Loktak Lake plays a crucial role in maintaining the ecological balance and is a significant source of livelihood for the local communities.
• Sambhar Lake:
• Sambhar Lake, located in Rajasthan, is the largest inland saltwater lake in India.
• It is an important wintering area for migratory birds, including flamingos, and is recognized as a Ramsar site.
• Sambhar Lake is known for its salt production, and salt pans can be seen around the lake's vicinity.
• The lake is surrounded by vast saline wetlands, giving it a unique landscape and attracting nature enthusiasts and birdwatchers.

​ 

Important Points

The correct answer is Lord Hastings.

Key Points

• Lord Hastings served as the Governor-General of India from 1813 to 1823.
• During his tenure, Lord Hastings initiated a policy of "paramountcy" in British India.
• The policy of paramountcy declared that the authority of the British East India Company was supreme and superior to that of Indian princely states.
• Under the doctrine of paramountcy, the Company claimed the power to intervene in the affairs of Indian states and asserted its dominance over them.

Additional Information

• Lord Amherst:
• Lord Amherst served as the Governor-General of India from 1823 to 1828.
• He oversaw the First Anglo-Burmese War (1824-1826), which resulted in the British acquisition of territories in Northeast India.
• Lord Amherst implemented various administrative and judicial reforms during his tenure.
• He faced criticism for his handling of the war and was recalled to England in 1828.
• Lord Cornwallis:
• Lord Cornwallis served as the Governor-General of India from 1786 to 1793.
• He is best known for his administrative reforms, including the introduction of the Permanent Settlement of Bengal in 1793.
• Lord Cornwallis played a significant role in shaping the administrative and legal structures of British India.
• He also led the British forces during the Third Anglo-Mysore War, culminating in the defeat of Tipu Sultan in 1792.
• Lord Auckland:
• Lord Auckland served as the Governor-General of India from 1836 to 1842.
• He pursued an expansionist policy in Afghanistan and became involved in the First Anglo-Afghan War (1839-1842).
• The war proved to be a military and political disaster for the British, and they faced significant setbacks and losses.
• Lord Auckland was criticized for his decisions and handling of the conflict, and he was replaced as Governor-General in 1842.

The correct answer is Wajid Ali Shah.

• Wajid Ali Shah was the last Nawab of Oudh (Awadh) and reigned from 1847 to 1856.
• He was a prominent patron of the arts and played a significant role in the development and promotion of Kathak, a classical dance form of India.
• Wajid Ali Shah himself was a skilled dancer, poet, and musician, and he actively supported Kathak performers and musicians during his reign.
• Under his patronage, Kathak reached its golden age in the nineteenth century, with the art form flourishing in the royal courts and gaining popularity among the masses.
• Asaf-ud-daula:
• Asaf-ud-daula was the fourth Nawab of Awadh, ruling from 1775 to 1797.
• He is known for his patronage of art, architecture, and literature in Lucknow.
• Asaf-ud-daula commissioned the construction of several architectural marvels, including the Bara Imambara and the Rumi Darwaza in Lucknow.
• He also promoted cultural activities and supported renowned poets and musicians of his time.
• Siraj-ud-daulah:
• Siraj-ud-daulah was the last independent Nawab of Bengal, reigning from 1756 to 1757.
• He is famously associated with the Battle of Plassey in 1757, where he faced defeat against the British East India Company forces led by Robert Clive.
• The British victory at Plassey marked a significant turning point in the British colonization of India.
• Siraj-ud-daulah's defeat and subsequent capture led to the British gaining control over Bengal and establishing their dominance in the region.
• Saadat Khan Burhanul mulk:
• Saadat Khan Burhanul mulk, also known as Burhan-ul-Mulk, was a prominent Persian noble and statesman.
• He served as the founder of the Nawab dynasty in Awadh and became the first Nawab of Awadh in 1722.
• Saadat Khan played a vital role in stabilizing and expanding the Awadh region and was known for his administrative and military reforms.
• Under his rule, Awadh witnessed significant development, and he established a well-organized administration and a strong revenue system.

The correct answer is Eighth.

Key Points

• The 71^st Amendment, enacted in 1992, added Konkani, Manipuri, and Nepali languages to the Eighth Schedule of the Indian Constitution, recognizing them as official languages of India.
• The amendment was a significant step towards linguistic inclusivity, acknowledging the cultural and linguistic diversity of India and granting official status to these languages.
• The 71^st Amendment highlighted the importance of preserving and promoting these languages, ensuring their protection, and facilitating educational resources, official documentation, and communication in these languages for their respective communities.
• The addition of Konkani, Manipuri, and Nepali languages to the Eighth Schedule aimed to provide representation and support to linguistic communities in **Goa, Manipur, and Sikkim, respectively.**​

Additional InformationThere are a total of 12 Schedules in the Indian Constitution.

The correct answer is Bodh Gaya.

