SSC CHSL Tier-1 2022: Official Paper (Held On: 21 March, 2023 Shift 1) (Previous Year Paper)

The paper when unfolded will appear as shown below:

Hence, the correct answer is "Option 3".

The logic followed here is:

Logic: The second word is a component or part of the first word.

Here,

Fan : Blade → A blade is a component of a fan.

Similarly,

Car : ? → Steering is a component of a car.

Hence, the correct answer is "Steering".

The logic followed here is:

Logic: (2^nd number - 1^st number) × 6 + 1^st number = 3^rd number.

Now,

For (7, 41, 211)

→ (41 - 7) × 6 + 7

→ 34 × 6 + 7

→ 204 + 7 = 211.

For (12, 66, 336)

→ (66 - 12) × 6 + 12

→ 54 × 6 + 12

→ 324 + 12 = 336.

Similarly, for (11, 61, 311)

→ (61 - 11) × 6 + 11

→ 50 × 6 + 11

→ 300 + 11 = 311.

Hence, the correct answer is "Option 4".

BODMAS Rule: 

According to the question:

Now,

Given equation: 34 P 17 S 9 ? 13 R 11 S 3 R 4 = -6

After replacing the symbols:

⇒ 34 ÷ 17 × 9 ? 13 - 11 × 3 - 4 = -6

⇒ 2 × 9 ? 13 - 11 × 3 - 4 = -6

⇒ 18 ? 13 - 33 - 4 = -6

⇒ 18 ? 13 - 37 = -6

We need to replace '? with +' to make the equation correct,

⇒ 18 + 13 - 37 = -6

⇒ 31 - 37 = -6.

Here, '+' makes the equation correct, and 'Q means +'.

So, 'Q' will be replace the '?' symbol in the given equation.

Hence, the correct answer is "Q".

From the given open Dice:

R and D is the opposite sides.

C and G is the opposite sides.

F and M is the opposite sides.

So, the face of 'F' is opposite to the face showing 'M'.

Hence, the correct answer is "Option 3".

The odd word pair from the given alternatives is:

Option 1) 6 - Hexagon → A hexagon has six sides.

Option 2) 5 - Rectangle → A Rectangle has four sides only.

Option 3) 3 - Triangle → A triangle has three sides.

Option 4) 4 - Square → A square has four sides.

Here, '5 - Rectangle' does not follow this pattern.

Hence, the correct answer is "Option 2".

The logic followed here is:

Step I: Symbol 

 is getting rotated in 'one place and then opposite' alternatively in clockwise direction.

Step II: Symbol  is getting rotated in 'one place and then opposite' alternatively in clockwise direction.

Step III: Symbol 

 is getting rotated in 'one place and then opposite' alternatively in clockwise direction.

Step IV: Symbol 

 is getting rotated in 'one place and then opposite' alternatively in clockwise direction.

So, the complete series is:

Hence, the correct answer is "Option 1".

The logic followed here is:

For, 'DEER' is written as 'EGHV',

For, 'ROOM' is written as 'SQRQ',

Similarly, for 'SOAP'

So, 'SOAP' is coded as 'TQDT'.

Hence, the correct answer is "Option 3".

Family Chart:

Given: 

Anjali is the sister of Mukesh.

Nikhil has two children and is the son-in-law of Archana.

Anjali is the maternal granddaughter of Archana.

Archana has only one child.

So, Nikhil's wife is Daughter of Archana.

Hence, the correct answer is "Option 1".

When the paper is unfolded, the image appears as follows:

Hence, the correct answer is "Option 1".

The logic followed here is:

So, '1072' will complete the series.

Hence, the correct answer is "Option 3".

The triangles are:

So, there are '17' triangles in the given figure.

Hence, the correct answer is "17".

The logic followed here is:

Given Sequence: t _ n s _ r t h _ s o _ t h _ s _ r

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

Option 1) nonrho → t n n s o r / t h n s o r / t h h s o r

Option 2) honrno → t h n s o r / t h n s o r / t h n s o r

Here, 'Option 2' followed a pattern.

Option 3) hornnr → t h n s o r / t h r s o n / t h n s r r

Option 4) hoonor → t h n s o r / t h o s o n / t h o s r r

Hence, the correct answer is "Option 2".

The logic followed here is:

Logic: The second word represents the currency of the respective country.

Bangladesh : Taka → Taka is the currency of Bangladesh.

Similarly:

Kuwait : Dinar → Dinar is the currency of Kuwait.

Hence, the correct answer is "Dinar".

When the paper is unfolded, the image appears as:

Hence, the correct answer is "Option 1".

Given Statements:

I. All blankets are bedsheet.

II. No bedsheet is a curtain.

The least possible Venn diagram for the given statement is:

Conclusions:

I. Some bedsheet are blanket - True (All blankets are bedsheet it means some blankets will be also bedsheet).

II. No curtain is a blanket - True (Because, All blankets are bedsheet and No bedsheet is a curtain, so all the Blankets are part of Bedsheet that is not Curtain, it also means No curtain is a blanket).

So, Both conclusion I and II follow.

Hence, the correct answer is "Option 1".

Given equation: 46 + 28 × 2 - 7 ÷ 13 = 41.

BODMAS Table: 

Let's check each option one by one.

Option 1) × and +

Given: 46 + 28 × 2 - 7 ÷ 13 = 41

After interchanging the numbers we get;

⇒ 46 × 28 + 2 - 7 ÷ 13 = 41

⇒ 46 × 28 + 2 - 0.54 = 41

⇒ 1288 + 2 - 0.54 = 41

⇒ 1290 - 0.54 = 41

⇒ 1289.46 ≠ 41

⇒ LHS ≠ RHS

Option 2) ÷ and -

Given: 46 + 28 × 2 - 7 ÷ 13 = 41

After interchanging the numbers we get;

⇒ 46 + 28 × 2 ÷ 7 - 13 = 41

⇒ 46 + 8 - 13 = 41

⇒ 54 - 13 = 41

⇒ 41 = 41

⇒ LHS = RHS

Option 3) + and ÷ 

Given: 46 + 28 × 2 - 7 ÷ 13 = 41

After interchanging the numbers we get;

⇒ 46 ÷ 28 × 2 - 7 + 13 = 41

⇒ 3.29 - 7 + 13 = 41

⇒ 16.29 - 7 = 41

⇒ 9.29 ≠ 41

⇒ LHS ≠ RHS

Option 4) ÷ and × 

Given: 46 + 28 × 2 - 7 ÷ 13 = 41

After interchanging the numbers we get;

⇒ 46 + 28 ÷ 2 - 7 × 13 = 41

⇒ 46 + 14 - 7 × 13 = 41

⇒ 46 + 14 - 91 = 41

⇒ 60 - 91 = 41

⇒ - 31 ≠ 41

⇒ LHS ≠ RHS

Hence, the correct answer is "Option 2".

The logic followed here is:

Logic: 1^st number × 3 = 2^nd number.

Now,

For, 54 : 162

⇒ 54 × 3 = 162.

For, 38 : 114

⇒ 38 × 3 = 114.

Similarly, for ? : 216

⇒ 72 × 3 = 216.

Hence, the correct answer is "Option 3".

The logic followed here is:

Logic: **(**Sum of the place value of all numbers) - 20 = Code of the word.

'PAIN' is written as '20'

⇒ (16 + 1 + 9 + 14) - 20

⇒ 40 - 20 = 20.

'HER' is written as '11'

⇒ (8 + 5 + 18) - 20

⇒ 31 - 20 = 11.

Similarly, for 'TIER'

⇒ (20 + 9 + 5 + 18) - 20

⇒ 52 - 20 = 32.

So, 'TIER' will be written as '32'.

Hence, the correct answer is "32".

The logic followed here is:

Logic: Each letter in the cluster is obtained by moving three positions forward in the English alphabet.

Let's check each option as per the logic:

Option 1) NOS → N + 1 = O, O + 4 = S.

Option 2) GHM → G + 1 = H, H + 4 = L ≠ M.

Option 3) BCG → B + 1 = C, C + 4 = G.

Option 4) JKO → J + 1 = K, K + 4 = O.

Based on the given logic, Option 2 (GHM) is different from the rest.

