SSC CHSL Tier-1 2022: Official Paper (Held On: 17 March, 2023 Shift 4) (Previous Year Paper)

The logic here followed is

The diagram is rotating 90° anticlockwise direction.

Hence, the correct answer is "Option 3".

The logic followed here is:

Logic: Second word = (First word + Third word) × 2

(4, 12, 2):

→ 12 = (4 + 2) × 2

→ 12 = 6 × 2

(7, 42, 14):

→ 42 = (7 + 14) × 2

→ 42 = 21 × 2

Let's check each option as per the logic,

1) (19, 62, 11):

→ 62 = (19 + 11) × 2

→ 62 ≠ 30 × 2

2) (25, 29, 5):

→ 29 = (25 + 5) × 2

→ 29 ≠ 30 × 2

3) (9, 26, 4):

→ 26 = (9 + 4) × 2

→ 26 = 13 × 2 ⇒ Follow the logic.

4) (15, 44, 9):

→ 44 = (15 + 9) × 2

→ 44 ≠ (23) × 2 

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

Hence, the correct answer is "(9, 26, 4)".

The correct order as per the dictionary is as follows:

5) Irradiation

1) Irreparable

2) Irreplaceable

3) Irrigated

4) Irritable

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

The least possible Venn diagram is:

Conclusions:

I. All T are L. → Follows (As, All T are P and All P are L, this conclusion is definitely true)

II. All L are P. → Does not follow (As, All P are L → Some P are L, So, this conclusion is possible but not definitely true)

III. Some P are T. → Follows (As, All T are P,  this conclusion is definitely true )

Hence, "Both conclusions I and III follows" is the correct answer.

Faces opposite to each other is shown below:

6 → 2

3 → 1

4 → 8

Clearly, '4' will be on the face opposite to the face showing '8'.

Hence, '4' is the correct answer.

Let's check each option,

1) × and –

→ 39 × 3 ÷ 13 + 16 – 8 = 17

→ 39 × 3/13 + 16 – 8 = 17

→ 9 + 16 – 8 = 17

→ 25 – 8 = 17

→ 17 = 17 → LHS = RHS.

2) + and –

→ 39 + 3 ÷ 13 – 16 × 8 = 17

→ 39 + 3/13 – 16 × 8 = 17

→ 39 + 3/13 – 128 = 17

→ 510/13 – 128 ≠ 17 → LHS ≠ RHS.

3) ÷ and –

→ 39 ÷ 3 – 13 + 16 × 8 = 17

→ 13 – 13 + 16 × 8 = 17

→ 13 – 13 + 128 = 17

→ 128 ≠ 17 → LHS ≠ RHS.

4) × and ÷

→ 39 – 3 × 13 + 16 ÷ 8 = 17

→ 39 – 3 × 13 + 2 = 17

→ 39 – 39 + 2 = 17 

→ 2 ≠ 17 → LHS ≠ RHS.

Here, we can see that only Option 1 gives the correct equation.

Hence, the correct answer is "× and –".

The logic followed here is:

Logic: The positional value of first letter is subtracted by 3 to get the corresponding first letter.

→ The opposite letter of the second letter as per the positional value table is the corresponding second letter.

XQ ∶ UJ

Similarly,

IH ∶ ?

Hence, the correct answer is "FS".

In the given pattern, the second number is obtained by doubling the first number and adding 1.

So,

46 * 2 = 92, 92 + 1 = 93 58 * 2 = 116, 116 + 1 = 117

Following the same pattern,

38 * 2 = 76, 76 + 1 = 77

Therefore, 77 is the correct answer.

The logic followed here is:

1. OQJL → O + 2 = Q and J + 2 = L 2. YAZB → Y + 2 = A and Z + 2 = B 3. UWDG → U + 2 = W and D + 3 = G 4. EGTV → E + 2 = G and T + 2 = V

Hence, 'UWDG' is the correct answer.

Given: _ fghi _ _ _ ghije _ ghi _ _ f _ hij

Let's check each options:

1) ejfffjeg → e f g h i j / f f g h i j / e f g h i j / e f g h i j

2) ejeffjgg → e f g h i j / e  f g h i j / e f g h i i / g f g h i j

3) ejeffjjg → e f g h i j / e f g h i j / e f g h i j / j f g h i j

4) ejeffjeg → e f g h i j / e f g h i j / e f g h i j / e f g h i j

Here, we can see that Option 4 forms repeating sequence of " e f g h i j ".

Hence, the correct answer is "ejeffjeg".

The logic followed here is:

Similarly,

Hence, 'SOQRZC' is the correct answer.

The logic followed here is:

• ‘FRIENDS * FANS’ is coded as ‘28’
• Number of letters in FRIENDS is 7 and in FANS is 4
• 7 × 4 = 28
• ‘INDIANS * PICKS’ is coded as ‘35’
• Number of letters in INDIANS is 7 and in PICKS is 5
• 7 × 5 = 35

Similarly,

• ‘INCREASES * PRICES’
• Number of letters on INCREASES is 9 and in PRICES is 6
• 9 × 6 = 54

Hence, '54' is the correct answer.

The mirror image of the given figure is shown below:

Hence, the correct answer is "ИIАТИUОМ".

The number of Black who are only white is 6.

Hence, the correct answer is "6".

The logic followed here is:

Logic: The left side word represent male and right side word represent female of the same species.

Let's check each option as per the logic,

1) Cock ∶ Hen

→ These are the male and female terms for chickens, so this fits the logic.

2) Stallion ∶ Horse

→ Stallion is a term for a male horse, but 'Horse' is a general term and not specifically female, so this doesn't match.

3) Witch ∶ Wizard

→ These terms are gender-specific, but they don't refer to the same species or occupation in the same way as the others, so this doesn't match as well.

4) Cow ∶ Bull

→ The order of the male and female is incorrect as per the logic.

Here, we can see that only Option 1 follow the logic.

Hence, the correct answer is "Cock ∶ Hen".

The logic followed here is:

1. 168 – 336 → 168 × 2 = 336 2. 512 – 1024 → 512 × 2 = 1024 3. 358 – 726 → 358 × 2 = 716 ≠ 726 4. 624 – 1248 → 624 × 2 = 1248

Hence, '358 – 726' is the correct answer.

Given equation: 84 × 7 ÷ 4 – 16 × 8 ÷ 2 + 14 =?

After changing the signs, the final equation we get:

→ 84 ÷ 7 × 4 + 16 ÷ 8 × 2 – 14 =?

→ 12 × 4 + 2 × 2 – 14 =?

→ 48 + 4 – 14 =?

→ 52 – 14 =?

→ 38 =?

Hence, the correct answer is "38".

The logic followed here is:

Logic: The first word is a specialist who treats the part of the body mentioned in the second word.

Dentist ∶ Teeth

→ Dentist treats teeth.

Orthopedician ∶ Bones

→ Orthopedician treats Bones.

Similarly,

Cardiologist ∶?

→ Cardiologist treats Heart.

Hence, the correct answer is "Heart".

The logic followed here is:

• (432, 348, 264) → (432 + 264) ÷ 2 = 696 ÷ 2 = 348
• (288, 337, 386) → (288 + 386) ÷ 2 = 674÷ 2 =  337

Similarly,

• (348, 317, 286) → (348 + 286) ÷ 2 = 634 ÷ 2 = 317

Hence, '(348, 317, 286)' is the correct answer.

Faces opposite to each other is shown below:

1. 

 → Cannot be made (As, 1 and 4 are faces opposite to each other, so they cannot appear on the dice at the same time)

2. 

 → Can be made

3. 

 → Can be made

4. 

 → Can be made

Hence, 'option 1' is the correct answer.

The number of triangles in the figure is shown below:

Hence, ‘22’ is the correct answer.

Faces opposite to each other is shown below:

1. 

 → Cannot be made (As, @ and + are faces opposite to each other, so they cannot appear on the dice at the same time)

2. 