Key Points

• Bodh Gaya is a small town in the state of Bihar, India, and it is one of the most sacred sites in Buddhism.
• It was at Bodh Gaya, under a peepal tree known as the Bodhi Tree, that Siddhartha Gautama, later known as Buddha, attained enlightenment.
• The site of Bodh Gaya is marked by the Mahabodhi Temple, which is a UNESCO World Heritage Site and an important pilgrimage destination for Buddhists worldwide.
• The temple complex houses the sacred Bodhi Tree, the Vajrasana (Diamond Throne) where Buddha meditated, and various other monastic structures.

Additional Information

• Sarnath:
• Sarnath, located near Varanasi in Uttar Pradesh, is where Buddha delivered his first sermon after attaining enlightenment.
• It is a significant pilgrimage site for Buddhists.
• Kushinagar:
• Kushinagar, also in Uttar Pradesh, is the place where Buddha attained Mahaparinirvana (passed away).
• It is an important Buddhist pilgrimage site and has several monastic ruins and stupas.
• Ujjain:
• Ujjain is an ancient city in Madhya Pradesh and holds religious importance in Hinduism.
• It is associated with the Kumbh Mela and is known for its ancient temples, but it is not directly linked to Buddha's life or enlightenment.

The correct answer is Sujata Mohapatra.

Key Points

• Sujata Mohapatra is a renowned Odissi dancer and Guru who has made significant contributions to the Odissi dance form.
• She is known for her graceful movements, intricate footwork, and emotive expressions that are characteristic of Odissi dance.
• Sujata Mohapatra was honoured with the Sangeet Natak Akademi Award in 2013, one of the highest recognition given for performing arts in India.
• As a Guru, Sujata Mohapatra has trained and mentored many students, passing on the rich traditions and techniques of Odissi dance.

Additional Information

• Shovana Narayan:
• Shovana Narayan is a renowned Kathak dancer who has contributed to the field of Kathak dance.
• She is known for her expressive storytelling, intricate footwork, and graceful movements in the Lucknow Gharana style of Kathak.
• Shovana Narayan received the Padma Shri award, one of the highest civilian honours in India, in the year 1992.
• She has also been actively involved in promoting cultural exchanges and collaborations between India and other countries.
• Birju Maharaj:
• Birju Maharaj is a legendary Kathak dancer, choreographer, and Guru.
• He belongs to the Lucknow Gharana and is recognized for his mastery of intricate footwork, graceful movements, and expressive storytelling.
• Birju Maharaj has received numerous national and international awards for his contribution to Kathak dance like Padma Vibhushan in 1986, Sangeet Natak Akademi Award in 1964, Kalidas Samman etc.
• He has played a vital role in preserving and popularizing Kathak through his performances, teaching, and choreographic works.
• Rukmini Devi:
• Rukmini Devi was a renowned Bharatanatyam dancer, choreographer, and the founder of Kalakshetra.
• She is credited with reviving and reforming Bharatanatyam, bringing it into the mainstream and removing social stigmas associated with the art form.
• Rukmini Devi's contributions include incorporating elements from other classical dance styles, introducing new themes and techniques, and establishing Kalakshetra as a leading institution for Indian classical arts.
• She was a strong advocate for animal rights and environmental conservation, and her work extended beyond dance to various social and cultural initiatives.

The correct answer is I, II and III.

Key Points

• Connective tissues provide structural support and integrity to the body, with diverse types such as loose, dense, adipose, cartilage, bone, and blood, each contributing unique properties and functions within the extracellular matrix. Hence, option 3 is the correct answer.
• The extracellular matrix, composed of protein fibres and ground substance, determines the flexibility, strength, and elasticity of connective tissues, allowing them to adapt to different mechanical demands.
• Apart from their structural roles, connective tissues also play a crucial role in immunity, with certain types housing immune cells and contribute to immune responses against pathogens and foreign substances.
• Connective tissues are essential components of the body, contributing to its overall architecture, supporting organs and tissues, storing energy, protecting vital structures, and participating in various physiological processes.​

Additional Information

• Blood:
• Blood is a type of connective tissue that consists of cells suspended in a liquid matrix called plasma.
• It plays a vital role in transporting oxygen, nutrients, hormones, and waste products throughout the body.
• Bone:
• Bone is a specialized connective tissue that forms the skeletal structure of the body.
• It provides support, protection, and facilitates movement.
• Bone tissue is composed of cells called osteocytes embedded in a matrix of collagen fibres and calcium salts.
• Ligament:
• Ligaments are fibrous connective tissues that connect bones to other bones in a joint.
• They provide stability and help limit excessive movement within the joint, contributing to joint strength and function.

The correct answer is Ireland.

Key Points

• Directive Principles of State Policy of the Indian constitution are borrowed from the constitution of Ireland.
• Directive Principles of State Policy (DPSP) in the Indian Constitution are mentioned in Part IV, Articles 36 to 51.
• The nomination of members to the Rajya Sabha and the Method of the election of the president is also taken from the Irish constitution.

