DSSSB Junior Secretariat Assistant Official paper (Held on: 8 April 2022 Shift 1 ) (Previous Year Paper)

The logic followed here is : 

Positional value of opposite letter is written in place of consonants and the vowels are written as it is. 

• GAMBLE is related to 20 - A - 14 - 25 - 15 - E​

• RETAIN is related to 9 - E - 7 - A - I - 13. ​

Similarly,

• FLOWER is related to

​

Thus, 'FLOWER' is related to '21 - 15 - O - 4 - E - 9'.

Hence, the correct answer is "21 - 15 - O - 4 - E - 9".

According to the given question,

Given Word : QUESTIONS

There are three such pairs in the word 'QUESTIONS'.

Forward Pairs : ST 

Backward Pairs : SU, NO

Hence, the correct answer is "Three".

According to the given information:

A fruit-seller has arranged different varieties of fruits consisting of apples, bananas, kiwis, mangoes, oranges and pears on a staircase.

1) Mangoes are placed on the bottom-most step.

2) On the topmost step, pears are placed.

3) Apples are placed on the step above bananas, but below kiwis.

4) Oranges are placed on the step below bananas.

Thus, 'Bananas' are placed between apples and oranges.

Hence the correct answer is "Bananas".

Given word: SIMPLIFIED

According to the given information :

If each vowel in the word SIMPLIFIED is changed to the letter preceding it in the English alphabetical order

Then, the new arrangement will be:

Clearly, only letter 'D' will appear twice in the new set of letters.

Hence, the correct answer is "D".

Given word: SUCCESSOR 

According to the given information :

If each of the letters in the word SUCCESSOR is arranged in alphabetical order.

Then, the new arrangement will be:

Clearly, The position of 'two' letters will remain unchanged.

Hence, the correct answer is "2".

The logic followed here is:

• 'DONUT' is coded as 17256 and 'TONED' is coded as 52187

​

​Codes in tabular form :

Thus, the code for 'E' is '8'.

Hence the correct answer is "8".

The logic followed here is : 

• PIKACOO is written as KRPZXLL

​

Similarly,

• JERRY be written as :

Thus, JERRY be written as QVIIB

Hence, the correct answer is "QVIIB".

According to the given information :

U scored more than X. V scored more than U but less than W. X scored more than Y. 

Thus, 'U' scored more than exactly two people and less than exactly two people.

Hence, the correct answer is "U".

The logic followed here is : 

• HENCE is related to NEEHC

 

• ALONG is related to OLGAN.

 

Similarly,

• QUIET is related to :

 

Thus, QUIET is related to IUTQE.

Hence, the correct answer is "IUTQE".

Given:

'X + Y' means 'X is the mother of Y',

'X * Y' means 'X is the father of Y',

'X - Y' means 'X is the daughter of Y',

'X % Y' means 'X is the wife of Y'.

Let us first decode the given symbols and then draw a family tree

On checking: 'A - B * C + D'

1) A - B

'A - B' means 'A is daughter of B'.

2) B * C

'B * C' means 'B is father of C'.

3) C + D

'C + D' means 'C is mother of D'.

• Thus, the following family tree can be drawn :

Clearly, A is 'Mother's sister' of D.

Hence, the correct answer is "Mother's sister".

According to the given information, 

Among five buildings, 1, 2, 3, 4 and 5 each was built in different time line.

Statements:

(I) 2 is older than 5 but younger than 4. 1 is older than only 3.

• 4 > 2 > 5 > 1 > 3

Clearly, we can conclude that building '4' is the oldest.

Thus, statement (I) is sufficient.

(II) Both 1 and 2 are younger than 4.

• 4 > 1, 2

​Clearly, we can not conclude which building is the oldest.

Thus, statement (II) is not sufficient.

Hence, the correct answer is "Only 1 is sufficient".

According to given information:

Thus, 'food' is coded as "bf".

Hence, the correct answer is "bf".

As per the given information, 

The circle represents 'Meat eaters', the triangle represents 'Vegetable eaters' and the rectangle represents 'Milk drinkers'.

The Venn diagram for the given representation is :

The shaded part represents the number of 'Milk drinkers' who are 'Vegetable eaters', but do NOT eat meat = 18

Hence, the correct answer is "18".

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

According to the given information :

• P and Q are brothers. T is the sister of P. Z's daughter's father is Q. P's mother is J. Y is the father of T. M is the sister of J.
• Thus, the following family tree can be drawn:

​

Thus, it is clear from the above diagram that 'M is Mother's sister of P'.

Hence, the correct answer is "Mother's sister".

Given Statement: S = Y ≤  M < B = O > L

Conclusions:

I.O > S  → TRUE (as S = Y ≤  M < B = O > L →  S < O , clear relationship between O and S can be determined)

II. O < Y → FALSE (as S = Y ≤  M < B = O > L → Y < O)

Hence, the correct answer is "Only I is true".

Statements:

All goats are lions.

Some deer are pandas.

Some goats are cheese.

The least possible diagram for the given statements is as follows :

Conclusions:

(I) Some lions are deer → False (Because their is no direct relation between 'lions' and 'deer' so it is possible but not definite)

(II) Some goats are pandas → False (Because their is no direct relation between 'goats' and 'pandas' so it is possible but not definite)

III) Some lions are cheese → True (Because 'Some goats are cheese' and 'All goats are lions', so the 'lions' that are 'goats' are also 'cheese',  thus it is definitely true)

Hence, the correct answer is "Only conclusion III follows".

Given:

In a certain code language,

'L + M' means 'L is the brother of M',

'L - M' means 'L is the mother of M',

'L × M' means 'L is the father of M',

'L ÷ M' means L is the son of M'.

Let us first decode the given symbols and then draw a family tree

On checking: 'P × Q - R + S ÷ T'

1)  P × Q

'P × Q' means 'P is father of Q'.

2. Q - R

'Q - R' means 'Q is mother of R'.

3. R + S

'R + S' means 'R is brother of S'.

4. S ÷ T

'S ÷ T' means 'S is son of T'.

Thus, the following family tree can be drawn:

Clearly, 'T is Daughter's husband of P'.

Hence, the correct answer is "Daughter's husband".

Given statement :  L = M > N < P ≥  Q > O

Conclusions:

I. L > N → TRUE (as L = M > N < P ≥  Q > O → L > N; clear relationship between L and N can be determined).

II. N < Q → FALSE (as L = M > N < P ≥  Q > O → clear relationship between N and Q cannot be determined).

Hence, the correct answer is "Only I is true".

According to the given information :

Shankar goes to office by car. He starts driving towards the north for 3 km. He takes a right turn and drives for 7 km. Again, he takes a right turn and drives for 11 km. Then he takes a turn towards the west and drives for 13 km. Lastly, he drives 8 km towards the north.

• Thus, the following diagram can be drawn according to the given information :

​

Clearly, Shankar is 6 km, West from the starting point.

Hence, the correct answer is "6 km, West".

According to the given information :

P is to the west of R, who is to the north of S . Q is to the east of S and north of T. 

