SSC CGL 2022 Tier-I Official Paper (Held On : 05 Dec 2022 Shift 4) (Previous Year Paper)

BODMAS rule:

I. 8 × 3 ÷ 6 + 9 – 7

After interchanging '× and ÷' and '7 and 9'

8 ÷ 3 × 6 + 7 – 9

⇒ 16 + 7 - 9

⇒ 23 - 9 = 14.

II. 9 – 7 × 1 + 6 ÷ 3

After interchanging '× and ÷' and '7 and 9'

⇒ 7 – 9 ÷ 1 + 6 × 3

⇒ 7 – 9 + 6 × 3

⇒ 7 – 9 + 18

⇒ 25 - 9 = 16.

Hence, the correct answer is "Option 2".

The pattern followed in the given options is:

Logic: (First term)² + 1 = Second term

Now we consider the given options:

Option 1) 12 – 145

⇒ (12)² + 1 = 145

⇒ 144 + 1 = 145

⇒ 145 = 145

Option 2) 16 – 257 

⇒ (16)2 + 1 = 257

⇒ 256 + 1 = 257

⇒ 257 = 257

Option 3) 14 – 193

⇒ (14)2 + 1 = 193

⇒ 196 + 1 = 193

⇒ 197 ≠ 193

Option 4) 10 –101

⇒ (10)2 + 1 = 101

⇒ 100 + 1 = 101

⇒ 101 = 101

We can see that 14 - 193 does not follow the pattern so it is the odd one.

Hence, the correct answer is "Option 3".

According to the English alphabet and its positional values:

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The pattern followed in the given series is:

The first alphabet is getting - 1.

The second alphabet is getting + 5.

The third alphabet is getting  -9.

Here, 'MGB' will complete the series.

Hence, the correct answer is "Option 2".

BODMAS rule:

Option 1) 7 × 8 ÷ 9 + 18 – 11 = 16.

After interchanging '× and +'.

⇒ 7 + 8 ÷ 9 × 18 – 11 = 16

⇒ 7 + 0.8 × 18 – 11 = 16 

⇒ 7 + 14.4 – 11 = 16 

⇒ 21.4 – 11 = 16

⇒ 10.4 ≠ 16 

Option 2) 24 – 8 – 5 × 5 + 3 = 14.

After interchanging '× and +'.

⇒ 24 – 8 – 5 + 5 × 3 = 14 

⇒ 24 – 8 – 5 + 15 = 14 

⇒ 39 – 8 – 5 = 14 

⇒ 26 ≠ 14

Option 3) 5 × 10 – 15 + 20 ÷ 25 = 8.

After interchanging '× and +'.

⇒ 5 + 10 – 15 × 20 ÷ 25 = 8 

⇒ 5 + 10 – 15 × 0.8 = 8

⇒ 5 + 10 – 12 = 8

⇒ 15 – 12 = 8 

⇒ 3 ≠ 8

Option 4) 24 × 8 + 6 ÷ 3 – 18 = 22.

After interchanging '× and +'.

⇒ 24 + 8 × 6 ÷ 3 – 18 = 22 

⇒ 24 + 8 × 2 – 18 = 22 

⇒ 24 + 16 – 18 = 22

⇒ 40 – 18 = 22

⇒ 22 = 22  

Hence, the correct answer is "Option 4".

The pattern followed in the given series is:

The figure with the arrow moves in clockwise direction.

<br>

The alphabet at the top changes moves left to right alternatively with the bottom.

The alphabet present in a step are one alphabet apart.

The alphabet at the bottom moves from left to right alternatively with the top.

<br>

    

Next step:

The arrow will point towards left.

The alphabet at the top will be at the left.

The alphabet at the bottom will be at the right.

                                   

Now we consider the given options:

Option 1) The places of the alphabets is interchanged.

Option 2) The positioning of the alphabets is incorrect.

Option 3) The pattern is correct.

Option 4) The arrow in the pattern is incorrect and the places of the alphabets is interchanged.

Hence, the correct answer is "option 3".

The correct order of words according to the English alphabet is:

1. Theogonic
2. Theologue
3. Theology
4. Theorem
5. Theory

From the order obtained, we can see that 'Theology' appears at the third position.

Hence, the correct answer is "Option 3".

Given statements:

Some coats are tables.

No table is a mirror.

All golds are tables.

The least possible Venn diagram for the given statements:

Conclusions:

I. Some coats being golds is a possibility → Follow → If the number of golds is equal to the number of tables then the conclusion 'Some coats are golds' follows.

II. No gold is a mirror → Follow → We have 'No table is a mirror' and 'All golds are tables' we can clearly see that no gold can be mirror therefore the conclusion follows.

III. All tables are golds → Does not follow → We do not have any information about all tables and thus we cannot assume for all tables so the conclusion does not follow.

IV. No coat is a mirror → Does not follow → No information is provided between coats & mirrors, we cannot rule out the possibility that some coats are mirror thus the conclusion does not follow.

So only conclusions I and II follow. 

Hence, the correct answer is "option 3".

According to the English alphabet and their positional values:

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The pattern followed in the given codes is:

Logic: Letters - 1.

Here, for 'PLAYGROUND' is written as ‘OKZXFQNTMC’.

And, for ‘SCIENCE’ is written as ‘RBHDMBD'

Similarly, for 'TYPEWRITER'

So, 'TYPEWRITER' will be written as 'SXODVQHSDQ'.

Hence, the correct answer is "Option 4".

The pattern followed in the given series is:

Logic: (First term - 1)³ = Second term

Now we apply the pattern on the given series:

For, 6 ∶ 125

(6 - 1)³ = 125

(5)3 = 125

125 = 125

For, 2 ∶ 1 

(2 - 1)3 = 1

(1)3 = 1

1 = 1

Similarly, for  5 ∶ ?

(5 - 1)3 = ?

(4)3 = ?

64 = Answer

Hence, the correct answer is "option 2".

The mirror image of the given combination is:

Now we consider the given options:

Option 1) 

The combination is correct.

Option 2) 

'2' and 'B' are not mirrored.

Option 3) 

'2' is not mirrored.

Option 4)  

The combination is mirrored sidewards.

Hence, the correct answer is "Option 1".

Statements:

I. All P are W.

II. No O is W.

Venn diagram:

Conclusion:

I. Some O are not P → Follow → From the statements we know that all 'P' are 'W' and no 'O' is a 'W' which means no 'O' is a 'P' which can be also stated as some 'O' are not 'P'. Therefore, the conclusion follows.

II. All W are O → Does not follow → We have 'No O is W' which clearly means that 'O' is not related to 'W' and therefore this conclusion is baseless thus the conclusion does not follow.

So, only conclusion I follows.

Hence, the correct answer is "option 2".

When we compare the figures 1 and 2, we get:

 

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When dice is rotated such that '3' and '6' are visible in both the cases, we get '2' on the left and '4' on the right which means '2' and '4' are opposite to each other.

So, the face opposite to '2' is '4'.

Hence, the correct answer is "option 1".

The mirror image of the given combination is:

Now we consider the given options:

Option 1)

'7' is missing.

Option 2)

The number '7' is misplaced and there is an extra 'I'.

Option 3)

There is an extra alphabet added i.e., 'I'.

Option 4)

The combination is correct.

Hence, the correct answer is "option 4".

We apply the options to the given equation and solve it using BODMAS rule:

Given equation: 248 ÷ 4 + 184 ÷ ( 4 × 6 – 2 × 8) = 77

Option 1) 8 and 4

After Interchanging:

⇒ 248 ÷ 8 + 184 ÷ ( 4 × 6 – 2 × 4) = 77

⇒ 248 ÷ 8 + 184 ÷ (24 – 8) = 77

⇒ 248 ÷ 8 + 184 ÷ 16 = 77

⇒ 31 + 11.5 = 77

⇒ 42.5 ≠ 77.

