DSSSB Junior Secretariat Assistant Official paper (Held on: 3 April 2022 Shift 3 ) (Previous Year Paper)

Decoding the information, 

 

Now check all the options:

Option (1) 66 H 18 M 9 R 13 D 26

After signs of M and R are interchanged.

= 66 H 18 R 9 M 13 D 26

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

= 66 × 18 ÷ 9 + 13 – 26

= 66 × 2 + 13 – 26

= 132 + 13 – 26

= 145 – 26

= 119 ≠ 141

Option (2) 26 R 66 H 18 M 13 D 9

After signs of M and R are interchanged.

= 26 M 66 H 18 R 13 D 9

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

= 26 + 66 × 18 ÷ 13 - 9

= 26 + 66 × 1.38 - 9

= 26 + 91.38 - 9

= 117.38 – 9= 108.38 ≠ 141

Option (3) 26 M 13 H 66 R 18 D 9

After signs of M and R are interchanged.

= 26 R 13 H 66 M 18 D 9

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

= 26 ÷ 13 × 66 + 18 – 9

= 2 × 66 + 18 – 9

= 132 + 18 - 9

= 150 - 9

= 141

Option (4) 18 H 26 M 13 R 9 D 66

After signs of M and R are interchanged.

= 18 H 26 R 13 M 9 D 66

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

= 18 × 26 ÷ 13 + 9 – 66

= 18 × 2 + 9 – 66

= 36 + 9 – 66

= 45 – 66

= - 21 ≠ 141

Hence, “Option(3)” is the correct answer.

The given statement is: P = Q > R = S > T

Conclusions:

I. P = S → False (as P = Q > R = S gives either P = Q, Q > R and R = S, So P > S).

II. P > T → True (as P = Q > R = S > T given; as P > R and R > T so P > T true).

Hence, the correct answer is “Only II is true”.

Given:

1. Leo is the only brother of John.

2. Leo is the paternal uncle of Tony.

4. Maddie is the wife of Leo.

5. Nick is the nephew of John.

7. Tony is the grandson of Ron.

8. Ron is the husband of Victoria.

 

6. Kate is the daughter-in-law of Victoria

 

Hence, Nick is the "Cousin" of Tony.

The table is alphabets place value:

Given:

GS - EV - CY

Similarly,

Option(2): XC - VF - TI

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

The table is alphabets place value:

The pattern followed here is:

IMAGE is written as RNZTV

Similarly,

OPTION is written as

Hence, 'OPTION' is coded as "LKGRLM".

Drawing the diagram according to the given information,

1. Ramesh walked 5 km towards the north.
2. Then he turned to his left and walked 5 km.
3. From there he took a right turn and walked 5 km.

Hence, Ramesh faces "North" direction

Given:

3 is related to 8 following a certain logic. Following the same logic, 15 is related to 22.

The logic followed here is:

Hence, "44" is the correct answer.

The pattern followed here is:

1^st number ÷ 4 = 2^nd number

Now follow the steps:

168 : 42 

= 168 ÷ 4

= 42 = 2^nd number

And,

624 : 156

= 624 ÷ 4

= 156 = 2^nd number

Similarly,

252 : ?

= 252 ÷ 4

= 63 = 2^nd number

Hence, "63" is correct answer.

Drawing the diagram according to the given information,

1. Lakshmi walked 10 km from her house towards the west.
2. From there she took a right turn and walked 5 km.
3. Then she turned right again and walked 10 km.

Hence, she is going in "East" direction.

The table is alphabets place value:

Given:

Similarly,

Option(3)

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

The given statement is: S > I = M > R = A > N

Conclusions:

I. A < S → True (as S > I = M > R = A gives as S > M, M > A and S > A, So A < S).

II. I > N → True (as I = M > R = A > N given; as I > R and R > N so I > N true).

Hence, the correct answer is “Both I and II”.

Decoding the information, 

Given:

(6 - 5 ÷ 40) + 35 × 2

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

= (6 × 5 + 40) ÷ 35 - 2

= (30 + 40) ÷ 35 - 2

= 70 ÷ 35 - 2

= 2 - 2

= 0

Hence, “0” is the correct answer.

Preparing the family tree using the following symbols,

Given:

'A + B' means 'A is the sister of B',

'A - B' means 'A is the father of B',

'A × B' means 'A is the mother of B',

'A ÷ B' means 'A is the daughter of B'.

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

 

Now break the code of ‘H × L - Q + R ÷ M’

1) H × L

‘H × L’ means ‘H is the mother of L’

2) L - Q

‘L - Q’ means ‘L is the father of Q’.

3) Q + R

'Q + R’ means ‘Q is the sister of R’

4) R ÷ M

‘R ÷ M’ means ‘R is the daughter of M’

Hence, H is the ‘Husband's mother’ of M.

Given:

LOCK READ LACK LAME

'C' is added before each word. We get,

CLOCK → An instrument that shows you what time it is

CREAD → Cread is the short form of "Cumulative Research Evidence Assessment Device"

CLACK → Make a sharp sound or series of sounds as a result of a hard object striking another

CLAME →  Not a meaningful word

There are two meaningful English words that will be formed

Hence, “Two” is the correct answer.

Table show alphabet serial number –

The pattern followed is,

 

All follow the same pattern, except ‘IMKO’.

Hence, “IMKO” is the odd one

Preparing the family tree using the following symbols,

Given:

1. Garima is the wife of Kanika's brother.

 

2. Kanika is the daughter of Kishore, who is the husband of Sujata.

3. Piyush is the son of Sujata's only son Aman.

• Sujata's only son means Garima is the wife of Aman.

Hence, Aman is the "Son" of Kishore.

Given:

1) L is shorter than N but taller than O.

• N > L > O

2) Only one person is shorter than P. O is the shortest.

• N > L > P > O

Hence, “N” is the tallest all of them.

The logic followed here is:​​

As per the above chart:

The addition of all the alphabet as per their numbers in the chart is even, except for "SQS" whose addition is an odd number.

Hence, the correct answer is "SQS".

13.39 multiplied by 2.7 gives approximately:

=> 13.39 × 2.7 = 36.153

=> approximately 36

Hence, “36” is the correct answer.

According to the given information

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‘rule’ is coded as "mt".

Hence, 'mt’ is the correct answer.

The table is alphabets place value:

Given:

FH - DB - AC

Similarly,

Option(1): VX - TR - QS

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

The pattern followed here is:

Hence, '3' is the correct answer.

Given:

1. Sixty-one women are sitting in a row facing north.

2)  Shalu sits fourth to the right of Manisha, who is twenty-seventh from the left.

• Manisha is twenty-seventh from the left.