 → Cannot be made (As, # and 6 are faces opposite to each other, so they cannot appear on the dice at the same time)

3. 

 → Cannot be made (As, 4 and % are faces opposite to each other, so they cannot appear on the dice at the same time)

4. 

 → Can be made

Hence, ‘option 4’ is the correct answer.

The logic followed here is:

Logic: Each of the groups generally consist of words that fall within the same category.

Let's check each option as per the logic,

1) (Truck, Scooter, Car):

→ These are all types of vehicles.

2) (Lizard, Crocodile, Jungle):

→ Lizard and Crocodile are both reptiles, Jungle is not a type of reptile but a type of habitat.

3) (Lion, Leopard, Fox):

→ These are all types of mammals.

4) (Pen, Pencil, Eraser):

→ These are all stationery items.

Here, we can see that Option 2 doesn't follow the logic.

Hence, the correct answer is "(Lizard, Crocodile, Jungle)".

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

Clearly, Esha is daughter-in-law of Aryan.

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

The logic followed here is:

Hence, '2511' is the correct answer.

The correct answer is rumen.

Key Points

• In ruminants like cattle, bacteria present in the rumen (the largest compartment of the stomach) play a crucial role in the digestion of cellulose.
• The rumen is a fermentation chamber where complex carbohydrates, such as cellulose from plant material, are broken down by microbial fermentation.
• Bacteria in the rumen possess cellulolytic enzymes that break down cellulose into simpler forms that can be further digested and utilized by the ruminant host.
• This symbiotic relationship between ruminants and rumen bacteria allows them to efficiently extract nutrients from plant-based diets.

Additional Information

The correct answer is UNESCO.

Key Points

• UNESCO launched a list of 50 iconic Indian heritage textiles
• The list was titled "Handmade for the 21^st Century: Safeguarding Traditional Indian Textiles​​.
• The list includes 50 exclusive and iconic heritage textile crafts of India. Some of these include Toda embroidery and Sungadi from Tamil Nadu, Himroo weaves from Hyderabad, and Bandha tie and dye weaving from Sambalpur in Odisha.
• The list documents various aspects of the textiles, including the histories and legends behind them, the complicated and secret processes behind their creation, the causes for their dwindling popularity, and strategies for their preservation​.
• The publication aims to address one of the major challenges to the safeguarding of Intangible Cultural Heritage in South Asia, which is the lack of proper inventory and documentation. It brings together years of research on the selected textiles​.
• Some of the iconic handcrafted textiles documented from north India include Khes from Panipat, Chamba rumors from Himachal Pradesh, Thigma or wool tie and dye from Ladakh, and Awadh Jamdani from Varanasi​.
• From the south, textiles like Ilkal and Lambadi or Banjara embroidery from Karnataka, and Sikalnayakanpet Kalamkari from Thanjavur are included​.
• Textiles from other regions like Kunbi weaves from Goa, Mashru weaves and Patola from Gujarat, Himroo from Maharashtra, and Garad-Koirial from West Bengal also find a place in the list​.
• The UNESCO publication also functions as a sample of endangered textile crafts and includes recommendations for the protection and revitalization of these textile crafts, covering issues ranging from policy to grass-root-based micro-interventions.

Additional Information

UNESCO Sites

The correct answer is Ctrl + N.

Key Points

• Ctrl + N -- Open a new/blank document.

​ 

Additional Information

Word shortcut keys

• Ctrl + A -- Select all contents of the page.
• Ctrl + B -- Bold highlighted selection.
• Ctrl + C -- Copy selected text.
• Ctrl + X -- Cut selected text.
• Ctrl + N -- Open new/blank document.
• Ctrl + O -- Open options.
• Ctrl + P -- Open the print window.

​

• Ctrl + F -- Open find box.
• Ctrl + I -- Italicise highlighted selection.
• Ctrl + K -- Insert link.
• Ctrl + U -- Underline highlighted selection.
• Ctrl + V -- Paste.
• Ctrl + Y -- Redo the last action performed.
• Ctrl + Z -- Undo last action.

​

• Ctrl + G -- Find and replace options.
• Ctrl + H -- Find and replace options.
• Ctrl + J -- Justify paragraph alignment.
• Ctrl + L -- Align selected text or line to the left.
• Ctrl + Q -- Removes all formatting from a highlighted paragraph
• Ctrl + E -- Align selected text or line to the centre.
• Ctrl + R -- Align selected text or line to the right.
• Ctrl + M -- Indent the paragraph.

​

• Ctrl + T -- Hanging indent.
• Ctrl + D -- Font options.
• Ctrl + Shift + F -- Change the font.
• Ctrl + Shift + > -- Increase selected font +1.
• Ctrl + ] -- Increase selected font +1.
• Ctrl + [ -- Decrease selected font -1.

​

• Ctrl + Shift + * -- View or hide nonprinting characters.
• Ctrl + (Left arrow) -- Move one word to the left.
• Ctrl + (Right arrow) -- Move one word to the right.
• Ctrl + (Up arrow) -- Move to the beginning of the line or paragraph.
• Ctrl + (Down arrow) -- Move to the end of the paragraph.
• Ctrl + Del -- Delete the word to the right of the cursor.

​

• Ctrl + Backspace -- Delete the word to the left of the cursor.
• Ctrl + End -- Move the cursor to the end of the document.
• Ctrl + Home -- Move the cursor to the beginning of the document.
• Ctrl + Space -- Reset highlighted text to the default font.
• Ctrl + 1 -- Single-space lines.
• Ctrl + 2 -- Double-space lines.
• Ctrl + 5 -- 1.5-line spacing.

​

• Ctrl + Alt + 1 Change text to heading 1.
• Ctrl + Alt + 2 Change text to heading 2.
• Ctrl + Alt + 3 Change text to heading 3.
• F1 -- Open help.
• Shift + F3 -- Change the case of the selected text.
• Shift + Insert -- Paste.

​

• F4 -- Repeat the last action performed (Word 2000+).
• F7 -- Spell check selected text and/or document.
• Shift + F7 -- Activate the thesaurus.
• F12 -- Save as.
• Ctrl + S -- Save.
• Shift + F12 -- Save.
• Alt + Shift + D -- Insert the current date.
• Alt + Shift + T -- Insert the current time.
• Ctrl + W -- Close document.

The correct answer is demand for a commodity and its price.

Key Points 

• According to the law of demand
• ​​​​when the price of a commodity increase, the quantity demanded decreases
• when the price of a commodity decreases, it’s the quantity demanded increases
• keeping other factors remains the same.
• The consumer’s demand for good must be inversely related to the price of the good.
• There is an inverse relationship between price and demand and due to this the demand curve always has a downward slope.
• The demand Curve is the relation between the quantity of the good chosen by a consumer and the price of the good.​

Additional Information

• ​Assumptions for the Law of Demand
• ​​No change in the income of consumers
• No change is the taste and preference of the consumers
• No change in price related to other goods.

The correct answer is HAL.

Key Points

• The ALH Mk-III helicopters, indigenously manufactured by Hindustan Aeronautics Limited (HAL),
• It features state-of-the-art equipment including advanced RADAR as well as Electro optical sensors, Shakti engines, a full glass cockpit, a high-intensity searchlight, advanced communication systems, an automatic identification system as well as search-and-rescue homer.
• This feature enables the helicopter to undertake maritime reconnaissance as well as carry out search and rescue at extended ranges while operating from ships, both by day and night.
• A total of 16 ALH Mk-III aircraft have been inducted into the Indian Coast Guard in a phased manner and four of these aircraft are positioned in Chennai.

Additional Information Hindustan Aeronautics Limited:

• Founded in: 1940
• Headquarters: Bengaluru, Karnataka
• Chairman: Mihir Kanti Mishra (as of May 2023)

The correct answer is Bharatnatyam and Odissi.