Given equation: 248 ÷ 4 + 184 ÷ ( 4 × 6 – 2 × 8) = 77

Option 2) 184 and 77

After interchanging:

⇒ 248 ÷ 4 + 77 ÷ ( 4 × 6 – 2 × 8) = 184

⇒ 248 ÷ 4 + 77 ÷ (24 – 16) = 184

⇒ 248 ÷ 4 + 77 ÷ 8 = 184

⇒ 62 + 9.6 = 184

⇒ 71.6 ≠ 184.

Given equation: 248 ÷ 4 + 184 ÷ ( 4 × 6 – 2 × 8) = 77

Option 3) 184 and 248

After Interchanging:

⇒ 184 ÷ 4 + 248 ÷ ( 4 × 6 – 2 × 8) = 77

⇒ 184 ÷ 4 + 248 ÷ (24 – 16) = 77

⇒ 184 ÷ 4 + 248 ÷ 8 = 77

⇒ 46 + 31 = 77

⇒ 77 = 77.

Given equation: 248 ÷ 4 + 184 ÷ ( 4 × 6 – 2 × 8) = 77

Option 4) 4 and 6

After Interchanging:

⇒ 248 ÷ 6 + 184 ÷ ( 4 × 4 – 2 × 8) = 77

⇒ 248 ÷ 6 + 184 ÷ (16 – 16) = 77

⇒ 248 ÷ 6 + 184 ÷ 0 = 77

⇒ 41.3 + 0 = 77 

⇒ 41.3 ≠ 77

Hence, the correct answer is "Option 3".

Given :

A # B means ‘A is the sister of B’.

A @ B means ‘A is the son of B’.

A & B means ‘A is the father of B’.

A % B means ‘A is the mother of B’.

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

W & Q # T & Y @ M % K → W is father of Q, Q is sister of T, T is father of Y, Y is son of M, M is mother of K.

W is the father's father to K.

Hence, the correct answer is "Option 3"

According to the English alphabets & their positional values:

The pattern followed is:

The first alphabet is increased by + 4 & positional value of the opposite alphabet is the code.

The second alphabet is increased by + 3 & positional value of the opposite alphabet is the code.

The third alphabet is increased by + 2 & positional value of the opposite alphabet is the code.

The fourth alphabet is increased by+ 1 & positional value of the opposite alphabet is the code.

Now,

 'BOSS’ is coded as '21967'.

'DEAL' is coded as '19192414'

Similarly, for GAIN:

'GAIN' will be coded as '16231612'.

Hence, the correct answer is "Option 3".

The pattern followed in the given series is:

(First term - Second term) × 8 + Second term = Third term 

Now we apply the pattern on the given rows:

First row - 15, 11, 43

(15 - 11) × 8 + 11 = 43

4 × 8 + 11 = 43

32 + 11 = 43

43 = 43

Second row - 13, 8, 48

(13 - 8) × 8 + 8 = 48

5 × 8 + 8 = 48

40 + 8 = 48

48 = 48

Third row - 9, 7, ?

(9 - 7) × 8 + 7 = ?

2 × 8 + 7 = ?

16 + 7 = ?

23 = Answer

Hence, the correct answer is "Option 1".

The figure that will replace the question mark(?) in the following figure series is shown below :

• The numbers in the middle of the box are multiplied by 2.
• The arrows change alternatively up and down.

lines are increasing one by one and making new figures in new series. as shown below

Hence, the correct answer is "Option 1".

The logic followed here is:

Logic : (First number)² + (Third number)² = Second number.

(5, 41, 4) 

→ (5)² + (4)² ⇒ 25 + 16 = 41

And,

(2, 68, 8) 

→ (2)2 + (8)2 ⇒ 4 + 64 = 68

Similarly,

(6, 100, 8) 

→ (6)2 + (8)2 ⇒ 36 + 64 = 100

Hence, the correct answer is 'Option 1'.

The logic followed here is: 

Ant ∶ Antling → Antling is a small immature or miniature ant.

Similarly,

Deer ∶ Fawn → Fawn is a young deer.

Hence, the correct answer is "Option 2".

The pattern followed here is : 

So, '267' will complete the series.

Hence, the correct answer is "Option 4".

K ÷ L → K is the mother of L

K – L →  K is the father of L

K × L→   K is the sister of L

By drawing family tree using the table above we get,

1) P ÷ Q × R 

Here, P is the father of R. 

2) R – Q ÷ P 

Here, P is the Grandchild of R.

3) P ÷ Q – R 

Here, P is the paternal grandmother of R.

4) Q ÷ P – R 

Here, P is the father of R.

Hence, the correct answer is "Option 3".

According to the English alphabets & their positional values:

The pattern followed is:

The first alphabet is increased by + 3.

The second & the Third alphabet are increased by + 2.

 

Hence, the correct answer is "Option 1".

According to the English alphabet & its positional value:

<br>

The pattern followed is:

Option 1) 

Option 2) 

Option 3) 

Option 4) 

Here, the odd one is 'ATRE'.

Hence, the correct answer is "Option 3".

The logic followed here is :

Rice ∶ Grain → Rice is a small seed that is cultivated from grain plants.

Lentils ∶ Pulses → Pulse is an edible seed from a legume plant (variation of pulses) 

Hence, the correct answer is "Option 1"

The correct answer is Chaitra.

Key Points

• Ugadi
• Ugadi, which is observed as Andhra Pradesh's Hindus' New Year's Day, is observed on the first day of the Hindu Luni-Solar Calendar in the month of Chaitra.
• According to the Gregorian calendar, it takes place in either March or April.
• This Indian holiday heralds the arrival of pleasure, joy, hope, and light.
• The Sanskrit words "Yuga," which means age, and "adi," which means the beginning, are combined to form the word "Ugadi."
• It denotes the start of a new era in plain terms.
• In Karnataka, Andhra Pradesh, and Telangana, this holiday is celebrated with great zeal and passion.

Additional Information

• The ninth month of the Hindu calendar is Agrahya or Mrga.
• The Hindu month of Vaisakha corresponds to April or May on the Gregorian calendar. in the national calendar of India.
• The fifth month of the Hindu calendar is shravan.

The correct answer is Raju Khan.

Key Points

• Raju Khan ​
• Raju Khan is a famous Bollywood Choreographer.
• He is the son of acclaimed choreographer Saroj Khan.
• He began his career in the late '80s with the movie Dacoit, Sadak, etc.
• He achieved greater success with movies like 'Koi Mil Gaya' and 'Lagaan' his work was most acknowledged and polished.
• In the year 2002, he went on to win the National Film Award for the Hindi movie 'Lagaan'.

Additional Information

• Ahmed Khan is an Indian Producer, Director, Writer, and Choreographer.
• Dinesh Kumar is an Indian Choreographer working in South Indian Films, he won The National Award for Best Choreography in the year 2011 for his work in Aadukalam.
• Shiamak Davar is an Indian Choreographer noted as the first to bring Contemporary Jazz and western forms of dance to India.

The correct answer is Consumption of one person does not affect the consumption of another person.

Key Points

• A public good is a good that is non-excludable and non-rivalrous.
• Non-rivalrous means the goods that do not diminish gradually in supply as more people consume them
• Non-excludable means that the goods are available to all citizens.
• These are the main features of public goods, available to all citizens and the supply does not affect the consumption of another person.

