DSSSB Junior Secretariat Assistant Official paper (Held on: 2 April 2022 Shift 2 ) (Previous Year Paper)

Drawing the diagram according to the given information:

• Town MAH is to the West of Town KOL.
• Town KER is to the south of Town MAH.
• Town GOA is to the West of Town KER.

​

From the above diagram, it is clear that Town GOA is towards the South-West direction of Town MAH.

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

Given Series,

(Left) Z 2 @ 6 K 4 G ∞ S D % 7 R C & T Σ 3 N 8 (Right)

We have to find out the element which is seventh to the right of the element which is fourteenth from the right end of the series.

Fourteenth from the right end of the series = G

Seventh to the right of the Fourteenth = C

From the above diagram;

It is clear that C is the element which is seventh to the right of the element which is fourteenth from the right end of the series .

Hence, the correct answer is C.

Given,

D, L, M, Z, B and K are six friends, each weighing differently on a weighing scale.

• M is heavier than only two friends.

• B is lighter than only D, but immediately heavier than K.

• Z is lighter than M but NOT the lightest.

​ 

From the given information, it is clear that K is heavier than M, Z and L.

Hence, the correct answer is Three.

BODMAS rule : 

149.99 - [10.25 + {23.98 - (19.76 - 4.98)}] = ?

 

Replacing the given values with their approximate values,

149.99 - [10.25 + {23.98 - (19.76 - 4.98)}]

= 150 - [10 + {24 - (20 - 5)}]

= 150 - [10 + {24 - 15}]

= 150 - [10 + 9]

= 150 - 19

= 131

Hence, the correct answer is "131".

The logic followed here is:

Given,

TX - IM - DH,

Similarly,

We have to go through all the options given,

Option 1) RV - GL - MQ

Option 2) AE - GK - MP

This pair doesn't follow the logic.

Option 3) AF - GK - MQ

This pair doesn't follow the logic.

Option 4)  AE - GK - SW

This pair follows the same logic.

Hence, the correct answer is "AE - GK - SW".

Given,

A's mother is the only daughter of B's father.

We have to determine the relation between B's husband and A.

From the above family tree,

It is clear that, B's husband is the father of A.

Hence, the correct answer is Father.

Given

Statement:

P > R ≥ Q = W ≤ S < E

Conclusions:

1) Q < E → True (As, Q = W ≤ S < E gives; → Q < E, So Q < E True)

2) R > S → False (As, R ≥ Q = W ≤ S gives; → There is no clear relation between R and S, So R > S is not True)

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

Given,

• Diya is the daughter of Anu.
• Anu is Raj's wife.
• Sagar is the brother of Raj.

​

​

From the above family tree, it is clear that, Diya is the daughter of Raj.

Hence, the correct answer is Daughter.

Given,

171 : 142 :: 283 : ? :: 315 : 286​

The logic followed here is:

171 is related to 142 by following logic,

• 171 - 29 = 142

And, 

315 is related to 286 by following logic,

• 315 - 29 = 286

Similarly,

283 will be related to,

• 283 - 29 = 254

Hence, the correct answer is 254.

BODMAS rule:

Decoding the information;

Given,​

Option 1) 6 × 16 + 2 ÷ 4 - 3 = 14 + 7 ÷ 4 - 2

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

⇒ 6 - 16 ÷ 2 + 4 × 3 = 14 ÷ 7 + 4 × 2

⇒ 6 - 8 + 4 × 3 = 2 + 4 × 2

⇒ 6 - 8 + 12 = 2 + 8

⇒ 18 - 8 = 10

⇒ 10 = 10

Option 1 satisfies the BODMAS rule. 

Option 2) 7 × 42 + 7 ÷ 3 - 4 = 42 + 6 ÷ 2 - 7

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

⇒  7 - 42 ÷ 7 + 3 × 4 = 42 ÷ 6 + 2 × 7

⇒  7 - 6 + 3 × 4 = 7 + 2 × 7

⇒  7 - 6 + 12 = 7 + 14

⇒ 19 - 6 = 21

⇒  13 ≠ 21

Option 2 doesn't satisfy the BODMAS rule.

Option 3) 50 × 49 + 7 ÷ 1 - 2 = 30 + 6 ÷ 9 - 5

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

⇒ 50 - 49 ÷ 7 + 1 × 2 = 30 ÷ 6 + 9 × 5

⇒ 50 - 7 + 1 × 2 = 5 + 9 × 5

⇒ 50 - 7 + 2 = 5 + 45

⇒ 45 ≠ 50

Option 3 doesn't satisfy the BODMAS rule.

Option 4) 9 × 16 + 8 ÷ 6 - 3 = 32 + 32 ÷ 4 - 8

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

⇒ 9 - 16 ÷ 8 + 6 × 3 = 32 ÷ 32 + 4 × 8

⇒ 9 - 2 + 6 × 3 = 1 + 4 × 8

⇒ 9 - 2 + 18 = 1 + 32

⇒ 25 ≠ 33

Option 4 doesn't satisfy the BODMAS rule.

Hence, the correct answer is "6 × 16 + 2 ÷ 4 - 3 = 14 + 7 ÷ 4 - 2".

Given,

37 : 216 :: 65 : ? :: 26 : 125​

The logic followed here is:

37 : 216

• ​37 ⇒ 36 + 1 ⇒ 6² + 1
• 216 ⇒ 6³

26 : 125

• 26 ⇒ 25 + 1 ⇒ 52 + 1
• 125 ⇒ 53

Similarly,

65 : ?

​65 ⇒ 64 + 1 ⇒ 82 + 1 

? ⇒ 83 ⇒ 512

Hence, the correct answer is "512".

Given

Statement:

I. P < Q ≤ W = R ≤ Y

II. R ≥ M

Conclusions:

1) P > M  → False (As, P < Q ≤ W = R, R ≥ M given; → no clear relation between P and M, So P > M false)

2) Y ≥ Q  → True (As, Q ≤ W = R ≤ Y given; → Y ≥ Q, So Y ≥ Q True)

Hence, the correct answer is "Only conclusion II is true".

The logic followed here is:

• FIRE is written as GHSD.

​

​Similarly, 

BURN will be written as,

Hence, the Correct answer is CTSM.

BODMAS rule:

Decoding the information;

Given,

6 L 25 M 15 N 45 O 5

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

= 6 × 25 - 15 + 45 ÷ 5

= 6 × 25 - 15 + 9

= 150 - 15 + 9

= 159 - 15

= 144

Hence, the correct answer is 144.

According to the given information:

The ascending order of the numbers is as follows,

• 295 < 345 < 469 < 505 < 678
• 295 is the smallest number, with 5 being its 3^rd digit.
• 678 is the highest number, with 7 being its 2^nd digit.
• 5 × 7 = 35

​

Hence, the correct answer is "35".

According to the given information:

1. ​Raghav is facing north
2. He goes straight for 45 meters,
3. Then he turns left and walks 30 meters,
4. Then turns right and goes 35 meters,
5. And then turns right again and covers a distance of 40 meters.

​So from the following, this diagram can be deduced,

As we can see from the diagram he is currently walking in the East direction.

