DSSSB Junior Secretariat Assistant Official paper (Held on: 5 April 2022 Shift 2 ) (Previous Year Paper)

As per the given information;

Alphabets in reverse order:  Z Y X W V U T S R Q P O N M L K J I H G F E D C B A 

• The 10th letter from the right end :

​ (Left)  Z Y X W V U T S R Q P O N M L K J I H G F E D C B A  (Right)

10^th letter = 'J'

• The 12th to the left of the 10th from the right end :

 (Left)  Z Y X W V U T S R Q P O N M L K J I H G F E D C B A   (Right)​

Therefore, the 12^th letter to the left of the 10^th letter from the right end is 'V'.

Hence, the correct answer is "V".

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

According to the given information :

1. A has two children C and E.
2. E is the only daughter of A and B.
3. D is the wife of A's son.
4. B is the mother of F's father.

Therefore, the following family tree can be drawn:

Thus, it is clear from the above diagram that 'A is Father's father of F'.

Hence, the correct answer is "Father's father".

The logic followed here is:

1. DGT

2. RUF

3. BEV

4) WYB

Thus, 'option 4' does not follow the same logic that is being followed by the other options, so it is different from other letter-cluster.

Hence, the correct answer is "WYB".

The logic followed here is:

• AN - EL - IJ

Similarly,

• CZ - GX - KV

Thus, CZ - GX - KV share the same relationship as AN - EL - IJ.

Hence, the correct answer is "CZ - GX - KV".

Decoding the information,

Given equation: 8 × 35 + X ÷ 2 - 6 = 15

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

New Equation: 8 - 35 ÷ X + 2 × 6 = 15

Here, we cannot start calculation from 'division' because we have a variable as divisior, thus we will start from multiplication.

⇒ 8 - 35 ÷ X + 2 × 6 = 15

⇒ 8 - 35 ÷ X + 12 = 15

⇒ 20 - 35 ÷ X = 15

⇒ (-35) ÷ X = 15 - 20

⇒ (-35) ÷ X = (-5)  

⇒ (-35) = (-5) × X

⇒  (-35) ÷ (-5) = X

⇒  X = 7

Hence, the correct answer is "7".

As per the given information:

• 'N' is added after each word and 'B' is added before each word.

Therefore, the newly formed words will be :

1. EAR → BEARN , 

2. BAT → BBATN

3. ROW → BROWN 

4. ACE → BACEN

Thus, the only meaningful word formed is "BROWN" from the word ''Row''.

• BROWN is a color.

Hence, the correct answer is "Row".

Given Statement : A > L < P = H > A > R > O > Y = Z

Conclusions:

I: Z < O → FALSE (as A > L < P = H > A > R > O > Y = Z → clearly 'Z < O' and not 'Z < O'; thus it is not true)

II: P > R → FALSE (as A > L < P = H > A > R > O > Y = Z→ clearly 'P > R' and not 'P > R'; thus it is not true)  

Hence, the correct answer is "Neither I nor II".

As per the given information:

• P is the second youngest among the six students. ​

• ​Only three students are older than T.

​

• Q is younger than only U. ​

• R is NOT the youngest.

• ​Thus, the final arrangement is :

Clearly, the third oldest among the six students is 'R'.

Hence, the correct answer is "R".

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

As per the given information: ​

• Max is the son of Joe.
• Max is the son-in-law of Abby.
• Lia is Joe's wife.

• Sam is the son of Abby.
• Rosa is the sister of Sam.
• Rosa is Tony's mother. ​
• If Abby has just one daughter.

• Therefore, the following family tree can be drawn:

Thus, it is clear from the above diagram that Tony is either a grandson or a granddaughter of Lia. But in options, only grandson is given thus "Tony is the grandson of Lia".

Hence, the correct answer is "Grandson".

Decoding the information,

Given equation: 10 × 5 - 4 + 2 ÷ 1     

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

New Equation: 10 ÷ 5 + 4 × 2 -1 

⇒ 10 ÷ 5 + 4 × 2 -1 

⇒ 2 + 4 × 2 -1  

⇒ 2 + 8 - 1    

⇒ 10 - 1  

⇒ 9

Hence, the correct answer is "9".

Given equation: [29.34 - (- 2) {5.90 - (7 - 2.5)}] ÷ [2.98 × {5.23 + (-3) × (-2)}] = ?

Concept used:

Follow the BODMAS rule as per the order given below:

Calculation:

⇒ [29.34 - (- 2) {5.90 - (7 - 2.5)}] ÷ [2.98 × {5.23 + (-3) × (-2)}] 

⇒ [29.34 - (- 2) {5.90 - 4.5}] ÷ [2.98 × {5.23 + 6}]

⇒ [29.34 - (- 2) 1.4] ÷ [2.98 × 11.23]

⇒ [29.34 - (-2.8)] ÷ [2.98 × 11.23]

⇒ [29.34 + 2.8)] ÷ 33.654

⇒ 32.14 ÷ 33.654

⇒ 0.9 ≈ 1

Hence, the correct answer is "1".

Alternate Method

Given equation: [29.34 - (- 2) {5.90 - (7 - 2.5)}] ÷ [2.98 × {5.23 + (-3) × (-2)}] = ?

Calculation:

 

Replacing the given values with approximate values,

⇒ [29 - (-2) {6 - (7 - 3)}] ÷ [3 × {5 + (-3) × (-2)}]

⇒ [29 - (-2) {6 - 4}] ÷ [3 × {5 + 6}]

⇒ [29 - (-2) 2] ÷ [3 × 11]

⇒ [29 - (-4)] ÷ 33

⇒ [29 + 4] ÷ 33

⇒ 33 ÷ 33

⇒ 1

Hence, the correct answer is "1".

Given:

In a certain code language,

'A ÷ B means 'A is the wife of B',

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

'A × B' means 'B is the mother of A',

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

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

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

 

On checking: 'P ÷ Q - R + S × T $ M' 

1) 'P ÷ Q'  

'P ÷ Q' means 'P is the wife of Q'.

2) 'Q - R'

'Q - R' means 'Q is the father of R'.