Additional Information

• In Economics, public goods are referred to as commodity or service that is made available to all members of society.
• These services are administered by governments and paid collectively through taxes.
• Examples of public goods include security, education, infrastructure, environment, and health.

The correct answer is Right to Property.

Key Points

• Article 300A
• Article 300A  deals with the Right to Property.
• Article 300A states that no person shall be deprived of his property, save by the authority of law.
• The right to property was declined from the Fundamental Right after the 44th Constitutional Amendment Act, of 1978.
• After the amendment, it was made a legal right under Article 300A in PART-XII of the Constitution.
• The Supreme Court reminded Government that the state had to follow the due procedure of law before taking the private property of a person.

Additional Information

The correct answer is 'Mawsynram'

Key Points

• Mawsynram is reported as the world's wettest place on earth.
• It is situated in The Khasi Hills in Meghalaya.
• It receives an average rainfall of 11,872 millimeters.
• The majority of its rainfall is received from the Bay of Bengal.
• People of these regions use grasses on the roofs to cover their huts from rain.

Additional Information

• Meghalaya is a North-Eastern state of India.
• It is famous for its highest rainfall, biodiversity, and sub-tropical forests.
• Shillong is the capital of the state.
• Khasi, Jaintia, and Garo Hills is an extension of the main Peninsular
  

plateau.

The correct answer is Gujarat.

Key Points

• Stray Cattle movement.
• In September 2022 Gujarat legislative assembly withdrew a bill aimed at prohibiting the movement of stray cattle on roads and public places in urban areas of the state, months after it was passed.
• After returning the "Gujarat Cattle Control (Keeping and Moving) In Urban Areas Bill" to the state's Bharatiya Janata Party (BJP) administration and asking them to "reconsider it and make necessary revisions," state governor AcharyaA few days later, Devvrat retracted the plan..
• The bill, which was approved by the Assembly in April of this year, required cattle-rearers to seek a licence in order to maintain certain animals, such as stray cows and bulls, in cities and towns and to have them tagged; if they failed to do so, they risked being imprisoned.

Additional Information

• On the first day of the two-day Assembly session, Minister of State for Urban Development Vinod Moradiya put the bill's withdrawal motion up for a vote.
• However, after receiving full support from the opposition Congress, the BJP administration withdrew the request.The opposition Congress protested the passage of the law during the last Assembly session on April 1, calling it a "black Act" while it was being discussed.

The correct answer is Siraj Ud Daulah.

 Key Points

• ​Siraj Ud Daulah 
• Siraj Ud Daulah became the Nawab of Bengal in 1756 after the death of Alivardi Khan.
• The last independent Nawab of Bengal was Mirza Muhammad Siraj-ud-Daulah, also known as Siraj-ud-Daulah[a] or Siraj ud-Daula.
• The East India Company began to dominate Bengal by the conclusion of his reign and, eventually nearly the entire Indian subcontinent.
• On June 23, 1757, Siraj was betrayed by Mir Jafar, the Nawab's army's commander, and lost the Battle of Plassey.
• The East India Company took over Bengal's government after an invasion by its armies, led by Robert Clive.

 

Additional Information 

• Nawab of Bengal in 1756
• The three territories of Bengal, Bihar, and Orissa, which today make up the independent nation of Bangladesh and the Indian states of West Bengal, Bihar, and Orissa, were de facto ruled independently by the Nawab of Bengal in the early 18th century.
• The Nawabs had their headquarters in Murshidabad, which was in the middle of Bengal, Bihar, and Odisha. The first Nawab was their leader, a former prime minister.

The correct answer is Baked brick.

Key Points

• Bhitargaon
• ​The greatest Indian brick temple to have survived from the Gupta Empire is located in Bhitargaon, a town close to Kanpur in the Kanpur region of Uttar Pradesh, India.
• Many of the original elements are still present despite the extensive restoration. It dates to the fifth century, late.
• A terracotta panel fronts the terraced brick structure that houses the Bhitargaon Temple.
• It is the earliest surviving brick/terracotta Hindu shrine with a roof and a towering shikhara, but its upper chamber did experience significant damage in the 18th century.
• It was constructed in the 5th century during the Gupta dynasty.

Additional Information

• The temple faces east and has a square construction with double-recessed corners.
• Overlooking the garbhagriha is an enormous pyramidal spire. Terracotta wall decorations with images of Shiva, Vishnu, and other deities adorn the walls.
• When Alexander Cunningham first arrived, the porch and the ardhamandapa, which eventually fell, were still in tact.

The correct answer is Rangabati.

Key Points

• Rangabati​
• Rangabati is a famous folk dance of Odisha.
• The most well-known recorded song in Sambalpuri/Odiya is probably "Rangabati."
• The song's male singer is 2017 Padma Shri recipient Jitendra Haripal. In the middle of the 1970s, the song was initially recorded for All India Radio.
• The song was redone in 1976 by the Indian Record Manufacturing Company Ltd (INRECO), a record label based in Calcutta at the time. The disc was finally published in 1978–1979 after a dispute caused a delay.
• Mitrabhanu Gauntia wrote the Sambalpuri song, which was performed by Jitendra Haripal and Krishna Patel and was produced by Prabhudatta Pradhan.

Additional Information

• Folk Dance of Odisha
• Various folk dance styles emerged in various parts of Odisha, including the well-known Odissi and Chhau.
• Many people adore the Sambalpuri dance, which is the most well-known dance in western Odisha.
• Some coastal areas of Odisha, including Cuttack, Jajapur, Jagatsinghpur, Puri, Khurda, Bhadrak, Baleswar, Dhenkanal, and Angul, practise the dance style known as Laudi Khela, also known as Gauda Nacha.
• The performers are mostly young boys from the "Gauda" or "Gopal" (Yadav) castes. During Dola Purnima, this dance is performed (Holi).
• One of Odisha's most popular and well-known folk dance styles is called Ghumura Dance (or Ghumra Dance).

The correct answer is Crystal field theory (CFT).

Key Points

• Crystal field theory (CFT)
• ​Crystal field theory (CFT) discusses the relationship between ligand binding and degradation of d orbitals in metal complexes, the geometry of metal complexes, and the splitting of d orbitals.
• The propensity of transition metals to form complexes is one of their key characteristics. A complex can be thought of as having several ligands encircling a core metal atom or ion.
• Crystal field theory governs how these ligands interact with the central metal atom or ion.
• The interaction between a metal ion and ligand is viewed by the 1929-founded crystal field theory as essentially an electrostatic phenomenon, with the ligands being considered as point charges close to the atomic orbitals of the central atom.
• Using molecular orbital theory, crystal field theory was developed and expanded to consider the partially covalent nature of bonding between the ligand and metal atom.

Additional Information

• The metal-ligand bond was defined by crystal field theory as an ionic bond that solely results from electrostatic interactions between the metal ions and ligands.
• In the crystal field theory, anions are viewed as point charges, whereas neutral molecules are viewed as dipoles. Transition metals' d orbitals degenerate, or have the same energy, when they are not bound to any ligands.
• Due to the varied symmetries of the d orbitals and the inductive influence of the ligands on the electrons, the d orbitals split apart and become non-degenerate when they begin bonding with other ligands.

The correct answer is Open air classroom.

Key Points

• Paray Shikshalaya’ programme
• ​The West Bengal state government unveiled its open-air learning project, known as "Paray Shikshalaya," on February 7.
• The state government's goal is to provide classes I through VII in elementary education in every neighbourhood within the state.
• This new campaign aims to encourage kids to pursue their education, especially those who have stopped attending school as a result of the Covid-19 epidemic issue.
• This project would involve both primary school teachers and paraprofessionals. Children in Classes 1–5 will receive an elementary education from them.