Key Points

• Sonal Mansingh is a prominent Indian classical dancer who specializes in Bharatanatyam and Odissi.
• For her contributions to promoting ‘Classical dances’, she has received accolades from many national and international organizations.
• She was the youngest recipient of Padma Bhushan in 1992.
• In 2003, Sonal became the first Indian woman dancer to be awarded Padma Vibhushan.

Additional Information

Correct Answer A = 100, MPC = 0.8

Key Points:

The consumption function you provided is in the form of a simple linear equation:

• C = A + MPC*Y

where:

• C represents consumption,
• A represents autonomous consumption,
• MPC represents the marginal propensity to consume, and
• Y represents income.

Comparing this with your given function C = 100 + 0.8Y, we can identify the values of A and MPC.

• A (Autonomous consumption) is part of consumption that occurs when income is zero.
• It's the intercept of the consumption function on the consumption axis.
• This is represented by the constant term in the equation, which in this case is 100.
• MPC (Marginal Propensity to Consume) is the change in consumption resulting from a one-unit change in income.
• It's the slope of the consumption function.
• In your given function, this is represented by 0.8.

So, in the given consumption function C = 100 + 0.8Y, autonomous consumption (A) is 100 and the marginal propensity to consume (MPC) is 0.8.

Correct Answer Archery

Key PointsList of games played in commonwealth games 2022:

Additional Information:

• The 2022 Commonwealth Games (officially known as the XXII Commonwealth Games) will be held in Birmingham, England.
• The 2022 Commonwealth Games is the third Commonwealth Games to be hosted in England following London 1934 and Manchester 2002.
• The motto of the 2022 Commonwealth Games is "Games for Everyone".
• Birmingham was announced as the host by the Commonwealth Games Federation in 2017.
• 72 Commonwealth nations are expected to participate in the 2022 Commonwealth Games.
• Australia hosted the Commonwealth Games the most (5) times.
• 2018 Commonwealth Games were held at Gold Coast, Australia.
• India won 26 Gold medals and a total of 66 medals and finished 3^rd for the tournament.
• Delhi in India hosted the Commonwealth Games in 2010.
• Edinburg in Scotand hosted the Commonwealth Games twice in 1970 and 1986.
• Perth in Australia hosted the Commonwealth Games in 1962.

The correct answer is Abul Fazl

Key Points:

• The Akbarnama, which translates to Book of Akbar (1556-1605), the 3^rd Mughal Emperor, was written by his court historian and biographer, Abul Fazl.
• It was written in Persian originally, which was the court language of the Mughals.
• The book includes vivid and detailed descriptions of his life and times during the reign of Akbar.
• It is believed it took seven years for the book to be completed.
• Abul Fazl was one of the Nine Jewels of the Akbar Court.
• The first volume of the book deals with the birth of Akbar, the history of Timur's family and the reigns of Babur and Humayun, and the Suri sultans of Delhi.
• The second volume describes the detailed history of the reign of Akbar till the year 1602 and records the events during Akbar's reign.
• It also throws light on how Bairam Khan and Akbar won the second Battle of Panipat (1556) against Hemu.
• The third volume of the Akbarnama describes the administrative system of the Empire. It also deals with Akbar's household, army, revenues, and geography of the Mughal Empire.
• It also provides us the information about the traditions and culture of the people living in India at that time.

Additional Information: About Abul Fazl :​

• Abul Fazl was the grand courtier of the Mughal emperor Akbar.
• He was the author of the Akbarnama, the official history of Akbar's reign.
• Apart from Akbarnama, Abul Fazl also wrote the Persian translation of the Bible.
• He was also one of the Nine Jewels of the Akbar's royal court and the brother of Faizi, the poet laureate of  Akbar.

Nine Jewels of Akbar: 

• The following were the Nine Jewels or Navratnas of the Akbar's Royal Court-
• Raja Birbal- He was a noble who won Akbar’s appreciation for his wits.
• Tansen-He was the musician in Akbar’s court.
• Abul Fazal- He was the chief advisor in the court of Akbar.
• Faizi- Faizi was a poet who was famous for his work Nal U Daman.
• Raja Man Singh- He was the General in the court of Akbar.
• Raja Todar Mal- He was the Finance minister in the court of Akbar.
• Mullah Do Piazza- Home Minister of Akbar.
• Fakir Aziao-Din- Religious Minister of Akbar.
• Abdul Rahim Khan-I-Khana- Defence Minister of Akbar and a renowned poet.

The correct answer is Article 131

Key Points:

• Supreme Court has exclusive original jurisdiction.
• In which no other court can decide such disputes and original means, the power to hear such disputes in the first instance, not by way of appeal.
• Under Article 131, the Supreme Court Supreme has original jurisdiction to deal with any dispute between
• the Centre and one or more states;
• the Centre and any state or states on one side and one or more states on the other;
• between two or more states.
• With regard to the exclusive original jurisdiction of the Supreme Court,
• the dispute must involve a question on which the existence or extent of a legal right depends.
• any suit brought before the Supreme Court by a private citizen against the Centre or a state cannot be entertained under this.
• In 1961, the first suit, under the original jurisdiction of the Supreme Court, was brought by West Bengal against the Centre.

Additional Information:

• The Jurisdiction and powers of the Supreme Court be classified into
• Original Jurisdiction
• Writ Jurisdiction
• Appellate Jurisdiction
• Advisory Jurisdiction
• A Court of Record
• Power of Judicial Review
• Article131, Original jurisdiction of the Supreme Court
• Article 132, Appellate jurisdiction of Supreme Court in appeals from high courts in certain cases
• Article 133, Appellate jurisdiction of Supreme Court in appeals from high courts in regard to civil matters
• Article 134, Appellate jurisdiction of Supreme Court in regard to criminal matters

The correct answer is Iga Swiatek.

Key Points:

• World No. 1 Iga Swiatek steamrolled her opponents to win her 2^nd French Open title.
• The Polish superstar defeated 18-year-old American 18^th seed Coco Gauff 6-1, 6-3 in a one-sided women's singles final at the Philippe Chatrier in Paris on Saturday, June 4.
• Spaniard Rafael Nadal on 5 June 2022 won the 14^th singles title of the French Open beating Casper Ruud of Norway 6-3, 6-3, 6-0 in the final.
• With this victory, 36-year-old Nadal has become the oldest champion of the French Open.
• It is his 22^nd Grand Slam title.
• In women's singles, World Number One Iga Swiatek of Poland won the 2022 title by beating Coco Gauf in Paris on 4 June 2022.
• | Grand Slam Title 2022 | Male Winner | Female Winner | | --- | --- | --- | | U.S. Open | Carlos Alcaraz | Iga Swiatek | | Wimbledon | Novak Djokovic | Elena Rybakina | | French Open | Rafael Nadal | Iga Swiatek | | Australian Open | Rafael Nadal | Ashleigh Barty
  |

Additional Information:

• The French Open, also known as Roland-Garros, is a major tennis tournament.
• It is held over two weeks at the Stade Roland Garros in Paris, France, beginning in late May each year.
• The tournament and venue are named after the French aviator Roland Garros.
• ​The French Open:
• Founded: 1891
• Location: Paris, France
• Surface: Clay – outdoors (1908–present); Sand – outdoors (1891–1907)
• Japan's Ena Shibahara and Wesley Koolhof of the Netherlands won the French Open mixed doubles title on 2 June 2022.

Correct Answer Dhirubhai Ambani

Key Points

• Dhirubhai Ambani was a successful Indian business tycoon.
• He was the founder of Reliance Industries.
• He started Reliance Industries in 1966 as a small textile manufacturer.
• Over the years, he expanded the company into a diverse range of businesses.
• These businesses include telecommunications, petrochemicals, and retail.
• His entrepreneurial efforts have had a significant impact on the Indian business landscape.

The correct answer is Option 3. 