3) 'R + S

'R + S'means S is the daughter of R.

4) 'S × T'

'S × T' means T is the mother of S.

5) 'T $ M'

'T $ M' means T is the sister of M. 

• Thus, the following family tree can be drawn:

• Clearly, P is Sister's husband's mother of M.

Hence, the correct answer is "Sister's husband's mother".

The logic followed here is:

• 'GUITAR' is written as 'SEQFYH'.

Similarly,

• 'VIOLEN' will be written as;

Thus, VIOLEN will be written as 'DQKNUL'.

Hence, the correct answer is "DQKNUL".

The logic followed here is:

Let (1st number : 2nd number)

(1st number)² - 5 = (2nd number)

According to above logic:

Missing term = (17)² - 5

Missing term = 289 - 5

Missing term = 284

Hence, the correct answer is "284".

According to the given information: 

• Swati walked 3 km from her house towards the south.
• From there she took a right turn and walked 1 km.
• Then she turned right again and walked 3 km.
• The diagram according to the given information is,

• Clearly, the direction in which Swati is going is 'North'.

Hence, the correct answer is "North".

According to the given information:

A walks towards the south, then turns to the right, then to the left, and then to the right

• The diagram according to the given information is;

• Thus, the direction in which A is going is 'West'.

Hence, the correct answer is "West".

The logic followed here is:

Let (1st number : 2nd number)

(1st number)³ = (2nd number)

According to above logic:

Missing term = (17)³ 

Missing term = 4913 

Hence, the correct answer is "4913".

Given statement: A = C > D < E = F > B

Conclusions :

I. A > D → TRUE (as A = C > D < E = F > B → clear relationship given between A and D, so A > D it is true)

II. D < F → TRUE (as  A = C > D < E = F > B → clear relationship given between D and F, so D < F it is true)

Hence, the correct answer is "Both I and II are true".

The logic followed here is: 

STEM is written as KJYQ

Similarly,

ROOT will be written as:

Thus, 'ROOT' will be written as 'LOOJ'.

Hence, the correct answer is "LOOJ".

The logic followed here is:

Letters are increased by +4 and Numbers are increased by +8.

• AC4 is related to EG12

And,

• IK20 is related to MO28

Similarly,

• QS36 is related to?

Thus, QS36 is related to 'UW44'.

Hence, the correct answer is "UW44".

The pattern followed here is:

• B is the mirror image of A and this mirror image inside the two square.

Similarly,

• D is the mirror image of C and this mirror image inside the two square.

Hence, 'Option (4)' is the correct answer.

The table is alphabets place value:

The pattern followed here is:

Hence, 'M3N' is the correct answer.

Statements:

Some doctors are teachers.

Some teachers are compounders. 

The least possible diagram for the given statements is as follows

Conclusions:

I. Some teachers are doctors → True (Because some doctors are teachers so some teachers are also doctors)

II. Some doctors are compounders → False (Because direct relationship between doctor and teachers is not given so it may be possible but not define)

Hence, “Only conclusion I follows” is the correct answer.

The logic is here:

Three small figures are given upper side using these three figures we create the middle figure.

• We are using a small middle figure for the outside shape of the middle figure.
• We are using a small left side figure for the middle shape of the middle figure.
• We are using a small right side figure for the inside shape of the middle figure.

Check all the options:

Option 1: 

don't follow the logic, the small middle figure doesn't use 

Option 2: 

follow the logic. 

Option 3: 

follow the logic. 

Option 4: 

follow the logic. 

Hence, "Option 1" is the correct answer.

The table is alphabets place value:

Given:

BA - DF - GK

Similarly,

Option(1): IH - KM - NR

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

Table show alphabet serial number –

The pattern followed is,

Option (1): AE - GK

Option (2): IM - OS

Option (3): CG - IM

Option (4): NR - TW

All follow the same pattern, except ‘NR - TW’.

Hence, “NR - TW” is the odd one.

Six friends Vinita, Rajat, Mohit, Gunjan, Lovely and Sanjay are sitting on a straight bench facing towards the North.

1. They are sitting in the alphabetical order of their names.

2. Gunjan and Mohit interchange their positions. 

Hence, "Gunjan" is sitting second to the left of Sanjay.

Given:

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

1. F sits third to the left of O.

2. B sits to the immediate right of O.
   

3. Exactly three people sit between M and O.

4. M sits sixth to the left of G.

Two condition are created:

Condition I:

Condition II:

5. G sits second to the right of L.

This means L sits second to the left of G, But in 'condition II' O already sits second to the left of G.

So condition II is the wrong arrangement.

Hence, "14" total number persons are seated.

Table show alphabet serial number –

The pattern followed is,

1) BNP : DMR

2)  FJT : HQV

3)  PGD : RTF

4)  LKS : NPT

All follow the same pattern, except 'LKS : NPT’.

Hence, “LKS : NPT” is the odd one.

The table is alphabets place value:

The pattern followed here is:

 

Hence, 'J19T' is the correct answer.

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

1. Dot rotates clockwise direction and one by one dot is increasing. 

2. Hexagon sides one by one removed.

3. 1st to 2nd figure increases one line with a dot.

2nd to 3rd figure one arrow is increased.

3rd to 4th figure increases one line with a dot.

Hence, ‘option 4’ is the correct answer.

Given;

'blue' is coded as 'white',

'White' is coded as 'green',

'green' is coded as 'yellow'

The colour of Milk is White, and White is coded as Green.

Hence, “Green” is the right answer.

Given:

X, Y, Z, W, O, A and K are sitting in a row facing north

1. A is sitting to the immediate left of K.
2. K is fourth to the right of Y.

3. Y is the neighbour of O and W.
4. X, who is third to the left of W, is at one of the ends.

Only S is left so final sitting arrangment is:

Hence, "W" is to the right of Y.

The logic followed here is:

Hence, the correct answer is "1302".

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

Hence, ‘option 3’ is the correct answer.

Table show alphabet serial number –

The pattern followed is,

Hence, “R32P” is the missing term.