• Thus, the following diagram can be drawn according to the given information :

Clearly, T is at South-East of R.

Hence, the correct answer is "South-East".

Decoding the information, 

Given:

37 + 73 - 23 ÷ 32 × 29 = ?

After replacing the signs from left to right and using the BODMAS rule,

= 37 × 73 ÷ 23 + 32 - 29

= 37 × 3.174 + 32 - 29

= 117.43 + 32 - 29

= 149.43 - 29

= 120.43

Hence, “120.43” is the correct answer.

The pattern followed here is:

• 2nd image is the mirror image of 1st image.

Similarly,

• 4th image is the mirror image of 3rd image.

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

The pattern followed here is,

Let (1st number : 2nd number)

(1st number)³ = 2nd number

Now follow the steps:

9 : 729

=> 9³ = 729 = 1st number

Similarly,

2 : ?

=> 23 = 8 = 1st number

Hence, "8" is correct answer.

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

Hence, ‘option 1’ is the correct answer.

Table show alphabet serial number –

The pattern followed is,

1)  KSJ : NQK

2)  MVK : PTL

3)  CYN : FWP

4)  GXQ : JVR.

All follow the same pattern, except 'CYN : FWP'

Hence, “CYN : FWP” is the odd one.

The pattern followed here is:

 

Hence, '28' is the correct answer.

The logic is here is,

(√1^st number + 4)² = 2nd number

Given:

9 is related to 49

=> (√9 + 4)² = (3 + 4)² = 7² = 49 = 2^nd number

And,

169 is related to 289

=> (√169 + 4)² = (13 + 4)² = 17² = 289 = 2^nd number

Similarly,

121 is related to

=> (√121 + 4)² = (11 + 4)² = 15² = 225 = 2^nd number

Hence, “225” is the correct answer.

Logic: If two dice have the same face value in the given image then their clockwise or anticlockwise wise number are known as opposite numbers in dice.

       ♦  If we rotate the second dice in a clockwise direction.

We get,

In first dice and second dice.

The number '8' is common.

      ♦  The left letter will be opposite to each other writing them clockwise starting from 8.

Hence, the face opposite to the 3 is “4”.

The table is alphabets place value:

 

Given: NR - SV - WZ

<br>

Similarly,

Option(1): LP - QT - UX

<br>

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

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

Square is divided into four parts:

1st to 2nd figure:

All shape shift in a clockwise direction and the square shape change into an arrow.

2nd to 3rd figure:

The two shape shift in a clockwise direction and the arrow shifts in front part of the square.

3rd to 4th  figure:

Follow the 1st to 2nd figure step.

4th to 5th figure:

Follow the 4th to 5th figure step.

Final series is

Hence, ‘option 4’ is the correct answer.

The table is alphabets place value:

Given: BAG : DEJ

Similarly,

Option(2): CAB : EEE

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

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

The Shape shifts alternate corner to corner,  corner to centre and centre to centre.

The Shape is alternate vertically flip and horizontally flip.

Final series is

Hence, ‘option 4’ is the correct answer.

The logic followed here is:

Option (1) 

→ The Back side line and curve area are in the same direction.

Option (2) 

→ The Back side line and curve area are in the same direction.

Option (3) 

→ The Back side line and curve area are in the same direction.

Option (4) 

→ The Back side line and curve area are NOT in the same direction.

All options are the same except Option (4).

Hence, “Option (4)” is an odd one.

The logic followed here is:

Option (1) 

 → Two leaf and black side area is the right side from the front.

Option (2) 

 → Two leaf and black side area is the left side from the front.

Option (3) 

→ ATwo leaf and black side area is the left side from the front.

Option (4) 

 → Two leaf and black side area is the left side from the front.

All options are the same except Option (1).

Hence, “Option (1)” is an odd one.

Now check all the options:

Option (1) 25 + 16 × 64 - 5 ÷ 8

After signs - and × are interchanged.

= 25 + 16 - 64 × 5 ÷ 8

Replacing the signs from left to right and using the BODMAS rule,

= 25 + 16 - 64 × 0.625

= 25 + 16 - 40

= 41 - 40

= 1 ≠ 97

Option (2) 8 ÷ 64 - 16 × 25 + 5

After signs - and × are interchanged.

= 8 ÷ 64 × 16 - 25 + 5

Replacing the signs from left to right and using the BODMAS rule,

= 0.125 × 16 - 25 + 5

= 2 - 25 + 5

= 7 - 25

= - 18 ≠ 97

Option (3) 16 + 64 ÷ 8 - 25 × 5

After signs - and × are interchanged.

= 16 + 64 ÷ 8 × 25 - 5

Replacing the signs from left to right and using the BODMAS rule,

= 16 + 8 × 25 - 5

= 16 + 200 - 5

= 216 - 5

= 211 ≠ 97

Option (4) 64 ÷ 16 - 25 × 8 + 5

After signs - and × are interchanged.

= 64 ÷ 16 × 25 - 8 + 5

Replacing the signs from left to right and using the BODMAS rule,

= 4 × 25 - 8 + 5

= 100 - 8 + 5

= 105 - 8

= 97 = 97

Hence, “Option(4)” is the correct answer.

The pattern followed here is:

92Hence, '110' is the correct answer.

The logic followed here is:

Option 1) Substitute-Replace → Replace is the SYNONYMS word of the substitute**.**

Option 2) Dearth-Abundance → Abundance is the ANTONYMS word of the Dearth.

Option 3) Haughty-Proud  → Proud is the SYNONYMS word of the Haughty.

Option 4) Abduct-Kidnap  → Kidnap is the SYNONYMS word of the Abduct.

Hence, “Dearth-Abundance” is an odd one.

The correct mirror image of the given figure when the mirror is held at the right side is:

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

The shaded part represents the number of people can play at least three musical instruments.

 

• The number representing  the number of people can play at least three musical instruments = 14 + 11 = 25

Hence, ‘25’ is the correct answer.

The shaded part represents the number of people can play only two musical instruments.

 

• The number representing  the number of people can play only two musical instruments = 12 + 7 + 5 + 9 + 21 = 54

Hence, ‘54’ is the correct answer.

The correct answer is Dharma, Artha, Kama, Moksha

Key Points

• The four aims of life as determined by the Vedic outlook are Dharma, Artha, Kama, and Moksha.
• Dharma refers to righteousness and ethical living.
• Artha pertains to wealth and prosperity.
• Kama encompasses desires and passions.
• Moksha signifies liberation and spiritual freedom.
• These aims guide individuals in balancing their personal aspirations with their duties towards society.

Additional Information

• The Vedic outlook forms the basis of many philosophical and spiritual traditions in India.
• It emphasizes a holistic approach to life, integrating material and spiritual pursuits.
• Dharma, Artha, Kama, and Moksha are collectively known as the Purusharthas.
• These aims are considered essential for achieving a balanced and fulfilling life.
• The concept of Purusharthas is deeply embedded in Hindu philosophy and culture.

