SSC CGL 2023 Tier-I Official Paper (Held On: 17 Jul 2023 Shift 4) (Previous Year Paper)

From the given two dices,

 

→ 3 and 2 are common surface in both Dice, therefore, '4' is the opposite surface of '1'.

Here, '4' is opposite to the face containing '1'.

Hence, the correct answer is "4".

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

So,

• (2, 1, 5)

2 × 2 = 5 - 1

4 = 4 (LHS = RHS)

And,

• (5, 12, 22)

5 × 2 = 22 - 12

10 = 10 (LHS = RHS)

Similarly,

• (6, 2, ?)

6 × 2 = ? - 2

12 + 2 = ?

14 = ?

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

Logic : (Cube of 1^st number + 1^st number) = 2^nd number

So,

• Option - (1) : 4 : 70

$(4)^3$ + 4 = 70

64 + 4 = 70

68 ≠ 70 (LHS ≠ RHS)

• Option - (2) : 3 : 30​

$(3)^3$ + 3 = 30 

27 + 3 = 30

30 = 30 (LHS = RHS)

• Option - (3) : 6 : 222

$(6)^3$ + 6 = 222

216 + 6 = 222

222 = 222 (LHS = RHS)

• Option - (4) : 7 : 350

$(7)^3$ + 7 = 350

343 + 7 = 350

350 = 350 (LHS = RHS)

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

Given statement : 100 + 100 × 50 - 2 ÷ 3 = 51 

According to the question, after interchanging the signs :

So,

• Option - (1) : + and ÷

100 + 100 × 50 - 2 ÷ 3 = 51 ⇒ 100 ÷ 100 × 50 - 2 + 3 = 51 

1 × 50 - 2 + 3 = 51

50 + 3 - 2 = 51

53 - 2 = 51

 

51 = 51 (LHS = RHS)

• Option - (2) : + and -

100 + 100 × 50 - 2 ÷ 3 = 51 ⇒ 100 - 100 × 50 + 2 ÷ 3 = 51

100 - 100 × 50 + 0.66 = 51

100 + 0.66 - 5000 = 51

100.66 - 5000 = 51

-4899.34 ≠ 51 (LHS ≠ RHS)

• Option - (3) : - and ×

100 + 100 × 50 - 2 ÷ 3 = 51 ⇒ 100 + 100 - 50 × 2 ÷ 3 = 51

100 + 100 - 50 × 0.66 = 51

100 + 100 - 33 = 51

200 - 33 = 51

167 ≠ 51 (LHS ≠ RHS)

• Option - (4) : ÷ and ×

100 + 100 × 50 - 2 ÷ 3 = 51 ⇒ 100 + 100 ÷ 50 - 2 × 3 = 51

100 + 2 - 2 × 3 = 51

100 + 2 - 6 = 51

102 - 6 = 51

96 ≠ 51 (LHS ≠ RHS)

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

Logic: No specific pattern is followed here, certain codes are assigned to each letter randomly.

C R O W → 6 9 7 0

O R C A → 7 5 6 9

There, are 3 letters common in both words (C, R and O) and 3 numbers are common (6, 9 and 7)

Thus, in 1^st word, the number remaining which is not assigned to (C, R and O) is '0'

Thus, the code for ‘W’ in the given code language is '0'

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

1. For '

' element → 

• '

' element is alternately replaced by '

' element.

• Shifting clockwise direction.

2. For '

' element → Rotation of 90º clockwise direction.

3) For '

' element → Number of '

' element are decreasing from the shaded region and increasing in the non shaded area.

Final series is

Hence, ‘option - (2)’ is the correct answer.

The least possible Venn diagram for the given statement is:

Conclusions:

I. No pen is a fan → Does not Follow (As, no box is a fan and some pens are fans. So, no direct negative or cross relation is given between pens and fan therefore it is definitely false)

II. No box is a pen → Does not Follow (As, some pens are boxes and no box is a fan. So, no direct negative or cross relation is given between pens and box therefore it is definitely false)

III. Some fans are pens → Follow (As, some pens are fans. So, as some part of pens is common with fans therefore it is definitely true.)

IV. Some boxes are pens → Follow (As, some pens are boxes. So, as some part of pens is common with boxes therefore it is definitely true.)

So, Only conclusions Ill and IV follow.

Hence, the correct answer is "Only conclusions Ill and IV follow".

Logic : Position values according to English alphabetic series written in reverse order and rearranged diagonally.

So,

• ‘STAR’ is written as ‘8110291’

And,

• ‘GIFT’ is written as '02697'

​Similarly,

• ‘DOLL’ will be written as :

​Hence, "2121514" is the correct answer.

The correct answer is Option (1).

Logic: (1^st Number + 3^rd Number) / 2 = 2^nd Number

Given :

• (12, 15, 18)

(12+18) / 2 = 15

• (10, 8, 6)

(10+6) / 2 = 8

So,

 (15+25) / 2 = 20

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

Alternate Method:

Logic : (2^nd number - 1^st number) = (3^rd number - 2^nd number)

Given : 

• (12, 15, 18)

15 - 12 = 18 - 15

3 = 3 (LHS = RHS)

• (10, 8, 6)

8 - 10 = 6 - 8

-2 = -2 (LHS = RHS)

So,

• Option - (1) : (15, 20, 25)

20 - 15 = 25 - 20

5 = 5 (LHS = RHS)

• Option - (2) : (14, 28, 14)

28 - 14 = 14 - 28

14 ≠ -14 (LHS ≠ RHS)

• Option - (3) : (13, 10, 17)

10 - 13 = 17 - 10

3 ≠ 7 (LHS ≠ RHS)

• Option - (4) : (19, 18, 1)

18 - 19 = 1 - 18

-1 ≠ -17 (LHS ≠ RHS) 

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

Given :

Given statement : H + I - J × K × L - M ÷ N

So,

• H + I → H is the father of I.

• I - J → I is the son of J.

• J × K → J is the sister of K.

• K × L → K is the sister of L.

​​

• L - M → L is the son of M.

• M ÷ N → M is the wife of N.

Thus, according to the final family tree :

• Option - (1) : H is the husband of the sister of K → Correct
• Option - (2) : J is the wife of the son of M → Incorrect as J is the sister of the son of M
• Option - (3) : H is the husband of the sister of L → Correct
• Option - (4) : H is the husband of the daughter of M → Correct

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

Logic : (1^st number + 2^nd number) = (3^rd number + 9)

Given : 

• (44, 63, 98)

44 + 63 = 98 + 9

107 = 107 (LHS = RHS)

• (59, 99, 149)

59 + 99 = 149 + 9

158 = 158 (LHS = RHS)

So,

• Option - (1) : (81, 15, 87)

81 + 15 = 87 + 9

96 = 96 (LHS = RHS)

• Option - (2) : (54, 73, 121)

54 + 73 = 121 + 9

127 ≠ 130 (LHS ≠ RHS)

• Option - (3) : (19, 32, 44)

19 + 32 = 44 + 9

51 ≠ 53 (LHS ≠ RHS)

• Option - (4) : (82, 13, 96)

82 + 13 = 96 + 9

95 ≠ 105 (LHS ≠ RHS) 

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

The least possible Venn diagram for the given statement is:

Conclusions:

I. Some black are spoons → Follow (As, some spoons are black. So, as some part of spoons is common with black therefore it is definitely true.)

II. All crows are black → Does not Follow (As, All black are crows. So, it is possible but not definitely true)

III. No plate is a crow → Follow (As, no crow is a plate. So, direct cross or negative relation is given between plate and crow therefore it is definitely true.)

So, Only conclusions I and Ill follow.

Hence, the correct answer is "Only conclusions I and Ill follow".