Additional Information Some other important features borrowed from Indian Constitution and their sources:

The correct answer is Bhawana Kanth.

Key Points

• Bhawana Kanth created history in May 2019 by becoming the first woman to qualify for combat missions on a fighter jet in the Indian Air Force.
• Her qualification opened up opportunities for women to serve in combat roles in the Indian armed forces.
• Bhawana Kanth received her initial training at the Air Force Academy in Dundigal, Telangana, and showcased exceptional skills and dedication during her training.
• Her accomplishment as a fighter pilot serves as a source of inspiration for women across the country.

Additional Information

• Priya Jhingan:
• Priya Jhingan is an Indian lawyer and a former officer in the Indian Army.
• She is notable for being one of the first women to join the Indian Army as a Short Service Commission officer.
• Priya Jhingan and another woman, Lt. G. R. Khanna, filed a landmark case in the Delhi High Court in 1992 challenging the denial of permanent commission to women officers in the Indian Army.
• Harita Kaur Deol:
• Harita Kaur Deol is an Indian Air Force officer who made headlines in 1994 for her pioneering achievements.
• She became the first woman to fly solo in a fighter aircraft when she flew a MiG-21 Bison.
• Unfortunately, she tragically lost her life in an air crash soon after, in 1996, during a routine training mission.
• Harita Kaur Deol's bravery and accomplishments continue to inspire generations of women aspiring to join the Indian Air Force.
• Shanti Tigga:
• Shanti Tigga made history in 2012 by becoming the first woman jawan (soldier) in the Indian Army.
• She joined the Corps of Signals in the Indian Army and served as a riflewoman.
• While Shanti Tigga's achievement is significant in breaking gender barriers in the Indian Army.
• Nonetheless, her determination and trailblazing role have contributed to women's empowerment and inclusion in the Indian armed forces.

The correct answer is Human faeces.

Key Points

• Human faeces are an organic impurity commonly found in sewage.
• Faecal matter is rich in organic matter and contains various bacteria, pathogens, and undigested food particles.
• The presence of human faeces in sewage poses a risk to public health due to the potential transmission of diseases and contamination of water sources.
• Proper sewage treatment processes are necessary to effectively manage and eliminate human faeces to prevent environmental and health hazards.

Additional Information

• Phosphates:
• Phosphates are inorganic compounds that can be found in sewage as an inorganic impurity.
• Phosphates mainly come from detergents, fertilizers, and human waste that enter the sewage system.
• Excessive levels of phosphates in sewage can contribute to water pollution and eutrophication when released into natural water bodies.
• Controlling and reducing the phosphate levels in sewage is important for environmental protection and maintaining water quality.
• Nitrates:
• Nitrates are inorganic compounds that can be present in sewage as an inorganic impurity.
• Nitrates can originate from various sources, including agricultural runoff, industrial waste, and domestic sewage.
• Elevated levels of nitrates in sewage can lead to water pollution and pose a risk to human health, especially when they contaminate drinking water sources.
• Metals:
• Metals, such as lead, mercury, cadmium, and copper, can be present in sewage as inorganic impurities.
• These metals can originate from various sources, including industrial discharges, domestic waste, and runoff from metal-contaminated areas.
• Elevated levels of metals in sewage can have detrimental effects on the environment and human health.
• Effective sewage treatment processes, including filtration and sedimentation, are employed to remove or reduce metal impurities in sewage before it is discharged or reused.

Shortcut Trick

For a Direct Common Tangent (DCT), the relationship between distance (d), radii (R, r), and length (L) is a Pythagorean triplet formed by L, (R − r), and d.

Difference in radii = 20 − 4 = 16 cm

Length of tangent = 30 cm

Distance (d) = √[30² + 16²]

d = √[900 + 256] = √1156 = 34 cm

∴ The correct answer is 34 cm.

Alternate Method

Given:

Radius of larger circle (R) = 20 cm

Radius of smaller circle (r) = 4 cm

Length of direct common tangent (DCT) = 30 cm

Formula Used:

Length of DCT = √[d² − (R − r)²]

Where d is the distance between the centers.

Calculations:

⇒ 30 = √[d² − (20 − 4)²]

⇒ 30 = √[d² − 16²]

Squaring both sides:

⇒ 30² = d² − 16²

⇒ 900 = d² − 256

⇒ d² = 900 + 256

⇒ d² = 1156

⇒ d = √1156

⇒ d = 34 cm

∴ The correct answer is 34 cm.

Additional Information

Transverse Common Tangent (TCT)

The length of the transverse common tangent is given by TCT = √[d² − (R + r)²], where the tangent crosses the line joining the centers.

Tangent Properties

A tangent is always perpendicular to the radius at the point of contact, and for two non-intersecting circles, there are 2 direct and 2 transverse common tangents.