The correct answer is Swara

Key Points

• Swara refers to the seven notes (Sa, Re, Ga, Ma, Pa, Dha, Ni) in Indian classical music.
• These notes form the foundation of melodies and are used in the creation of various ragas.
• Each swara has a specific pitch and is essential for the practice and performance of Indian classical music.
• Swara is different from raga, which is a framework for musical composition and improvisation.

Additional Information

• A raga is a melodic framework for improvisation akin to a melodic mode in Indian classical music.
• Taal refers to the rhythmic pattern and cycle in Indian classical music.
• The concept of swara is foundational and is taught to beginners as the first step in learning Indian classical music.

The correct answer is Pteridophyta-Marsilea

Key Points

• Pteridophyta-Marsilea is the correct pair of plant group and its example.
• Marsilea is a genus of aquatic ferns found in the Pteridophyta group.
• Pteridophytes are vascular plants that reproduce via spores and do not produce seeds or flowers.
• Other options provided are incorrect:
• Thallophyta includes algae, and Marchantia is a Bryophyte.
• Gymnosperms include conifers, and Bromeliads are angiosperms.
• Bryophyta includes mosses and liverworts, and Cladophora is an alga.

Additional Information

• Thallophyta is a division of the plant kingdom that includes simple plants like algae.
• Bryophyta includes non-vascular plants like mosses and liverworts that reproduce via spores.
• Gymnosperms are seed-producing plants like conifers that do not form flowers.
• Pteridophyta includes ferns and their allies, which are vascular plants reproducing via spores.

The correct answer is Igneous rock

Key Points

• Granite is classified as an igneous rock.
• Igneous rocks are formed through the cooling and solidification of magma or lava.
• Granite is known for its coarse-grained texture and is composed mainly of quartz, feldspar, and mica.
• This type of rock is commonly found in the continental crust and is extensively used in construction due to its durability and aesthetic appeal.

Additional Information

• Igneous rocks can be divided into two main types: intrusive (plutonic) and extrusive (volcanic).
• Granite is an example of an intrusive igneous rock, meaning it forms from magma that cools slowly beneath the Earth's surface.
• Other examples of igneous rocks include basalt (extrusive) and gabbro (intrusive).
• Granite's high resistance to weathering makes it a popular choice for monuments, buildings, and countertops.

The correct answer is Mysore

Key Points

• Mysore is the location of the Central Institute of Indian Languages (CIIL).
• The CIIL was established in 1969 under the Department of Higher Education, Ministry of Education, Government of India.
• It plays a vital role in the promotion and development of Indian languages.
• The institute focuses on research, training, and the development of language technologies.
• CIIL also conducts various programs to support the teaching and learning of Indian languages.

Additional Information

• The CIIL is located in Hunsur Road, Manasagangothri, Mysore, Karnataka.
• It aims to coordinate the development of Indian languages by conducting fundamental research in linguistics and language technology.
• The institute's activities include the creation of linguistic resources, language documentation, and the development of educational materials.
• CIIL also collaborates with various national and international organizations to promote multilingualism and language preservation.
• The institute has several regional language centers across India to support its mission.

The correct answer is Dr. Amit Singh and Dr. Arun Kumar Shukla

Key Points

• Dr. Amit Singh and Dr. Arun Kumar Shukla have been conferred the Shanti Swarup Bhatnagar Prize for Science and Technology, 2021, for biological science.
• The Shanti Swarup Bhatnagar Prize is one of the most prestigious awards in India for recognizing excellence in scientific research.
• The award is named after the founder Director of the Council of Scientific & Industrial Research (CSIR), Shanti Swarup Bhatnagar.
• It is awarded annually by the CSIR for notable and outstanding research, applied or fundamental, in biological, chemical, earth, atmosphere, ocean and planetary, engineering, mathematical, medical, and physical sciences.
• The prize comprises a citation, a plaque, and a cash award.

Additional Information

• Dr. Amit Singh is known for his work in the field of microbial pathogenesis and tuberculosis.
• Dr. Arun Kumar Shukla is recognized for his contributions to the understanding of G protein-coupled receptors (GPCRs) and their signaling mechanisms.
• The Shanti Swarup Bhatnagar Prize was first awarded in 1958 and has since been awarded annually.
• The award aims to encourage and nurture young scientists to pursue high-quality research in their respective fields.
• Recipients of the Shanti Swarup Bhatnagar Prize often go on to receive further national and international recognition for their work.

The correct answer is Refraction due to difference in the layers of gases reflection

Key Points

• The twinkling of stars is primarily caused by the refraction due to the difference in the layers of gases in the Earth's atmosphere.
• As starlight enters the Earth's atmosphere, it passes through various layers of air with different temperatures and densities, causing the light to bend (refract).
• This refraction causes the star's light to change direction multiple times, making the star appear to move slightly and change in brightness, which is perceived as twinkling.
• Scattering of light, reflection, and simple refraction are not the primary reasons for the twinkling effect observed.

Additional Information

• The phenomenon of twinkling is more pronounced for stars because they are point sources of light, unlike planets which appear larger and their light averages out the refraction effects.
• The scientific term for the twinkling of stars is stellar scintillation.
• Atmospheric turbulence is the main cause of the varying refraction index in different layers of the atmosphere.
• This effect can be minimized by observing stars from higher altitudes or using adaptive optics in telescopes.

The correct answer is Yakshagana

Key Points

• Yakshagana is a traditional dance form that originated in the state of Karnataka, India.
• It combines dance, music, dialogue, costume, make-up, and stage techniques with a unique style and form.
• Yakshagana is performed typically during the night and can last for several hours, sometimes till dawn.
• This dance form is known for its vibrant costumes and elaborate headgears, which are intrinsic to its performance.
• The themes of Yakshagana are usually drawn from Hindu epics like the Ramayana and the Mahabharata.

Additional Information

• Chhau is a semi-classical Indian dance with martial, tribal, and folk origins, found in Eastern India.
• Kalaripayattu is a martial art form that originated in Kerala.
• Theyyam is a popular ritual form of worship in Kerala, known for its vibrant costumes and body painting.
• These dance forms, though culturally rich, are not associated with Karnataka like Yakshagana.
• Yakshagana has a long history and is a significant part of Karnataka's cultural heritage.

The correct answer is 100 joules

Key Points

• 100 joules is the kinetic energy of the object when it is halfway down.
• An object falling freely under gravity converts its potential energy at the starting height into kinetic energy as it falls.
• When the object is halfway down, it has converted half of its initial potential energy into kinetic energy.
• The initial potential energy (PE) at 10 meters is given by PE = mgh, where m = 2 kg, g = 10 m/s², and h = 10 m.
• Thus, PE = 2 kg * 10 m/s² * 10 m = 200 joules.
• When the object is halfway down (at 5 meters), it has lost half of its initial potential energy, which is 100 joules.
• This 100 joules of lost potential energy is converted into kinetic energy.
• Thus, the kinetic energy of the object halfway down is 100 joules.

Additional Information

• The acceleration due to gravity (g) is approximately 10 m/s².
• Energy conservation principles state that the total mechanical energy (potential + kinetic) of an object in free fall remains constant if air resistance is negligible.
• The potential energy lost by the object as it falls is converted into kinetic energy, increasing its velocity.
• At the halfway point, the potential energy is equally split into kinetic energy, illustrating the conservation of energy in a gravitational field.