Key Points

• Central Highlands: The Central Highlands are located north of the Narmada River.
• They cover parts of Madhya Pradesh, Chhattisgarh, and Maharashtra.
• This region consists of a series of plateaus, hills, and valleys.
• It is characterized by its average elevation of about 600-900 meters above sea level, making it relatively higher in comparison to the surrounding plains.
• The Central Highlands are known for their rugged terrain, with prominent hill ranges such as the Vindhya Range and the Satpura Range. These ranges act as a natural boundary between northern and southern India.
• Deccan Plateau: The Deccan Plateau is situated south of the Narmada River and covers a significant portion of peninsular India.
• It spans across several states, including Maharashtra, Karnataka, Andhra Pradesh, and Tamil Nadu.
• The Deccan Plateau is a vast elevated region with an average height of about 600-900 meters above sea level, although there are certain areas where it reaches higher elevations.
• It is characterized by its gently rolling terrain, with extensive lava flows and volcanic activity in the past.
• The plateau is composed of layers of basaltic lava flows, giving rise to black soil, which is highly fertile and suitable for agriculture.

Additional Information

• The Peninsular Plateau, also known as the Deccan Plateau, is a large plateau region in India.
• It is located in the southern part of the Indian subcontinent and covers a major portion of the country.

The correct answer is Option 3. 

Key Points

• When sunlight falls on the leaves of green plants, a process called photosynthesis occurs.
• Photosynthesis is the biological process by which plants convert sunlight, carbon dioxide, and water into glucose (a form of sugar) and oxygen. This process takes place in specialized structures within plant cells called chloroplasts, which contain a pigment called chlorophyll that gives plants their green color.
• During photosynthesis, chlorophyll absorbs the energy from sunlight.
• This energy is used to power a series of chemical reactions that convert carbon dioxide and water into glucose.
• The glucose produced is then used by the plant as a source of energy for various metabolic processes, such as growth, reproduction, and maintenance of cellular functions.
• However, not all the energy from sunlight can be captured and converted by plants. Sunlight consists of a broad spectrum of electromagnetic radiation, including visible light.
• other factors such as the angle and intensity of sunlight, the availability of water and nutrients, and the efficiency of the plant's photosynthetic apparatus can influence the amount of energy that plants capture and convert into food energy.
• On average, it is estimated that green plants in a terrestrial ecosystem are able to capture and convert approximately 1 percent of the total energy from sunlight into food energy through photosynthesis.

The correct answer is Option 1. 

Key Points

• World Earth Day, also known as International Mother Earth Day, is celebrated every year on April 22.
• The theme of Earth Day 2022 is to ‘Invest in our planet’.
• The Day will be celebrated all over the world to spread awareness for Earth’s wellbeing and to encourage people to support environmental protection.
• The day focuses on the global climate crisis that is worsening with each passing day.
• World Earth Day 2022 will mark the 52^nd Anniversary of the day since it started being observed in 1970.
• Earth Day was renamed officially by the UN in 2009 as International Mother Earth Day.
• The day was observed when the peace activist John Mc Connell proposed to honour Mother Earth and the concept of peace during a UNESCO conference in San Francisco.

The correct answer is Wine.

Key Points

• Nashik is known for its wine production and is referred to as the "Wine capital of India."
• Nashik's pursuit of becoming the wine capital of India received a significant boost when the Indian government bestowed it with the prestigious Geographical Indication (GI) tag. To further promote wine production, the city has been branded as "Nashik Valley Wine."
• The city's favorable climate, fertile soil, and proximity to the Sahyadri mountain ranges make it ideal for grape cultivation.

Additional Information

• Gold:
• Mumbai and Kolkata are renowned for their gold trading and jewelry manufacturing industries in India.
• These cities have a long-standing history and reputation for gold-related businesses, including gold bullion trading, jewelry design, and craftsmanship.
• Orange:
• Nagpur, known as the "Orange City," is famous for its high-quality oranges in India.
• The region's unique climate and fertile soil contribute to the cultivation of delicious and flavorful oranges.
• Nagpur is recognized as a prominent orange-growing region in India and produces a significant portion of the country's oranges.
• Cotton:
• Ahmedabad, located in Gujarat, is widely recognized as the major cotton hub in India.
• The city has a thriving cotton textile industry and significant cotton production.
• Ahmedabad is home to the Cotton Corporation of India (CCI) and serves as a prominent center for cotton trade and manufacturing.

The correct answer is Hemant Karkare.

Key Points

• Hemant Karkare led the ATS team in response to the coordinated terrorist attacks that took place in Mumbai in November 2008.
• He played a crucial role in neutralizing the terrorists at various locations, including the iconic Taj Mahal Palace Hotel.
• Tragically, Hemant Karkare lost his life in the line of duty during the attacks while fighting against the terrorists.
• In recognition of his exceptional bravery and supreme sacrifice, he was posthumously honoured with the Ashok Chakra, India's highest peacetime gallantry award.

Additional Information

• Mohan Chand Sharma:
• He was an Indian Police Service (IPS) officer serving with the Delhi Police's Special Cell.
• He led the operation against terrorists in the Batla House encounter, which took place in Delhi in 2008.
• Sharma displayed exemplary courage and professionalism during the operation, where he lost his life in the line of duty.
• In recognition of his bravery and sacrifice in the Batla House encounter, Mohan Chand Sharma was posthumously awarded the Ashok Chakra, India's highest peacetime gallantry award.
• Mohit Sharma:
• Major Mohit Sharma, an Indian Army Officer from the elite 1^st Para SF, was posthumously awarded the Ashoka Chakra, India's highest peace-time military decoration.
• He engaged in an encounter with terrorists in Jammu and Kashmir, killing four terrorists and rescuing two teammates before succumbing to multiple gunshot wounds.
• Major Sharma had previously received two gallantry decorations and was honoured by having a Delhi Metro station named after him in 2019.
• R P Diengdoh:
• R P Diengdoh, an Indian Army soldier, was awarded the Ashok Chakra for his bravery and sacrifice during an operation against militants in Jammu and Kashmir in 2018.

The correct answer is Option 4. 

Key Points

• In the 2011 population census, a person aged 7 years and above, who can read and write with understanding in any language, is treated as literate.
• The 2011 population census was conducted in India, aiming to gather demographic data and other relevant information about the population.
• The census covered various aspects, including population size, growth rate, literacy rate, sex ratio, and other socio-economic indicators.
• It provided valuable insights into the population distribution across different states, districts, and cities within the country.
• The census data helped in understanding trends, patterns, and disparities in terms of population, literacy, education, employment, and other important factors.
• It served as a crucial tool for policy-making, planning development initiatives, and resource allocation at national, state, and local levels.
• The census was conducted through a door-to-door survey method, collecting data from households and individuals to ensure comprehensive coverage of the population.

The correct answer is Shore temple.

Key Points

• The Shore Temple is situated in Tamil Nadu.
• It is a complex of temples and shrines that overlooks the shore of the Bay of Bengal.
• It is located in Mahabalipuram, about 60 kilometres (37 mi) south of Chennai in Tamil Nadu, India.

Important Points

• The Shore Temple is one of the Group of Monuments at Mahabalipuram, which is a UNESCO World Heritage Site in the year 1984.
• It was built during the Pallava dynasty, which ruled over Tamil Nadu from the 6^th to the 9^th centuries.
• It is a Dravidian temple, which is a style of architecture that is found in South India.
• It is dedicated to Shiva and Vishnu, who are two of the most important Hindu gods.
• It is a popular tourist destination, and it is one of the most visited temples in Tamil Nadu.

Additional Information 

The correct answer is National Commission for Scheduled Tribes.