3) Shalu position from the left.

= Manisha position from left + Shalu position from manisha = 27 + 4 = 31^st

=> The total number of women = Shalu position from left + Shalu position from right - 1

=> 61 = 31 + Shalu position from right – 1

=> 61 = 30 + Shalu position from right

=> Shalu position from right = 61 – 30 = 31^st

Hence, Shalu's position from the right is “31st”.

The logic is here:

The total number of light small figures in half of the square is equal to the total number of dark and light figures in the second half of square.

Now check all the options,

Option (1):

Option (2):

Option (3):

Option (4):

Hence, "Option (1)" is different.

The pattern followed here is:

1. Middle figure rotates anticlockwise direction.

2. Upper figure flip horizontal one by one.

Final series is:

Hence, ‘Option 3’ is the correct answer.

Statements:

All passion fruits are custard apples.

Some custard apples are bananas.

The least possible diagram for the given statements is as follows

Conclusions:

I. Some custard apples are passion fruits → True (Because all passion fruits are custard apples so definitely some custard apples are also passion fruits)  

II. All bananas are custard apples → False (Because some custard apples are bananas so all bananas are custard apples is false)  

Hence, “Only conclusion I follows".

Table show alphabet serial number –

The pattern followed is,

Hence, “RI3” is the complete series.

The pattern followed here is:

1. Figure 1st to 2nd one diagonal line increase.

2. Figure 2nd to 3rd one cross diagonal line increase.

3. Figure 3rd to 4th one vertical line increase.

4. Figure 4th to 5th one horizontal line increase and cross the vertical line.

Final series is:

Hence, ‘option 2’ is the correct answer.

Given:

Six boys Vansh, Ritik, Surya, Kapil, Pawan and Mihir are sitting on a straight bench facing the North.

1. Pawan is sitting to the left of Surya and to the right of Mihir.

2. Vansh is sitting to the right of Surya and to the left of Ritik.

3. Kapil is sitting at the extreme right end.

So, "Pawan" is sitting at the second position from the left end.

Hence, the correct answer is "Pawan".

The embedded part of this image is:

Hence, option (2) is the correct answer.

The table is alphabets place value:

The pattern followed here is:

 

Hence, '48M19' is the correct answer.

Table show alphabet serial number –

The pattern followed is,

Option (1): JEQ : LCS

Option (2): PUN : RSP

Option (3): PLT : RJV

Option (4): JHQ : KFS

All follow the same pattern, except 'JHQ : KFS’.

Hence, “JHQ : KFS” is the odd one.

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

Hence, ‘option 4’ is the correct answer.

The pattern followed here is:

• Image B is the water image of image A.

Similarly,​

• Image D will be the water image of image C.

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

The table is alphabets place value:

The pattern followed here is:

Hence, '17DE13P' is the correct answer.

Given:

A certain number of people are sitting in a row, facing North.

1. R is to the immediate left of O.

2. Z is fourth to the right of R.

3. Only three people sit between G and R.

4. W is at the immediate right of Z.

5. Only three people sit between X and O.

Hence, "10" total number persons are seated.

The pattern followed here is:

Hence, '353' is the correct answer.

Table show alphabet serial number –

The pattern followed is,

All follow the same pattern, except 'UXW’.

Hence, “UXW” is the odd one.

According to the given information:

The shaded part represents the number of people studying only English (A) and the number of people studying both Physics and Maths but NOT English (B).

 

The number of people studying only English (A) = 45

The number of people studying both Physics and Maths but NOT English (B) = 49

• A + B = 45 + 49 = 94

Hence, ‘94’ is the correct answer.

The shaded part represents people study Maths in the given college.

 

The numbers representing people study Maths in the given college = 23 + 12 + 49 + 52 = 136

Hence, ‘136’ is the correct answer.

The correct answer is 'Mohenjo-Daro'.

Key Points

• The Great Bath was excavated from Mohenjo-Daro.
• Mohenjo-Daro was the largest Harappan site situated on the Indus river currently in Pakistan.
• The Great Bath was the largest building of Harappan Civilisation (also known as Indus Civilisation).
• In addition to this, Great Granary, Assembly Hall, etc. were also excavated.
• The excavators were Rakhal Das Bannerji (1922), Mackay (1927) & Wheeler (1930).
• Thus, the correct answer is Mohenjo-Daro.

 Additional Information

• Let's have a look at other options:
• Harappa was the Capital city situated on the Ravi river in Pakistan. 6 Granaries in a row, working floors, workmen's quarters, etc. were excavated from here.
• Rakhigarhi is the largest Indian site of Indus Civilisation.
• Dholavira is situated on the Luni river in Gujarat, India. A unique water harnessing system and its stormwater drainage system, a large well, and a bath (giant water reservoirs), were excavated from here.

The correct answer is 'Sponges'.

Key Points

• Symmetry​
• It is an important point for the basis of classification of Kindom Animalia.
• There are two types of Body Symmetry -
• Asymmetrical (Irregular Shapes)
• Symmetrical (Regular Shapes)
• The symmetrical animals may have any one of the following symmetry -
• Bilateral Symmetry
• Radial Symmetry
• Spherical Symmetry
• Phylum Porifera
• They are organisms with holes in the body.
• It includes all the Sponges.
• They are non-motile, attached to a solid support, asymmetric creatures, mainly found in marine habitats.
• Thus, the correct answer is Sponges.

Additional Information

• Let's have a look at other options:

The correct answer is 'Helium'.

Key Points

• ​Helium
• Its atomic number is 2.
• It has the lowest boiling point and melting point among all the elements.
• Liquid helium is used to cool substances to very low temperatures.​
• It is used for inflating aeroplane tyres & filling balloons for metrological observations.
• Deep-sea divers use a mixture of helium and oxygen in place of air for breathing.
• Thus, the correct answer is Helium.

Additional Information

• Inert Gas
• Inert gas is that gas which generally does not participate in chemical reactions and is always available in a free state.
• Its examples are helium, neon, argon, krypton, xenon and radon.
• All inert gases are colourless, odourless and tasteless.
• They are also known as Noble Gases.

The correct answer is '2017'.

Key Points

• Ravi Shastri had been appointed as the new coach of Team India in 2017.
• Shastri's appointment followed Kumble's resignation as coach after the Champions Trophy in June.
• Prior to this, he was the director of Team India from 2014 to 2016.
• Ravi Shastri has left the post of head coach of Team India after the ICC T20 World Cup-2021.
• Ravi Shastri has been included as a commissioner for the retired players in the Legends League Cricket (LLC) starting in January next year.