The correct answer is West Bengal

Key Points

• West Bengal is the state where most of the jute mills are located in India.
• The state has a long history and tradition in jute manufacturing, which is one of the major industries contributing to its economy.
• The jute mills in West Bengal are concentrated along the banks of the Hooghly River, which provides the necessary water and transportation facilities for the industry.
• The favorable geographical conditions, such as the availability of raw jute, skilled labor, and proximity to ports, have made West Bengal the hub of the jute industry in India.

Additional Information

• Jute, often referred to as the 'golden fiber,' is a natural fiber with high tensile strength and low extensibility.
• It is used in the production of various goods such as hessian cloth, jute bags, carpets, and ropes.
• The jute industry in India is regulated by the Jute Commissioner, who oversees the production, distribution, and export of jute products.
• West Bengal's jute industry also contributes significantly to the employment sector, providing jobs to thousands of workers in the region.
• Efforts are being made to modernize the jute industry in West Bengal to enhance productivity and sustainability.

The correct answer is Minerals and vitamins

Key Points

• Minerals and vitamins are classified as micronutrients because they are required by the body in small amounts.
• These nutrients are essential for various bodily functions, including growth, disease prevention, and well-being.
• Micronutrients differ from macronutrients (carbohydrates, proteins, and fats), which are needed in larger quantities.
• Deficiencies in micronutrients can lead to serious health problems, emphasizing their importance in a balanced diet.

Additional Information

• Minerals include elements like iron, calcium, and potassium, which are crucial for processes such as oxygen transport, bone formation, and nerve function.
• Vitamins are organic compounds, such as vitamin C, vitamin D, and B-vitamins, that play roles in immune function, energy production, and cellular repair.
• Both types of micronutrients must be obtained through diet as the human body cannot produce them in sufficient quantities.
• A diverse and balanced diet typically provides all the necessary micronutrients to maintain health and prevent deficiencies.

The correct answer is R. K. Narayan

Key Points

• R. K. Narayan is the author famous for creating the fictional town named Malgudi.
• Malgudi is a fictional town in South India that serves as the setting for most of Narayan's stories and novels.
• The town of Malgudi was first introduced in Narayan's debut novel, "Swami and Friends", published in 1935.
• R. K. Narayan is one of the most celebrated Indian authors in English literature, known for his simplicity and humor in storytelling.
• His works have been translated into many languages and have earned him international acclaim.

Additional Information

• R. K. Narayan was born on October 10, 1906, in Madras (now Chennai), India.
• He has been honored with several awards, including the Sahitya Akademi Award and the Padma Bhushan.
• R. K. Narayan's other notable works include "The Guide," "The Bachelor of Arts," "The English Teacher," and many more.
• His writing often explores the intricacies of Indian middle-class life and the human condition.
• R. K. Narayan passed away on May 13, 2001, leaving behind a rich legacy in Indian literature.

The correct answer is The US

Key Points

• India launched the Artificial Intelligence Initiative in collaboration with The US on 18 March 2021.
• The initiative aims to foster AI innovation by sharing ideas and experiences.
• It focuses on identifying new opportunities in research and development.
• The initiative also emphasizes bilateral collaboration between India and the US.

Additional Information

• The collaboration is expected to enhance the AI capabilities of both nations.
• This initiative is part of a broader effort to strengthen the technological partnership between India and the US.
• Artificial Intelligence (AI) is a key area of mutual interest for both countries.
• The initiative will contribute to the global AI ecosystem by fostering innovation and development.

The correct answer is The planets orbit around the sun

Key Points

• Nicolas Copernicus proposed the heliocentric model of the universe.
• In this model, the planets, including Earth, orbit around the Sun.
• This was a revolutionary idea at the time, as the prevailing belief was the geocentric model, which posited that the Earth was the center of the universe.
• Copernicus' work laid the foundation for future astronomers like Galileo and Kepler to further develop and confirm the heliocentric theory.
• His seminal work, "De revolutionibus orbium coelestium" (On the Revolutions of the Celestial Spheres), was published in 1543.

Additional Information

• Nicolaus Copernicus was a Renaissance-era polymath who made significant contributions to astronomy, mathematics, and economics.
• His heliocentric theory challenged the long-standing Ptolemaic system, which held that the Earth was the center of the universe.
• Copernicus' ideas were initially met with resistance but eventually gained acceptance, profoundly influencing the Scientific Revolution.
• The heliocentric model simplified the explanation of the retrograde motion of planets and provided a more accurate framework for understanding celestial mechanics.
• Copernicus' work paved the way for the development of modern astronomy and our current understanding of the solar system.

The correct answer is 4

Key Points

• Lysosome is a membrane-bound cell organelle that contains digestive enzymes.
• Lysosomes are involved in various cell processes, including the breakdown of excess or worn-out cell parts.
• They can be used to destroy invading viruses and bacteria.
• Lysosomes are known as the cell's waste disposal system; they digest unwanted materials in the cytoplasm.
• They play a key role in cellular homeostasis, autophagy, and apoptosis.

Additional Information

• Lysosomes are found in nearly all animal cells, but are rare in plant cells.
• The enzymes within lysosomes are synthesized in the rough endoplasmic reticulum and transported to the Golgi apparatus for further processing.
• Lysosomal storage diseases are a group of disorders caused by defects in lysosomal function.
• Examples of lysosomal storage diseases include Tay-Sachs disease, Gaucher's disease, and Pompe disease.
• Proper lysosomal function is crucial for the health and survival of cells.

The correct answer is Mohammad Hamid Ansari

Key Points

• The book 'By Many a Happy Accident: Recollections of a Life' was authored by Mohammad Hamid Ansari.
• Mohammad Hamid Ansari served as the 12th Vice President of India from 2007 to 2017.
• The book was published in February 2021 and provides a detailed account of his life and career, including his tenure as Vice President.
• In the book, Ansari shares his experiences and insights from his public service and diplomatic career.

Additional Information

• Mohammad Hamid Ansari has had a distinguished career in the Indian Foreign Service and has served as India's ambassador to several countries.
• He has also been the Permanent Representative of India to the United Nations.
• In addition to his diplomatic roles, Ansari has been a distinguished academician and has served as the Vice-Chancellor of Aligarh Muslim University.
• His book provides valuable insights into India's foreign policy and governance from the perspective of someone who has been at the helm of affairs.

The correct answer is Sandesh Jhingan

Key Points

• Sandesh Jhingan received the Arjuna Award 2020 for football.
• The Arjuna Award is one of the prestigious awards given by the Ministry of Youth Affairs and Sports, Government of India, to recognize outstanding achievements in sports.
• Sandesh Jhingan is a well-known Indian footballer who has represented the national team and played for various clubs in the Indian Super League (ISL).
• His contributions to Indian football have been significant, earning him this honor in 2020.

Additional Information

• The Arjuna Award was instituted in 1961 to recognize outstanding achievements in national sports.
• Recipients of this award are given a bronze statue of Arjuna, a certificate, ceremonial dress, and a cash prize.
• The award not only honors the sports achievements but also encourages young athletes to strive for excellence in their respective fields.
• Other notable recipients of the Arjuna Award in 2020 include Deepti Sharma for cricket and Ishant Sharma for cricket.

The correct answer is Bases

Key Points

• Bases are substances that are bitter in taste and slippery to touch.
• They can turn red litmus paper blue, indicating their basic nature.
• Common examples of bases include sodium hydroxide (NaOH), potassium hydroxide (KOH), and ammonia (NH₃).
• Bases react with acids to form water and salts in a neutralization reaction.

Additional Information

• Acids are substances that are sour in taste and can turn blue litmus paper red.
• Salts are ionic compounds that result from the neutralization reaction of an acid and a base.
• Water is a neutral substance and does not exhibit the properties of acids or bases.
• The pH scale is used to measure the acidity or basicity of a solution, with values less than 7 indicating acidic solutions and values greater than 7 indicating basic solutions.

The correct answer is Odisha

Key Points

• Odisha is rich in bauxite, the primary raw material used for obtaining aluminium.
• Bauxite deposits in Odisha are considered one of the largest in India, making it a significant contributor to the aluminium industry.
• The state has several bauxite mines and is home to key aluminium production facilities.
• Bauxite mining in Odisha contributes to the state's economy and provides employment opportunities.

Additional Information

• Bauxite is primarily found in the eastern ghats of Odisha.
• Major bauxite mines in Odisha are located in the districts of Koraput, Kalahandi, and Rayagada.
• Odisha's bauxite reserves are estimated to be around 1,530 million tonnes, which is approximately 50% of India's total bauxite reserves.
• Companies like National Aluminium Company Limited (NALCO) have established their operations in Odisha due to the abundance of bauxite.
• The aluminium industry in Odisha also supports ancillary industries and contributes to infrastructure development.

The correct answer is Telangana

Key Points

• Telangana planned to conduct a dry run of India's first smartphone-based e-voting system in October 2021.
• This initiative aims to facilitate easier and more accessible voting processes, especially for those unable to physically visit polling stations.
• The e-voting system leverages advanced technology to ensure security, transparency, and reliability in the voting process.
• This move is part of broader efforts to incorporate technology into governance and public administration to enhance efficiency and inclusivity.

Additional Information

• Electronic voting or e-voting is a term used to describe the act of voting using electronic means to either aid or take care of the chores of casting and counting votes.
• India has been exploring various electronic voting systems to enhance the electoral process, ensuring that it is more accessible, secure, and efficient.
• The smartphone-based e-voting system is a significant step towards digitizing the electoral process and making it more adaptable to the needs of the modern electorate.
• Successful implementation of this system could pave the way for wider adoption in future elections, potentially transforming how voting is conducted in India.

The correct answer is 1685; 1687

Key Points

• Aurangzeb annexed Bijapur in 1685 and Golconda in 1687 into the Mughal Empire.
• These annexations were part of Aurangzeb's Deccan campaign which aimed to expand Mughal territory in southern India.
• Bijapur and Golconda were significant Sultanates in the Deccan region and their annexation marked the expansion of Mughal influence in the south.
• Aurangzeb's campaign in the Deccan was both prolonged and expensive but ultimately successful in terms of territorial gains.

Additional Information

• Aurangzeb was the sixth Mughal emperor, ruling from 1658 to 1707.
• His reign is often characterized by his efforts to expand the Mughal Empire to its greatest territorial extent.
• The Mughal Empire under Aurangzeb extended over most of the Indian subcontinent.
• Aurangzeb's policies and military campaigns had long-lasting impacts on the region, both politically and culturally.
• The annexation of Bijapur and Golconda significantly weakened the power of the Deccan Sultanates and paved the way for the eventual rise of the Maratha Empire.

The correct answer is Government of India Act, 1935

Key Points

• The Government of India Act, 1935 was based on the recommendations of the Simon Commission Report.
• The Simon Commission was formed in 1927 to review the working of the Government of India Act, 1919, and suggest reforms.
• The Commission's recommendations were published in 1930 and formed the basis for the Government of India Act, 1935.
• This Act introduced significant changes, including the establishment of provincial autonomy and the federal structure.
• The Act also proposed the creation of an All-India Federation, although this part was never implemented.

Additional Information

• The Simon Commission faced significant opposition in India because it did not include any Indian members.
• The Commission's report recommended the abolition of dyarchy and the introduction of provincial autonomy in its place.
• The Government of India Act, 1935, is considered a significant step towards the eventual independence of India.
• It laid down the principles that were later adopted in the Constitution of India, which came into effect on 26th January 1950.
• The Act also provided for the establishment of a Federal Court, which later evolved into the Supreme Court of India.

The correct answer is Majuli

Key Points

• Majuli is the largest inhabited river island in India.
• It is located on the Brahmaputra River in the Indian state of Assam.
• The island has a rich cultural heritage and is known for its vibrant festivals and traditional Assamese culture.
• Majuli is also recognized for its unique biodiversity and is home to various species of flora and fauna.
• The island is an important center for the Vaishnavite culture and houses numerous Satras (monasteries).

Additional Information

• Majuli has been recognized by the Guinness World Records as the world's largest river island.
• The island is subject to frequent flooding and erosion due to its location on the Brahmaputra River.
• Efforts are being made to preserve Majuli's unique ecosystem and cultural heritage through various conservation initiatives.
• Majuli is accessible by ferries from the city of Jorhat, making it a popular tourist destination.
• The island's scenic beauty and serene environment attract visitors from around the world.

The correct answer is 2015

Key Points

• The Ek Bharat Shreshtha Bharat initiative was launched in the year 2015.
• This initiative aims to enhance understanding and bonding between the states of India, thus strengthening the unity and integrity of India.
• It promotes cultural exchange and mutual understanding among different states and union territories of India.
• Under this initiative, states and UTs are paired with each other for a fixed time period, during which they carry out activities to promote a sustained and structured cultural connection.

Additional Information

• The initiative was announced by the Hon'ble Prime Minister on 31st October 2015, the 140th birth anniversary of Sardar Vallabhbhai Patel.
• It aims to celebrate the cultural diversity of India and to foster a spirit of national integration.
• Activities under this initiative include cultural performances, literary events, and reciprocal visits by students and teachers, among others.
• The initiative is managed by the Ministry of Education and other relevant ministries and departments.
• It seeks to create an environment of learning between the states by sharing best practices and experiences.

The correct answer is Candela

Key Points

• Candela is a unit of luminous intensity, not a unit of temperature.
• Units of temperature include Celsius, Kelvin, and Fahrenheit.
• The Celsius scale is commonly used in most parts of the world for everyday temperature measurement.
• The Kelvin scale is used in scientific contexts and is the SI base unit for temperature.
• The Fahrenheit scale is primarily used in the United States for weather forecasts and other applications.

Additional Information

• Candela (cd) is one of the seven base units in the International System of Units (SI).
• It measures the amount of light emitted in a particular direction by a source.
• The unit is critical in fields such as lighting design, photography, and vision science.
• Understanding the distinction between units of temperature and luminous intensity is essential in science and engineering.

The correct answer is Q = A L^(α) K^(\beta)

Key Points

• Q = A L^(α) K^(\beta) is the mathematical form of the Cobb-Douglas production function.
• The Cobb-Douglas production function represents the relationship between two or more inputs (typically labor and capital) and the amount of output produced.
• In the function, Q denotes the total output, A is a constant representing total factor productivity, L is the quantity of labor, K is the quantity of capital, and α and β are the output elasticities of labor and capital, respectively.
• The function is widely used in economics to represent production processes where inputs are substitutable but exhibit diminishing returns.
• The sum of the exponents (α + β) determines the returns to scale of the production function.

Additional Information

• The Cobb-Douglas production function was developed by economist Charles Cobb and mathematician Paul Douglas in the 1920s.
• It has been used to empirically analyze the production processes of various industries and economies.
• The function assumes that the production process is efficient and that the inputs are used optimally.
• The output elasticities (α and β) are typically estimated using statistical methods such as regression analysis.
• The Cobb-Douglas function can be extended to include more than two inputs, making it a flexible tool for economic analysis.

The correct answer is 6

Key Points

• The Super Highways in the Golden Quadrilateral have 6 lanes.
• The Golden Quadrilateral is a highway network connecting major industrial, agricultural, and cultural centers of India.
• This project was initiated by the National Highways Development Project (NHDP) and is maintained by the National Highways Authority of India (NHAI).
• It forms a quadrilateral connecting Delhi, Mumbai, Chennai, and Kolkata, and spans over 5,846 kilometers.

Additional Information

• The Golden Quadrilateral is one of the largest highway projects in India and significantly reduces travel time between the major cities.
• The project was launched in 2001 and was completed in 2012.
• It has improved the transportation infrastructure, boosted trade and commerce, and contributed to the economic growth of the country.
• The highways in the Golden Quadrilateral are designed to handle heavy traffic and support high-speed travel.

The correct answer is none of the given answers

Key Points

• None of the given answers is not a method of rainwater harvesting.
• The other options listed are valid methods of rainwater harvesting:
• Surface runoff harvesting: This method involves collecting rainwater runoff from surfaces like roads, gardens, and fields.
• Rooftop rainwater harvesting: This method involves collecting rainwater from rooftops and directing it to storage tanks or recharge pits.
• First flush: This method involves diverting the initial flow of rainwater away from the storage system to avoid contamination.

Additional Information

• Rainwater harvesting is a sustainable practice that helps in conserving water, reducing runoff, and recharging groundwater levels.
• It is especially beneficial in areas facing water scarcity and can significantly contribute to water security.
• Implementing rainwater harvesting systems can also reduce the dependency on conventional water supply systems and promote environmental sustainability.

The correct answer is electromagnetic induction

Key Points

• The process of rotating a coil in a magnetic field of an electric generator is known as electromagnetic induction.
• Electromagnetic induction is the production of an electromotive force across a conductor when it is exposed to a varying magnetic field.
• This principle is the fundamental operation mechanism of electric generators, transformers, and many other electrical devices.
• The phenomenon was discovered by Michael Faraday in 1831, and it is described by Faraday's Law of Induction.
• In an electric generator, the mechanical energy of rotating the coil is converted into electrical energy through electromagnetic induction.

Additional Information

• Michael Faraday is often credited with the discovery of electromagnetic induction, which laid the foundation for modern electromagnetic technology.
• Faraday's Law of Induction states that the induced electromotive force in any closed circuit is equal to the negative of the time rate of change of the magnetic flux through the circuit.
• Electromagnetic induction has numerous applications, including in the generation of electricity, induction cooking, and wireless power transfer.
• The efficiency and functionality of electric generators are critical for power generation in both industrial and residential settings.
• Understanding the principles of electromagnetic induction is essential for fields such as electrical engineering, physics, and various applied sciences.

The correct answer is quasi-federal in nature

Key Points

• The Indian Constitution is described as quasi-federal in nature, meaning it has features of both federal and unitary government systems.
• It establishes a dual polity with a clear division of powers between the Union and the States, but with a strong centralizing tendency.
• In case of conflict between central and state laws on a subject in the Concurrent List, the central law prevails.
• The Constitution provides for a strong central government with the power to override states in certain situations, reflecting its quasi-federal character.

Additional Information

• The Constitution of India is the longest written constitution of any sovereign country in the world.
• It establishes India as a sovereign, socialist, secular, and democratic republic.
• The Constitution provides for the division of powers through three lists in the Seventh Schedule: Union List, State List, and Concurrent List.
• The Union government has exclusive powers to legislate on subjects in the Union List, which includes areas of national importance like defense, foreign affairs, and railways.
• The Indian Constitution was adopted on 26th November 1949 and came into effect on 26th January 1950.
• Amendments to the Constitution can be made through the procedure outlined in Article 368.
• The quasi-federal nature allows for a balance of power, ensuring both central authority and state autonomy.

The correct answer is Repo rate

Key Points

• Repo rate is the rate at which the Reserve Bank of India (RBI) lends short-term money to commercial banks.
• This rate is used by monetary authorities to control inflation and regulate the supply of money in the economy.
• When the repo rate increases, borrowing from the central bank becomes more expensive, which can reduce the money supply and control inflation.
• Conversely, a decrease in the repo rate can encourage banks to borrow more, increasing the money supply and stimulating economic activity.

Additional Information

• The Reverse Repo Rate is the rate at which RBI borrows money from commercial banks, which can be used to control liquidity in the economy.
• The Bank Rate is the rate at which RBI lends money to commercial banks without any security.
• The Cash Reserve Ratio (CRR) is the percentage of a bank's total deposits that must be maintained with the central bank as reserves.
• These tools are part of the monetary policy used by the RBI to regulate the economy's money supply and maintain financial stability.

The correct answer is Both (a) and (b)

Key Points

• Legal tender can be limited or unlimited in character.
• Limited legal tender:
• Coins are a function of limited legal tender in India.
• It is because up to a certain limit, coins can be offered as limited legal tender.
• 50 paise coins can be offered as legal tender for dues up to Rs. 10 and smaller coins for dues up to Rs. 1.
• They are accepted up to a maximum sum.
• Unlimited legal tender:
• Currency notes and paper notes are regarded as unlimited legal tender.
• They are considered as an important form of medium of exchange.
• There is no limit for their issue.
• Hence, it can be concluded that both statements are correct.

The correct answer is Harishena

Key Points

• Harishena was a maha-danda-nayaka or chief judicial officer during the Gupta Period.
• The title "maha-danda-nayaka" indicates a high-ranking official responsible for judicial and legal matters.
• Harishena was also a renowned poet and is known for his eulogy of the Gupta emperor Samudragupta in the Allahabad Pillar inscription.
• His dual role as a judicial officer and a poet highlights the multifaceted nature of scholars during the Gupta era.
• The Gupta Period is often considered a golden age of Indian culture, literature, and governance.

Additional Information

• The Gupta Empire, which lasted from around 320 to 550 CE, is noted for its achievements in arts, science, and political administration.
• Other notable poets and scholars of the Gupta period include Kalidasa and Aryabhata.
• The period saw the composition of significant literary works, advancements in mathematics and astronomy, and the flourishing of classical art forms.

The correct answer is veena

Key Points

• Samudragupta was depicted playing a veena on his coins.
• The veena is a traditional Indian string instrument, which highlights the cultural and artistic achievements during Samudragupta's reign.
• Samudragupta's coins are a significant source of historical information, providing insights into the Gupta period's art, culture, and administration.
• His portrayal with a veena reflects his patronage of music and the arts, showcasing the importance of cultural activities in his empire.

Additional Information

• Samudragupta, often referred to as the 'Napoleon of India,' was a prominent ruler of the Gupta dynasty who reigned from approximately 335–375 CE.
• His reign is noted for its military conquests, which expanded the Gupta Empire across much of the Indian subcontinent.
• Samudragupta was also a patron of learning and the arts, and his court was a hub of cultural and scholarly activity.
• The Gupta period is often considered a golden age of Indian culture, marked by significant achievements in literature, science, and the arts.

The correct answer is Density of population

Key Points

• Density of population refers to the number of persons per unit area.
• It is a crucial metric for understanding the concentration of people in a given geographical area.
• A higher density indicates more people living in a smaller area, which can have implications for resources, infrastructure, and services.
• Conversely, a lower density suggests fewer people spread over a larger area, which might mean less strain on local resources but possibly less efficient service delivery.

Additional Information

• Population density is calculated by dividing the total population by the total land area.
• This metric is essential for urban planning, resource allocation, and understanding demographic trends.
• High population density areas often require more robust infrastructure and services to support the larger number of residents.
• Conversely, low population density areas might face challenges related to economic development and accessibility of services.

The correct answer is Limestone

Key Points

• Limestone primarily consists of the mineral calcite (calcium carbonate, CaCO3).
• It is a sedimentary rock that forms from the accumulation of shell, coral, algal, and fecal debris, or by the precipitation of calcium carbonate from lake or ocean water.
• Other rocks listed, such as Granite and Gabbro, are composed of multiple minerals, including quartz, feldspar, and mica in granite, and pyroxene, plagioclase, and olivine in gabbro.
• Pumice is a volcanic rock that typically contains multiple minerals and glassy materials.

Additional Information

• Limestone is used in a variety of applications, including construction, agriculture, and industry.
• It is a key ingredient in the production of cement and is also used as a building stone and for road base.
• The purity of limestone can vary, and it may contain small amounts of impurities such as clay, sand, and organic remains.
• Limestone can also form through biological processes, contributing to the formation of coral reefs and other marine structures.

The correct answer is State of Bihar V. Subhash Singh 1997

Key Points

• State of Bihar V. Subhash Singh 1997 is a landmark case where it was observed that courts have the authority to determine not only the constitutionality of the law but also the procedural part of administrative action.
• This case highlights the judiciary's role in ensuring that administrative actions comply with procedural requirements established by law.
• The decision underscores the importance of procedural fairness and the need for administrative bodies to adhere strictly to legal norms and standards.
• The case serves as a precedent for future cases involving the review of administrative actions and their procedural aspects.

Additional Information

• Cooper V. Union of India is another significant case that deals with judicial review but is more focused on the substantive aspects rather than procedural fairness.
• The importance of both procedural and substantive review by courts ensures a comprehensive check on administrative actions, safeguarding citizens' rights and upholding the rule of law.

The correct answer is potential energy

Key Points

• Potential energy is stored in water when it is at a higher level in a hydroelectric power station.
• This potential energy is converted into mechanical energy as the water moves downstream through turbines.
• The mechanical energy is then used to generate electricity in the power station.
• Hydroelectric power is a renewable source of energy, making it an important part of sustainable energy solutions.

Additional Information

• Hydroelectric power stations are often located near dams or reservoirs where large amounts of water can be stored.
• The process of converting potential energy to electrical energy involves multiple steps, including the operation of turbines and generators.
• Hydropower is one of the oldest and most widely used forms of renewable energy.
• It provides a significant portion of the world's electricity and contributes to reducing greenhouse gas emissions.

The correct answer is Pre-monsoon period

Key Points

• Mango showers are pre-monsoon rainfall which occurs in the Indian subcontinent.
• These showers are significant for the ripening of mangoes and thus are called mango showers.
• Mango showers usually occur in the months of April and May before the onset of the southwest monsoon.
• This phenomenon is observed primarily in the states of Kerala, Karnataka, and Tamil Nadu.
• The showers help in reducing the heat and providing relief from the scorching summer temperatures.

Additional Information

• Pre-monsoon showers are also known as blossom showers in Kerala and Karnataka.
• These showers are crucial for the coffee plantations in Kerala and Karnataka as they help in the blossoming of coffee flowers.
• Similar pre-monsoon showers are known as Nor'westers in West Bengal and Assam, locally called Kalbaishakhi.

The correct answer is Battle of Plassey, 1757

Key Points

• The Battle of Plassey, 1757, was a decisive victory for the British East India Company over the Nawab of Bengal and his French allies.
• This battle marked the beginning of British political control in India, eventually leading to the establishment of the British Raj.
• Robert Clive led the British forces to victory, and the battle significantly weakened the Mughal Empire's influence in India.
• Following their success in Plassey, the British East India Company gained significant control over Bengal, which was a wealthy and strategically important region.

Additional Information

• The Anglo-Mysore War, 1769, was a series of conflicts between the British East India Company and the Kingdom of Mysore but did not directly lead to British political control over India.
• The Partition of Bengal, 1905, was an administrative division by the British government, which was later annulled in 1911 due to widespread protests.
• Pitt's India Act, 1784, was a British parliamentary act that aimed to address the administration of the British East India Company's territories in India but came after the Battle of Plassey.

Given:

Principle = Rs. 6500, rate = 2%, time = 2 years.

Formula used:

CI = principle[(1 + $\dfrac{rate}{100}$)^time - 1]

Calculations:

CI = 6500[(1 + $\dfrac{2}{100}$)² - 1]

CI = 6500[(1 + $\dfrac{1}{50}$)² - 1]

CI = 6500[($\dfrac{51}{50}$)² - 1]

CI = 6500 × [$\dfrac{2601}{2500}$ - 1]

CI = 6500 × [$\dfrac{2601 - 2500}{2500}$]

CI = 6500 × [$\dfrac{101}{2500}$]

CI = $\dfrac{6565}{25}$

CI = Rs. 262.60

∴ The answer is Rs. 262.60

Given:

Group of 5 students scored 55, 48, 97, 88 and 72 marks in science test.

Formula used:

Average = $\dfrac{sum}{number}$

Calculations:

Average = $\dfrac{55 + 48 + 97 + 88 + 72}{5}$

Average = $\dfrac{360}{5}$

Average = 72

∴ The answer is 72.