Hence, the correct answer is "Option 2".

The logic followed here is:

Logic → The given words represent body parts, progressing from the upper part to the lower part of the body.

The correct logical order is:

1. Eyes

2. Lips

4) Neck

3. Stomach

4. Legs

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

The logic followed here is:

SH : IT

Similarly, for LM : ?

 

So, 'LM : NM' would be the related letters.

Hence, the correct answer is "Option 3".

According to the given Venn diagram:

The shaded area shows the "total number of horses are neither clips nor bags".

So, the total number of 'horses are neither clips nor bags' = 5.

Hence, the correct answer is "5".

The logic followed here is:

Logic: Difference of First number and Last number = Middle number.

Now,

For (141, 13, 128)

→ 141 - 128 = 13.

For (238, 164, 402)

→ 402 - 238 = 164.

Similarly, for (48, 31, 79)

→ 79 - 48 = 31.

Hence, the correct answer is "Option 3".

The logic followed here is:

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

Now,

For (80, 72, 64)

→ (80 + 64) ÷ 2

→ 144 ÷ 2 = 72.

For (64, 56, 48)

→ (64 + 48) ÷ 2

→ 112 ÷ 2 = 56.

Similarly, for (63, 56, 49)

→ (63 + 49) ÷ 2

→ 112 ÷ 2 = 56.

Hence, the correct answer is "Option 4".

Correct Answer Pranav Anand

Key Points

• 15-year-old Pranav Anand became the 76^th Grand Master of India.
• He achieved this feat by crossing 2500 ELO ratings at the ongoing World Youth Chess Championship in Mamaia, Romania.
• The 15-year-old had already met the rest of the criteria to earn the Grand Master title.
• To become a Grand Master, a player has to achieve three Grand Master norms and in addition, his 'Live Rating' must exceed 2500 ELO points.
• Pranav achieved the third and final grandmaster norm at the Biel Chess Festival in Switzerland in July.

Additional Information Rameshbabu Praggnanandhaa

• Grandmaster of chess Rameshbabu "Pragg" Praggnanandhaa was born in India on August 10, 2005.
• He was a chess prodigy who became the second-youngest grandmaster at the time at age 12 after becoming the youngest international master at age 10 at the time.
• He defeated world number one chess champion, Magnus Carlsen, of Norway , at the age of 16 in a rapid game on February 22, 2022, at the Airthings Masters Rapid tournament of the Champions Chess Tour 2022.
• After the legendary chess players P Harikrishna and Vishwanathan Anand, he is the third Indian to defeat Magnus Carlsen.
• He makes the history of the youngest player to ever do so.
• He again defeated Carlsen in the Chessable Masters online rapid chess competition in May 2022, his second victory against him in three months.
• After Abhimanyu Mishra, Sergey Karjakin, Gukesh D, and Javokhir Sindarov, Pragganandhaa is the fifth person under the age of 30 to hold the title of Grandmaster.

Viswanathan Anand is the first Indian chess grandmaster in 1988 and a former world chess champion.

• At the age of 15, Anand became the youngest Indian to win the title of International Master (IM) 1984.
• Anand won his first National Chess Championship in 1986.
• The title of Grandmaster was awarded to ‘Vishy’ in 1988.
• He won the Chess Oscar six times.
• He won the Fédération Internationale des Échecs (FIDE; international chess federation) world championship in 2000, 2007, 2008, 2010, and 2012.

Pentala Harikrishna is an Indian chess player. He became the youngest grandmaster from India.

• He was Commonwealth Champion in 2001, World Junior Champion in 2004, and Asian Individual Champion in 2011.

The correct answer is Saina Nehwal.

Key Points:

• Saina Nehwal is the first Indian Badminton player to have won an Olympic medal.
• ​She won the Bronze medal in women's singles at the London Olympics in 2012.
• She defeated China's, Wang Xin to clinch the medal.

Additional InformationP.V. Sindhu:

• She is an India Badminton player from Hyderabad, Telangana.
• She won a bronze medal in the 2020 Summer Olympics (Tokyo).
• She fetched the Silver medal at Rio Olympics, 2016, South Asian Games, 2016 and Commonwealth Games held at Gold Coast Australia, 2018.
• She won the Badminton World Federation (BWF) Championships and clinched a Gold.
• She has been honoured with Arjuna Award (2013), Padma Shri (2015), Rajiv Gandhi Khel Ratna (2016) and Padma Bhushan (2020).

Srikanth Kidambi:

• Srikanth Kidambi is a famous Indian Badminton player hailing from Hyderabad.
• He was awarded the Padma Shri (fourth highest civilian award) in the year 2018.
• He was also awarded the 'Arjuna Award' in 2015.

Chirag Shetty:

• Chirag Shetty is an accomplished professional badminton player from India.
• At the Asia Team Championships in Hyderabad in 2016, he made his international debut and took home the bronze medal.
• At the 2018 Commonwealth Games, he earned the Mixed Team Gold Medal and the Men's Doubles Silver Medal.
• At the 2022 Commonwealth Games, he won the men's doubles gold medal.
• In 2020, he received the Arjuna Award.

The correct answer is Ring Worm.

**Key Points:**Ringworm

• It is caused by fungus that live on dead tissues like skin, hair and nail.
• It causes Jock Itch and Athlete’s foot.
• A red patch that may itch often turns into a raised ring-shaped patch of skin over time.
• It is highly contagious and can be transmitted by skin to skin contact or contact with pets.
• Creams and medicated ointments are often enough to treat it.
• Basic hygiene can prevent it.

**Additional Information:**Cholera:

• It is a life-threatening infectious disease and a public health hazard.
• Cholera is an acute, diarrheal illness caused by infection of the intestine with the bacterium Vibrio cholerae.
• The infection is often mild or without symptoms, but sometimes can be severe.

Symptoms:

• Profuse watery diarrhoea
• Vomiting
• Leg cramps

Transmission:

• A person may get cholera by drinking water or eating food contaminated with the cholera bacterium.
• The disease can spread rapidly in areas with inadequate treatment of sewage and drinking water.

Vaccine:

• Currently there are three WHO pre-qualified oral cholera vaccines (OCV), Dukoral, Shanchol, and Euvichol-Plus.
• All three vaccines require two doses for full protection.

Tuberculosis:

• TB is caused by a bacterium called Mycobacterium tuberculosis, belonging to the Mycobacteriaceae family consisting of about 200 members.
• In humans, TB most commonly affects the lungs (pulmonary TB), but it can also affect other organs (extra-pulmonary TB).
• It can spread from person to person through the air.

COVID-19:

• The new coronavirus – COVID-19 – was first identified in Wuhan, China in December 2019.
• Coronaviruses belong to a family of viruses called Coronaviridae and the order Nidovirales.
• Coronaviruses get their name from their crown-like shape (corona is Latin for crown).
• They are found in animals and birds and are zoonotic – as they are transmitted between animals and people.

Correct Answer Akbar

Key Points

• The royal city at Fatehpur Sikri was built by the Mughal emperor Akbar during the second half of the 16^th century.
• It was celebrated as the city of Victory of the Mughal Empire, which was the capital city for more than 10 years from 1571 to 1585.
• It was turned as Fatehabad (the city of Victory) where the legendary sons of Akbar were born.
• It’s also known for the complex of monuments and temples all in uniform architectural style.

Additional InformationAkbar (1542- 1605)

• He reigned from 1556 to 1605.
• He constructed Fatehpur Sikri and made it his capital in 1569.
• Buland Darwaza was constructed at the gate.
• He started a new religion Din-i Ilahi in 1581-82.
• Abul Fazl wrote his biography titled Akbarnama.
• Nine of his courtiers were known as Navratnas.
• They were Todar Mal, Abul Fazal, Faizi, Birbal, Tansen, Abdur Rahim Khana-i-Khana, Mullah-do-Pyaza, Raja Man Singh, and Fakir Aziao-Din.
• He married a Hindu princess Harka Bai who is commonly known as Jodha Bai.
• Akbar captured the historic fortress of Chitor in 1568.
• He abolished the pilgrimage tax by Hindus in 1563.
• He also abolished the Jizyah tax in 1564.
• He also introduced the Mansabdari System or the rank-holder system to organize the nobility and army.

