SSC CGL 2023 Tier-I Official Paper (Held On: 18 Jul 2023 Shift 2) (Previous Year Paper)

Given:

Weight : Pounds → Pounds is a measurement unit of weight.

Similarly,

Height : Metres → Metres is a measurement unit of height.

Here, 'Height : Metres' is the correct pair.

Hence, the correct answer is "Option (2)".

Here, we use the BODMAS table given below:

Given:

⇒ 55 * 63 * 9 * 8 * 3 = 38

(1) ÷, ×, -, +

⇒ 55 * 63 * 9 * 8 * 3 = 38

After putting the signs:

⇒ 55 ÷ 63 × 9 - 8 + 3 = 38

Apply BODMAS rule:

⇒ 0.873 × 9 - 8 + 3

⇒ 7.857 - 8 + 3

⇒ 10.857 - 8 = 2.857

Here, the equation is not satisfied.

(2) ×, ÷, +, -

⇒ 55 * 63 * 9 * 8 * 3 = 38

After putting the signs:

⇒ 55 × 63 ÷ 9 + 8 - 3 = 38

Apply BODMAS rule:

⇒ 55 × 7 + 8 - 3

⇒ 385 + 8 - 3

⇒ 393 - 3 = 390

Here, the equation is not satisfied.

(3) +, -, ×, ÷

⇒ 55 * 63 * 9 * 8 * 3 = 38

After putting the signs:

⇒ 55 + 63 - 9 × 8 ÷ 3 = 38

Apply BODMAS rule:

⇒ 55 + 63 - 9 × 2.66

⇒ 55 + 63 - 23.94

⇒ 118 - 23.94 = 94.06

Here, the equation is not satisfied.

(4) +, ÷, -, ×

⇒ 55 * 63 * 9 * 8 * 3 = 38

After putting the signs:

⇒ 55 + 63 ÷ 9 - 8 × 3 = 38

Apply BODMAS rule:

⇒ 55 + 7 - 8 × 3

⇒ 55 + 7 - 24

⇒ 62 - 24 = 38

⇒ '55 + 63 ÷ 9 - 8 × 3 = 38'

Here, the equation is satisfied.

Hence, the correct answer is "Option (4)".

Logic: First no. = [(Second no. - 1) ÷ 2]²

Checking all the given options:

(1) 81 : 19 →

⇒ [(19 - 1) ÷ 2]²

⇒ ( 18 ÷ 2)²

⇒ (9)² = 81

(2) 121 : 23 →

⇒ [(23 - 1) ÷ 2]2

⇒ ( 22 ÷ 2)2

⇒ (11)2 = 121

(3) 1 : 3 →

⇒ [(3 - 1) ÷ 2]2

⇒ ( 2 ÷ 2)2

⇒ (1)2 = 1

(4) 64 : 9 →

⇒ [(9 - 1) ÷ 2]²

⇒ (8 ÷ 2)2 

⇒ (4)² = 16

Here, in '64 : 9' logic is not followed.

Hence, the correct answer is "Option (4)".

Preparing the family tree diagram by using the following symbol:

As per the given information:

1. F is C’s son and C is the only daughter of B.

2. B is C’s father and A is B's wife.

3. D is A’s only son-in-law.

Here, D is the father of F.

Hence, the correct answer is "Option (2)".

The mirror image of the given figure is:

Hence, the correct answer is "Option (1)".

Statements:

All fruits are wines.

Some wines are juices.

All juices are alcohols.

The Venn diagram as per the given statements:

Conclusions:

I. Some alcohols are juices. → Follow (All juices are alcohols, which means some alcohols are juices is definitely true)

Il. Some wines are alcohols. → Follow (Some wines are juices, and All juices are alcohols, which means some wines are alcohols is definitely true)

III. Some wines are fruits. → Follow  (All fruits are wines, which means some wines are fruits is definitely true)

Hence, the correct answer is "All conclusions follow".

Given:

(5, 19, 4)

(1, 7, 4)

(6, ?, 1)

Logic: 'Row wise'

First row → Second no. = [(First no.) × 3 + Third no.]

First row (5, 19, 4) →

⇒ [(5 × 3) + 4]

⇒ (15 + 4) = 19

Second row (1, 7, 4) →

⇒ [(1 × 3) + 4]

⇒ (3 + 4) = 7

Similarly, for the third row (6, ?, 1):

⇒ [(6 × 3) + 1]

⇒ (18 + 1) = 19

Here, the question mark is replaced by '19'.

Hence, the correct answer is "Option (3)".

The logic followed in the given figure series is:

From Figure (1) to (2):

One triangle increases.

From Figure (2) to (3):

One triangle increases.

From Figure (3) to (4):

One triangle increases.

From Figure (4) to Answer Figure (5):

One triangle increases.

Hence, the correct answer is "Option (2)".

The correct order of words as they would appear in the English dictionary is:

6. Banter
7. Believe
8. Bereave
9. Blight
10. Brave 2. Breathe

The correct order is '6, 1, 3, 4, 5, 2'.

Hence, the correct answer is "Option (1)".

Given:

King : Palace → The king lived in the palace.

Similarly,

Nun : Convent → The nun lives in the convent.

Here, 'Nun : Convent' is the correct pair.

Hence, the correct answer is "Option (2)".

Given:

(7, 5, 10)

(2, 1, 5)

(16, 6, ?)

Logic: 'Row wise'

First row → Third no. = [(First no. - Second no.) × 5]

First row (7, 5, 10) →

⇒ [(7 - 5) × 5]

⇒ (2 × 5) = 10

Second row (2, 1, 5) →

⇒ [(2 - 1) × 5]

⇒ (1 × 5) = 5

Similarly, for the third row (16, 6, ?) →

⇒ [(16 - 6) × 5]

⇒ (10 × 5) = 50

Here, the question mark is replaced by '50'.

Hence, the correct answer is "Option (2)".

Here, we use the BODMAS table given below:

Given:

⇒ 3 - 21 + 153 × 17 ÷ 26

As per the given data:

After changing the sign as per the table:

⇒ 3 × 21 - 153 ÷ 17 + 26

Apply BODMAS rule:

⇒ 3 × 21 - 9 + 26

⇒ 63 - 9 + 26

⇒ 89 - 9 = 80

Here, the value of the expression is '80'.

Hence, the correct answer is "Option (2)".

The logic followed in the given figure series is:

From Figure (1) to (2):

The symbols move as shown below.

From Figure (2) to (3):

The symbols move as shown below.

.

From Figure (3) to (4):

The symbols move as shown below.

From Figure (4) to Answer Figure (5):

The symbols move as shown below.

Hence, the correct answer is "Option (2)".

Given:

49, 54, 44, 59, ?, 64, 34 

The logic followed in the given series is:

Logic: 'Doble series'

Here, '39' is the missing term.

Hence, the correct answer is "Option (3)".

Given:

DY_GMI_ _YTG_ILDYT_MILD_TGM_L

Checking all the given options:

1. TLDGMIY

DYTGMIL / DYTGGIL / DYTMMIL / DITGMYL

2. TDLGMYI

DYTGMID / LYTGGIL / DYTMMIL / DYTGMIL

3. TLDMGYI

DYTGMIL / DYTGMIL / DYTGMIL / DYTGMIL

Here, the series is completed.

4. TLDYMIG

DYTGMIL / DYTGYIL / DYTMMIL / DITGMGL

Hence, the correct answer is "Option (3)".

The correct order of words as they would appear in the English dictionary is:

1. Decline
2. Decode
3. Decorate
4. Decorum 2. Decouple
5. Decrease

Here, the correct order is '1, 6, 4, 5, 2, 3'.

Hence, the correct answer is "Option (1)".

The mirror image of the given figure is:

Hence, the correct answer is "Option (1)".

Here, we use the table given below:

Logic: Addition of 4, 3 and 1 in the positional value of the first, second and third letter.

1. HLOP →

2. FHJL →

3. AEHI →

4. QUXY →

Here, in 'FHJL' different logic is followed.

Hence, the correct answer is "Option (2)".

Given:

(8, 388, 18)

(11, 137, 4)

Logic: Second no. = [(First no.)² +(Third no.)²]

(8, 388, 18) →

⇒ [(8)² + (18)²]

⇒ (64 + 324) = 388

(11, 137, 4) →

⇒ [(11)2 + (4)2]

⇒ (121 + 16) = 137

Checking all the given options:

1. (15, 230, 2) →

⇒ [(15)2 + (2)2]

⇒ (225 + 4) = 229

2. (3, 51, 7) →

⇒ [(3)2 + (7)2]

⇒ (9 + 49) = 58

3. (10, 118, 9) →

⇒ [(10)2 + (9)2]

⇒ (100 + 81) = 181

4. (14, 221, 5) →

⇒ [(14)2 + (5)2]

⇒ (196 + 25) = 221

Here, (14, 221, 5) shows a similar relation to the given set of numbers.

Hence, the correct answer is "Option (4)".