The pattern followed here is:

Hence, '102' is the correct answer.

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

• The small figure inside the square rotates anticlockwise direction.
• The small figure outside the square rotates clockwise direction.

Final series is

Hence, ‘option 1’ is the correct answer.

Confusion Points In option (4)

 the circle is outside the square but we want a new figure and a circle is already repeated in the 3rd figure.

The shaded part represents Cricketers are graduates.

 

The numbers representing Cricketers are graduates = 6 + 3 = 9

Hence, ‘9’ is the correct answer.

The shaded part represents Australians who are neither graduates nor Cricketers.

 

The numbers representing Australians who are neither graduates nor Cricketers = 17

Hence, ‘17’ is the correct answer.

The correct answer is Conduction.

Key Points

• Conduction is the movement of something such as heat or electricity through a medium or passage.
• Because ceramic is more porous than glass, conduction occurs slower in ceramic mugs, thus keeping liquids warmer for longer.
• When a skillet touches the burner, heat is conducted, when a piece of food touches the heated skillet, heat is conducted again, aiding cooking.

Additional Information

• Motion in a gas or a liquid in which the warmer portions rise and the colder portions sink, thus transferring heat, is called convection.
• Example - a radiator puts warm air out at the top and draws in cooler air at the bottom.
• Evaporation is the change of liquid into vapor without reaching at its boiling point and it often has a cooling effect on its surroundings.
• Example - Vaporization of water from the leaves of a tree , cools the surroundings.
• Thermal radiation is electromagnetic radiation emitted from a material that is due to the heat of the material, the characteristics of which depend on its temperature.
• Example - solar radiations, energy radiated by incandescent lamps.

The correct answer is Damodar.

Key Points

• Damodar River is a river flowing across the Indian states of Jharkhand and West Bengal.
• Rich in mineral resources, the valley is home to large-scale mining and industrial activity.
• It was earlier known as the "River of Sorrows" as it used to flood many areas of Bardhaman, Hooghly, Howrah and Medinipur districts.

Additional Information

• The Yamuna is the second-largest tributary river of the Ganges by discharge and the longest tributary in India.
• The Ganga is a trans-boundary river of Asia which flows through India and Bangladesh.
• The river flows through well-populated regions of the Indian subcontinent, providing fresh water to the millions of people living in these regions.
• The Krishna River is a river in the Deccan plateau, the third-longest river of India, after the Ganges and Godavari, and the fourth-largest in terms of water inflows and river basin area in India, after the Ganges, Indus and Godavari.

The correct answer is Hockey.

Key Points

• Rani Rampal is an Indian field hockey player.
• At the age of 15, she was the youngest player in the national team which participated in the 2010 World Cup.
• In 2020, the Government of India honoured her with the Padma Shri and the Major Dhyan Chand Khel Ratna.

Additional Information

• The Khel Ratna Award, officially known as the Major Dhyan Chand Khel Ratna Award, is the highest sporting honour of India.
• It was formerly known as the Rajiv Gandhi Khel Ratna Award.
• It is awarded annually by the Ministry of Youth Affairs and Sports.
• In 2020, Rohit Sharma received the award for cricket, Mariyappan Thangavelu for Paralympic High Jump, and Vinesh Phogat for Freestyle Wrestling.

The correct answer is revenue budget and capital budget.

Key Points

• The Government Budget is an annual financial statement that is prepared to account for the revenue and expenditure of a government for the upcoming fiscal year.
• The Revenue Budget consists of the Government's revenue receipts and the expenditure that is met using said revenue.
• The capital Budget is the Government's plan to purchase, build, maintain, repair and replace assets including infrastructure.

Additional Information

• A balanced budget occurs when revenues are equal to or greater than total expenses.
• A budget deficit occurs when expenses exceed revenue, and it can indicate the financial health of a country.
• Revenue receipts can be defined as those receipts which neither create any liability nor cause any reduction in the assets of the government.
• Revenue expenditures are short-term expenses used in the current period or typically within one year.
• Capital receipts are receipts that create liabilities or reduce financial assets.
• Capital expenditure is the money spent by the government on the development of machinery, equipment, building, health facilities, education, etc.

The correct answer Blue shift.

Key Points

• For visible light, the bluer part of the spectrum has shorter wavelengths, and the redder part of the spectrum has longer wavelengths.
• Thus, the Doppler effect for light is called a 'blueshift' if the light source is coming toward an observer, and a 'redshift' if it is moving away.
• 

Additional Information

• The Doppler effect, or Doppler shift, describes the changes in frequency of any kind of sound or light wave produced by a moving source with respect to an observer.
• Waves emitted by an object traveling toward an observer get compressed — prompting a higher frequency — as the source approaches the observer, and vice versa.

The correct answer is Karnataka and Andhra Pradesh.

Key Points

• Krishna-Godavari dispute was due to the objections raised by Karnataka and Andhra Pradesh back in 1969.
• The diversion of more water at Koyna river which a tributary of Krishna river for a multi-purpose project was the root cause of the dispute.
• The provisions of Interstate River Water Disputes Act, 1956 were utilitsed to reach a common ground.

Additional Information

• In 2022, Assam and Nagaland have said they are ready for out-of-court settlement of their decades old state border dispute and have agreed to share royalty from petroleum from the disputed area.
• In 2022, a 21-year-old issues on the division of assets between Uttar Pradesh and Uttarakhand has been resolved with dialogue.
• Uttarakhand was formed on the 9th November 2000 as the 27th State of India, when it was carved out of northern Uttar Pradesh.
• Gujarati-speaking areas of Bombay State were partitioned into the state of Gujarat following Mahagujarat Movement on May 1, 1960.

The correct answer is Akbar.

Key Points

• The Agra fort was built with red sandstone in its exteriors and bricks in its inner core.
• Though the construction of the Agra Fort is attributed to Akbar, it was built into what we see today under the reign of Shah Jahan, the grandson of Akbar.
• Akbar was the third Mughal emperor, who reigned from 1556 to 1605.