Aurangzeb (1658 AD-1707 AD):

• Aurangzeb defeated Dara at Dharmat (1658 AD), Samugarh (1658 AD), and Deorai, in which Samugarh was the decisive one and Deorai was the last one.
• After the victory, Aurangzeb was crowned at Delhi under the title Alamgir. He died in February 1707 in Ahmadnagar.
• Aurangzeb captured Guru Teg Bahadur, the 9^th Guru of Sikhs in 1675 AD and executed him when he refused to embrace Islam.
• The 10^th and last Sikh Guru, Guru Gobind Singh, son of Guru Teg Bahadur, organized his followers into a community of warriors called Khalsa to fight against the Muslims.
• Chhatrapati Shivaji Maharaj was the most powerful Maratha king and an arch-enemy of Aurangzeb.
• The Mughal conquests reached a climax during Aurangzeb’s reign as Bijapur and Golconda were annexed in 1686 AD and 1687 AD, respectively.
• Under him, the Mughal empire reached its greatest extent and the largest single-state ever known in India.
• He forbade the inscription of Kalma on the coins, also forbade sati and Jharokha-darshan.
• He ended the celebration of Navroz and, in 1679 AD, reimposed Jizya.

Shah Jahan:

• On 5 January 1592, Shahab-ud-din Muhammad Khurram, later known as Shah Jahan, was born to Mughal Emperor Jahangir and his wife Jagat Gosaini.
• Shah Jahan was an able military commander.
• On becoming the emperor, Shah Jahan executed many of his former rivals including his own brother Shahryar.
• Before becoming king, as a prince, he had been the governor of the Deccan, Bihar, Bengal, Gujarat, and Delhi.
• As king, Shah Jahan expanded the military and promoted the production of arms. He annexed several territories.
• Shah Jahan married multiple times as was the custom.
• His favorite was said to be Arjumand Banu Begum who is better known as Mumtaz Mahal.
• She died during childbirth in 1631 and Shah Jahan was said to be depressed.
• He got the Taj Mahal built in her honor and perhaps, he is most famous for this architectural feat.
• He also created many other architectural marvels including the Pearl Mosque at Agra, the Red Fort, the Jama Masjid at Delhi, the Shalimar Gardens, and some other buildings in present Pakistan.
• He also got the famous Peacock Throne built.

Jahangir

• In 1605, Prince Salim succeeded with the title Jahangir (Conqueror of World) when he assumed the throne after the death of Akbar.
• He issued 12ordinances. He is known for his strict administration of justice.
• He established Zanjir-i-Adil (chain of justice) at Agra for the seekers of royal justice.
• He is the eldest son of Akbar was born at Fatehpur Sikri near Agra in 1569.
• In 1611, he married Mehr-un-Nisa whom he gave the title of Nur Jahan (light of the world).
• Nurjahan exercised tremendous influence over state affairs. She was made the official Badshah Begum.
• Jahangir issued coins jointly in Nurjahan's name and his own.
• Jahangir also married Manbai in 1585 AD and Jodhbai in 1587 AD.
• He defeated and imprisoned his son, Khusrau Mirza.
• He also beheaded Guru Arjun, the 5^th Sikh Guru and one of the supporters of Khusrau Mirza.
• Captain Hawkins (1608-1611) and Sir Thomas Roe (1615-1616) visited Jahangir's court.
• Production of Tobacco started in his reign.
• He wrote his autobiography Tuzuk-i-Jahangir.
• He was buried in Lahore in 1627.

Correct Answer 16

Key Points

• India has won a total of 61 medals in the Commonwealth Games 2022.
• 22 gold,
• 16 silver, and
• 23 bronze
• In the 2018 Commonwealth Games, India won a total of 66 medals out of which 16 were in shooting.
• This time shooting was not included.
• India finished fourth in the medal tally.
• Australia took first place.
• England finished second and Canada third.
• New Zealand finished fifth.

Additional Information:

• India has won the total number of gold medals in the history of the Commonwealth Games (CWG Upto 2022) is 203.
• Australia (1003 gold medals) is at the top in terms of the total number of gold medals in the Commonwealth Games, while England (773) is second and Canada (510) is in third place.
• India won its first gold in the Commonwealth Games in 1958 which was won by legendary sprinter Milkha Singh.
• India has won a gold medal in every Commonwealth Games since then (didn't participate in 1962 and 1986).
• The 2010 Commonwealth Games in Delhi has been the most successful for India in which it won 38 gold medals.

The correct answer is 74.04 percent

Key Points:

• As per the census 2011, the literacy rate of India is 74.04%, 82.14% for males and 65.46% for females.
• For the purpose of census 2011, a person aged seven and above, who can both read and write with understanding in any language, is treated as literate.
• A person, who can only read but cannot write, is not literate.
• Kerala retained its position by being on top with a 93.91% literacy rate, followed by Lakshadweep (92.28%) and Mizoram (91.58%).
• Bihar with a literacy rate of 63.82% ranks last in the country preceded by Arunachal Pradesh (66.95%t) and Rajasthan (67.06%).

Hence, the correct answer is 74%.

**Additional Information:**Census in India:

• It was done for the first time in 1872 under the British Viceroy Lord Mayo.
• After that, it is conducted at intervals every 10 years.
• However, the first complete census of India was conducted in 1881.
• Since 1949, it is conducted by the Registrar General and Census Commissioner of India under the Ministry of Home Affairs, Government of India.
• All censuses after 1951 were conducted under the 1948 Census Act.
• As of 2011, the Census of India has been conducted 15 times.

Correct Answer is IIT Guwahati

Key Points:

• President of India Droupadi Murmu, on October 13, inaugurated ‘PARAM Kamrupa’ Supercomputer facility and a high-power active and passive component laboratory of SAMEER at the Indian Institute of Technology, Guwahati on the first day of her visit to the State.
• The Society for Applied Microwave Electronics Engineering and Research (SAMEER) is a Research & Development Institute under the administrative control of the Ministry of Electronics and Information Technology (MeitY), Government of India.
• Centre for High Power Microwave Tube & Component Technology (CHMTCT) under SAMEER, located in IIT Guwahati, Assam, has been started in 2015 with a specialization in the area of high-power microwave tube and component technology.
• The PARAM Kamrupa, one of its kind supercomputer in the North East region, is installed under the National Supercomputing Mission.
• The Super Computer Param Kamrupa will provide advanced computing, and healthcare techniques along with solutions for many issues to this region.
• She also informed that many components of this supercomputer were developed indigenously.

Additional Information

• The performance of a supercomputer is commonly measured in floating-point operations per second (FLOPS) instead of million instructions per second (MIPS).
• Since 2017, there have existed supercomputers that can perform over 1017 FLOPS (a hundred quadrillion FLOPS, 100 petaFLOPS or 100 PFLOPS).

The correct answer is surface-to-air

Key Points:

• S-400 is called Triumf(read Triumph).
• S-400 is a missile defense system.
• India signed a deal with Russia in October 2018 for the delivery of 5 missile defense systems.
• The deal was for US $5.43 billion.
• India faced the threat of sanctions at the time of signing of the deal by Countering America’s Adversaries Through Sanctions Act (CAATSA).
• The system can engage in all types of aerial targets:

1. Aircraft
2. Unmanned Aerial Vehicle
3. Ballistic Missiles
4. Cruise Missiles

• S-400 can track 100 airborne targets and engage 6 targets simultaneously.
• S-400 is developed by Almaz Central Design Bureau, Russia.

Additional Information:

• The first successful test was carried out by Russia in 1999.
• S-400 was inducted by the Russian Army in 2001.
• Dr. Alexander Lemanskiy was the Chief Engineer for S-400.
• Terminal High Altitude Area Defence System(THAAD) is a US-developed missile defense system equivalent to S-400$.

Correct Answer Balloon Mortgage

Key Points In this type of loan, borrowers make low payments for a certain period of time and then pay off the remaining balance in one large lump sum, or "balloon" payment, at the end of the loan term.

Initial Low Payments:

• Balloon loans typically have lower initial payments compared to traditional loans.
• This is because these payments are primarily based on the interest of the loan, not the principal.