The mirror image of the given figure is:

Hence, the correct answer is "Option (1)".

Here, we use the table given below:

Logic: [(Addition of positional values of all alphabet) × Number of alphabet]

'ROSE' is coded as ‘228’ →

'TULIP'is coded as ‘390' →

Similarly, 'LOTUS' will be coded as:

Here, 'LOTUS' is coded as '435'.

Hence, the correct answer is "Option (1)".

The embedded part of this image is:

Hence, the correct answer is "Option (2)".

Here, we use the table given below:

The logic followed in the given codes:

‘PLACE’ is written as ‘CONHA’ →

‘SHOCK’ is written as ‘QKQNA’ →

Similarly, 'FROWN' will be coded as:

Here, 'FROWN' is coded as 'QUDQU'.

Hence, the correct answer is "Option (1)".

Given:

(24, 3, 10)

(144, 9, 18)

Logic: First no. = [Second no. × (Third no. - 2)]

(24, 3, 10) →

⇒ [3 × (10 - 2)]

⇒ (3 × 8) = 24

(144, 9, 18) →

⇒ [9 × (18 - 2)]

⇒ (9 × 16) = 144

Checking all the given options:

1. (54, 9, 4) →

⇒ [9 × (4 - 2)]

⇒ (9 × 2) = 18

2. (156, 8, 19) →

⇒ [8 × (19 - 2)]

⇒ (8 × 17) = 136

3. (72, 8, 9) →

⇒ [8 × (9 - 2)]

⇒ (8 × 7) = 56

4. (133, 7, 21) →

⇒ [7 × (21 - 2)]

⇒ (7 × 19) = 133

Here, (133, 7, 21) shows a similar relation to the given set of numbers.

Hence, the correct answer is "Option (4)".

Here, we use the table given below:

The logic followed in the given pairs:

FUELED : DXBOAG →

GELATO : EHIDPR →

Similarly, for 'HEARTY : ?' →

Here, 'HEARTY : FHXUPB' is the correct pair.

Hence, the correct answer is "Option (3)".

The correct answer is Overcoming social exclusion through Bharatanatyam dance performances 

Key Points

• Padma Shri Awards:-
• Padma Shri is the fourth highest civilian award in the Republic of India, after the Bharat Ratna, the Padma Vibhushan, and the Padma Bhushan. It is awarded by the President of India to recognize exceptional service or achievements in various fields.
• The award is given across various categories including art, social work, public affairs, science and engineering, trade and industry, medicine, literature, education, sports, and more.
• The Padma Shri was established in 1954 by the government of India. It was originally a part of the Bharat Ratna awards but was separated into a distinct award later.
• The award is given annually on the occasion of India's Republic Day. It honors individuals from diverse backgrounds who have made significant contributions to society.
• Nominations are made by the public as well as government bodies and organizations. The recommendations go through a rigorous screening process before being finalized.
• The Padma Shri is often seen as a recognition of notable achievements and contributions at the national level. It's a prestigious honor that brings attention to the recipient's work and accomplishments.
• Narthaki Nataraj:-
• ​Narthaki Nataraj is an accomplished Indian classical dancer known for her expertise in the art form of Bharatanatyam, which is a traditional dance style originating from the southern part of India.
• She holds the distinction of being one of the most prominent transgender women to have gained recognition in the field of classical dance.
• Narthaki Nataraj was born in 1964 in Madurai, Tamil Nadu, India.
• From a young age, she displayed a keen interest and talent in Bharatanatyam.
• She trained rigorously in this dance form, honing her skills and mastering the intricate techniques and expressions that are integral to Bharatanatyam.
• She was awarded the Padma Shri in 2019 for her significant contributions to the field of Indian classical dance, specifically for her exceptional skills and dedication to the art of Bharatanatyam.

Additional Information

• List of other awardees of Padma Shree in 2019:-
• Manoj Bajpayee: Actor
• Gautam Gambhir: Cricketer
• Sunil Chhetri: Footballer
• Kader Khan (Posthumous): Actor and Comedian
• Prabhu Deva: Choreographer and Actor
• Kailash Madbaiya: Social Worker
• Muktaben Pankajkumar Dagli: Social Worker
• Shadab Mohammad: Mathematician

The correct answer is Jital.

Key Points

• Muhammad bin Tughlaq:-
• Muhammad Bin Tughlaq was the son of Ghiyasuddin Tughlaq.
• His real name was Ulugh Khan or Fakhruddin Jauna.
• He ruled over Delhi sultanate from 1325 to 1351.
• Muhammad Bin Tughlaq introduced copper currency system in India.
• Ibn Battuta was a famous Moroccan Muslim scholar and traveller came to India during his reign.
• Muhammad Bin Tughlaq Transferred his capital from Delhi to Daulatabad in 1326 A.D.
• Muhammad bin Tughlaq introduced a copper coin called "Jital" in place of the silver coin.

The correct answer is between 17% and 25% 

Key Points

• Silica:-
• Silica is an oxide of silicon that is found in nature as the major constituent of sand in many parts of the world and as quartz and also in various living organisms.
• Sandy soils have the highest source of silica. (85.9%)
• Silica in free and combined forms is a dominant component of the solid material of many soils, and dissolved silica is commonly a major solute of soil solutions.
• The approximate amount of silica present In cement Is between 17% and 25%.
• Cement:-
• ​Cement is a binder material used in construction to bind or glue different materials together.
• It's typically a fine powder made from a mixture of limestone, clay, shale, and other minerals that are heated at high temperatures to form a substance called clinker.
• When mixed with water, cement reacts chemically to form a strong, solid material that

The following table gives the ingredients of cement

The correct answer is 51A.

Key Points

• Article 51A:-
• ​Article 51A deals with fundamental duties of citizens of India.
• These fundamental duties were added to the Constitution by the 42nd Amendment Act in 1976, and they provide a set of moral and civic obligations that citizens are expected to follow for the betterment of society and the nation as a whole.
• There are 11 fundamental duties listed in Article 51A:-
• To abide by the Constitution and respect its ideals and institutions, the National Flag, and the National Anthem.
• To cherish and follow the noble ideals that inspired the national struggle for freedom.
• To uphold and protect the sovereignty, unity, and integrity of India.
• To defend the country and render national service when called upon.
• To promote harmony and the spirit of common brotherhood among all people of India transcending religious, linguistic, and regional or sectional diversities.
• To value and preserve the rich heritage of our composite culture.
• To protect and improve the natural environment, including forests, lakes, rivers, and wildlife, and to have compassion for living creatures.
• To develop scientific temper, humanism, and the spirit of inquiry and reform.
• To safeguard public property and to abjure violence.
• To strive towards excellence in all spheres of individual and collective activity.
• To provide opportunities for education to their children or wards between the ages of six and fourteen years.

The correct answer is Monsoon with dry winter.

Key Points

• Köppen's scheme:-
• It is also known as the Köppen climate classification, is a widely used system for classifying and describing the world's climates based on temperature and precipitation patterns.
• It was developed by the Russian-German climatologist Wladimir Köppen in the early 20th century and has undergone several modifications since then.
• The Köppen climate classification system divides the Earth's climates into five main types, each designated by a specific letter code:
• Tropical (A): These climates are characterized by high temperatures year-round and abundant precipitation. They are typically found in equatorial regions and include tropical rainforests and savannas.
• Dry (B): Dry climates are characterized by low precipitation levels. They are further divided into three subtypes:
• BWh: Hot desert climates, with extremely high temperatures and very low rainfall.
• BWk: Cold desert climates, similar to hot deserts but with colder winters.
• BSh/BSk: Steppe climates, with moderate temperatures and low rainfall.
• Temperate (C): Temperate climates have distinct seasons and moderate precipitation. They are divided into three subtypes: Cfa/Cwa,  Cfb/Cwb, Csa/Csb:
• Continental (D): Continental climates have a wide temperature range and moderate precipitation. They are divided into two subtypes: Dfa/Dwa, Dfb/Dwb.
• Polar (E): Polar climates are characterized by extremely cold temperatures and very low precipitation. They are divided into two subtypes: ET, EF.
• Koeppen's climate classification scheme designates the "Cwg" code for a specific type of climate in India.
• In this classification system, "C" represents a temperate or mesothermal climate, "w" indicates a dry winter season, and "g" stands for a hot summer.
• Therefore, the "Cwg" climate in India is a temperate climate with a dry winter and a hot summer.
• This type of climate is found in certain regions of northern India, particularly in areas such as parts of Punjab, Haryana, and western Uttar Pradesh

The correct answer is Buddhism.

Key Points

• Hemis Festival:-
• The Hemis Festival is a traditional religious festival celebrated in Ladakh, a region in northern India.
• This festival has a significant influence from Tibetan Buddhism.
• It is dedicated to Lord Padmasambhava, also known as Guru Rinpoche, who is considered the founder of Tibetan Buddhism in Tibet.
• The Hemis Monastery, where the festival takes place, is one of the most important and largest monasteries in Ladakh and holds great significance in the Tibetan Buddhist tradition.
• The festival usually includes colorful masked dances, rituals, and other cultural performances that are deeply rooted in the Buddhist religious beliefs and practices.