Hence, the correct answer is "East"

The logic followed here is:

CONCEPT is written as XLMXVKG,

• The alphabets are placed right below their opposite alphabets as they are placed in the chart.

Similarly,

ATTAINMENT will be written as,

Hence, the correct answer is "ZGGZRMNVMG"

The logic followed here is:

• According to the chart, the alphabets have numbers corresponding to the middle number.
• The initial alphabet has the previous number and the last alphabet has the following number.

J11L is related to M14O.

And, 

S20U is related to G8I.

Similarly

N15P is related to,

Only K12M follows a similar pattern as above.

Hence, the correct answer is "K12M".

According to the given information: ​

If 7 U Σ @ are written as @ Σ U 7, K 6 ≠ 3 are written as 3 ≠ 6 K.

Let's rearrange all the component of the given series in this manner.

@ Σ U 7 3 ≠ 6 K 2 ≤ 9 H E 4 $ T 8 P L % ¥ 6 G \(\mho \) & C 8 B

Hence, the correct answer is "$".

According to the given information:

 

1. P - Q × R + J → P is the sister of Q, Q is the father of R and R is the brother of J.

​

R is the nephew of P.

2. J - R + Q × P → J is the sister of R, R is the brother of Q and Q is the father of P.

​

R is the uncle of P.

3) P × Q - R + J → P is the father of Q, Q is the sister of R, and R is the brother of J.

​

R is the son of P.

4. Q + P - J × R → Q is the brother of P, P is the sister of J, and J is the father of R.

​

R is either niece or nephew of P as R's gender is not defined. 

From the above diagram, only option 3 satisfies the condition of "R" being the son of P.

Hence, the correct answer is "P × Q - R + J".

According to the given information:

Friends: L, O, S, T and Q are facing north.

• L is at the extreme left. Q is at the extreme right.
• T is in the middle of the row.

​

• S is not sitting with L, so he will be next to Q.
• So, the only position left for O is 2^nd from left.

Thus, O is sitting next to L.

Hence, the correct answer is "O".

The logic followed here is:

• The difference between the difference of numbers is increasing by +2.

​Hence, the correct answer is "104".

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

1. Upper three and lower three small figures interchange their position in a clockwise direction alternatively.

2. The sides of the bigger figure in the middle increase by +1 in every step.

Hence, the correct answer is "option 4"

The logic followed here is:

• The 1^st alphabet of the series is increased by +2.
• The number changes by n, where n = +1, -2, +3, -4... in every step simultaneously.
• The 2^nd alphabet of the series is increased by +2.

Hence, the correct answer is "N52M".

The logic followed here is:

• The number increases by +n, where n = odd number > 0 in every step.
• The 1^st alphabet of the series is increased by +1.
• The 2^nd alphabet of the series is increased by +1.

Hence, the correct answer is "51 NM"

The logic followed here is:​​

1. POR-QNS

2. TER-UDS

3. BRI- CQJ

4) GHT-HIU

All follow the same pattern, except GHT-HIU.

Hence, the correct answer is "GHT-HIU".

The logic followed here is:

The different numbers in this series follow a sequence n2 where n = 1, 2, 3, 4...

• 47 - 46 = 1 = 12
• 51 - 47 = 4 = 22

​​Therefore the difference between the next number should be 32 i.e 9.

• 60 - 51 = 9 = 32
• 60 + 14 = 76

​Hence, the correct answer is "60".

The logic followed here is:

1. XUR

2. YVS

3) WTR

4. ZWT

All follow the same pattern, except WTR.

Hence, the correct answer is "WTR".

The logic followed here is:

WTQ : KHE

The alphabets are decreasing by - 3 in both letters.

Among the given options only PMJ : DAX follows the same logic.

Hence, the correct answer is "PMJ: DAX".

The logic followed here is:

• The line in the diagram rotates 3 edges in a clockwise direction keeping the other edged endpoint constant.

​

• After the 3 clockwise rotations, the fixed endpoint of the line shifts one place in the clockwise direction.
• By keeping the new endpoint fixed the other end shifts 3 edges clockwise.

​

Hence, the correct answer is "option 4"

According to the given information:

Friends: Raj, Amit, Varun, Kanchan, and Tiya are sitting facing the North.

• Three friends are sitting between Tiya and Raj.
• There are 2 possible cases.

Case I -

​

Case II -

• Varun is sitting to the immediate left of Raj and second to the right of Amit.
• If Raj sits to the extreme left Varun cant be seated to the immediate left of Raj, hence case II gets eliminated.

​

• The only position left for Kanchan is in the middle.

Thus, Kanchan sits in the middle position.

Hence, the correct answer is *"Kanchan".*​

The logic followed here is:

Option 1) The inward arrow has a clockwise bend, and the outward arrow has an anticlockwise bend.

Option 2) The inward arrow has an anticlockwise bend, and the outward arrow has a clockwise bend.

Option 3) The inward arrow has an anticlockwise bend, and the outward arrow has a clockwise bend.

Option 4) The inward arrow has an anticlockwise bend, and the outward arrow has a clockwise bend.

Thus, all diagrams follow the same pattern except option 1.

Hence, the correct answer is "option 1"

Alternate MethodOutward arrow is left to the inward arrow in every option except option (1).

Therefore, option (1) is different from all.

Hence, the correct answer is "option 1".

The paper when unfolded will appear as follows:

When we unfold the given question figure the top triangles will be the water image of the bottom triangles.

Hence, the correct answer is "Option 4".

Confusion Points Option 1:

• The position of inner triangles is inverted.

Thus only option figure "

" will be correct.

The logic followed here is:

The first figure is related to the second figure as follows:

• The number of sides of the first figure + 1 = The number of sides of the second figure.

​

• The figure itself is placed on the edges of the figure in small size.
• The intersecting area of the two figures is shaded.

​

​Hence, the correct answer is "option 1"

The logic followed here is:

• The shaded part in the small figure shifts 90° anti-clockwise whilst going in the anticlockwise direction.

​.

• The diamond is partially shaded, so the missing part won't have the shaded region.

​

Hence, the correct answer is "option 4"

The logic followed here is:

• The alphabets are decreasing by -3.
• The numbers are increasing by n × 3 - 2, where n is the previous number of the series.

Hence, the correct answer is "TR82".

According to the given information:

• Purvi is in the 7^th position from the right.
• Twisha is in the 18^th position from the left.

​

If their positions are interchanged,

• Twisha's position will become 20^th from the left and 7^th from the right.
• This means there are 6 more people on the right of Twisha.
• ​20 + 6 = 26

​ Thus, the number of people in the row is 26.

Hence, the correct answer is "26".

The least possible diagram is as follows:

Conclusions:

I. Some pins are papers - True (From the figure we can clearly see that some part of the pins intersects with papers).

II. Some papers are bins - True (From the figure we can clearly see that some part of the papers intersects with bins).

​Hence, the correct answer is "Both the conclusions follow".

According to the given information:

From the given figure;

We can see that the shaded part denotes the number of people who speak German and French but not English.

That is given as "35".

​Hence, the correct answer is "35".

According to the given information:

From the given figure;

We can see that the shaded part denotes the number of people who speak German.

That equals to,

• 56 + 48 + 25 + 35 = 164.