Given statement : 56 * 8 * 4 * 7 * 50 * 15

According to the question, after replacing the * signs :

So,

• Option - (1) : +, =, ÷, ×, +

56 * 8 * 4 * 7 * 50 * 15 ⇒ 56 + 8 = 4 ÷ 7  × 50 + 15 

64 = 0.57 × 50 + 15

64 = 28.5 + 15

64 ≠ 43.5 (LHS ≠ RHS)

• Option - (2) : ÷, ×, =, +, +

56 * 8 * 4 * 7 * 50 * 15 ⇒ 56 ÷ 8 × 4 = 7 + 50 + 15

7 × 4 = 72

28 ≠ 72 (LHS ≠ RHS)

• Option - (3) : ÷, ×, -, =, ×

56 * 8 * 4 * 7 * 50 * 15 ⇒ 56 ÷ 8 × 4 - 7 = 50 × 15

7 × 4 - 7 = 750

27 - 7 = 750

20 ≠ 750 (LHS ≠ RHS)

• Option - (4) : ÷, ×, +, =, -

56 * 8 * 4 * 7 * 50 * 15 ⇒ 56 ÷ 8 × 4 + 7 = 50 - 15

7 × 4 + 7 = 35

28 + 7 = 35 

35 = 35 (LHS = RHS)

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

Given:

 

• The image must not to be rotated

  

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

Logic : (1^st number - 3^rd number) = (2^nd number ÷ 2)

So, 

• (14, 10, 9)

14 - 9 = 10 ÷ 2

5 = 5 (LHS = RHS)

And,

• (6, 8, 2)

6 - 2 = 8 ÷ 2

4 = 4 (LHS = RHS)

Similarly,

• (8, 4, ?)

8 - ? = 4 ÷ 2

8 - 2 = ?

6 = ?

Hence, "6" is the correct answer.

Logic : Term : Synonym

• Explicit is a synonym of open.

Similarly,

• Confidential is a synonym of secret.

Hence, "Secret" is the correct answer.

Additional Information

1. Clean → Synonyms are neat, tidy, pure etc.
2. Free → Synonyms are liberated, open, independent etc.
3. Indirectly → Synonyms are implicitly, not directly, subtly etc.
4. Secret → Synonyms are confidential, hidden, private etc.

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

1. For '

' element → Rotation of 90º in the anti-clockwise direction.​

2. For '

' element → Rotation of 90º in the anti-clockwise direction

Final series is

Hence, ‘option - (2)’ is the correct answer.

Logic : Consecutive decreasing multiples of (9) are subtracted from each number subsequently.

So,

325 - 54 = 271

271 - 45 = 226

226 - 36 = 190

190 - 27 = 163

163 - 18 = 145

145 - 9 = 136

Hence, "190" is the correct answer.

Given:

 

• The image must not to be rotated

  

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

Given : _B_T F H B N_F I_N T F_B N T F    

By checking options :

1. G N T B J → GBNT F H B NTF IBN T FJB N T F → (It follows the pattern of : 

) 2. G T N J B → GBTT F H B NNF IJN T FBB N T F → (It doesn't Follows the pattern) 3. G J N T B → GBJT F H B NNF ITN T FBB N T F → (It doesn't Follows the pattern) 4. G B N T B → GBBT F H B NNF ITN T FBB N T F → (It doesn't Follows the pattern)

⇒Option - (1) gives the pattern of "GBNT F - H B NTF - IBN T F - JB N T F"

Hence, "G N T B J" is the correct answer.

According to the sequence in the dictionary:

1. Lambast
2. Languish
3. Laughter
4. Legacy

2, Lighten

6. Lightly 

Hence, the correct option is "1, 4, 5, 3, 2, 6".

The correct mirror image of the given figure when mirror is placed at MN is as shown below:

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

Logic : (2) is added to the position value according to English alphabetic series diagonally.

So,

• PLANT : VPCNR

And,

• STOMP : ROQVU

​Similarly,

• BOARD : ?

​Hence, "FTCQD" is the correct answer.

​So,

• Option - (1) : CAX

​

• Option - (2) : AYZ

​

• Option - (3) : FDU

​

• Option - (4) : HDS

​

Thus, out of all the options 'HDS' is the odd one out as H - 4 = D 

​Hence, "HDS" is the correct answer.

Logic : 

• First letter → Increasing number series is subtracted from the position value according to English alphabetic series.
• Second letter → Increasing number series is added to the position value according to English alphabetic series.
• Third letter → (1) is subtracted from the position value according to English alphabetic series.

So,

​

​Hence, "IRL" is the correct answer.

The correct answer is use of more labour and capital inputs on the given land under cultivation.

Key Points

• Intensive agriculture, also known as intensive farming, maximizes agricultural production from a given area of land using higher inputs of labour, machinery, and other farming resources.
• This method represents a stark contrast to extensive farming, where the land is used more broadly with less management or fewer inputs per unit area.
• Intensive agriculture uses practices like irrigation, advanced fertilizers, and other technological inputs to generate a high output per unit of land, making it well-suited for regions with high population density where land is in short supply.
• The aim of this agricultural practice is to grow plentiful crops and raise large numbers of animals cheaply and rapidly, which often leads to higher environmental impact compared to less intensive farming systems.

Additional Information

• Extensive Farming:
• Extensive farming is characterized by low inputs of labour and capital per unit area of land.
• This farming method is traditionally used in regions with low agricultural productivity, such as remote, mountainous, or dry regions, where arable land is abundant.
• It has less of an impact on the environment per unit of area compared to intensive farming, as it tends not to employ large amounts of harmful fertilizers or pesticides.
• However, it usually generates less production per unit of land, which can be a potential downside in areas where the population is growing and food demand is high.
• Mechanized Farming:
• Mechanized farming is characterized by the use of machinery for various farming operations, replacing traditional manual and animal labour.
• This type of farming is usually employed in developed countries and in places where the cost of labour is high or labour is scarce.
• Mechanized farming significantly increases the efficiency and productivity of the land, making large-scale farming feasible.
• On the downside, it requires significant investment in machinery, which can be a barrier for small-scale farmers.
• Diversified Farming:
• Diversified farming involves growing a variety of crops or raising various types of livestock on the same farm to maximize output and reduce risk.
• This type of agriculture provides a variety of products, promoting food security, and can help to safeguard against the failure of a single crop or livestock.
• Diversified farming can be beneficial to the environment, promoting biodiversity and reducing the need for chemical inputs as different plants and livestock can help to control pests and replenish soil nutrients.
• However, it can require more labour, knowledge, and management compared to monocultures due to the complexity of farming multiple crops or livestock types.

The correct answer is Baji Rao ll.

Key Points

• Nana Sahib, born as Dhondu Pant, was an Indian Peshwa (prime minister) of the Maratha empire.
• He was adopted by Baji Rao II, who was the last Peshwa of the Maratha Empire.
• Nana Sahib played a significant role in the Indian Rebellion of 1857 (also known as the First War of Independence or the Sepoy Mutiny).
• He led the revolt in the region of Kanpur (Cawnpore) and despite initial successes, was defeated by British forces later on.
• After the Indian rebellion, he disappeared, and his ultimate fate was never known, leading to various theories and speculations.

Additional Information

• Baji Rao I:
• Baji Rao I served as the seventh Peshwa of the Maratha Empire from 1720 to 1740.
• Exemplifying Maratha's chivalry and valour, he is recognized for expanding the Maratha Empire, especially in the north, during his tenure.
• Some of Baji Rao's notable achievements include his victories in the Battle of Palkhed and the Battle of Bhopal.
• Baji Rao I was instrumental in the spread of Maratha influence which marked a significant shift in the Indian subcontinent's power dynamics.
• Balaji Baji Rao:
• Also known as Nana Saheb Peshwa, Balaji Baji Rao was the eldest son of Baji Rao I and served as the Peshwa of the Maratha Empire from 1740 to 1761.
• His regime in power was marked by territorial expansion via wars and the prosperity of Pune. He made Pune the effective capital of the Maratha empire and commissioned several landmark building constructions.
• However, his tenure ended tragically with the crushing Maratha defeat at the Third Battle of Panipat in 1761, leading to his death from shock.
• Balaji Vishwanath:
• Serving as the first of a series of hereditary Peshwas hailing from the Bhat family, Balaji Vishwanath held tenure from 1713 to 1720.
• Known for his diplomatic proficiency, he played a key role in consolidating Maratha power in Maharashtra and beyond.
• He managed to pacify the Mughal emperor, thereby gaining crucial legitimacy for the expansionist policies of his Maratha successors.

The correct answer is Ooty.

Key Points

• Ooty, also known as Udhagamandalam, is in the southern Indian state of Tamil Nadu.
• Despite being a hill station and experiencing lower temperatures compared to the surrounding areas, the climate doesn't become cold enough for it to experience snowfall during winters.
• This is in stark contrast to the other places listed - Nainital, Shimla, and Srinagar - which are all located in the northern part of India, and they do experience snowfall during winter due to their much colder climates.

The correct answer is Netaji Subhas Chandra Bose.