Additional Information

• Currently, Rahul Dravid is the new coach of the Indian Cricket Team.
• Before the 90s in Team India, the team manager was appointed instead of the coach.
• The process of selecting a full-time coach for the Indian team took place in 1992 with Ajit Wadekar becoming the coach.
• Lalchand Rajput was appointed as manager only for the 2007 T20 World Cup.

The correct answer is 'Kerala'.

Key Points

• Thus, the correct answer is Kerala.

The correct answer is 'Eid-ul-Fitr'.

Key Points

• Eid-ul-Fitr is a religious festival celebrated by Muslims at the end of the holy month of Ramzan.
• It is celebrated on the first day of Shawwal, the tenth month of the Islamic calendar.
• This festival of Muslims is basically a festival promoting brotherhood.
• Everyone celebrates this festival together and prays to God for happiness, peace, and prosperity.
• The joy of Eid-ul-Fitr is celebrated with full enthusiasm all over the world.
• Thus, the correct answer is Eid-ul-Fitr.

Additional Information

• Let's have a look at other options:

The correct answer is 'Rukmani Devi and Padma Subrahmanyam'.

Key Points

• Rukmani Devi Arundale
• Rukmini Devi Arundale (29 February 1904 – 24 February 1986) was a famous Indian dancer.
• She was filled with devotion to Bharatanatyam and started her own tradition of dance.
• She was awarded the Padma Bhushan in 1956 in the field of arts.
• In the 1920s, when Bharatanatyam was not considered a good dance form and people opposed it, she not only supported it but also adopted the art.
• Padma Subrahmanyam
• Padma Subrahmanyam (born 4 February 1943, in Madras), is an Indian classical Bharatanatyam dancer.
• She is also a research scholar, choreographer, music composer, singer, teacher, Indologist, and author.
• She is famous in India as well as abroad. Several films and documentaries have been made in her honour by countries such as Japan, Australia, and Russia.
• Thus, the correct answer is Rukmani Devi and Padma Subrahmanyam

Additional Information

• Let's have a look at other options:

The correct answer is 'Ladakh'.

Key Points

• Dosmoche Festival is celebrated in Ladhak in the second week of February.
• This is one of the new festivals of Ladakh. Mask dances are performed in various monasteries every year during this festival.
• Apart from this religious symbols are held outside Ladhakh by adorning the flag on wooden pillars.
• The Dosmoche festival lasts for two days in which Buddhist monks dance, offer prayers, and perform rituals to ward off bad luck and evil spirits from the area.
• Thus, the correct answer is Ladhak.

Additional Information

• Let's have a look at other options:

The correct answer is 'Osmium'.

Key Points

• Osmium
• ​Symbol - ​Os
• Atomic weight -190
• Atomic number - 76
• It is the heaviest of the known substances.
• Thus, the correct answer is Osmium.

Additional Information

• Metals
• According to chemistry, metals are those elements that readily give up electrons to form cations and form metallic bonds with atoms of metals.
• Metals have lustre, metallurgical properties, high tensile strength and are good conductors of heat and electricity.
• Gold - It is a chemical element with the symbol Au and atomic number 79, making it one of the higher atomic number elements that occur naturally. It is a bright, slightly orange-yellow, dense, soft, malleable, and ductile metal in a pure form. Chemically, gold is a transition metal and a group 11 element.
• Mercury - It is a chemical element with the symbol Hg and atomic number 80. It is also known as quicksilver and was formerly named hydrargyrum from the Greek words, hydor and argyros.
• Silver - It is a chemical element with the symbol Ag and atomic number 47. A soft, white, lustrous transition metal, it exhibits the highest electrical conductivity, thermal conductivity, and reflectivity of any metal.

The correct answer is 'Venus''.

Key Points

• Thus, the correct answer is Venus.

Additional Information

• Venus
• ​Venus is the second planet from the Sun.
• It is the brightest planet.
• It is called Earth's Sister Planet or Twin Planet.

Confusion Points

• Venus is entirely covered with a thick carbon dioxide atmosphere and sulphuric acid clouds which give it a light yellowish appearance.
• Jupiter is a giant gas planet with an outer atmosphere that is mostly hydrogen and helium with small amounts of water droplets, ice crystals, ammonia crystals, and other elements. Clouds of these elements create shades of white, orange, brown and red.

The correct answer is is seven.

Key Points

• Udyam Express of MSME is an initiative of Ministry of Micro, small and Medium Enterprises (MSME).
• These are the mobile vans will go to the villages and make people aware of all aspects of entrepreneurship along with imparting training to them.

Additional Information

• The Ministry of Micro, Small and Medium Enterprises, a branch of the Government of India, and an apex executive body.
• Objective: formulation and administration of rules, regulations and laws relating to micro, small and medium enterprises in India.
• The current Minister of Micro, Small and Medium Enterprises is Narayan Rane.

The correct answer is Mycoplasmas.

Key Points

• Mycoplasma is a genus of bacteria that lack a cell wall around their cell membranes.
• Peptidoglycan is absent and this characteristic makes them naturally resistant to antibiotics that target cell wall synthesis.

Additional Information

• Caulerpa taxifolia is a species of green seaweed native to tropical waters of the Pacific Ocean, Indian Ocean, and Caribbean Sea.
• The species name taxifolia arises from the resemblance of its leaf-like fronds to those of the yew.
• Acetabularia is a genus of green algae typically found in subtropical waters.
• They are a single-celled organism, but gigantic in size and complex in form, making them an excellent model organism for studying cell biology.
• Sporozoites is a motile spore-like stage in the life cycle of some parasitic sporozoans (e.g. the malaria organism), that is typically the infective agent introduced into a host.

The correct answer is Metamorphic rocks.

Key Points

• Metamorphic rocks result from the alteration of preexisting rocks in response to changing environmental conditions, such as variations in temperature, pressure, and mechanical stress, and the addition or subtraction of chemical components.
• Some examples of metamorphic rocks are gneiss, slate, marble, schist, and quartzite.

Additional Information

• Igneous rocks are defined as types of rocks that are formed when molten rock or lava cools to a solid state eg. Granite, Basalt, etc.
• Volcanic rocks are igneous rocks.
• Sedimentary rocks are types of rock that are formed by the accumulation or deposition of mineral or organic particles at Earth's surface, followed by cementation eg. sandstone, limestone, and shale.

The correct answer is the slow process of conversion of organic matters into coal.

Key Points

• Carbonization is the conversion of organic matters like plants and dead animal remains into carbon through destructive distillation.
• Carbonization of coal is its decomposition by heat, out of contact with air, into a solid residue, coke, and liquid and gaseous distillation products.
• The main objective of the process of carbonization is the production of either hard coke or gas, the liquor being a valuable product in each case.

Additional Information

• Over millions of years, the absence of air, high temperature, and high pressure transformed the dead organisms into petroleum and natural gas.
• Polyethylene is made through an addition polymerization reaction that utilizes an ethylene monomer (–C2H4–) repeated along the chain.
• The process of separating the various constituents/ fractions of petroleum is known as refining.
• At the refinery, the crude oil mixture is 'fractionated' into different components by fractional distillation.

The correct answer is Deepika Kumari.

Key Points

• Deepika Kumari is an Indian professional archer.
• She is currently ranked the World's No. 1.
• She won a gold medal in the 2010 Commonwealth games in the women's individual recurve event.

Additional Information

• Ankita Bhakat is an Indian recurve archer who is currently ranked world number 20 by the World Archery Federation.
• Komalika Bari is the only third Indian player to win the world title at the Tata Archery Academy's Cadet World Youth Archery Championships.
• She is currently ranked world number 53 by the World Archery Federation.
• Bombayla Devi Laishram is an Indian archer with a current world ranking of 412.
• She has won a silver medal at the World Archery Championships, and four gold, five silver, and four bronze medals at various editions of the Archery World Cup.

The correct answer is Sclerenchyma.

Key Points

• Sclerenchyma is a general term used to denote a tissue or cell type that has lignified walls.
• The main function of sclerenchyma is to provide mechanical support and strength to the plants.
• They provide structural support to the plant organs.
• They form protective coverings around nuts and seeds.

Additional Information

• Meristems form anew from other cells in injured tissues and are responsible for wound healing.
• Unlike most animals, plants continue to grow throughout their entire life span because of the unlimited division of meristematic regions.
• Collenchyma tissue is composed of elongated living cells of uneven primary thick walls.
• It provides support, structure, mechanical strength, and flexibility to the petiole, leaf veins, and stem of young plants, allowing for easy bending without breakage.
• Parenchyma is a type of simple permanent tissue that makes a major part of ground tissues in plants.
• They primarily store food and nutrients, provide support and foundation, and are involved in growth and development.

The correct answer is I and II.

Key Points

• Venus is the second planet from the Sun.
• It is known as the Earth's twin because they're almost similar in size and structure.
• Venus has extreme surface heat and a dense, toxic atmosphere, making it the hottest planet in our solar system with surface temperatures hot enough to melt lead.
• Thus, option 4 is the correct answer.

Additional Information

• The coldest planet in our solar system on record goes to Uranus which is about 20 times further away from the Sun than the Earth is.
• The lowest temperature recorded there was minus 224 degrees Celsius.

The correct answer is Amiya Kumar Mallick.

Key Points

• Amiya Kumar Mallick is an Indian sprinter who holds the 100 metres national record of 10.26 seconds.
• He is the fastest Indian on the tracks as of today.
• For women, the record is held by Dutee Chand with a timing of 11:22 seconds.

Additional Information

• Sanjeet Singh is an Indian athlete and sprinter specialising in 200 metres distance.
• Seaman Muhammed Anas Yahiya is an Indian sprinter who specialises in the 400 metres distance.
• He holds the national record in the 400 metres, which he set at the 2019 Czech Athletics Championships.
• Sapper Anil Kumar Prakash is a retired Indian sprinter.
• He held the 100 metres national record of 10.30 s set at the National Circuit Athletic Meet held in New Delhi in 2005 which was broken in 2016 by Amiya Kumar Mallick.

The correct answer is ₹181 lakh crore.

Key Points

• The relationship between Gross Value Added (GVA) and  Gross Domestic Product (GDP) is defined as -
• GVA= GDP + subsidies on products – taxes on products.
• Thus, GDP = ₹170 lakh crore + ₹2 lakh crore - ₹13 lakh crore = ₹181 lakh crore.

Additional Information

• In economics, gross value added is the measure of the value of goods and services produced in an area, industry or sector of an economy.
• Gross domestic product is a monetary measure of the market value of all the final goods and services produced in a specific time period by countries.

The correct answer is 9:1.

Key Points

• The ratio of widths to that of intensity to that of amplitude in Young's double slit experiment is as follows =
• W₁:W₂ = I₁:1₂
• **I₁:I₂ = A₁2:A₂**2
• ⇒ W1:W2 = A12:A22
• As per the value given in the problem, 
• ​W1:W2 = 3²:1² = 9:1

Additional Information

• In modern physics, the double-slit experiment is a demonstration that light and matter can display characteristics of both classically defined waves and particles.
• It also displays the fundamentally probabilistic nature of quantum mechanical phenomena.

The correct answer is British India and Nepal.

Key Points

• The Treaty of Sugauli established the boundary line of Nepal.
• It was signed on 4 March 1816 between the East India Company and Guru Gajaraj Mishra following the Anglo-Nepalese War of 1814–16.

Additional Information

• The Anglo-Afghan Treaty of 1919, also known as the Treaty of Rawalpindi, was a treaty which brought the Third Anglo-Afghan War to an end.
• It was signed on 8 August 1919 in Rawalpindi by the United Kingdom and the Emirate of Afghanistan.
• The Treaty of Srirangapatanam, signed 18 March 1792, ended the lodar.
• Its signatories included Charles Cornwallis, on behalf of the British East India Company; representatives of the Nizam of Hyderabad and the Maratha Empire; and Tipu Sultan, the ruler of Mysore.
• The Treaty of Salbai was signed on 17 May 1782.
• It was signed between Warren Hastings on behalf of the British East India Company and Mahadaji Sindhia, a Maratha statesman and ruler of Ujjain.

The correct answer is Quo Warranto.

Key Points

• The term 'Quo Warranto' means 'what is your authority'.
• It is a judicial order asking a person, who occupies public office, to show by what authority s/he holds the office.
• If it is found that the holder of the office has no valid title, then this writ is issued to him to oust from the office.
• Article 32 empowers Supreme Court and Article 226 empowers High Courts to issue these writs.

Additional Information

• 'Habeas Corpus' literally means “to have a body of”.
• This writ is used to release a person who has been unlawfully detained or imprisoned.
• 'Mandamus' means 'we command'.
• It is issued by the Court to direct a public authority to perform the legal duties which it has not or refused to perform.
• 'Certiorari' means 'To be certified' or 'To be informed'.
• This writ is issued by a court higher in authority to a lower court or tribunal ordering them either to transfer a case pending with them to itself or quash their order in a case.

The correct answer is Odisha.

Key Points

• In a recently released NITI Aayog report, Odisha is ranked eighth from the bottom with 29.35% of the State's population found to be multi-dimensionally poor.
• This is a drastic improvement from the 1973-74 era and an appreciable effort by the government.
• The state is home to 13 particularly vulnerable tribal groups.
• The State is disaster prone to cyclones, floods and drought.
• The latest was the Cyclone Yaas, which created havoc along the coastline of the state.

Additional Information

• West Bengal has population of 19.98% living below poverty lines.
• Madhya Pradesh has population of 31.65% living below poverty lines.
• Bihar has population of 33.74% living below poverty lines.
• The all-India percentage is 21.92.

The correct answer is Babur.

Key Points

• The first Battle of Panipat happened on 21 April 1526.
• It was fought between the invading forces of Babur and the Lodi dynasty.
• With Lodi being defeated by Babur, it marked the beginning of the Mughal Empire and the end of the Delhi Sultanate.

Additional Information

• Jahangir was the fourth Mughal Emperor who ruled from 1605 until his death in 1627.
• He is famous for his 'golden chain of justice'.
• Humayun was the second emperor of the Mughal Empire from 1530 to 1540 and again from 1555 to 1556.
• He defeated Mahmud Lodi in the decisive battle of Dauhariya in 1532.
• Akbar was the third Mughal emperor, who reigned from 1556 to 1605.
• Akbar won the Second Battle of Panipat on 5 November 1556 with the Hindu king of Delhi, Hemu.

The correct answer is surfactant intermediate.

Key Points

• Many items are derived from crude petroleum, which provide raw materials for many new industries, collectively known as petrochemical industries.
• This group of industries is divided into four sub-groups: Polymers, Synthetic fibres, Elastomers and Surfactant intermediate.
• Surfactants are compounds that lower the surface tension between two liquids, between a gas and a liquid, or between a liquid and a solid.
• Surfactants may act as detergents, wetting agents, emulsifiers, foaming agents, or dispersants.

Additional Information

• Resin, like plastic, is a byproduct of petroleum or crude oil.
• It is suitable for use in paints and varnishes, coatings, printing ink, lithographic inks, paper, adhesives, rubber, concrete-curing compounds.
• Polyethylene or polythene is the most common plastic.
• It is used in in packaging film, garbage bags, grocery bags, insulation for wires and cables, agricultural mulch, bottles, toys, houseware, etc.
• Paint stays on the surface of something and creates a colored coating whereas dye soaks into the fibers, or skin in this case, and changes the color of the thing itself.
• Both can be petroleum products.

The correct answer is a Theosophist and Irish socialist.

Key Points

• Annie Besant was a British socialist, theosophist, women's rights activist, writer, orator, political party member, educationist, and philanthropist.
• Regarded as a champion of human freedom, she was an ardent supporter of both Irish and Indian self-rule.
• She was elected as president of the Indian National Congress in the 1917 Calcutta session.

Additional Information

• Sri Aurobindo was an Indian philosopher, yoga guru, maharishi, poet, and Indian nationalist.
• He was also a journalist, editing newspapers such as Vande Mataram.
• Literary works -  The Life Divine, Synthesis of Yoga, Savitri: A Legend and a Symbol.

The correct answer decreases.

Key Points

• The average summer temperature drops to 15°C and the average winter temperature is below freezing point at the middle range of the Himalayas Mountains.
• Over 5000 meters, the temperature is below freezing point all year round, and the mountain top is always covered by snow.

Additional Information

• Near the Earth's surface, the air gets cooler the higher you climb.
• As you climb a mountain, you can expect the air temperature to decrease by 6.5 degrees C for every 1000 meters you gain.
• This is called the standard (average) lapse rate.

The correct answer is Mattur.

Key Points

• Mattur is a village in Shivamogga district near the city of Shivamogga in Karnataka state.
• It is known for the usage of Sanskrit for day-to-day communication.
• The general language of the state is Kannada.

Additional Information

• Punsari village in Gujarat became India's first Adarsh Gram in 2020.
• Malana is an ancient Indian village in the state of Himachal Pradesh and famous for its Malana cream.
• Madhapar from the Kutch district of Gujarat is one of the richest villages in India in terms of bank deposits.

The correct answer is 30 years.

Key Points

• Qualifications to be eligible as a Rajya Sabha member -
• Must be an Indian Citizen
• Must be not less than 30 years of age
• Must be registered as an elector for a parliamentary constituency.

Additional Information 

• Qualifications to be eligible as a Lok Sabha member -
• Must be an Indian Citizen
• Must be not less than 25 years of age
• Must be registered as an elector for a parliamentary constituency.

The correct answer is Article 32.

Key Points

• Article 32 makes the Supreme Court both the guarantor and the defender of 'Fundamental Rights.
• It provides for a mechanism or an instrument through which an individual whose fundamental rights have been infringed can approach the Apex Court i.e. Supreme Court of India to seek remedy as well as enforcement of these rights.
• B.R. Ambedkar described 'The Right to Constitutional Remedy' as the 'heart and soul' of the Indian constitution because when any of our rights are violated, we can seek a remedy through the courts.

Additional Information

• Article 15 of the Constitution of India forbids discrimination on grounds only of religion, race, caste, sex, or place of birth.
• Article 17 ensures that untouchability is abolished and its practice in any form is forbidden.
• The preamble is an introduction to the highest law of the land; it is not the law.
• It sets the stage for the Constitution.

The correct answer is Part IV.

Key Points

• Part IV (Articles 36 – 51) of the Indian Constitution deals with the provisions of the Directive Principles of State Policy.
• The directive principles ensure that the State shall strive to promote the welfare of the people by securing a social order in which social, economic and political justice is animated/informed in all institutions of life.

Additional Information

• Part IX - Deals with Panchayats, Municipalities, and Cooperative societies.
• Part III - Deals with the Fundamental Rights.
• Part V - Deals with the Union government.

The correct answer is Mizoram.

Key Points

• Mizoram has huge number of mountains and formation of most of the mountains is accompanied by formation of valley type depression which runs parallel to mountains.
• These depressions get accumulated with unconsolidated deposits known as molasses basin.

Additional Information

• Arunachal Pradesh is land of peanuts in the foothills of the Himalayas in northeast India.
• Tripura has three distinct physiographic zones - i) hill ranges ii) undulating plateau land and iii) low-lying alluvial land.
• The Khasi Hills and Jaintia Hills which form the central and eastern parts of Meghalaya are an imposing plateau with rolling grassland, hills and river valley.

The correct answer is 12.

Key Points

• The Khelo India initiative has been organised into 12 verticals -
• Play field development
• Community coaching development
• State-level Khelo India centres
• Annual sports competition
• Talent search and development
• Utilisation and creation/upgrade of sports infrastructure
• Support to national/regional/state sports academics
• Physical fitness of school children
• Sports for women
• Promotion of sports amongst people with disabilities
• Sports for peace and development
• Promotion of rural and indigenous/tribal games

Additional Information

• Khelo India Programme is a national scheme for the development of sports in India.
• It was launched in the year 2018 by the Sports Ministry.
• This program has been launched to improve the sports culture in India.

The correct answer is Tarapur.

Key Points

• Tarapur Atomic Power Station is located in Tarapur, Palghar, Maharashtra.
• It was the first commercial nuclear power station built in India and became operational in 1969.
• Kalpakkam is known for its nuclear plants and affiliated research installations.
• These include the Madras Atomic Power Station (MAPS), a nuclear power plant, the Indira Gandhi Centre for Atomic Research (IGCAR), an affiliate of the Department of Atomic Energy (DAE) and the Bhabha Atomic Research Centre (BARC).
• The nuclear power plant in Rawatbhata, Kota, Rajasthan is India's second pair of indigenously designed Nuclear Power Plant of 700 MW unit size.
• Narora Atomic Power Station is a nuclear power plant located in Narora, Bulandshahar District in Uttar Pradesh.

The correct answer is monotonic.

Key Points

• A monotonic preference means that a rational consumer always prefers more of a good as it offers the consumer a higher level of satisfaction.
• A consumer may have different preference sets corresponding to the different levels of income.

Additional Information

• The law of diminishing returns is an economic principle stating that as investment in a particular area increases, the rate of profit from that investment, after a certain point, cannot continue to increase if other variables remain at a constant.
• A substitute is a product or service that can be easily replaced with another by consumers.
• In economics, products are often substitutes if the demand for one product increases when the price of the other goes up.

The correct answer is 'Bangladesh'

Key Points

• Population Density:
• The population density of a country is the number of people living per unit area, typically expressed as inhabitants per square kilometer.
• Bangladesh has an exceptionally high population density, making it one of the most densely populated countries in the world.
• Comparative Analysis:
• India, while having a very large population, has a vast land area that results in a lower population density compared to Bangladesh.
• As of the latest data, Bangladesh's population density is over 1,200 people per square kilometer, whereas India's is significantly lower, around 460 people per square kilometer.

Additional Information

• China:
• China has a very large population, even more than India, but its land area is also comparably vast.
• This results in a population density of around 150 people per square kilometer, which is lower than India's population density.
• Indonesia:
• Indonesia has a large population distributed across a vast archipelago comprising numerous islands.
• Its population density is approximately 140 people per square kilometer, which is lower than that of India.
• Pakistan:
• Pakistan also has a high population density but not as high as India or Bangladesh.
• Pakistan’s population density is around 260 people per square kilometer, which is still lower than that of India.

Important Points

• Population density can reflect various socio-economic factors, including the level of urbanization and the capacity for resource availability.
• High population densities can lead to challenges such as congestion, inadequate infrastructure, and resource depletion.
• Country-specific policies and planning are essential to manage the impacts of population density on development and quality of life.

The correct answer is Primary deficit = fiscal deficit - interest payment.

Key Points

• Primary deficit refers to the difference between the current year's fiscal deficit and interest payment on previous borrowings.
• It indicates the borrowing requirements of the government, excluding interest..

Additional Information

• The fiscal deficit is the difference between total expenditure and revenue of the government.
• It indicates the total borrowing that are needed by the government.

The correct answer is Uttar Pradesh.

Key Points

• The Uttar Pradesh Legislative Council has 100 members.
• 90 of them are elected and 10 are nominated by the governor of the state.

Additional Information

• Karnataka Legislative Council has 75 members - 64 elected and 11 nominated.
• Maharashtra Legislative Council has 78 members - 66 elected and 12 nominated.
• Andhra Pradesh Legislative Council has 58 members - 50 elected and 8 nominated.

The correct answer is Shudra.

Key Points

• Dvija means "twice-born" in ancient Indian Sanskrit.
• The concept is premised on the belief that a person is first born physically and at a later date is born for a second time spiritually.
• Dvija, in medieval Indian texts, refers to a member of the first three varnas – Brahmins, Kshatriyas, and Vaishyas.
• ​Thus, Shudras are not included in this grouping.

Additional Information

• The traditional caste system consists of a hierarchy of four castes (varnas) - Brahmins (priests and teachers), Kshatriyas (rulers and warriors), Vaishyas (merchants and cultivators), and Shudras (servants).
• Members of the lowest Hindu varna, the Shudras and people below the four-varna system altogether are regarded as theoretically ineligible to study or even to listen to the Vedas.
• However, the Asvalayana sutra indicates that a non-dvija child may also be inducted into the Dvija category, if he wishes to pursue the duties associated with these varnas.
• The position of women in the dvija system is anomalous as even high-caste women are not considered eligible for Vedic study according to traditional canons.

The correct answer is Prakrit, Greek and Aramaic.

Key Points

• The inscriptions found in the central and eastern part of India were written in Magadhi Prakrit using the Brahmi script.
• Prakrit using the Kharoshthi script, Greek and Aramaic were used in the northwest.
• The edicts are composed in non-standardized and archaic forms of Prakrit.

Additional Information

• Brahmi -  Its best examples are found in the rock-cut edicts of Asoka.
• Kharosthi - Its inscriptions have been found in the form of Buddhist Texts from present clay Afghanistan and Pakistan.
• Sanskrit - Conquests of Samudragupta written by Harisena are in Sanskrit language and Brahmi script.
• Pali - The Asokan edicts were in Pali using Brahmi script.
• Persian - Jahangir’s Allahabad inscriptions in Persian.
• Greek - The Kandahar inscription of Ashoka is written in Greek and Aramaic (Armenian) languages and is hence bilingual.

Given:

The base of a cylinder having an area(a) is 10.24 π.

The height of the cylinder is 5.

Formula used:

Area of Base of Cylinder = πr²

Curved surface area of the cylinder = 2πrh (where, r = radius and h = height.)

Calculations:

Area of the base = 10.24 π

πr² = 10.24 π

r = 3.2 

Curved surface area = 2 × π × 3.2 × 5 = 32 π.

∴ The answer is 32 π.

Given:

Discount scheme as "Buy 1 saree and get 75% off on another saree of the same price".

Cost price is below 75% of the marked price.

Formula used:

Selling price(S.P.) = Marked price(M.P) - Discount percentage on marked price(D%)

Profit percentage(P%) = $\dfrac{S.P. - P.}{C.P.} \times 100$

Calculations:

Let the marked price of one saree be 100.

If a person buy 1 saree at Rs. 100 he can get another saree of same price at 75% off that means the price for the second price is 100 - 75 = Rs. 25.

So, the total discount percentage for two sarees will be $\dfrac{{75}}{{2}}$% = 37.5%.

S.P. = 100 - 37.5 = Rs. 62.5

And, the corresponding C.P. will be = 100 - 75% of 100 = Rs. 25

P% = $\dfrac{{62.5 - 25}}{{25}}$ × 100 = 150%.

∴ The answer is 150%.

Given:

The average marks of 23 children is 62.

A new student with 86 marks joins the class.

Formula used:

A =$\dfrac{{S}}{{N}}$(where, A is the average, S is the sum of observations and N is the number of observations)

Calculations:

A = $\dfrac{{S}}{{N}}$

62 × 23 = S

S = 1426

Now, when a new student joins the class with 86 marks, then the total number of students becomes 23 + 1 = 24.

The new average thus forms = $\dfrac{{1426 + 86}}{{24}}$

= $\dfrac{{1512}}{{24}}$ = 63

∴ The answer is 63.

Given:

The sum of the cubes of two numbers (a³ + b³) is 1755.

The sum of the numbers (a + b) is 15.

Formula used:

(a + b)³ = a³ + b³ + 3ab(a + b)

(a - b)² = (a + b)² - 4ab

Calculations:

(a + b)³= a³ + b³ + 3ab(a + b)

15³ = 1755 + 3ab(15)

$\dfrac{{3375 - 1755}}{{15}}$ = 3ab

ab = $\dfrac{{108}}{{3}}$ = 36

(a - b)²= (a + b)² - 4ab

= 15² - 4 × (36)

(a - b)²= 225 - 144 = 81

a - b = 9

∴ The answer is 9.

Given:

2^n-1 + 2ⁿ⁺¹ = 320

Formula used:

1. a^m+n = a^m × aⁿ
2. am - n = am × a^- n = a^m/aⁿ
3. a^m = aⁿ ⇒ m = n

Calculations:

2n-1 + 2n+1 = 320

By using the above formula,

2ⁿ × $\dfrac{{1}}{{2}}$ + 2ⁿ × 2 = 320

2ⁿ × ($\dfrac{{1}}{{2}}$+ 2) = 320

2ⁿ × $\dfrac{{5}}{{2}}$ = 320

2ⁿ = $\dfrac{{320 × 2}}{{5}}$

2ⁿ = 128 

2ⁿ = 2⁷

n = 7

∴ The answer is 7.

Given:

The cost price of an encyclopedia is Rs.10,080, which is 20% below its marked price.

Discount = 30%

Concept used:

Let the marked price be 100.

Therefore, the cost price which is 20% below the Marked price = 100 - (20% of 100) = 80.

Formula used:

Selling price = marked price - discount percentage on marked price.

Calculations:

Cost price is Rs. 10080.

80% of x = 10080

10080 × $\dfrac{{100}}{{80}}$ = 12600

Therefore, the marked price = 12600.

Required Selling Price = 12600 - (30% of 12600)

Selling Price = 12600 - 3780 = Rs. 8220.

∴ The answer is Rs. 8820.

Given:

The strength of a school increased from 400 to 500.

Calculations:

Percentage increase = $\dfrac{{500 - 400}}{{400}}$ × 100.

Percentage increase = $\dfrac{{100}}{{4}}$ × 100.

Percentage increase = 25%.

∴ The answer is 25%.

Given:

Cubical vessel of side 30 cm.

Concept used:

The length of longest rod that can be fit is the length of the diagonal of the cubical vessel.

Formula used:

Diagonal of the cube = a$\sqrt {3}$

Calculations:

Length of diagonal = a$\sqrt {3}$ = 30$\sqrt {3}$ cm.

∴ The answer is 30$\sqrt {3}$ cm.

Given:

The average of six numbers is x.

The average of three of these numbers is y.

The average of remaining three is z.

Concept used:

Let, the six numbers be a, b, c, d, e, f.

Calculations:

a + b + c + d + e + f = 6x (eqnA)

Again, a + b + c = 3y (eqn1) and,

d + e + f = 3z (eqn2)

Putting eqn1 and eqn2 in eqnA,

3y + 3z = 6x

y + z = 2x

z = 2x - y

∴ The answer is z = 2x - y.

Given:

The interest on a sum of ₹4,096 for 3 years, when interest is compounded annually at a certain rate of interest, is ₹817.

Formula used:

C.I. = P[(1 +$\frac{{R}}{{100}}$)ⁿ - 1]

Where, P is the principle, R is the rate and n is the time.

Calculations:

817 = 4096 × [(1 +$\frac{{R}}{{100}}$)³ - 1]

$\dfrac{{817}}{{4096}}$ + 1 = (1 + $\frac{{R}}{{100}}$ )³

$\dfrac{{4913}}{{4096}}$ = (1 +$\frac{{R}}{{100}}$)³

Cube rooting both sides we get,

$\dfrac{{17}}{{16}}$ = 1 + $\frac{{R}}{{100}}$

$\dfrac{{17}}{{16}}$ - 1 = $\frac{{R}}{{100}}$

$\dfrac{{1}}{{16}}$ = R/100

R = $\dfrac{{100}}{{16}}$ = $6\frac{1}{4}\%$

∴ The answer is $6\frac{1}{4}\%$

Given:

$(\frac{3}{5})^x \times (\frac{5}{3})^{2x} = \frac{625}{81}$

Formula used:

(a/b)ⁿ = (b/a)^-n

a^m × aⁿ = a^m+n

Calculations:

$(\frac{3}{5})^x \times (\frac{5}{3})^{2x} = \frac{625}{81}$

⇒ $(\frac{5}{3})^{-x} \times (\frac{5}{3})^{2x} = (\frac{5}{3})^4$

⇒ $(\frac{5}{3})^{-x + 2x} = (\frac{5}{3})^4$

⇒ $(\frac{5}{3})^x = (\frac{5}{3})^4$

⇒ x = 4

∴ The correct answer is option (2).

Given:

Ice-cream cone with a radius of 2 cm and a height of 7 cm to the brim will be used.

To distribute a cubical ice-cream brick with a 22-cm edge among some children.

Formula used:

Volume of cone = $\dfrac{{1}}{{3}}$ πr²h

Volume of cubical = a³

Where, r is the radius, h is the height, a is the side of the cube.

Calculations:

Number of children = $\dfrac{{Volume\ of \ cubical}}{{Volume \ of \ cone}}$

= $\dfrac{{22 × 22 × 22}}{{1/3 × π × 2² × 7}}$

= $\dfrac{{10648}}{{88/3}}$

= $\dfrac{{10648 × 3}}{{88}}$ = 363

∴ The answer is 363.