Special Case: Touching Circles

If two circles touch externally, the distance between centers d = R + r. In this case, the length of the DCT becomes 2√(R × r).

Given:

If 6m61 is completely divisible by 11

Calculation:

For divisibility by 11,

The Sum of digits at even places minus the sum of digits at odd places should be 0 or divisible by 11

6 + 6 – M – 1 = 0 or a multiple of 11

∴ If the value of M is 0, then it is divisible by 11.

Calculation:

Minimum export = 20000

Average export in the given period = (47000 + 59000 + 99000 + 20000 + 85000)/5

⇒ 310000/5 = 62000

Minimum export less than average export = 62000 - 20000 = 42000

Percentage = 42000/62000 × 100

⇒ 67.74%

∴ Option 1 is the correct answer.

Calculation:

The average cost price of J and K together = (700 + 900)/2 = 800

The average selling price of L and M together = (600 + 800)/2 = 700

Difference = 800 - 700 = 100

Percentage = 100/700 × 100 = 14.28%

∴ Option 2 is the correct answer.

Concept:

Some useful formulas are,

sec2 θ - tan2 θ = 1

tan θ = $\rm 1\over \cot θ$

Calculation:

We know that, 

sec2 θ - tan2 θ = 1; which can be written as,

(sec θ + tan θ)(sec θ - tan θ) = 1

Since,sec β + tan β = 2       ....(1)

We can write the above equation as,

⇒ (sec β  - tan β ) =  $1\over 2$         ...(2)

By solving eq(1) and eq(2) we get,

2 tan β  = 2 - $\rm 1\over 2$ = $\rm 3\over 2$

⇒ tan β = $\rm 3\over 4$

⇒ cot β = $\rm 4\over 3$

∴ Option 3 is the correct answer.

Given:

SecA = 9/4

Formula used:

Sec2A – Tan2A = 1,

CotA = 1/TanA

Calculation:

⇒ Sec2A – Tan2A =1

⇒ Tan2A =Sec2A – 1

⇒ Tan2A = (9/4)2 – 1

⇒ Tan2A = (81 – 16)/16

⇒ Tan2A = 65/16

⇒ TanA = √65/4

⇒ CotA = 1/TanA

⇒ CotA = 1/√65/4

⇒ CotA = 4**/√65**

∴ Option 1 is the correct answer.

Given:

In ΔPQR, PN is the median on QR.

PN = QN

Concept Used:

Median divide the side into two equal parts.

Calculation:

In ΔPQR, PN is the median,

QN = NR

PN = QN        [given]

In ΔPQN

PN = QN

∠QPN = ∠NQP = θ 

Similarly, In ΔPNR

PN = NR

∠PNR = ∠NRP = α 

∴ ∠ QPR = θ + α 

In ΔPQR, apply Angle-Sum-Property

∠QPR +∠QRP + ∠RQP = 180° 

(θ + α) + θ + α = 180° 

2(θ + α) = 180° 

(θ + α) = 90° 

∴ ∠ QPR = 90°

∴ Option 1 is the correct answer.

Given: 

L is the incentre of ΔONP.

∠OLP + ∠ONP = 195.

Concept Used:

If L is the incentre.

∠OLP = 90° + ∠ONP/2

Calculation:

∠OLP + ∠ONP = 195

∠OLP = 195 - ∠ONP

L is the incentre.

∠OLP = 90° + ∠ONP/2

195 - ∠ONP = 90° + ∠ONP/2

105 = 3∠ONP/2

∠ONP = 70°

∠OLP = 195 - 70 

∠OLP = 125°

∴ Option 4 is the correct answer.

Shortcut Trick

Apply the algebraic identity for the square of a trinomial: (a + b + c)² = (a² + b² + c²) + 2(ab + bc + ca).

Substitute the given values: 0² = 40 + 2(ab + bc + ca).

0 = 40 + 2(ab + bc + ca) → 2(ab + bc + ca) = −40.

Dividing by 2, we get ab + bc + ca = −20.

∴ The correct answer is −20.

Alternate Method

Given:

a + b + c = 0

a² + b² + c² = 40

Formula Used:

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

⇒ Substitute the known values into the identity:

⇒ (0)² = 40 + 2(ab + bc + ca)

⇒ 0 = 40 + 2(ab + bc + ca)

⇒ 2(ab + bc + ca) = −40

⇒ ab + bc + ca = −40 ÷ 2

⇒ ab + bc + ca = −20

∴ The correct answer is −20.

Additional Information

Algebraic Identity - Square of Trinomial

The formula (a + b + c)² = a² + b² + c² + 2(ab + bc + ca) connects the sum of three numbers, the sum of their squares, and the sum of their pairwise products.

Special Case: Sum is Zero

If a + b + c = 0, then a² + b² + c² = −2(ab + bc + ca). This implies that the sum of pairwise products must be negative if the squares are positive.

Cubic Identity when Sum is Zero

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

Given:

The sum of a number and its reciprocal is 4.