Key Points

• In a tribute to Netaji Subhas Chandra Bose, the Ministry of Education has decided to name residential schools and hostels funded under the Samagra Shiksha Scheme as "Netaji Subhas Chandra Bose residential schools/hostels".
• This is reflective of the central government's effort to honour the memory and contributions of the legendary freedom fighter, acknowledging his role as a key figure in India's freedom struggle.
• This renaming further promotes nationalistic pride and engenders a sense of historical connection among the younger generation towards the country's rich past.
• While each of the personalities listed in the options made significant contributions to India's socio-political landscape, it is Bose's name that is specifically chosen for this initiative by the Ministry of Education.

Additional Information

• Shyama Prasad Mukherjee:
• Mukherjee was an Indian politician, barrister, and academician.
• He was also the Minister for Industry and Supply in Prime Minister Jawaharlal Nehru's cabinet.
• He founded the Bharatiya Jana Sangh in 1951, which later evolved into the Bharatiya Janata Party (BJP).
• Mukherjee strongly opposed the Indian National Congress and their policies, particularly with regard to Jammu and Kashmir.
• He passed away under mysterious circumstances during a visit to Kashmir, which led to widespread protests and demands for investigations.
• Deen Dayal Upadhyaya:
• Upadhyaya was an Indian philosopher, economist, sociologist, historian, journalist, and political scientist.
• He was one of the most important leaders of the Bharatiya Jana Sangh, the forerunner of the Bharatiya Janata Party.
• Upadhyaya championed the philosophy of integral humanism, which is a synthesis of the material and the spiritual, the individual and the collective.
• He also served as the president of the Jana Sangh and strongly criticized the policies of Nehru and the Congress Party.
• Sardar Vallabhbhai Patel:
• Patel was an Indian barrister and statesman and one of the leaders of the Indian National Congress.
• He played a key role in the country's struggle for independence.
• He served as India's first Deputy Prime Minister and first Minister of Home Affairs from 1947 to 1950.
• Patel is credited with achieving political integration in India, persuading almost every princely state to accede to India.
• He is often referred to as the "Unifier of India" and his birthday, 31 October, is celebrated as Rashtriya Ekta Diwas (National Unity Day) in his honour.

The correct answer is 553^rd.

Key Points

• On 7^th November 2022, Indian Prime Minister Narendra Modi attended the celebration of the 553^rd Prakash Parv of Shri Guru Nanak Dev Ji in New Delhi.
• This event marks the birth anniversary of Guru Nanak Dev Ji, the founder of Sikhism.
• It is a significant occasion for Sikhs worldwide, celebrated with prayers and festivities.
• The Prime Minister was honoured with traditional Sikh gifts at the event - a Shawl, Siropa (a respectful term for a ceremonial robe of honour), and a Sword.
• The celebration reinforces India's commitment to upholding the teachings and values of Guru Nanak Dev Ji including equality, fraternity, and service to others.

The correct answer is a - iv, b - iii, c - ii, d - i.

Key Points

• Blue-green Algae (Cyanobacteria)
• Blue-green algae are actually bacteria and are also known as Cyanobacteria.
• They are photosynthetic organisms and can live in a wide variety of environments, including freshwater, seawater, damp soil, or rocks.
• Cyanobacteria are known for their significant contribution to the Earth's oxygen atmosphere.
• They can exist as single cells or can form colonies.
• Red Algae (Rhodophyta)
• Red algae, often called Rhodophyta, have been identified as one of the oldest groups of eukaryotic algae.
• They are mostly found in the warmer waters of the ocean.
• Red algae are of great economic value because of their use in the production of agar and carrageenan, substances used as thickening agents in various food products.
• Their red colour is due to the pigment, phycoerythrin.
• Green Algae (Chlamydomonas)
• Green algae are a diverse group of algae from which plants evolved. Chlamydomonas is a genus of unicellular green algae.
• Chlamydomonas species are widely distributed worldwide and are found in soil and freshwater.
• They have two flagella that allow them to move.
• They are known for their green colour due to the presence of chlorophyll.
• Brown Algae (Sargassum)
• Brown algae are the most complex type of algae; many are seaweeds.
• Sargassum is a brown algae, known for forming massive floating forests in the ocean.
• It is primarily marine and is found in warm-temperate and tropical oceans.
• They provide important ecological functions such as providing habitats for a wide variety of marine species.
• The brown colour is due to the presence of a pigment called fucoxanthin, which masks the green colour of chlorophyll.

The correct answer is Bile juice.

Key Points

• Bile juice is secreted by the liver and stored in the gallbladder. It is released into the small intestine when food enters.
• Bile neutralizes the acid in chyme, raising its pH and making the intestinal environment more alkaline.
• This is a critical step, as the enzymes in the small intestine that further digest food work optimally in an alkaline condition.
• Along with neutralizing the acid, bile aids in the emulsification of dietary fat, which helps in its digestion.
• It's important to note that excessive bile or reflux of bile into the stomach can cause discomfort and affect the digestive process.​

Additional Information

• Pepsin:
• Pepsin is an enzyme that is released in the stomach to break down proteins into smaller peptides during digestion.
• It is produced by the chief cells in the stomach lining and is activated by the acidic environment of the stomach.
• Pepsin is not involved in making food alkaline, instead, it assists in further breaking down food particles.
• Faulty regulation or overproduction of pepsin can lead to peptic ulcers or other gastric disorders.
• Gastric Juice:
• Gastric juice, a combination of pepsin, hydrochloric acid, and other enzymes, is secreted into the stomach to aid in the digestion of food.
• It is acidic in nature, with a pH ranging from 1.5 to 3.5, which is essential for pepsin's protein digestion process.
• The acidity of gastric juice also kills many bacteria that enter the stomach, providing a protective function against infection.
• Gastric juice is not responsible for making food alkaline, but rather for launching the initial stages of digestion in a highly acidic environment.
• Hydrochloric Acid:
• Hydrochloric acid (HCl) is one of the main components of gastric juice.
• It creates the acidic environment in the stomach needed to activate pepsin and other enzymes.
• HCl helps to break down food and kill ingested pathogens.
• Like pepsin and gastric juice, hydrochloric acid participates in digestion within the stomach, but it does not play a part in making the chyme alkaline.

The correct answer is Discovery of transistor effect.

Key Points

• In 1956, William Bradford Shockley, John Bardeen, and Walter Houser Brattain jointly received the Nobel Prize in Physics for their research on semiconductors and their discovery of the transistor effect.
• The transistor effect they discovered is a fundamental principle that forms the basis for the functioning of transistors, pivotal components in virtually all modern electronic devices.
• The development of the transistor, a semiconductor device capable of amplifying electrical signals, was instrumental in paving the path for the electronic age.
• Their work has had profound impacts on technology, including the development of computers, smartphones, audio and video devices, medical equipment, and much more.

​

Additional Information

Noble Prize:

• The Nobel Prize was established in the will of Alfred Nobel, a Swedish inventor, engineer, and industrialist. He signed his last will and testament on 27 November 1895, giving the largest share of his fortune to a series of prizes in physics, chemistry, physiology or medicine, literature, and peace - the Nobel Prizes.
• The prizes were first awarded in 1901. Each prize consists of a medal, a diploma, and a cash award, which varies each year.
• The Nobel Prizes are internationally recognized as the most prestigious awards available in their respective fields.
• They are awarded yearly by various committees and organizations. The Royal Swedish Academy of Sciences selects the Physics and Chemistry laureates, the Nobel Assembly at the Karolinska Institute selects Medicine laureates, the Swedish Academy chooses Literature, and the Nobel Peace Prize is awarded by the Norwegian Nobel Committee.
• In 1968, Sveriges Riksbank (Sweden's central bank) established The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel. Although not one of the prizes established in Alfred Nobel's will, it is widely considered to be a "Nobel Prize" in Economics.
• A Nobel Prize can be shared by up to three persons. They can either divide it equally or two together can receive a one-half share.

The correct answer is Mahanadi and Godavari.

Key Points

• Mahanadi and Godavari are two of the major rivers that are part of the Peninsular drainage system in India.
• The Peninsular River System, unlike the Himalayan River System, is mainly composed of older rivers that have a fixed course and do not substantially change direction or characteristics with seasons.
• The major rivers in this system are the Mahanadi, Godavari, Krishna, Kaveri (also known as Cauvery), Narmada, and Tapti.
• These rivers mainly drain in the rural areas of India and have not just geographical but also cultural and religious significance to the Indian people.