​Hence, the correct answer is "164".

The correct answer is Vitamin D.

Key Points

• Vitamin D helps the human body absorb calcium, one of the main building blocks for strong bones and teeth.
• Vitamin D thus helps prevent Osteoporosis, a disease that thins and weakens the bones and makes them brittle and more likely to break.
• Source - oily fish, egg yolks, red meat, etc.

Additional Information

• Vitamin A is retinol or retinoic acid.
• It helps with
• vision
• growth
• cell division
• reproduction
• immunity.
• It also has some antioxidant properties.
• SourceB - Leafy vegetables, milk, eggs, etc.
• Vitamin C is ascorbic acid**.**
• It helps the body form
• blood vessels
• cartilage
• muscle
• collagen in bones.
• It is also vital to your body's healing process.
• Sources - citrus fruit, peppers, broccoli, etc.
• There are many different types of vitamin B, such as B1, B2, etc.
• They help in metabolism.
• They help form red blood cells.
• Sources - poultry, soya beans, bananas, etc.

The correct answer is Johann Wolfgang Döbereiner.

Key Points

• Johann Wolfgang Döbereiner was a German scientist.
• He is credited with inventing the first lighter, known as the Döbereiner's lamp.
• He observed the similarities among certain elements and anticipated the development of the periodic system of elements.
• This is the principle on which the periodic table is built.

Additional Information

• AEB de Chancourtois was a French geologist and mineralogist.
• He was the first to arrange chemical elements in order of atomic weights.
• Dmitri Ivanovich Mendeleev was a Russian chemist.
• He formulated the Periodic Law.
• This led to the creation of a framework that became the modern periodic table.
• John Alexander Reina Newlands was a British chemist.
• He was the first to arrange the elements into a periodic table with increasing order of atomic masses.
• He found that every eight elements had similar properties and called this the law of octaves.

The correct answer is Barren Island.

Key Points

• Barren Island is an island located in the Andaman Sea.
• It is the only confirmed active volcano in the Indian subcontinent.
• The first recorded eruption was in 1787.
• Since then, the volcano has erupted more than ten times.
• The most recent eruption was in November 2020.

 

Additional Information

• Mount Etna is in Sicily, Italy and last erupted in February 2021.
• Mt. Fuji is in Tokyo, Japan, and last erupted in December 1707.
• Krakatoa is located between the islands of Java and Sumatra, Indonesia, and last erupted in June 2020.

The correct answer is Pandit Birju Maharaj.

Key Points

• Pandit Birju Maharaj was an Indian dancer, composer, and singer.
• He was an exponent of the Lucknow "Kalka-Bindadin" Gharana of Kathak dance in India.
• He received the Padma Vibhushan award in 1986.

Additional Information

• Gopi Krishna was an exponent of the Benares Gharana style of Kathak.
• He received the Padma Shri award in 1975.
• Mrinalini Vikram Sarabhai was a Bharatnatyam and Kathakali connoisseur.
• She received the Padma Shri award in 1965 and the Padma Bhushan award in 1992.
• Rukmini Devi Arundale was a Bharatanatyam danseuse, and an activist for animal welfare.
• She was the first woman in Indian history to be nominated as a member of the Rajya Sabha.
• She received the Padma Bhushan award in 1956.

The correct answer is Gujarat.

Key Points

• The Saptak Annual Festival of Music is an annual thirteen-day Indian classical music festival held in Ahmedabad.
• Besides pure classical music, it also includes performances of folk music, classical dance forms, and semi-classical forms such as thumri.

Additional Information

• Madhya Pradesh has several music festivals such as Dhrupad Samaroh, Allauddin Khan Sangeet Samaroh, Kabir Samaroh, Krishna Rao Samaroh, Tansen Sangeet Samaroh, etc.
• Rajasthan has several music festivals such as Udaipur World Music Festival, Jodhpur RIFF, the Sacred Pushkar, World Sacred Spirit Festival, etc.
• Maharashtra has several music festivals such as Swami Haridas Sangeet Sammelan, Sawai Gandharva Bhimsen Festival, Dumru Percussion Festival, etc.

The correct answer is Patiala.

Key Points

• The Athletics Federation of India (AFI) held the Indian Grand Prix IV in June 2021.
• It was held at the National Institute of Sports (NIS) in Patiala.

Additional Information

• The Grand Prix for athletics is a bunch of athletic events organised by the AFI.
• It helps athletes achieve qualification standards for world events.

The correct answer is Dharmendra Pradhan.

Key Points

• Dharmendra Pradhan is the Minister for Education and Minister for Skill Development and Entrepreneurship.
• This ministry is responsible for the coordination of all skill development efforts across the country.
• Aim: To skill on a large scale with speed and high standards.
• Vision: 'Skilled India'.

Additional Information

• Sarbananda Sonowal is the current Cabinet Minister of Ports, Shipping and Waterways and Cabinet Minister of AYUSH in the Government of India.
• Pralhad Venkatesh Joshi is the current Union Minister of Parliamentary Affairs, Coal and Mines of India.
• Piyush Vedprakash Goyal is a Cabinet Minister of the Government of India, having portfolios such as Minister of Textiles, Minister of Commerce and Industry and Minister of Consumer Affairs, Food and Public Distribution.

The correct answer is Fluorine.

Key Points

• Fluorine is an element with the symbol F and atomic number 9.
• It is the lightest halogen and exists under standard conditions as a highly toxic, pale yellow diatomic gas.
• It is the most electronegative element and is extremely reactive, as it reacts with all other elements except argon, neon, and helium.

Additional Information

• Sodium (Na) is a very soft silvery-white metal.
• It is the most common alkali metal and the sixth most abundant element on Earth.
• The human body requires a small amount of sodium to conduct nerve impulses, contract and relax muscles, and maintain the proper balance of water and minerals.
• Magnesium (Mg) is a shiny grey solid metal.
• It is a key factor in making several parts of the body run smoothly such as the heart, bones, muscles, nerves, and others.
• Aluminium (Al) is a light, silvery metal extracted from bauxite.
• It has a density lower than those of other common metals and is hence used to build aircraft components.

The correct answer is Punjab.

Key Points

• The Shahpurkandi Fort was built by Shah Jahan's Rajput Chief Jaspal Singh Pathania in 1505.
• It was built to protect the regions of Nurpur and Kangra.

Additional Information

• Some forts in Gujarat - Bhadra Fort in Ahmedabad, Surat Fort in Surat, Bhujia Fort in Bhuj, Roha Fort in Kutch.
• Some forts in Rajasthan - Chittor Fort at Chittorgarh, Ranthambore Fort at Sawai Madhopur, Gagron Fort at Jhalawar, Amer Fort at Jaipur.
• Some forts in Haryana - Fatehabad Fort of Firuz Shah Tuglaq in Fatehabad, Farrukhnagar Fort in Gurgaon, Asigarh Fort  in Hisar.

The correct answer is 7.0 μm in diameter.

Key Points

• Red blood cells get their bright red colour from a protein called haemoglobin.
• They have the shape of a flat disk or doughnut.
• They carry oxygen from your lungs to your tissues.
• They also bring carbon dioxide back to your lungs.
• They make up almost half of your blood.
• The lifespan of a red blood cell is around 120 days.