Concept Used:

If a + 1/a = k

a² + 1/a² = k² - 2

Calculation:

Let the nuumber be a.

Reciprocal = 1/a

According to question,

⇒ a + 1/a = 4

⇒ a2 + 1/a2 = 42 - 2

⇒ a2 + 1/a2 = 14

∴ Option 3 is the correct answer.

Shortcut Trick

Use the Net Percentage Change formula: a + b + (ab ÷ 100)%

Here, Price decrease (a) = −30 and Sales increase (b) = +40.

Net change in Revenue = −30 + 40 + [(−30 × 40) ÷ 100]

Net change = 10 − 12 = −2%

A negative sign indicates a percentage decrease.

∴ The correct answer is 2 percent decrease.

Alternate Method

Given:

Decrease in Price = 30%

Increase in Sales (Quantity) = 40%

Formula Used:

Revenue = Price × Quantity

⇒ Let the initial Price be 100 and initial Sales be 100.

⇒ Initial Revenue = 100 × 100 = 10,000

⇒ New Price = 100 − (30% of 100) = 70

⇒ New Sales = 100 + (40% of 100) = 140

⇒ New Revenue = 70 × 140 = 9,800

⇒ Decrease in Revenue = 10,000 − 9,800 = 200

⇒ Percentage Decrease = (200 ÷ 10,000) × 100 = 2%

∴ The correct answer is 2 percent decrease.

Additional Information

Successive Percentage Change

When a value is changed by x% and then by y%, the net change is [x + y + (xy/100)]%. Use negative for decrease.

Revenue and Expenditure Relationship

Revenue = Price × Consumption. If Price increases and Expenditure is constant, Consumption must decrease by [r/(100+r)] × 100%.

Percentage Base Change

Percentage change is always calculated on the initial value: [(Final − Initial) ÷ Initial] × 100%.

Given: 

The average age of Rustam and Preetam is 30 years.

The average age of Preetam and Geetam is 20 years.

The average age of Rustam and Geetam is 26 years.

Calculation:

Let the ages of Rustam, Preetam and Geetam be r, p and g respectively.

(r + p)/2 = 30 ⇒ r + p = 60        ----(1)

⇒ (p + g)/2 = 20 ⇒ p + g = 40        ----(2)

⇒ (r + g)/2 = 26 ⇒ r + g = 52         ----(3)

Substituting the value of p and g in terms of r from (1) and (3) in (2):

⇒ 60 - r + 52 - r = 40

⇒ 112 - 2r = 40

⇒ 2r = 112 - 40 = 72

∴ r = 36

⇒ p = 60 - 36 = 24 and

⇒ g = 52 - 36 = 16

∴ Youngest is Geetam of 16 years.

∴ Geetam’s age after 5 years = 16 + 5 = 21 years.

∴ Option 1 is the correct answer.

Given:

First selling price of a table = Rs. 210

Another selling price of a table = Rs. 420

There will be loss of L1% and L2 % respectively.

L1 - L2 = 7

Concept Used:

Cost Price = 100 × Selling Price/(100 - Loss%)  

Calculation:

SP₁ = Rs. 210

⇒ CP = 100 × 210/(100 - L₁%) 

⇒ SP₂ = Rs. 420

⇒ CP = 100 × 420/(100 - L₂%) 

Since both CP equal, 

⇒ 100 × 210/(100 - L1%) = 100 × 420/(100 - L2%) 

⇒ 210/(100 - L1%) = 420/(100 - L2%)

⇒ 2(100 - L1%) = (100 - L2%)

⇒ 200 - 2L₁ = 100 - L₂

⇒ 2L₁ - L₂ = 100

Given, L1 - L2 = 7. 

⇒ L₁ = 7 + L₂

Put the value of L₁

⇒ 2(7 + L₂) - L2 = 100

⇒ 14 + 2L₂ - L₂ = 100

⇒ L₂ = 86%

⇒ CP = 100 × 420/(100 - 86) 

⇒ CP = 100 × 420/14

⇒ CP = 100 × 30

⇒ CP = Rs.3000

∴ Option 2 is the correct answer.

Formula used:

• cos θ = 1/sec θ
• sin2 θ + cos2 θ = 1

 

Calculation:

We have,

⇒ sec x + cos x = 5/2

⇒ 1/cos x  + cos x = 5/2

Above equation satisfy for x = 60°, 

Hence,

sin²x = sin260° = (√3/2)2 

sin2x = 3/4

∴ Option 1 is the correct answer.

Calculation:

Jobs held in 2010 = 30

Jobs held in 2011 = 50

Jobs held in 2012 = 70

Jobs held in 2013 = 60

Jobs held in 2014 = 80

Minimum jobs held by Indians in 2010.

∴ Option 2 is the correct answer.