The correct answer is Amjad Ali Khan.

Key Points

• After India's Kailash Satyarthi and Pakistan's Malala Yousafzai received the prestigious award, sarod master Amjad Ali Khan and his sons Amaan and Ayaan gave a performance at the Nobel Peace Prize Concert. With a special "Raga For Peace" written for the occasion, the group promoted a message of peace, harmony, and nonviolence.
• After the congratulatory remarks for Malala and Satyarthi, Amjad Ali, Amaan, and Ayaan ascended the stage to perform their "Raga for Peace."
• Peace Through RAGA: It is a subsidiary of the Russia & America Goodwill Association (RAGA.org), a group that unites Russians and Americans for friendship and peace. All official Soviet and pro-Soviet "friendship associations," including The National Council of American-Soviet Friendship, ceased to exist when the USSR fell at the end of 1991 (NCASF).

Additional Information

• Bahadur Khan​​
• ​Bengali Ustad Bahadur Khan was born in Shibpur, Brahmanbaria, Bangladesh, on January 19, 1931. (then British India). He came from a musical background and was linked to sitarist Pandit Ravi Shankar.
• He was the son of Indian classical musician Ayet Ali Khan. Before he ultimately settled in Calcutta, Khan first learned how to play the sarod from his father and his uncle Alauddin Khan in Maihar. In the future, he worked alongside his relatives Ali Akbar Khan and Shrimati Annapurna Devi after also honing his vocal music skills.
• Buddhadev Das Gupta
• ​Buddhadeb Dasgupta was the third of nine siblings and was born in a Vaidya family in 1944 in Anara, a town close to Puruliya in southern West Bengal.
  

Buddhadeb began his teaching career as an economics instructor at the University of Burdwan's Shyamsundar College before moving on to City College in Calcutta. He started making films in 1976 after becoming frustrated with the disconnect he saw between the socio-political reality and the economic theory he was teaching.

• Satyaki Banerjee
• ​Indian Bengali composer Satyaki Banerjee hails from India. He is a member of a London- and Kolkata-based Anglo-Bengali band. He performs using both classical and folk styles and plays instruments such as the sarod and dotara. He trained under Pandit Tejendra Narayan Majumdar after studying the sarod with the late Pandit Dipak Chowdhury.

The correct answer is Samir V Kamat.

Key Points

• On August 26, 2022, Dr Samir V. Kamat was named Chairman of the DRDO and Secretary of the Department of Defence R&D.
• Dr Kamat earned his PhD in Materials Science and Engineering from The Ohio State University, USA, in 1988 after completing his B. Tech. (Hons.) in Metallurgical Engineering at IIT-Kharagpur in 1985. He joined the DRDO in 1989.
• Dr Kamat has led and directed a number of crucial material programmes at DRDO, including the development of high-strength steels for naval ship hulls, high-temperature titanium alloys, and nickel base superalloy based components for aero-engines, the development of tungsten heavy alloys for kinetic energy penetrators, the development of fused silica radomes for missile seekers, and the development of armour solutions for personnel as well as combat vehicles and scout vehicles. These have been used in a number of the systems that the DRDO laboratories are creating.

Additional Information

• Defence Research and Development Organisation
• ​The Ministry of Defence of the Government of India's Department of Defence Research and Development, which has its main office in Delhi, India, and is responsible for the research and development of the military, is home to the Defence Research and Development Organisation (DRDO), the leading organisation in that department.
• It was created in 1958 by the union of the Defence Science Organisation and the Technical Development Establishment and Directorate of Technical Development and Production of the Indian Ordnance Factories.
• The Defense Research & Development Service (DRDS) was later established by the Ministry of Defence in 1979 as a service for Group "A" Officers and Scientists, directly under its administrative jurisdiction.

The correct answer is Mesoglea.

Key Points

• Mesoglea is a gelatinous substance that is undifferentiated and found in jellyfish and other coelenterates between the outer layer and inner cellular layer.
• Mesoderm creates the intermediate layer in the early trilaminar embryo germ layers. Triploblastic animals contain it.
• The epiblast cells begin converging at the midline and ingressing at the major streak during gastrulation in both birds and mammals.

Additional Information

• Coeliac
• ​Coeliac disease, sometimes known as celiac disease in American English, is a chronic autoimmune condition that mostly affects the small intestine and causes intolerance to the protein gluten, which is found in grains including wheat, rye, and barley.
• The basic symptoms of gastrointestinal problems include chronic diarrhoea, abdominal distention, malabsorption, appetite loss, and failure to grow normally in children.
• This frequently begins between the ages of six months and two years. Non-classical symptoms are more common, especially in people older than two years.
• Any part of the body could be affected by a wide range of symptoms, there can be none at all, or there might be barely perceptible gastrointestinal symptoms.

​Acoelomata

• ​An animal without a coelom, or formal bodily cavity, is said to be an acoelomate. Only multicellular organisms with real tissues can develop true body cavities. There are creatures like coral and jellyfish in this class, the eumetazoan, which have just two fundamental tissues. Three different tissue types exist in triploblastic eumetazoan.
• The simplest type of animal, an acoelomate has three genuine tissues. In that order from the inside to the outside, these tissues are the endoderm, mesoderm, and ectoderm. These tissues touch back-to-back with no room in between in an acoelomate. The mesoderm surrounds the organs as they develop inside of them. The digestive tract is formed by the endoderm, while the ectoderm makes up the skin.

The correct answer is Site.

Key Points

• Site
• The location where a structure or settlement grows is referred to as its site.
• A site is described as a location where something is built, or constructed, or as a location where a major or historical event took place.
• A site would be the property you purchase and plan to build your new home on.
• The physical qualities of the local terrain are included in the term "site," which refers to the actual location of a colony on Earth.
• Climate, landforms, water, vegetation, accessibility, soil quality, minerals, and animals are some of the site-specific characteristics.

Additional Information

• Settlements
• Humans who have established a stable community over an extended period of time in a particular location are considered to live in settlements.
• A modest fishing town on a river in a distant place can be considered a settlement, as opposed to a metropolis, which is a sophisticated population hub.
• Towns, villages, cities, hamlets, bases, and camps are some of the several names for settlements.
• Any planned pattern of human living can be categorized as a settlement.

The correct answer is Erosion.

Key Points

• Exogenic force
• ​Exogenic forces, often known as external forces, are those that originate in the earth's atmosphere or get their energy from the outside of the planet.
• While pressure that arises from within the earth is referred to as endogenic forces, also known as internal forces.
• Denudation, which meaning to strip off or uncover, is a broad term used to describe all exogenic processes.
• Geomorphic agents are the parts of nature that can carry out these exogenic processes (or exagenic geomorphic agents). the waves, water, wind, etc.

Additional Information

• ​The atmosphere, which is influenced by the sun's primary energy as well as the gradient that tectonic forces create, provides the exogenic forces with their energy.
• Slopes on the earth's surface are mostly produced by tectonic pressures or earth movements brought on by endogenic processes,

The correct answer is 4. 

Key Points

• ICC Men’s Cricket World Cup 
• 4 times times has India hosted the ICC Men’s Cricket World Cup (One Day)
• ​The One Day International (ODI) Cricket World Cup, also known as the ICC Men's Cricket World Cup, is the sport's global championship.
• Every four years, the International Cricket Council (ICC), the sport's governing body, hosts the competition, which consists of preliminary qualification stages and a finals tournament.
• The competition is one of the most watched athletic events in the world, according to the ICC, who also refer to it as the "flagship event of the international cricket calendar."