Additional Information

• List of some important festivals in Jainism:-
• Mahavir Jayanti
• Paryushana Parva (Das Lakshana Parva)
• Diwali (Jain Diwali)
• Samvatsari or Kshamavani Parva
• Navapad Oli (Ayambil Oli)
• Gyan Panchami
• Mauni Ekadashi
• Akshaya Tritiya
• List of some important festivals in Islam:-
• Eid al-Fitr
• Eid al-Adha
• Mawlid al-Nabi
• Ashura
• Lailat al-Qadr
• Islamic New Year (Hijri New Year)
• List of some important festivals in Hinduism:-
• Diwali
• Holi
• Navaratri
• Durga Puja
• Ganesh Chaturthi
• Janmashtami
• Raksha Bandhan

The correct answer is Ribosome. 

Key Points

• Ribosomes:-
• They are complex molecular machines composed of RNA and protein molecules.
• They exist in all living cells, from bacteria to eukaryotes, and are essential for protein synthesis.
• The primary function of ribosomes is to synthesize proteins through a process called translation.
• They read the genetic information encoded in mRNA (messenger RNA) and use it to assemble amino acids in the correct order to form a protein chain.

Additional Information

• Mitochondria:-
• Mitochondria are double-membraned organelles found in the cells of eukaryotic organisms.
• They have an outer membrane and an inner membrane that encloses the mitochondrial matrix.
• The inner membrane is highly folded into structures called cristae, which increase its surface area for energy production.
• One of the primary functions of mitochondria is to generate energy through aerobic respiration.
• This process involves the conversion of nutrients, particularly glucose, into adenosine triphosphate (ATP), which is the cell's primary energy currency.
• This process occurs in the mitochondria's inner membrane, specifically in the cristae.
• Golgi apparatus:-
• It is also known as the Golgi complex or Golgi body
• It is a membranous organelle found in eukaryotic cells.
• It consists of a series of flattened membrane-bound sacs or cisternae arranged in stacks, along with associated vesicles.
• Nucleus:-
• It is a membrane-bound organelle found in eukaryotic cells.
• It contains the cell's genetic material, including DNA, and serves as the control center of the cell.
• The nucleus is typically spherical and surrounded by a double-layered membrane known as the nuclear envelope.

The correct answer is MM Keeravani.

Key Points

• M. M. Keeravani:-
• He is a well-known Indian film composer and playback singer in the Telugu and Hindi film industries.
• He has composed music for a wide range of movies and is particularly known for his work in the Indian cinema.
• Some of his notable works include the background score and songs for films like "Baahubali: The Beginning," "Baahubali: The Conclusion," "Magadheera," "Pelli Sandadi," and many others.
• He won a Golden Globe for the Natu Natu song.

Additional Information

• The Golden Globe Awards:-
• It is an annual awards ceremony that honors outstanding achievements in film and television, both domestic and foreign.
• The awards are presented by the Hollywood Foreign Press Association (HFPA), an organization of journalists and photographers who cover entertainment in the United States for international media outlets.
• The Golden Globes are considered one of the major awards shows in the entertainment industry, alongside events like the Oscars (Academy Awards) and the Emmys.

The correct answer is 3.

Key Points

• NIPUN:-
• It stands for National Initiative for Proficiency in Reading with Understanding and Numeracy
• The vision of the NIPUN Bharat Mission is to create an enabling environment to ensure the universal acquisition of foundational literacy and numeracy.
• NIPUN Bharat will be implemented by the Department of School Education and Literacy.
• NIPUN Bharat aims to cover the learning needs of children in the age group of 3 to 9 years.
• A five-tier implementation mechanism will be set up at the national- state- district- block- school level in all states and UTs.
• NIPUN Bharat envisages making the experience of learning at the foundational stage Holistic, Integrated, Inclusive, Enjoyable, and Engaging.
• It comes under the aegis of the centrally sponsored scheme of Samagra Shiksha.
• It attains foundational literacy and numeracy by the end of Grade 3.

The correct answer is Bharatanatyam.

Key Points

• Bharatanatyam:-
• It originated in Tamil Nadu.
• Bharatanatyam is the oldest Indian classical dance and it originated hundreds of years ago in the Indian state of Tamil Nadu.
• This dance form expresses the religious themes and spiritual ideas of South India.
• The ancient Tamil epic Silappatikaram contains the description of Bharatanatyam.
• ‘Alarippu’ is a dance piece from Bharatanatyam classical dance.
• The Sangeet Natak Akademi currently confers classical status on eight Indian classical dance styles: Bharatanatyam (Tamil Nadu), Kathak (North, West and Central India), Kathakali (Kerala), Kuchipudi (Andhra Pradesh), Odissi (Odissa), Manipuri (Manipur), Mohiniyattam (Kerala), and Sattriya (Assam).

Additional Information

• 8 Classical Dances of India and States: 

The correct answer is Blind snake .

Key Points

• Typhlops:-
• It is a genus of blind snakes, also known as worm snakes, which belong to the family Typhlopidae.
• These snakes are found in various regions around the world, including Africa, Asia, the Americas, and some islands in the Pacific.
• Blind snakes are characterized by their small size, cylindrical bodies, and reduced eyes covered by scales. They are non-venomous and mainly feed on ants and termites, using their specialized jaws and teeth to consume their prey. Due to their fossorial (burrowing) nature and secretive habits, they are not commonly encountered by humans.

Additional Information 

• Sea snake: Sea snakes belong to a completely different family and environment. They are part of the Elapidae family and are adapted to living in marine environments. They are venomous and possess fully functional vision to navigate and hunt in the water.
• Glass snakes: "Glass snakes" actually refer to legless lizards, primarily belonging to the genus Ophisaurus. They are not snakes at all, despite their snake-like appearance. They differ from snakes in several key ways, such as having eyelids and external ear openings.
• Grass snake: Grass snakes belong to the genus Natrix, specifically in places like Europe. They are non-venomous snakes that live in terrestrial habitats, often near water sources, and are known for their distinctive collar or ring around the neck. They are not fossorial and have functional eyes.

The correct answer is 1901 - 1921. 

Key Points

• Period of stagnant:-
• The period referred to as a "stagnant or stationary phase of growth" of India's population is a demographic concept known as the "demographic transition."
• This refers to the transition from a high birth rate and high death rate society to a low birth rate and low death rate society, typically accompanied by an intermediate phase of rapid population growth.
• During the early stages of demographic transition, a country experiences high birth rates due to factors such as lack of family planning, high infant mortality rates (leading to a need for larger families), and traditional cultural norms.
• 1901 - 1921 is referred to as a period of stagnant or stationary phase of growth of India’s population.

Additional Information

• Census 2011:-
• It was the 15th Census of India and the 7th Census of Independent India.
• Census 2011 Commissioner: C. Chandramouli
• Slogan: Our Census, Our Future
• No. of districts: 640
• No. of towns: 7933
• No.of villages: 640930
• The total population of India as per the Census 2011 is 1210.19 million of which 623.7 million were males and 586.46 million were females.
• Sex Ratio: 943 Females/1000
• Child Sex Ratio: 919( Rural- 923, Urban- 905)
• The density of Population: 382 Person/Km2
• Literacy Rate: 74.04% of the total population( males: 82.14% and females: 65.46%)
• Population Growth Rate during the decade: 17.7%

The correct answer is Eighth.

Key Points

• Eighth Five Year Plan:-
• In India was implemented from 1992 to 1997.
• It aimed to achieve a growth rate of 5.6% per annum and focused on economic liberalization, industrial development, and infrastructure improvement.
• The plan emphasized the role of private sector participation, globalization, and market-oriented reforms.
• The process of economic reforms in India was introduced during the Eighth Five-Year Plan (1992-1997).
• This period marked a significant turning point in India's economic policies, with the initiation of liberalization measures aimed at opening up the economy, encouraging private investment, and reducing government intervention in various sectors.

Additional Information

• Five-year plans :​
• | Plan | Period | | --- | --- | | First Five year Plan | 1951-1956 | | Second Five year Plan | 1956-1961 | | Third Five year Plan | 1961-1966 | | Plan Holidays – Annual Plans | 1966-1969 | | Fourth Five year Plan | 1969-1974 | | Fifth Five year Plan | 1974-1978 | | Sixth Five year Plan | 1980-1985 | | Seventh Five year Plan | 1985-1990 | | Annual Plans | 1989-1991 | | Eighth Five year Plan | 1992-1997 | | Ninth Five year Plan | 1997-2002 | | Tenth Five year Plan | 2002-2007 | | Eleventh Five year Plan | 2007-2012 | | Twelfth Five year Plan | 2012-2017 |

 

Important Points

• In 1978, the Janta Party came to power, and the 5th Five Year Plan was terminated.
• There was a rolling plan from 1978-80.