Additional Information

• Shah Jahan was the fifth Mughal emperor from 1628 to 1658.
• He is best remembered for the grand monuments constructed during his reign like the Taj Mahal and the Moti Masjid in Agra and the Jama Masjid and Red Fort in Delhi.
• Babur was the founder of the Mughal Empire in the Indian subcontinent in 1526.
• Some of his famous works included Babri Masjid, Jama Masjid, Panipat Mosque and Kabuli Bagh Mosque.
• Aurangzeb was the sixth emperor of the Mughal Empire, ruling from July 1658 until his death in 1707.
• He was the last of the great Mughal architects and built the Badshahi Mosque, Bibi Ka Maqbara, Moti Masjid (Red Fort) etc.

The correct answer is Ministry of Law and Justice.

Key Points

• Ministry of Law and Justice launched the “Ek Pahal” campaign to encourage mass registration under Tele-Law in 2021.
• Tele-Law means the use of communications and information technology for the delivery of legal information and advice.
• The Ministry of Law and Justice in the Government of India is a cabinet ministry which deals with the management of the legal affairs, legislative activities and administration of justice in India.

Additional Information

• The Ministry of Social Justice and Empowerment is responsible for welfare, social justice and empowerment of disadvantaged and marginalised sections of society.
• It is currently being headed by Dr. Virendra Kumar.
• The Ministry of Women and Child Development is an apex body for formulation and administration of the rules and regulations and laws relating to women and child development in India.
• It is currently being headed by Smt. Smriti Irani.
• The Ministry of Home Affairs is mainly responsible for the maintenance of internal security and domestic policy.
• It is currently being headed by Shri Amit Shah**.**

The correct answer is Torana.

Key Points

• Torana, also referred to as Vandanamalikas, is a free-standing ornamental or arched gateway for ceremonial purposes.
• It is seen in the Hindu, Buddhist and Jain architecture of the Indian subcontinent, Southeast Asia and parts of East Asia.
• Toranas are associated with Buddhist stupas like the Great Stupa in Sanchi, as well as with Jain and Hindu structures, and also with several secular structures.

Additional Information

• Parikrama or Pradakshina is the clockwise circumambulation of sacred entities, and the path along which this is performed, as practiced in the Indic religions - Hinduism, Buddhism, Sikhism and Jainism.
• In Buddhist architecture, a square fence-like enclosure symbolizes heaven on top of the dome of a stupa eg. the harmika of the Great Stupa, Sanchi, Madhya Pradesh.
• A vedika was a wooden fence that surrounded a sacred place that can be free-standing at ground level or attached to the stupa in an elevated position.

The correct answer is Sundari.

Key Points

• Sundarbans is a mangrove area in the delta formed by the confluence of the Padma, Brahmaputra and Meghna Rivers in the Bay of Bengal.
• The name Sundarbans is thought to be derived from sundri or sundari (Heritiera fomes), the name of the large mangrove trees that are most plentiful in the area.
• According to several investigations, the Sundari tree possesses significant antinociceptive, antioxidant, antihyperglycemic, antimicrobial and anticancer properties.

Additional Information

• Peepal tree is grown throughout India, mainly grown in the states of Haryana, Bihar, Kerala and Madhya Pradesh.
• Sal tree are found in Assam, Nepal, Bengal, on the bank of the Yamuna river, and also in some parts of Haryana.
• Chir pine is found in Darjeeling in North Bengal and in Kamen District in Arunachal Pradesh.

The correct answer is hydrogen and helium.

Key Points

• In the core of the Sun hydrogen is being converted into helium by a process called nuclear fusion.
• During the process some of the mass is converted into energy.
• This is why the sun is so hot and bright.

Additional Information

• On the Earth, most helium is a radioactive decay product of uranium and thorium.
• It is found under the Earth's crust with other natural gases.
• Neon is present in the Earth's atmosphere at a concentration of just 18 parts per million.
• It is extracted by fractional distillation of liquid air, which produces helium as well.
• On Earth, hydrogen is found in the greatest quantities as water.
• It is present as a gas in the atmosphere only in tiny amounts – less than 1 part per million by volume.
• Nitrogen, the most abundant element in our atmosphere, is crucial to life.
• It is found in soils and plants, in the water we drink, and in the air we breathe.

The correct answer is Evolutionary relationships.

Key Points

• Evolutionary relationships refers to the similarities in structure, breeding behavior, geographical distribution, chromosomes, and biochemistry of the living organisms evolved from the common ancestors.
• Simply put, it means how closely related two organisms are in evolution.

Additional Information

• Vertebrae are the small circular bones that form the spine of a human being or animal.
• The average person is born with 33 individual bones (the vertebrae) that interact and in an adult, some vertebrae at the bottom end of the spine fuse together and the number becomes 24.
• A cell consists of three parts: the cell membrane, the nucleus, and, between the two, the cytoplasm.
• Within the cytoplasm lie intricate arrangements of fine fibers and hundreds or even thousands of miniscule but distinct structures called organelles.
• Ribonucleic acid (RNA) is a molecule that is present in the majority of living organisms and viruses
• It is made up of nucleotides, which are ribose sugars attached to nitrogenous bases and phosphate groups.

The correct answer is Polyphenol oxidase.

Key Points

• Polyphenol oxidase is an quinone and enzyme involved in fruit browning.
• It is a tetramer that contains four atoms of copper per molecule.
• Such quinones are very reactive and can react with each other and surrounding proteins to generate a black pigment called melanin causing browning.

Additional Information

• Carbonic anhydrase is an enzyme that assists rapid inter-conversion of carbon dioxide and water into carbonic acid, protons and bicarbonate ions.
• This enzyme was first identified in 1933, in red blood cells of cows.
• Hydrolases are the group of enzymes whose natural function is digestive to break down nutrients into smaller units for digestion.
• An acid hydrolase is an enzyme that works best at acidic pHs.
• It is commonly located in lysosomes, which are acidic on the inside.
• A phospholipase is an enzyme that hydrolyzes phospholipids into fatty acids and other lipophilic substances.
• They are widespread in nature and play very diverse roles from aggression in snake venom to signal transduction, lipid mediator production, and metabolite digestion in humans.

The correct answer is 19.

Key Points

• India won 5 gold medals - 2 each in shooting and badminton, and 1 in athletics.
• India won 8 silver medals - 5 in athletics, and 1 each in table tennis, badminton, and shooting.
• India won 6 bronze medals - 2 each in athletics and shooting, and 1 each in badminton and archery.

Additional Information

• Table tennis player Bhavina Patel won India's first olympics (Paralympic) medal in Table Tennis.
• Shooter Avani Lekhara scripted history as she became the first Indian to win a medal in Shooting in the Paralympics.
• Archer Harvinder Singh became the first Indian to win a medal in Archery at the olympics (Paralympic).
• In badminton, Indian shuttlers won a record number of medals including two golds.

The correct answer is 5^th September.

Key Points

• In India, September 5 is celebrated as Teachers' Day as a tribute to the contribution made by teachers to society.
• It also honours the memory of India's first Vice President, Sarvepalli Radhakrishnan, September 5 being his birthday.

Additional Information

• The International Day of Non-Violence is marked on 2 October, the birthday of Mahatma Gandhi, leader of the Indian independence movement and pioneer of the philosophy and strategy of non-violence.
• The World Teachers Day is celebrated on October 5, which commemorates the signing of the 1966 UNESCO/ILO Recommendation concerning the Status of Teachers, which is a standard-setting instrument that addresses the status and situations of teachers around the world.

The correct answer is Saptak.

Key Points

• Saptak stands for “gamut” or “series of seven notes”.
• The seven svaras or bands of the saptak are the fundamentals of heptatonic scales or melakarta ragas and thaats in Carnatic and Hindustani classical music.
• The seven svara are Shadja, Rishabh , Gandhar , Madhyam , Pancham , Dhaivat  and Nishad.

Additional Information

• The shruti is the smallest interval of pitch that the human ear can detect and a singer or musical instrument can produce.
• The concept is found in ancient and medieval Sanskrit texts such as the Natya Shastra, the Dattilam, the Brihaddeshi, and the Sangita Ratnakara.
• Many ancient Sanskrit and Tamil works refer to the 22 shrutis as the foundation of the Indian Music Scale.
• The Saptarshi is a Sanskrit word meaning "seven sages".
• They are the seven greatest sages of the Vedic realm who have attained a semi-immortal status.
• The asterism of the Big Dipper, which is part of the constellation of Ursa Major, is called saptarishi, with the seven stars representing seven rishis.
• A raga is a collection of pitches.
• Each raga is defined not only by the pitches themselves, but also by specific formulas for using them.
• There are 83 ragas but the six main Ragas, from which all other Ragas emanate, are Raga Bhairav (dawn), Raga Hindol (spring, morning), Raga Megh (monsoon), Raga Shri (dusk), Raga Deepak (evening), and Raga Malkauns (late night, winter).

The correct answer is DNA.

Key Points

• DNA, or deoxyribonucleic acid, is the hereditary material in humans and almost all other organisms.
• Nearly every cell in a person's body has the same DNA.
• DNA is made of chemical building blocks called nucleotides.
• These building blocks are made of three parts: a phosphate group, a sugar group and one of four types of nitrogen bases.
• DNA contains the instructions needed for an organism to develop, survive and reproduce.

Additional Information

• Plastids are pivotal subcellular organelles that have evolved to perform specialized functions in plant cells, including photosynthesis and the production and storage of metabolites.
• Mitochondria are membrane-bound cell organelles that generate most of the chemical energy needed to power the cell's biochemical reactions.
• Chemical energy produced by the mitochondria is stored in a small molecule called adenosine triphosphate (ATP).

The correct answer is Nagaland.

Key Points

• Nagaland is a mountainous state in northeast India, bordering Myanmar.
• It's home to diverse indigenous tribes, with festivals and markets celebrating the different tribes' culture.
• Its capital city is Kohima.
• The major folk dances of Nagaland include Modse, Agurshikukula, Butterfly Dance, Aaluyattu, Sadal Kekai, Changai Dance, Kuki Dance, Leshalaptu, Khamba Lim, Mayur Dance, Monyoasho, Rengma, Seecha and Kukui Kucho, Shankai and Moyashai etc, however, the prominent ones are War Dance and Zeliang Dance.

Additional Information

• Famous dance forms of Odisha are Odissi, Sambalpuri, Chhau, Paika, Changu Dance, Gumura, Bandi Nacha, etc.
• Famous dance forms of Madhya Pradesh are Jawara, Matki, Aada, Khada Nach, Phulpati, Grida Dance, Selalarki, Selabhadoni, Maanch, Lehangi, etc.
• Famous dance forms of Bihar are Bidesia, Paika, Jhijhian, Kajari dance, Jat-Jatin, Karma, Jhumar, Jharni, Jhumeri, etc.

The correct answer is Akash Prime.

Key Points

• Akash is a medium-range mobile surface-to-air missile system developed by the Defence Research and Development Organisation and produced by Bharat Dynamics Limited.
• In September 2022, the Akash Prime missile had successfully intercepted and destroyed an unmanned aerial target that mimicked an enemy aircraft.

Additional Information

• The Defence Research and Development Organisation is the premier agency under the Department of Defence Research and Development in Ministry of Defence of the Government of India.
• It is charged with the military's research and development, headquartered in Delhi, India.
• Bharat Dynamics Limited is one of India's manufacturers of ammunitions and missile systems.
• It was founded in 1970 in Hyderabad, Telangana, India.

The correct answer is Desmosomes are specialised adhesive protein complexes that localise to intercellular junctions of animal cells.

Key Points

• Desmosomes are adhesive intercellular junctions that mechanically integrate adjacent cells by coupling adhesive interactions mediated by desmosomal cadherins to the intermediate filament cytoskeletal network.
• They are one of the stronger cell-to-cell adhesion types and are found in tissue that experience intense mechanical stress, such as cardiac muscle tissue, bladder tissue, gastrointestinal mucosa, and epithelia.

Additional Information

• Desmosomal cadherins are a dense adhesion complex required for tissues to withstand mechanical stress.
• The cytoskeleton is a complex, dynamic network of interlinking protein filaments present in the cytoplasm of all cells, excluding bacteria and archaea.

The correct answer is 'MPC + MPS = 1'.

Key Points

• Marginal Propensity to Save (MPS) is measured as the ratio of change in savings to change in income.
• Marginal Propensity to Consume (MPC) is the proportion of an increase in income that gets spent on consumption.
• Also, marginal propensity to save is the opposite of marginal propensity to consume.
• Mathematically, in a closed economy, MPS + MPC = 1, since an increase in one unit of income will be either consumed or saved.

Thus, the correct answer is MPC + MPS = 1.

The correct answer is 'AB Vajpayee'.

Key PointsPradhan Mantri Gram Sadak Yojana (PMGSY)

• The first phase of PMGSY was started in the year 2000 by then Prime Minister Atal Bihari Vajpayee.
• The main objective of PMGSY is the socio-economic empowerment of rural areas by providing rural connectivity to unconnected habitations with a defined population.
• The primary objective of the scheme is to provide a road network meeting the prescribed standards.
• PMGSY-II was launched for the upgradation of 50,000 km of the rural road network by the Government of India in the year 2013 to improve overall efficiency.
• In 2019, PMGSY-III was launched for the integration of 1,25,000 km to connect Gramin Agricultural Markets (GrAMs), higher secondary schools and hospitals with major rural connectivity routes.
• Targets are allocated on the basis of eligible habitations under PMGSY-I and on the basis of the length of roads in the case of PMGSY-II and PMGSY-III.

Thus, the correct answer is AB Vajpayee.

The correct answer is 'Satapatha Brahmana'.

Key PointsSatapatha Brahmana

• Satapatha Brahmana is the Brahmana text of Shukla Yajurveda.
• It is considered to be the most authentic among the Brahmin texts.
• Maharishi Yajnavalkya was the first preceptor of the Satapatha Brahmana.
• It has 100 Chapters and 14 Kandas.
• It is probably named Satapatha because of having one hundred chapters.
• In this, a detailed explanation has been given of all the rituals and it is impossible to understand the Yajurveda without the knowledge of this Brahmana.
• Linguistically, Shatapatha Brahmana belongs to the later part of the Brahmanical period of Vedic Sanskrit.
• According to the Satapatha Brahmana, the wife is one-half of her husband and she alone completes him.

Thus, the correct answer is Satapatha Brahmana.

Additional InformationLet's have a look at other options:

• Kaushitiki Brahmana
• ​Kaushitaki Brahman Upanishad is the full name of Kaushitaki Upanishad.
• It is a Rigvedic Upanishad.
• The Kaushitaki Upanishad is a part of the Kaushitaki Brahmana of the Angveda.
• It has a total of four chapters.
• In this Upanishad, light has been laid on the worship of the soul and the Brahmaloka, Pranopasana, Agnihotra, various worships, the glory of the Pranatattva and the celestial element present in the sun, moon, electric cloud, sky, air, fire, water, mirror and resonance.
• In the end, the nature of 'Atma-tattva' and the fruit obtained from its worship have been discussed.
• Aitareya Brahmana
• ​The Aitareya Brahmana is a branch of the Rigveda of which only "Brahmins" are available, not the Samhita.
• The Aitareya Brahmana holds first place among the Rigvedic Brahmins because of its importance.
• This "Brahmin" is a very complete indicator of the subjects related to Hautkarma and this is its importance.
• Other parts of this "Brahmin" are also available which are called "Aitareya Aranyaka" and "Aitareya Upanishad".
• Jaiminiya Brahmana
• ​It is mainly divided into three parts in which there are 360 ​​sections in the first part, 437 in the second part and 385 sections in the third part.
• The total number of blocks is 1182.

The correct answer is 'The Government of India Act, 1935'.

Key Points

The Government of India Act

• The Government of India Act was considered one of the longest pieces of legislation passed by the British Parliament for British India containing 321 sections and 10 schedules.
• The Government of India Act, 1935 was passed by the British Parliament in August 1935.
• Regarding the Government of India Act, J.L. Nehru remarks, 'It was a new charter of Slavery'.

Additional Information Its main features were -

• All India Union Proposal
• Provincial Autonomy
• Duplex Governance System at the Centre
• Division of Powers
• Federal Administrator
• Federal Court
• Reservation and Protection
• End of Indian Council
• Supremacy of British Parliament, etc.

The correct answer is '44th Amendment Act'.

Key PointsRight to Property

• Citizens were granted 7 freedoms by Article 19 of the original constitution, and the sixth of these freedoms was "Freedom of Property".
• It was later defined by the 44^th Constitutional Amendment, 1978 of the Indian Constitution as the fundamental right to property as well as "Freedom of Property" has been abolished.
• But the right to property is still not completely separated from the Indian Constitution.
• The Right to Property is still a constitutional right and is described in Article 300 'A' of the Indian Constitution.

Thus, the correct answer is 44th Amendment Act.

Additional InformationLet's have a look at other options:

The correct answer is 2005.

Key PointsThe Mahatma Gandhi National Rural Employment Guarantee Act

• ​The Mahatma Gandhi National Rural Employment Guarantee Act (MNREGA ) is an employment guarantee scheme implemented in India, enacted by legislation on 7 September 2005.
• The scheme provides 100 days of employment in every financial year to adult members of any rural household who are willing to do public work-related unskilled labour at a statutory minimum wage of Rs.220 per day.
• This act was initiated with the aim of increasing the purchasing power of rural people, mainly for people living in rural India with semi-skilled or unskilled jobs, whether they are below the poverty line or not.
• About a third of the fixed workforce is made up of women.
• It was initially called the National Rural Employment Guarantee Act (NREGA) but was renamed on 2 October 2009.

Thus, the correct answer is 2005.

The correct answer is 'Influenza'.

Key PointsInfluenza Epidemic

• The Spanish flu was a worldwide pandemic in 1918, also known as the Influenza pandemic, 1918-19.
• It originated in January 1918 and lasted until December 1920 and infected 500 million people which was one-quarter of the world's population at that time.
• The death toll from this is estimated to be 170 lakh in India.
• It was one of the deadliest pandemics in human history.

Thus, the correct answer is Influenza.

The correct answer is 'Fundamental rights are absolute rights'.

Key Points

• Article 19(2) - Based on this, the state has the right to impose reasonable restrictions on the freedom of expression. The following is a declaration of reasonable restrictions:
• India's security and sovereignty
• Defamation
• Friendly relations with foreign states
• Public order
• Etiquette
• Contempt of court. Hence, option 1 cannot be the answer.
• It also means that fundamental rights are not absolute rights as there are certain restrictions. Hence, option 3 can be the correct answer.
• Judicial review - The power of the Supreme Court of India to enforce and implement these fundamental rights is derived from Article 32 of the Constitution. It means Judiciary has the power and responsibility to protect fundamental rights. Hence, option 2 cannot be the answer.
• Supreme Court held that the power to amend the Constitution, including Fundamental Rights is contained in Article 368. Hence, option 4 cannot be the answer.

Thus, the correct answer is Fundamental rights are absolute rights.

Additional Information

Fundamental Rights

• Fundamental rights are said to be those rights which, being fundamental to the life of the individual, are provided to the citizens by the constitution and which cannot be interfered by the state.
• These are such rights which are necessary for the full development of the personality of the individual and without which man cannot develop himself fully.
• Fundamental rights cannot be violated.
• Fundamental rights are justifiable and are equally available to every person in society.

The correct answer is 'Khasi'.

Key Points Khasi

• Khasi is a language spoken by the Khasi community in the state of Meghalaya in Northeast India.
• It is a member of the Austro-Asiatic language family.
• It is not one of the major languages mentioned in the 8th Schedule.

Thus, the correct answer is Khasi.

Additional Information The official languages ​​of the Republic of India are listed in the eighth schedule. Articles 343 to 351 included in Part XVII of the Indian Constitution deal with official languages.

The following 22 languages ​​are included in the Eighth Schedule of the Constitution:

• Assamese, Bengali, Gujarati, Hindi, Kannada, Kashmiri, Konkani, Malayalam, Manipuri, Marathi, Nepali, Odia, Punjabi, Sanskrit*,* Sindhi, Tamil, Telugu, Urdu, Bodo, Santali, Maithili and Dogri.
• Out of these languages, 14 were included at the very beginning of the constitution.
• Konkani, Manipuri and Nepali were included in the year 1992 by the 71st Amendment Act.
• Bodo, Dogri, Maithili and Santali were included in the Eighth Schedule in the year 2003 by the 92nd Constitutional Amendment Act which came into effect from the year 2004.

The correct answer is '1962'.

Key Points Article 239 A

• It was introduced in the Indian Constitution in 1962.
• It empowers Parliament to create a Legislature or Council of Ministers or both for some of the Union Territories.
• It states that -
• Parliament may by law create for the Union territory of Puducherry —
• a body, whether elected or partly nominated and partly elected, to function as a Legislature for the Union territory, or
• a Council of Ministers,
• or both with such constitution, powers and functions, in each case, as may be specified in the law.
• Any such law as is referred to in clause (1) shall not be deemed to be an amendment of this Constitution for the purposes of article 368 notwithstanding that it contains any provision which amends or has the effect of amending this Constitution.

Thus, the correct answer is 1962.

The correct answer is '1987'.

Key Points Arunachal Pradesh

• Arunachal Pradesh is a northeastern state of India.
• Arunachal means "mountain of the rising sun" in Hindi.
• The state borders Assam in the south, Nagaland in the southeast, Burma/Myanmar in the east, Bhutan in the west and Tibet in the north.
• Itanagar is the capital of the state.
• The main spoken language of the state is Hindi.
• Before 1962, this state was known as the North-East Frontier Agency (NEFA).
• Constitutionally it was a part of Assam itself, but due to its strategic importance, till 1965, the administration was looked after by the Ministry of External Affairs.
• After 1965, the administration here came under the Home Ministry by the Governor of Assam.
• Arunachal Pradesh was made a union territory in 1972 and was named 'Arunachal Pradesh'.
• After all this, on 20 February 1987, it was made the 24th state of the Indian Union.

Thus, the correct answer is 1987.

The correct answer is 'L-shaped to the origin'.

Key PointsComplementary Goods

• Complementary goods are those which are used to fulfill a specific need such as cars and petrol, shoes and polishes, pencils and erasers, etc.
• There is a negative relationship between the prices of complementary goods and the quantity demanded of a given commodity. This implies that as the price of complementary goods rises, the quantity demanded of a given good decreases, other things remaining constant and vice versa.
• For example, as the price of pencils increases, the quantity of erasers in demand decreases because they will become expensive when used together. Therefore, the demand for a commodity is inversely affected by the price of complementary goods.
• If the two goods are perfect complements the indifference curve is right-angled or L-shaped, as shown in Figure.

• The vertical portion of the I1, curve reveals that no amount of reduction in good Y will lead even to a slight increase in good X. For example, point A, M and В are all on the curve It but point В involves the same amount of Y but more of X than point M.
• Thus MRSXY is zero. The two goods X and Y are consumed in the desired ratio, as indicated by the slope of the ray OR at point M.

Thus, the correct answer is L-shaped to the origin.

The correct answer is 'special slaves purchased for military service'.

Key Points

Bandagan

• Bandagan is a Persian term used for special slaves who are purchased for military service during the early period of Delhi Sultanate, especially by sultan Iltutmish.
• They were carefully trained to man some of the most important political offices in the kingdom.
• As they were totally dependent on their master, the Sultan could trust and rely on them.
• They were slaves who were given the posts of generals and governors generally by the rulers of the slave dynasty.

Thus, the correct answer is special slaves purchased for military service.

The correct answer is '1932'.