Additional Information

• The first ODI cricket match had been played just four years prior, in June 1975, when England hosted the first World Cup.
• The first men's event was preceded by a Women's Cricket World Cup, while a competition with multiple international teams was held as early as 1912 when Australia, England, and South Africa competed in a triangular tournament of Test matches.

Note -

• The 1987 World Cup was jointly hosted by India and Pakistan, with matches played across both countries.
• India co-hosted the 1996 World Cup with Pakistan and Sri Lanka, and the tournament was played across 22 venues in the three countries.
• In 2011 India,Sri Lanka, and Bangladesh Host the ICC Men's Cricket World Cup.
• The most recent World Cup held in India was in 2023.

The correct answer is Mumbai.

Key Points

• IPL 2022
• ​A men's T20 franchise cricket league in India is known as the Indian Premier League (IPL).
• Ten teams from seven cities and three states compete in it every year.
• The Board of Control for Cricket in India (BCCI) established the league in 2007. IPL's current chairman is Arun Dhumal.
• It typically takes place in India's warm months of March through May and has a special window in the ICC Future Tours Programme.

Additional Information

• The IPL is the cricket league with the highest attendance worldwide.
• It placed sixth in terms of average attendance across all sports leagues in 2014.
• In 2010, the IPL became the first sporting event ever to feature a live YouTube broadcast.
• The IPL's brand value in 2022 was 90,038 crore ($11 billion).

The correct answer is 2 million hectares.

Key Points

• HYVP
• In India initially HYVP was implemented in 2 million hectares
• ​The High Yielding Variety Programme (HYVP), which had as its goal the achievement of food self-sufficiency by 1970–1971, was introduced in the Kharif of 1966–1967.
• The program's main goal was to boost food grain productivity by using the most recent agricultural input kinds. introduction of new, higher yielding seed varieties, improved fertiliser treatment, and prolonged pesticide use.
• The Reserve Bank of India provided financing to the Farmers via a loose system via the Central Cooperative Banks.

Additional Information

• This initiative from the fourth five-year plan was a significant advancement and turning point in India's history of agricultural development.
• The programme was successful in the areas of the nation that produce wheat, and some success was also shown in the production of rice and other crops.

The correct answer is Water Vapour.

Key Points

• Greenhouse gasses
• A greenhouse gas, often known as a greenhouse gas (GHG or GhG), is a gas that creates the greenhouse effect by absorbing and radiating heat infrared light.
• Water vapour (H2O), carbon dioxide (CO2), methane (CH4), nitrous oxide (N2O), and ozone are the planet's main greenhouse gases (O3).
• Without greenhouse gases, the average surface temperature of the Earth would be closer to -18 °C (0 °F) than it is today, which is 15 °C (59 °F).
• Greenhouse gases are found in the atmospheres of Venus, Mars, and Titan.

Additional Information

• Water Vapour 
• Water vapour, or aqueous vapour are all terms for the gaseous state of water.
• It is a particular kind of water condition inside the hydrosphere.
• Water vapour can be created by the boiling or evaporation of liquid water as well as by the sublimation of ice.
• Water vapour is continuously produced by evaporation and eliminated by condensation in a normal atmosphere.
• It causes convection currents that can result in clouds since it is less dense than the majority of the other air constituents.

Important Points

• Carbon dioxide
• The most significant contributor to the warming effect, accounting for 64% of the total.
• Carbon dioxide is long-lived in the atmosphere, with 40% remaining after 100 years, 20% after 1,000 years, and 10% after 10,000 years.
• Methane
• The second-largest contributor, accounting for 19% of the total.
• Methane is more potent than carbon dioxide, with a global warming impact that's almost 30 times greater over 100 years.
• Chlorofluorocarbons (CFCs)
• The third-largest contributor, accounting for 8.1% of the total.
• CFCs were widely used in the mid-1900s, but they are still long-lived in the atmosphere.
• Nitrous oxide
• A powerful greenhouse gas with a GWP that's around 270 times that of carbon dioxide.
• It remains in the atmosphere for a little more than a century.
• Other greenhouse gases include:
• Fluorinated gases
• Hydrochlorofluorocarbons (HCFCs)
• Hydrofluorocarbons (HFCs)
• Perfluorocarbons (PFCs)
• Sulfur hexafluoride (SF6)
• Nitroge n triflouride (NF3)

The correct answer is Prithviraja III .

Key Points

• Prithviraja III
• Prithviraja III was the best-known Chahamana ruler.
• From 1177 to 1192 CE, Prithviraja III, sometimes referred to as Prithviraj Chauhan or Rai Pithora, ruled Sapadalaksha.
• He belonged to the Chauhan (Chahamana) dynasty, and his capital was Ajmer in modern-day Rajasthan. In 1177 CE, when Prithviraj ascended the throne as a boy, he inherited a kingdom that ran from Thanesar in the north to Jahazpur (Mewar) in the south.
• He sought to enlarge this realm by engaging in military operations against nearby countries, most notably by defeating the Chandelas.

Additional Information

• In 1191 AD, Prithviraj oversaw a coalition of Rajput princes that routed Muhammad Ghori's Ghurid army near Taraori.
• However, Ghori reappeared with a force of mounted Turkish archers in 1192 CE and overcame the Rajput army there. However, Prithviraj was killed in the battlefield and lost the war.
• In numerous semi-legendary texts, most notably the Prithviraj Raso, his defeat at Tarain is described as a turning point in the Islamic conquest of India.

The correct answer is 1949.

Key Points

• Indian Parliamentary
• The Indian Parliamentary Group established in 1949.
• The Parliament is the supreme legislative body of the Indian Republic  Bhratya Sansad.
• The two houses that make up India's bicameral legislature are the Lok Sabha and the Rajya Sabha (Council of States) (House of the People).
• In his capacity as head of the legislature, the president has full authority to prorogue either house of Parliament or dissolve the Lok Sabha.
• The president can only use these powers if they are recommended by the prime minister and his Union Council of Ministers.

Additional Information

• Members of Parliament are those chosen by voters or proposed by the president for a seat in either house (MPs).
• The members of the Rajya Sabha are chosen by the members of all state legislative assemblies via proportional representation, whereas the members of the Lok Sabha are chosen by the Indian population directly through voting in single-member districts.
• The authorised membership of the Parliament is 543 in the Lok Sabha and 245 in the Rajya Sabha, including 12 candidates with experience in a variety of literary, artistic, scientific, and social service disciplines.

The correct answer is 1972.

Key Points

• Family Planning Programme
• The government of India initiated the comprehensive family planning programme in the year 1972.
• ​In 1952, India became the first nation in the world to introduce a national programme for family planning.
• The programme has changed over the years in terms of policy and actual programme execution.
• It is currently being repositioned to meet goals for population stabilisation as well as reproductive health promotion and a decrease in maternal, newborn, and child mortality and morbidity.

Additional Information

• The National Population Policy of 2000, NHP, and other policy documents (NPP: Family Welfare Goals and Objectives) serve as the foundation for the goals, strategies, and initiatives developed and implemented by the Family Planning division.
• National Health Policy 2017, and NHM: National Rural Health Mission) (including ICPD: International Conference on Population and Development, MDG: Millennium Development Goals, SDG: Sustainable Development Goals, and others).

The correct answer is Santhal Revolt 

Key Points

• Santhal Revolt 
• Santhal Revolt was led by Kanhu and Sidhu.
• The Santhal revolt, often referred to as the Sonthal uprising or the Santhal Hool, was an uprising by the Santhal people in what are now Jharkhand and West Bengal, Eastern India, against the British East India Company (BEIC) and the zamindari system.
• The East India Company declared martial law on November 10, 1855, which lasted until January 3, 1856, when it was suspended and the revolt was finally put down by the Presidency soldiers.
• It began on June 30, 1855. The four brothers who made up the insurrection were Sidhu, Kanhu, Chand, and Bhairav.