Additional Information

• The Himalayan Rivers
• The Himalayan Rivers are perennial, fed by both rainfall and the melting snow of the Himalayas. They flow throughout the year.
• Major rivers in this system include the Indus, Ganga, and Brahmaputra.
• These rivers have long courses, are often involved in power generation, irrigation, and they carry significant amounts of silt.
• The basin area of the Himalayan rivers is shared by several countries such as China, India, Nepal, and Bangladesh.
• Many of these rivers have spiritual and cultural significance in India.
• The Peninsular Rivers
• The Peninsular Rivers are seasonal as their flow is dependent on rainfall.
• The main rivers of this system include the Mahanadi, Godavari, Krishna, and Kaveri in the east and the Narmada and Tapti in the west.
• These rivers have shorter and shallower courses compared to the Himalayan Rivers.
• Unlike the Himalayas rivers, most of the rivers of the Peninsular system end in the Bay of Bengal, except the Narmada and Tapti which end in the Arabian Sea.
• The rivers in the peninsular system have less impact in terms of flooding and causing significant damage, unlike the rivers in the Himalayan system.
• Inland Drainage System
• This is a smaller drainage system where the rivers do not have an outlet to the sea and drain in the form of lakes and marshes.
• The Western Rajasthan, part of Gujarat, and the southern part of Punjab form the region where inland drainage prominently occurs in India.
• Luni, Machhu, Rupen, and Saraswati are rivers featured in this system.
• These water bodies sometimes disappear during the dry season, are saline, and are not very suitable for irrigation or navigation.

The correct answer is Ceylon.

Key Points

• Emperor Ashoka sent Buddhist missions to various places to spread the principles of Dhamma (Buddhist teachings).
• His son, Mahendra (also referred to as Mahinda), and daughter, Sanghamitra, were sent to Ceylon (present-day Sri Lanka).
• They played a key role in establishing Theravada Buddhism as the major religion in the region.
• Sanghamitra is known for carrying a sapling of the sacred Bodhi Tree under which Buddha achieved enlightenment, to Anuradhapura, Sri Lanka.
• The tree that grew from the sapling is known as the Jaya Sri Maha Bodhi and is one of the most sacred relics of Buddhists in Sri Lanka.
• As a result of their efforts, Buddhism grew strong roots in Sri Lanka and continues to be the majority religion there today.

Additional Information

• Ashoka:
• Ashoka, the third emperor of the Mauryan dynasty, ruled almost the entire Indian subcontinent from 268 to 232 BCE.
• He is notably remembered for his conversion to Buddhism following the Kalinga War in 262-261 BCE. The war resulted in a vast loss of life and suffering, which deeply impacted him and led to his embrace of Buddhism.
• Post-conversion, Ashoka became known for his principles of non-violence (ahimsa), love, truth, tolerance, and vegetarianism, which he called "Dhamma" or "Dharma".
• He attempted to spread these principles throughout his empire, as well as neighbouring states, via envoys and inscriptions on pillars known as the "Edicts of Ashoka".
• Ashoka is credited for significant efforts in spreading Buddhism beyond the Indian subcontinent. His son Mahendra and daughter Sanghamitra were sent on a Buddhist mission to Ceylon (current Sri Lanka).
• He also built and supported numerous stupas (Buddhist monuments), sponsored the Buddhist council, and played a pivotal role in ordaining monks and nuns.
• Ashoka's emblem of the "Lion Capital" atop the Ashoka Pillar at Sarnath, Uttar Pradesh, India, is adopted as the National Emblem of India.

The correct answer is revenue deficit.

Key Points

• When a government's revenue expenditure exceeds revenue receipts, it is termed as a revenue deficit.
• Revenue expenditure refers to the day-to-day operational expenses incurred by the government, such as salaries, pensions, and interest payments on debt. Revenue receipts are the funds that the government receives from tax collections and other sources during the normal course of operations.
• A revenue deficit essentially means that the government's own earnings are insufficient to meet the operational costs of running government departments and provision of services.
• To cover this deficit, the government may need to borrow or sell assets, which could further affect its fiscal position. It may also hint at the possibility of structural economic imbalances.​

Additional Information

• Primary Deficit:
• Primary deficit refers to the difference between the current year's fiscal deficit and interest payments on previous borrowings.
• It shows how much of the government's expenses, other than interest payments, exceed revenue.
• If the primary deficit is zero, it means that the current borrowings of the government are being used only for making interest payments.
• Capital Deficit:
• This term is not as commonly recognized in economic parlance, especially in the context of government budgeting.
• However, generally, a capital deficit could refer to a situation where a government's capital expenditures (money spent on acquiring or maintaining fixed assets like land, buildings, and equipment) exceed its capital receipts.
• Fiscal Deficit:
• A fiscal deficit is the difference between the total income of the government (total taxes and non-debt capital receipts) and its total expenditure.
• A fiscal deficit is regarded by some as a favourable economic policy, especially during times of slowdown or recession, as governments might invest in infrastructure to stimulate economic growth. However, sustained and large deficits can lead to serious problems, such as high-interest rates, inflation, and devaluation.
• Fiscal deficit gives the signal that the government is undertaking borrowings to meet its expenditure, and it is a key economic indicator, closely watched by analysts and policymakers.

The correct answer is Republic Day.

Key Points

• The Param Vir Chakra, Ashoka Chakra, and Vir Chakra, which are among India's highest military honours, are usually presented during the Republic Day celebrations.
• Republic Day, which is celebrated on January 26 every year, marks the day on which the Constitution of India came into effect, establishing India as a republic.
• The awards are presented by the President of India. It's during the Republic Day parade, that bravery and gallantry awards for military personnel are generally announced.
• It's important to note that the Ashoka Chakra can be awarded to military as well as civilian personnel and can be awarded posthumously.

​

Additional Information

• Independence Day:
• Independence Day is celebrated in India on August 15 every year, marking the country's independence from British rule in 1947.
• The Prime Minister of India hoists the Indian flag at the Red Fort in Delhi and delivers a speech addressing the nation.
• The day is marked with various cultural and patriotic events, but military awards are not typically presented on this day.
• Gandhi Jayanti:
• Gandhi Jayanti is celebrated on October 2 each year to honour the birth of Mahatma Gandhi, fondly known as the "Father of the Nation".
• This day is marked by prayer services and tributes across India, including at Raj Ghat, Mahatma Gandhi's memorial in New Delhi.
• Events like art exhibitions and essay competitions are also held, but military awards are not presented on this day.
• Indian Air Force Day:
• Indian Air Force Day is celebrated on October 8 each year to mark the foundation of the Air Force in India.
• This day is typically marked by air displays and parades at various Air Force Stations in India.
• While recognition and awards specific to the air force may be distributed, the highest military honours like the Param Vir Chakra, Ashoka Chakra, and Vir Chakra are not typically presented on this day.

The correct answer is Drums.

Key Points

• Sivamani, known by his stage name Drums Sivamani, is a renowned percussionist from India. He plays many instruments including drums, octoban, darbuka, udukai, ghatam, and kanjira.
• Over his career, he has performed in various stages and for different types of events, including the IPL Championships in 2008 and 2010.
• He has been associated with prominent musicians, like A.R. Rahman, and has performed for various compositions across film industries.

​

Additional Information

• List of Famous Musicians with Instruments:
• Santoor: Pt Shiv Kumar Sharma
• Sarod: Allauddin Khan,Amjad Ali Khan.
• Sitar: Pt Ravi Shankar, Budhaditya Mukherjee.
• Surbahar: Annapurna Devi, Sajjad Hussain.
• Rudra Veena: Asad Ali Khan, Zia Moin-ud-din Khan.

The correct answer is Malik Kafur.

Key Points

• Malik Kafur was the slave-general of Alauddin Khilji.
• He led Alauddin Khilji's army in the battle against Ramachandra of Devagiri.
• Malik Kafur's military leadership and strategic skills were instrumental in the Khilji dynasty's expansion.
• His successful campaigns contributed to the establishment of a powerful empire under Alauddin Khilji's rule.
• Malik Kafur played a key role in the history of medieval India as a **trusted general and commander in various battles.**​

Additional Information

• Alauddin Khilji was the second sultan of the Khilji dynasty.
• He was the most powerful king of this dynasty.
• He ruled for about twenty years from 1296 to 1316.
• He became the sultan of Delhi after killing his uncle and father-in-law Jalaluddin Khilji, the founder of the Khilji dynasty.
• Alauddin was a very ambitious person and a warmonger.
• He liked to call himself ‘The Second Alexander’.
• During his regime, he expanded his kingdom to a large area. He conquered Gujarat, Ranathambor, Mewar, Malwa, Jalore, Warangal, and Madurai.