The correct answer is 25.

Key Points

• Volleyball:-
• Volleyball is a team sport.
• It is played between two teams of six players.
• Teams are separated by a net.
• Each team tries to score points by grounding a ball on the other team's court under organised rules.
• Volleyball has come a long way from the dusty-old YMCA gymnasium of Holyoke, Massachusetts, USA.
• Dimensions:
• The dimension of the court is18m/9m.
• The width of the net is 1m.
• The height of the net is 2.43m for men and 2.24m for women.
• A 3 m line in each court is marked to determine the front court and back court.
• A regulation volleyball should be 65-67 centimeters in circumference and weigh 260-280 grams.
• William G. Morgan invented the sport back in 1895.
• It was started because the game of basketball was considered violent.
• It was designed as an indoor sport.

 Additional Information

Volleyball Pointing System:

The volleyball point system uses a rally scoring system, meaning a point is awarded on every rally, regardless of which team serves. Here's a breakdown of the key points:

Sets:

• Most matches are played as best-of-five sets.
• The first four sets are played to 25 points, with a two-point lead required to win. So, a set can continue until one team leads by two points, even if the score goes beyond 25-25.
• The final set (if necessary) is played to 15 points, again with a two-point lead requirement.

Scoring:

A point is awarded to the opposing team whenever your team commits a fault, such as:

• Hitting the ball out of bounds.
• Touching the net during play.
• Four touches by your team before returning the ball over the net.
• Foot faults or other technical violations.
• Serving errors also result in a point for the opposing team.

The correct answer is Vallabhbhai Patel 

Key Points

• Vallabhbhai Patel:-
• He was also related to Bardoli Satyagraha.
• He is known as the Iron Man of India.
• The women of Bardoli bestowed the title "Sardar" on Vallabhbhai Patel for his leadership during the Bardoli Satyagraha in 1928.
• It was during the struggle and after the Indian National
• Congress victory in Bardoli Satyagraha, that Patel first began to be referred to as Sardar.
• He is also known as the Bismarck of India because he had played a major role in uniting India.
• Bardoli Satyagraha:-
• It is an event in the Indian Freedom struggle against the rise in tax during times of financial troubles.
• It took place in the town of Bardoli (Gujarat) in the year 1928.

Additional Information

• Lala Lajpat Rai (1865 – 1928):-
• He is also known as "Punjab Kesari" (Lion of Punjab).
• He was an Indian freedom fighter, politician, and social reformer who played a significant role in India's struggle for independence from British rule.
• He was born in Punjab, which is now in modern-day Pakistan. Rai was one of the prominent leaders of the Indian National Congress during the early 20th century.
• Motilal Nehru (1861 – 1931):-
• He was an Indian lawyer, politician, and prominent leader in the Indian National Congress during the colonial era.
• He was a key figure in the Indian independence movement and played a significant role in shaping the political landscape of pre-independence India.
• He was the father of Jawaharlal Nehru, who later became the first Prime Minister of India.
• Chakravarti Rajagopalachari:-
• He was commonly known as C. Rajagopalachari or Rajaji (1878 – 1972),
• He was an Indian lawyer, statesman, freedom fighter, and one of the prominent leaders in the Indian National Congress.
• He played a multifaceted role in the struggle for India's independence and later in the post-independence period.
• He is also known for being the last Governor-General of India before the country became a republic.

The correct answer is Commercial bank.

Key Points

• Commercial bank:-
• It is an institution that accepts deposit, makes business loans and offer related services to various like accepting deposits and lending loans and advances to general customers and business man.
• These institutions run to make profit.
• Commercial banks is an institutional source of credit in India.
• They cater to the financial requirements of industries and various sectors like agriculture, rural development, etc. it is a profit making institution owned by government or private of both.
• Commercial bank includes public sector, private sector, foreign banks and regional rural banks:

Additional Information

• Money lenders:-
• Money lenders provide an alternative source of credit for individuals and small businesses who may have difficulty accessing loans from formal financial institutions like banks.
• This can help to bridge the gap between credit demand and supply.
• Commission agents:-
• Commission agents, also known as brokers or intermediaries, are individuals or firms that facilitate transactions between buyers and sellers in various markets.
• They play a significant role in economics by connecting buyers with sellers and helping to efficiently allocate resources.
• Traders:-
• These are individuals or entities that engage in the buying and selling of goods, services, or financial assets with the primary goal of generating profits.
• Traders play a significant role in economics and financial markets by facilitating the exchange of assets, contributing to market liquidity, and influencing price movements.

The correct answer is Governor.

 Key Points

• State Election Commissioner (SEC):-
• The role of the State Election Commissioner is primarily defined under Article 243K of the Indian Constitution.
• It is a crucial constitutional and administrative figure responsible for conducting and supervising elections within a particular state or union territory in India.
• The State Election Commissioner is usually appointed by the Governor of the state.
• The appointment is made after consultation with the State Government, but it is important that the Commissioner is not under the direct influence of the government to ensure the autonomy of the election process.
• The tenure of the State Election Commissioner is usually determined by the Governor, and it may vary from state to state.
• Governor:-
• Governor is the chief executive head of a state.
• He is appointed by the President for a term of 5 years and is subjected to pleasure of the President.
• The President may transfer a Governor to another state.
• The Constitution does not provide any cases of contingency in regard to Governor for example death of the Governor.
• Article 160 states that The President can make such provisions as he thinks fit for the discharge of functions of governor in any contingency.
• When the Governor of a state dies in office, anyone designated by the President takes over as acting Governor.

Additional Information

• Chief Justice of India (CJI):-
• It is the highest-ranking judicial officer in India.
• It serves as the head of the Indian judiciary.
• President:-
• President of a country is typically the ceremonial head of state and holds a position of constitutional importance.
• The President is elected by an Electoral College comprising elected members of both houses of Parliament and state legislative assemblies.
• Chief Minister:-
• It is the head of the state government in a particular state or union territory.

The correct answer is Pierre Laplace.

Key Points

• Nebular Hypothesis:-
• Nebular hypothesis of Solar System's origin:
• The Nebular Hypothesis of the origin of the Solar System was given by Laplace in 1796.
• Laplace imagined that the planets had condensed from the primitive solar atmosphere.
• It was originally extended far beyond the limits of the present-day system.
• Our solar system formed at the same time as our Sun as described in the nebular hypothesis.
• The nebular hypothesis is the idea that a spinning cloud of dust made of mostly light elements, called a nebula, flattened into a protoplanetary disk, and became a solar system consisting of a star with orbiting planets.
• The stages of formation are
• ​There was a Nebula formed by interstellar dust and cloud.
• The Nebula started to collapse and condense.
• The nebula flattened into a disk called the Protoplanetary Disk.
• The solar system started forming
• Pierre Laplace:-
• Pierre-Simon Laplace was a French mathematician and astronomer who made significant contributions to celestial mechanics and statistics.​
• He revised the nebular hypothesis in 1796.

Additional Information

• Neville Chamberlain:-
• Neville Chamberlain (1869-1940) was a British statesman who served as the Prime Minister of the United Kingdom from 1937 to 1940.
• He is primarily known for his policy of appeasement towards Nazi Germany in the lead-up to World War II.
• Edwin Hubble:- 
• Edwin Hubble (1889-1953) was an American astronomer.
• He is best known for his significant contributions to our understanding of the universe and for providing evidence that the universe is expanding.
• Harold Jeffrey:-
• He was an American mathematician who worked on the theory of partial differential equations and geophysics.

The correct answer is Ranjitsinh Disale

Key Points

• Ranjitsinh Disale:-
• Ranjitsinh Disale has been appointed as the World Bank Education Advisor for the period June 2021 to June 2024.
• He is a government school primary teacher from Maharashtra's Solapur.
• He has also won the Global Teacher Prize 2020.
• He’s been honoured for “transforming the life chances” of girls at Zilla Parishad Primary School in Paritewadi – a poor village in Maharashtra state where tribal communities have traditionally kept females away from formal education.
• The Global Teacher Prize, which has been referred to by journalists as the Nobel Prize for teaching, highlights and celebrates the profession while giving greater recognition to the work of teachers all over the world.

Additional Information

• Peter Tabichi:-
• He is a Kenyan science teacher and Franciscan friar who gained international recognition for his exceptional contributions to education.
• He was awarded the Global Teacher Prize in 2019, which is a prestigious award presented annually to an outstanding teacher who has made a significant impact on their students and community.
• Vishwavir Ahuja:-
• Vishwavir Ahuja is an Indian business executive and banker.
• He is known for his role as the Managing Director and CEO of RBL Bank (Ratnakar Bank Limited), a private sector bank in India.
• Ahuja has been associated with RBL Bank for a significant period and has played a key role in the bank's growth and transformation.

The correct answer is Chota Nagpur plateau.