Additional Information

• A white blood cell is known as a leukocyte or white corpuscle.
• They are 12 to 15 µm in diameter.
• They lack haemoglobin.
• They defend the body against infection and disease.

The correct answer is Maihar Gharana.

Key Points

• Ali Akbar Khan was an Indian Hindustani classical musician of the Maihar gharana.
• He is known for his virtuosity in playing the sarod.
• Khan was awarded the Padma Bhushan in 1967 and the Padma Vibhushan in 1989.
• He received a MacArthur Fellowship in 1991, the first Indian musician to receive the so-called "genius grant".

Additional Information

• There is a rich tradition of Gharanas or styles in classical Hindustani music.
• These schools or Gharanas have their basis in the traditional mode of musical training and education.
• Every Gharana has its own distinct features.
• Examples - Gwalior gharana, Agra gharana, Jaipur gharana, etc.
• Allahabad Gharana:
• Basically, it is not a Gharana but a place of many famous music personalities.
• It includes: Jankibai, Kesari Bai, Muneer Khatoon Begum, Ramdas Mishra, Yusuf Khan, Karmatullah Khan, Kishan Maharaj, etc.
• Krishna Devi is associated with Allahabad Gharana.
• Jaipur Gharana:
• The Jaipur-Atrauli Gharana (also known as the Jaipur Gharana) is a Hindustani music apprenticeship fraternity (Gharana), founded by Alladiya Khan (1855–1946) in the late 19^th century.

The correct answer is the Mediterranean region.

Key Points

• The  Mediterranean region has a mostly Mediterranean climate.
• It is characterised by mild to cool, rainy winters and warm to hot, dry summers.
• Landforms found in this region are Mediterranean forests, woodlands, and scrub vegetation.

Additional Information

• The South Pole is located in Antarctica, one of the Earth's seven continents.
• It is extremely cold year-round, approx. -20°C to -60°C monthly averages with clear skies and constant light winds from the South.
• There are no trees or shrubs, and only two species of flowering plants are found.
• Greenland is an island country located between the Arctic and Atlantic oceans.
• It has an Arctic climate with average temperatures that do not exceed 10°C in the warmest summer months.
• Its vegetation is dominated by the Arctic tundra, with subarctic forests.
• North America is a continent in the Northern Hemisphere and almost entirely within the Western Hemisphere.
• Most part of North America is cold in the winter and warm in the summer, with moderate precipitation.
• There is a great variety of vegetation such as tropical forests, Mediterranean vegetation, coniferous forests, and tundra vegetation.

The correct answer is the lithosphere.

Key Points

• The lithosphere is the solid, outer part of the Earth.
• It is an irregular surface with various landforms such as mountains, plateaus, deserts, plains, valleys, etc.
• It includes the brittle upper portion of the mantle and the crust.
• It is bounded by the atmosphere above and the asthenosphere below.

Additional Information

• The mesosphere is the 3^rd layer of Earth's atmosphere.
• It extends from about 50 to 85 km above our planet.
• The mesosphere burns up most meteors and asteroids before they are able to reach the earth's surface.
• The stratosphere is the 2^nd layer of Earth's atmosphere.
• It extends around 6 to 20 km above the Earth's surface.
• This is where you'll find the very important ozone layer which helps protect us from ultraviolet radiation (UV) from the sun.
• The asthenosphere is the mechanically weak and ductile region of the upper mantle of Earth.
• It lies below the lithosphere, between approximately 80 and 200 km below the surface, and extends as deep as 700 km.
• It enables the tectonic plates to move because the material under can flow.

The correct answer is Ellora.

Key Points

• Ellora is a UNESCO World Heritage Site.
• It is located in Maharashtra.
• It is one of the largest rock-cut Hindu temple cave complexes in the world.
• It has artwork dating from the period 600–1000 CE.

Additional Information

• The Ajanta Caves in Maharashtra are approximately 30 rock-cut Buddhist cave monuments.
• It dates from the 2^nd century BCE to about 480 CE.
• The Karla Caves in Maharashtra are a complex of ancient Buddhist Indian rock-cut caves.
• They were developed over the period from the 2^nd century BCE to the 5^th century CE.
• Bhaja Caves in Maharashtra is a group of caves that include 22 caves and is one of the earliest Buddhist rock-cut monasteries in Deccan.
• It dates back to the 2^nd Century CE.

The correct answer is Barsha Ritu Goswami.

Key Points

• The INSA Young Historian of Science Award was established in 2014.
• Aim: Recognizing young historians of science of extraordinary promise and creativity with notable research contributions in the area.
• It is made annually to historians of science, working in India or abroad.
• The awardees receive a certificate‚ a bronze medal, honorarium of Rs. 1,00,000/-.

Additional Information

• The Indian National Science Academy (INSA) is a national academy in New Delhi.
• It is meant for Indian scientists in all branches of science and technology.
• It was founded on 7 January 1935.
• It plays a role in promoting, recognising and rewarding excellence in scientific research.
• Rohit Sharma
• He is an Indian cricket player.
• Rohit Sharma became the first captain in cricketing history to win 13 consecutive T20Is.
• Rohit achieved this feat during the first T20I match of the three-match series against England on 7 July 2022 at Southampton.
• Named the ICC ODI Cricketer of the Year for 2019, Rohit became the first player in the history of the game to score five ODI centuries in one edition of the World Cup.
• BCCI has nominated Rohit Sharma for the prestigious Rajiv Gandhi Khel Ratna Award 2020.

The correct answer is food absorption in small intestine.

Key Points

• Every cell lining the small intestine bristles with thousands of tightly packed microscopic projections of a tissue, cell, or cell organelle called microvilli.
• They project into the gut lumen, forming a brush border that absorbs nutrients and protects the body from intestinal bacteria.

Additional Information

• Food assimilation in the stomach is done by very strong acids and enzymes.
• These break the food further into various nutrients such as carbohydrates, proteins, and fatty acids.
• The kidneys are the main osmoregulatory organs.
• They function to filter blood and maintain the dissolved ion concentrations of body fluids.
• The liver filters toxins through the sinusoid channels, which are lined with immune cells called Kupffer cells.
• These engulf the toxin, digest it and excrete it in a process called phagocytosis.

The correct answer is primary deficit.

Key Points

• Primary deficit refers to the difference between the current year's fiscal deficit and the interest payment on previous borrowings.
• It indicates the borrowing requirements of the government, excluding interest.
• As per the Union Budget 2022-23, the target for the primary deficit in 2021-22 is 2.8% of GDP.

Additional Information

• A fiscal deficit is a shortfall in a government's income compared with its spending.
• A revenue deficit occurs when the actual amount of revenue and/or the actual amount of expenditures do not correspond with budgeted revenue and expenditures.
• A fiscal imbalance is the result of a gap between expenditures and income in the public sector - central government, local governments and social insurance.

The correct answer is Eldhose Paul.

Key Points

• Eldhose Paul is a Men's Triple Jump athlete from Kerala, India.
• At the Grand Prix event in Patiala, he did his Personal Best leap of 16.95m.

Additional Information

• Arpinder Singh won a Gold Medal for India in Men's triple jump event after a gap of 48 years in the Asian Games in Jakarta in 2018.
• Before Arpinder, the previous champion was Mohinder Singh Gill in 1970.

The correct answer is it is the distance travelled by light in one year.

Key Points

• Light-year is the distance light travels in one year.
• It is a unit for distance.
• Light travels through space at 300,000 kilometres per second and travels 9.46 trillion kilometres per year.
• A light year is how we measure the distance between celestial bodies.

Additional Information

• Light takes 499.0 seconds for light to travel from the Sun to the Earth.
• This distance is called 1 Astronomical Unit.
• The speed of a sound wave in air depends upon the properties of the air, mostly the temperature, and to a lesser degree, the humidity.
• Ideally, it is around the speed of sound is 331.5 meters/sec.
• Sound cannot travel in outer space due to the lack of a medium.

The correct answer is heat of vaporization.

Key Points

• The heat of vaporization is defined as the amount of heat needed to turn 1 g of a liquid into a vapour, without a rise in the temperature of the liquid.
• Water's heat of vaporization is around 540 cal/g at 100 °C, water's boiling point.

Additional Information

• The heat of condensation is defined as the quantity of heat that is evolved when the unit mass of vapour is changed at a specified temperature to a liquid.
• It equals the heat of vaporization.
• The heat of combustion of a substance can be defined as the amount of heat liberated when a given amount of the substance undergoes combustion.
• It is also known as the calorific value or the energy value.
• The heat of ionization is defined as the quantity of heat that is absorbed when the 1g equivalent of a substance is broken up completely into positive and negative ions.

The correct answer is Tehri Dam

Key Points

• Tehri Dam is a multi-purpose rock and earth-fill embankment dam on the Bhagirathi River in New Tehri, Tehri Garhwal district in Uttarakhand, India.
• With a height of 260.5 m (855 ft) Tehri Dam is the tallest dam in India.
• It is currently ranked No. 10 on the List of Tallest Dams in the world.
• The Tehri Dam withholds a reservoir for irrigation, municipal water supply and the generation of 1,000 megawatts.

Additional Information

• The Koyna Dam is one of the largest dams in Maharashtra, India. It is a rubble-concrete dam constructed on Koyna River which rises in Mahabaleshwar, a hillstation in Sahyadri ranges.
• The Ranjit Sagar Dam, also known as the Thein Dam, is part of a hydroelectric project constructed by on the Ravi River on the border of Union Territory, Jammu and Kashmir and state Punjab.
• Gandhisagar Dam is constructed on the Chambal River. It is in Mandsaur district of Madhya Pradesh.

The correct answer is Kolkata

Key Points

• The institute at Calcutta was established first, on 13 November 1961.
• The Indian Institutes of Management (IIMs) are central government-owned-public business schools for the management profession.
• It is offering undergraduate, postgraduate, doctoral and executive programmes along with some additional courses in the field of business administration.

Additional Information

• The establishment of IIMs was initiated by Jawaharlal Nehru, the first prime minister of India, based on the recommendation of the Planning Commission of India.
• IIM Banglore was established in 1973 as the third Institute of Management.
• IIM(International Institution of Management) New Delhi was established in 1981. It was India's first corporate-sponsored business school.

The correct answer is Ivor Jennings

Key Points

• Ivor Jennings was a British lawyer and academic. He served as constitutional adviser to the Government of Pakistan. In 1959, he was an advisor to the committee to draft the constitution of Nepal.
• The Directive Principles of State Policy of India are the guidelines or principles given to the institutes for governing India and are provided in Part IV (Article 36-51) of the Constitution of India.
• They are not enforceable by any court.

Additional Information

• Vallabhbhai Patel endeared as Sardar, was an Indian statesman. He is also called the "Unifier of India".
• L. M  Singhvi was an Indian jurist, parliamentarian, scholar, writer and diplomat. He was, after V. K. Krishna Menon, the second-longest-serving High Commissioner for India in the United Kingdom.
• B. N. Rau was an Indian civil servant, jurist, diplomat and statesman known for his key role in drafting the Constitution of India.

The correct answer is Delhi

Key Points

• Firoz Shah's tomb is located in Hauz Khas (New Delhi), close to the tank built by Alauddin Khalji.
• Sultan Firoz Shah Tughlaq (1309 – 20 September 1388) was a ruler from the Tughlaq dynasty, who reigned over the Sultanate of Delhi from 1351 to 1388.
• Firoz Shah Tughluq contributed to architecture in a similar manner as Shah Jahan did years later.
• Firoz Shah Tughlaq wrote an autobiography, titled Futuhat-e-firozshahi.

Additional Information

• Tughlaq Dynasty was a Muslim dynasty of Turkic origin that ruled over the Delhi sultanate in medieval India.
• Its reign started in 1320 in Delhi when Ghazi Malik assumed the throne under the title of Ghiyath al-Din Tughluq. The dynasty ended in 1413.

Rulers of the Tuglaq dynasty:

• 1321–1325 - Ghiyath al-Din Tughluq
• 1325–1351 - Muhammad ibn Tughluq
• 1351–1388 - Firuz Shah Tughlaq
• 1388–1413 - Ghiyath-ud-din Tughluq Shah / Abu Bakr Shah / Muhammad Shah / Mahmud Tughlaq / Nusrat Shah.

The correct answer is 0.0099

Key Points

• Population growth is the increase in the number of people in a population of a dispersed group.
• The population growth rate for 2020 is projected at 0.97%, which is the 112^th highest among 235 countries.
• The population growth reached a peak in 1974 with an annual growth rate of 2.36%.
• The percentage of decadal growth during 2001-2011 was 17.70%, 3.84% lower than the 1991-2001 period.

Additional Information

• Census has been conducted in India since 1872 and 2011 marks the first time biometric information was collected.
• The 2011 Census of India was the 15^th Indian Census.
• Uttar Pradesh is the most populous state in India and Bihar has the highest density of population according to the census 2011.

The correct answer is the Himalayas and the Northern Plains.

Key Points

• The Himalayan range is one of the youngest mountain ranges on the planet and consists mostly of uplifted sedimentary and metamorphic rock.
• Its formation is a result of a continental collision or orogeny along the convergent boundary (Main Himalayan Thrust) between the Indo-Australian Plate and the Eurasian Plate.
• Northern plains are the youngest physiographic feature in India. They lie to the south of the Shivaliks, separated by the Himalayan Frontal Fault.
• The southern boundary is a wavy irregular line along the northern edge of the Peninsular India. On the eastern side, the plains are bordered by the Purvanchal hills.

Additional Information

• The Peninsular plateau is a tableland composed of the old crystalline, igneous and metamorphic rocks. It was formed due to the breaking and drifting of the Gondwana land and thus, making it a part of the oldest landmass.
• The coastal plain is flat, low-lying land adjacent to the sea coast. The Coastal Plains of India lie on either side of the Peninsular Plateau, along the western and eastern coasts of India.
• The major island groups of India are the Andaman and Nicobar Archipelago (A chain of islands similar in origin) in the Bay of Bengal and Lakshadweep islands in the Arabian Sea.