Key Points

• The Eighty-ninth Amendment Act, 2003 of the Indian Constitution established the National Commission for Scheduled Tribes.
• The Commission was established to protect the interests of the Scheduled Tribes and to ensure their development.
• The Commission has the following powers and functions:
• To investigate and monitor the implementation of safeguards provided for the Scheduled Tribes under the Constitution and other laws.
• To inquire into specific complaints of deprivation of rights and safeguards of the Scheduled Tribes.
• To advise the Central Government and State Governments on all matters relating to the welfare of the Scheduled Tribes.
• To make recommendations for the protection, development and advancement of the Scheduled Tribes.
• To publish reports on its activities and findings.
• The Commission is headed by a Chairperson who is appointed by the President of India.
• The Chairperson is assisted by a Vice-Chairperson and a few members.
• The Commission has its headquarters in New Delhi and has regional offices in different parts of the country.

Important Points

The correct answer is February 1922.

Key Points

• The Non-Cooperation Movement was a major political protest in India that began in 1920 and lasted for two years.
• The movement was led by Mahatma Gandhi and was aimed at achieving independence from British rule.
• The movement was successful in mobilizing a large number of people and in bringing about a number of changes, such as the repeal of the Rowlatt Act.
• However, the movement was also marked by violence, and in February 1922, a crowd of peasants set fire to a police station in Chauri Chaura, killing 22 policemen.
• This incident led to Gandhi calling off the movement, as he believed that it had become violent and that it was no longer in the best interests of India.
• The Chauri Chaura incident was a major setback for the Indian independence movement, but it also served as a reminder of the importance of non-violence.
• Gandhi's decision to call off the movement was a difficult one, but it was a decision that he believed was in the best interests of India.

Additional Information

• About Mahatma Gandhi:
• Mahatma Gandhi (Mohandas Karamchand Gandhi) was born on October 2, 1869.
• He died January 30, 1948, in Delhi, and the day is celebrated as Shaheed Diwas or Martyrs' Day.
• His autobiography is titled My Experiments with Truth.
• Other Important movements led by Mahatma Gandhi:
• ​Champaran Movement (1917)
• Kheda Movement (1918)
• Khilafat Movement (1919)
• Civil Disobedience Movement: Dandi March (1930)
• Quit India Movement (1942)

The correct answer is 3214 km.

Key Points

• Indira Point is the southernmost point of India's Union.
• Indira point is also known as Pygmalion point.
• It got its name in 1985.
• It was renamed in honour of former Indian prime minister Indira Gandhi.
• Indira Point is located near Great Nicobar.
• It is located at 6°8′ N latitude.

Important Points 

• The north-south extent from Indira Col in Kashmir to Kanyakumari is 3,214 km.
• The east-west width from the Rann of Kutch to Arunachal Pradesh is 2,933 km.
• With an area of 32,87,263 sq km, India is the seventh-largest country in the world.
• India accounts for about 2.4 per cent of the total surface area of the world.

Additional Information

• Extreme points of India:

The correct answer is Mosaic.

Key Points

• The first web browser developed by the National Center for Supercomputing Applications (NCSA) was Mosaic.
• Mosaic was released in 1993 and was one of the first graphical web browsers.
• It was developed by Marc Andreessen and Eric Bina at the National Center for Supercomputing Applications (NCSA) at the University of Illinois at Urbana–Champaign.
• Mosaic was a significant improvement over previous web browsers, as it allowed users to view images and other multimedia content on web pages.
• Mosaic was also the first web browser to support multiple protocols, such as HTTP, FTP, and Gopher.
• Mosaic was a popular web browser for several years, but it was eventually replaced by other browsers, such as Netscape Navigator and Internet Explorer.
• However, Mosaic is still considered to be an important milestone in the history of the web, as it helped to popularize the use of graphical web browsers.

Important Points

The correct answer is Both I and II.

Key Points

• The power of a lens is a measure of its ability to bend light.
• The power of a lens is measured in diopters, and the diopter is defined as the reciprocal of the focal length in meters.
• A convex lens has a positive focal length, and a concave lens has a negative focal length.
• Therefore, the power of a convex lens is positive, and the power of a concave lens is negative.
• Here is a more detailed explanation of each statement:
• Statement I: The power of a convex lens is represented as a positive number.
• A convex lens is a lens that is thicker in the middle than at the edges.
• When light passes through a convex lens, it is bent inward or converged.
• This convergence of light rays causes objects to appear larger and closer than they actually are.
• The power of a convex lens is positive because it converges light rays.
• Statement II: The power of a concave lens is represented as a negative number.
• A concave lens is a lens that is thinner in the middle than at the edges.
• When light passes through a concave lens, it is bent outward, or diverged.
• This divergence of light rays causes objects to appear smaller and farther away than they actually are.
• The power of a concave lens is negative because it diverges light rays.

Important Points

• Do not confuse between Concave/Convex Lens and Mirror
• Convex lens
• The convex lens is also called a converging lens.
• Concave lens
• The concave lens is also called a diverging lens.

Correct answer is Ukraine.

Key Points

• India hosted the Chess Olympiad for the first time.
• It consisted of open and women’s tournaments.
• The opening and closing ceremonies were held at the Jawaharlal Nehru Stadium.
• The 44^th Chess Olympiad was organised by the International Chess Federation or World Chess Federation (FIDE) in Chennai, India from July 28 to August 09, 2022.
• Ukraine won the gold medal in the women's section of the 44^th Chess Olympiad.
• Team Armenia won silver while the India-2 team settled for bronze in Open Section.

Additional Information

• The Chess Olympiad is an international chess competition between national teams.
• The first Chess Olympiad was held in Paris in 1927.
• The Chess Olympiad is held every two years.
• The current world champion, Magnus Carlsen, has won the Chess Olympiad three times.
• The most successful country in the **Chess Olympiad is the Soviet Union, which has won 25 titles.**​

Shortcut Trick

Sum of ages of Ram, Shyam, and Rahim = Sum of all given averages = 28 + 26 + 30 = 84 years.

Ram's age = 84 − (26 × 2) = 84 − 52 = 32 years.

Shyam's age = 84 − (30 × 2) = 84 − 60 = 24 years.

Rahim's age = 84 − (28 × 2) = 84 − 56 = 28 years.

∴ The correct answer is 32 years, 24 years and 28 years.

Alternate Method

Given:

Average age of Ram (R) and Shyam (S) = 28 years

Average age of Rahim (Rh) and Shyam (S) = 26 years

Average age of Ram (R) and Rahim (Rh) = 30 years

Formula Used:

Sum of observations = Average × Total number of observations

⇒ R + S = 28 × 2 = 56 --- (i)

⇒ Rh + S = 26 × 2 = 52 --- (ii)

⇒ R + Rh = 30 × 2 = 60 --- (iii)

Adding equations (i), (ii), and (iii):

⇒ 2(R + S + Rh) = 56 + 52 + 60 = 168

⇒ R + S + Rh = 168 ÷ 2 = 84 --- (iv)

Subtracting (ii) from (iv):

⇒ Ram's age (R) = 84 − 52 = 32 years

Subtracting (iii) from (iv):

⇒ Shyam's age (S) = 84 − 60 = 24 years

Subtracting (i) from (iv):

⇒ Rahim's age (Rh) = 84 − 56 = 28 years

∴ The correct answer is 32 years, 24 years and 28 years.

Additional Information

Definition of Average

Average is the ratio of the sum of values to the number of values. Formula: Average = Sum ÷ n.

Sum of Pairs Property

In a group of three (A, B, C), if sums of pairs (A+B, B+C, C+A) are known, the total sum (A+B+C) is exactly half of the sum of the three pair sums.

Weighted Average

When two groups with averages A₁ and A₂ and sizes n₁ and n₂ are combined, the new average is (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Shortcut Trick

Sum of present ages = 94 years.

Sum of ages 8 years ago = 94 − (2 × 8) = 78 years.

Divide 78 in the ratio 2 : 1 ⇒ Father = 52, Son = 26.

Age 10 years from now (Total gap of 18 years from past) ⇒ Father = 52 + 18 = 70, Son = 26 + 18 = 44.

Required ratio = 70 : 44 = 35 : 22.

∴ The correct answer is 35 : 22.

Alternate Method

Given:

Present sum = 94 years.

Ratio 8 years ago = 2 : 1.

Formula Used:

Total Age = Sum of individual ages.

Let the ages of Father and Son 8 years ago be 2x and x.

⇒ Present age of Father = 2x + 8

⇒ Present age of Son = x + 8

⇒ (2x + 8) + (x + 8) = 94

⇒ 3x + 16 = 94

⇒ 3x = 78

⇒ x = 26

⇒ Father's age 10 years from now = (2x + 8) + 10 = 2(26) + 18 = 52 + 18 = 70 years.

⇒ Son's age 10 years from now = (x + 8) + 10 = 26 + 18 = 44 years.

⇒ Ratio = 70 : 44 = 35 : 22.

∴ The correct answer is 35 : 22.

Additional Information

Constant Age Difference

The difference between the ages of two people remains constant throughout their lives, regardless of the time elapsed.

Age Sum Adjustment

To find the sum of ages 'n' years ago for 'k' people, subtract (n × k) from the present sum.

Ratio and Proportion in Ages

If ages are in ratio a : b, they can be represented as ax and bx to set up linear equations based on the given sum or difference.

Given:

Sum of diameter of these two circles is 84 cm

Calculation:

Diameter of one circle = 84/2 = 42 cm

Radius of the circle = 42/2 = 21 cm

According to the diagram,

AD = DB

O1O2 = 21

Again O1A = O2A = 21 [Radius of the circle]

∠ADO1 = 90°

O1D = O2D = 21/2

AD = √(441 - 441/4)

⇒ 21√3/2 

AB = 2 × 21√3/2  = 21√3

∴ The length of the common chord is 21√3 cm

Given:

982 − 972 + 962 − 952 + 942 − 932 + ...... 122 − 11²

Expand using identity a² - b² = (a + b)(a - b)

(98 + 97)(98 - 97) + (96 + 95)(96 - 95) + (94 + 93)(94 - 93) + .......................... + (12 + 11)(12 - 11)

(98 + 97) + (96 + 95) + (94 + 93) + .......................... + (12 + 11)

It is an AP with a = 98, d = -1, and l = 11

T_n = a + (n - 1)d

11 = 98 + (n - 1)(-1)

Solving this

n = 88

Sum = n/2 × (a + l)

88/2 × (98 + 11)

Sum = 4796

∴ Option 2 is the correct answer.

Calculation:

Bike: 900 + 650 + 700 + 450 + 500 = 3200 units

Truck: 700 + 500 + 400 + 800 + 850 = 3250 units

I. The total production of trucks by all 5 companies is 201.50 percent of the total production of bikes by all 5 companies.

3250/3200 × 100 = 101.56%

So, a statement I is NOT correct.

II. The average production of bikes and trucks by company R is 800.

(900 units for bikes + 700 units for trucks)/2 = 800 units

This is equal to 800 units, so statement II is correct.

Only statements I is NOT correct based on the given data.

Calculation:

Distance between A and B = 220 km

A starts moving towards B at 11 AM with speed of 40 km/hr

B starts moving Away from A at 12 PM with speed of 30 km/hr

At 12 PM A travelled 40 km

Now distance reduced to 180 km

Now both starts moving and difference between their speed is 10 km/hr

Since A’s speed is 10 km more than B so they will meet after 180 km / 10 km/hr = 18 hr = at 6 AM on next day

∴ Option 4 is the correct answer.

Shortcut Trick

Subtract 2 from both sides of the given equation: (x − 2) + 1/(x − 2) = 6.

Apply the algebraic shortcut: If k + 1/k = n, then k² + 1/k² = n² − 2.

Substitute n = 6 into the formula: 6² − 2 = 36 − 2 = 34.

∴ The correct answer is 34.

Alternate Method

Given: 1/(x − 2) + x = 8

Formula Used: (a + b)² = a² + b² + 2ab

⇒ 1/(x − 2) + x = 8

⇒ x − 2 + 1/(x − 2) = 8 − 2

⇒ (x − 2) + 1/(x − 2) = 6

⇒ Squaring both sides: [(x − 2) + 1/(x − 2)]² = 6²

⇒ (x − 2)² + [1/(x − 2)]² + 2 × (x − 2) × [1/(x − 2)] = 36

⇒ (x − 2)² + 1/(x − 2)² + 2 = 36

⇒ (x − 2)² + 1/(x − 2)² = 36 − 2 = 34

∴ The correct answer is 34.

Additional Information

Algebraic Expansion

The square of a binomial is given by (a + b)² = a² + b² + 2ab and (a − b)² = a² + b² − 2ab.

Reciprocal Property

If the sum of a number and its reciprocal is k (i.e., x + 1/x = k), then the sum of their squares is always k² − 2.

Higher Power Relation

If x + 1/x = k, then the sum of their cubes is given by x³ + 1/x³ = k³ − 3k.

Given:

P is a point on side YZ.

XY = XZ

∠XPY = 90° 

YP = 9 cm

Calculation:

The given triangle is isosceles triangle.

In ΔXPY and ΔXPZ

XY = XZ        [given]

XP = XP        [common]

∠ XYZ = ∠ XZY          [Isosceles triangle]

ΔXPY ~ ΔXPZ

∴ YP = PZ = 9 cm

YZ = YP + PZ = 9 + 9

YZ = 18 cm

∴ Option 2 is the correct answer.

Concept Used:

tan θ = cot(90 - θ)

cot θ = 1/tan θ 

Calculation:

⇒ (tan 10° tan 80° + tan 20° tan 70° + tan 30° tan 60° + tan 40° tan 50°)

⇒ (tan 10° cot 10° + tan 20° cot 20° + tan 30° cot 30° + tan 40° cot 40°)

⇒ 1 + 1 + 1 + 1

⇒ 4

∴ Option 1 is the correct answer.

Calculation:

The average production of refrigerator by all six companies = (200 + 140 + 120 + 80 + 40 + 100)/6

⇒ 680/6 = 113.33

∴ Option 2 is the correct answer.

Shortcut Trick

Let the Cost Price (CP) be 100 units.

Selling Price (SP) with 20% profit = 120 units.

New Selling Price = Double the initial SP = 120 × 2 = 240 units.

New Profit = New SP − CP = 240 − 100 = 140 units.

Profit % = (140 ÷ 100) × 100 = 140%.

∴ The correct answer is 140%.

Alternate Method

Given:

Profit percentage initially = 20%

Condition: The new selling price is double the initial selling price.

Formula Used:

Profit = Selling Price (SP) − Cost Price (CP)

Profit % = (Profit ÷ CP) × 100

CP = 100

SP = 120

New SP = 240

+20%

× 2

Overall Profit = +140%

Calculations:

⇒ Let the Cost Price (CP) of the calculator be 100 units.

⇒ Since the profit is 20%, Initial Selling Price (SP₁) = 100 + (20% of 100) = 120 units.

⇒ The new selling price is double the initial selling price.

⇒ New Selling Price (SP₂) = 2 × 120 = 240 units.

⇒ New Profit = SP₂ − CP = 240 − 100 = 140 units.

⇒ New Profit % = (New Profit ÷ CP) × 100 = (140 ÷ 100) × 100 = 140%.

∴ The correct answer is 140%.

Additional Information

Marked Price & Discount

Discount is always calculated on Marked Price (MP). Selling Price = MP − Discount.

Successive Percentage Change

When two successive changes of x% and y% occur, net change = x + y + (x × y)/100.

Dishonest Dealer

If a dealer sells goods at CP but uses a false weight, Profit % = (True Weight − False Weight) ÷ False Weight × 100.

Given:

3 cosec A = 7

Calculation:

3 cosec A = 7

⇒ cosec A = 7/3

⇒ sin A = 1/cosec A = 3/7

cos A tan A = cos A × sin A/cos A

⇒ sin A = 3/7

∴ Option 2 is the correct answer.