Key Points

• Chota Nagpur plateau:-
• The Chota Nagpur Plateau is known as the 'mineral heart-land of India'.
• It is located in eastern India. Most of the parts of Jharkhand state, Orissa, West Bengal, Bihar and Chhattisgarh fall in this plateau.
• To its east is the Indus-Ganga Plain and to the south is the Mahanadi.
• This plateau is rich in minerals.
• Major minerals of India bauxite, mica and coal are found here.
• It has the maximum concentration of iron and steel industries in India

Additional Information

• The Deccan Plateau:
• It is a large plateau in western and southern India.
• It covers an area of 500,000 square kilometres and extends over eight Indian states.
• The word “Deccan” comes from the Sanskrit word Dakshina, meaning “south”.
• It lies between the Western and Eastern Ghats and is informally described as the peninsular territory south of the Narmada River between these mountains.
• The Malwa Plateau:-
• It is a region located in central India, covering parts of the states of Madhya Pradesh and southeastern Rajasthan.
• It is characterized by its undulating topography, diverse landscapes, and historical significance.
• The Chhattisgarh Plateau:-
• It is also known as the Chhattisgarh Basin, is a region located in central India, primarily within the state of Chhattisgarh.
• It is characterized by its unique geological and geographical features, as well as its cultural and historical significance.

The correct answer is Trishul and Garuda 

Key Points

• Indian Railways:-
• Indian Railways is one of the world's largest railway networks, covering extensive routes across India.
• The network is divided into zones and divisions for efficient management and operations.
• The first passenger train ran in 1853 between Bombay (now Mumbai) and Thane, marking the beginning of Indian Railways.
• Indian Railways offers various types of trains including express, passenger, local, luxury, and freight trains.
• Indian Railways has embraced technology with online booking, GPS tracking, and station modernization.
• The Indian Railways on October 7, 2021, launched and operated two long-haul freight trains named Trishul and Garuda, to provide a very effective solution to the problem of capacity constraints in critical rail sections.

The correct answer is 10.

Key Points

• ODI:-
• It stands for "One Day International," which is a format of limited-overs cricket.
• In ODI cricket, each team faces a set number of overs, typically 50 overs per side, to bat and bowl. ODI matches are played over a single day, as opposed to Test matches, which can last up to five days.
• In One Day International (ODI) cricket matches, a bowler can bowl a maximum of 10 overs in a single innings.
• This rule is designed to ensure fairness and to prevent any single bowler from dominating the match by consistently bowling long spells.

The correct answer is Ashoka.

Key Points

• Ashoka:-
• ​Ashoka, also known as Ashoka the Great, was an Indian emperor who ruled the Maurya dynasty from approximately 268 to 232 BCE.
• He is considered one of the most significant and impactful rulers in Indian history.
• Ashoka is particularly renowned for his transformation from a fierce and expansionist ruler to a promoter of Buddhism and a proponent of moral and ethical governance.
• Ashoka's early reign was marked by military conquests and expansion of the Maurya Empire across a large part of the Indian subcontinent.
• However, after the Kalinga War in 261 BCE, which resulted in massive loss of life and suffering, Ashoka experienced a profound change of heart.
• He renounced violence and sought a path of moral and ethical conduct.

Additional Information

• Chandragupta Maurya:-
• Chandragupta Maurya established Mauryan emipre in the Magadha Kingdom.
• Kautilya was the mentor of Chandragupta Maurya.
• In his later years, Chandragupta Maurya became a Jain Monk.
• He defeated Dhana Nanda, the last ruler of the Nanda Dynasty.
• Bindusara:-
• He was the second Mauryan emperor of India.
• He was the son of the dynasty's founder Chandragupta and he was the father of the most famous ruler Ashoka.
• Bindusara was known as “Amitro Chates” to the Greeks.
• Bindusara was interested in Ajivika Sect. of Jains.

The correct answer is Sayyid Ahmad Khan.  

Key Points

• The Mohammedan Anglo-Oriental College was founded by Sayyid Ahmed Khan in 1875 at Aligarh.
• Later it became the Aligarh Muslim University.
• His objective was to build a college in tune with the British education system but without compromising its Islamic values.
• The institution offered modern education, including Western science, to Muslims. Hence statement 1 is correct.
• The Aligarh Movement had an enormous impact in the area of educational reforms and contributed greatly to establishing the college.
• Sayyid Ahmad Khan was a great believer in religious toleration.
• He believed that all religions had a certain underlying unity which could be called practical morality.
• Hindus, Parsis, and Christians had contributed freely to the funds of his college whose doors were open for all the Indians.

Additional Information

• Mirza Ghulam Ahmad (1835-1908):-
• He was a religious leader, theologian, and the founder of the Ahmadiyya movement in Islam.
• He was born in Qadian, Punjab, India (now in Pakistan). He claimed to be the Messiah and Mahdi prophesied in Islamic tradition, as well as a reformer sent by God to restore the true teachings of Islam.
• Muhammad Iqbal:-
• He is also known as Allama Iqbal, was a prominent philosopher, poet, and politician in British India.
• He is widely regarded as one of the most important figures in Urdu and Persian literature and is often referred to as the national poet of Pakistan.
• Iqbal's philosophical and poetic works had a profound impact on the intellectual and political landscape of his time, as well as on the subsequent development of the Muslim world.
• Abdul Ghaffar Khan:-
• He is also known as Bacha Khan, was a prominent Indian independence activist and a key figure in the nonviolent struggle for Indian freedom from British colonial rule.
• He is best remembered for his efforts to promote education, social reform, and nonviolent resistance among the Pashtun community in what is now Pakistan and Afghanistan.
• He was a close associate of Mahatma Gandhi and played a significant role in the Indian freedom movement.

The correct answer is Boron, silicon, antimony.

 Key Points

• Metalloids:-
• These are elements that have properties similar to both metals and non-metals. In some of their properties, they show similarity with metals and in others with non-metals.
• They are hence placed in between metals and non-metals.
• Metalloids can also be called semimetals.
• They are found in groups 13, 14, 15, 16 and 17 of the p-block.
• Metalloids include Boron, Silicon, Germanium, Arsenic, Antimony, Tellurium and Polonium.
• Total elements are 118 out of which 91 are metals, 7 are metalloids, and 20 are non-metals.
• In the modern periodic table, metalloids are in Right of the periodic table

Given:

Area of △ABC : Area of △DEF = 196 : 625

Formula used:

Area of △₁/Area of △₂ = (side of △₁)²/(side of △₂)²

Calculation:

Area of △ABC/Area of △DEF = (AB)2/(DE)2

⇒ 196/625 = (AB/DE)²

⇒ AB/DE = √196/√625 = 14/25

∴ The correct option is 1.

Shortcut Trick

If sec θ + tan θ = k, then sec θ − tan θ = 1/k.

Given sec θ + tan θ = 5, then sec θ − tan θ = 1/5.

Subtracting the two equations: 2 tan θ = 5 − 1/5 = 24/5.

⇒ tan θ = 12/5.

∴ The correct answer is 12/5.

Alternate Method

Given: sec θ + tan θ = 5

Formula Used: sec² θ − tan² θ = 1

⇒ (sec θ + tan θ)(sec θ − tan θ) = 1

⇒ 5 × (sec θ − tan θ) = 1

⇒ sec θ − tan θ = 1/5

Let sec θ + tan θ = 5 be Equation (1) and sec θ − tan θ = 0.2 be Equation (2).

Subtracting Eq(2) from Eq(1):

⇒ (sec θ + tan θ) − (sec θ − tan θ) = 5 − 1/5

⇒ 2 tan θ = 24/5

⇒ tan θ = 24 / (5 × 2)

⇒ tan θ = 12/5

∴ The correct answer is 12/5.

Additional Information

Trigonometric Identity

The identity 1 + tan² θ = sec² θ is a fundamental relation derived from the Pythagorean theorem.

Cosecant and Cotangent Identity

Similarly, cosec² θ − cot² θ = 1. If cosec θ + cot θ = x, then cosec θ − cot θ = 1/x.

Pythagorean Triplets

In this case, since tan θ = 12/5 (P/B), the hypotenuse H is √(12² + 5²) = 13. Thus (5, 12, 13) is the triplet.

Given:

Length of each equal side of an isosceles triangle (b) = 3x

Length of an unequal side of an isosceles triangle (a) = 5x

Area of triangle = 30√11 cm² 

Formula used:

Area of isosceles triangle = (a/4) × √{(4 × b²) - a²}

Calculation:

Area of isosceles triangle = (a/4) × √{(4 × b2) - a2}

⇒ 30 × √11 = (5x/4) × √{(4 × (3x)²) - (5x)²}

⇒ 30 × √11 = (5x/4) × √{(4 × 9x2) - 25x2}

⇒ 30 × √11 = (5x/4) × √{36x2 - 25x2}

⇒ 30 × √11 = (5x²/4) × √11

⇒ x2/4 = 6

⇒ x = √24  = 2√6

Length of an unequal side of an isosceles triangle (a) = 5x

⇒ 5 × 2√6 = 10√6 cm

∴ The correct answer is 10√6 cm.