GIVEN:

Distance = 720 km

Speed = 20 m/s

Starting time = 6 am

Stoppage = 1 hrs 30 min

FORMULA USED:

Speed = Distance/Time

CALCULATION:

20 × 18/5 = 72 km/h

Traveling time = 720/72 = 10 hrs

Total time = 10 + 1.5 = 11.5 hrs

Arrival time = 6 am + 11.5 hrs =  5 : 30 pm

∴ Train will arrive at 5 : 30 pm.

Calculation:

Total production of taxi by J = 90 + 70 + 50 + 45 + 40 = 295

Total production of taxi by K = 55 + 60 + 90 + 80 + 65 = 350

Difference = 350 - 295 = 55

Statement I is wrong

The production of taxi by J in year P and Q together = 90 + 70 = 160

The production of taxi by K in years R and S together = 90 + 80 = 170

Percentage = 160/170 × 100 = 94.11%

Statement II is wrong.

Both statement is Incorrect.

∴ Option 2 is the correct answer.

Shortcut Trick

For half-yearly compounding, the rate becomes half (20% ÷ 2 = 10%) and time doubles (1 year × 2 = 2 periods).

Effective percentage for 2 periods at 10% = 10 + 10 + (10 × 10)/100 = 21%.

Compound Interest = 21% of ₹18000 = 18000 × 0.21 = ₹3780.

∴ The correct answer is ₹3780.

Alternate Method

Given: Principal (P) = ₹18000, Annual Rate (R) = 20%, Time (T) = 1 year, Compounded Half-Yearly.

Formula Used: Amount (A) = P(1 + r/100)ⁿ; Compound Interest (CI) = A − P.

⇒ For half-yearly compounding, new rate (r) = 20% ÷ 2 = 10% per half-year.

⇒ Total periods (n) = 1 year × 2 = 2 half-years.

⇒ A = 18000 × (1 + 10/100)²

⇒ A = 18000 × (11/10) × (11/10)

⇒ A = 18000 × 1.21 = ₹21780.

⇒ CI = A − P = 21780 − 18000 = ₹3780.

∴ The correct answer is ₹3780.

Additional Information

Half-Yearly Compounding Rule

When interest is compounded half-yearly, the annual rate is divided by 2 and the time is multiplied by 2.

Effective Rate Formula

For two successive changes of x% and y%, the net change is (x + y + xy/100)%. For 2 periods of 10% each, it is 21%.

Quarterly Compounding

In quarterly compounding, the rate is divided by 4 and the time is multiplied by 4 (n = 4T, r = R/4).

Given:

Marked Price = Rs. 13000

Discount = 10%

Profit = 30%

Concept Used:

Selling price  = 13000 – 10% of 13000

Cost price = SP × 100/(100 + Profit%) 

Calculation:

Marked Price = Rs. 13000

After Discount selling price  = 13000 – 10% of 13000 = 11700

Now, cost price = 11700 × 100/130 = 9000

∴ Option 3 is the correct answer.

Given:

The angles of a triangle are in the ratio 2 ∶ 2 ∶ 5.

Concept:

The angle sum property of a triangle states that the sum of all three angles of a triangle is 180o .

Solution:

As per the question,

The angles of a triangle are in the ratio 2 ∶ 2 ∶ 5

Using the angle sum property of the triangle, we have

2x + 2x + 5x = 180o 

9x = 180o 

x = 20o

The largest angle of the triangle is 5x i.e., 100o .

Hence,, option 4 is correct.

Calculation:

$\rm \frac{\frac{5}{6}\ of\ \frac{1}{3}\times \frac{12}{25}-\frac{1}{3}\ of\ \frac{5}{6}\times \frac{18}{25}} {\frac{25}{12}\ of\ \frac{1}{6} \times \frac{2}{5}+\frac{3}{8}\ of \ \frac{12}{25}\times\frac{5}{6}}$

$\rm \frac{\frac{5}{6}\ \times \ \frac{1}{3}\times \frac{12}{25}-\frac{1}{3}\ \times \ \frac{5}{6}\times \frac{18}{25}} {\frac{25}{12}\ \times\ \frac{1}{6} \times \frac{2}{5}+\frac{3}{8}\ \times \ \frac{12}{25}\times\frac{5}{6}}$

$\rm \frac{ \frac{1}{3}\times \frac{2}{5}- \frac{1}{5}} {\frac{5}{36} +\frac{3}{20}}$

$\rm \frac{\frac{2}{15}- \frac{1}{5}} {\frac{5}{36} +\frac{3}{20}}$

$\rm \frac{\frac{2-3}{15}} {\frac{25 + 27}{180}}$

$\rm \frac{\frac{-1}{15}} {\frac{52}{180}}$

$\frac{-1 \times 180}{15 \times 52}$

-3/13

∴ Option 1 is the correct answer.

Given:

Rani can do a work in 10 days.

Priya can do the same work in 15 days.

Guddu can do the same work in 12 days.

All three of them do the same work together and they are paid Rs. 9000.