Lump Sum Payment:

• The defining feature of a balloon loan is the large "balloon" payment due at the end of the loan term.
• This payment covers the remaining principal of the loan.

Short Term:

• Balloon loans usually have shorter terms than traditional installment loans.
• The term is often 5 to 7 years, but the balloon payment is based on what the balance would be after a longer term, often 30 years.

Risk of Default:

• There is a higher risk of default with balloon loans.
• If borrowers cannot make the large balloon payment at the end of the term, they may need to refinance the loan, sell the asset, or default on the loan.

Common in Real Estate:

• Balloon loans are often used in real estate transactions, particularly for commercial properties or short-term real estate investments.
• They can also be used for personal loans and auto loans.

The Correct answer is Hubble constant

Key Points:

• 'Expanding Universe'
• Edwin Hubble, an American astronomer, was the first to prove that the universe is expanding.
• According to Expanding Universe theory, the universe is presently expanding.
• Hubble proved that there is a direct relationship between the speeds of distant galaxies and their distances from Earth.
• This is now known as Hubble’s Law.

Additional Information:Faraday:

• When an electric current passes up to 1 second due to 96485 C, through an electrolyte then the equivalent weight of the electrolyte deposited is one & this amount of electric current is called 1 Faraday.
• Faraday constant (F) = 96485C mol−1
• The constant is named after the British physicist Michael Faraday.
• It is a universal constant.
• It is the amount of electric charge carried by 1 mole of electrons.
• Represented by F & its measuring unit is Coulombs per mole (C.mol-1 ).

Correct Answer Popular Front of India (PFI)

Key Points:

• The Ministry of Home Affairs (MHA) of India declared the Popular Front of India (PFI) and its front organizations, including its student wing- the Campus Front of India (CFI), as an “unlawful association” under the Unlawful Activities (Prevention) Act (UAPA) in September 2022.
• The Muslim organization has been banned for five years along with eight associates or front organizations.
• The MHA has also issued another order empowering States to notify places associated with PFI and its front organizations where unlawful activity is taking place.
• The ban comes close on the heels of a countrywide raid on September 22 when 109 members of the groups were arrested by the National Investigation Agency (NIA) and other agencies.

**Additional Information:**About the Unlawful Activities (Prevention) Act:

• Passed in 1967, the law aims at the effective prevention of unlawful activity associations in India.
• The Act assigns absolute power to the central government, by way of which if the Centre deems an activity as unlawful then it may, by way of an Official Gazette, declare it so.
• It has the death penalty and life imprisonment as the highest punishments.
• Under UAPA, both Indian and foreign nationals can be charged.
• It will be applicable to the offenders in the same manner, even if the crime is committed on foreign land, outside India.
• Under the UAPA, the investigating agency can file a charge sheet in a maximum of 180 days after the arrests and the duration can be extended further after intimating the court.

The correct answer is USA

Key Points

• NASA's Double Asteroid Redirection Test (DART), the world's first full-scale mission to test technology for defending Earth against potential asteroid or comet hazards.
• Launched from Space Launch Complex 4 East at Vandenberg Space Force Base in California.
• DART is the first-ever mission dedicated to investigating and demonstrating one method of asteroid deflection by changing an asteroid's motion in space through kinetic impact.
• DART is a joint project between NASA and the Johns Hopkins Applied Physics Laboratory (APL).
• NASA stands for National Aeronautics and Space Administration.
• The National Aeronautics and Space Administration is an independent agency of the USA which is responsible for the civilian space program, aeronautics, and aerospace research.
• It was established in 1958 with headquarters at Two Independence Square, Washington, D.C., United States.
• Dwight D. Eisenhower was its founder.

Additional Information:

• Headquater of Roscosmos - Moscow.
• Its launch facilities include Baikonur Cosmodrome in Kazakhstan, the world's first and largest spaceport, and Vtochny Cosmodrome, which is being built in the Russian Far East in Amur Oblast.
• The launch of Chandrayaan-3 is planned for August 2022.
• On July 22, 2019, Chandrayaan-2's rocket successfully lifted off with the Vikram Lander and Pragyan rover housed in it.
• ISRO built India's first satellite, Aryabhata, which was launched by the Soviet Union in 1975.
• JAXA
• JAXA was formed on 1 October 2003.
• It is responsible for research, technology development, and the launch of a satellite into orbit and is involved in many more advanced missions such as asteroid exploration and possible human exploration of the moon.

The correct answer is 1927.

Key Points

• Dr. Ambedkar start a temple entry movement in 1927.
• It was a movement to allow lower caste people to enter temples.
• Ambedkar led three such movements for temple entry between 1927 and 1935.
• One of them was the Kalaram Temple entry movement initiated under the guidance of Dr B.R. Ambedkar on 2^nd March 1930.​

Additional Information

• Dr. Bhimrao Ambedkar is known as the father of the Indian constitution.
• Dr. Ambedkar fought to eradicate social evils like untouchability and for the rights of the Dalits and other socially backward classes throughout his life.

The correct answer is 1%.

Key Points

• Public healthcare spending refers to the funds allocated by the government towards healthcare services, infrastructure, and programs to benefit the general public.
• According to the Economic Survey 2020-21, India's public healthcare spending as a percentage of GDP stood at around 1%.
• This percentage reflects the proportion of the country's total economic output (GDP) that is dedicated to public healthcare expenditures.
• The low percentage of public healthcare spending highlights the relatively limited financial resources allocated by the government toward healthcare infrastructure, services, and programs.
• The low level of public healthcare spending has implications for the overall accessibility and quality of healthcare services available to the general population.
• Insufficient public healthcare spending can lead to challenges such as inadequate healthcare infrastructure, shortages of medical equipment and supplies, limited availability of healthcare professionals, and difficulties in providing affordable and accessible healthcare services to all citizens.
• The COVID-19 pandemic has further emphasized the need for increased healthcare spending to strengthen the healthcare system, enhance preparedness for emergencies, and improve the overall health outcomes of the population.
• The Indian government has been working towards increasing public healthcare spending to address the existing gaps in the healthcare system. However, the target of increasing spending to 2.5% of GDP, as recommended by the National Health Policy 2017, is yet to be achieved.
• Increasing public healthcare spending is crucial for improving healthcare infrastructure, ensuring the availability of essential medicines, enhancing preventive healthcare programs, expanding healthcare coverage, and providing quality healthcare services to all citizens.
• Higher public healthcare spending can contribute to improved healthcare outcomes, reduced healthcare costs for individuals, enhanced disease prevention and control, and overall better health and well-being of the population.

Additional Information

Here are some key facts from the Economic Survey of India 2020-21:

• Economic Growth: The Economic Survey provides an analysis of India's economic performance. According to the Economic Survey 2020-21, India experienced a sharp contraction of 7.7% in real GDP during the financial year 2020-21 due to the impact of the COVID-19 pandemic.
• Agriculture Sector: The survey highlights the importance of the agriculture sector in the Indian economy. It states that the agriculture sector remained resilient during the pandemic, recording positive growth of 3.4% in 2020-21.
• Manufacturing and Services Sectors: The survey analyzes the performance of the manufacturing and services sectors. It indicates that both sectors were significantly affected by the pandemic-induced disruptions, leading to a contraction in output and employment.
• Fiscal Deficit: The Economic Survey provides insights into the fiscal health of the country. As per the survey, India witnessed a sharp increase in the fiscal deficit, reaching 9.5% of GDP in 2020-21. This increase was primarily driven by higher expenditure to mitigate the impact of the pandemic.
• Investment and Savings: The survey emphasizes the importance of investment and savings for economic growth. It highlights the need for higher investment rates to stimulate economic activity and generate employment.
• Financial Sector: The Economic Survey discusses various aspects of the financial sector, including banking, insurance, and capital markets. It provides an analysis of the reforms undertaken in the sector and their impact on financial stability and inclusion.
• Infrastructure Development: The survey recognizes the significance of infrastructure development for economic growth. It emphasizes the need for increased investment in infrastructure sectors such as transportation, energy, and telecommunications.
• Ease of Doing Business: The survey evaluates the ease of doing business in India and identifies areas for improvement. It discusses reforms implemented to enhance the business environment, attract investments, and promote entrepreneurship.
• Social Sectors: The Economic Survey sheds light on various social sectors such as education, healthcare, and poverty alleviation. It highlights the progress made in these sectors and outlines policy measures for inclusive growth and development.
• Sustainable Development: The survey recognizes the importance of sustainable development and discusses environmental challenges. It emphasizes the need for balancing economic growth with environmental conservation and climate change mitigation.