The correct answer is Baiga.

Key Points

• Arjun Singh Dhurve, a tribal artist, was awarded the prestigious Padma Shri in 2022.
• Dhurve is known for his contribution to the traditional Baiga dance.
• This dance form belongs to the Baiga tribe, an ancient and significant tribe mainly residing in states like Madhya Pradesh, Chhattisgarh, Jharkhand, and Odisha.
• The Baiga dance is a folk and tribal dance that carries deep cultural and traditional significance for the Baiga tribe.
• Arjun Singh Dhurve has made significant efforts to preserve and promote this traditional dance form, ensuring its cultural heritage continues to enrich and perpetuate in contemporary society.
• The Padma Shri has been accorded to him in recognition of his invaluable contribution and efforts towards keeping the traditional art form alive and relevant.

Additional Information

• Chhau:
• Chhau is a traditional dance form originating from eastern India, particularly regions of Jharkhand, West Bengal, and Odisha.
• It's a unique fusion of martial arts, folk traditions, and classical Indian dance elements.
• The dance is notable for its mask use, dramatic representations, and storytelling through movement.
• Santhal:
• The Santhal dance is a folk dance performed by the Santhal tribes, one of the largest tribal communities in India.
• Predominantly found in West Bengal, Bihar, Orissa, Jharkhand and Assam, the dance is a major part of their cultural identity.
• Santhal dance is often performed in large groups and is prominently accompanied by musical instruments like drums, flutes, and fiddles.
• Tertali:
• The Tertali dance is a ritualistic dance form performed by the Kamar tribes, who primarily inhabit areas of Madhya Pradesh.
• The dance usually involves two or three women sitting on the ground while clanging small metal cymbals (Manjiras) tied to their hands and singing folk tales.
• The Tertali dancers often channel unseen forces during their performances, making this dance form a captivating spiritual experience.

The correct answer is 2.

Key Points

• Generally, there are two on-field umpires in cricket matches.
• One umpire typically stands behind the stumps at the bowler's end, which provides a clear view of the bowler's action, the line and length of the delivery, and the batsman's shots.
• The second umpire stands at square leg or a little behind, allowing them to judge line calls more accurately, such as wides or no-balls due to front foot faults. They can also observe short runs and can assist the main umpire with decisions that require a side-on perspective.
• The umpires have the power to make decisions according to the 'Laws of Cricket' regarding all aspects of play, such as fair and unfair play, player conduct, and decisions on whether batsmen are out or not.
• In addition to these two on-field umpires, there is also usually a third (off-field) umpire and sometimes a fourth umpire, who assist the on-field umpires with certain decisions using video replays and other technologies, among other duties.

The correct answer is Sattriya.

Key Points

• Borgeet is associated with the Sattriya Indian classical dance form.
• It is a genre of devotional music from Assam, composed to praise Lord Krishna.
• Borgeet adds a spiritual dimension to Sattriya dance performances.
• It combines rhythmic movements with soulful melodies, creating a harmonious expression of devotion.
• Sattriya dance, accompanied by Borgeet, offers a unique cultural and artistic experience from the northeastern region of India.

Additional Information

Eight Classical Dances of India and States: 

The correct answer is Insurance.

Key Points

• 'BFSI' stands for Banking, Financial Services, and Insurance in India.
• It represents a wide range of industries that provide financial products and services to individuals and businesses.
• The term encompasses banking, involving deposit and loan services.
• It includes financial services like investment advice and wealth management.
• Insurance, a key component, offers risk coverage and financial protection.
• The BFSI sector is crucial for the economy, contributing to financial stability and growth.

The correct answer is Increases.

Key Points

• The atomic size increases as you go down a group in the periodic table.
• This increase is due to the addition of new electron shells or energy levels.
• As more electron shells are added, the outermost electrons are farther from the nucleus.
• The increased shielding effect from inner electrons also contributes to the larger atomic size.
• This trend of increasing atomic size down a group is observed across the periodic table's elements.

The correct answer is Swaran Singh Committee.

Key Points

• The Fundamental Duties of citizens were incorporated into the Constitution of India.
• This addition was based on the recommendations of the Swaran Singh Committee.
• The committee, chaired by Swaran Singh, was tasked with studying the feasibility of including Fundamental Duties.
• The 42^nd Amendment Act of 1976 introduced these Fundamental Duties to the Indian Constitution.
• These duties emphasize the **responsibilities of citizens towards the nation's integrity, harmony, and progress.**​

Additional Information

• Raja Chelliah Committee:
• The Raja Chelliah Committee was formed in 1991 to suggest tax reforms in India.
• It focused on economic and taxation policies, aiming to improve revenue collection and promote economic growth.
• Its recommendations led to significant changes in India's tax structure and policies.
• Santhanam Committee:
• The Santhanam Committee, officially known as the Committee on Prevention of Corruption, was established in 1962.
• It aimed to examine measures to combat corruption in various government departments and organizations.
• The committee's findings and recommendations contributed to the strengthening of anti-corruption efforts in India.
• Kelkar Committee:
• The Kelkar Committee, led by Vijay Kelkar, has been associated with multiple economic and financial reforms in India.
• It has provided recommendations on fiscal policies, taxation, and economic reforms to boost growth and development.
• The committee's reports have influenced important economic decisions taken by the Indian government.

The correct answer is James Augustus Hickey.

Key Points

• The first newspaper in India, "The Bengal Gazette," was established by James Augustus Hickey.
• James Augustus Hickey was an Irishman who started the newspaper in 1780 during the colonial period.
• "The Bengal Gazette" is also known as the Calcutta General Advertiser.
• This newspaper marked a significant milestone in Indian media history, becoming the pioneer of journalism in the country.
• James Hickey's initiative laid the foundation for the development and growth of the press in India.

Additional Information

• Deen Bandhu Mitra:
• Deen Bandhu Mitra was a Bengali playwright, poet, and journalist during the 19^th century.
• He is best known for his play "Nil Darpan," which highlighted the oppression faced by indigo farmers under British rule.
• Deen Bandhu Mitra made significant contributions to Bengali literature and social issues.
• Hem Chandrakar:
• Hem Chandrakar was an Indian social worker and a prominent figure in the tribal and rural development movement.
• He worked towards the welfare and upliftment of tribal communities, focusing on education and empowerment.
• However, Hem Chandrakar was not associated with the publication of the first newspaper in India.
• Harishchandra Mukherjee:
• Harishchandra Mukherjee was an influential journalist and reformer in 19^th-century India.
• He was the editor of "Hindu Patriot," a newspaper that was instrumental in promoting the Indian nationalistic sentiment during the British Raj.
• Mukherjee was also heavily involved in social reform, contributing notably to the cause of widow remarriages in India.
• He was a supportive voice for the Indian Rebellion of 1857 through his writings in the Hindu Patriot.

The correct answer is India and Bangladesh

Key Points

• The 2031 Cricket World Cup will be co-hosted by India and Bangladesh.
• The decision was announced by the International Cricket Council (ICC) confirming the landmark event.
• This event is significant as it showcases the collaboration between two major cricketing nations in South Asia.
• Cricket is exceedingly popular in both countries, and jointly hosting the World Cup symbolizes their strong commitment towards promoting and developing the sport.
• It will also be an opportunity for these nations to showcase their unique culture, hospitality, and the big strides they have made in infrastructure and facilities necessary to host such a major global sporting event.

Additional Information

• International Cricket Council (ICC):
• The ICC is the global governing body for the sport of cricket.
• The organization was originally founded as the 'Imperial Cricket Conference' in 1909 by representatives from Australia, England, and South Africa. It was renamed to the 'International Cricket Conference' in 1965, and then took its current name in 1987.
• The ICC’s main activities include governing cricket internationally, organizing international tours, competitions, and managing the rules, regulations, and equipment for the game.
• It is also responsible for the staging of all ICC Events, including the Cricket World Cup, among others.
• The ICC presides over the ICC Code of Conduct, playing conditions, the Decision Review System, and other related matters.
• The headquarters of the ICC is in Dubai, United Arab Emirates. It manages all operational matters from Dubai and administrates the game globally.