Calculation:

Total plates = 3260

Out of the total plates, 40% plates are manufactured by Plant B

⇒ Plates manufactured by Plant B = 3260 × (40/100)

⇒ Plates manufactured by Plant B = 1304

∴ Plant B manufactured 1304 plates.

Given:

$\rm \left(\frac{1}{\sin θ}+\frac{1}{\tan θ}\right)\rm \left(\frac{1}{\sin θ}-\frac{1}{\tan θ}\right)$

Formula used:

(A² - B²) = (A + B) × (A - B)

Cosec² θ - cot² θ = 1

Calculation:

$\rm \left(\frac{1}{\sin θ}+\frac{1}{\tan θ}\right)\rm \left(\frac{1}{\sin θ}-\frac{1}{\tan θ}\right)$

⇒ (cosec θ + cot θ) × (cosec θ - cot θ)

⇒ Cosec2 θ - cot2 θ

⇒ 1

∴ The correct answer is 1.

Shortcut Trick

When the Percentage Profit at SP₁ equals the Percentage Loss at SP₂ for the same article, the Cost Price (CP) is the average of the two Selling Prices.

CP = (2000 + 1200) ÷ 2 = 3200 ÷ 2 = Rs. 1600.

To gain 20%, New SP = 1600 × 1.2 = Rs. 1920.

∴ The correct answer is Rs. 1,920.

Alternate Method

Given: SP₁ = Rs. 2,000, SP₂ = Rs. 1,200, Profit% = Loss%, Target Profit = 20%.

Formulas: Profit% = [(SP − CP) ÷ CP] × 100 | Loss% = [(CP − SP) ÷ CP] × 100 | New SP = CP × (100 + P%) ÷ 100.

⇒ Let CP be x. Since Profit% = Loss%, we have (2000 − x)/x = (x − 1200)/x.

⇒ 2000 − x = x − 1200 ⇒ 2x = 3200 ⇒ x = Rs. 1,600.

⇒ Required Profit = 20% of 1600 = 1600 × (20/100) = Rs. 320.

⇒ New Selling Price = 1600 + 320 = Rs. 1,920.

∴ The correct answer is Rs. 1,920.

Additional Information

Cost Price relation with Profit and Loss

If the numerical value of Profit equals Loss, the CP is the midpoint. If the Percentage values are equal, the CP is also the arithmetic mean of the two prices.

Calculating Final SP

To find the SP for a desired profit, multiply the CP by the factor (1 + Profit%/100). For a 20% profit, the multiplier is 1.2.

Concept used:

Dividend = (divisor × quotient) + remainder

the if remainder = 0, then dividend is divisible by the divisor.

Calculation:

We need to check it by options.

Option 1:

number = 24973

While dividing with 7.

Dividend = (divisor × quotient) + remainder

⇒ 24973 = (7 × 3567) + 4

So this number is not divisible by 7.

Option 2:

number = 24983

While dividing with 7.

Dividend = (divisor × quotient) + remainder

⇒ 24983 = (7 × 3569) + 0

So, this number is divisible by 7.

∴ The correct option is 2.

Given:

sin 2x + 2 sin 4x + sin 6x 

Formula used:

sin C + sin D = 2 × sin (C + D)/2 × cos (C - D)/2

cos 2θ = (2 × cos 2 θ  - 1)

Calculation:

sin 6x + sin 2x + 2 sin 4x

⇒ 2 × sin (6x + 2x)/2 × cos (6x - 2x)/2 + 2 sin 4x

⇒ 2 × sin 4x × cos 2x + 2 sin 4x

⇒ 2 × sin 4x (cos 2x + 1)

⇒ 2 × sin 4x {(2 × cos²x - 1) + 1) }

⇒ (2 × sin 4x) × (2 × cos2 x) 

⇒ 4 cos2 x  sin 4x

∴ The correct answer is 4 cos2 x  sin 4x.

Given:

⇒ 405 : y :: y : 125

Concept used:

a : b : : c : d

⇒ a/b = c/d

Calculation:

405 : y :: y : 125

⇒ 405/y = y/125

⇒ y² = 125 × 405

⇒ y = √{25 × 5 × 81 × 5}

⇒ y = 25 × 9 = 225 

∴ The correct answer is 225.

Given:

Distance between policeman and thief = 600 m

Speed of policeman = 10 km/h

Speed of thief = 8 km/h

Formula used:

Distance = relative speed × time

Calculation:

Distance = relative speed × time

⇒ 600 = (10 - 8) × (5/18) × time

⇒ Time = (600 × 18)/(2 × 5)

⇒ Time = (60 × 18) = 1080 sec

⇒ Time = 1080 sec. = 1080/60 = 18 minutes

∴ The correct answer is 18 minutes.

Shortcut Trick

For a number to be divisible by 36, it must be divisible by its co-prime factors, 4 and 9.

Rule for 4: Last two digits must be divisible by 4 → 47502 is eliminated (02 is not divisible by 4).

Rule for 9: Sum of digits must be a multiple of 9.

Checking remaining options: Sum of digits for 29412 = 2 + 9 + 4 + 1 + 2 = 18 (Divisible by 9).

∴ The correct answer is 29412.

Alternate Method

Given:

Numbers to check: 47502, 29412, 54732, 87064

Concept Used:

Since 36 = 4 × 9 and gcd(4, 9) = 1, any number divisible by 36 must be divisible by both 4 and 9.

Divisibility by 4: The number formed by the last two digits is divisible by 4.

Divisibility by 9: The sum of the digits of the number is divisible by 9.

Calculations:

⇒ Step 1: Check divisibility by 4 (Last two digits)

⇒ 47502 → 02 is not divisible by 4.

⇒ 29412 → 12 is divisible by 4.

⇒ 54732 → 32 is divisible by 4.

⇒ 87064 → 64 is divisible by 4.

⇒ Step 2: Check divisibility by 9 for the remaining numbers (Sum of digits)

⇒ 29412 → 2 + 9 + 4 + 1 + 2 = 18 (18 is divisible by 9)

⇒ 54732 → 5 + 4 + 7 + 3 + 2 = 21 (21 is not divisible by 9)

⇒ 87064 → 8 + 7 + 0 + 6 + 4 = 25 (25 is not divisible by 9)

⇒ Hence, only 29412 satisfies both conditions.

∴ The correct answer is 29412.

Additional Information

Divisibility by Composite Numbers

If a number is divisible by a composite number, it must be completely divisible by all of its co-prime factors (e.g., for 72, check 8 and 9).

Divisibility Rule of 8

A number is divisible by 8 if the number formed by its last three digits is divisible by 8.

Divisibility Rule of 11

A number is divisible by 11 if the difference between the sum of its digits at odd places and the sum of its digits at even places is either 0 or a multiple of 11.

Given:

Amar can complete a work = 15 days

Prem can complete a work = 12 days

Formula used:

Total work = efficiency × time

Calculation:

Now,

(Amar + Prem) = 4 + 5 = 9 units = 2 days

⇒ (9 × 6) = 54 units =  (2 × 6) = 12 days

⇒ 58 units = 13 days

⇒ 60 units = 13 + (2/5) = 13$2\over5$ days

∴ The correct answer is 13$2\over5$ days.

Shortcut Trick

Total Work (LCM of 4, 9) = 36 units.

Efficiency: B = 4, A = 9.

2-day cycle (B + A) = 4 + 9 = 13 units.

In 2 cycles (4 days), work done = 13 × 2 = 26 units. Remaining = 36 − 26 = 10 units.

Day 5 (B) does 4 units. Remaining = 6 units. Day 6 (A) takes 6/9 = 2/3 days.

Total time = 5 + 2/3 = 5(2/3) days.

∴ The correct answer is 5(2/3) days.

Alternate Method

Given: Time taken by A = 4 days, Time taken by B = 9 days.

Formula Used: Total Work = Efficiency × Time

⇒ Work starts with B on alternate days.

⇒ Day 1 (B): 4 units | Day 2 (A): 9 units.

⇒ Work in 1 cycle (2 days) = 4 + 9 = 13 units.

⇒ Work in 2 cycles (4 days) = 13 × 2 = 26 units.

⇒ Remaining work = 36 − 26 = 10 units.

⇒ Day 5 (B's turn): B completes 4 units. Remaining = 10 − 4 = 6 units.

⇒ Day 6 (A's turn): Time taken by A = Remaining work ÷ Efficiency = 6 ÷ 9 = 2/3 days.

⇒ Total time = 4 days + 1 day + 2/3 days = 5(2/3) days.

∴ The correct answer is 5(2/3) days.

Additional Information

Alternate Day Work

In alternate work, the sequence of workers matters. If the total work is not a multiple of the cycle sum, the remaining work is handled by the person whose turn follows.

Efficiency and Time

Efficiency is inversely proportional to the time taken to complete a task. Efficiency = Total Work ÷ Time.

LCM Method

Using the Least Common Multiple (LCM) of individual days as the Total Work simplifies calculations by avoiding fractions until the final step.