Calculation:

Total income of M and N = 850 + 350 = 1200

The total expenditure in year J, K and L = 350 + 250 + 350 = 950

Ratio

1200 : 950

24 : 19

∴ Option 3 is the correct answer.

Shortcut Trick

In an equilateral triangle, the centroid is the same as the incenter.

The distance from the centroid to any side is the inradius (r) of the triangle.

Shortcut formula: Inradius (r) = side ÷ (2√3)

⇒ Distance = (16√3) ÷ (2√3)

⇒ Distance = 16 ÷ 2 = 8 cm

∴ The correct answer is 8 cm.

Alternate Method

Given:

Side of equilateral triangle ABC (a) = 16√3 cm.

Point P is the centroid.

Formula Used:

Height (h) of equilateral triangle = (√3 ÷ 2) × side

Centroid divides the median in the ratio 2 : 1 from the vertex.

Calculations:

⇒ Height (AD) = (√3 ÷ 2) × 16√3

⇒ AD = (16 × 3) ÷ 2

⇒ AD = 24 cm

⇒ The centroid (P) divides median AD in ratio AP : PD = 2 : 1.

⇒ Distance of P from side BC = PD

⇒ PD = (1 ÷ (2 + 1)) × AD

⇒ PD = (1 ÷ 3) × 24

⇒ PD = 8 cm

∴ The correct answer is 8 cm.

Additional Information

Equilateral Triangle Centroid

In an equilateral triangle, the centroid, orthocenter, circumcenter, and incenter all lie at the same point.

Inradius and Circumradius

For an equilateral triangle with side a, Inradius (r) = a / (2√3) and Circumradius (R) = a / √3. Note that R = 2r.

Median Property

The centroid divides each median into two segments with lengths in the ratio 2 : 1 from the vertex to the midpoint of the opposite side.

Given:

The marked price of an article is 40 percent more than its cost price.

Calculation:

Let the cost price be 100

⇒ Marked price = 140

Selling Price = 140 – 0.20 × 140 = 112

Profit% = [(112 – 100)/100] × 100 = 12%

∴ Option 2 is the correct answer.

Calculation:

Rama can finish the work in 5 days working 4 hours a day, that's 5 × 4 = 20 hours.

Seema can finish the work in 3 days working 10 hours a day, that's 3 × 10 = 30 hours.

So, we can say that Rama's work rate is 1/20 of the work per hour, and Seema's work rate is 1/30 of the work per hour.

So, their combined rate is 1/20 + 1/30 = (3 + 2)/60 = 5/60 = 1/12 of the work per hour.

If they want to finish the work in 6 days, and they work together at the combined rate of 1/12 of the work per hour, then they need to work:

6 days × x hours/day = 1 work

x = 1 work / (6 days × 1/12 work/hour)

x = 1 / (6/12) = 2 hours/day

So, Rama and Seema need to work together for 2 hours each day to finish the work in 6 days.

Shortcut Trick

Identify the Algebraic Identity for the sum of two cubes.

Standard Formula: (a + b)(a² − ab + b²) = a³ + b³

Here, let a = x and b = 1.

Substitute these values: (x + 1)(x² − (x)(1) + 1²) = x³ + 1³ = x³ + 1.

∴ The correct answer is x³ + 1.

Alternate Method

Given: (x + 1)(x² − x + 1)

Method: Expand the brackets using the distributive property of multiplication.

⇒ x(x² − x + 1) + 1(x² − x + 1)

⇒ (x × x²) − (x × x) + (x × 1) + (1 × x²) − (1 × x) + (1 × 1)

⇒ x³ − x² + x + x² − x + 1

⇒ x³ + (−x² + x²) + (x − x) + 1

⇒ x³ + 0 + 0 + 1

⇒ x³ + 1

∴ The correct answer is x³ + 1.

Additional Information

Difference of Two Cubes

The identity for the subtraction of cubes is a³ − b³ = (a − b)(a² + ab + b²).

Perfect Cube Binomial

The expansion of (a + b)³ is a³ + 3a²b + 3ab² + b³, which is different from a³ + b³.

Difference of Squares

Another essential identity is a² − b² = (a − b)(a + b).

Given:

An equilateral triangle inradius is 4 cm.

Concept used:

In equilateral triangle, 

Circumradius  = a/√ 3

Inradius of equilateral triangle = a/2√ 3

Calculation:

Inradius of equilateral triangle = 4

⇒ a/2√ 3 = 4

⇒ a = 8√3

Circumradius  = a/√ 3 = 8√3/√3

⇒ 8

Given:

1440 − 200 ÷ 50 × 2 + 3

Concept used:

Calculation:

1440 − 200 ÷ 50 × 2 + 3

⇒ 1440 − 4 × 2 + 3

⇒ 1440 − 8 + 3

⇒ 1440 − 5

⇒ 1435

∴ Option 3 is the correct answer.

Calculation:

Let's denote the total number of students as 100% 

The students who passed in history are 45% and those who passed in Hindi are 60%.

So, the total percentage who passed either in history or Hindi (or both) is 45% + 60% = 105%.

But this sum also includes the students who passed in both subjects twice (once for history and once for Hindi).

Also, we know that 8% of students failed in both subjects. That means the total percentage of students who passed in at least one subject is 100% - 8% = 92%.

Percentage of students who passed in both subjects = Total pass percentage in history or Hindi - the percentage of students who passed in at least one subject

= 105% - 92% = 13%

So, 13% of students passed in both subjects.

Shortcut Trick

Ratio of Volumes = (Ratio of Radii)² × (Ratio of Heights)

Ratio of Volumes = (6 / 5)² × (2 / 3)

Ratio of Volumes = (36 / 25) × (2 / 3)

Ratio of Volumes = 12/25 × 2 = 24 / 25

∴ The correct answer is 24 : 25.

Alternate Method

Given:

Ratio of heights (h₁ : h₂) = 2 : 3

Ratio of radii (r₁ : r₂) = 6 : 5

Formula Used:

Volume of a cylinder (V) = πr²h

Calculations:

⇒ V₁ = π × (6x)² × (2y) = π × 36x² × 2y = 72πx²y

⇒ V₂ = π × (5x)² × (3y) = π × 25x² × 3y = 75πx²y

⇒ V₁ : V₂ = 72πx²y : 75πx²y

⇒ V₁ : V₂ = 72 : 75

⇒ V₁ : V₂ = 24 : 25 (Dividing both sides by 3)

∴ The correct answer is 24 : 25.

Additional Information

Volume of Cylinder

The amount of space occupied by a three-dimensional object is its volume. For a cylinder, V = πr²h.

Curved Surface Area (CSA)

The area of the curved surface of a cylinder excluding its base and top is given by CSA = 2πrh.

Total Surface Area (TSA)

The sum of the curved surface area and the areas of the two circular bases is TSA = 2πr(h + r).

Ratio Property of Volume

If heights are equal, the volume ratio is the ratio of the squares of the radii: V₁/V₂ = (r₁/r₂)².

Given:

2Cos2 θ − 9 cos θ + 7 = 0

Concept Used:

cos θ = 1/sec θ 

Calculation:

2Cos2 θ − 9 cos θ + 7 = 0

Solving for secθ, we have a quadratic equation in secθ:

2Cos2 θ − 9 cos θ + 7 = 0

This can be factored as follows:

(2 cos θ - 7)(cos θ - 1) = 0.

Setting each factor equal to zero gives the solutions cos θ = 3.5 or cos θ = 1.

As cos θ = 3.5 is not possible so we take cos θ = 1.

cos2 θ + sec2 θ

1/sec2 θ + sec2 θ

1 + 1 = 2

∴ Option 1 is the correct answer.

Calculation:

J1, we need to find the sum of the bike production and divide it by the number of  companies (5 in this case):

J1 = (300 + 175 + 200 + 75 + 100)/5

J1 = 850/5

J1 = 170

To calculate J2, we need to find the sum of the truck production and divide it by the number of companies:

J2 = (200 + 100 + 50 + 250 + 275)/5

J2 = 875/5

J2 = 175

(J1 ∶ J2) is 170 ∶ 175.

34 : 35

∴ Option 3 is the correct answer.

Calculation:

If the sum amounts to Rs. 6580 in 2 years and Rs. 7896 in 3 years, the difference (Rs. 7896 - Rs. 6580 = Rs. 1316) would be the interest earned in the third year.

So, the interest for the third year, Rs. 1316, was obtained from the amount that was there at the end of two years, which is Rs. 6580.

Interest for third year = Sum after 2 years × annual interest rate

1316 = 6580 × r

Solving this equation for r gives us:

r = 1316/6580 × 100 = 20%

So, the annual rate of interest is 20%.

Given:

$\frac{\frac{5}{12} \text { of } \frac{6}{25}−\frac{5}{6} \times \frac{12}{33}+\frac{5}{11} \div \frac{25}{33}}{\frac{1}{6} \div \frac{1}{2}+\frac{1}{6} \times \frac{1}{2}−\frac{1}{2} \text { of } \frac{1}{6}}$

Concept used:

Calculation:

$\frac{\frac{5}{12} \text { of } \frac{6}{25}−\frac{5}{6} \times \frac{12}{33}+\frac{5}{11} \div \frac{25}{33}}{\frac{1}{6} \div \frac{1}{2}+\frac{1}{6} \times \frac{1}{2}−\frac{1}{2} \text { of } \frac{1}{6}}$

$\frac{\frac{5}{12} \times \frac{6}{25}−\frac{5}{6} \times \frac{12}{33}+\frac{5}{11} \times \frac{33}{25}}{\frac{1}{6} \times 2+\frac{1}{6} \times \frac{1}{2}−\frac{1}{2} \times \frac{1}{6}}$

$\frac{\frac{1}{10} −\frac{10}{33}+\frac{3}{5}}{\frac{1}{3}+\frac{1}{12}−\frac{1}{12}}$

$\frac{\frac{33-100+198}{330}}{\frac{1}{3}}$

$\frac{131}{110}$

∴ Option 1 is the correct answer.

The correct answer is 'Option 3' i.e. 'Inessential'.

Key Points

• The word "indispensable" means absolutely necessary, essential, or requisite.(अपरिहार्य).
• The most appropriate antonym of "indispensable" is: Inessential
• "Inessential" means not absolutely necessary. In other words, something that is inessential could be done without. (अवश्यकता से परे).

Therefore, the correct answer is: 'Inessential'.

Additional Information

• Here's an explanation for the other options:
• "Fundamental" - This word refers to the basic, underlying, or essential foundations or principles of something.(मौलिक).
• "Crucial" - This word means of great importance, or necessary for the success of something. (महत्वपूर्ण).
• "Basic" - This word refers to the essential facts or principles of a subject or skill.(मूल).

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

Key Points

• The incorrectly spelled word here is: 'Prepaer'
• The correct spelling is "Prepare".
• It means to make something or someone ready for some activity, purpose, use, etc. (तैयार करना).

Therefore, the correct spelling is: 'Prepare'.

Additional Information

• Here's the explanation for the other options:
• "Mushy" - This word is spelled correctly. It means like mush in consistency or firmness.(नरम और गीला)
• "Busiest" - This word is also spelled correctly. It's the superlative form of "busy," meaning the most occupied or engaged(सबसे व्यस्त).
• "Matter" - This word is spelled correctly. "Matter" has various meanings, it can refer to a subject or topic of concern or it can refer to physical substance in general, as distinct from mind and spirit.(मुद्दा)

The correct answer is 'Option 4' i.e. 'Inarticulate'.

Key Points

• The most appropriate option to fill in the blank is: inarticulate
• "Inarticulate" means unable to speak distinctly or express oneself clearly.
• It fits the context of the sentence as Howard is trying to speak but is unable to do so in a clear and understandable manner.

Therefore, the correct sentence is: Howard tried to speak but all that came out was an inarticulate, squeaky gargle. 

Additional Information

• Here's why the other options are not appropriate:
• "Implausible" means not seeming reasonable or probable; failing to convince. It doesn't fit the context here because it doesn't describe the quality of speech or sound.
• "Sincere" refers to a person, feeling, or expression that is free from pretense or deceit; proceeding from genuine feelings. It doesn't describe the physical sound of someone's voice.
• "Easy" could refer to something requiring no great labor or effort, but it doesn't fit in this context because it doesn't describe a characteristic of someone's voice or speech.

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

Key Points

• The word that is opposite in meaning to the given word "Ignominy" is: 'Esteem'
• "Ignominy" refers to public shame or disgrace(अपमान).
• "Esteem" is the opposite of "Ignominy". It refers to respect and admiration.(सम्मान).

Therefore, the correct answer is: 'Esteem'.

Additional Information

• Here's the explanation for the other options:
• "Disrepute" - It means the state of being held in low regard by the public.(बदनामी).
• "Stigma" - It refers to a mark of disgrace associated with a particular circumstance, quality, or person.(कलंक).
• "Infamy" - It refers to the state of being well known for some bad quality or deed.(कुख्याति).

The correct answer is 'Option 4' i.e. 'Drowned'.

Key Points

• The correct answer is 'drowned'.
• The reason it is correct is that the verb 'sink' needs to be replaced with the past tense form 'sank' in passive voice, which is 'was sunk'.
• However, in the given options, the option 'was sunk' is not provided.
• Out of the available options, 'drowned' is the most fitting, although it slightly changes the meaning of the sentence.
• 'Drowned' typically refers to a person or animal dying due to submersion in water, but it can be metaphorically used to refer to a ship being submerged in water.

Therefore, the correct sentence is: Titanic drowned after midnight.

The correct answer is 'To give great importance to trifles'.

Key Points

• The idiom "to make a mountain out of a molehill" means to exaggerate or put too much focus on a minor issue and turn it into a major one.
• A molehill is a small mound of earth created by moles, and it's small compared to a mountain.
• So this idiom is used to point out that someone is making a big deal out of something that isn't a big problem.

Therefore, the correct answer is: To give great importance to trifles.

Additional Information

• Here's why the other options are incorrect:
• "To violate the rules" - This means to break the rules or not follow the established guidelines.
• "To make unnecessary comments" - While this can sometimes be a part of making a mountain out of a molehill, it's not a direct interpretation of the idiom.
• "To achieve big success" - This suggests a positive outcome or reaching a high level of achievement.

The correct answer is 'Option 3'.

Key Points

• When converting direct speech into reported speech, the tense of the verb usually moves one step back in time. This is known as backshifting.
• However, if the direct speech is in the past perfect (as is the case with "The prisoner had slept throughout the journey"), it does not change when turned into reported speech because the past perfect tense is already the most 'remote' tense possible in English.
• So "had slept" remains "had slept" in reported speech.

Therefore, the correct answer is: 'Pritam said that the prisoner had slept throughout the journey.'

The correct answer is 'Option 2'.

Key Points

• The idiom "A bite at the cherry" is used to refer to an opportunity to achieve something or a chance to do something.
• It often refers to a second chance or another opportunity after missing out on a previous attempt.

Therefore, the correct answer is: 'An attempt or opportunity to do something.'

Additional Information

• Here's why the other options are incorrect:
• "A wrong move" - This phrase means to make an incorrect decision or action, which does not relate to the concept of an opportunity presented in "a bite at the cherry."
• "To have a leverage over someone" - This phrase means to have a form of power or advantage over another person, which does not correspond with the idea of an opportunity or attempt expressed in the idiom.
• "A dog bite" - This is a literal translation and does not convey the metaphorical meaning of the idiom "a bite at the cherry," which is about opportunities or attempts, not about physical biting.