Given:

Price of pen increased by 20% and then decreasea by 10%.

Formula used:

Single discount = x + y + $\dfrac{xy}{100}$ (where, x and y are successive discounts)

Calculations:

Single discount = + 20 - 10 + $\dfrac{(+20)(-10)}{100}$

= + 10 - 2

= + 8%

∴ The answer is 8%

Given:

Three digit numbers divisible by 5 or 9.

Formula used:

Divisibility rules of 5:

Number having zero or five at the end divisible by 5.

Divisibility rules of 9:

When the sum of all the digits of a number is divisible by 9 then the number is also divisible by 9.

Calculations:

Total number of positive multiples of 5 upto 1,000 = $\dfrac{1000}{5}$ = 200. Discarding the 2-digit numbers and 1000 itself we get 200 - (19 + 1), i.e. 180 elements.

Similarly there are $\dfrac{999}{9}$ = 111 multiples of 9 up to 1,000. Removing the 2-digit multiples of 9, gives us 111 - ($\dfrac{99}{9}$) = 111 – 11 = 100 three digit multiples of 9.

To get the answer we have to remove the count of the common terms in the lists so as not to count them twice. These are all the multiples of their LCM which is 45.

$\dfrac{999}{45}$ = 22.2. Hence there are 22 multiples of 45 up to 999, out of which there are two, viz, 45 and 90 which are of two digits. Thus there are (22 – 2) = 20 multiples of 45 which are of 3 digits.

Therefore the number of 3-digit numbers which are divisible by 5 or 9 = 180 + 100 – 20 = 260.

∴ The answer is 260.

Shortcut Trick

Identify the Pythagorean triplet: 8, 15, 17.

Given Diagonal (Hypotenuse) = 85 m = 17 × 5.

Given Length = 77 m (This does not fit the 8, 15, 17 triplet directly).

Using b = √(d² − l²): b = √(85² − 77²) = √((85+77)(85−77)) = √(162 × 8) = √1296 = 36 m.

Perimeter = 2 × (77 + 36) = 2 × 113 = 226 m.

∴ The correct answer is 226 m.

Alternate Method

Given:

Diagonal (d) of the rectangular park = 85 m

Length (l) of the rectangular park = 77 m

Formula Used:

In a rectangle, d² = l² + b² (Pythagoras Theorem)

Perimeter = 2 × (l + b)

Calculations:

⇒ 85² = 77² + b²

⇒ b² = 85² − 77²

⇒ b² = (85 + 77)(85 − 77)

⇒ b² = 162 × 8 = 1296

⇒ b = √1296 = 36 m

⇒ Perimeter = 2 × (77 + 36)

⇒ Perimeter = 2 × 113 = 226 m

∴ The correct answer is 226 m.

Additional Information

Rectangle Properties

A rectangle is a quadrilateral with four right angles. Opposite sides are equal and parallel. Area = l × b.

Pythagorean Triplets

Common triplets include (3, 4, 5), (5, 12, 13), (7, 24, 25), (8, 15, 17), (9, 40, 41), and (20, 21, 29).

Diagonal of a Rectangle

The diagonal divides the rectangle into two congruent right-angled triangles. Diagonal = √(l² + b²).

Given:

$49^{7.5} \div 49^{\frac{3}{2}} \times 49^{-3}=(\sqrt[3]{49})^{x}$

Calculations:

$49^{7.5} \div 49^{\frac{3}{2}} \times 49^{-3} = (\sqrt[3]{49})^{x}$

49^7.5 ÷ 49^1.5 × 49^-3 = $\sqrt[3]{49})^{x}$

49^(7.5-1.5-3) = $\sqrt[3]{49})^{x}$

49^(7.5-4.5) = $\sqrt[3]{49})^{x}$

49³ = $\sqrt[3]{49})^{x}$

49³ = 49^x/3

49³ = 49^x/3

3 = x/3

x = 9

∴ The answer is 9.

Given:

Amount = Rs. 1323, principle = Rs. 1200, rate = 5%

Formula used:

Amount = principle[(1 + $\dfrac{rate}{100}$)^time]

Calculations:

1323 = 1200[(1 + $\dfrac{5}{100}$)^time]

$\dfrac{1323}{1200}$ = [(1 + $\dfrac{1}{20}$)^time]

$\dfrac{441}{400}$ = ($\dfrac{21}{20}$)^time

($\dfrac{21}{20}$)² = ($\dfrac{21}{20}$)^time

Time = 2 years.

∴ The answer is 2 years.

Shortcut Trick

Convert all terms to a common base of 3 to equate exponents.

Base 3 exponent of 27 is 3, and for 9ⁿ⁺⁴, it is 2(n + 4).

Sum of exponents on LHS: 3 + 2n + 8 = 2n + 11.

Equating to RHS exponent: m = 2n + 11.

∴ The correct option is D.

Alternate Method

Given:

27 × 9ⁿ⁺⁴ = 3^m

Formula Used:

a^x × a^y = a^x+y and (a^x)^y = a^xy

⇒ 3³ × (3²)ⁿ⁺⁴ = 3^m

⇒ 3³ × 3²⁽ⁿ⁺⁴⁾ = 3^m

⇒ 3³ × 3²ⁿ⁺⁸ = 3^m

⇒ 3^{3 + 2n + 8} = 3^m

⇒ 3²ⁿ⁺¹¹ = 3^m

⇒ m = 2n + 11

∴ The correct option is D.

Additional Information

Product Law of Exponents

When multiplying powers with the same base, add the exponents: a^m × aⁿ = a^m+n.

Power of a Power Law

When an exponential expression is raised to a power, multiply the exponents: (a^m)ⁿ = a^mn.

Equality of Bases Rule

If a^x = a^y (where a ≠ 0, 1, −1), then the exponents must be equal: x = y.

Given:

Discount = 5%, marked price = Rs. 550

Formula used:

Selling price = marked price - discount% on marked price

Calculations:

Selling price = 550 - 550 × 5%

= 550 - 550 × $\dfrac{5}{100}$

= 550 - 550 × $\dfrac{1}{20}$

= 550 - 27.5

= Rs. 522.5

∴ The answer is Rs. 522.5

Given:

(2.43 + 1.62)² - ? = 4 × 2.43 × 1.62

Calculations:

(2.43 + 1.62)² - ? = 4 × 2.43 × 1.62

(4.05)² - ? = 15.7464

16.4025 - ? = 15.7464

16.4025 - 15.7464 = ?

= 0.6561

∴ The answer is 0.6561

Given:

Radius of cylinder = 2 units and height = 5 units.

Another cylinder having radius and height is the reciprocal of the original radius and height.

Formula used:

Volume of cylinder = π × radius² × height

Calculations:

Radius = 2 units, new radius = $\dfrac{1}{2}$ units

Height = 5 units, new height = $\dfrac{1}{5}$ units

New volume = π × $\dfrac{1}{2}$ × $\dfrac{1}{2}$ × $\dfrac{1}{5}$

New volume = π × $\dfrac{1}{20}$ units³

∴ The answer is $\dfrac{π}{20}$ units³