The correct answer is 16.68%

Key Points

• The literacy rate in the country is 74.04 per cent, 82.14 for males and 65.46 for females.
• The national literacy rate, according to the 2011 census, was 74.04 percent.
• The Census 2011 defines a literate person as, “a person aged seven and above who can both read and write with understanding in any language, is treated as literate.

Additional Information

• Among the Indian states, Kerala has the highest literacy rate 93.91% and then Mizoram 91.58%.
• As per the 2011 census, among states, Bihar has the lowest literacy rate of 61.8%.
• The literacy rate went up from 64.83% in 2001 to 74.04% in 2011 showing an increase of 9.21%. Interestingly, females literacy level saw a significant jump as compared to males between 2001-2011. While female literacy in 2001 stood at 53.67%, it has gone up to 65.46% in 2011.

The correct answer is High Powered Money

Key Points

• High-powered money is the liability of the monetary authority of the country.
• This is also called the monetary base and is created by the RBI.
• In short, it is the total amount of money created by the central bank.
• This includes: The total currency circulating in the public, plus the currency that is physically held in the vaults of commercial banks, plus the commercial banks' reserves held in the central bank.

Additional Information

• Bank money refers to money held in the form of demand deposits with commercial banks.
• Also known as M0, narrow money refers to physical money, such as coins and currency, demand deposits, and other liquid assets, that are easily accessible to central banks.
• Broad money is a measure of the amount of money, or money supply, in a national economy including both highly liquid "narrow money" and less liquid forms.

The correct answer is  $ 1.90 per day

Key Points

• The 'international poverty line' is currently set at $1.90 a day at 2011 international prices.
• The World Bank produced its first global poverty estimates for  developing countries for World Development Report 1990: Poverty (World Bank 1990) using household  survey data for 22 countries .
• When measuring the international poverty of a country, the international poverty line at PPP is converted to local currencies in 2011 price.
• It is then converted to the prices prevailing at the time of the relevant household survey using the best available Consumer Price Index (CPI).

The correct answer is Assam

The Tropic of Cancer does NOT pass through Assam.

Key Points

• In India, the Tropic of Cancer passes through 8 states - Gujarat, Rajasthan, Madhya Pradesh, Chattisgarh, Jharkhand, West Bengal, Tripura and Mizoram.
• The Tropic of Cancer (23.5°N) divides India into two almost equal climatic zones, namely, the Northern Zone and the Southern zone.

Additional Information

• The tropic is one of the five major latitudinal circles on the earth, the other four being the Tropic of Capricorn, the Arctic Circle, the Antarctic Circle and the Equator.
• Africa is the only continent, which is crossed by the Tropic of Cancer, Equator and Tropic of Capricorn.
• Mahi River is the only river in India that cuts the Tropic of Cancer twice first in Madhya Pradesh and second in Gujarat.

The correct answer is The President

Key Points

• The judges of a high court are appointed by the President.
• While appointing the judges, the President consults the Chief Justice of India and the Governor of the concerned state.
• For the appointment of other judges, the chief justice of the concerned high court is also consulted.
• In the case of a common high court for two or more states, the governors of all the states concerned are consulted by the President.

Additional Information

• The Indian President is the head of the state and he is also called the first citizen of India.
• He is a part of the Union Executive, provisions of which are dealt with in Articles 52-78 including articles related to the President (Article 52-62).

The correct answer is Mahavir

Key PointsVardhaman Mahavira (540 – 468 B.C.)

• He was born at Kundagrama near Vaisali.
• At the age of 30, Vardhaman renounced his home and became a wandering ascetic.
• After 13 years of penance, he attained the highest spiritual knowledge called Kevala Jnan.
• He attained Kevala Jnan at Jimbhikagrama village under a sal tree aged 42. This is called Kaivalya.
• Thereafter, he was called Mahavira, Jina, Jitendriya (one who conquered his senses), Nigrantha (free from all bonds), and Kevalin.

Additional Information

• Mahavira is considered the last Tirthankara.
• He preached his teachings for 30 years and died at Pava (near Rajagriha) aged 72.
• A Jina is said to possess ‘Avadhijnana,’ (Superhuman cognition or psychic power.)
• The other name for ‘Jina’ is ‘Tirthankara,’ which means ford builder.

The correct answer is 72.

Key PointsDadra and Nagar Haveli:

The 10^th amendment to the Constitution in 1961 made Dadra and Nagar Haveli a part of India and in 1987 the area was given the title of a Union Territory.

Recently, Daman and Diu is merged into Dadra and Nagar Haveli to form a single Union Territories.

From 1954 till 1961, the territory functioned almost independently by what was known as the " Free Dadra and Nagar Haveli Administration". However, the territory was merged with the Indian Union on 11 August 1961, and since then, is being administered by the Government of India as a Union Territory.

The correct answer is Article 15 (1)

Key Points

• Article 15 (1) prohibits discrimination by the state against any citizen on grounds 'only' of caste, religion, sex, race, and place of birth.
• Fundamental rights are provided to every citizen of the country without any discrimination.
• The word "discrimination" refers to making adverse distinctions with regard to or to distinguish un-favourable from others.
• The term 'only' means that discrimination can be done on the basis of other grounds.

Additional Information

• There are six fundamental rights of the Indian Constitution along with the constitutional articles:

1. Rights to equality (Article 14-18)
2. Rights to freedom (Article 19-22)
3. Right against exploitation (Article 23-24)
4. Right to freedom of religion (Article 25-28)
5. Cultural and educational rights (Article 29-30)
6. Rights to constitutional remedies (Article 32)

The correct answer is Pushyamitra Sunga

Key Points

• Pushyamitra Shunga was the founder and first ruler of the Shunga Empire in East India.
• Pushyamitra was originally a Senapati "General" of the Maurya Empire.
• In 185 BCE he assassinated the last Mauryan Emperor, Brihadratha Maurya, during an army review, and proclaimed himself emperor.
• Patanjali, the second great grammarian of Ancient India, was a contemporary Pushyamitra Sunga.

Additional InformationGautamiputra Satakarni: 

• He is considered the greatest king of the Satavahana dynasty.
• He called himself the only Brahmana who defeated the Shakas and destroyed many Kshatriya rulers.
• He was given the titles Rajaraja and Maharaja.
• He donated land to the Buddhist monks.
• He was succeeded by his son Vasisthiputra Sri Pulamavi/Pulumavi or Pulamavi II.

Agnimitra Sunga:

• He Was Pushyamitra’s son who succeeded him on the throne.
• His reign lasted from about 149 BC to 141 BC.
• By this time, Vidarbha broke away from the empire.
• Agnimitra is the hero of Kalidasa’s poem, Malavikagnimitram.
• His son Vasumitra succeeded him as king.

Vasudeva Kanva:

• The Kanva dynasty was established by Vasudeva Kanva in 75 BC.
• Vasudeva was initially a minister of the Shunga Emperor Devabhuti, who then assassinated the former emperor and usurped the throne.

The correct answer is capital expenditure

Key Points

• Capital expenditure is the money spent by the government on the development of machinery, equipment, building, health facilities, education, etc.
• It also includes the expenditure incurred on acquiring fixed assets like land and investment by the government that gives profits or dividends in future.

Additional Information

Revenue Receipt: 

• Revenue receipts can be defined as those receipts that neither create any liability nor cause any reduction in the assets of the government.
• They are regular and recurring in nature and the government receives them in the normal course of activities.

Revenue Expenditure:

• Revenue Expenditure is one that neither creates assets nor reduces any liability of the government. Salaries of employees, interest payments on past debt, subsidies, pension, etc, fall under the category of revenue expenditure.
• It is recurring in nature.

Capital Receipt:

• Capital receipts are receipts that create liabilities or reduce financial assets.
• They also refer to incoming cash flows.
• Capital receipts can be both non-debt and debt receipts.
• Loans from the general public, foreign governments and the Reserve Bank of India (RBI) form a crucial part of capital receipts.

The correct answer is Partition of Bengal

Key Points

• The partition of the undivided Bengal Presidency in 1905 was one of Curzon’s most criticised moves which triggered widespread opposition not only in Bengal but across India and gave impetus to the freedom movement.
• In July 1905, Curzon announced the partition of the undivided Bengal Presidency.
• A new province of East Bengal and Assam was announced, with a population of 3.1 crores with a Muslim-Hindu ratio of 3:2.
• Curzon’s actual motive was to crush the increasingly loud political voices of the literate class in the province and to provoke religious strife and opposition against them.

Additional Information

• George Nathaniel Curzon, 1^st Marquess Curzon of Kedleston (11 January 1859 – 20 March 1925) was known commonly as Lord Curzon.
• He was appointed as the Viceroy of India in 1899.
• He was reappointed as the Viceroy of the country in 1904.
• Rabindranath Tagore led the marches at many places, and composed many patriotic songs, most famously ‘Amar Sonar Bangla’ (My Golden Bengal), which is now the national anthem of Bangladesh.

Important Points

Reform in various fields

• Army: In 1902, Lord Kitchener came to India as the Commander-in-Chief and carried out much-needed reforms in the army. The factories were established in India to produce guns, gunpowder and rifles.
• Judiciary: Under the judiciary reforms, the number of judges of the Calcutta High Court was increased, the salaries of the judges of the High Courts and subordinate courts were enhanced and the Indian Code of Civil Procedure was revised.
• Monument Act, 1904: The Act established an Archaeological Department under a director. It was assigned the responsibility of repair, restoration and protection of historical monuments.

The correct answer is 22 members

Key Points

• Public Accounts Committee was introduced in 1921 after its first mention in the Government of India Act, 1919 also called Montford Reforms.
• The Public Accounts Committee has 22 members.
• All the members are taken from the Indian Parliament.
• Out of 22 members, 15 are elected from Lok Sabha (Lower House) and 7 members are elected from Rajya Sabha (Upper House).

Additional Information

• The Public Accounts Committee examines public expenditure.
• Main Function: To examine the annual audit reports of the Comptroller and Auditor General of India (CAG), which are laid before the Parliament by the President.
• Note: CAG submits three reports – a report on appropriation accounts, an audit report on finance accounts, and an audit report on public undertakings.

The correct answer is Andhra Pradesh

Key Points

• In the Gudem Hills of Andhra Pradesh, a militant guerrilla movement spread in the early 1920s.
• Gudem rebels attacked police stations, attempted to kill British officers and continued guerrilla warfare to achieve Swaraj.
• The movement was basically a protest against forest laws.
• This movement was led by Alluri Sitaram Raju, a follower of Mahatma Gandhi.

The correct answer is Article 51 A.

Key Points

• ​The Fundamental Duties are dealt with in Article 51A under Part-IV A of the Indian Constitution.
• 42^nd Amendment Act of 1976 added 10 Fundamental Duties to the Indian Constitution.
• 86^th Amendment Act 2002 later added the 11^th Fundamental Duty to the list.
• Swaran Singh Committee in 1976 recommended Fundamental Duties, the necessity of which was felt during the internal emergency of 1975-77.

Additional Information

Article 31 A: 

• Article 31A  saves five categories of laws from being challenged and invalidated on the ground of contravention of the fundamental rights conferred by Article 14 and Article 19.
• It also provides the guaranteed right to compensation in case of acquisition or requisition of private property by the state.

Article 61:

• Article 61 of the Constitution of India prescribes the procedure for impeachment of the President.
• When the President is to be impeached for violation of the Constitution, the charge shall be preferred by either House of Parliament

Article 55:

• Manner of election of President.

Given:

Smallest five digits number exactly divisible by 252

Formula used:

Dividend = Quotient × Divisor + Remainder

Calculation:

Lets take the Smallest five digit number 10000

if 10000 is divided by 252

10000 = 252 × 39 + 172(remainder)

to get the smallest five digit number divisible by 252

Remainder + x = 252 (let x be the number added to 10000 to make the number divisible by 252)

172 + x = 252

x = 80

10000+80 = 10080

10080 is the smallest five digit number divisible by 252

Answer is 10080.

Given:

10% of x is equal to 4% of y

Calculation:

10% of x is equal to 4% of y

10% × x = 4% × y

10x = 4y

5x = 2y

let x be 2 and y be 5

16% of x will be equal to A% of y

16% × 2 = A% × 5

32 / 5 = A%

A% = 6.4

16% of x will be equal to 6.4% of y

Answer is 6.4%.

Given:

Present Value of the house = ₹40,00,000,

Decrease percent = 10% per year

Years = 3

Formula used:

Value after increase or decrease = (100 ± decrease or increase) % × Initial Value

Calculation:

Value after 3 years = (100 - 10) % × (100 - 10) % × (100 - 10) % ×  4000000

= \(\frac{90×90×90}{1000000}\) ×  4000000

= 2916000

Value after 3 years = ₹2916000

Answer is ₹2916000.

Given:

Side of Small cube = 20cm

Side of large cube = 2m

Formula used:

Volume of cube = side³

Concept used:

if some number of small cubes are filled in a large cubical box then,

Volume of the larger cube = sum of the volume of smaller cube

Calculation:

Let n be the number of cubes of 20cm edges

1m = 100cm

Volume of the larger cube = sum of the volume of smaller cube

200 × 200  × 200 = n  × 20  × 20  × 20

n = 1000

Number of cubes of 20cm edge put in a cubical box of 2m edge is 1000

Answer is 1000.

Additional InformationDiagonal of a square = \(\sqrt{2}\) side

Diagonal of a cube = \(\sqrt{3}\) side

Shortcut Trick

Multiplying factor for a 25% annual increase is 1 + 1/4 = 5/4.

To find the past population, we multiply the current population by the reverse factor, which is 4/5.

Population 2 years ago = 1,00,00,000 × (4/5)² = 64,00,000.

Population 3 years ago = 64,00,000 × (4/5) = 51,20,000.

Required difference = 64,00,000 − 51,20,000 = 12,80,000.

∴ The correct answer is 12,80,000.