The correct answer is C. V. Raman.

Key Points

• The Nobel Prize in Physics 1930 was awarded to Sir Chandrasekhara Venkata Raman for his work on the scattering of light and for the discovery of the effect named after him.
• Scattering of Light 
• If the molecules of a medium, after absorbing incoming radiations, emit them in all possible directions, the process is called scattering. Rayleigh has shown that the intensity of scattered light is inversely proportional to the fourth power of wavelength (or directly proportional to the fourth power of frequency).​

Additional Information

• Facts About Dr. C V Raman:
• Name: Dr. Chandrashekhra Venkataraman or C.V. Raman
• Born on: 7 November 1888
• Place of Birth: Tiruchirappalli, Tamil Nadu
• Father's Name: R. Chandrashekhara Aiyer
• Mother's Name: Parvathi Ammal
• Spouse Name: Lokasundari Ammal
• Died on: 21^st November 1970
• Place of Death: Bangalore, India
• Discovery: Raman Effect
• Awards: Matteucci Medal, Knight Bachelor, Hughes Medal, Nobel Prize in Physics, Bharat Ratna, Lenin Peace Prize, Fellow of the Royal Society.

The correct answer is The areas where the warm and cold currents meet provide the best fishing grounds.

Key Points

• Ocean currents are streams of water flowing constantly on the ocean surface in definite directions.
• The ocean currents may be warm or cold.
• Generally, the warm currents originate near the equator and move toward the poles.
• The cold currents carry water from polar or higher latitudes to tropical or lower latitudes.
• The Ocean current influences the temperature conditions of the area.
• The areas where the warm and cold currents meet provide the best fishing grounds of the world.
• Seas around Japan and the eastern coast of North America are such examples.

Additional Information

The correct answer is dBase.

Key Points

• What is a Database?
• A database is a collection of related data which represents some aspect of the real world. A database system is designed to be built and populated with data for a certain task.
• What is DBMS?
• Database Management System (DBMS) is a software for storing and retrieving users' data while considering appropriate security measures. It consists of a group of programs that manipulate the database. The DBMS accepts the request for data from an application and instructs the operating system to provide the specific data. In large systems, a DBMS helps users and other third-party software to store and retrieve data.
• DBMS allows users to create their own databases as per their requirements. The term “DBMS” includes the use of the database and other application programs. It provides an interface between the data and the software application.
• Some DBMS examples include MySQL, PostgreSQL, Microsoft Access, SQL Server, FileMaker, Oracle, RDBMS, dBASE, Clipper, and FoxPro. Since there are so many database management systems available, it is important for there to be a way for them to communicate with each other. For this reason, most database software comes with an Open Database Connectivity (ODBC) driver that allows the database to integrate with other databases. For example, common SQL statements such as SELECT and INSERT are translated from a program's proprietary syntax into a syntax other databases can understand.
• dBase is considered to be the 1^st DBMS software for all types of microcomputer systems.

The Correct Answer is Hyderabad.

 Key Points

• Hyderabad recently received the prestigious World Green City Award 2022.
• Hyderabad has beaten the cities like Paris, Bogota, Mexico City, Montreal, and Fortaleza to receive World Green City Award 2022 – the best across all six categories.
• Hyderabad received the award at the International Association of Horticulture Producers (AIPH) 2022.
• The announcement of the winners under six categories and the grand winner was made during the special gala dinner at the IUCN Leaders Forum held in Jeju, South Korea.
• The six categories of the award are Living Green for Biodiversity, Living Green for Climate Change, Living Green for Health and well-being, Living Green for Water, Living Green for Social Cohesion and Living Green for Economic Recovery and Inclusive Growth.
• Hyderabad won “Living Green for Economic Recovery and Inclusive Growth” during the AIPH event.

Additional Information About Hyderabad 

• Hyderabad is located in the southern state of Telangana, India. It is the capital of Telangana and the fifth-largest city in India.
• The population of Hyderabad is over 10 million people. It is a cosmopolitan city with people from all over India and the world living there.
• Hyderabad has a hot, dry climate. The summers are very hot and humid, while the winters are mild.
• The official language of Hyderabad is Telugu. However, English is widely spoken in the city.
• The majority of the people in Hyderabad are Hindu, but there are also significant populations of Muslims, Christians, and Jains.
• Hyderabad is a major economic hub in India. It is home to many software companies, IT firms, and educational institutions.
• Hyderabad is a popular tourist destination. The city has many historical monuments, including the Charminar, Golconda Fort, and the Qutub Shahi Tombs. It also has a number of parks, gardens, and museums.

The correct answer is Power of the President to consult the Supreme Court.

Key Points

• As per Article 143, the President has the power to address questions to the Supreme Court, that he deems important for public welfare.
• The Supreme Court “advises” the President by answering the query put before it.
• Article 143 of the Constitution confers Advisory Jurisdiction to the Supreme Court of India.

Additional Information

• Article 143: Power of President to consult Supreme Court.

1. If at any time it appears to the President that a question of law or fact has arisen, or is likely to arise, which is of such a nature and such public importance that it is expedient to obtain the opinion of the Supreme Court upon it, he may refer the question to that Court for consideration and the Court may, after such hearing as it thinks fit, report to the President its opinion thereon.
2. The President may, notwithstanding anything in the proviso to article 131, refer a dispute of the kind mentioned in the said proviso to the Supreme Court for opinion and the Supreme Court shall, after such hearing as it thinks fit, report to the President its opinion thereon.

The correct answer is President.

Key Points

• Article 72 of the Constitution empowers the President to grant pardons to persons who have been tried and convicted of any offence in all cases where the:
• Punishment or sentence for an offence against a Union Law.
• Punishment or sentence is by a court-martial (military court).
• Punishment is a Death sentence.​
• Pardoning Power of President
• Article 72 empowers the President the power to grant pardons, reprieves, respites or remissions of punishment or to suspend, remit or commute the sentence of any person convicted of any offence.
• The meaning of these terms is as follows:
• Pardon: It removes both the sentence and the conviction and completely absolves the convict from all sentences, punishments, and disqualifications.
• Commutation: It denotes the substitution of one form of punishment with a lighter form of punishment. For example, a death sentence may be commuted to rigorous imprisonment.
• Remission: It implies reducing the period of the sentence without changing its character. For example, a sentence of rigorous imprisonment for five years may be remitted to rigorous imprisonment for one year.
• Respite: It denotes awarding a lesser sentence in place of one originally awarded due to some special fact, such as the physical disability of a convict or the pregnancy of a woman offender.
• Reprieve: It implies a stay of the execution of a sentence (especially that of death) for a temporary period. Its purpose is to enable the convict to have time to seek pardon or commutation from the President.

Additional Information

The correct answer is 1859.

Key Points

The Indigo Rebellion (Neel Bidroho) started in Bengal in March 1859 and was a revolt by the farmers against British planters who had forced them to grow indigo under terms that were greatly unfavorable to the farmers.

• The indigo farmers revolted in the Nadia district of Bengal by refusing to grow indigo.
• They attacked the policemen who intervened.
• The planters, in response to this, increased the rents and evicted the farmers which led to more agitations.
• In April 1860, all the farmers in the Barasat division of the districts Nadia and Pabna went on a strike and refused to grow indigo.
• The strike spread to other parts of Bengal.
• The anger of the peasants exploded in 1859 when led by Digambar Biswas and Bishnu Biswas of Nadia district, they decided not to grow indigo under duress and resisted the physical pressure of the planters.
• The revolt was suppressed and many farmers were slaughtered by the government and some of the zamindars.
• The revolt was backed by the Bengali intelligentsia, Muslims, and missionaries. The whole of the rural population supported the revolt.
• The press also supported the revolt and played its part in portraying the plight of the farmers and fighting for their cause.