Additional Information

• The British East India Company's (BEIC) revenue system, usury practises, and the zamindari system in India's tribal region, then known as the Bengal Presidency, were all put a stop to as a result of the Santhals' uprising.
• It was a revolt against the oppression of colonial rule, which was upheld by the police, the courts, and the local zamindars under the British East India Company's legal system. A distorted revenue structure served as the vehicle for this persecution.

The correct answer is Coelenterates.

Key Points

• Coelenterates.
• ​The name "Coelenterata" refers to the animal phylum Cnidaria.
• They have radial symmetry and a very basic tissue structure with just two cell layers (ectoderm and endoderm). Examples include hydrae, jellyfish, and sea anemones, which are solitary, as well as corals, which are frequently colonial.
• Coelenterata rely on diffusion across the tissue layers rather than a specific circulatory system.

Additional Information

• Coelenterates are all aquatic, primarily marine, creatures. The body morphology is diploblastic, radially symmetric, and lacks a coelom.
• The hypostome, the body's only aperture, is encircled by sensory tentacles that are either nematocyst- or colloblast-equipped to acquire primarily planktonic prey.
• The gastrovascular cavity, also known as the coelenteron, is a large cavity that encircles these tentacles. Digestion occurs both within and outside of cells. Simple diffusion is used to perform breathing and excretion. The body is covered in a network of nerves.

Given:

No. of lecturers in state A in 2017 = 10

No. of lecturers in state B in 2019 = 22

Formula used:

Percentage = $\frac{\text{Lecturer in state A}}{\text{Lecturer in state B}}\times 100$

Calculations:

According to the formula,

⇒ Percentage = $\frac{10}{22}\times100$ = 45.45%

⇒ Hence, No. of lecturers in state A in 2017 is 45.45% of state B in 2019

Given:

x = 1

x2 + y2 + z2 = xy + yz + zx

Calculations:

x² + y2 + z2 - xy - yz - zx = 0

⇒(1/2)[(x - y)² + (y - z)² + (z - x)²] = 0

⇒x = y , y = z and z = x

But x = y = z = 1

so, $\rm \frac{10x^4+5y^4+7z^4}{13x^2y^2+6y^2z^2+3z^2x^2}$

= {10(1)⁴ + 5(1)⁴ + 7(1)⁴}/{13(1)²(1)²+ 6(1)²(1)² + 3(1)²(1)²}

= 22/22

= 1

Hence, the required value is 1.

Given:

Mp = Rs. 90

Sp = Rs. 68

Formula used:

Discount % = $\frac{Discount}{Mp}\times 100$

Calculation:

⇒ Discount = Mp - Sp = 90 - 68 = Rs. 22

⇒ Discount % = $\frac{22}{90}\times 100$

⇒ Discount % = 24.44%

⇒ Hence, Discount % on cap is 24.44%

10 cm

∴ The correct answer is 10 cm.

• Alternate Method: Header Given: ΔABC ~ ΔQRP, ar(ΔABC) / ar(ΔQRP) = 9 / 4, AB = 18 cm, BC = 15 cm. Formula Used: ar(ΔABC) / ar(ΔQRP) = (BC / PR)² SVG Calculations: ⇒ 9 / 4 = (15 / PR)² ⇒ √(9 / 4) = 15 / PR ⇒ 3 / 2 = 15 / PR ⇒ 3 × PR = 30 ⇒ PR = 10 cm Final Answer Line.

• Wait, the prompt says "Always end with the FINAL ANSWER LINE RULE." for the Alternate Method too.

• One last check on the SVG colors: Circle fill: #ddeeff (not used here) Main shape fill: #ddeeff Main shape stroke: #2255cc Points: #cc0000 Labels: #cc5500 Dimension labels: #2255cc

• Wait, the prompt says "Regular points A,B,C etc : fill="#cc0000" r="5"".

• "Point labels (A,B,C etc) : font-size="14" font-weight="bold" fill="#cc5500"".

• "Dimension labels : font-size="12" fill="#2255cc"".

• Okay, I'm ready.

• Wait, the prompt says "Use × instead of * for multiplication everywhere."

• I'll use ×.

• Wait, the prompt says "Never use " anywhere in the output."

• I'll use single quotes ' for all HTML attributes.

• Wait, the style example shows double quotes: src="//cdn.testbook.com/...".

• If I use double quotes, I must not use the entity ".

• The rule "Never use " anywhere in the output" usually means "don't use the literal string "". It doesn't mean "don't use double quotes".

• However, to be safe, I'll use single quotes for attributes.

• Wait, the prompt says "Use ⇒ for ⇒ | ∴ for ∴ | → for → | × for ×".

• I'll use these.

• Final check on the "Additional Information" section: "Identify 2 to 4 closely related concepts..." I'll use 3 concepts.

• Final check on the "Shortcut Trick" section: "No algebra. No step-by-step derivation." I'll remove the ⇒ and keep it simple.

• Shortcut Trick:

Shortcut Trick

Ratio of corresponding sides = √(Ratio of areas)

Side Ratio = √(9 ÷ 4) = 3 : 2

Since ΔABC ~ ΔQRP, side BC corresponds to PR.

3 units (BC) = 15 cm → 1 unit = 5 cm

2 units (PR) = 2 × 5 = 10 cm

∴ The correct answer is 10 cm.

• Alternate Method: Header Given: ΔABC ~ ΔQRP, ar(ΔABC) / ar(ΔQRP) = 9 / 4, AB = 18 cm, BC = 15 cm. Formula Used: ar(ΔABC) / ar(ΔQRP) = (BC / PR)² SVG Calculations: ⇒ 9 / 4 = (15 / PR)² ⇒ √(9 / 4) = 15 / PR ⇒ 3 / 2 = 15 / PR ⇒ 3 × PR = 30 ⇒ PR = 10 cm Final Answer Line.

• Wait, the prompt says "Always end with the FINAL ANSWER LINE RULE." for the Alternate Method too.

• One last check on the SVG colors: Circle fill: #ddeeff (not used here) Main shape fill: #ddeeff Main shape stroke: #2255cc Points: #cc0000 Labels: #cc5500 Dimension labels: #2255cc

• Wait, the prompt says "Regular points A,B,C etc

Given:

x + $\frac{1}{2x}$ = 3

Concept Used:

Simple calculations is used

Calculations:

⇒ x + $\frac{1}{2x}$ = 3

On multiplying 2 on both sides, we get

⇒ 2x + $\frac{1}{x}$ = 6  .................(1)

Now, On cubing both sides,

⇒ $(2x + \frac{1}{x})^3 = 6^3$

⇒ $8x^3 + \frac{1}{x^3} + 3(4x^2)(\frac{1}{x})+3(2x)(\frac{1}{x^2})=216$

⇒ $8x^3 + \frac{1}{x^3} + 12x+\frac{6}{x}=216$

⇒ $8x^3 + \frac{1}{x^3}= 216 - 6(2x+\frac{1}{x})$

⇒ $8x^3 + \frac{1}{x^3}= 216- 6(6)$  ..............from (1)

⇒ $8x^3 + \frac{1}{x^3}= 216- 36$

⇒ $8x^3 + \frac{1}{x^3}= 180$

⇒ Hence, The value of the above equation is 180

Given:

$\rm \sqrt{\frac{1+sinA}{1-sinA}}$

Concept Used:

The concept of conjugation is used here

Calculation:

⇒ $\rm \sqrt{\frac{1+sinA}{1-sinA}}$

Now, Conjugate the above equations

⇒ $\rm {\sqrt{\frac{1+sinA}{1-sinA} \times \rm {\frac{1+sinA}{1+sinA}}}}$

⇒ $\rm \sqrt{\frac{(1+sinA)^2}{1-sin^2A}}$

⇒ $\rm \sqrt{\frac{(1+sinA)^2}{cos^2A}}$

⇒ $\rm {\frac{(1+sinA)}{cosA}}$

⇒ $\frac{1}{ cos A} +\frac{sin A}{ cosA}$

⇒ sec A + tan A 

⇒ Hence, Value of the given part is sec A + tan A

Shortcut Trick

Since the buses move at right angles, the distance between them is the hypotenuse of a right-angled triangle.