The correct answer is Matrushakti Udaymita Scheme.

Key Points

• Matrushakti Udaymita Scheme was announced to facilitate women entrepreneurs in Haryana and to provide them with a supportive ecosystem for business.
• The primary aim of this scheme is to create better opportunities for women in the business sector and to uplift their socioeconomic status.
• This initiative by the Haryana government reflects their efforts toward gender equality and women's empowerment.
• The announcement was notably made on International Women's Day 2022, which emphasizes the significance of the initiative in promoting gender parity.
• The Matrushakti Udaymita Scheme is a part of several initiatives being undertaken by various governments in India to encourage female entrepreneurship and to reduce gender disparity in the business environment.

Additional Information

• UJJWALA Scheme:
• The Pradhan Mantri Ujjwala Yojana (PMUY), also known as the UJJWALA Scheme, is a social welfare program initiated by the Indian Government.
• It was launched with the primary objective of providing clean cooking fuel to poor households in rural and semi-urban areas.
• The scheme supports providing LPG connections to families below the poverty line.
• Mahila E-Haat Scheme:
• Mahila E-haat was launched by the Ministry of Women and Child Development, Government of India, to encourage women entrepreneurs and self-help groups (SHGs).
• This direct online marketing platform provides a space for women to showcase their products across the globe without any charge.
• The objective is to strengthen the financial inclusion of women entrepreneurs in the economy by providing a platform where they can market their products worldwide.
• SWADHAR Scheme:
• The SWADHAR Scheme is an effort by the Ministry of Women and Child Development in India to uplift and provide a better life to women in moral danger due to circumstances.
• The scheme provides a supportive institutional framework where women can be protected and rehabilitated.
• Services provided under this scheme include food, shelter, counselling, vocational training, and legal aid to manage their personal and social issues.

The correct answer is A and B only.

Key Points

• The subjects which are not included in any of the three lists are called Residuary subjects.
• According to the Indian Constitution, the residuary subjects, or those subjects that are not mentioned in any of the three lists (Union List, State List, or Concurrent List), fall under the authority of the Central Government. Hence, Statement A is correct.
• If there is any conflict between the Union List and the State List, then the former prevails.
• In case of a conflict between the Union and State Lists, the law made by the Union Parliament prevails over the State law.
• This is to ensure the supremacy of the national perspective over regional interests. Hence, Statement B is also correct.
• When the Parliament enacts a law on the request of two or more states, then that law made by the Parliament on the State List is applicable to all the states. This is incorrect.
• If two or more states request the Parliament to enact a law on a subject that falls under the State List, then this law is applicable only to those states that requested it and any other states that later adopt it, not to all states. Hence, Statement C is incorrect.

The correct answer is 919 females per 1000 males.

Confusion Points

• SSC has given 914 as the correct answer, but according to census 919 is the correct answer. So we have updated the option and answer accordingly.

Key Points

• The child sex ratio in India, according to the 2011 Census, was 919females per 1000 males.
• This ratio is a noteworthy demographic indicator that reflects the societal condition and status of females in the country.
• The ratio is calculated among children aged 0-6 years, considered to be a crucial age group due to the particular attention required for their growth and development.
• The data from the 2011 census has been utilized in setting up and implementing various child welfare, gender equality and female empowerment measures within the country.
• Low sex ratio in India is a subject of concern for policymakers, as it may suggest gender-based discrimination. Therefore, measures are continuously undertaken to improve this scenario.

Additional Information

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

Important Points

• According to the State Census 2011,
• The most populated state in India is Uttar Pradesh with a population of 19.96 crores.
• The least populated state in the country is Sikkim with a population of 6,07,688.
• Mizoram is the second least populous state in India with around 1,091,014 population.
• Arunachal Pradesh is the third least populous state.

Concept used:

Calculation:

18 ÷ {(6 of 2 - 4)} × 5(6 - 3)

⇒ 18 ÷ {(12 - 4)} × 5 × 3

⇒ 18 ÷ 8 × 5 × 3

⇒ (9/4) × 5 × 3

⇒ 135/4

∴ The correct answer is 135/4.

Calculation:

Total fund got by school = 100% = 1000000

Funds got through donation = 35%

Scholarship paid = 26% 

Required percentage = 26/35 × 100

⇒ 2600/35 = 74.285% ≈ 74.29%

∴ The correct answer is 74.29%.

Given:

15 men + 21 women can do a job = 56 days

12 men + 24 women can do a job = 64 days

Formula used:

Total work = efficiency × time

Calculation:

Let, the man efficiency = M

The woman efficiency = W

According to the question:

⇒ (15 M + 21 W) × 56 = (12 M + 24 W) × 64

⇒ (15 M + 21 W) × 7 = (12 M + 24 W) × 8

⇒ 105 M - 96 M =  192 W - 147 W

⇒ 9 M = 45 W

⇒ M/W = 5/1

Total work = (15 M + 21 W) × 56

⇒ {(15 × 5) + 21) × 56} = (96 × 56) units

Total efficiency = 18 M + 24 W

⇒ (18 × 5) + 24 × 1 = 114 units

Required time taken to complete work = Total work/total efficiency

⇒ (96 × 56)/114 = (16 × 56)/19 = 47$\frac{3}{19}$ days

∴ The correct answer is 47$\frac{3}{19}$ days.

Given:

New dividend = 110% × original dividend

New divisor = 125% × original divisor

Formula used:

Dividend = divisor × quotient + remainder 

Calculation:

Let the original dividend = 100x

Mistakenly increased dividend = 100 × 110% = 110x

Let original divisor = 100y

Mistankenly increased divisor = 100y × 125% = 125y

Dividend = divisor × quotient + remainder 

100x = 100y × 25 + 0

x/y = 25/1

Increased dividend = 110x = 110 × 25 = 2750

Increased divisor = 125y = 125 × 1 = 125

Quotient = 2750/125 = 22

∴ The correct answer is 22.

Shortcut Trick

Let CP = x and SP = y. Original Profit = y − x.

New SP = 2y. New Profit = 2y − x.

According to the question: 2y − x = 4 × (y − x).

⇒ 2y − x = 4y − 4x ⇒ 3x = 2y ⇒ y/x = 3/2.

Profit % = (3 − 2) ÷ 2 × 100 = 1/2 × 100 = 50%.

∴ The correct answer is 50%.

Alternate Method

Given: New SP is twice the original SP; New Profit is four times the original profit.

Formulas: Profit = SP − CP | Profit% = (Profit ÷ CP) × 100

⇒ Let CP = 100 and Profit = P. Then SP = 100 + P.

⇒ New SP = 2 × (100 + P) = 200 + 2P.

⇒ New Profit = New SP − CP = (200 + 2P) − 100 = 100 + 2P.

⇒ According to the condition: 100 + 2P = 4P.

⇒ 2P = 100 ⇒ P = 50.

⇒ Profit% = (50 ÷ 100) × 100 = 50%.

∴ The correct answer is 50%.

Additional Information

Profit and Loss Basic Concepts

Profit occurs when the selling price (SP) is greater than the cost price (CP). Profit = SP − CP.

Percentage Calculation

Profit percentage is always calculated on the Cost Price (CP) unless stated otherwise. Profit% = (Profit/CP) × 100.

Given:

Height of building = 1000 m

Angle of elevation = 30°

Formula used:

Tan θ = perpendicular/Base = P/B

Tan 30° = 1/√3

Value of √3 = 1.732 

Calculation:

 

Tan 30° = AB/BC

⇒ 1/√3 = 1000/BC

⇒ BC = 1000√3

⇒ BC = 1000 × 1.732 = 1732 m

∴ The correct answer is 1732 m.

Given:

A can do 20% of a job = 7 days

B can do 25% of the job = 7 days

Formula used:

Total work = efficiency × time

Calculation:

A can do 20% of a job = 7 days

A can do 100% of a job = 7 × 5 = 35 days

B can do 25% of the job = 7 days

B can do 100% of the job = 7 × 4 = 28 days

According to the question:

⇒ A × 35 = B × 28

⇒ A/B = 4/5

Total work = A × 35 = 4 × 35 = 140 units

Both work together for 7 days = (5 + 4) × 7

⇒ 9 × 7 = 63 units

Percentage job complete in 7 days = (63 × 100)/140

⇒ 9 × 5 = 45%

∴ The correct answer is 45%.