From the above, we can conclude that the 'Indigo Revolt' took place in Bengal in March 1859.

Additional Information

The correct answer is Dzongkha.

Key Points 

• The official Language of Bhutan is Dzongkha.
• The capital of Bhutan is Thimphu.
• The national animal is Takin (cattle chamois or gnu goat)
• The national bird is Common Raven
• The national flower is Blue poppy.
• The national sport is Archery.
• The national tree is Bhutan Cypress.

Additional Information

The correct answer is Frigid zone.

Key Points 

• Frigid Zone
• In the Southern Hemisphere, the frigid zone is the area located between the South Pole and Antarctic Circle.
• In the Northern Hemisphere, the frigid zone is the area located between the North Pole and the Arctic circle.
• The Frigid zones are located near the poles. Hence, Option 1 is correct.
• They are the coldest zones and are covered with ice and snow, most of the time. Hence, they are called frigid zones. Only slanting rays of the sun reach these zones as they are located at distance from the Equator. Thus, very little heat reaches these zones.
• The northern frigid zone lies between the North Pole and the Arctic Circle. It covers an area of 4.12 percent of the total earth’s surface.
• The other frigid zone is the southern frigid zone which lies between the Antarctic Circle and the South Pole.
• Northern Temperate zone and Northern Frigid zone lies between the Tropic of Cancer and the Arctic Circle, and the Arctic Circle and the North Pole respectively.
• Frigid Zones are very cold areas.
• There is very little heat since the rays from the sun are slanting.
• In this zone, the sun does not rise much above the horizon.

Additional Information 

The correct answer is 1990.

Key Points

• Tim Berners-Lee, a British computer scientist, generally credited as the inventor of the World Wide Web.
• The development of the World Wide Web was begun in 1989 by Tim Berners-Lee and his colleagues at CERN, an international scientific organization based in Geneva, Switzerland.
• In 2004 he was awarded a knighthood by Queen Elizabeth II of the United Kingdom and the inaugural Millennium Technology Prize by the Finnish Technology Award Foundation.

Additional Information

 

NOTE: -

• Tim Berners-Lee indeed began working on the idea for the World Wide Web in 1989 while at CERN, the European physics research center. However, the first successful communication between a web browser and a server via the Internet happened on December 25, 1990. Because the options provided do not include 1989, the closest accurate option would be:

1990

This represents the year when the World Wide Web became a functioning entity. However, if 1989 were an option, it would be the most accurate choice to represent when Berners-Lee first started developing the concept.

The correct answer is Four.

Key Points

• The Vedas are considered the earliest literary record of Indo-Aryan civilization.
• There are four Vedas: Rigveda, Samaveda, Yajurveda and the fourth one is Atharvaveda.

Additional Information

• Rigveda
• Rigveda is regarded as one of the most sacred texts of Hinduism.
• It has fascinated scholars and historians due to its significance and antiquity.
• It is a collection of ancient Indian collections of Vedic Sanskrit hymns.
• The Rigveda is divided into ten books which are known as Mandalas.
• It is a collection of 10,600 verses and 1,028 hymns.
• It is the oldest text in any Indo-European language.
• It has originated as early as 1700 BC.
• The Angiras (rishi family) has composed 35% of the hymns and the Kanva family has composed 25% of Rig Veda.​
• Yajurveda
• The Yajurveda is the Veda primarily of prose mantras for worship rituals.
• An ancient Vedic Sanskrit text is a compilation of ritual offering formulas that were said by a priest while an individual performed ritual actions such as those before the yajna fire.
• Yajurveda is one of the four Vedas, and one of the scriptures of Hinduism.
• The exact century of Yajurveda's composition is unknown and estimated by Witzel to be between 1200 to 800 BCE, contemporaneous with Samaveda and Atharvaveda.
• Atharvaveda
• The Atharva Veda is the "knowledge storehouse of atharvaṇas, the procedures for everyday life".
• The text is the fourth Veda but has been a late addition to the Vedic scriptures of Hinduism.
• It is a collection of 730 hymns with about 6,000 mantras, divided into 20 books.
• About a sixth of the Atharvaveda texts adapts verses from the Rigveda, and except for Books 15 and 16, the text is in poem form deploying a diversity of Vedic matters.
• Two different recensions of the text – the Paippalada and the Śaunakiya – have survived into modern times.
• Samaveda
• The Samaveda is the Veda of melodies and chants.
• It is an ancient Vedic Sanskrit text, and part of the scriptures of Hinduism.
• One of the four Vedas is a liturgical text which consists of 1,549 verses.
• All but 75 verses have been taken from the Rigveda.
• Three recensions of the Samaveda have survived, and variant manuscripts of the Veda have been found in various parts of India.

Shortcut Trick

By observing the equation sin θ + cos θ = √2, we identify that this condition is satisfied when θ = 45°.

Substituting θ = 45°: sin 45° + cos 45° = 1/√2 + 1/√2 = 2/√2 = √2.

Now, calculate the required value: cosec 45° + cot 45°.

cosec 45° = √2 and cot 45° = 1.

Result = √2 + 1.

∴ The correct answer is √2 + 1.

Alternate Method

Given: sin θ + cos θ = √2

Formula Used: (sin θ + cos θ)² = sin²θ + cos²θ + 2 sin θ cos θ ; sin²θ + cos²θ = 1

⇒ Square both sides of the given equation: (sin θ + cos θ)² = (√2)²

⇒ sin²θ + cos²θ + 2 sin θ cos θ = 2

⇒ 1 + 2 sin θ cos θ = 2

⇒ 2 sin θ cos θ = 1

⇒ sin 2θ = 1 ⇒ 2θ = 90° ⇒ θ = 45°

⇒ Now, cosec θ + cot θ = cosec 45° + cot 45°

⇒ cosec 45° = √2 and cot 45° = 1

⇒ Final value = √2 + 1. This corresponds to Option (4).

∴ The correct answer is √2 + 1.

Additional Information

Trigonometric Identity

The fundamental square identity is sin²θ + cos²θ = 1, which applies to all values of θ.

Reciprocal Relations

cosec θ = 1 / sin θ and cot θ = 1 / tan θ = cos θ / sin θ.

Values for 45°

For θ = 45°, sin θ = 1/√2, cos θ = 1/√2, tan θ = 1, and cot θ = 1.

Complementary Angles

If sin θ = cos α, then θ + α = 90°. In this problem, sin 45° = cos 45°.

Given:

AB = 20 cm

BC = 16 cm

AC = 12 cm

Radius of incircle = 4 cm

Formula used:

Area of triangle = semi–perimeter of triangle × radius of incircle

Calculation:

Area of triangle = [(20 + 16 + 12)/2] × 4

⇒ 24 × 4

⇒ 96 cm2

∴ The area of ΔABC is 96 cm2

Calculation:

$9x^2 + 12xy + 4y^2 = (3x + 2y)^2$

Now we can substitute this expression back into the original fraction:

$\frac{(9x^2 + 12xy + 4y^2)}{36}$

$\frac{ [(3x + 2y)^2]}{6^2}$

$(\frac {x} {2}+ \frac{y} {3})^2$

Therefore, the simplified expression is $(\frac {x} {2}+ \frac{y} {3})^2$

Given:

The marked price of the chair = Cost price + 30% of the cost price

Selling price after discount = Rs. 200

Discount amount = Rs. 40

Formula:

Profit percentage = (Profit / Cost price) * 100

To solve the question, we need to find the cost price, and profit.

Calculation:

The selling price after a discount of Rs. 40 is Rs. 200:

Selling price = Marked price - Discount

MP = 200 + 40

240

According to the question:

CP × 130% = 240

CP = 2400/13 = 184.6

Profit = Selling price - Cost price

Profit = 200 - 184.6

Profit = 15.38 

Profit percentage = (15.38/184.62) × 100

Profit percentage = 8.34% 

So, the profit percentage is approximately 8.34%.