Resultant Speed = √(48² + 36²) = √(2304 + 1296) = √3600 = 60 km/h.

Convert speed to m/s: 60 × (5/18) = 50/3 m/s.

Distance after 15 seconds = Speed × Time = (50/3) × 15 = 50 × 5 = 250 m.

∴ The correct answer is 250 m.

Alternate Method

Given:

Speed of Bus 1 (S₁) = 48 km/h

Speed of Bus 2 (S₂) = 36 km/h

Time (t) = 15 seconds

Formula Used:

Distance = Speed × Time

Conversion: 1 km/h = 5/18 m/s

Hypotenuse (H) = √(Base² + Perpendicular²)

Calculations:

⇒ Speed of Bus 1 in m/s = 48 × (5/18) = 40/3 m/s

⇒ Distance covered by Bus 1 (D₁) = (40/3) × 15 = 200 m

⇒ Speed of Bus 2 in m/s = 36 × (5/18) = 10 m/s

⇒ Distance covered by Bus 2 (D₂) = 10 × 15 = 150 m

⇒ Distance between buses = √(D₁² + D₂²)

⇒ Distance = √(200² + 150²)

⇒ Distance = √(40000 + 22500) = √62500

⇒ Distance = 250 m

∴ The correct answer is 250 m.

Additional Information

Pythagorean Triplets

Sets of three integers like (3, 4, 5) satisfy a² + b² = c². Scaling them (30, 40, 50) or (150, 200, 250) helps solve geometry problems instantly.

Unit Conversion

To convert km/h to m/s, multiply by 5/18. To convert m/s to km/h, multiply by 18/5.

Perpendicular Motion

When two objects move perpendicularly, their relative distance is calculated using the Pythagoras theorem based on the linear distance covered by each.

Given:

Table :

Calculations:

Total earning of P = 105 + 96 + 65 + 115 + 130 = 511

Total earning of Q = 150 + 110 + 122 + 106 + 68 = 556

Ratio of P's earning to Q's earning = 511 : 556 

Hence, The Required value is 511 : 556.

Given:

Calculations:

Cost of production by company A= 90 

Cost of production by company E = 36

Total cost of production by A and E together = 90 + 36 = 126

So, Total cost required=  126 × 5,000 × 8,00,000/360 = 1,400,000,000 or 140 crores

Hence, The Required value is 140 crores.

Given:

∆ABC ~ ∆DEF, and BC = 4 cm, EF = 5 cm and the area of triangle ABC = 80 cm².

Concept used:

In two similar triangles, 

Ratio of their area is equal to ratio of the squares of their corresponding sides.

Calculations:

According to the question,

Area of ∆ABC : Area of ∆DEF = BC² : EF²

⇒80 : Area of ∆DEF = 4² : 5²

⇒Area of ∆DEF = 25 × 80/16

⇒Area of ∆DEF = 125

Hence, The Required value is 125 cm².

Given:

Amount after 2 years = Rs 3,640

Amount after 8 years = Rs. 4,060

Calculations:

Simple interest of 6 years

= Amount after 8 years - Amount after 2 years 

= Rs.(4060 - 3640)

= Rs.420

= Interest in 1 year = 420/6 = 70

Principal

= Amount after 2 years - interest in 2 years

= 3640 - 140

= Rs.3500

Interest of 1 year = 420/6 = Rs.70

Rate = 70 × 100/3500 = 2%

Hence, The Required value is 2%.

Shortcut Trick

Given: 8 cot θ = 6 ⇒ cot θ = 6/8 = 3/4.

Divide numerator and denominator of the expression by sin θ.

Expression = (1 + cot θ) / (1 − cot θ)

Expression = (1 + 3/4) / (1 − 3/4) = (7/4) / (1/4) = 7.

∴ The correct answer is 7.

Alternate Method

Given: 8 cot θ = 6

Formula Used: cot θ = Base / Perpendicular; sin θ = Perpendicular / Hypotenuse; cos θ = Base / Hypotenuse.

⇒ 8 cot θ = 6 ⇒ cot θ = 6/8 = 3/4

⇒ Let Base (B) = 3 and Perpendicular (P) = 4

⇒ Hypotenuse (H) = √(P² + B²) = √(4² + 3²) = √25 = 5

⇒ sin θ = P/H = 4/5 and cos θ = B/H = 3/5

⇒ Expression = (sin θ + cos θ) / (sin θ − cos θ)

⇒ Expression = (4/5 + 3/5) / (4/5 − 3/5)

⇒ Expression = (7/5) / (1/5) = 7

∴ The correct answer is 7.

Additional Information

Quotient Identities

The ratio of trigonometric functions are given as tan θ = sin θ / cos θ and cot θ = cos θ / sin θ.

Pythagorean Identity

The fundamental relation between sine and cosine is sin² θ + cos² θ = 1.

Pythagorean Triplets

Sets of three positive integers (a, b, c) such that a² + b² = c², commonly used are (3, 4, 5), (5, 12, 13), and (8, 15, 17).

Given:

The following chart shows the scores of employees is a company's annual performance.

Calculations:

Kartik's marks = 80

Total marks = 80 + 90 + 75 + 70 + 85 = 400

Percentage required

= 80 × 100/400

= 20%

Hence, The Required value 20%.

Given:

Diagonal of cube = 6√3 cm

Calculations:

Diagonal of cube = √3 × side 

⇒ 6√3 = side √3

Hence, side = 6

So, length of cuboid = 3 × 6 = 18 

Breadth = 6 and height= 6

So, the surface area of the cuboid

= 2(lb + bh + lh)

= 2(108 + 36 + 108)

= 2 × 252 cm²

= 504 cm²

Hence, The Required value is 504 cm².

Given:

 tan A = $\rm \frac {5}{12}$

Calculations:

tan A = 5/12 

Then, sec A

= √(1 + tan²A)

= √(1 + 25/144)

= √(169/144)

= 13/12

So, cos A = 12/13

Hence, The Required value is 12/13.

Given:

LCM = 4104 , HCF = 9, one of the number = 171

Concept used:

LCM × HCF = Product of the numbers

Calculations:

LCM × HCF = Product of the numbers

⇒ 4104 × 9 = 171 × other number

⇒ other number = 4104 × 9/171 = 216

Hence, The Required value is 216.

Given:

x2 − 2xy = 84

x = y - 10

Calculations:

According to question,

x2 − 2xy = 84 ------------(1)

And x = y - 10

now, put x = y - 10 in eq(1)

(y - 10)² - 2y(y - 10) = 84

⇒y² - 20y + 100 - 2y² + 20y = 84

⇒- y² = 84 - 100

⇒ y² = 16 

⇒ y = 4

Hence, The Required value is 4.