Formula used:

W = E × T     Where, W = Work, E = Efficiency, and T = Time

Calculation:

Let the total work be a units

Work done by Rani in 1 day = a/10

Work done by Priya in 1 day = a/15

Work done by Guddu in 1 day = a/12

Ratio of work done by Rani, Priya and C:

⇒ Rani : Priya : Guddu = 1/10 : 1/15 : 1/12

⇒ Rani : Priya : Guddu = 18 : 12 : 15 = 6 : 4 : 5

Total amount paid to them = Rs. 9000

Share of Priya = Rs. 9000 × (4)/(6 + 4 + 5)

Share of Priya = Rs. 9000 × (4)/(15)

Share of Priya = Rs. 2400

∴ The share (in Rs.) of Priya is 2400.

Shortcut Trick

Length (L) = 8 cm

Breadth (B) = 2 × 8 = 16 cm

Height (H) = 8 ÷ 2 = 4 cm

TSA = 2 × (LB + BH + HL) = 2 × (8×16 + 16×4 + 4×8)

TSA = 2 × (128 + 64 + 32) = 2 × 224 = 448 cm²

∴ The correct answer is 448 cm².

Alternate Method

Given:

⇒ Length (L) of the cuboid = 8 cm

⇒ Breadth (B) = 2 × Length = 2 × 8 = 16 cm

⇒ Height (H) = Length ÷ 2 = 8 ÷ 2 = 4 cm

Formula Used:

⇒ Total Surface Area (TSA) = 2(LB + BH + HL)

Calculations:

⇒ TSA = 2 × (8 × 16 + 16 × 4 + 4 × 8)

⇒ TSA = 2 × (128 + 64 + 32)

⇒ TSA = 2 × (224)

⇒ TSA = 448 cm²

∴ The correct answer is 448 cm².

Additional Information

Volume of Cuboid

The space occupied by a cuboid is calculated as Volume = L × B × H.

Lateral Surface Area (LSA)

The area of the four side faces (excluding top and bottom) is LSA = 2H(L + B).

Diagonal of a Cuboid

The longest rod that can be placed inside a cuboid is given by Diagonal = √(L² + B² + H²).

Given:

a = 12, b = -7 and c = -5

Concept Used:

If, a + b + c = 0

then, a3 + b3 + c³ = 3abc

Calculation:

⇒ 12 - 7 - 5 = 0

⇒ a3 + b3 + c3 = 3 × 12 × (-7) × (-5)

⇒ 1260

Given:

Total = 13000

2X = 3Y = 4Z

Solution:

X = 3/2Y

Z = 3/4 Y

Total = 3/2 Y + Y + 3/4 Y = 13000

6Y + 4Y + 3Y = 4 x 13000

13Y = 4 x 13000

Y = 4 x 1000 = Rs. 4000

Hence, the correct option is 4.

The correct answer is 'Option 2' i.e. 'To get into trouble'.

Key Points

• The phrase "Get into hot water" is an English idiom that means "to get into trouble".
• It refers to finding oneself in a difficult or precarious situation.
• The phrase originated from the idea that hot water can burn or scald, implying danger or trouble.

Therefore, the correct answer is: 'To get into trouble'.

Additional Information

• Let's examine all the options one by one:
• To get a costly gift: This option does not align with the idiom. Getting a costly gift is generally considered a positive event (महंगा उपहार पाना)
• To reach nowhere: This suggests that no progress or achievement has been made.(कहीं नहीं पहुंचना) It doesn't align with the meaning of the idiom.
• A private end to serve: This phrase implies having a personal or private goal to achieve, often in a somewhat selfish or secretive manner.(निजी उद्देश्य की सेवा करना)

The correct answer is 'Option 1'.

Key Points

• The sentence contains an error in option 1: "has becoming increasingly scarce".
• The problem lies in the verb tense.
• In English, the present perfect tense is formed by using "has" or "have" followed by a past participle (in most cases, a verb ending in -ed).
• The verb "become" should be used in its past participle form, "become", not "becoming".
• The phrase should be corrected to "has become increasingly scarce".

Therefore, the correct sentence is: "More than 40 percent of the world’s population lives in regions where water has become increasingly scarce."

The correct answer is 'Option 1' i.e. 'Amorphous'.

Key Points

• The word "Shapeless" refers to something that does not have a definite shape, form, or structure.
• It can describe physical objects or more abstract concepts, like a shapeless plan or argument.
• Amorphous: "Amorphous" describes something that lacks a clear shape or form or has no specific shape or form.(अनियमित आकार)
• It comes from the Greek words 'a-' (without) and 'morphē' (shape or form).

Therefore, the correct answer is: 'Amorphous'.