Calculation:

Income of company D = 500 + 300 = 800

Income of company E = 1000 + 600 = 1600

Income of company F = 800 + 500 = 1300

Income of company G = 500 + 400 = 900

Income of company H = 600 + 1200 = 1800

Total income of all 5 companies = 800 + 1600 + 1300 + 900 + 1800 = 6400

Total expenditure of all 5 companies = 300 + 600 + 500 + 400 + 1200 = 3000

Percentage of total income to total expenditure = 6400/3000 × 100 = 213.33%

∴ Option 1 is the correct answer.

Calculation:

Total runs = 700

Run scored by L, N and R = 29% + 12% + 13% = 54%

Total runs scored by L, N and R = 54/100 × 700 = 378

∴ Option 4 is the correct answer.

Given:

25 ÷ 10 - $(\frac {7} {4} × \frac {1} {3})$ of $\frac {6} {5}$ + $\frac {14} {3}$ × $\frac {9} {10}$ + $(\frac {1} {5} \div \frac {1} {25})$ 

Concept used:

Calculation:

⇒ 25 ÷ 10 - $(\frac {7} {4} × \frac {1} {3})$ of $\frac {6} {5}$ + $\frac {14} {3}$ × $\frac {9} {10}$ + $(\frac {1} {5} \div \frac {1} {25})$

⇒ $5\over 2$ - $\frac {7} {12}$ ×  $\frac {6} {5}$ + $\frac {21} {5}$ + 5

⇒ $5\over 2$ - $\frac {7} {10}$ + $\frac {21} {5}$ + 5

⇒ $(25 + 42)\over 10$ - $\frac {7} {10}$ + 5

⇒ 60/10 + 5

⇒ 6 + 5

⇒ 11

Hence the value is 11.

Given:

In triangle XYZ. ∠Y is the smallest angle and ∠Y = 25 degrees.

The ratio of the angle is 20 ∶ 11 ∶ 5.

Calculation:

Now, the measure of the largest angle of △XYZ = 25° × $\frac {20}{5}$ = 100°

∴ The largest angle of △XYZ is 100°.

Given:

The medians QT and RS intersect at right angles.

QT = 18 cm, RS = 27 cm

Concept used:

The centroid is the intersection point of all three medians.

Centroid divides the median in the ratio 2 : 1

Calculation:

The two medians intersect at G. Hence G is the centroid of the triangle and the centroid divides the median in the ratio 2 : 1

∴ QG : GT = 2 : 1 ⇒ QG = 18 × 2/3 = 12 cm 

Also, RG : GS = 2 : 1 ⇒ GS = 27 × 1/3 = 9 cm

∴ In ΔGQS, ∠QGS = 90° (∵ medians intersect at 90°)

Using Pythagoras theorem,

QG2 + GS2 = QS2 

⇒ 122 + 92 = QS2

⇒ QS2 = 225

⇒ QS = √ 225 = 15 cm.

∴ The length of QS = 15 cm.

Given:

cot (P + Q) = 0

tan (P - Q) = 1/√3

Concept:

Cotangent and tangent are reciprocal trigonometric functions and tan(π/3) = √3.

Calculation:

⇒ cot (P + Q) = 0

⇒ (P + Q) = 90°.

⇒ tan (P - Q) = 1/√3

⇒ (P - Q) = 30°.

Add these two equations to solve for P and subtract to solve for Q:

⇒ P = (90° + 30°) / 2 = 60°.

⇒ Q = (90° - 30°) / 2 = 30°.

Therefore, ∠P = 60° and ∠Q = 30°.

Concept Used:

New Value = Original Value × (1 ± Percentage/100)

Calculation:

For the third year, the salary increased by 25%, so the original salary before this increase was:

23,000 ÷ (1 + 25/100) = 23,000 ÷ 1.25 = Rs. 18,400

For the second year, the salary decreased by 20%, so the original salary before this decrease was:

18,400 ÷ (1 - 20/100) = 18,400 ÷ 0.8 = Rs. 23,000

For the first year, the salary increased by 15%, so the original salary before this increase was:

23,000 ÷ (1 + 15/100) = 23,000 ÷ 1.15 = Rs. 20,000 

So, Tilak's salary at the beginning of these three years was Rs. 20,000.

Given:

$\frac{1-\tan^245° }{1 + \cos^2 90° }$

Formula:

tan 45° = 1

cos 90° = 0

Calculation:

⇒ (1−tan² 45°)/(1+cos² 90°)

⇒ (1 − 1²)/(1 + 0²) = 0/1 = 0.

Hence, the value is 0.

Given:

Capital ratio of Nikhil and Neha = 5 ∶ 4

Profit ratio = 6 ∶ 5

Concept:

The formula for profit distribution is (capital × time).

Calculation:

Let the time invested by Nikhil be T, then time invested by Neha is (T+1).

⇒ 5T/4(T+1) = 6/5

⇒ 25T = 24T + 24

⇒ After solving this equation, T = 24.

Therefore, Neha invested the money for (T + 1) = 24 + 1 = 25 years.

∴ Option 4 is the correct answer.

Given:

(p + 2q)² - (p - 2q)²

Concept:

The formula a² - b² = (a + b)(a - b).

Calculation:

⇒ (p + 2q)2 - (p - 2q)2

⇒ p² + 4q² + 4pq - p2 - 4q2 + 4pq

= 8p × q.

Hence, the value is 8pq.

Given:

60% of articles sold at a 20% loss

40% of articles sold at a 5% profit

Concept:

The formula for overall profit or loss percentage = [(total cost price - total selling price) / total cost price] × 100.

Calculation;

⇒ 20% Loss on 60% of articles = 60 × 0.2 = 12.

⇒ 5% Profit on 40% of articles = 40 × 0.05 = 2.

⇒ Overall loss percentage = 12 - 2 = 10%.

Hence, the overall loss percentage is 10%.

Given:

224 of 4 ÷ 7 - 250 × 3

Concept:

Calculation:

⇒ 224 of 4 ÷ 7 - 250 × 3

⇒ 224 ×  4 ÷ 7 - 750

⇒ 896 ÷ 7 - 750

⇒ 128 - 750

⇒ -622

Hence, the value is -622.

Shortcut Trick

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

Sum of sides = 15 + 9 = 24 cm; Height = 6 cm

Area = 1/2 × 24 × 6 = 72 cm²

Total cost = Area × Rate = 72 × 3 = 216

∴ The correct answer is Rs. 216.

Alternate Method

Given:

Parallel side 1 (a) = 15 cm

Parallel side 2 (b) = 9 cm

Distance between them (h) = 6 cm

Rate of copper plating = Rs. 3 per cm²

Formula Used:

Area of a trapezium = 1/2 × (a + b) × h

Calculations:

⇒ Area = 1/2 × (15 + 9) × 6

⇒ Area = 1/2 × 24 × 6

⇒ Area = 12 × 6 = 72 cm²

⇒ Total cost = Area × Rate

⇒ Total cost = 72 × 3

⇒ Total cost = Rs. 216

∴ The correct answer is Rs. 216.

Additional Information

Area of a Trapezium

The area is the product of the average of the parallel sides and the distance between them: A = [(a + b)/2] × h.

Median of a Trapezium

The segment connecting the midpoints of the non-parallel sides is called the median, and its length is (a + b) / 2.

Costing Problems

Total cost for surface work is always the calculated surface area multiplied by the rate per unit area.

Given:

Difference in speed = 40 km/hour

Sum of speed = 60 km/hour

Concept:

Time = Distance / Speed, and in this case, time difference is given.

Calculation:

Let Farhan's speed = x, then

Aman's speed = y.

According to question,

x + y = 60           ..........(i)

x - y = 40            ..........(ii)

After solving we get,

x = 50 km/h and y = 10 km/h

Using any of the speeds and time difference to find the distance:

⇒ D/10 - D/50 = 8/60

⇒ D[5 - 1]/50 = 2/15

⇒ 4D/50 = 2/15

⇒ D = 2/15 × 50/4

⇒ D = 5/3 km

Therefore , the distance they both should cover is 5/3 km.

Calculation:

Total runs = 500

Runs scored by R = 32% = 32/100 × 500

⇒ 160

∴ Option 1 is the correct answer.

Given:

A can complete 3/8 work in 36 days

B can complete 1/2 work in 27 days

Concept: Work efficiency is inversely proportional to time taken.

Calculation:

⇒ A's full work will take (36 / 3) × 8 = 96 days.