Calculations:

The capacity of the tank

= LCM(10, 20 and 25) = 100

Efficiency of A = 100/10 = 10

Efficiency of B = 100/20 = 5

Efficiency of C = 100/25 = 4

Tank filled in 2 hours by A, B, and C

= (10 + 5 + 4) × 2 = 38 unit

According to the question, 

After 4 hours from the beginning, tap B is also closed

Tank filled in 2 hours by A & B

= (10 + 5) × 2 = 30 unit

Now, tap B is also closed

Remiang capacity of tank = 100 - 38 - 30 = 32 unit

These 32 unit is filled by A alone.

So, the total work done by A 

= Work done in (1st 2 hr + next 2 hr + 32 unit)

= 10 × 2 + 10 × 2 + 32 = 72 unit

Percentage of a tank filled by A = (72/100) × 100 = 72%.

Hence, The Required value is 72%.

Mistake PointsNote that, B closed after 4 hr form the beginning, not after closing the C.

Given:

Prasad goes 96 kilometres on a bike at a speed of 16 km/h, 124 kilometres at 31 km/h in a car, and 105 kilometres at 7 km/h in a horse cart.

Calculations:

Total distance 

= 96 + 124 + 105

= 325 km

Total time 

= 96/16 + 124/31 + 105/7

= 6 + 4 + 15

= 25

Average speed

= total distance/total time taken

= 325/25

= 13 km/h

Hence, The Required value is 13 Km/h.

Given:

CP of 100 apples = Rs 350

SP of 1 dozen apples = Rs 48

Concept Used:

Gain Percentage = $\frac{Gain}{CP}\times 100$

Calculation:

⇒ SP of 12 apples = Rs 48

⇒ So, SP of 1 apple = $\frac{48}{12}$ = Rs 4

⇒ SP of 100 apples = Rs 400

As can be seen, SP > CP.

⇒ Gain = 400 – 350 = Rs 50

⇒ Profit Percentage = $\frac{50}{350}\times 100$ = $\frac{100}{7}=14\frac{2}{7}\%$

Therefore, the profit percentage is 14$\frac{2}{7}$%.

Given:

In a ∆ABC, AB = BC, and P, Q and R are the mid points of the sides AB, BC and AC, respectively.

PR = 5 cm

Calculations:

According to the question,

PR = 5 cm 

Then 

BC = 2 × PR = 10 cm

[The line segment in a triangle joining the midpoint of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.]

In ∆ABC, If AB = BC,

Then,

AB = 10 cm

So

the From mid-point theorem,

QR = AB/2 = 10/2 = 5 cm

Hence, The Required value is 5 cm.

Given:

Ratio of two numbers = 5 : 7

When 6 is added to each, new ratio = 3 : 4

Calculation:

Let the numbers be 5x and 7x.

According to the question,

⇒ $\frac{5x+6}{7x+6}=\frac{3}{4}$

⇒ 4(5x + 6) = 3(7x + 6)

⇒ 20x + 24 = 21x + 18

⇒ 21x – 20x = 24 – 18

⇒ x = 6

First number = 5x = 5 × 6 = 30

Second number = 7x = 7 × 6 = 42

Therefore, the two numbers are 30 and 42.

Given:

First year increase rate = 12%

Second year decrease rate = 8%

Calculations:

Let the initial population be x.

Then, According to question,

92% of 112% of x = 64,400

⇒ 0.92 × 1.12x = 64,400

⇒ x = 64,400/(0.92×1.12)

⇒ x = 64,400/1.0304

⇒ x = 62,500

Hence, The Required value is 62,500.

Given:

9-digit number = 83P93678Q

Divisor = 72

Concept Used:

Divisibility of 8 = Last three digits should be divisible by 8.

Divisibility of 9 = Sum of digits is divisible by 9.

Calculation:

As the divisor 72, is divisible by 8 and 9, so the divisibility will be checked.

For divisible by 8,

78Q should be divisible by 8, so, Q should be 4 as 784 is divisible by 8.

For divisible by 9,

⇒ 8 + 3 + P + 9 + 3 + 6 + 7 + 8 + 4 = 48 + P

For being divisible by 9, the nearest number to be added is 6 which gives 54.

Now, $\sqrt{P^2+Q^2+12}=\sqrt{6^2+4^2+12}$

⇒ $\sqrt{36+16+12}=\sqrt{64}=8$

Therefore, the required value is 8.

Given:

Three circles of radius 4 cm are kept touching each other.

Calculation:

The length of the string not in contact with the circle = 2r + 2r + 2r

⇒ 6r = 6 × 4

⇒ 24

As we can say the angle covered by the string is 120º

Or we can say it covered 1/3 part of the circle

Length of string touching circle = 2πr/3 + 2πr/3 + 2πr/3

⇒ 2πr = 2 × 4 × π

⇒ 8π

Total length = 24 + 8π

∴ The required answer is 24 + 8p cm. (here pi means π)

The correct answer is "A scholarship was conferred to Kailash by the department".

Key Points

• As we can see the given sentence is in the active voice format of the simple past tense as the past participle (conferred) is applied in the sentence, so we have to change the active voice as per the same tense rules.
• Active voice: Subject + V2 + object
• Passive voice: Object + was/were + V3 + by + subject
• Example:
• Active voice: Maya cleaned the dishes.
• Passive voice: The dishes were cleaned by Maya.
• By following the above-mentioned rules, we have to change the active to passive by applying the third form of the verb (conferred) and past helping verb (was) in the sentence.
• Therefore, the correct answer is: A scholarship was conferred to Kailash by the department.

Additional Information

Let us take a look at the rules of simple past active passive voice:

• Active voice: Subject + V2 + object
• Passive voice: Object + was/were + V3 + by + subject
• Active voice: Subject + did + not + v1 + object
• Passive voice: Object + was/were + not + V3 + by Subject
• Active voice: Did + subject + V1 + object +?
• Passive voice: Was/were + Object + V3 + by subject +?

The correct answer is "Madhurima explained that she was planning to quit her graduation".

Key Points

• As we can see, the direct speech is in the present continuous tense form (am planning), we have to change the indirect speech according to the same tense rules.
• Direct speech: Subject + is/am/are + V1 + ing + Object
• Indirect speech: Subject + was/were + V1 + ing+ Object
• Example: Direct speech: Bhumika Said, “I am washing the fruits.”
• Indirect speech: Bhumika said that she was washing the fruits.
• Furthermore, "inverted commas" will be replaced with "that" and "I and my" will be substituted with "she and her".
• Consequently, the same rule would be applied in the given sentence.
  

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Therefore, the correct answer is: Madhurima explained that she was planning to quit her graduation.

Additional Information

• Indirect communication is referred to as reporting the words, but direct speech is regarded as reciting the exact same words said.
• Modals, reporting verbs, place, time, tense, pronouns, and other elements all affect how direct and indirect speech is changed.
• Depending on the subject of the reporting speech, the first-person pronoun shifts.
• Eliminate the comma and the inverted commas, between the reporting and the reported speech, insert "that."
• Example:
• Arun Said, “They will be cleaning the car.”
• Arun said that they would be cleaning the car.

The correct answer is "Dimolish".

Key Points

• The given words, 'conduct, biopic and handful' are correctly spelt, holding appropriate meaning except 'dimolish'.
• The incorrectly spelt word when corrected, results in the formation of "demolish".
• Let us take a look at the meaning of correctly spelt word:
• Demolish: pull or knock down (a building).
• Example: The house was demolished to make way for the shopping center.
• Example: I looked forward keenly to demolishing my opponent.
• Therefore, the only incorrect spelt word is 'dimolish'.

Additional Information

• Let us take a look at the meaning of correctly spelt words: