SSC CGL 2023 Tier-I Official Paper (Held on: 27 Jul 2023 Shift 3) (Previous Year Paper)

The logic followed here is :-

(First number × 2) - 4

• 19 : 34 → (19 × 2) - 4 = 38 - 4 = 34

and

• 5 : 6 → (5 × 2) - 4 = 10 - 4 = 6

Similarly,

• 27 : ? → (27 × 2) - 4 = 54 - 4 = 50

Hence, the correct answer is "50".

The logic followed here is :-

(First number × Second number) + 4

• (4, 3, 16) → (4 × 3) + 4 = 12 + 4 = 16

and

• (6, 4, 28) → (6 × 4) + 4 = 24 + 4 = 28

Similarly,

• (8, 2, 20) → (8 × 2) + 4 = 16 + 4 = 20

Hence, the correct answer is "(8, 2, 20)".

The logic followed here is :-

By using BODMAS RULE :

Option 1) : × and –

Given equation is : 171 ÷ 3 – 16 + 72 × 412 = 572 

After interchanging the two signs the equation is as follows : 171 ÷ 3 × 16 + 72 - 412 = 572

⇒ 171 ÷ 3 × 16 + 72 - 412 = 572

⇒ 57 × 16 + 72 - 412 = 572

⇒ 912 + 72 - 412 = 572

⇒ 984 - 412 = 572

⇒ 572 = 572

LHS = RHS

Option 2) : ÷ and –

Given equation is : 171 ÷ 3 – 16 + 72 × 412 = 572 

After interchanging the two signs the equation is as follows : 171 - 3 ÷ 16 + 72 × 412 = 572

⇒ 171 - 3 ÷ 16 + 72 × 412 = 572

⇒ 171 - 0.1875 + 72 × 412 = 572

⇒ 171 - 0.1875 + 29664 = 572

⇒ 29835 - 0.1875 = 572

⇒ 29834.1875 ≠ 572

LHS ≠ RHS

Option 3) : ÷ and +

Given equation is : 171 ÷ 3 – 16 + 72 × 412 = 572 

After interchanging the two signs the equation is as follows : 171 + 3 - 16 ÷ 72 × 412 = 572

⇒171 + 3 - 16 ÷ 72 × 412 = 572

⇒171 + 3 - 0.22 × 412 = 572

⇒171 + 3 - 91.55 = 572

⇒174 - 91.55 = 572

⇒82.44 ≠ 572

LHS ≠ RHS

Option 4) : – and +

Given equation is : 171 ÷ 3 – 16 + 72 × 412 = 572 

After interchanging the two signs the equation is as follows : 171 ÷ 3 + 16 - 72 × 412 = 572

⇒ 171 ÷ 3 + 16 - 72 × 412 = 572

⇒ 57 + 16 - 72 × 412 = 572

⇒ 57 + 16 - 29664 = 572

⇒ 73 - 29664 = 572

⇒ -29591 ≠ 572

LHS ≠ RHS

Hence, the correct answer is "× and –".

The logic followed here is :-

1) EBV

2) GET

3) BYY

4) JGQ

∴ Here, 'GET' is different from other three alternatives.

Hence, the correct answer is "GET".

The logic followed here is :-

By using BODMAS RULE :

Option 1) : + and ×

Given equation is : 17 × 4 + 6 ÷ 2 – 27 = 92

After interchanging the two signs the equation is as follows : 17 + 4 × 6 ÷ 2 - 27 = 92

⇒ 17 + 4 × 6 ÷ 2 - 27 = 92

⇒ 17 + 4 × 3 - 27 = 92

⇒ 17 + 12 - 27 = 92

⇒ 29 - 27 = 92

⇒ 2 ≠ 92

LHS ≠ RHS

Option 2) : ÷ and ×

Given equation is : 17 × 4 + 6 ÷ 2 – 27 = 92

After interchanging the two signs the equation is as follows : 17 ÷ 4 + 6 × 2 - 27 = 92

⇒ 17 ÷ 4 + 6 × 2 - 27 = 92

⇒ 4.25 + 6 × 2 - 27 = 92

⇒ 4.25 + 12 - 27 = 92

⇒ 16.25 - 27 = 92

⇒ 10.75 ≠ 92

LHS ≠ RHS

Option 3) : + and -

Given equation is : 17 × 4 + 6 ÷ 2 – 27 = 92

After interchanging the two signs the equation is as follows: 17 × 4 - 6 ÷ 2 + 27 = 92

⇒ 17 × 4 - 6 ÷ 2 + 27 = 92

⇒ 17 × 4 - 3 + 27 = 92

⇒ 68 - 3 + 27 = 92

⇒ 95 - 3 = 92

⇒ 92 = 92

LHS = RHS

Option 4) : ÷ and +

Given equation is : 17 × 4 + 6 ÷ 2 – 27 = 92

After interchanging the two signs the equation is as follows : 17 × 4 ÷ 6 + 2 - 27 = 92

⇒ 17 × 4 ÷ 6 + 2 - 27 = 92

⇒ 17 × 0.66 + 2 - 27 = 92

⇒ 11.33 + 2 - 27 = 92

⇒ 13.33 - 27 = 92

⇒ 13.66 ≠ 92

LHS ≠ RHS

Hence, the correct answer is "+ and -".

The position and positional values of English Alphabets are as:

The logic followed here is:

So, 'XMYR' will replace the question mark in the given series.

Hence, the correct answer is 'Option 1'.

Family Chart:

Decoding the given information:

<br>

Given Equation: ‘N + D # Z $ B’

It means: N is husband of D, D is Mother of Z, Z is Father of B.

So, N is Paternal Grandfather of B.

Hence the correct answer is 'Option 1'.

Given Statements:

I. Some rings are fingers.

II. Some fingers are toes.

III. No toe is an earring.

The least possible Venn diagram for the given statements is:

Conclusions:

I. No earring is a ring. → False (Because, No definite relation given between Earring and Ring, so it can be possibly only)

II. Some toes are rings. → False (Because, No definite relation given between Toes and Rings, so it can be possibly only).

So, Neither conclusion I and conclusion II follows.

Hence, the correct answer is 'Option 1'.

The logic followed here is:

Given Sequence: S _ U C T S R _ _ T _ R U E _ S R _ _ T

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

Option 1) R U E S T V G → S R U C / T S R U / E T S R / U E T S / R V G T →(Does not follow pattern).

Option 2) R V D S T U F → S R U C / T S R V / D T S R / U E T S / R U F T →(Does not follow pattern).

Option 3) R U D S T U F → S R U C T /  S R U D T / S R U E T/ S R U F T/ →(Follows pattern of SRU_T and +1 in the letter before T)

Option 4) R V E S T U F → S R U C / T S R V / E T S R / U E T S / R U F T → (Does not follow pattern).

Here, 'R U D S T U F' followed a pattern.

Hence, the correct answer is 'Option 3'.

The logic followed here is:

Step 1: The letters in each image is shifting +1 in their positional values in English Alphabetical series and in anticlockwise direction.

Step 2: The image in centre is filled and empty alternatively and its sides and vertices are by increasing +1.

So, Image 5 will replace the question mark in the series.

Hence, the correct answer is 'Option 4'.

The logic followed here is:

Logic: The second word is the national animal of the first country.

Here,

India : Royal Bengal Tiger → The Royal Bengal Tiger is the national animal of India.

Similarly,

Australia : Kangaroo → The Kangaroo is the national animal of Australia.

So, Kangaroo is second word.

Hence, the correct answer is 'Option 3'.

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

1. For '

' element → 90ºShifting one step forward and one step backward direction

Final series is

Hence, ‘option - (4)’ is the correct answer.

Logic : Squares of whole number series is added subsequently. 

Hence, "72" is the correct answer.

Logic : Alternately (2) and (3) are added to the position value according to English alphabetic series.

So,

• ‘FARM’ is coded as HDTP

And,

• ‘EGGS’ is coded as GJIV

​Similarly,

• ‘FOOD’ is coded as :

​Hence, the correct answer is "HRQG".

The image embedded in given figure is as shown below :

∴ Here, Option figure 4 is embedded in given figure.

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

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

Given : 

• (13, 17, 23)

(13 + 23) ÷ 2 - 1 = 17

36 ÷ 2 - 1 = 17

18 - 1 = 17

17 = 17 (LHS = RHS) 

• (8, 12, 18)

(8 + 18) ÷ 2 - 1 = 12

26 ÷ 2 - 1 = 12

13 - 1 = 12

12 = 12 (LHS = RHS) 

So,

• Option - (1) : (17, 21, 15)

(17 + 15) ÷ 2 - 1 = 21

32 ÷ 2 - 1 = 21

16 - 1 = 21

15 ≠ 21 (LHS ≠ RHS)

• Option - (2) : (18, 22, 28)

(18 + 28) ÷ 2 - 1 = 22

46 ÷ 2 - 1 = 22

23 - 1 = 22

22 = 22 (LHS = RHS)

• Option - (3) : (11, 15, 23)

(11 + 23) ÷ 2 - 1 = 15

34 ÷ 2 - 1 = 15

17 - 1 = 15

16 ≠ 15 (LHS ≠ RHS)

• Option - (4) : (5, 9, 16)

(5 + 16) ÷ 2 - 1 = 15

21 ÷ 2 - 1 = 15

10.5 - 1 = 15

9.5 ≠ 15 (LHS ≠ RHS)

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

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

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

Given : 7 * 5 * 4 * 2 * 3 * 7

According to the question, by replacing the *signs :

So,

• Option - (1) : ÷, −, +, ×, =

7 * 5 * 4 * 2 * 3 * 7 ⇒ 7 ÷ 5 − 4 + 2 × 3 = 7

1.4 − 4 + 2 × 3 = 7

1.4 + 6 - 4 = 7

7.4 - 4 = 7

3.4 ≠ 7 (LHS ≠ RHS)

• Option - (2) : +, −, ÷, −, =

7 * 5 * 4 * 2 * 3 * 7 ⇒ 7 + 5 − 4 ÷ 2 − 3 = 7

7 + 5 − 2 − 3 = 7

12 − 2 − 3 = 7

7 = 7 (LHS = RHS)

• Option - (3) : ÷, +, ÷, +, =

7 * 5 * 4 * 2 * 3 * 7 ⇒ 7 ÷ 5 + 4 ÷ 2 + 3 = 7

1.4 + 2 + 3 = 7

6.4 ≠ 7 (LHS ≠ RHS)

• Option - (4) : −, ÷, +, ×, =

7 * 5 * 4 * 2 * 3 * 7 ⇒ 7 − 5 ÷ 4 + 2 × 3 = 7

7 - 1.25 + 2 × 3 = 7

7 + 7 - 1.25 = 7

14 - 1.25 = 7

12.75 ≠ 7 (LHS ≠ RHS)

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

Logic : 

• First four letters → Written diagonally.
• Last three letters → Written diagonally.

So,

• COMFORT : FMOCTRO

 

And,

• DIGNITY : NGIDYTI

​Similarly,

• FOREIGN : ?

​Hence, the correct answer is "EROFNGI".

Given : L _ _ RALMT _ _ _ _ TRALM_ R _    

By checking options :

1. TRMALMTA → L T R RALMT M A L M TRALMT R A → (It doesn't Follows the pattern)
2. MRTLAMTA → L M R RALMT T L A M TRALMT R A → (It doesn't Follows the pattern)
3. MTRALMTA → L M T RALMT R A L M TRALMT R A → (It follows the pattern of : LMTRA - LMTRA - LMTRA - LMTRA)
4. MTRLAMTA → L M T RALMT R L A M TRALMT R A → (It doesn't Follows the pattern)

⇒Option - (3) gives the pattern of "L M T RA - LMT R A - L M TRA - LMT R A"

Hence, "MTRALMTA" is the correct answer.

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

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

The least possible Venn diagram for the given statements is as shown below :

Conclusions:

I. Some flashes are streaks → Does not follow (As no streak is a line, some lines are bands and all bands are flashes. So, it is possible but not definitely true)

II. No flash is a line → Does not follow (As some lines are bands and all bands are flashes. So, no direct relation is given between flash and line thus cannot be proved therefore it is definitely false)

∴ Here, Neither conclusion I nor II follows.

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

Logic : (2nd number + 3rd number) - 100 = 1st number

Given : 

• (239, 127, 212)

127 + 212 - 100 = 239

339 - 100 = 239

239 = 239 (LHS = RHS)

• (96, 64, 132)

64 + 132 = 196 

196 - 100 = 96 (LHS = RHS)

So,

• Option - (1) : (262, 132, 240)

132 + 240 - 100 = 262

372 - 100 = 262

272 ≠ 262 (LHS ≠ RHS)

• Option - (2) : (140, 76, 181)

76 + 181 - 100 = 140

257 - 100 = 140

157 ≠ 140 (LHS ≠ RHS)

• Option - (3) : (167, 89, 178)

89 + 178 - 100 = 167

267 - 100 = 167

167 = 167 (LHS = RHS)

• Option - (4) : (110, 91, 159)

91 + 159 - 100 = 110

250 - 100 = 110

150 ≠ 110 (LHS ≠ RHS) 

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

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

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

Logic :

• Consonants → (4) is added to from the position value according to English alphabetic series.
• Vowels → (3) is subtracted from the position value according to English alphabetic series.

So,

• HEROES : LBVLBW

And,

• INVEST : FRZBWX

​Similarly,

• KIDNAP : ?

​Hence, the correct answer is "OFHRXT".

The correct answer is Tamil Nadu. 

Key Points

• The Shevaroy Hills is a mountain range located in the Eastern Ghats of Tamil Nadu.
• It is situated near the town of Yercaud, which is a popular tourist destination known for its scenic beauty and pleasant weather.
• The Shevaroy Hills are home to a variety of flora and fauna, including several rare and endangered species of plants and animals.
• The hills are also known for their coffee and spice plantations, which are a major source of livelihood for the local communities.

Additional Information

• The Eastern Ghats run almost parallel to the east coast of India leaving broad plains between their base and the coast.
• It is a chain of highly broken and detached hills starting from the Mahanadi in Odisha to the Vagai in Tamil Nadu.
• They almost disappear between the Godavari and the Krishna.
• The Eastern Ghats reappear as more or less a continuous hill range in Cuddapah and Kurnool districts of Andhra Pradesh where they are called as Nallamala Range with a general elevation of 600-850 m.
• Located south of the Krishna River, the hills run north to south, parallel to the Coromandel Coast on the Bay of Bengal.
• The rugged, sparsely populated hills are composed for the most part of jumbled quartzites and slates and exemplify the mountain scenery of the Eastern Ghats.
• The southern part of this range is called the Palkonda range.
• The hills trend northwest to southeast and form the central part of the Eastern Ghats.
• Geologically, they are relicts of ancient mountains formed during the Cambrian Period that were subsequently eroded by the Penneru River and its tributaries.
• Javadi Hills, range of hills, one of the larger of the Eastern Ghats, in northern Tamil Nadu state, southeastern India.
• Their steep southeastern flanks are forested with sandalwood.
• The hills are sparsely populated.
• Grains, legumes, and oilseeds are the chief crops.

The Correct answer is President

Key PointsPardoning Power of President

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

Additional Information

The correct answer is Kathakali.

Key Points

• Nalacharitam is a play that originated in the state of Kerala, which is known for its rich cultural heritage and traditional dance forms.
• Nalacharitham was written by Unnayi Warrier in the 18th century.
• The play Nalacharitam is a popular performance in Kathakali, which tells the story of King Nala and his struggles.​

Important Points

• Kathakali is a classical Indian dance form which is a story play genre of art is the folk dance form of Kerala.
• It is a combination of 5 forms of fine art which are –
• Natyam (expressions)
• Nritham (dance)
• Nrithyam (enactment)
• Sangeetam (music)
• Vadya (instruments)
• Various costumes of characters of Kathakali –
• Sathwika (Hero)
• Katti (Villain)
• Minukku (females)
• Thathi (other characters)
• Types of Drums used in Kathakali – Maddalam, Chenda, and Idakka
• Kathakali is the most difficult style of the traditional dance form in which actors speak ‘sign language’ where hand gestures are used to dictate word part of the character and facial and eye movements express emotions and mood.
• Kathakali is based on the epics of Ramayana and Mahabharata.

Additional Information

• Kathak, on the other hand, is a classical dance form that originated in North India and is known for its intricate footwork and graceful movements.
• Sattriya is a classical dance form from the state of Assam.
• Odissi is a classical dance form from the state of Odisha.

The correct answer is Indonesia

Key Points

• The first Republic Day Parade was held on 26 January 1950, during which the President of Indonesia Sukarno was the chief guest.
• Between 1950 and 1954, Republic Day parades were held at Irwin Stadium (now National Stadium), Kingsway, Red Fort and Ramlila Maidan.
• Dr Rajendra Prasad began his first tenure as President of the Indian Union on this day.
• The President addresses the country on the eve of Republic Day.
• The republic day celebrations are majorly divided into three parts i.e. the Republic Day Parade, the Beating Retreat, and the Award Distributions.

The correct answer is Both I and II.

Key Points Ethanol

• Ethanol is still a liquid at room temperature, and it has a melting point of 156 K and a boiling point of 351 K.
• It is used as a preservative in paints because it is an efficient solvent and often used in cleaning materials to prevent breach of organisms.
• It is used in gasoline to avoid piston knocking and to preserve driveability.
• It is a strong, water-mixable solvent containing other organic solvents, including acetone, tetrachloride carbon, ethylene glycol, chloroform, benzene, diethyl alcohol, glycerol, pyridine, nitromethane, and toluene.

Acetic acid

• Acetic acid is an organic compound that belongs to a group of acids called carboxylic acids.
• The formula of acetic acid is CH3COOH with a methyl group is attached to a carboxyl functional group.
• The melting point of acetic acid is 290 K or 16.5°C and hence it often freezes during winter in cold climates.
• The IUPAC name of acetic acid is ethanoic acid. Acetic acid is the main component of vinegar.
• 5-8% solution of acetic acid in water is called vinegar and is used widely as a preservative in pickles.
• Vinegar's sour taste and pungent smell are due to the presence of acetic acid.
• Uses of Acetic Acid:
• Acetic acid is used in the production of a wide range of dyes, rayons, silk, and perfumes.
• Acetic acid is also used in the production of rubber.
• It is mostly used in a pickle preservative as vinegar.
• It is injected directly into the tumour during cancer treatment.
• Therefore Both I and II are correct.

Additional Information

The correct answer is Structural unemployment.

Key Points

• Structural unemployment occurs when there is a mismatch between the skills possessed by the workforce (including educated youths) and the requirements of the job market.
• In the context of India, the lack of employable skills among educated youths is a classic example of structural unemployment, as the education system often fails to align with the evolving needs of industries.

Additional Information

• Educated unemployment is often considered a specific subset or manifestation of structural unemployment in the Indian economic context, but structural unemployment is the broader, primary economic classification for skill mismatches.
• Cyclical unemployment is caused by fluctuations in the business cycle, where there is a decrease in demand for goods and services, leading to layoffs and unemployment.
• Technological unemployment is caused by the automation of jobs, where machines and technology replace human labor.

The correct answer is Nikhat Zareen (52 kg) and Nitu (48 kg).

Key Points 

• Nitu Ghanghas is an Indian boxer (48 kg) and was one of the gold medal winners at the 73rd Strandja Memorial Boxing Tournament, held in Sofia, Bulgaria in February 2022.
• Nitu (48 kg) prevailed 5-0 over Italy's Erika Prisciandaro, a former youth world championship bronze-medallist.
• Nikhat Zareen:
• Indian boxer Nikhat Zareen won a gold medal in the 52kg category at the 73rd Strandja Memorial Tournament in Sofia, Bulgaria on 27 Feb 2022, by defeating Ukraine's Tetiana Kob.
• She has become the 1st Indian boxer to win 2 gold medals at Strandja Memorial Boxing.

The correct option is Bal Gangadhar Tilak.

Key Points

• The Fergusson College was developed from the New English School, which was founded in 1880 by four young men: Bal Gangadhar Tilak, Vishnushastri Chiplunkar, Gopal Ganesh Agarkar, and Madhavrao Namjoshi.
• The school was established to provide modern education to Indians, and it quickly became one of the most prestigious schools in the country.
• In 1884, the Deccan Education Society was formed to manage the New English School and to establish a college.
• The college, which was named after Sir James Fergusson, the then Governor of Bombay, opened its doors in 1885.
• The Fergusson College was one of the first colleges in India to offer a liberal arts education.
• It was also one of the first colleges to be established by Indians, and it quickly became a center of Indian nationalism.
• The college's alumni include many prominent figures in Indian history, including Lokmanya Tilak, Gopal Ganesh Agarkar, and R.G. Bhandarkar.
• The Fergusson College has continued to be a leading institution of higher education in India.
• It is now a constituent college of the University of Pune, and it offers a wide range of undergraduate and postgraduate programs.
• The college is also home to a number of research centers and institutes, and it has produced many notable scholars and scientists.
• The Fergusson College is a proud institution with a long and distinguished history.
• It is a testament to the vision and dedication of its founders, and it continues to play an important role in the development of India.

Additional Information

• Deccan English School:
• ​There was no Deccan English School in India.
• The Deccan Education Society was founded in Pune, India by a group of Indian intellectuals, including Lokmanya Bal Gangadhar Tilak, Gopal Ganesh Agarkar, and Mahadev Govind Ranade.
• ​Anglo-British School:
• ​The Anglo-British School was a school for the children of British residents in India.
• It was founded in 1854 by the East India Company and was located in Simla, Himachal Pradesh.
• The school was co-educational and offered a British-style education. It was closed in 1947, after India gained independence.
• Poona English School :
• ​The Poona English School was founded in 1824 by the British East India Company.
• The school was located in Poona (now Pune), Maharashtra, India.
• The school was initially intended for the children of British officials and military personnel, but it was later opened to Indian students as well.
• The school offered a British-style education, including instruction in English, mathematics, science, and history.
• The school was a popular institution and had a good reputation.
• The school closed in 1947, after India gained independence.

The correct answer is Basavanna.

Key Points

• The twelfth century witnessed the emergence of a new movement in Karnataka, led by a Brahmana named Basavanna (1106-68) who was a minister in the court of a Kalachuri ruler.
• His followers were known as Virashaivas (heroes of Shiva) or Lingayats (wearers of the linga).

Additional Information

• Lingayats continue to be an important community in the region to date.
• They worship Shiva in his manifestation as a linga, and men usually wear a small linga in a silver case on a loop strung over the left shoulder.
• Those who are revered include the jangama or wandering monks.
• Lingayats believe that on death the devotee will be united with Shiva and will not return to this world.
• Therefore they do not practise funerary rites such as cremation, prescribed in the Dharmashastras.
• Instead, they ceremonially bury their dead.
• The Lingayats challenged the idea of caste and the “pollution” attributed to certain groups by Brahmanas.
• They also questioned the theory of rebirth.
• These won them followers amongst those who were marginalised within the Brahmanical social order.
• The Lingayats also encouraged certain practices disapproved in the Dharmashastras, such as post-puberty marriage and the remarriage of widows.
• Our understanding of the Virashaiva tradition is derived from vachanas (literally, sayings) composed in Kannada by women and men who joined the movement.

The correct answer is 44th.

Key PointsRight to Property:

• The right to property was removed from the list of Fundamental Rights by the 44th Amendment Act, of 1978.
• It is made a legal right under Article 300-A in Part XII of the Constitution. So at present, there are only six Fundamental Rights.
• Article 19 provides to all citizens the right to acquire, hold, and dispose of their property whereas Article 31 provides that "no person shall be deprived of his property save by authority of law."
• Later, in 44thAmendment of 1978 removed the right to property from the list of fundamental rights.
• This amendment was made to prevent the misuse of the right to property by individuals and to ensure that it is used for the welfare of society as a whole.
• Hence, the right to property is no longer a fundamental right, however, it is still a constitutional right.​

Additional Information Fundamental Rights:

• Presently there are 6 fundamental rights.
• Supreme Court is the custodian or protector of fundamental rights.
• It was borrowed from U.S. Constitution.
• Articles:
• Right to equality (14 - 18)
• Right to freedom (19 - 22)
• Right against exploitation (23 - 24)
• Right to freedom of religion(25 - 28)
• Cultural and educational rights (29 - 30)
• Right to constitutional remedies (32)

The Correct Answer is Janaki Prasad.

Key Points

• Janaki Prasad
• The Banaras Gharana of Kathak developed under the leadership of Janaki Prasad.
• He was originally a resident of Bikaner.
• Imparting the intricate knowledge of this ancient dance to his disciple, he founded the Banaras Gharana of Kathak.
• Practitioners of Kathak Banaras Gharana are unique in that they often take turns to both the right and left with equal assurance.
• This Banaras gharana is different from other gharanas in many ways, including thaat (a piece of performance) and tatkar (use of steps).

Additional Information

• Kathak
• The spiritual center of India and one of the oldest cities in the world is Banaras. Kathak and a particular gharana Kathak was popular in Banaras.
• The three main gharanas of Kathak, a traditional dance form originating in Uttar Pradesh, are located in Lucknow, Jaipur and Banaras.
• The Vedic Sanskrit word "Katha", meaning "story", is where the word "Kathak" originates from.
• The resulting text-based analysis suggests that Kathak is an old style of traditional Indian dance.
• With the entry of the British in India, Kathak started declining. Artists passed on their knowledge to the next generation within the family as there were no written texts to preserve this art style.

The correct answer is Stomatal pores open.

Key Points

• Stomata are tiny pores present on the surface of the leaves.
• Massive amounts of gaseous exchange take place in the leaves through these pores for the purpose of photosynthesis.
• But it is important to note here that the exchange of gases occurs across the surface of stems, roots, and leaves as well.
• Since large amounts of water can also be lost through these stomata, the plant closes these pores when it does not need carbon dioxide for photosynthesis.
• The opening and closing of the pore is a function of the guard cells.
• The guard cells swell when water flows into them, causing the stomatal pore to open. Similarly, the pore closes if the guard cells shrink.

The correct answer is A is true and R is false.

Key Points

Explanation:

Assertion (A): India did indeed have a surplus in its balance of trade during most of the British Raj.

• This means that the value of its exports exceeded the value of its imports.
• This was due to several factors, including:
• Forced cultivation of cash crops: The British forced Indian farmers to grow crops like indigo and cotton for export, even if it meant neglecting food production for domestic consumption.
• Deindustrialization: British policies destroyed India's traditional industries, making the country more dependent on imported manufactured goods.
• Drain of wealth: A significant portion of the trade surplus was not reinvested in India, but sent back to Britain as tribute and profits for British companies.

Reason (R): However, the statement that the surplus of the balance of trade was used for the growth and development of India is false.

• The benefits of the trade surplus primarily accrued to the British, while India suffered from:
• Underdevelopment: The drain of wealth and focus on cash crops over food production stunted India's economic development and exacerbated poverty.
• Exploitation: Indian farmers and laborers were often exploited by British companies and landowners, receiving meager wages and working in poor conditions.
• Lack of infrastructure: Despite the trade surplus, the British invested very little in India's infrastructure, such as roads, railways, and education, which further hampered development.

 

Therefore, while it is true that India had a positive balance of trade under British rule, the surplus was not used for its growth and development, but rather benefited the British at the expense of the Indian people.

The correct answer is Sarnath.

Key Points

• Mauryan Pillar Capital found at Sarnath is popularly known as Lion Capital.
• It is one of the finest examples of Mauryan sculpture.
• Lion Capital is located at Sarnath, near Varanasi.
• It was built in 250 BCE.
• It is made up of polished sandstone. The surface is highly polished.
• Originally the Capital has 5 components

1. ​The shaft (now broken into many parts)
2. A lotus baseball
3. A drum on the base bell with 4 animals processing clockwise.
4. Figures of 4 lions
5. The crowning part, a large wheel (this is also broken)

Additional Information

• The Lion Capital is the National Emblem of India.
• The inscription Satyamev Jayate is taken from the Mundaka Upanishad.
• Gautam Buddha gave his first sermon at Sarnath.

The correct answer is Seven.

Key Points

• A revolutionary strategy for sustainable development and economic prosperity is PM GatiShakti. Seven engines—roads, railways, airports, ports, mass transit, waterways, and logistics infrastructure—power the strategy.
• The Gati Shakti initiative is also known as the National Master Plan for Multimodal Connectivity.
• The Indian government introduced it.
• It strives to reduce logistics costs through coordinated planning and execution of infrastructure projects.
• The National Infrastructure Pipeline, introduced in 2019 and costing Rs 110 lakh crore, would be absorbed by the Gati Shakti scheme.
• The program also aims to speed up turnaround times at ports and increase cargo handling capacity to increase trade.
• In addition, it plans to create two new defence corridors, one in Tamil Nadu and the other in Uttar Pradesh, and 11 industrial corridors.
• Another goal is to extend 4G access to every town.
• The network of gas pipelines will be expanded by 17,000 kilometres.​

Important Points

• Gati Shakti Digital Platform:
• It entails the development of a common platform under which infrastructure projects may be efficiently planned and carried out through real-time collaboration across various ministries and departments.

The correct answer is New Delhi. 

Key Points The National Dope Testing Laboratory (NDTL) 

• It functions under the Ministry of Youth Affairs and Sports.
• The NDTL in India was established in 2008 to get permanently accredited by International Olympic Committee (IOC) and World Anti Doping Agency (WADA) to do the testing for the banned drugs in human sports.
• It is a dope testing lab aiming to get permanent accreditation from the World Anti-Doping Agency (WADA) and the International Olympic Committee (IOC).
• India signed the Copenhagen Declaration on Anti-Doping, post which it set up the National Anti-Doping Agency in December 2004.
• The National Dope Testing Lab is headed by the Chief Executive Officer, who is generally a Sports Secretary.
• National Anti Doping Agency is headed by the Director-General.
• Recently, NDTL was banned from carrying out any doping test for six months after it failed to meet the standards set up by the World Anti-Doping Agency (WADA).
• The Lab has completed sample testing for numerous major International as well as National events since its inception.
• The lab was earlier located in the Jawaharlal Nehru Stadium and is shifted to the new site on May 14, 2009, with better facilities.
• The area of the new NDTL lab is 2700 square meters as against the earlier area of only 900 square meters.

The correct answer is Sarangi.

Key Points

• The sarangi is a bowed instrument that was made popular by Indian artist Pandit Ram Narayan as a solo performance instrument in Hindustani classical music.
• He also became the first sarangi performer to achieve fame on a global scale.
• The sarangi is played with a bow just like a violin, but in contrast to the violin, it is held vertically with the sound chamber below.
• It normally has three primary strings, with a fourth string serving as a drone occasionally.
• A solo concerto is a type of music in which an orchestra plays behind a single solo instrument that plays the melodic line.
• A solo concerto has three movements: a quick section, a slow section, and then another fast section.

Additional Information

The correct answer is 1956.

Key Points

• On 20 January 2022, the Supreme Court gave a judgment dealing with the property rights of Hindu women and widows under the Hindu Succession Act 1956 .
• Key points from the final verdict-
• The daughters of a male Hindu dying without a will would be entitled to inherit self-acquired and other properties obtained in the partition by the father.
• The daughters would get preference over other collateral members of the family such as sons and daughters of brothers of the deceased father.
• In case a female Hindu dies without leaving a will, the property she inherited from her father or mother would go to the heirs of her father while the property she inherited from her husband or father-in-law would go to the heirs of the husband.

Additional Information

• The Hindu Succession Act 1956 was enacted to amend and codify the law related to unwilled succession among Hindus, Jains, Sikhs, Buddhists.
• The act gives a uniform system according to which property of an unwilled deceased person is given.
• The act was amended in 2005 to give girls equal rights in the property.

The correct answer is Ralph H Fowler.

Key Points

• Zeroth law of thermodynamics is one of the four laws of thermodynamics.
• Its creation is credited to Ralph H. Fowler.
• The Zeroth law of thermodynamics frames the concept of temperature as an indicator of thermal equilibrium.
• According to the Zeroth Law of Thermodynamics, "two systems in thermal equilibrium with a third system separately are in thermal equilibrium with each other."
• The Zeroth Law plainly states that when two systems A and B are in thermal equilibrium, there must be a physical quantity that has the same value for both.
• Temperature is a thermodynamic variable whose value is the same for two systems in thermal equilibrium (T ).

Additional Information

• The first law of thermodynamics states that energy can neither be created nor destroyed, only altered in form.
• The total entropy of an isolated system (the thermal energy per unit temperature that is unavailable for doing productive work) can never decrease, according to the second law of thermodynamics.
• When a current 'i' travels through a conductor of resistance 'r' for time 't,' Joule's law of heating states that the heat created in the conductor is equal to the product of the square of the current, the resistance, and the duration.

The correct answer is Taxes.

Key Points

• Capital Receipts:
• All those receipts of the government which either create liability or reduce financial assets are capital receipts.
• Receipts that generate liability or decrease the financial assets of the government.
• It includes borrowings from the Reserve Bank of India and commercial banks and other financial institutions.
• It also consists of loans received from foreign governments and international organizations and repayment of loans granted by the Union government.
• Taxes are part of Revenue receipts.
• Examples:
• Market borrowings by the government from the public
• Borrowings from the RBI
• Borrowings from commercial banks or financial institutions through the sale of T-BILLS,
• Loans received from foreign governments or international financial institutions
• A small savings, post office savings, post office saving certificates, Provident Fund
• PSU’s Disinvestment

Additional Information

• Capital Expenditure:
• All those expenditures of the government either result in the creation of physical/financial assets or a reduction in financial liabilities.
• Spending incurred by the government results in the formation of physical or financial possessions of the union government or a decrease in financial liabilities of the union government.
• It contains expenditure on procuring land, equipment, infrastructure, expenditure in shares.
• It also includes mortgages by the Union government to Public Sector Undertakings, state and union territories
• Examples:
• Purchase of land,
• Purchase of machinery,
• Building and equipment
• Investment in shares,
• Loans and advances by the central government to state governments and UTs.
• Capital Expenditure is also classified as plan and non-plan capital expenditure.
• Plan expenditure relates to central Five-year Plan and Non-Plan relates to expenditure not covered under the Five-year

The correct answer is Jan Samarth.

Key Points

• Jan Samarth is a digital platform launched by the Government of India to simplify the loan application and disbursement process for small businesses and entrepreneurs.
• The platform is designed to offer a hassle-free experience to borrowers by providing end-to-end loan services, including loan application, verification, and disbursal.
• The portal will also provide customized loan options based on the borrower's credit history, repayment capacity, and other relevant parameters.
• The platform will also offer various other financial services like insurance, investment, and pension schemes for the benefit of small businesses and entrepreneurs.

Additional Information

• Swayatta is a digital platform launched by the Government of India to promote self-employment and entrepreneurship among the youth.
• It offers various services like skill development, mentorship, and financial assistance to aspiring entrepreneurs.
• E-Shram is a digital platform launched by the Government of India to provide social security benefits to the unorganized sector workers.
• It offers services like registration, enrollment, and tracking of social security schemes like insurance, pension, and healthcare.
• Yukti is a digital platform launched by the Government of India to promote research and innovation in the field of science and technology.
• It offers various services like funding, collaboration, and networking opportunities to researchers, scientists, and entrepreneurs.

The correct answer is 2014.

Key Points

• Narendra Modi proposed to celebrate a day for yoga as 'International Day of Yoga' while speaking at the United Nations General Assembly on September 27, 2014.
• The proposal was accepted by the United Nations, and the first International Day of Yoga was celebrated on June 21, 2015.
• Narendra Modi is the current Prime Minister of India.

Additional Information

• Yoga is a form of physical, mental, and respiratory integration.
• It enhances general health through physical postures, breathing techniques, and meditation.
• Thousands of years ago, yoga was created as a spiritual exercise.
• The ancient Hindu text known as the Rigveda is where yoga-like activities were first discussed.
• There are several references to yoga throughout the Upanishads.

The correct answer is 'Below average and late monsoon.'

Key Points

• Monsoon Dynamics:
• The Indian monsoon is significantly influenced by atmospheric pressure differences between the Indian Ocean and the Pacific Ocean.
• NORM (Negative Outgoing Radiation Mode) signifies that the pressure difference is such that the central and eastern Pacific (Tahiti) have lower pressure.
• During El Niño events, there is often higher pressure in the western Pacific (Darwin, Australia), leading to weakened monsoon activity in South Asia.
• El Niño Impact:
• El Niño is characterized by the periodic warming of sea surface temperatures in the central and eastern Pacific Ocean.
• It disrupts normal weather patterns, often leading to dryness and drought in regions that rely heavily on monsoonal rains, like India.
• Monsoon Timing and Intensity:
• A negative pressure difference in Tahiti generally correlates with delayed and weakened monsoon rains.
• This results in below-average rainfall, adversely affecting agriculture and water supplies in the affected regions.

Additional Information

• Above average late monsoon:
• An above-average late monsoon would imply more rainfall but delayed. This is typically not associated with a negative pressure difference in Tahiti during El Niño events.
• El Niño usually causes reduced and late seasonal rains rather than increased rainfall.
• Drought:
• While El Niño can lead to drought conditions, the term "drought" broadly refers to prolonged periods of insufficient rainfall, not necessarily aligning with the specific timing of monsoon seasons.
• In this context, "below average and late monsoon" more accurately describes the seasonal impact rather than the general condition of drought.
• Above average and early monsoon:
• An early and above-average monsoon occurs under conditions opposite to those seen during El Niño events, such as La Niña, where pressures are higher in the central Pacific and lower in the western Pacific.
• This option is inconsistent with the impact of a negative pressure difference in Tahiti.

Important Points

• The Southern Oscillation Index (SOI) is crucial to understanding pressure differences. A negative SOI often indicates El Niño conditions.
• The Walker Circulation, an east-west atmospheric circulation pattern, is disrupted during El Niño, affecting monsoon patterns.
• Monitoring sea surface temperatures and atmospheric pressures are vital in predicting monsoon onset and intensity.
• El Niño and La Niña are part of the broader El Niño-Southern Oscillation (ENSO) cycle, significantly impacting global climate systems.

The correct answer is 1988.

Key Points

• Joint Forest Management (JFM) is a collaborative effort between the forest department and local communities to manage and protect forest resources.
• JFM was launched in 1988 in the context of the National Forest Policy of India, which aimed to involve local communities in forest conservation and management.
• The program has been successful in improving forest cover and reducing deforestation in several parts of India.

Additional Information

• The National Forest Policy, 1952, was implemented by the Indian government after the country gained its independence in 1947.
• It categorized wooded regions into four categories: village forests, protected forests, national forests, and common trees between people's dwelling places.
• The primary goal of the National Forest Policy of 1988 is to maintain ecological balance, including atmospheric equilibrium, and environmental stability, all of which are essential for the survival of all living things, including humans, animals, and plants.

The correct answer is Lucknow.

Key Points

• The Lucknow Pact was signed between the Indian National Congress and the All India Muslim League in December 1916.
• The pact aimed at creating a united front against British colonialism in India and to secure greater self-governance for Indians.
• The agreement was significant because it marked the first time the Congress and the Muslim League had come to a compromise on the issue of self-government.
• The pact also led to the formation of the League-Congress joint committee, which worked towards the goal of Indian independence.

Additional Information

• The Indian National Congress was founded in Bombay in 1885.
• It was founded by Allan Octavian Hume.
• However, there was no joint front between the Congress and the Muslim League at this time.
• The Allahabad Address was given by Allama Iqbal in 1930, where he proposed the idea of a separate Muslim state in India, which later became Pakistan.
• The Delhi Durbar of 1911 was a grand imperial gathering held in Delhi to celebrate the coronation of King George V as Emperor of India.

Given:

The Right-angle triangle

Concept:

The sum of all angles of right-angle triangle = 180° 

One of the angles of the Right-angle triangle = 90° 

Calculation:

Let the smallest angle of the right-angle triangle be X

According to the question

The second angle = X + 30

The sum of all angles of the right-angle triangle = X + X + 30° + 90° 

⇒ 180° = 2X + 120

⇒ 180° - 120° = 2X

⇒ 60° = 2X

⇒ X = 30° 

∴ The required result will be 30°.

Given:

The number = 5826, 5964, 6039, 6336, 6489, 6564, 6867, and 6960

Concept:

A number is divisible by 3 then sum of the digits of the number is also divisible by 3.

A number is divisible by 9 then sum of the digits of the number is also divisible by 9..

Calculation:

For number 5826

⇒ 5 + 8 + 2 + 6 = 21

This number is divisible by 3 but not by 9

For number 5964

⇒ 5 + 9 + 6 + 4 = 24

This number is divisible by 3 but not by 9

For number 6039

⇒ 6 + 0 + 3 + 9 = 18

This number is divisible by 3 and 9 both

For number 6336

⇒ 6 + 3 + 3 + 6 = 18

This number is divisible by 3 and 9 both

For number 6489

⇒ 6 + 4 + 8 + 9 = 27

This number is divisible by 3 and 9 both.

For number 6564

⇒ 6 + 5 + 6 + 4 = 21

This number is divisible by 3 but not by 9.

For number 6867

⇒ 6 + 8 + 6 + 7 = 27

This number is divisible by 3 and 9 both

For number 6960

⇒ 6 + 9 + 6 + 0 = 21

This number is divisible by 3 but not by 9.

∴ The total numbers which is divided by 3 and not by 9 are 4.

Given:

The monthly income of Ramesh = Rs. 45000

The monthly expenditure on housing = 25%

The monthly expenditure on transportation = 10%

Concept:

$X\%={X\over 100}$

Calculation:

Let the total monthly expenditure of Ramesh on housing and transportation together be X

⇒ X = (25% + 10%) of 45000

⇒ X = 35% of 45000

⇒ X = ${35\over 100}\times 45000={35\ \times 450}=15750$

∴ The required result will be 15750.

Given:

The sum of the cubes of two numbers (a³ + b³) is 9728.

The sum of the numbers (a + b) is 32 ..(1)

Formula used:

(a + b)³ = a³ + b³ + 3ab(a + b)

(a - b)² = (a + b)² - 4ab

Calculations:

(a + b)³= a³ + b³ + 3ab(a + b)

32³ = 9728 + 3ab(32)

32768 - 9728 = 96ab

ab = 23040/96

⇒ ab = 240

(a - b)²= (a + b)² - 4ab

⇒ (a - b)2  = 32² - 4 × (240)

⇒  (a - b)² = 1024 - 960= 64

⇒  a - b = 8    ..(2)

Solving both,

⇒ 2a = 40

⇒ a = 20  ⇒  b = 12

a3 - b³ = 20³ - 12³

= 8000 - 1728 = 6272

The answer is 6272

Given:

The radius = 4 cm

The angle = 45° 

Concept:

Arc length = r × θ     Where r = Radius, and θ = Angle

Perimeter = 2r + arc length

Calculation:

Let the perimeter be X

⇒ 45° in radian = 45° × ${π \over 180}$ = ${π \over 4}$

The perimeter of the sector = 2r + arc length = 2 × 4 + 4 × ${{22\over 7}\over 4}$ = 8 +  ${22\over 7}$

∴ The required result will be ${78\over 7}$.

Alternate MethodFormula Used:

Length of the arc = (Angle/360) × Perimeter of circle

Perimeter of sector = 2r + Length of the arc

Calculation:

Length of the arc = (45/360) × 2 π × 4

⇒ L = π = 22/7

Perimeter of sector = 2 × 4 + 22/7 = 8 + 22/7 = 78/7

∴ The correct answer is 78/7cm.

Given:

The numbers = 11368, 11638, 11863 and 12638

Concept:

A number divided by 11only when the difference of the sum of the digits at odd positions and sum of the digits at even positions is zero of multiple of 11.

Calculation:

For number 11368

⇒ (1 + 3 + 8) - (1 + 6)

⇒ 12 - 7 = 5 

Not divisible by 11

For number 11638

⇒ (1 + 6 + 8) - (1 + 3)

⇒ 15 - 4 = 11

Number 11638 is divisible by 11

For number 11863

⇒ (1 + 8 + 3) - (1 + 6)

⇒ 12 - 7 = 5

This number is not divisible by 11

For number 12638

⇒ (1 + 6 + 8) - (2 + 3)

⇒ 15 - 5 = 10

This number is not divisible by 11

∴ The required result will be 11638.

 

Alternate Method

Let's apply this rule to each of the given numbers.

11368:

Odd position digits: 1, 3, 8

Even position digits: 1, 6

Sum of odd position digits: 1 + 3 + 8 = 12

Sum of even position digits: 1 + 6 = 7

Difference: 12 - 7 = 5 (not divisible by 11)

12638:

Odd position digits: 1, 6, 8

Even position digits: 2, 3

Sum of odd position digits: 1 + 6 + 8 = 15

Sum of even position digits: 2 + 3 = 5

Difference: 15 - 5 = 10 (not divisible by 11)

11638:

Odd position digits: 1, 6, 8

Even position digits: 1, 3

Sum of odd position digits: 1 + 6 + 8 = 15

Sum of even position digits: 1 + 3 = 4

Difference: 15 - 4 = 11 (divisible by 11)

11863:

Odd position digits: 1, 8, 3

Even position digits: 1, 6

Sum of odd position digits: 1 + 8 + 3 = 12

Sum of even position digits: 1 + 6 = 7

Difference: 12 - 7 = 5 (not divisible by 11)

Therefore, the number among 11368, 11638, 11863, and 12638 that is divisible by 11 is:

∴ The required result will be 11638.

Shortcut Trick

Direct formula for Curved Surface Area (CSA) using Diameter (d): π × d × h = 1408

(22/7) × d × 56 = 1408

22 × d × 8 = 1408

176 × d = 1408

d = 1408 ÷ 176 = 8 cm = 0.08 m

∴ The correct answer is 0.08 m.

Alternate Method

Given:

Height (h) of the cylinder = 56 cm

Curved Surface Area (CSA) = 1408 cm²

Formula Used:

Curved Surface Area of a right circular cylinder = 2 × π × r × h

Where r is the radius and h is the height.

Calculations:

⇒ 2 × (22/7) × r × 56 = 1408

⇒ 44 × r × (56 ÷ 7) = 1408

⇒ 44 × r × 8 = 1408

⇒ 352 × r = 1408

⇒ r = 1408 ÷ 352

⇒ r = 4 cm

⇒ Diameter (d) = 2 × r = 2 × 4 = 8 cm

⇒ In meters: d = 8 ÷ 100 m = 0.08 m

∴ The correct answer is 0.08 m.

Additional Information

Total Surface Area (TSA) of Cylinder

The total surface area includes the curved surface and the areas of the two circular bases: TSA = 2 × π × r × (h + r).

Volume of Cylinder

The space occupied by the cylinder is given by the formula: Volume = π × r² × h.

Metric Conversion

To convert centimeters to meters, divide the value by 100 (1 m = 100 cm).

Given:

Select the correct statement about the properties of a triangle.

Concept:

Triangle inequality theorem states that for any triangle the sum of the length of the two side of the triangle always greater that the third side of the triangle

Calculation:

The correct statement is = The sum of two sides is always greater than the third side.

∴ The required result will be "The sum of two sides is always greater than the third side".

Given:

Sara can finish a work = 18 days

Tara can finish a work = 15 days

Formula used:

Work = Efficiency × Time

Calculation:

Let the Sara can finish the remaining work in X days.

One day work of Sara = ${1\over18}$

One day work of Tara = ${1\over15}$

Tara worked for 10 days = ${10\over15}={2\over3}$

The remaining work = ${1-{2\over3}}={3-2\over3}={1\over3}$

⇒ X = ${{1\over3}\over{1\over18}}={18\over3}=6\ days$

∴ The required result will be 6 days.

Given

x + 1/x = 6

Formula used

x² - 1/x² = (x + 1/x)(x - 1/x)

(x + 1/x)² - 4 = (x - 1/x)²

Calculation

(x- 1/x)² = 6² - 4

(x- 1/x)2 = 32

(x- 1/x) = 4√2

x2 - 1/x2 = 4√2 × 6

x2 - 1/x2 = 24√2

The answer is 24√2.

Shortcut Trick

For two numbers a and b, the third proportional is calculated as b² ÷ a.

Given: a = 7 and b = 63.

Third Proportional = (63 × 63) ÷ 7

⇒ 9 × 63 = 567.

∴ The correct answer is 567.

Alternate Method

Given: First number (a) = 7, Second number (b) = 63.

Formula Used: If x is the third proportional to a and b, then a : b :: b : x.

Calculations:

⇒ 7 / 63 = 63 / x

⇒ 1 / 9 = 63 / x

⇒ x = 63 × 9

⇒ x = 567

∴ The correct answer is 567.

Additional Information

Mean Proportional

The mean proportional between two numbers a and b is given by √(a × b).

Fourth Proportional

If a : b :: c : d, then d is the fourth proportional, calculated as d = (b × c) ÷ a.

Continued Proportion

Three numbers a, b, c are in continued proportion if a/b = b/c, which implies b² = ac.

Given:

40 men can complete the work in = 30 days

Formula used:

Work = Efficiency × Time

Calculation:

Let they can complete the work in X days

⇒ 30 × 40 = (40 - 10) × X

⇒ 1200 = 30 × X

⇒ X = 40

∴ The required result will be 40.

Given

The cost price of 28 oranges is equal to selling price of 24 oranges

Formula used

Profit = SP - CP

Calculation

CP × 28 = SP × 24

CP/SP = 6/7

Profit% = (7 - 6)/6 × 100

= 50/3 or 16(2/3)%

The answer is 16(2/3)%.

Given:

The length of the train = 252 m

The speed of the train = 125 km/h

The speed of the man = 17 km/h

Concept:

The relative speed of two objects that are moving toward the same direction = (Speed of the first object) - (The speed of the second object)

Formula used:

${Speed}={Distance\over Time}$

Calculation:

According to the question

The length of the train = 252 m

The relative speed = 125 - 17 = 108 km/h = 108 × 5/18 = 30 m/s

The time taken by train to pass the man 

⇒ 252/30 sec

⇒ 8.4 sec

∴ The required result will be 8.4 seconds.

Given:

The expression = tan4θ + tan2θ = 1

Formula used:

sec²θ = 1 + tan²θ 

Calculation:

According to the question

⇒ tan4θ + tan2θ = 1

⇒ tan²θ × (tan²θ + 1) = 1

⇒ tan²θ  × sec²θ = 1

⇒ tan²θ = ${1\over sec^2θ}$

⇒ tan²θ = cos²θ      -----(1)

Now,

11 (cos4θ + cos2θ)

⇒ 11 (tan⁴θ + tan²θ)

⇒ 11 × 1 = 11

∴ The required result will be 11.

Given:

The expression = $\sqrt{2+\sqrt{2+\sqrt{2+2cos8θ}}}$

Formula used:

1 + cosθ = 2cos²(θ/2)

Calculation:

According to the question

⇒ $\sqrt{2+\sqrt{2+\sqrt{2+2cos8θ}}}$

⇒ $\sqrt{2+\sqrt{2+\sqrt{2({1+cos8θ})}}}$

⇒ $\sqrt{2+\sqrt{2+\sqrt{2({2cos^24θ})}}}$

⇒ $\sqrt{2+\sqrt{2+2cos4θ}}$

⇒ $\sqrt{2+\sqrt{2(1+cos4θ)}}$

⇒ $\sqrt{2+\sqrt{2(2cos^22θ)}}$

⇒ $\sqrt{2+2\cos2θ}$

⇒ $\sqrt{2\ (1+\cos2θ)}$

⇒ $\sqrt{2\ (2\cos^2θ)}$

⇒ 2cosθ 

∴ The required result will be 2cosθ.

Shortcut Trick

The expression follows the algebraic identity a² − b² = (a + b)(a − b).

Here, a = 7.35 and b = 2.25.

Numerator = (7.35 + 2.25) × (7.35 − 2.25) = 9.6 × 5.1

Expression = (9.6 × 5.1) ÷ 0.24 = 40 × 5.1 = 204

∴ The correct answer is 204.

Alternate Method

Given Expression: (7.35 × 7.35 − 2.25 × 2.25) ÷ 0.24

Formula Used: a² − b² = (a + b)(a − b)

⇒ Expression = (7.35² − 2.25²) ÷ 0.24

⇒ Expression = [(7.35 + 2.25) × (7.35 − 2.25)] ÷ 0.24

⇒ Expression = (9.60 × 5.10) ÷ 0.24

⇒ Expression = 48.96 ÷ 0.24

⇒ Expression = 4896 ÷ 24

⇒ Expression = 204

∴ The correct answer is 204.

Additional Information

Algebraic Identities

The identity a² − b² = (a + b)(a − b) is used to simplify the difference of squares without calculating the actual squares.

BODMAS Rule

Always solve expressions in the order: Brackets, Orders (powers), Division/Multiplication, and Addition/Subtraction.

Decimal Division

When dividing decimals, multiply both the numerator and denominator by the same power of 10 to remove the decimal point (e.g., 48.96/0.24 = 4896/24).

Shortcut Trick

Savings = Income − Expenditure

Radha's savings = 60,000 − 24,000 = 36,000

Avinash's savings = 50,000 − 18,000 = 32,000

Ratio (Radha : Avinash) = 36 : 32 = 9 : 8

∴ The correct answer is 9 : 8.

Alternate Method

Given:

Avinash's salary = ₹50,000, Expenditure = ₹18,000

Radha's salary = ₹60,000, Expenditure = ₹24,000

Formula Used:

Savings = Income − Expenditure

Radha

₹36,000 (9 parts)

Avinash

₹32,000 (8 parts)

Ratio = 9 : 8

Calculations:

⇒ Avinash's savings = 50,000 − 18,000 = ₹32,000

⇒ Radha's savings = 60,000 − 24,000 = ₹36,000

⇒ Ratio of Radha's savings to Avinash's savings = 36,000 : 32,000

⇒ Dividing both sides by 4000, we get:

⇒ Ratio = 9 : 8

∴ The correct answer is 9 : 8.

Additional Information

Income, Expenditure & Savings

The basic fundamental rule used in all such personal finance problems is: Income = Expenditure + Savings.

Compound Ratio

If two ratios are given as a : b and c : d, their compound ratio is formed by multiplying the antecedents and consequents respectively to get (a × c) : (b × d).

Duplicate & Sub-duplicate Ratio

The duplicate ratio of any ratio a : b is a² : b², whereas the sub-duplicate ratio is √a : √b.

Given:

A can finish a job in = 8 hours

B can finish a job in = 12 hours

Formula used:

Work = Efficiency × Time

Calculation:

Let they together can complete the work in X days.

One day work of A = ${1\over8}$

One day work of B = ${1\over12}$

One day work of when they work together = ${1\over X}$

⇒ ${1\over8}+{1\over 12}={1\over X}$

⇒ ${3+2\over 24}={1\over X}$

⇒ ${5\over24}={1\over X}$

⇒ X = ${24\over5}=4.8$ hours

∴ They can complete the work in 4.8 hours.

Shortcut Trick

Given:

The total number of students appeared = 1800

The total number of students passed = 800

The students appeared from section C = 100° 

The percentage of students passed from section C = 25%

Concept:

$X\%={X\over100}$

A circle has total = 360° 

Calculation:

Let the total failed students from section C be X

The total appeared students from section C = ${{100\over360}\times {1800}}={100\times 5}=500$

The total passed students from section C = ${{25\over100}\times 800}=200$

The total failed students from section C = X = 500 - 200 = 300

∴ The required result will be 300.

Shortcut Trick

Convert Rohit's speed to m/s: 5.4 × (5/18) = 1.5 m/s.

Relative speed in opposite directions = 2.85 + 1.5 = 4.35 m/s.

Meeting time in seconds = Distance ÷ Relative Speed = 600 ÷ 4.35 ≈ 137.93 s.

Meeting time in minutes = 137.93 ÷ 60 ≈ 2.298 min.

Rounding to one decimal point gives 2.3 minutes.

∴ The correct answer is 2.3 minutes.

Alternate Method

Given: Track Length = 600 m, Speed_Pankaj = 2.85 m/s, Speed_Rohit = 5.4 km/h.

Formula: Time = Distance ÷ Relative Speed; Relative Speed (Opposite) = S₁ + S₂

⇒ Rohit's speed in m/s = 5.4 × (1000/3600) = 5.4 × (5/18) = 1.5 m/s.

⇒ Relative Speed = 2.85 + 1.5 = 4.35 m/s.

⇒ Time taken to meet (seconds) = 600 ÷ 4.35 = 137.931 s.

⇒ Time taken to meet (minutes) = 137.931 ÷ 60 = 2.2988... min.

⇒ Rounding to one decimal point = 2.3 min.

∴ The correct answer is 2.3 minutes.

Additional Information

Relative Speed on Circular Track

When two objects move in opposite directions, relative speed is S₁ + S₂. When in the same direction, it is |S₁ − S₂|.

Unit Conversion

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

Meeting at Start Point

The time taken to meet at the starting point is the LCM of the time taken by each individual to complete one full lap.

Shortcut Trick

List all prime numbers between 32 and 69: 37, 41, 43, 47, 53, 59, 61, 67.

Total count of prime numbers (n) = 8.

Sum using pairing: (37+67) + (41+61) + (43+59) + (47+53) = 104 + 102 + 102 + 100 = 408.

Average = Total Sum ÷ Count = 408 ÷ 8 = 51.

∴ The correct answer is 51.

Alternate Method

Given: Prime numbers between 32 and 69.

Formula: Average = (Sum of all observations) ÷ (Total number of observations)

⇒ Prime numbers between 32 and 69 are: 37, 41, 43, 47, 53, 59, 61, 67

⇒ Sum of primes = 37 + 41 + 43 + 47 + 53 + 59 + 61 + 67

⇒ Sum = 408

⇒ Total count of prime numbers = 8

⇒ Average = 408 ÷ 8

⇒ Average = 51

∴ The correct answer is 51.

Additional Information

Prime Numbers

A prime number is a natural number greater than 1 that has exactly two divisors: 1 and itself. The only even prime number is 2.

Arithmetic Mean

For any set of numbers, Average = (Σx) ÷ n, where Σx is the sum of terms and n is the total number of terms.

Checking for Primes

To verify if a number N is prime, check its divisibility by prime numbers up to √N. If none divide N, then N is prime.

Given:

7 cot P = 24

Formula used:

In Right-angle triangle

cotθ = ${Base\over Perpendicular}$

sinθ = ${Perpendicular\over Hypotenuse}$

Calculation:

In Δ ABC

⇒ By Pythagoras theorem

⇒ AB2 = 242 + 7²

⇒ AB2 = 576 + 49 = 625

⇒ AB = √625 = 25

Now, sin P = ${7\over25}$

∴ The required result will be ${7\over25}$.

Given:

The principle = Rs. 3720

The amount = Rs. 5282.4

The rate of interest = 12%

Formula used:

${S.I.}={P × R × T\over100}$     Where S.I. = Simple interest, P = Principle, R = Rate, and T = Time

Calculation:

Let the time is T years.

According to the question

Simple interest = 5282.4 - 3720 = 1562.4

⇒ $1562.4={3720\ × 12\ × T\over100}$

⇒ 156240 = 44640 × T

⇒ T = ${156240\over44640}= 3.5\ years$

∴ The required result will be 3$\frac{1}{2}$ years.

Given:

Ram can complete a piece of work = 15 days

Rohan can complete a piece of work = 25 days

Rohit can complete a piece of work = 30 days

Formula used:

Total work = efficiency × time

Calculation:

According to the question:

⇒ (Rohan + Rohit) × 2 +  (Rohan + Ram) × D = 150

⇒​ (6 + 5) × 2 +  (6 + 10) × D = 150

⇒ 16 × D = (150 - 22)

⇒ D = 128/16 = 8 days

<br>

Total days required to finish the work = 8 + 2 = 10 days

∴ The correct answer is 10 days.

The correct answer is "may be converted."

 

Key Points 

• The reason for selecting "may be converted" as the most appropriate option lies in the context of the sentence.
• The sentence is discussing the versatility of polyethylene terephthalate (PET) and how it can be transformed into various products.
• The word "converted" is suitable in this context because it accurately reflects the process of changing or transforming one form into another, which aligns with the idea of transforming PET into different products like polyester fabric and automotive parts. (इस संदर्भ में "परिवर्तित" शब्द उपयुक्त है क्योंकि यह एक रूप को दूसरे रूप में बदलने या बदलने की प्रक्रिया को सटीक रूप से दर्शाता है)
• Options like "might be placed," "might be evolved," and "may be devaluated" do not convey the intended meaning of transformation in this context.
• Therefore, the​ correct answer is Option 3.
  

Correct sentence: Polyethylene terephthalate, one of the most often recycled plastics and the material used in the majority of water and soda bottles, may be converted into everything from polyester fabric to automotive parts.

The correct answer is "insight."

 

Key Points

   

  

• The word "wisdom" means the ability to make sensible decisions and judgements because of your knowledge or experience. ((ज्ञान या अनुभव के आधार पर) विवेकपूर्ण निर्णय लेने की क्षमता, समझदारी, बुद्धिमानी, अक़लमंदी)
• Example: I don’t see the wisdom of this plan.
• The synonym of "wisdom" is "insight."
• The word "insight" means a clear, deep, and sometimes sudden understanding of a complicated problem or situation. (किसी जटिल समस्या या स्थिति की स्पष्ट, गहरी और कभी-कभी अचानक समझ)
• Example: It was an interesting book, full of fascinating insights into human relationships.
• Therefore, the​ correct answer is Option 3.
  

Additional Information 

       

• Clarity: the quality of being clear and easy to understand. (स्‍पष्‍टता और सुबोधता)
• Folly: an act that is not sensible and may have a bad result. (विवेकहीन कार्य या क्रिया जिसका दुष्‍परिणाम हो सकता है; मूर्खता का काम; नासमझी)
• Emotion: a strong feeling such as love, anger, fear, etc. ((प्रेम, क्रोध, भय आदि) मनोभाव, भावना, भावावेश)