⇒ B's full work will take (27 / 1) × 2 = 54 days.

I. A is less efficient than B - Correct, since A takes more time than B.

II. A and B working together can complete 11/15 work in 36 days - Incorrect, as working together they can complete (1/96 + 1/54) × 36 = ~0.73 of the work in 36 days.

Hence, only statement I is correct.

Calculation:

The average of salary of employees C, D and E = (300 + 200 + 400)/3 

900/3 = 300

∴ Option 2 is the correct answer.

Given:

x + y + z = 0

Concept used:

If (a + b + c) = 0 then a³ + b³ + c³ = 3abc

Calculation:

According to the concept,

$\frac {x} {(yz)^2}+ \frac {y} {(xz)^2} + \frac {z} {(xy)^2}$

⇒ $\frac {(x\times x^2)\ +\ (y\times y^2)\ +\ (z\times z^2)}{(xyz)^2}$

⇒ $\frac {x^3\ +\ y^3\ +\ z^3}{(xyz)^2}$

⇒ $\frac {3xyz}{(xyz)^2}$ (∵ x + y + z = 0, so x³ + y³ + z³ = 3xyz)

⇒ $\frac {3} {xyz}$

∴ The value of $\frac {x} {(yz)^2}+ \frac {y} {(xz)^2} + \frac {z} {(xy)^2}$ is $\frac {3} {xyz}$.

Calculation:

The formula for simple interest is:

I = PRT/100,

where:

I = interest earned,

P = principal amount (initial investment),

R = annual interest rate (in percentage),

T = time (in years).

If a sum of money becomes three times of itself at a rate of 10 percent per annum, it means that twice the initial sum was earned as interest (because the initial sum plus twice the sum gives three times the sum). So:

2P = PRT/100

Substituting the given R = 10, we get:

2P = P × 10 × T/100

Solving for T:

T = 2 × 100/10 = 20 years.

Now, for the two statements:

I. For the money to become 5 times of itself at the rate of 20 percent per annum in the same time period (20 years), the interest earned must be four times the principal. So:

4P = P × 20 ×T/100 = P× 20 × 20/100 = 4P.

So, Statement I is correct.

II. For the money to become 7 times of itself at the rate of 30 percent per annum in the same time period (20 years), the interest earned must be six times the principal. So:

6P = P × 30 × T/100 = P × 30 × 20/100 = 6P.

So, Statement II is also correct.

Thus, both statements I and II are correct.

Given:

If in triangle ABC, D is a point on the side BC such that the line joining AD bisects the angle A.

The length of BD and BC are 4 cm and 10 cm respectively.

Concept used:

The Angle Bisector Theorem states that in a triangle, the angle bisector of a vertex divides the opposite side into segments that are proportional to the lengths of the other two sides.

Calculation:

DC = BC - BD = 10 - 4 = 6 cm

According to the concept,

Since AD is the angle bisector of ∠BAC, AB : AC = BD : DC

So, AB : AC

⇒ 4 : 6 = 2 : 3

∴ The ratio of the lengths of AB and AC is 2 : 3.

Given:

Average of 5 numbers = 60

Sum of remaining two numbers = 120

Concept:

Average = Total sum / Number of elements.

Calculation:

Let's call the first number x. Then we know:

⇒ The second number = x/2, the third number = 3x/2, and the remaining two numbers = 120.

⇒ The sum of all 5 numbers = 60 × 5 = 300.

⇒ x + x/2 + 3x/2 + 120 = 300

⇒ 3x = 180

⇒ x = 60

We find that x = 60.

The third number is therefore 3x/2 = 3 × 60/2 = 90

Therefore, the value of the 3^rd number is 90.

The correct answer is 'Option 1'.

Key Points

• The most appropriate meaning of the idiom "Be my guest" is "Please do it".
• "Be my guest" is a polite way of giving someone permission to do something, or to invite them to do something as if they were a welcome guest.
• The idiom conveys a sense of generous hospitality.

Therefore, the correct answer is: 'Please do it'.

The correct answer is 'Option 4'.

Key Points

• The segment in the sentence that contains a grammatical error is "hardly picture in Rome I was unable".
• The error lies in the missing article before "picture".
• In English, countable singular nouns usually need an article or other kind of determiner like 'a', 'an', or 'the'.
• Article 'A' will be used before word 'Picture' as it is starting with a consonant.

Therefore, The correct sentence is: "And, indeed, there was hardly a picture in Rome I was unable to reattribute to its rightful owner."

The correct answer is 'She said that she would be available the next day'.

Key Points

• The correct indirect form of the sentence "She said, 'I will be available tomorrow.'" is "She said that she would be available the next day."
• When changing direct speech into indirect speech, the verb tense typically shifts back (this is known as "backshifting").
• In this case, "will" becomes "would".
• Moreover, words indicating nearness in time or place in direct speech are generally changed into words showing distance in indirect speech.
• Here, "tomorrow" changes to "the next day".

Therefore, the correct sentence is: 'She said that she would be available the next day.'

Additional Information

• Option 1, "She said that she would be available tomorrow," is incorrect because "tomorrow" should be changed to "the next day" in indirect speech.
• Option 3, "She said that she must be available the next day," is incorrect because "will" should not change to "must" in indirect speech. "Must" changes the meaning, implying a necessity or obligation that wasn't present in the original sentence.
• Option 4, "She said that she will be available the next day," is incorrect because the verb "will" should be backshifted to "would" in indirect speech.

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

Key Points

• The correct word that can substitute the group of words "Belonging to the same kind" is "Homogeneous."
• "Homogeneous" describes something that is made up of elements of the same kind or that have the same properties.(समरूप).

Therefore, the correct answer is: 'Homogeneous'.

Additional Information

• "Sebaceous" relates to oil or fat, specifically to the secretion of sebum, a substance produced by the sebaceous glands in the skin. (वसायुक्त)
• "Heterogeneous" is used to describe a group that contains items or individuals of different types. (विषम).
• "Casserole" is a type of dish, both a type of food and the container it's cooked in. It's usually a hearty, slowly cooked meal that is baked in the oven.(कैसरोल).

The correct answer is "False".

Key Points

• The word "bogus" means not genuine or true (fake).
• It is used to describe something that is a counterfeit or deceptive representation.
• The word that is closest in meaning (synonym) to "bogus" among the provided options is "false".
• "False" is used to describe something that is not true or correct(झूठा).

Therefore, the correct answer is 'option 3'.

Additional Information

• Let's look at the other options:
• "Humane" means having or showing compassion or benevolence.(मानवता संबंधी)
• "Strong" means having the power to move heavy weights or perform other physically demanding tasks.(मजबूत)
• "Criticize" means to indicate the faults of (someone or something) in a disapproving way.(आलोचना करना)

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

Key Points

• The correctly spelled word among the provided options is "MALODOROUS".
• "Malodorous" is an adjective that means smelling very unpleasant.(बदबूदार)

Therefore, the correct answer is: 'Malodorous'.

Additional Information

• Now, let's look at the incorrectly spelled words and provide their correct spellings and meanings:
• "HEIRARCHY" is misspelled. The correct spelling is "HIERARCHY", which refers to a system in which members of an organization or society are ranked according to relative status or authority.(पदानुक्रम)
• "APPAULLING" is misspelled. The correct spelling is "APPALLING", which means causing shock or dismay; horrific.(भयानक)
• "PESTILLENTIAL" is misspelled. The correct spelling is "PESTILENTIAL", which means relating to or tending to cause infectious diseases.(महामारी संबंधी)

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

Key Points

• The most appropriate one-word substitution for "a person who is experiencing dementia brought about by old age" is "Senile".
• "Senile" refers to the weakness or mental infirmity of old age, and it is often used to describe conditions like dementia that are associated with aging. (जरा संबंधी)

Therefore, the correct answer is: 'Senile'.

Additional Information

• Let's look at the other options:
• "Sentinel" is a guard whose job is to stand and keep watch. (पहरेदार).
• "Primal" means essential; fundamental. It's often used to refer to something that is original or has existed from the beginning.(मूल)
• "Primitive" means relating to an early stage of evolutionary development; primeval.(प्राचीन)