Additional Information

• Let's examine all the options one by one:
• Amortization: This term refers to the process of gradually reducing a debt through installment payments of principal and interest over a certain period of time, especially in accounting and finance.(मूलधन का अपवर्तन)
• Amoral: An "Amoral" person or behavior is one that is not influenced by moral standards or principles.(नैतिकताहीन)
• Amorous: This term describes feelings or actions that are strongly related to love, or showing strong sexual attraction.(कामुक or प्रेमी).

The correct answer is 'Option 1' i.e. 'Leonine'.

Key Points

• The phrase "Lion like characteristics" refers to attributes or qualities that are similar to those of a lion.
• Leonine: "Leonine" comes from 'leo', the Latin word for lion, and it specifically refers to characteristics or attributes similar to those of a lion. (सिंह समान)

Therefore, the correct answer is: 'Leonine'.

Additional Information

• Let's examine all the options one by one:
• Feline: This term refers to the cat family (Felidae), which includes not just domestic cats but also larger cats like lions and tigers. (बिल्ली संबंधी)
• Porcine: This term is related to pigs and does not pertain to characteristics of a lion. It comes from the Latin word 'porcus', meaning pig. (सुअर संबंधी)
• Lionize: This is a verb that means to treat someone as a celebrity or to give a lot of public attention and approval.(प्रशंसा करना)

The correct answer is 'Option 3'.

Key Points

• The correct sentence with no spelling errors is option 3: "They give the impression that you are desperate."
• In option 1, the word "impressin" is misspelled. The correct spelling is "impression".
• In option 2, the word "desparate" is misspelled. The correct spelling is "desperate".
• In option 4, the word "impresion" is misspelled. The correct spelling is "impression".
• The word "impression" means an idea, feeling, or opinion about something or someone, especially one formed without conscious thought or on the basis of little evidence.
• "Desperate" means having a great need or desire for something, or feeling of despair.

Therefore, the correct sentence is: "They give the impression that you are desperate".

The correct answer is 'Option 1'.

Key Points

• The phrase "Penny wise and pound foolish" is an English idiom that refers to the act of being careful about small amounts of money while carelessly spending larger amounts, often resulting in more significant financial loss.(छोटी राशियों के साथ सतर्क, लेकिन बड़ी राशियों के साथ लापरवाह)
• Careless with large amounts, but not small: This is the correct answer.
• It exactly matches the meaning of the idiom "Penny wise and pound foolish".
• The idiom suggests a lack of understanding of the bigger picture.

Therefore, the correct answer is: Careless with large amounts, but not small.

Additional Information 

• Here are explanations for all options:
• To act like a fool: Although the idiom contains the word "foolish", the phrase does not simply mean to act like a fool. It has a specific connotation related to financial management.(मूर्ख की तरह व्यवहार करना)
• An intelligent person who behaves foolishly: This doesn't capture the specific context of careful and careless financial management that is expressed in the idiom.(एक बुद्धिमान व्यक्ति जो मूर्खतापूर्ण व्यवहार करता है)
• Dissipating money without caring about consequences: This doesn't capture the full meaning of the idiom, which includes being careful with small amounts while being careless with larger ones.(परिणामों की परवाह किए बिना धन का विसर्जन करना)

The correct answer is 'Option 1'.

Key Points

• The correct indirect form of the given sentence is option 1: "He said that I had been making excuses."
• In reported speech, if the reporting verb (like "said" in this case) is in the past tense, then we usually shift the tenses back in the reported clause.
• When, the given direct sentence is in 'Past continuous tense' , the indirect sentence will be changed to 'Past perfect continuous tense'.
• 'Were' will be changed into 'Had been'.
• 'You' will be changed into 'I'.

Therefore, the correct answer is: 'He said that I had been making excuses.'

The correct answer is 'Option 4'.

Key Points

• The sentence contains an error in option 4: "even thousands of mile."
• The correct term is "miles" not "mile" when referring to multiple units of distance.
• In English, we usually use the plural form of a noun when we are talking about more than one of something.
• Therefore, "mile" should be in its plural form "miles" when referring to "thousands" of them.

Therefore, the correct sentence is: "Balloons filled with helium travel hundreds or even thousands of miles."

The correct answer is 'Option 1' i.e. 'Gluttony'.

Key Points

• "Abstinence" refers to the act of voluntarily refraining from indulging in something, usually pertaining to pleasurable activities like eating certain foods or drinking alcohol.
• Gluttony: This is the correct answer. "Gluttony" is the habit or act of eating or consuming to excess.(भोजन की अत्यधिक तृष्णा)
• It represents indulgence in the very activities from which one abstains when practicing "abstinence".

Therefore, the correct answer is: 'Gluttony'.

Additional Information

• Let's examine all the options one by one:
• Celibacy: This refers to the state of abstaining from marriage and sexual relations. It is actually a form of abstinence(ब्रह्मचर्य)
• Continence: This is the ability to control movements of the bowels and bladder, but it can also mean self-restraint or abstinence, especially in regard to sexual activity.(संयम)
• Control: This refers to the power to influence or direct people's behavior or the course of events. (नियंत्रण)