Formula used:

sin4 θ + cos4 θ = (sin2θ + cos2θ)2 - 2 sin2  θ × cos2 θ = 1 - 2 sin2  θ × cos2 θ

Calculation:

(sin4 θ + cos4 θ)/(1 - 2 sin2 θ × cos2 θ)  

⇒ (1 - 2 sin2 θ × cos2 θ)/(1 - 2 sin2 θ × cos2 θ)

⇒ 1

∴ The correct answer is 1.

Given:

$\rm \frac{X-5Y}{X+5Y}=\frac{7}{13}$

Calculation:

⇒ $\rm \frac{X-5Y}{X+5Y}=\frac{7}{13}$

⇒ 13 × (X - 5Y) = 7 × (X + 5Y)

⇒ 13 X - 65 Y = 7 X + 35 Y

⇒ 13 X - 7 X = 65 Y + 35 Y

⇒ 6 X = 100 Y

⇒ X/Y = 100/6 = 50/3

∴ The correct answer is 50/3.

Calculation:

Average score of Angela = (62.50 + 65 + 64.5)/3 = 192/3 = 64

Average score of Maria = (69.05 + 70 + 67.52)/3 = 206.57/3 = 68.85

Average score of Sareena = (73.81 + 72.5 + 74.2)/3 = 220.51/3 = 73.50

Average score of Preeti = (74.3 + 75 + 77.5)/3 = 226.8/3 = 75.6

Average score of Deepika = (64.29 + 67.50 + 63.28)/3 = 195.07/3 = 65.02

∴ The correct answer is Preeti.

Shortcut Trick

If x + 1/x = k, then x² + 1/x² = k² − 2.

Given k = 10, then x² + 1/x² = 10² − 2 = 98.

To find x⁴ + 1/x⁴, apply the same logic to x² + 1/x².

x⁴ + 1/x⁴ = 98² − 2 = 9604 − 2 = 9602.

∴ The correct answer is 9602.

Alternate Method

Given: x + 1/x = 10

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

Step 1: Square both sides of the given equation.

⇒ (x + 1/x)² = 10²

⇒ x² + (1/x)² + 2 × x × (1/x) = 100

⇒ x² + 1/x² + 2 = 100

⇒ x² + 1/x² = 98

Step 2: Square both sides of the resulting equation to find the value of the fourth power.

⇒ (x² + 1/x²)² = 98²

⇒ (x²)² + (1/x²)² + 2 × x² × (1/x²) = 9604

⇒ x⁴ + 1/x⁴ + 2 = 9604

⇒ x⁴ + 1/x⁴ = 9604 − 2

⇒ x⁴ + 1/x⁴ = 9602

∴ The correct answer is 9602.

Additional Information

Algebraic Identity for Squares

The fundamental identity used is (a + b)² = a² + b² + 2ab. When b is the reciprocal of a, the term 2ab simplifies to 2.

Successive Squaring Property

To reach power 4, we must square the base expression twice. If x + 1/x = k, then x² + 1/x² = k² − 2, and x⁴ + 1/x⁴ = (k² − 2)² − 2.

Shortcut for Squaring Numbers near 100

To calculate 98², use (100 − 2)² = 10000 − 400 + 4 = 9604. This helps in speeding up algebraic simplifications.

Given:

Marked price (M.P) = 120% × cost price (C.P)

Discount (D%) = 15%

Formula used:

C.P/M.P = (100 - D%)/(100 + P%)

Calculation:

Marked price (M.P) = 120% × cost price (C.P)

M.P/C.P = 120/100 = 6/5

According to the question:

C.P/M.P = (100 - D%)/(100 + P%)

⇒ 5/6 = (100 - 15)/(100 + P%)

⇒ 5/6 = 85/(100 + P%)

⇒ (100 + P%) = (85 × 6)/5

⇒ P% = 102 - 100 = 2%

∴ The correct answer is 2%.

Shortcut Trick

Let the six-digit number be N, where N is divisible by 33.

New number = N + 54.

Since 33 is a multiple of 3 (33 = 3 × 11), N is also divisible by 3.

The number 54 is also divisible by 3 (5 + 4 = 9).

Sum of two numbers divisible by 3 is always divisible by 3.

∴ The correct answer is 3.

Alternate Method

Given:

Original number (N) is divisible by 33.

Addition constant = 54.

Calculations:

⇒ If N is divisible by 33, then N = 33k (where k is an integer).

⇒ New number = 33k + 54.

⇒ Factor out the common divisor: 3(11k + 18).

⇒ Since 3 is a factor of the expression, the new number must be divisible by 3.

⇒ Checking other options: 54 is not divisible by 33, 11, 2 (if N is odd), 5, or 7.

∴ The correct answer is 3.

Additional Information

Divisibility Rule of 3

A number is divisible by 3 if the sum of its digits is divisible by 3.

Divisibility Rule of 33

A number is divisible by 33 if it is simultaneously divisible by both 3 and 11.

Property of Divisors

If d divides a and d divides b, then d must divide (a + b).

Given:

AD ⊥ BC ; ∠D = 90° 

AC = 26 units; CD = 10 units; BC = 42 units

∠DAC = x and ∠B = y

Formula used:

Pythagorean theorem:

H² = P² + B²

Cos θ = B/H ; tan θ = P/B

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

Calculation:

In △DAC

⇒ AC² = AD² + CD²

⇒ 26² = AD2 + 10²

⇒ 676 = AD2 + 100

⇒ AD = √(676 - 100) = √576 = 24 units

In △ADB

BD = (BC - CD) = (42 - 10) = 32 units

⇒ AB2 = AD2 + BD2

⇒ AB2 = 242 + 322

⇒ AB2 = 576 + 1024

⇒ AB = √1600 = 40 units

From the question:

$\rm \frac{6}{\cos x}-\frac{5}{\cos y}+8\tan y$

⇒ 6/(AD/AC) - 5/(BD/AB) + 8 × (AD/BD)

⇒ 6/(24/26) - 5/(32/40) + 8 × (24/32)

⇒ (6 × 26/24) - (5 × 40/32) + 8 × (24/32)

⇒ 6.5 - 6.25 + 6

⇒ 6.25 = 25/4 units

∴ The correct answer is 25/4 units.

Given:

Radius of circle = 10 cm

Angle subtended at center = 60° 

Formula used:

Area of sector = (π × R² × θ)/360

Calculation:

Area of sector = (π × R2 × θ)/360

⇒ (3.14 × 10² × 60)/360 = 314/6 = 52.33 cm²

∴ The correct answer is 52.33 cm2.

Shortcut Trick

When melting and recasting spherical balls, the sum of the cubes of the diameters of the smaller balls equals the cube of the diameter of the original ball.

D³ = d₁³ + d₂³ + d₃³

3³ = (1.5)³ + 2³ + d₃³

27 = 3.375 + 8 + d₃³ ⇒ d₃³ = 15.625

d₃ = 2.5 cm (Since 2.5 × 2.5 × 2.5 = 15.625)

∴ The correct answer is 2.5 cm.

Alternate Method

Given: Diameter of the large lead ball (D) = 3 cm. Diameters of the two smaller balls are d₁ = 3/2 = 1.5 cm and d₂ = 2 cm.

Formula Used: Volume of a sphere = (4/3) × π × r³ = (1/6) × π × D³.

⇒ Total Volume of large ball = Sum of Volumes of three smaller balls.

⇒ (π/6) × (D)³ = (π/6) × (d₁)³ + (π/6) × (d₂)³ + (π/6) × (d₃)³

⇒ D³ = d₁³ + d₂³ + d₃³

⇒ (3)³ = (1.5)³ + (2)³ + d₃³

⇒ 27 = 3.375 + 8 + d₃³

⇒ 27 = 11.375 + d₃³

⇒ d₃³ = 27 − 11.375 = 15.625

⇒ d₃ = ³√15.625

⇒ d₃ = 2.5 cm

∴ The correct answer is 2.5 cm.

Additional Information

Volume of a Sphere

The amount of space occupied by a 3D circle is given by V = (4/3)πr³, where r is the radius.

Volume in Terms of Diameter

Substituting r = D/2 into the volume formula gives V = (π/6)D³.

Conservation of Volume

In melting and recasting problems, the total volume remains constant as long as there is no wastage during the process.

Surface Area of Sphere

The total surface area is given by A = 4πr² or A = πD².