Shortcut Trick

Weighted Average method: Price = (Price₁ × Ratio₁ + Price₂ × Ratio₂) ÷ Total Ratio

Price = (100 × 7 + 150 × 20) ÷ (7 + 20)

Price = (700 + 3000) ÷ 27 = 3700 ÷ 27

Price ≈ 137.03

∴ The correct answer is ₹137.

Alternate Method

Given:

Price of pulse X = ₹100 per kg

Price of pulse Y = ₹150 per kg

Mixing ratio X : Y = 7 : 20

Calculations:

⇒ Let the price of the mixture be M.

⇒ Using the alligation or weighted mean formula: M = (n₁c₁ + n₂c₂) ÷ (n₁ + n₂)

⇒ M = (7 × 100 + 20 × 150) ÷ (7 + 20)

⇒ M = (700 + 3000) ÷ 27

⇒ M = 3700 ÷ 27

⇒ M = 137.037...

⇒ Rounding to the nearest Rupee, M = 137.

∴ The correct answer is ₹137.

Additional Information

Alligation Rule

It states that (Quantity of cheaper) ÷ (Quantity of dearer) = (CP of dearer − Mean Price) ÷ (Mean Price − CP of cheaper).

Weighted Average

For two components with values v₁, v₂ in ratio n₁:n₂, the average is (n₁v₁ + n₂v₂) ÷ (n₁ + n₂).

Profit/Loss in Mixtures

If the mixture is sold at a certain profit %, the Mean CP must be calculated first: CP = [SP × 100] ÷ [100 + Profit %].

Shortcut Trick

If x − 1/x = k, then x⁵ − 1/x⁵ = (k² + 2)(k³ + 3k) − k.

Given k = −6, then k² + 2 = 38 and k³ + 3k = −234.

Value = (38 × −234) − (−6) = −8892 + 6 = −8886.

∴ The correct answer is -8886.

Alternate Method

Given: x − 1/x = −6

Formula Used: x⁵ − 1/x⁵ = (x² + 1/x²)(x³ − 1/x³) − (x − 1/x)

⇒ x² + 1/x² = (x − 1/x)² + 2 = (−6)² + 2 = 38

⇒ x³ − 1/x³ = (x − 1/x)³ + 3(x − 1/x) = (−6)³ + 3(−6) = −216 − 18 = −234

⇒ x⁵ − 1/x⁵ = (x² + 1/x²)(x³ − 1/x³) − (x − 1/x)

⇒ x⁵ − 1/x⁵ = (38 × −234) − (−6) = −8892 + 6 = −8886

∴ The correct answer is -8886.

Additional Information

Square Relation

For a given x − 1/x = k, the identity used for squares is x² + 1/x² = k² + 2.

Cube Relation

For a given x − 1/x = k, the identity used for cubes is x³ − 1/x³ = k³ + 3k.

Expansion of Power 5

The term x⁵ − 1/x⁵ is derived from (x² + 1/x²)(x³ − 1/x³) = x⁵ − 1/x + x − 1/x⁵.

Calculation:

Sale of XYZ mobile in 2019 = 18

Sale of XYZ mobile in 2020 = 40

Percentage increase = (22 × 100)/18 = 1100/9 = 122.22%

∴ The correct answer is 122.22%.

Given:

48% × male workers = (2/3) × female workers

Calculation:

⇒ 48% × male workers = (2/3) × female workers

⇒ Male workers/female workers = 200/(3 × 48)

⇒ Male workers : female workers = 200 : (3 × 48) = 25 : 18

∴ The correct option is 4.

Shortcut Trick

Direct Algebraic Identity: (a − b)² + (b − c)² + (c − a)² = 3(a² + b² + c²) − (a + b + c)²

Given: (a + b + c) = 19 and (a² + b² + c²) = 155

Substitute values: 3 × 155 − 19²

Calculation: 465 − 361 = 104

∴ The correct answer is 104.

Alternate Method

Given: (a + b + c) = 19 and (a² + b² + c²) = 155

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

Calculations:

⇒ (19)² = 155 + 2(ab + bc + ca)

⇒ 361 = 155 + 2(ab + bc + ca)

⇒ 2(ab + bc + ca) = 361 − 155 = 206

⇒ Required expression: (a − b)² + (b − c)² + (c − a)²

⇒ (a² − 2ab + b²) + (b² − 2bc + c²) + (c² − 2ca + a²)

⇒ 2(a² + b² + c²) − 2(ab + bc + ca)

⇒ 2(155) − 206

⇒ 310 − 206 = 104

∴ The correct answer is 104.

Additional Information

Sum of Squares of Differences

The expression (a − b)² + (b − c)² + (c − a)² is equivalent to 2(a² + b² + c² − ab − bc − ca).

Standard Algebraic Identity

a³ + b³ + c³ − 3abc = (a + b + c) × [ (a − b)² + (b − c)² + (c − a)² ] ÷ 2.

Derived Relation

3(a² + b² + c²) = (a + b + c)² + (a − b)² + (b − c)² + (c − a)². This is useful for finding the sum of squares of differences directly.

Given:

Marked price (M.P) = Rs.3600

Concept used:

Discount% = M.P × D%

Effective discount (D) = (D₁) + (D₂) - (D1 × D2)/100

Calculation:

Discount (D1) = 3600 × 35%

⇒ 36 × 35 = Rs.1260

Effective discount = 30 + 5 - (30 × 5)/100

⇒ 35 - 1.5 = 33.5%

Discount (D2) = 3600 × 33.5% = Rs.1206

Difference between two discount = (1260 - 1206) = Rs.54

∴ The correct answer is Rs.54.

Given:

(Raja + Rocky) can complete painting work = 5 days

Formula used:

Total work = efficiency × time

Calculation:

According to the question:

⇒ (Raja + Rocky) × 2 + Raja × 4 = (Raja + Rocky) × 5

⇒ Raja × 4 = (Raja + Rocky) × 3

⇒ Raja × 1 = Rocky × 3

⇒ Raja/Rocky = 3/1

Total work = (Raja + Rocky) × 5

⇒ (3 + 1) × 5 = 4 × 5

⇒ 20 units

Time taken by Rocky alone to complete the painting work = 20/1 = 20 days

∴ The correct answer is 20 days.

Given:

Sin A = (- 3/5)

A lies in the 3rd quadrant.

Formula used:

Sin θ = P/H

Sec θ = H/B

Where, H = hypotenuse ; P = perpendicular ; B = base

Calculation:

Sin A = - (3/5) = P/H

By Pythagorean theorem:

⇒ H² = P² + B²

⇒ 5² = 3² + B²

⇒ B² = 25 - 9 

⇒ B = √16 = 4

Now, sec A = - (H/B) = - (5/4)

∴ The correct answer is - (5/4).

Given:

A can do a piece of work = 5 days

B can do a piece of work = 10 days.

Formula used:

Total work = efficiency × time

Calculation:

Let the number of days work together by (A + B) = D

According to the question:

⇒ (A + B) × D + B × 8 = 10

⇒ (2 + 1) × D + 1 × 8 = 10

⇒  3 × D = (10 - 8)

⇒ D = 2/3 days

∴ The correct answer is 2/3 days.

Shortcut Trick

Shortcut Trick

Downstream speed = 144 ÷ 9 = 16 km/h

Upstream speed = 144 ÷ 12 = 12 km/h

Speed of stream = (Downstream speed − Upstream speed) ÷ 2

Speed of stream = (16 − 12) ÷ 2 = 2 km/h

∴ The correct answer is 2 km/h.

Alternate Method

Given:

Distance (D) = 144 km

Time taken upstream (T_u) = 12 hours

Time taken downstream (T_d) = 9 hours

Formula Used:

Speed = Distance ÷ Time

Speed of stream (S_s) = (Speed downstream − Speed upstream) ÷ 2

Distance = 144 km

Downstream: 9 hours (16 km/h)

Upstream: 12 hours (12 km/h)

Speed of stream = (16 − 12) ÷ 2 = 2 km/h

Calculations:

⇒ Speed downstream (S_d) = 144 ÷ 9 = 16 km/h

⇒ Speed upstream (S_u) = 144 ÷ 12 = 12 km/h

⇒ Speed of stream = (S_d − S_u) ÷ 2

⇒ Speed of stream = (16 − 12) ÷ 2

⇒ Speed of stream = 4 ÷ 2

⇒ Speed of stream = 2 km/h

∴ The correct answer is 2 km/h.

Additional Information

Speed of Boat in Still Water

It is calculated as half the sum of downstream and upstream speeds: S_b = (S_d + S_u) ÷ 2

Downstream Speed

When the boat moves in the same direction as the flow of the river, speeds are added: S_d = S_b + S_s

Upstream Speed

When the boat moves against the flow of the river, speeds are subtracted: S_u = S_b − S_s

Average Speed for Round Trip

If a boat goes a certain distance and returns, the average speed = (2 × S_u × S_d) ÷ (S_u + S_d)

Shortcut Trick

Side of Equilateral Triangle = Perimeter ÷ 3 = 48 ÷ 3 = 16 cm.

