SSC CHSL Tier-1 2022: Official Paper (Held On: 15 March, 2023 Shift 3) (Previous Year Paper)

The logic followed here is:

Logic: **(**1^st number + 2)² = 2^nd number.

Now,

For 27 ∶ 841

→ (27 + 2)²

→ 29² = 841.

For 18 ∶ 400

→ (18 + 2)2

→ 202 = 400.

Similarly, for ? ∶ 324

→ (16 + 2)2

→ 182 = 324.

Hence, the correct answer is "Option 1".

According to the sequence in the dictionary: 

The correct order of the given words is:

4. Ectasia
5. Emergence
6. Energetic
7. Engine
8. Envelope 

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

Additional Information

1. First of all, check the common letter in all.
2. Arrange them according to the alphabet they come first. 
3. When common letters are arranged, then go for the rest.

The logic followed here is:

Consonants: +1

Vowels: Next Vowel

'CLOUD' is written as 'DMUAE'.

'WHITE' is written as ‘XIOUI’

Similarly, for 'WATER'

'WATER' is coded as 'XEUIS'.

Hence, the correct answer is "Option 1".

From the given open Dice:

7 and 2 is the opposite sides.

3 and 6 is the opposite sides.

4 and @ is the opposite sides.

And, two opposite sides can not be the adjacent surfaces, so it can't be shows in a dice.

Now,

Option 1) 

→ Can not be made, because 4 and @ is the opposite sides.

Option 2) 

→ Can not be made, because 7 and 2 is the opposite sides.

Option 3) 

→ Can not be made, because 3 and 6 is the opposite sides

Option 4) 

→ Can be made, because all the surfaces are adjacent sides.

Hence, the correct answer is "Option 4".

For find the opposite faces of '8', we need to compare the common surface in the given dices,

Now,

From Dice 1 and Dice 3,

Here, 3 and 7 is the common surfaces in both dice, so 8 and 6 is the opposite sides.

Hence, the correct answer is "Option 3".

The logic followed here is:

Option 1) IJK → I + 1 = J; J + 1 = K.

Option 2) GIK → G + 2 = I; I + 2 = K.

Option 3) LNP → L + 2 = N; N + 2 = P.

Option 4) TVX → T + 2 = V; V + 2 = X.

So, 'IJK' odd among the all options.

Hence, the correct answer is "Option 1".

Statements:

l. All parrots are birds.

ll. Some birds are butterflies.

The least possible Venn diagram for the given statement is:

Conclusion:

I. All butterflies are parrots - False (No definite relation given between butterflies and parrots, so it can be possible only).

II. Some parrots are butterflies - False (No definite relation given between butterflies and parrots, so it can be possible only).

So, Neither conclusion I or II follow.

Hence, the correct answer is "Option 3"

The logic followed here is:

Logic: (Sum of the place value) ÷ 7.

Now,

'N' is written as '2'

⇒ 14(N) ÷ 7 = 2.

For, 'KAW' is written as '5'

⇒ (11 + 1 + 23) ÷ 7.

⇒ 35 ÷ 7 = 5.

Similarly, for ‘MAN’

⇒ (13 + 1 + 14) ÷ 7

⇒ 28 ÷ 7 = 4.

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

Hence, the correct answer is "4".

According to the given Venn diagram:

The shaded area shows the "total number of brown are pink".

So, the total number of 'brown are pink' = 2 + 7 = 9.

Hence, the correct answer is "9".

For find the adjacent faces of '3', we need to compare the common surface in the given dices,

Now,

From Dice 1 and Dice 3,

2 and 5 is the common surface, so 3 and 7 will be the opposite surfaces.

From Dice 1 and Dice 2,

7 is the opposite surface of 3, so 2,5,4,6 these all are the adjacent surface of 7 and 3.

So, according to the options '6 and 4' will be the adjacent surfaces of 3.

Hence, the correct answer is "Option 3".

Family Chart:

Given: 

Mukesh's sister is the wife of Ramesh.

Ramesh is Rani's only brother.

Ramesh's father is Madhur.

Sheetal is Ramesh's paternal grandmother.

Rema is Sheetal's daughter-in-law.

Ronit is Rani's brother's son.

So, Ronit is Nephew of Mukesh.

Hence, the correct answer is "Option 2".

The logic followed here is:

For, MAKE : KEMA

For, CAMP : MPCA

Similarly, for STAY : ?

Hence, the correct answer is "Option 1".

The logic followed here is:

Logic: The first word is the object of study or interest for the discipline or branch mentioned as the second word.

Here,

Heart : Cardiology → Heart is studied in Cardiology.

Similarly,

Earthquakes : ? → Earthquakes are studied in Seismology.

Hence, the correct answer is "Seismology".

The logic followed here is:

Step I: Symbol '÷' has shifting a place in anti-clockwise direction in next images.

Step II: Symbol '+' has shifting a place in anti-clockwise direction in next images.

Step III: Symbol 'Square' has shifting a place in anti-clockwise direction in next images.

Step IV: Symbol '=' has shifting a place in anti-clockwise direction in next images.

Step V: Symbol 'O' has shifting a place in anti-clockwise direction in next images.

So, the complete series will be:

So, 'Option 3' will replace the question mark.

Hence, the correct answer is "Option 3".

From the given open Dice:

P and T is the opposite sides.

Q and S is the opposite sides.

R and U is the opposite sides.

And, two opposite sides can not be the adjacent surfaces, so it can't be shows in a dice.

Now,

Option 1) 

→ Can be made, because no opposite sides in the given Dice.

Option 2) 

→ Can be made, because no opposite sides in the given Dice.

Option 3) 

→ Can not be made, because Q and S are the opposite sides.

Option 4) 

→ Can be made, because no opposite sides in the given Dice.

Hence, the correct answer is "Option 3".

The logic followed here is:

Logic: The first word is the unit of measurement for the quantity mentioned as the second word.

Here,

Radians : Angle →.Radians is the unit of measurement for Angle.

Similarly,

Ampere : ? → Ampere is the unit of measurement for Electric Current.

Hence, the correct answer is "Electric Current".

The quadrilaterals are:

So, there is '17' quadrilaterals in the given figure.

Hence, the correct answer is "17".

The logic followed here is:

Given Sequence: n o _ m _ l _ o _ m _ l n _ r _ a l

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

Option 1) naromra → n o n m a l / r o o m m l / n r r a a l

Option 2) ranraom → n o r m a l / n o r m a l / n o r m a l

Option 3) noamrna → n o n m o l / a o m m r l / n n r a a l

Option 4) manrmao → n o m m a l / n o r m m l / n a r o a l

Here, 'Option 2' followed a pattern.

Hence, the correct answer is "Option 2".

The logic followed here is:

Option 1) Howrah Bridge → Howrah Bridge is a structured situated in India.

Option 2) Eiffel Tower → Eiffel Tower is a structured situated in France.

Option 3) Taj Mahal → Taj Mahal is a structured situated in India.

Option 4) Red Fort → Red Fort is a structured situated in India.

Here, 'Eiffel Tower' is odd among the options.

Hence, the correct answer is "Option 2".

The logic followed here is:

So, '616' will complete the series.

Hence, the correct answer is "616".

The logic followed here is:

Logic: 1^st number + 6 = 2^nd number,

2^nd number + 6 = 3^rd number.

Now,

(9, 15, 21)

⇒ 9 + 6 = 15,

⇒ 15 + 6 = 21.

(31, 37, 43)

⇒ 31 + 6 = 37,

⇒ 37 + 6 = 43.

Similarly, for (65, 71, 77) 

⇒ 65 + 6 = 71,

⇒ 71 + 6 = 77.

Hence, the correct answer is "Option 3".

Given equation: 13 × 12 ÷ 36 + 11 – 7 = 35 .

BODMAS Table: 

Let's check each option one by one.

Option 1) + and ×, 36 and 7

Given: 13 × 12 ÷ 36 + 11 – 7 = 35 

After interchanging the numbers we get;

⇒ 13 + 12 ÷ 7 × 11 – 36 = 35 

⇒ 13 + 1.72 × 11 – 36 = 35 

⇒ 13 + 18.92 – 36 = 35 

⇒ 31.92 - 36 = 35 

⇒ -4.08 ≠ 35

⇒ LHS ≠ RHS

Option 2) + and –, 12 and 7

Given: 13 × 12 ÷ 36 + 11 – 7 = 35 

After interchanging the numbers we get;

⇒ 13 × 7 ÷ 36 - 11 + 12 = 35 

⇒ 2.53 + 11 – 12 = 35

⇒ 13.53 – 12 = 35

⇒ 1.53 ≠ 35

⇒ LHS ≠ RHS

Option 3) × and ÷, 13 and 36 

Given: 13 × 12 ÷ 36 + 11 – 7 = 35 

After interchanging the numbers we get;

⇒ 36 ÷ 12 × 13 + 11 – 7 = 35 

⇒ 3 × 13 + 11 – 7 = 35 

⇒ 39 + 11 – 7 = 35 

⇒ 50 - 7 = 35

⇒ 43 ≠ 35

⇒ LHS ≠ RHS

Option 4) × and ÷, 11 and 7

Given: 13 × 12 ÷ 36 + 11 – 7 = 35 

After interchanging the numbers we get;

⇒ 13 ÷ 12 × 36 + 7 – 11 = 35 

⇒ 39 + 7 – 11 = 35 

⇒ 46 - 11 = 35

⇒ 35 = 35

⇒ LHS = RHS

Hence, the correct answer is "Option 4".

The logic followed here is:

Logic: (√1^st number × 2) × 2^nd number = 3^rd number.

Now,

For (25, 13, 130)

→ (√25 × 2) × 13

→ (5 × 2) × 13

→ 10 × 13 = 130.

For (49, 32, 448) 

→ (√49 × 2) × 32

→ (7 × 2) × 32

→ 14 × 32 = 448.

Similarly, for (36, 12, 144)

→ (√36 × 2) × 12

→ (6 × 2) × 12

→ 12 × 12 = 144.

Hence, the correct answer is "Option 1".

Given: Six friends Uday, Vikrant, William, Xena, Yasir and Ziya.

Given that no two friends have the same height

1. Vikrant is taller than only three other friends.

__ > __ > Vikrant > __ > __ > __

2. Ziya is only taller than Xena and William is only shorter than Uday.

Uday >  William > Vikrant > __ > Ziya > Xena

So, Yasir will sit on the remaining place bacause, no two friends have the same height.

Uday >  William > Vikrant > Yasir > Ziya > Xena

Here, 'Yasir' is the third shortest among all the friends.

Hence, the correct answer is "Yasir".

The logic followed here is:

Logic: The gap between the numbers are square of consecutive numbers.

Now,

For (83, 119, 168)

→ 83 + 6² 

→ 83 + 36 = 119.

→ 119 + 72 

→ 119 + 49 = 168.

For (76, 101, 137) 

→ 76 + 52 

→ 76 + 25 = 101.

→ 101 + 62 

→ 101 + 36 = 137.

Similarly, for (78, 87, 103)

→ 78 + 32 

→ 78 + 9 = 87.

→ 87 + 42 

→ 87 + 16 = 103.

Hence, the correct answer is "Option 2".

The correct answer is Option 4. 

Key Points

• Bihu is the famous dance form of Assam, a state located in northeastern India.
• It is an integral part of the Bihu festival, which is the most important festival in Assam and is celebrated to mark the agricultural cycle.
• Bihu is characterized by energetic movements, rhythmic footwork, and graceful hand gestures.
• The Bihu dance is performed by both men and women, usually in groups.
• It is accompanied by traditional Bihu music, which includes the use of instruments like the dhol (a double-headed drum), pepa (a buffalo hornpipe), and taal (a cymbal).
• The dancers wear colorful traditional attire, with women typically dressed in Mekhela Chador, a two-piece garment, and men wearing dhoti and kurta.

Additional Information

• Kalbeliya is a famous dance form of Rajasthan, a state in northwestern India.
• It is primarily associated with the Kalbeliya community, a nomadic tribe known for their snake-charming skills and their distinctive dance style.
• The Kalbeliya dance is an integral part of their cultural expression and has gained recognition and popularity worldwide. The Kalbeliya dance is characterized by its graceful and rhythmic movements, which imitate the fluid and sinuous movements of a snake.
• Kathak is one of the major classical dance forms of India, originating from the northern region of the country, particularly in the states of Uttar Pradesh and Rajasthan.
• It is a highly expressive dance form that combines rhythmic footwork, intricate hand gestures, facial expressions, and storytelling.
• Bhangra is a lively and energetic dance form that originated in the Punjab region of India and Pakistan.
• It is a traditional folk dance and music style that has become popular worldwide.
• Bhangra is associated with the harvest season and is often performed during festivals and celebrations.

The correct answer is Option 3. 

Key Points

• Australia is the world's largest producer of bauxite, with production amounting to an estimated 100 million metric tons in 2022.
• Formation and Composition: Bauxite is a sedimentary rock that is primarily composed of aluminum hydroxide minerals, iron oxides, and various impurities. It is formed through the weathering and erosion of rocks in tropical and subtropical areas, where high rainfall and prolonged exposure to moisture contribute to its development over millions of years.
• Aluminum Ore: Bauxite is the primary source of aluminum metal. It contains a significant amount of alumina (aluminum oxide), which is extracted from the bauxite ore through a refining process known as the Bayer process. Alumina is then further processed to obtain aluminum metal used in a wide range of industries, including transportation, construction, packaging, and electrical applications.
• Global Reserves and Production: Bauxite reserves are found in various countries around the world, with the largest deposits located in Australia, Guinea, Brazil, China, and India. These countries account for the majority of global bauxite production. The availability and accessibility of bauxite deposits, along with economic factors and environmental considerations, influence production levels in different regions.
• Environmental Impact and Sustainability: Bauxite mining and processing can have significant environmental impacts. The extraction of bauxite often involves clearing forests, disrupting ecosystems, and generating large amounts of waste, including red mud, which is a byproduct of the refining process. Sustainable mining practices, land rehabilitation efforts, and technological advancements are being pursued to mitigate these environmental concerns and promote responsible bauxite production.

The correct answer is Option 3. 

Key Points

• India and France were re-elected as the president and co-president of the International Solar Alliance (ISA) for a term of two years at the virtual meeting of the third assembly.
• A total of 53 member countries and 5 signatory and prospective member countries participated in the assembly.

Additional Information

• At the virtual meeting of the third assembly, the International Solar Alliance (ISA) appointed four new Vice-Presidents to represent different regions.
• The Asia Pacific Region was represented by Fiji and Nauru, while Mauritius and Niger represented the Africa Region.
• The Europe and others Region had representatives from the UK and Netherlands, and the Latin America and Caribbean Region was represented by Cuba and Guyana.
• These Vice-Presidents assumed their positions. During the assembly, the initiatives of the ISA Secretariat to establish the Coalition for Sustainable Climate Action (CSCA) and enhance engagement with the private and public corporate sector were approved.
• As a significant step, ten public sector organizations in India presented a cheque of 1 million USD each to support these initiatives at the assembly.

The correct answer is Option 2. 

Key Points

• The correct height of Kanchenjunga, the third highest peak in the world, is approximately 8,598 meters (28,209 feet).
• Kanchenjunga is indeed a magnificent mountain located in the Himalayan range, straddling the border between Nepal and the Indian state of Sikkim.

Additional Information

• The name "Kanchenjunga" means "Five Treasures of Snow" in Tibetan, referring to its five peaks, which are said to represent the five repositories of God: gold, silver, gems, grain, and holy books.
• The mountain is located on the border of Nepal and the Indian state of Sikkim.
• It has been a prominent feature in the local cultures and religions due to its imposing presence.
• Kanchenjunga was first climbed on May 25, 1955, by a British expedition led by Charles Evans.
• However, out of respect for local religious beliefs, they stopped a few feet short of the actual summit.Despite being one of the highest peaks in the world, Kanchenjunga is less frequently climbed than Everest or K2 due to its remote location and the difficulty of its ascent, which is considered one of the most challenging in mountaineering.

The correct answer is Option 2. 

Key Points

• The equinox falls on 21 March and 23 September, approximately.
• On 21 March, it is known as the vernal equinox or spring equinox in the Northern Hemisphere and the autumnal equinox in the Southern Hemisphere.
• On 23 September, it is known as the autumnal equinox in the Northern Hemisphere and the vernal equinox or spring equinox in the Southern Hemisphere.
• These dates can vary by a day or so depending on the year and time zone.

The correct answer is Kerala.

Key Points

• The 2022 Santosh Trophy was won by Kerala, who triumphed over West Bengal in a 5-4 penalty shootout victory.
• The thrilling final took place at the Manjeri Payyanad Stadium in Malappuram, Kerala.
• The victory was especially memorable for Kerala as they lifted the Santosh Trophy for the **seventh time.**​

Additional Information

• The Santosh Trophy is one of India's most prestigious football tournaments, organized by the All India Football Federation (AIFF).
• Named after the late Maharaja Sir Manmatha Nath Roy Chowdhary of Santosh (now in Bangladesh).
• it has been held annually since 1941.
• The tournament involves teams representing different states and government institutions.

The correct answer is Attorney General for India.

Key Points

• The Attorney General (AG) of India
• This is a part of the Union Executive. AG is the highest law officer in the country.
• Article 76 of the Constitution provides for the office of AG of India.
• AG is appointed by the President on the advice of the government.
• S/he must be a person who is qualified to be appointed a judge of the Supreme Court, i.e. s/he must be a citizen of India and must have been a judge of some high court for five years or an advocate of some high court for ten years or an eminent jurist, in the opinion of the President.
• Term of the Office: Not fixed by the Constitution.

Additional Information

• Vice President of India 
• The vice pres ident of India is the deputy to the head of state of the Republic of India, i.e. the president of India.
• The Vice-President is elected by an electoral college consisting of members of both Houses of Parliament, in accordance with the system of proportional Representation.
• Article 324 of the Constitution read with the Presidential and Vice-Presidential Elections.
• The 14^th and current vice president of India is Jagdeep Dhankar.

Thus, the Vice-Pres ident of India is elected by Members of Parliament

• Chief Justice of India
• The Chief Justice of India (CJI) is appointed by the President of India under clause (2) of Article 124 of the Constitution.
• The chief justice is appointed by the president after consultation with such judges of the Supreme Court and high courts as he

deems necessary.

• The other judges are appointed by the president after consultation with the chief justice and such other judges of the Supreme Court and the high courts as he deems necessary.
• Consultation with the chief justice is obligatory in the case of the appointment of a judge other than the Chief justice.
• ​Solicitor General of India
• The Solicitor General of India is a Legal advisor.
• The Solicitor General of India is subordinate to the Attorney General of India.
• He himself assisted by several Additional Solicitor Generals of India.

The correct answer is 5.7%.

Key Points

• India's economic growth is expected to decline to 5.7% in 2022 from 8.2% in 2021, according to the United Nations Conference on Trade and Development (UNCTAD) Report 2022.
• India's GDP will further decelerate to 4.7% growth in 2023, as per this report.
• The report has cited higher financing costs & weaker public expenditures for this decline in growth.

Additional Information

• The United Nations Conference on Trade and Development (UNCTAD) is an intergovernmental organization.
• It aims to promote the interests of developing states in world trade.
• UNCTAD is part of the United Nations Secretariat dealing with trade, investment, and development issues.
• UNCTAD:
• Headquarters: Geneva, Switzerland
• Founded: 1964
• Founder: United Nations General Assembly
• Secretary-General: Rebeca Grynspan

The correct answer is Ahmedabad.

Key Points

• Prime Minister Narendra Modi inaugurated Phase 1 of Modi Shaikshanik Sankul, an educational complex in Ahmedabad, Gujarat in October 2022.
• The project is a part of the government's efforts to provide quality education to all sections of society.
• The complex will provide facilities for holistic development of students, including hostel, classrooms, laboratories, and sports facilities.
• It will also have a library, an auditorium, and a cafeteria.
• The complex is expected to benefit over 1,000 students.

Additional Information

• Some points about Gujarat
• Present Chief Minister: Bhupendrabhai Patel
• Governor: Acharya Devvrat
• Rajya Sabha Seats: 11
• Lok Sabha Seats: 26

The correct answer is Kuchipudi.

Key Points

• Deepika Reddy is an acclaimed Kuchipudi dancer.
• She started her journey 50 years ago and she had her Rangapravesham in 1976.
• She has performed across the world, including at the Rashtrapati Bhavan, Sri Lankan parliament, Hiroshima in Japan, and France.
• She received the prestigious Sangeet Natak Akademi Award for her contribution to the Kuchipudi dance from President Ram Nath Kovind at Rashtrapati Bhavan.

Additional Information Important dance form and performing states. 

Correct Answer Java

Key PointsPython:

• A very user-friendly language for beginners that supports multiple programming paradigms, including object-oriented programming (OOP).
• It's commonly used in data analysis, machine learning, web development, and many other fields.

Java:

• One of the most popular object-oriented languages used globally.
• It is widely used in enterprise environments and for building large-scale applications.

C++:

• A highly efficient and flexible language that supports OOP.
• It's typically used for system/software development, game development, and other performance-critical areas.

C#:

• Developed by Microsoft, this language is primarily used for Windows desktop applications and game development (with the Unity engine), but it's versatile enough for just about anything.

JavaScript:

• Though primarily a prototype-based language, JavaScript also supports object-oriented programming.
• It is the main language for web development.

The correct answer is 'Ahmedabad'.

Key Points:

• The International Kite Festival 2023 began in Ahmedabad, Gujarat on January 08.
• The festival is being organized by Gujarat Tourism on the G20 theme of 'One Earth, One Family, One Future', and will be held from January 8 to 14.
• Apart from Ahmedabad, the International Kite Festival will also be organized in Surat, Vadodara, Rajkot, Dwarka, Somnath, Dhordo, and Kevadia.
• More than 800 kite flyers from across India and the world(65 countries) will participate and display their unique creations in this Festival.
• This year, kite enthusiasts from different countries will fly Kites at the same time attempting to create a Guinness World Record for the maximum number of kite flyers.
• A special Parade by international and national kite flyers, a theme pavilion displaying the history of kites, and workshops on making and flying kites are among the major attractions of the festival this year.

Additional Information:

• Ahmedabad is the most populous city in the Indian state of Gujarat. It is the administrative headquarters of the Ahmedabad district and the seat of the Gujarat High Court.
• It is the second-largest producer of cotton in India, due to which it was known as the 'Manchester of India' along with Kanpur.
• In July 2017, the Historic City of Ahmedabad, or Old Ahmedabad, was declared a UNESCO World Heritage City.

The correct answer is 40^th

Key Points:

• ​The Global Innovation Index 2022 rankings released by World Intellectual Property Organization. Hence, statement A is incorrect.
• In 2022, India was ranked 40^th position out of 132 countries. Hence, statement B is incorrect.
• Switzerland is the most innovative economy in the world in 2022 ranked 01^st on the list. Hence, statement C is incorrect.
• India and Turkiye enter the top 40 for the first time as innovation leaders. Hence, statement D is correct.

Additional Information:

• World Intellectual Property Organization published the Global Innovation Index ranking the countries and their economies through innovational measures, environments, and outputs.
• It was first published in 2007 by INSEAD and World Business, a British magazine until 2020. In 2021 it was published by the World Intellectual Property Organization.
• ​The theme for 2022 is What is the future of innovation-driven growth?
• In 2021 India was ranked 46^th on the list.
• Consecutively, Switzerland has ranked first from 2011 up to 2022.
• South Korea is the only Asian country holding the 06^th position in the top 10 in 2022.

Important Points:

• ​World Intellectual Property Organization (WIPO):
• Founded: 14 July 1967
• Headquarters: Geneva, Switzerland
• Director General: Daren Tang;

The correct answer is Karnataka.

Key PointsKolar Gold Fields:

• The Kolar Gold Fields is located are in the Kolar District of Karnataka.
• The mines were nationalized in 1956 and were closed in 2001 due to environmental, pricing, and lack of investments.
• The Kolar Goldfields is about 100 kilometers from Bangalore.
• Operated by the Bharat Gold Mines Limited (BGML), a public sector undertaking.
• The KGF was the world’s second deepest gold mine at a depth of 3,000 meters.
• The river Kaveri makes the second biggest waterfall in India, known as Shivasamudram Falls.
• The hydroelectric power generated from the falls is supplied to Mysuru, Bengaluru, and the Kolar Gold Field nearby it.
• The mines remained active for 121 years before they experienced an unsystematic closure on February 28, 2001.
• The mines were closed owing to high operational costs and low revenues.
• The late Prime Minister Jawaharlal Nehru had pledged the mines as a security deposit to the World Bank.

Correct Answer Only I

Key Points

• The pH value of salts of strong acid and strong base is 7.
• The salts are from a strong acid and strong base that do not hydrolyze and the resulting salt pH will remain 7.
• The anion in the salt form's strong base does not attract the H+ from the water.
• Salt of a strong acid and a weak base is acidic with a pH value less than 7 because acid is strong which retains the pH value less than 7. Statement I is correct
• Salt of a weak acid and strong base is base with a pH value of more than 7 because the base is strong hence pH of the whole solution will be more than 7.
• Salt of a strong acid and strong base is neutral because both are strong and cancels strong effects of each other, the pH will be 7.

Statement II:(Incorrect)

• When electricity is passed through an aqueous solution of sodium Chloride (brine), it decomposes to form NaOH + H₂ + CI₂.
• Brine is a saturated solution of NaCl (Sodium chloride).
• Electrolytic decomposition of solution gives Cl₂ (Chlorine) at the anode and H₂ (Hydrogen) is formed at the cathode and NaOH (Sodium hydroxide ) is formed near to the cathode.
• This process is known as chor- alkali process.

The correct answer is Mother Teresa.

Key Points

• Mother Teresa, officially known as Saint Teresa of Calcutta, was a Roman Catholic missionary who worked in Bengal, particularly in Kolkata (formerly known as Calcutta), for the majority of her life.
• She dedicated her life to serving the poor, sick, and marginalized people in Kolkata, establishing the Missionaries of Charity and receiving worldwide recognition for her humanitarian work.
• Mother Teresa, originally named Anjezë Gonxhe Bojaxhiu, was born on August 26, 1910, in Skopje, now North Macedonia.
• She joined the Sisters of Loreto at the age of 18 and moved to Ireland to train as a missionary.
• In 1929, Mother Teresa arrived in Kolkata (formerly Calcutta), India, where she taught at St. Mary's School for girls.
• During a train ride to Darjeeling in 1946, she experienced what she referred to as a "call within a call" from God to work among the poorest of the poor.
• In 1950, Mother Teresa founded the Missionaries of Charity, a Roman Catholic religious congregation dedicated to serving the destitute and dying.
• The Missionaries of Charity focused on providing care, shelter, and support to the sick, homeless, orphans, lepers, and individuals dying on the streets of Kolkata.
• Mother Teresa's selfless and dedicated service to the poor and marginalized garnered global attention, and the Missionaries of Charity expanded internationally.
• She received numerous awards and honors for her humanitarian work, including the Nobel Peace Prize in 1979.

Additional Information

The correct answer is West Bengal.​

Key Points

• West Bengal has been accredited with the International Travel Award 2023, for 'best destination for culture' by the Pacific Area Travel Writers Association (PATWA), an affiliate of the UN World Tourism Organisation.
• The award will be conferred in Berlin, at the World Tourism & Aviation Leaders' Summit on March 9, 2023.
• PATWA is an organisation of travel writers that was founded in 1998.​

Additional Information

• West Bengal is a state in eastern India.
• It is the fourth-most populous state and the thirteenth-largest state by area in India.
• It also borders the Indian states of Odisha, Jharkhand, Bihar, Sikkim and Assam.
• West Bengal includes the Darjeeling Himalayan hill region, the Ganges delta, the coastal Sundarbans and the Bay of Bengal.
• West Bengal:
• Capital: Kolkata
• Chief Minister: Mamata Banerjee
• Established: 26 January 1950
• Districts: 23
• Sex ratio (2011): 947 /1000
• Literacy (2011): 77.08%

The correct answer is High Yielding Variety.

Key Points

• The Green Revolution started in 1965 with the first introduction of High Yielding Variety (HYV) seeds in Indian agriculture.
• In 1965, the government with the help of Indian geneticists M.S. Swaminathan, known as the father of the Green Revolution, launched the Green Revolution.
• The movement lasted from 1967 to 1978 and was a great success.
• This was coupled with better and efficient irrigation and the correct use of fertilizers to boost the crop.
• The result of the Green Revolution was to make India self-sufficient when it came to food grains.
• These HYV seeds had more success with the wheat crop and were highly effective in regions that had proper irrigation.

Additional Information

Other Revolutions:

The correct answer is Sergio Perez.

Key Points

• Sergio Perez won the race, becoming the first Mexican driver to win in Formula 1.
• Charles Leclerc finished second, while Carlos Sainz Jr. finished third.
• Max Verstappen retired from the race with a mechanical problem.
• The race was held in wet conditions, making it a challenging one for the drivers.
• Perez started the race from pole position and led from start to finish.
• Leclerc made a late charge for the lead, but was unable to pass Perez.
• Sainz Jr. finished third after a strong drive from the back of the grid.
• The win for Perez was his fourth of the season and moved him up to third in the Drivers' Championship.
• The result also extended Red Bull's lead in the Constructors' Championship.

Additional Information

Formula 1 Grand Prix 

• Formula 1 Grand Prix is a motor race for single-seat Formula One cars that is sanctioned by the Fédération Internationale de l'Automobile (FIA).
• The races are held on purpose-built circuits and public roads around the world.
• The Formula One World Championship is the highest class of single-seater auto racing sanctioned by the FIA.
• The championship consists of a series of races held over a period of several months.
• The drivers and constructors with the most points at the end of the season are crowned champions.
• The first Formula One Grand Prix was held in 1950 at Silverstone Circuit in England.
• The current Formula One World Championship consists of 22 races held over a period of nine months.
• The races are held in a variety of countries around the world, including Australia, Austria, Bahrain, Belgium, Canada, China, France, Germany, Hungary, Italy, Japan, Mexico, Monaco, Netherlands, Russia, Saudi Arabia, Singapore, Spain, Turkey, United Arab Emirates, and the United States.

The correct answer is PM Narendra Modi.​

Key Points

• PM Narendra Modi will dedicate 75 Digital Banking Units (DBUs) to the nation on 16 Oct 2022.
• As part of the Union budget speech for 2022-23, the Finance Minister had announced the setting up of the 75 DBUs in 75 districts of the country to commemorate the 75 years of independence of the country.
• The DBUs are being set up to ensure benefits of digital banking reach all corners of the country.

Additional Information

• ​Important Current Affairs Related to PM Narendra Modi:​ 
• PM Modi inaugurated Phase 1 of Modi Shaikshanik Sankul, an educational complex for needy students in Ahmedabad, Gujarat on 10^th Oct 2022.
• PM Modi on 9^th Oct 2022 declared Modhera in Gujarat's Mehsana district as India's first 24x7 solar-powered village.
• Prime Minister Narendra Modi inaugurated the Akshaya Patra Foundation’s new midday meal kitchen in Varanasi on 7 July 2022.
• PM Narendra Modi on 7 July 2022 inaugurated 'Akhil Bhartiya Shiksha Samagam' on implementation of the National Education Policy (NEP) in Varanasi.
• PM Modi laid the foundation stone and inaugurated several projects worth 33000 crore rupees in Bengaluru on 20 June 2022.
• Prime Minister Narendra Modi inaugurated ‘Kranti Gatha’ on 14 June 2022.
• PM Modi on 10 June 2022 inaugurated the headquarters of the Indian National Space Promotion and Authorisation Centre (IN-SPACe) at Bopal in Ahmedabad, Gujarat.

The correct answer is Gujarat Titans.

Key Points

• The Indian Premier League (IPL) 2022 ended with Gujarat Titans (GT) lifting the trophy by defeating inaugural champions Rajasthan Royals (RR) at the Narendra Modi Stadium, Ahmedabad.
• The Indian Premier League (IPL) 2022, was the 15^th edition of the professional Twenty20 cricket league established by the Board of Control for Cricket in India (BCCI).
• The host country for IPl 2022 was India.
• The Orange Cap title winner is Jos Butler (Rajasthan Royals) with Total runs: 863 runs.
• The Purple Cap title winner is Yuzvendra Chahal (Rajasthan Royals) with total of 27 Wickets.
• IPL 2022 Sponsorer was TATA.

Additional Information

• TATA group has been adjudged as the sponsor of WPL 2023.
• The media rights for the Women's IPL have been sold for INR 951 crores.
• The Women's IPL is set to get underway in 2023.
• Franchise-based model is likely to see five teams in the inaugural season.
• The Board of Control for Cricket in India (BCCI) was formed in 1928  as a society.
• ​BCCI does not depend on the Government for its finances.
• Roger Binny is the incumbent BCCI president and Jay Shah is the secretary.

The correct answer is September 1932.

Key Points

• Poona Pact: (1932)
• Poona Pact was signed in the year 1932.
• The reason for the Poona Pact was the Communal Award of August 1932 which provided a separate electorate for depressed classes.
• Poona pact signed between Dr B R Ambedkar and Gandhiji.
• Poona pact was signed on September 24, 1932, at Yerwada Jail in Pune.
• Madan Mohan Malaviya signed it on behalf of upper-caste Hindus and Gandhi.
• Ambedkar signed on behalf of depressed classes.
• The final outcome of the Poona pact was 147 electoral seats.
• Provisions of the Poona Pact: 
• Seats would be reserved for the ‘Depressed classes’ in the Provincial Councils.
• The number of seats reserved for the provinces depended on the strength of the provinces:
• Madras: 30; Punjab: 8; Bombay and Sindh: 15; Central Provinces: 20; Bihar and Orissa: 18; Bengal: 30; United Provinces: 20; and Assam: 7 (Total reserved: 148)
• In the Central Legislature, 19% of the seats would be reserved for the Depressed Classes.
• The members of the depressed classes who were eligible to vote would form an electoral college.
• This College would elect four candidates among the depressed classes on the basis of a single vote.
• That is, the candidates with the four highest numbers of votes would form the panel of four).
• Then, these four candidates would stand for election with the general candidates for election to the assembly.
• This time, the general electorate would vote. Thus, in effect, the depressed classes got a ‘double vote’ since they formed part of the general electorate also.

This principle of ‘Joint electorate and reserved seats’ was to be followed in the Central Assembly too.

• It was agreed that this system would continue for ten years unless it was ended by mutual consent sooner.
• It was also agreed upon to allocate a certain portion of money from the educational grant for the education of the depressed classes in all the provinces.
• Nobody would be discriminated against because they belonged to the depressed classes in the matter of election to the local bodies or appointment to government service.

The correct answer is Geostationary orbit.

Key Points

• The satellites that circle Earth directly above the equator are in a Geostationary orbit.
• Geostationary Orbit:
• ​This is a type of geosynchronous orbit, which means the satellite's orbital period is the same as the rotation period of the Earth.
• A satellite in a Geostationary orbit appears stationary with respect to an observer on the Earth's surface.
• Location:
• ​Geostationary orbits are directly above the Earth's equator and follow the direction of the Earth's rotation.
• Applications:
• ​These orbits are particularly useful for communication, weather observation, and other satellites that need a constant view of one area of the surface.
• Orbit Height:
• ​The geostationary orbit is at an altitude of approximately 35,786 kilometers (22,236 miles) above Earth's equator.
• Satellite Speed:
• ​Satellites in geostationary orbit travel at the same rotational speed as the Earth, which allows them to stay in the same position relative to the Earth's surface.

Additional Information

The correct answer is Freedom to manage religious affairs.

• There are six fundamental rights provided in the Constitution of India. Part III and Article 12 – 35 deal with fundamental rights in the Constitution of India.
• Right to freedom of religion - Articles 25-28
• The right to freedom of religion finds its mention under Articles 25-28.
• Article 25 refers to the freedom of conscience and free profession, practice, and propagation of religion.
• Article 26 refers to the freedom to manage religious affairs.
• Article 27 refers to freedom as to the payment of taxes for the promotion of any particular religion.
• Article 28 refers to freedom as to attendance at religious instruction or religious worship in certain educational institutions.
• Six fundamental rights provided in the Constitution of India are:

The correct answer is Projector.

Key Points

• Projector: A projector is an output device that projects an image from a computer screen onto a larger surface, such as a wall or a whiteboard.
• This allows users to share their work with a larger audience.
• Scanner:  A scanner is an input device. It converts images or text into a digital format.
• This allows users to store and edit their work electronically.
• OCR: An OCR device is an input device that converts text from a scanned image into a digital format.
• This allows users to extract text from documents that are not in a digital format.
• MICR: A MICR device is an input device that reads numbers and letters that are printed in magnetic ink.
• This is used in banking applications to read account numbers and other data on checks.

Additional Information

Given:

Cost price of 60 chairs = Rs. 24,560

Profit = 20%

Formula:

Profit = (Selling price - Cost price)/Cost price ×100

Solution:

Cost price per chair = 24,560/60 = Rs. 409.33

Calculate the selling price of one chair to earn a 20% profit:

Selling price per chair = Cost price per chair + (Profit / 100) × Cost price per chair

= 409.33 + (20/100) × 409.33 = Rs. 491.19

Calculate the number  of chairs that must be sold to earn a profit of Rs. 24,560:

Number of chairs = Total profit/Selling price per chair

= 24,560/491.19 = 50

Therefore, 50 chairs must be sold to earn a profit of Rs. 24,560.

Calculation:

According to the question:

Salary of J = 75

Salary of M = 100

The ratio is:

75 : 100

3 : 4

∴ Option 2 is the correct answer.

Given:

 

Calculation:

Total savings = Sum of savings for all companies

Total savings = 400 + 900 + 700 + 400 + 500 = 2900

Total expenditure = Sum of expenditure for all companies

Total expenditure = 200 + 500 + 400 + 300 + 1100 = 2500

Percentage difference = ((Total savings - Total expenditure)/Total savings) × 100

Percentage difference = ((2900 - 2500)/2900) × 100

Percentage difference = (400/2900) × 100

Percentage difference ≈ 13.79%

Therefore, the total expenditure of all the companies is approximately 13.79% less than the total savings.

Shortcut Trick

For small values, use hit and trial by identifying factors or pairs of numbers.

Given p + q = 7 and p² + q² = 25, check pairs that sum to 7:

(3, 4) ⇒ 3 + 4 = 7 and 3² + 4² = 9 + 16 = 25. This satisfies both conditions.

The product pq = 3 × 4 = 12.

∴ The correct answer is 12.

Alternate Method

Given values: p + q = 7 and p² + q² = 25

Formula used: (p + q)² = p² + q² + 2pq

Applying the algebraic identity:

⇒ (p + q)² = 7²

⇒ p² + q² + 2pq = 49

⇒ 25 + 2pq = 49

⇒ 2pq = 49 − 25

⇒ 2pq = 24

⇒ pq = 24 ÷ 2

⇒ pq = 12

∴ The correct answer is 12.

Additional Information

Square of a Difference

(p − q)² = p² + q² − 2pq. This formula is used when the difference and sum of squares are known.

Difference of Squares

p² − q² = (p − q)(p + q). This identity helps in factorizing quadratic expressions.

Relationship between Identities

(p + q)² − (p − q)² = 4pq. This is useful for finding the product directly from the sum and difference.

Given:

4-digit number: XY7B

The number is divisible by 4.

Formula:

A number is divisible by 4 if the last two digits form a number divisible by 4.

To find the largest value of B, we need to determine the largest possible value for the last two digits that forms a number divisible by 4.

Solution:

Since XY7B is a 4-digit number divisible by 4, B must be even. The possible values for B are 0, 2, 4, 6, and 8.

So the last two digits will be 70, 72, 76, and 78.

Note that only 72 and 76 are divisible by 4

So the largest value of B is 6

Therefore, the largest value of B is 6.

Shortcut Trick

Ratio of Time (Upstream : Downstream) = 2 : 1

Since Distance is constant, Speed ratio is inverse of Time ratio: (U : D) = 1 : 2

Speed in Still Water (u) : Speed of Stream (v) = (D + U) : (D − U) = (2 + 1) : (2 − 1) = 3 : 1

Given 3 units = 12 km/h ⇒ 1 unit = 12 ÷ 3 = 4 km/h

∴ The correct answer is 4 km/h.

Alternate Method

Given:

Speed in still water (u) = 12 km/h

Let the rate of flow of the river (v) = x km/h

Time taken to row upstream = 2 × Time taken to row downstream

Formula Used:

Speed = Distance ÷ Time

Downstream Speed = u + v

Upstream Speed = u − v

Calculations:

Let the distance be D km.

⇒ D ÷ (12 − x) = 2 × (D ÷ (12 + x))

⇒ 1 ÷ (12 − x) = 2 ÷ (12 + x)

⇒ 12 + x = 2 × (12 − x)

⇒ 12 + x = 24 − 2x

⇒ x + 2x = 24 − 12

⇒ 3x = 12

⇒ x = 4 km/h

∴ The correct answer is 4 km/h.

Additional Information

Downstream and Upstream Concepts

When a boat moves with the flow of the river, it is Downstream (Speed = u + v). When it moves against the flow, it is Upstream (Speed = u − v).

Speed of Still Water and Stream

Still water speed (u) = (Downstream Speed + Upstream Speed) ÷ 2. Stream speed (v) = (Downstream Speed − Upstream Speed) ÷ 2.

Ratio Relationship

If time taken to travel a distance upstream is n times the time taken downstream, then u/v = (n + 1) / (n − 1).

Given:

A circle is circumscribing a triangle whose sides are 30 cm, 40 cm and 50 cm

Concept Used:

Circumference of circle = 2πr

Calculation:

The triangle described is a right triangle (since    $30^2 + 40^2 = 50^2$), also known as a Pythagorean triplet.

In a right triangle, the circumradius (radius of the circle circumscribing the triangle) is half the length of the hypotenuse.

Since the hypotenuse is 50 cm, the circumradius is 50/2 = 25 cm.

The circumference of the circumscribing circle is 2 ×  π ×  25 cm = 50π cm.

∴ Option 4 is the correct answer.

Given:

32 + 12 × 36 ÷ 4 + 4 - 22 ÷ 11 × 3

Concept used:

Calculation:

⇒ 32 + 12 × 36 ÷ 4 + 4 - 22 ÷ 11 × 3

⇒ 32 + 12 × 9 + 4 - 2 × 3

⇒ 32 + 108 + 4 - 2 × 3

⇒ 144 - 2 × 3

⇒ 144 - 6

⇒ 138

Therefore, the simplified value of the expression 32 + 12 × 36 ÷ 4 + 4 - 22 ÷ 11 × 3 is 138.

Given:

$\frac{1+\sin^245^\circ}{1-cos^245^\circ}$

Calculation

sin 45° = 1/√2

sin² 45° = (1/√2)² = 1/2

cos 45° = 1/√2

cos² 45° = (1/√2)2 = 1/2

Using these values

$\frac{1+\sin^245^\circ}{1-cos^245^\circ}$

$\frac{1+ \frac{1}{2}}{1-\frac{1}{2}}$

$\frac{\frac{3}{2}}{\frac{1}{2}}$

3

∴ Option 2 is the correct answer.

Given:

Angle P = 88

PQ and PR produced to point S and T respectively.

The bisectors of angle SQR and TRQ meet at the point O.

Formula used:

External Bisectors = 90 - (P / 2)

Solution:

Angle QOR = 90 - 88 / 2 

⇒ 90 - 44 = 46

Angle QOR = 46° 

∴ Option 2 is the correct answer.

Given:

sin(x - y) = 1/2

cos(x + y) = 1/2

Calculation:

sin(x - y) = 1/2

⇒ sin(x - y) = sin 30° 

⇒ x - y = 30°       ...............(i)

cos(x + y) = 1/2

⇒ cos(x + y) = cos 60° 

⇒ x + y = 60°     .................(ii)

Add equation (i) and (ii), we get

⇒ 2x = 90°

⇒ x = 45° 

sin x cos x + 2sin2x + cos3x sec x

⇒ sin x cos x + 2sin2x + cos²x

Put the value of x in above equation

⇒ sin 45° × cos 45° + 2sin² 45° + cos² 45°

⇒ 1/√2 × 1/√2 + 2(1/√2)² + (1/√2)²

⇒ 1/2 + 1 + 1/2

⇒ 2

∴ Option 1 is the correct answer.

Given:

The average age of Ram, Raman, and Rohan = 23 years

Average age of Raman and Rohan = 27 years

Formula used:

Average = Sum of values/Number of values

Solution:

Let's assume the current age of Ram is R, Raman is Rm, and Rohan is Rh.

Using the formula for average, we can write the following equations:

(R + Rm + Rh)/3 = 23 ---(Equation 1)

(Rm + Rh)/2 = 27 ---(Equation 2)

To find Ram's age 5 years ago, we need to determine Ram's current age.

Solving Equation 2 for Rm + Rh:

Rm + Rh = 2 × 27

Rm + Rh = 54 ---(Equation 3)

Substituting Equation 3 into Equation 1:

(R + 54)/3 = 23

R + 54 = 3 × 23

R + 54 = 69

R = 69 - 54

R = 15

Ram's current age is 15 years.

Ram's age 5 years ago:

Ram's age 5 years ago = 15 - 5

Ram's age 5 years ago = 10 years old.

Therefore, Ram's age 5 years ago was 10 years.

Given:

The ratio of prices of A and B: 5 : 9

Ratio of prices of C and D: 24 : 13

Price of C is Rs. 1,500 more than the price of B

Price of D is Rs. 1,300

Formula used:

Ratio = Value 1/Value 2

Solution:

From the given ratios, we can write the following equations:

A/B = 5/9 ---(Equation 1)

C/D = 24/13 ---(Equation 2)

C = B + 1,500 ---(Equation 3)

D = 1,300 ---(Equation 4)

From Equation 1, we can express A in terms of B:

A = (5/9) × B

Substituting Equation 3 into Equation 2:

(B + 1,500)/1,300 = 24/13

(B + 1,500) × 13 = 24 × 1,300

13B + 19,500 = 31,200

13B = 31,200 - 19,500

13B = 11,700

B = 11,700 / 13

B = 900

Substituting the value of B into Equation 1:

A = (5/9) × 900

A = 500

Therefore, the price of A is Rs. 500.

Given:

Dimensions of each brick: 25 cm × 12.5 cm × 16 cm

Dimensions of the wall: 8 m long, 5 m high, and 22.5 cm thick

Formula used:

The volume of a brick = Length × Width × Height

To find the number of bricks needed, we need to calculate the volume of the wall and divide it by the volume of each brick.

Solution:

Converting the dimensions of the wall to centimeters:

Length = 8 m = 800 cm

Height = 5 m = 500 cm

Thickness = 22.5 cm

The volume of the wall = Length × Height × Thickness

800 cm × 500 cm × 22.5 cm

9,000,000 cm³

Volume of each brick = 25 cm × 12.5 cm × 16 cm

5,000 cm³

Number of bricks needed = Volume of the wall / Volume of each brick

9,000,000 cm³/5,000 cm³

1800

Therefore, you would need 1800 bricks, each measuring 25 cm × 12.5 cm × 16 cm, to construct the wall.

Given:

In the isosceles triangle, ΔABC with BC is the unequal side of the triangle,

line AD is median drawn from the vertex A to the side BC.

AC = 5 cm

AD = 4 cm (Median)

Concept used:

Apollonius's theorem:

For a triangle, ΔABC with AD is median on the side BC, 

AB2 + AC2 = 2(AD2 + DC2)

Calculation:

According to the question, the required figure is:

Since ΔABC is an isosceles triangle,

Therefore, AB = AC = 5 cm

Apply Apollonius's theorem:

⇒ 52 + 52 = 2(42 + DC2)

⇒ 25 + 25 = 2(16 + DC2)

⇒ 50 = 2(16 + DC2)

⇒ 25 = 16 + DC2

⇒ DC2 = 25 - 16

⇒ DC2 = 9

⇒ DC = 3 cm

Since D is the median point on the side BC, 

Therefore, BD = DC = 3 cm

⇒ BC = BD + CD

⇒ BC = 3 + 3 = 6 cm

Therefore, '6 cm' is the required answer.

Given:

O, T, and P can do a piece of work in 3, 4, and 6 hours respectively

Formula used:

Work done = (1/Time taken)

Solution:

The LCM of 3, 4, and 6 is 12.

Work done by O in one hour = 1/3 × 12 = 4

Work done by T in one hour = 1/4 × 12 = 3

Work done by P in one hour = 1/6 × 12 = 2

Total work done in one hour = 4 + 3 + 2 = 9

Time taken to finish the work = 1/(Total work done in one hour)

= 12/9

= 4/3

= 1 + 1/3

= 1 hour and 20 minutes

Therefore, when O, T, and P work together, they will finish the work in 1 hour and 20 minutes.

Shortcut Trick

Amount saved due to 30% reduction = 30% of Rs. 140

⇒ Savings = 0.30 × 140 = Rs. 42

This saved amount of Rs. 42 allows the customer to buy 5 more pens.

⇒ Reduced rate of Pen = Total savings ÷ Extra quantity = 42 ÷ 5 = Rs. 8.4

∴ The correct answer is Rs. 8.4.

Alternate Method

Given: Total expenditure = Rs. 140, Price reduction = 30%, Extra quantity = 5 pens.

Formula Used: Price × Consumption = Expenditure (If expenditure is constant, Price ∝ 1 / Consumption)

⇒ Let original price be 100 units. After 30% reduction, new price = 70 units.

⇒ Price Ratio (Old : New) = 100 : 70 = 10 : 7

⇒ Since expenditure is constant (Rs. 140), Consumption Ratio (Old : New) = 7 : 10

⇒ Increase in consumption = 10 − 7 = 3 units

⇒ According to question: 3 units = 5 pens

⇒ New consumption (10 units) = (5 ÷ 3) × 10 = 50/3 pens

⇒ Reduced rate = Total expenditure ÷ New consumption

⇒ Reduced rate = 140 ÷ (50/3) = (140 × 3) ÷ 50

⇒ Reduced rate = 420 ÷ 50 = Rs. 8.4

∴ The correct answer is Rs. 8.4.

Additional Information

Price-Consumption Relation

When the expenditure remains constant, the percentage increase in consumption due to a reduction in price is given by: [x / (100 − x)] × 100, where x is the reduction percentage.

Direct Formula for Reduced Price

Reduced Price = (Total Amount × Reduction %) ÷ Extra Quantity. Similarly, Original Price = Reduced Price × 100 ÷ (100 − Reduction %).

Percentage and Ratio Conversion

A reduction of 30% means the new value is 7/10 of the original value. The consumption must increase in the ratio of 10/7 to keep the product constant.

Given:

$a^4 + \frac{1}{a^4} = 194$

Identity used:

(a + b)2 = a2 + b2 + 2ab

If (x + 1/x) = p then (x3 + 1/x3) = p3 - 3p

Calculation:

a4 + 1/a4 = 194

Adding 2 on both sides we'll get

⇒ a4 + 1/a4 + 2 = 194 + 2 = (a2 + 1/a2)2

Then, (a2 + 1/a2) = √196 = 14

Again adding 2 on both sides, we'll get

⇒ a2 + 1/a2 + 2 = 14 + 2 = (a + 1/a)2

Then, (a + 1/a) = √16 = 4

⇒ a3 + 1/a3 = (a + 1/a)3 - 3 × (a + 1/a) = 43 - 3 × 4 

⇒ a3 + 1/a3 = 52

∴ Option 2 is the correct answer.

Calculation:

Here is the calculation of the difference for each year:

Year 2010: Difference = 150 - 100 = 50

Year 2011: Difference = = 120 - 80 = 40

Year 2012: Difference = 120 - 100 = 20

Year 2013: Difference = 200 - 150 = 50

Year 2014: Difference = 170 - 100 = 70

From the above calculations, we can see that the maximum difference occurs in

the year 2014, where the difference between the exports from Company A and

Company B was 70.

Therefore, the year in which the difference between the exports from Company A and Company B was maximum is 2014.

Given

Formula used:

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

Calculation

$(x - 8)^2 - (x + 8)^2 = 0$

Expanding the squared terms using the difference of squares formula $(a^2 - b^2 = (a + b)(a - b))$:

$[(x - 8) + (x + 8)][(x - 8) - (x + 8)] = 0$

Simplifying further:

[2x][-16] = 0

Now we have:

-32x = 0

Dividing both sides by -32:

x = 0

Therefore, the value of x is 0.

Given:

 $\frac{4}{3}$ (sin2 35° + sin2 55°)

Concept used:

1. sin θ = cos (90° - θ)
2. tan θ = cot (90° - θ)
3. sin2 θ + cos2 θ = 1

Calculation: 

 $\frac{4}{3}$ (sin2 35° + sin2 55°)

⇒  $\frac{4}{3}$ (sin2 35° + cos2 (90°  - 55°)

⇒   $\frac{4}{3}$ (sin2 35° + cos2 (35°))

⇒  $\frac{4}{3}$ (1)

⇒ 4/3

∴ The simplified value is 4/3.

Given:

Principal amount = Rs. P

Interest rate = 5% per annum

Interest earned = Rs. 82

Total amount = Rs. 902

Formula used:

Simple interest = (P x R x T)/100

Solution:

The interest earned is Rs. 82.

Amount = SI + P

902 = 82 + P

P = 820

The interest earned for T years

(820 x T x 5)/100 = 82

T = 10/5

T = 2

Therefore, the value of T is 2 years.

Shortcut Trick Total ratio parts = 1 + 2 + 6 = 9 parts. Sum of angles in a triangle = 180°. Smallest angle corresponds to the smallest ratio part (1). Smallest angle = (1 ÷ 9) × 180° = 20°. ∴ The correct answer is 20 degree.

Alternate Method Given: Ratio of angles = 1 : 2 : 6 Formula Used: Sum of all interior angles of a triangle is always 180°.

6x 1x 2x Sum of Angles: 1x + 2x + 6x = 180°

Let the angles be 1x, 2x, and 6x. ⇒ 1x + 2x + 6x = 180° ⇒ 9x = 180° ⇒ x = 180° ÷ 9 ⇒ x = 20° ⇒ Smallest angle = 1x = 1 × 20° = 20° ⇒ Other angles are 2 × 20° = 40° and 6 × 20° = 120° ∴ The correct answer is 20 degree.

Additional Information Angle Sum Property The sum of the measures of the interior angles of any triangle is always 180°. Exterior Angle Theorem The measure of an exterior angle of a triangle is equal to the sum of the measures of its two remote interior angles. Types of Triangles by Angles Acute triangle (all angles < 90°), Right triangle (one angle = 90°), and Obtuse triangle (one angle > 90°). Triangle Inequality Theorem The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Shortcut Trick

$CP\over MP$ = $100 - Discount\over 100 + Profit$ = $100 - 10 \over100+ 10$ = $90\over110$

⇒ Profit = 20 

⇒ %Profit =  $20\over90$ × 100 = $200\over9$ = 22.22%

Alternate Method 

Given:

After giving a 10 percent discount on an article there is still a profit of 10 percent.

Formula used:

$SP = MP\left( {\frac{{100 - discount}}{{100}}} \right)$

Calculation:

Let the Marked Price of the article be 100

Discount = 10%

$SP = 100\left( {\frac{{100 - 10}}{{100}}} \right) = 90$

Still, there is a profit of 10%

So,

$CP = 90× \frac{{100}}{{100 + 10}} = 90 × \frac{{100}}{{110}} =\frac{900}{11}$

If no discount was given

Profit $= \frac{{200 - 120}}{{120}} × 100\% = \frac{{80}}{{120}} × 100\%$ 

Profit = 22.22%

Calculation:

 The total marks obtained by X = 120 + 160 + 240 + 200 + 40 + 220 = 980

 The total marks obtained by Y = 60 + 280 + 260 + 140 + 180 + 80 = 1000

The ratio is:

980 : 1000

98 : 100

49 : 50

∴ Option 3 is the correct answer.

The correct answer is 'Option 4'

Key Points

• The part of the sentence that contains a grammatical error is: everyone were up and buzzing.
• The error lies in the verb agreement.
• The subject "everyone" is singular and hence should be followed by a singular verb form "was" instead of the plural form "were".
• Everyone was up and buzzing: This phrase suggests that all people (perhaps referring to the people on watch and the watchkeepers) were awake (up) and active or excited (buzzing).

Therefore, he corrected sentence would be: "Although people had been on watch and the watchkeepers were very tired, everyone was up and buzzing."

The correct answer is 'Option 3'.

Key Points

• "Pedal to the metal" means "To go full speed, especially while driving a vehicle" (गाडी को पूरी स्पीड पर चलाना).
• This is a common idiom used to describe someone driving very fast.

Therefore, the correct answer is: 'To go full speed, especially while driving a vehicle.'

Additional Information

• Very excessive (बहुत अधिक) does not match with the idiom.
• To enjoy yourself by going out (बाहर जाकर आनंद लेना) does not convey the same meaning.
• Avoid responsibility by giving it to someone else (जिम्मेदारी से बचना और उसे किसी और को देना) is not related to the idiom.

The correct answer is 'Option 1'.

Key Points

• In the original indirect speech, the person is reporting what someone else said.
• To convert it to direct speech, we need to change the pronouns, verb tenses, and other details to match the original speaker's words.
• Here's an explanation of why option 1 is the correct answer:
• The reporting verb "said" remains the same.
• The pronoun "he" changes to "I" to match the original speaker's perspective.
• The verb "would be taking" changes to "will be taking" to reflect the original speaker's intention.
• The time reference "two weeks" remains unchanged.
• The phrase "as there has been a death in my family" changes to "as there had been a death in his family" in indirect speech because the tense shifts from Present Perfect ("has been") in direct speech to Past Perfect ("had been") in indirect speech.

Therefore, the correct sentence is: "He said, 'I will be taking a leave of absence for two weeks as there has been a death in my family'."

The correct answer is 'Option 1'.

Key Points

• The sentences follow a logical flow, starting with the general concept of fasting leading to a feeling of rejuvenation and extended life expectancy (P).
• Then it introduces a possible reason for this effect, which is the detoxification effect of fasting (Q).
• The sentence then provides specific evidence of a study performed on earthworms that showed the extension of life due to fasting (R).
• Finally, it describes the experiment performed in the 1930s, isolating one worm and observing its extended lifespan and maintained youthful characteristics (S).

The correct arrangement is as follows:

• P. Fasting also leads to a feeling of rejuvenation and extended life expectancy.
• Q. This might be due to the detoxification effect of fasting.
• R. A study was performed on earthworms that showed the extension of life thanks to fasting.
• S. The experiment was performed in the 1930s by isolating one worm and putting it on a cycle of fasting and feeding.
• The isolated worm outlived the other worms by 19 generations while still maintaining its freshness and youthful physiological characteristics.

Therefore, the correct order is: 'PQRS'.

The correct answer is 'Option 3'.

Key Points

• The part of the sentence that contains a grammatical error is: given to both Neha and I.
• In this case, "I" should be replaced with "me." The pronoun "I" is used as a subject, while "me" is used as an object.
• When you remove "Neha and," it becomes clear that "me" is the correct form to use: "The credit...was given to me."
• Given to both Neha and me: This indicates that the credit (or recognition) for organizing the successful event was attributed to both Neha and the speaker.

Therefore, the corrected sentence is: "The credit for organizing the successful event was given to both Neha and me."

The correct answer is 'Option 4'.

Key Points

• The given sentence "Shivam does not play football" is in the active voice, where the subject "Shivam" is performing the action of not playing football.
• To change it to the passive voice, we need to make the object of the active sentence (football) the subject of the passive sentence.
• The object of the active sentence (Shivam) becomes the agent in the passive sentence.

Therefore, the correct passive transformation is: "Football is not played by Shivam."

The correct answer is 'Option 3' i.e. 'Picture of a witch riding'.

 Key Points

• The original sentence is grammatically incorrect because the phrase "picture by which a witch is riding" is not idiomatic and does not convey the intended meaning clearly.
• Option 3 corrects this by using the phrase "picture of a witch riding."
• This phrase is more concise and effectively conveys that the picture depicts a witch riding a broomstick.
• It maintains the intended meaning of the sentence in a clearer and more grammatically correct way.
• However, in option 2, 'pictures' is wrong because it is a plural noun & in the sentence after the article 'a' we will use a singular noun i.e. Picture.
• In option 4, the use of the conjunction 'that' is incorrect as per the grammatical context of the sentence.

Therefore, the correct sentence is: There's even a picture of a witch riding a broomstick on the sides of the police cars.

The correct answer is 'Option 1' i.e. 'No improvement'.

Key Points

• The underlined part of the sentence, "chased the ball," is already grammatically correct.
• It uses the simple past tense to describe the action of the dog chasing the ball.
• This construction effectively conveys the past event of the dog pursuing and moving the ball into the neighbor's yard.

Therefore, the correct sentence is: The dog chased the ball into the neighbour's yard.

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

Key Points

• The word "malign" is a verb that means to speak ill or unfavorably about someone or something.
• It involves making harmful, false, or derogatory statements that can damage the reputation or character of the person or thing being discussed.
• "Baleful" is an adjective that means threatening harm or menacing. It signifies a sense of danger, evil, or harm.(अमंगलकारी)

Therefore, the correct answer is: 'Baleful'.

Additional Information

• "Insurgent" refers to a person who rises in active revolt against an established authority or government.(विद्रोही)
• "Radical" refers to someone who advocates for extreme or fundamental changes in political, social, or economic systems. (जरुरत से ज्यादा परिवर्तनशील)
• "Nihilistic" is an adjective that relates to the philosophy of nihilism, which rejects or denies the existence of inherent meaning or values in life. (निरर्थक)

The correct answer is 'Option 2' i.e. 'Anything'.

Key Points

• In this context, "anything" is the most suitable choice because it implies that out of all possible comparisons, the most fitting one is an old-time magician.
• The word "anything" is often used in comparative structures to mean "any other thing."

Therefore, the correct sentence is: He made me think of an old time magician more than anything.

Additional Information

• Here is a brief explanation of the other options:
• A thing: This is grammatically correct, but it sounds somewhat unnatural in this context. It doesn't have the same emphasis as "anything."
• Everything: This doesn't make logical sense in this context because it implies that he made the speaker think of an old-time magician more than all things combined, which is likely not the intended meaning.
• Something: This could potentially work, but "anything" is a more common choice in comparative structures and sounds more natural in this sentence.

The correct answer is 'Option 1'.

Key Points

• "Blessing in disguise" means "Bad thing that turns out to be good".
• It refers to an unexpected positive outcome from a challenging or difficult situation.

Therefore, the correct answer is: 'Bad thing that turns out to be good'.

Additional Information

• A good thing introduced into your life as a blessing (आशीर्वाद के रूप में आपके जीवन में पेश की गई अच्छी चीज़) does not match with the idiom.
• A good deed rewards as a blessing (एक अच्छा कार्य एक आशीर्वाद के रूप में इनाम देता है) is not the same as the idiom.
• Something that happens very rarely (ऐसी चीज़ जो बहुत कम होती है) does not convey the same meaning.