Given:

The time taken to complete first part of the journey = 37.5 minutes

The speed of a person in first part of the journey = 90 km/h

The time taken to complete remaining part of the journey = 14 minutes

The speed of a person for remaining part of the journey = 80 km/h

Formula used:

Distance = speed × time

Calculation:

Distance travelled by a person in first part = (90 × 37.5)/60 = 225/4 = 56$\frac{1}{4}$ km

Distance travelled by a person in second part = (80 × 14)/60 = 56/3 = 18$\frac{2}{3}$ km

Total distance covered by the person = 56$\frac{1}{4}$ + 18$\frac{2}{3}$ 

⇒ (56 + 18) + $\frac{1}{4}$ +  $\frac{2}{3}$ = 74 + $\frac{11}{12}$ = 74$\frac{11}{12}$ km

∴ The correct answer is 74$\frac{11}{12}$ km.

Shortcut Trick

The extra amount spent by the 20^th student over the average is shared by the other 19 students.

Increase in average per student = Extra amount ÷ Remaining students

⇒ Increase = 19 ÷ 19 = ₹1

Actual Average = Individual spend + Increase = 175 + 1 = ₹176

Total money spent = Total students × Average = 20 × 176 = ₹3,520

∴ The correct answer is ₹3,520.

Alternate Method

Given:

Total number of students = 20

Amount spent by 19 students = ₹175 each

Amount spent by 20^th student = Average + ₹19

Formula Used:

Total Expenditure = Average (A) × Total Students (n)

Let the average expenditure of all 20 students be x.

⇒ Total expenditure = 20 × x

⇒ Total expenditure = (Sum of 19 students) + (Expenditure of 20^th student)

⇒ 20x = (19 × 175) + (x + 19)

⇒ 20x = 3325 + x + 19

⇒ 20x − x = 3344

⇒ 19x = 3344

⇒ x = 3344 ÷ 19 = 176

⇒ Total money spent = 20 × 176 = 3520

∴ The correct answer is ₹3,520.

Additional Information

Concept of Average

Average is the sum of all observations divided by the total number of observations. Average = Sum ÷ n.

Net Deviation Method

The sum of deviations of all observations from the Arithmetic Mean is always zero. This property is used to solve complex average problems quickly.

Weighted Average

When different groups have different averages, the combined average is (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Shortcut Trick

Total Simple Interest percentage = (3 ÷ 5) × 100 = 60%

We know directly that Total SI% = Rate × Time

60% = Rate × 12

Rate = 60 ÷ 12 = 5%

∴ The correct answer is 5% p.a.

Alternate Method

⇒ Let the Principal amount be P and the Rate of interest be R% p.a.

⇒ Given Time (T) = 12 years

⇒ Simple Interest (SI) after 12 years = (3 ÷ 5) × P

⇒ Formula: Simple Interest = (P × R × T) ÷ 100

⇒ (3 ÷ 5) × P = (P × R × 12) ÷ 100

⇒ 3 ÷ 5 = (12 × R) ÷ 100

⇒ R = (3 × 100) ÷ (5 × 12)

⇒ R = 300 ÷ 60

⇒ R = 5

∴ The correct answer is 5% p.a.

Additional Information

Simple Interest vs Compound Interest

Simple Interest is strictly calculated only on the principal amount, whereas Compound Interest is calculated on the principal amount as well as the accumulated interest from previous periods.

Difference between CI and SI

For 2 years, Difference = P × (R ÷ 100)². For 3 years, Difference = P × (R ÷ 100)² × (3 + R ÷ 100).

Compound Interest Formula

Amount = P × (1 + R ÷ 100)ⁿ, where n is the number of years or compounding periods. The Compound Interest is obtained by subtracting the Principal from the Amount (CI = Amount − P).

Formula used:

(A² - B²) = (A - B) × (A + B)

Calculation:

$\frac{3.35^2-1.25^2}{3.35+1.25}$

⇒ {(3.35 - 1.25) × (3.35 + 1.25)}/(3.35 + 1.25)

⇒ (3.35 - 1.25) = 2.10

∴ The correct answer is 2.10.

Shortcut Trick

Relation between Area of Sector (A), Radius (r), and Arc Length (l) is A = (1/2) × l × r.

32π = (1/2) × l × 12

32π = 6 × l

l = 32π / 6 = 16π / 3

∴ The correct answer is 16/3 π cm.

Alternate Method

Given:

Radius (r) = 12 cm

Area of Sector = 32π cm²

Formula Used:

Area of Sector = (θ/360°) × πr²

Length of Arc (l) = (θ/360°) × 2πr

Calculations:

⇒ 32π = (θ/360°) × π × (12)²

⇒ 32π = (θ/360°) × 144π

⇒ θ/360° = 32 / 144 = 2 / 9

⇒ Length of Arc (l) = (2 / 9) × 2 × π × 12

⇒ l = (2 / 9) × 24π

⇒ l = (2 × 8π) / 3

⇒ l = 16π / 3 cm

∴ The correct answer is 16/3 π cm.

Additional Information

Area and Arc Relationship

The Area of a sector is also given by (l × r) / 2, where l is the arc length and r is the radius.

Perimeter of Sector

The Perimeter of a sector is the sum of the arc length and twice the radius: P = l + 2r.

Circumference of Circle

The total circumference of a circle is 2πr, representing a central angle of 360°.

Concept used:

The diameter is the longest chord of a circle.

Calculation:

Radius is not a chord. so this statement that states that radius is the longest chord of a circle is incorrect.

∴ The correct option is 1.

Given:

A can complete a work = 18 days.

B can complete a work = 12 days.

Formula used:

Total work = efficiency × time

Calculation:

According to the question:

⇒ (B × 4) + A × D = 36

⇒ (3 × 4) + 2 × D = 36

⇒ 2 × D = 36 - 12

⇒ D = 24/2 = 12

∴ The correct answer is 12 days.

Given:

Total race between A and B = 18 km

Length of a circular track = 800 m

Time taken by A to complete the 1^st round = 200 sec

Time taken by B to complete the 1^st round = 250 sec

Formula used:

Distance = speed × time

Calculation:

Total race between A and B = 18 km = 18000 m

Number of rounds to complete the race = 18000/800 = 22.5 rounds

Time taken by A to complete the 1^st round = 200 sec

For 22.5 round = 200 × 22.5 = 4500 sec.

When A and B start running,

The first meeting will occur at L.C.M (200, 250) = 1000 sec.

Fourth meet will be = 1000 × 4 = 4000 sec.

For the next meeting,

Time would be 5000 sec, which is impossible as A completes the race in 4500 sec.

But, to complete 22.5 rounds A takes 4500 sec. So the time cannot be more than 4500 sec.

So, the faster person meets the slower person at 4000 sec.

∴ The correct option is 2.

Calculation:

(3x - 2y)³ = (3x)³ - (2y)³ - 3 × (3x)² × (2y) + 3 × 3x × (2y)²

⇒ 27x³ - 8y³ - 54x²y - 4x²y + 36 xy² - 5xy² = (3x - 2y)3 - 4x²y - 5xy²

⇒ 27x3 - 58x2y + 31xy2 - 8y3 = (3x - 2y)3 - 4x2y - 5xy2

Now we put the value of x = - 5 and y = - 7

(3x - 2y)3 - 4x2y - 5xy2 

⇒ {3 × (- 5) - 2 × (- 7)}³ - 4 × (- 5)² × (- 7) - 5 × (- 5) × (- 7)²

⇒ {- 15 + 14}³ + 4 × 25 × 7 + 25 × 49

⇒ (-1)³ + 700 + 1225

⇒ 1925 - 1 = 1924

∴ The correct answer is 1924.

The correct answer is: Be in a difficult situation from where escape is difficult

Key Points

• The idiom 'back against the wall' means being in a difficult or hopeless situation. (किसी कठिन या निराशाजनक स्थिति में होना)
• For example: With his back against the wall, he had no choice but to come up with a creative solution to the challenging problem.
• It implies that there are no options left to escape or find a way out.
• The phrase is often used in situations where one is facing a challenge or an obstacle that seems insurmountable.
• The origin of the idiom is unclear, but it may have come from the idea of being trapped in a corner with no way out.

Therefore, the correct answer is option 2.

Additional Information

• Option 1: It is the opposite of the correct meaning of the idiom.
• Option 3: It is not related to the idiom and is a misinterpretation.
• Option 4: It is the opposite of the correct meaning of the idiom.