Area = (√3 ÷ 4) × Side².

Area = (√3 ÷ 4) × 16 × 16 = 64√3 cm².

∴ The correct answer is 64√3 cm².

Alternate Method

Given:

Perimeter of Equilateral Triangle = 48 cm.

Formula Used:

Perimeter = 3 × a (where a is the side).

Area = (√3 / 4) × a².

Calculations:

⇒ 3 × a = 48

⇒ a = 48 ÷ 3 = 16 cm

⇒ Area = (√3 / 4) × (16)²

⇒ Area = (√3 / 4) × 256

⇒ Area = 64√3 cm²

∴ The correct answer is 64√3 cm².

Additional Information

Equilateral Triangle Properties

All three sides are equal and each internal angle is 60°.

Height of Equilateral Triangle

The height (h) is given by (√3 / 2) × side.

Inradius and Circumradius

Inradius (r) = a / (2√3) and Circumradius (R) = a / √3.

Given:

The cost of 32 pens and 12 pencils = Rs.790

Calculation:

The cost of 32 pens and 12 pencils = Rs.790

Divide both sides by 4

The cost of 8 pens and 3 pencils = 790/4 = Rs.197.5

∴ The correct answer is Rs.197.5.

The correct answer is: Extravagant

Key Points

• The sentence talks about people paying high prices for houses because they need accommodation.
• The word 'frugal' means being economical or thrifty. (किफायती या मितव्ययी होना)
• For example: He lived a frugal lifestyle, always saving money and avoiding unnecessary expenses.
• The antonym of 'frugal' is 'extravagant', which means spending money without restraint or being wasteful. (बिना रोक-टोक के पैसा खर्च करना या फिजूलखर्ची करना)
• For example: They had an extravagant wedding with luxurious decorations and gourmet food.
• Therefore, the word opposite in meaning to 'frugal' in the given sentence is 'extravagant'.

Hence, option 4 is the correct answer.

Additional Information

• 'Prices' is not the antonym of 'frugal'. It is a noun that refers to the amount of money that is required to purchase something. (वह धनराशि जो किसी वस्तु को खरीदने के लिए आवश्यक होती है)
• 'Accommodation' is not the antonym of 'frugal'. It is a noun that refers to a place where someone lives or stays. (वह स्थान जहाँ कोई रहता या ठहरता हो)
• 'Present' is not the antonym of 'frugal'. It is an adjective that means existing or occurring now. (विद्यमान या अभी घटित होने वाला)

The incorrectly spelt word is: Ignision 

Key Points

• The correct spelling of the word is 'ignition'.
• Ignition means the process of starting a fire or combustion. (आग या दहन शुरू करने की प्रक्रिया)
• For example: The ignition of the campfire required some kindling and a match.
• The incorrect spelling 'ignision' has an extra 'i' between 'g' and 'n'.
• The mistake is a common misspelling error due to the similar sound of 'i' and 'g'.
• To avoid such errors, it is important to practice spelling and pay attention to the correct sequence of letters.

Therefore, the correct answer is option 2.

Additional Information

• Horticulture is the science of plant cultivation. (बागवानी पौधों की खेती का विज्ञान है)
• Copulate means to engage in sexual intercourse. (संभोग में संलग्न होना)
• Portion is a part or share of something. (किसी चीज़ का हिस्सा या हिस्सा)

The correct answer is: It rains

Key Points

• The original sentence is in the present tense.
• The correct option also uses the present tense but replaces "is" with "it".
• "It" is a pronoun that refers to the rain.
• This sentence means that the speaker will only go out if it's not raining.

Therefore, the correct answer is option 2.

Corrected sentence: I will not go out if it rains.

Additional Information

• "raining" is a present participle, which can be used as a verb or adjective, but it does not fit in this sentence as the main verb.
• "will rain" is in the future tense, which changes the meaning of the sentence.
• "rained" is in the past tense, which also changes the meaning of the sentence.

The correct answer is: get off my

Key Points

• The correct preposition to use in this context is "off".
• "Get of mine" and "get off mine" are incorrect because "mine" is a possessive pronoun and cannot be used as an object of a preposition.
• The correct possessive pronoun to use is "my" because the speaker is referring to their own couch.

Therefore, the correct answer is option 2.

Corrected sentence: Please ask the dog to get off my couch. 

Additional Information

• "get of mine" is grammatically incorrect because it uses the wrong preposition and the wrong possessive pronoun.
• "get off mine" is also grammatically incorrect because it uses the wrong possessive pronoun.
• "No substitution" is not applicable because the underlined segment needs to be corrected.

The erroneous part of the sentence is: I read

Key Points

• The sentence is in the past tense, indicating that the action of falling asleep and reading the book happened in the past.
• The verb "fell" is in the past tense and correctly describes the action of falling asleep.
• The word "asleep" is an adverb describing how the action of falling asleep occurred.
• The segment "I read" contains a grammatical error because the verb "read" is in the present tense, which does not match the past tense of the rest of the sentence.

Therefore, the correct answer is option 2.

Corrected sentence: I fell asleep while I was reading the book. 

Additional Information

• "the book", is a noun phrase that correctly identifies the object being read.
• "asleep while", is a prepositional phrase that correctly describes the circumstance in which the action of falling asleep occurred.
• "I fell", is a verb phrase that correctly describes the action of falling asleep.

The correct answer is: Crowded

Key Points

• The given word is 'lonely' which means without company or solitary. (बिना किसी कंपनी या अकेले के)
• The antonym of 'lonely' would be a word that means crowded or full of people. (भीड़भाड़ वाला या लोगों से भरा हुआ)
• So, 'crowded' is the most appropriate antonym as it means a place or area filled with many people or things.

Therefore, the correct answer is option 1.

Additional Information

• Isolated means separated from others or alone, but not necessarily crowded. (दूसरों से अलग या अकेला)
• Empty means having nothing inside or vacant, which is not opposite to 'lonely'. (अंदर कुछ भी न होना या खाली होना)
• Remote means far away or distant, but not necessarily crowded. (बहुत दूर)

The incorrectly spelt word is: Concieve 

Key Points

• The word "Conceive" means to form or develop in the mind, to imagine or understand. (मन में बनना या विकसित होना, कल्पना करना या समझना)
• For example: It's fascinating to watch an artist conceive a new painting from their imagination.
• The correct spelling of the word is with the letter "i" after the letter "e".
• The incorrect spelling "Concieve" is a common misspelling of the word.

Therefore, the correct answer is option 1.

Additional Information

• "Detect" means to discover or identify something. (किसी चीज़ की खोज या पहचान करना)
• "Predict" means to forecast or estimate something based on available information. (उपलब्ध जानकारी के आधार पर किसी चीज़ का पूर्वानुमान या अनुमान लगाना)
• "Stimulate" means to encourage or excite something to happen. (किसी चीज़ को घटित होने के लिए प्रोत्साहित या उत्साहित करना)

The correct answer is: went on the rampage

Key Points

• The verb "went" is more appropriate than "played", "ran", or "strolled" because it conveys a sense of purposeful movement.
• "On the rampage" is an idiomatic expression meaning to behave violently or destructively.
• The sentence is in the past tense, so the correct form of the verb is "went" instead of "go".

Therefore, the correct answer is option 2.

Corrected sentence: The mob went on the rampage and looted several shops in the locality. 

Additional Information

• "played on the rampage" does not accurately convey the seriousness of the situation and is not a commonly used phrase.
• "ran on the rampage" could be used in certain contexts but does not fit well in this sentence.
• "strolled on the rampage" is completely inappropriate as it suggests a leisurely walk rather than violent behaviour.

The correct answer is: Conspiracy

Key Points

• One-word substitute for a secret plan made to do something wrong is Conspiracy.
• Conspiracy refers to a secret plan by a group of people to do something unlawful or harmful. (लोगों के एक समूह द्वारा कोई गैरकानूनी या हानिकारक कार्य करने की गुप्त योजना)
• The word conspiracy is a noun and is pronounced as kuh n-spir-uh-see.
• For example: The politician was accused of being involved in a conspiracy to rig the election.

Therefore, the correct answer is option 4.

Additional Information

• Strategy refers to a plan of action or policy designed to achieve a major or overall aim. It is not necessarily a secret plan and may not involve any wrongdoing. (किसी प्रमुख या समग्र लक्ष्य को प्राप्त करने के लिए बनाई गई कार्य योजना या नीति)
• Planning refers to the process of making plans for something. It is not necessarily a secret plan and may not involve any wrongdoing. (किसी चीज़ के लिए योजना बनाने की प्रक्रिया)
• Conditioning refers to the process of training or accustoming a person or animal to behave in a certain way. It is not related to a secret plan. (किसी व्यक्ति या जानवर को एक निश्चित तरीके से व्यवहार करने के लिए प्रशिक्षित करने या आदी बनाने की प्रक्रिया)