Given:

$2.\overline{6}$

Calculations:

Let x = $2.\overline{6}$      ----(1)

Multiply by 10 in equation (1)

10 x = 26.66      ----(2)

Subtract equation 1 by equation 2

10x - x = 26.666 - 2.666

9x = 24

x = $\dfrac{24}{9}$

x = $\dfrac{8}{3}$

∴ The answer is $\dfrac{8}{3}$

Given:

The HCF of $\dfrac{2}{5}$, $\dfrac{3}{5}$ and $\dfrac{1}{2}$

Formula used:

H.C.F. of fractions = $\dfrac{{H.C.F. \ of \ numerators}}{{L.C.M. \ of \ denominators}}$

Calculations:

$\dfrac{H.C.F.(2, 3, 1)}{L.C.M.(5, 5, 2)}$

H.C.F. of 2, 3, 1 = 1 (as, these numbers are prime numbers in which the factors can only be 1 and the number itself)

L.C.M. of 5, 5, 2 = 10

The HCF of $\dfrac{2}{5}$, $\dfrac{3}{5}$ and $\dfrac{1}{2}$ = $\dfrac{1}{10}$

∴ The answer is $\dfrac{1}{10}$

Shortcut Trick

Diagonal of a cube = Side × √3 ⇒ 15√3 = Side × √3 ⇒ Side = 15 cm.

Volume of 1 cube = Side³ = 15³ = 3375 cm³.

Total Volume of 3 cubes joined = 3 × 3375 = 10125 cm³.

∴ The correct answer is 10125 cm³.

Alternate Method

Given: Diagonal of each cube = 15√3 cm; Number of cubes = 3.

Formula Used: Diagonal of cube = a√3; Volume of cuboid = L × B × H.

⇒ Side of each cube (a) = 15√3 / √3 = 15 cm.

⇒ When 3 cubes are joined in a row, the length (L) of the cuboid = 15 + 15 + 15 = 45 cm.

⇒ The breadth (B) remains the same = 15 cm.

⇒ The height (H) remains the same = 15 cm.

⇒ Volume of the cuboid = 45 × 15 × 15 cm³.

⇒ Volume = 45 × 225 = 10125 cm³.

∴ The correct answer is 10125 cm³.

Additional Information

Total Surface Area of Cuboid

The total surface area is given by the formula: TSA = 2(LB + BH + HL).

Diagonal of a Cuboid

The longest rod that can be placed in a cuboid has length D = √(L² + B² + H²).

Cube Properties

For a cube of side 'a', Volume = a³ and Total Surface Area = 6a².

Given:

A car travels 20 m in 4 minutes.

Later, it travels 20 km at a speed of 80 km/h.

Formula used:

Average speed = Total distance/ total time

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

Calculations:

In first case,

Distance = 20 m and Time = 4 mins

Conversion from minute to seconds.

Time = 4 mins = (4 × 60 = 240 seconds) as, 1 min = 60 seconds.

For, second case,

Distance = 20 km = 20 × 1000 = 20,000 m.

Time = $\frac{{20}}{{80}}$ = $\frac{{1}}{{4}}$ hour = 900 seconds. (as, 1 hour = 3600 seconds)

Average speed = $\frac{{20 + 20000}}{{240 + 900}}$

$\frac{{20020}}{{1140}}$ = 17.56 m/sec.

∴ The answer is 17.56 m/sec.

Given:

$\frac{{1}}{{(√18 - √16)}}$

Calculations:

$\frac{{√18 + √16}}{{(√18 - √16)(√18 + √16)}}$ [multiplying both the numerator and the denominator by (√18 + √16)]

$\frac{{√18 + √16}}{{18 - 16}}$ [as, (a - b)(a + b) = a² - b²)]

$\frac{{√(3 × 3 × 2) + 4}}{{2}}$

$\frac{{3√2 + 4}}{{2}}$

∴ The answer is $\frac{1}{2}\left( {3\sqrt 2 + 4} \right)$

Given:

The difference between compound interest and simple interest for 2 years at 10% per annum, compounded annually, is Rs.64.

The interest is reckoned half-yearly.

Formula used:

S.I. = $\dfrac{{PRT}}{{100}}$

C.I. = P[(1 + $\frac{{R}}{{100}}$ )ⁿ - 1]

Where, P is the principle, R is the rate and n or T is the time.

Calculations:

For the first case,

C.I. - S.I. = 64

P[(1 +$\frac{{10}}{{100}}$)² - 1] - $\frac{{P × 2 × 10}}{{100}}$ = 64

P[($\frac{{11}}{{10}}$)² - 1] - $\frac{{P × 2 × 10}}{{100}}$ = 64

P($\frac{{121 - 100}}{{100}}$) - $\frac{{P × 2 × 10}}{{100}}$ = 64

$\frac{{21P}}{{100}}$- $\frac{{20P}}{{100}}$ = 64

P = 6400

Now, for the second case, when the interest is calculated half yearly. In such case, rate becomes R/2 and time becomes 2n.

C.I. = 6400[(1 + $\frac{{10}}{{2 × 100}}$)⁴ - 1]

C.I. = 6400[(1 + $\frac{{1}}{{20}}$)⁴ - 1]

C.I. = 6400[($\frac{{21}}{{20}}$)⁴ - 1]

6400 × $\frac{{194481 - 160000}}{{160000}}$

6400 × $\frac{{34481}}{{160000}}$

C.I. = Rs. 1379.24

S.I = $\frac{{6400 × 10 × 4}}{{2 × 100}}$

S.I. = Rs. 1280

Difference between the two interests will be = 1379.24 - 1280 = Rs. 99.24

∴ The answer is Rs. 99.24.

Given:

$x + \dfrac{1}{x} = 2$

Calculations:

x + $\dfrac{1}{x} = 2$

x² + 1 = 2x

x² - 2x + 1 = 0

x² - x - x + 1 = 0

(x - 1)(x - 1) = 0

x = 1

Now putting the values of x = 1 in the following equation,

x¹⁰¹⁷ + x^-(1024)

= 1¹⁰¹⁷ + 1^-(1024)

= 1 + $\dfrac{{1}}{{1}}$

= 1 + 1 = 2

∴ The answer is 2.

Given:

Radius of solid metallic sphere are is 64 cm

Radius of spherical ball are is 4 cm.

Formula used:

The number of spherical balls obtained = (volume of solid metallic sphere) / (volume of spherical ball)

Volume of solid metallic sphere =$\frac{{4}}{{3}}$πR³

Volume of spherical ball = $\frac{{4}}{{3}}$ πr³.

Calculations:

$\frac{{4/3πR³}}{{4/3πr³}}$ = (R/r)³

(64/4)³ = 16³ = 4096

∴ The answer is 4096.