Alternate Method

Given:

Present Population (P₀) = 1,00,00,000

Annual increase rate (R) = 25% = 1/4

Formula Used:

Past Population = Present Population × [1 / (1 + R)]ⁿ

Calculations:

⇒ Multiplier for past population = 1 / (1 + 1/4) = 4/5

Population 2 years ago (P₂):

⇒ P₂ = 1,00,00,000 × (4/5)²

⇒ P₂ = 1,00,00,000 × 16/25 = 64,00,000

Population 3 years ago (P₃):

⇒ P₃ = 64,00,000 × (4/5)

⇒ P₃ = 51,20,000

Difference between the population 3 years ago and 2 years ago:

⇒ Difference = P₂ − P₃

⇒ Difference = 64,00,000 − 51,20,000 = 12,80,000

∴ The correct answer is 12,80,000.

Additional Information

Population Growth Formula

If a population grows at R% annually, the population after 'n' years is given by P × (1 + R/100)ⁿ.

Population Decay Formula

If a town's population decreases by R% annually, the population after 'n' years is given by P × (1 − R/100)ⁿ.

Successive Percentage Change

If the population changes by A%, B%, and C% in three successive years, the final population is P × (1 ± A/100) × (1 ± B/100) × (1 ± C/100).

Finding Past Population

To find the population 'n' years ago when the present population 'P' and growth rate 'R' are known: Past Population = P ÷ (1 + R/100)ⁿ.

Shortcut Trick

Let the fourth number be 1 unit.

Average of first three numbers = 3 × 1 = 3 units.

Sum of first three numbers = 3 × 3 = 9 units.

Total Sum of four numbers = 9 + 1 = 10 units.

Given Average of four numbers = 14 ⇒ Total Sum = 14 × 4 = 56.

10 units = 56 ⇒ 1 unit = 56 ÷ 10 = 28/5.

∴ The correct answer is 28/5.

Alternate Method

Given:

Let the four numbers be n₁, n₂, n₃, and n₄.

Formula Used:

Average = Sum of observations ÷ Number of observations

Calculations:

⇒ Let the fourth number (n₄) = x

⇒ Average of first three numbers = (n₁ + n₂ + n₃) ÷ 3 = 3x

⇒ Sum of first three numbers (n₁ + n₂ + n₃) = 9x

⇒ Average of all four numbers = (n₁ + n₂ + n₃ + n₄) ÷ 4 = 14

⇒ 9x + x = 14 × 4

⇒ 10x = 56

⇒ x = 56 ÷ 10

⇒ x = 28/5

∴ The correct answer is 28/5.

Additional Information

Basic Average Formula

The average of n numbers is the sum of the numbers divided by n. Sum = Average × n.

Weighted Average

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

Concept of Deviation

The sum of deviations of all observations from their mean is always zero.

Given:

Perimeter of the rectangle = 40cm

Formula used:

Perimeter of the rectangle = 2(Length + Breadth) 

Calculation:

let the two consecutive odd number is x and x+2

Length = x+2

Width = x

Perimeter of the rectangle = 2(Length + Breadth) 

40 = 2( x+2+x )

20 = 2x + 2

2x = 18

x = 9

length of the shorter side is x 

Shorter side is 9

Answer is 9.

Additional InformationArea of rectangle = Length × breadth

Diagonal of rectangle = \(\sqrt{length^2+breadth^2}\)

Given:

Traffic lights at three different road crossings change after 24 seconds, 36 seconds and 54 seconds, respectively

Concept used:

LCM - Highest common factor

Calculation:

They all change simultaneously at 10:15:00 a.m

They all change simultaneously again in,

LCM ( 24 seconds, 36 seconds and 54 seconds )

= LCM (24, 36, 54)

= 216 seconds

= 3 minutes 36 seconds

They all change simultaneously again in 3 minutes 36 seconds

=10:15:00 a.m + 00:03:36

= 10:18:36a.m.

Answer is 10:18:36a.m.

Shortcut Trick

Assume total distance as LCM of speeds or a convenient number like 100 km.

Distances are 50 km, 25 km, and 25 km.

Total Time = (50 ÷ 30) + (25 ÷ 25) + (25 ÷ 20) = 5/3 + 1 + 5/4 = (20 + 12 + 15) ÷ 12 = 47/12 hours.

Average Speed = Total Distance ÷ Total Time = 100 ÷ (47/12) = 1200/47 = 25 25/47 km/h.

∴ The correct answer is 25 25/47 km/h.

Alternate Method

Given:

Speed₁ = 30 km/h (50% distance), Speed₂ = 25 km/h (25% distance), Speed₃ = 20 km/h (Remaining 25% distance).

Formula Used:

Average Speed = Total Distance ÷ Total Time

Calculations:

⇒ Let total distance be D.

⇒ Time T₁ = (0.50D) ÷ 30 = D/60

⇒ Time T₂ = (0.25D) ÷ 25 = D/100

⇒ Time T₃ = (0.25D) ÷ 20 = D/80

⇒ Total Time = D/60 + D/100 + D/80

⇒ Total Time = D × (20 + 12 + 15) ÷ 1200 = 47D/1200

⇒ Average Speed = D ÷ (47D/1200) = 1200/47

⇒ Average Speed = 25 25/47 km/h

∴ The correct answer is 25 25/47 km/h.

Additional Information

Average Speed (Equal Distances)

If a journey is divided into two equal distances with speeds x and y, the average speed is 2xy/(x + y).

Relative Speed

For objects moving in the same direction, relative speed = s₁ − s₂. In opposite directions, relative speed = 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.

Shortcut Trick

Use the Successive Multiplier method to find the original price.

Selling Price = Original Price × (1 − d₁/100) × (1 − d₂/100)

1938 = Original Price × 0.85 × 0.95

Original Price = 1938 ÷ (0.85 × 0.95) = 1938 ÷ 0.8075 = 2400

∴ The correct answer is ₹2,400.

Alternate Method

Given:

Final Selling Price (SP) = ₹1,938

First Discount (d₁) = 15%

Second Discount (d₂) = 5%

Formula:

Marked Price (MP) × (100 − d₁)/100 × (100 − d₂)/100 = Selling Price (SP)

Calculations:

⇒ Let the Original Price be x.

⇒ x × (85/100) × (95/100) = 1938

⇒ x × (17/20) × (19/20) = 1938

⇒ x × (323/400) = 1938

⇒ x = (1938 × 400) ÷ 323

⇒ x = 6 × 400

⇒ x = 2400

∴ The correct answer is ₹2,400.

Additional Information

Equivalent Single Discount

For two successive discounts of a% and b%, the single equivalent discount is (a + b − ab/100)%.

Marked Price and Selling Price Relation

Selling Price = Marked Price − Discount. Discount is always calculated on the Marked Price (MP).

Successive Percentage Change

If a value is changed by x% and then by y% successively, the net percentage change is [x + y + (xy/100)]%.

Given:

Radius = 21cm

Height = 28cm

Formula used:

Pythagoras Theorem,

Slant height² = Radius² + Height²

Total Surface area of the cone = π r (l + r) [ where r is radius and l is slant height]

Calculation:

let l be the slant height 

Slant height2 = 212 + 28² 

l = \(\sqrt{441+784}\)

l = \(\sqrt{1225}\)

l = 35

Total Surface area of the cone = π r (l + r)

= \(\frac{22}{7}\) × 21 × (35 + 21)

= 22  × 3  × 56

= 3696

Answer is 3696.

Additional InformationVolume of the cone = \(\frac{1}{3}\)πr²h