Key PointsThe Communal Award

• On 16th August 1932, British Prime Minister Ramsay Mac Donald announced a plan for the representation of minorities.
• This came to be known as the Communal Award.
• The award not only expanded a separate electoral system for Muslims, Sikhs, Christians, Europeans and Anglo-Indians, but it was also extended to Dalits.
• Gandhi was very upset with the separate electoral system for Dalits and he started a fast in Yerwada Jail in Poona to amend the award.
• Eventually, an agreement was reached between the Congress leaders and the Dalit leaders, which came to be known as the Poona Pact.
• In this, the joint Hindu electoral system was maintained and seats were also reserved for the Dalits.

Thus, the correct answer is '1932'.

The correct answer is 'Chennai'.

Key PointsIntegral Coach Factory

• Integral Coach Factory is one of the earliest production units of independent India.
• Integral Coach Factory (ICF) is located at Perambur in Chennai, Tamil Nadu.
• It was inaugurated by the first Prime Minister of India Jawaharlal Nehru on 2 October 1955.
• The first of India's four railway coach manufacturing factories and the world's largest producer of railway coaches, Integral Coach Factory has been making a significant contribution to the progress of Indian Railways since 1955.
• Spread over 511 acres, this factory has about 10,000 workers, who manufacture more than 4000 coaches every year.
• These include conventional and self-propelled coaches, LHB and other designs.
• Integral Coach Factory is capable of manufacturing multiple variants at once.
• Since its inception, ICF has produced over 63,000 coaches in over 500 different designs.
• In the year 2018-19, ICF prepared and dispatched the coach set of India's first semi-high speed train Vande Bharat.

Thus, the correct answer is Chennai.

The correct answer is 'Mausim'.

Key PointsMonsoon

• The word monsoon is derived from the Arabic word 'Mausin' which means season.
• The seafarers who landed in Arabia with a boat in the sea invented the word Mawsim (monsoon). After this, the monsoon winds came to be called the monsoon.
• Monsoon originating from the Indian Ocean and the Arabian Sea are the winds coming to the south-west coast of India, which cause heavy rains in India, Pakistan, Bangladesh etc.
• These are seasonal winds, which are active in the southern Asia region, usually from June to September, for four months.

Thus, the correct answer is Mausim.

The correct answer is 'Article 368'.

Key Points Let's have a look at all options:

Thus, the correct answer is Article 368.

Confusion PointsArticle 32 - Right to Constitutional Remedies

Article 368 - Powers of Parliament to amend the Constitution.

The correct answer is 'rock edicts, pillar edicts and cave inscriptions'.

Key PointsAshokan Inscriptions

• A total of 33 inscriptions are inscribed by Emperor Ashoka of the Maurya dynasty during his reign from 269 BC to 231 BC.
• They are divided into rock edicts, pillar edicts and cave inscriptions.
• They are found in places in modern Bangladesh, India, Afghanistan, Pakistan and Nepal and are among the oldest evidence of the existence of Buddhism.

Thus, the correct answer is rock edicts, pillar edicts and cave inscriptions.

Additional InformationLet's have a look at the detailed classification:

• Rock Edicts
• ​Major Rock Edicts
• ​Ashoka's 14 Major Rock Edicts are a set of different inscriptions found at 8 different places.
• Minor Rock Edicts
• ​There are 15 Minor Rock Edicts of Ashoka.
• Pillar Edicts
• ​Major Pillar Edicts
• ​There are 7 Major Pillar Edicts of Ashoka which have been found inscribed on stone pillars in 6 different places.
• Minor Pillar Edicts
• ​The pillars on which the official declarations of Ashoka are inscribed are called Minor Pillar Edicts.​
• Cave Inscriptions
• ​Cave inscriptions of Ashoka have been found on the walls of three caves named Barabar located in the Gaya district of South Bihar.

The correct answer is 'Delhi'.

Key PointsLet's have a look at all options:

Thus, Delhi is the only union territory which has its own High Court. Other union territories share their high court with other states.

Hence, the correct answer is Delhi.

The correct answer is 'south'.

Key Points

Climate of India

• The Tropic of Cancer passes through the middle of the country, and this makes its climate more tropical.
• India is a big tropical country and is famous for its diverse climatic features.
• The Tropic of Cancer passes through the middle of India and extends from Mizoram in the east and Rann of Kutch in the west; and considerably affects the climate of the country.
• To the south of the Tropic of Cancer lies the southern part of the country which belongs to the tropical area and its north lies the northern half of India which belongs to the sub-tropical zone. Therefore, India experiences both sub-tropical and tropical climates.

Thus, the correct answer is South.

HintTrick to learn the name of states through which Tropic of Cancer passes:

GAMCHA JHAR MITRA PAR

GA - Gujarat

M - Madhya Pradesh

CHA - Chattisgarh

JHAR - Jharkhand

MI - Mizoram

TRA - Tripura

PA - Paschim Bengal (West Bengal)

R - Rajasthan

Given:

Radius of the sphere is 7 cm.

Formula used:

Curved surface area of the sphere = 4πr² [ where, r is the radius of the sphere]

Calculations:

Curved surface area of the sphere = 4πr² = 4 × π × 7²

= 4 × $\dfrac{22}{7}$ × 7 × 7

= 4 × 22 × 7 = 616 cm³. ( using π = $\frac{22}{7}$)

∴ The answer is 616 cm³.

Given:

\(\rm \begin{array}{l} ,,,,;;;A,B\ × ,;;,;;;6\ _______\ B;B,;B \end{array}\)

Concept:

Following are the rules to solve Cryptarithmetic Questions:

1. Every Character/letter must have a unique and distinct value.
2. The values of a character/letter can not be changed and should remain the same throughout.
3. Starting character of a number can not be zero example – 0341 should be simply 341.
4. The problem will have only and only one solution.
5. The addition of two similar numbers is always even.
6. In the case of the addition of two numbers, if there is carry then, the carry can only be 1.
7. Once all the characters/letters are replaced with numbers, arithmetic operations must be correct.

Calculation:

From first multiplication i.e. (B × 6 = KB), the possibilities would be

[(2 × 6 = 12), (4 × 6 = 24), (6 × 6 = 36), and (8 × 6 = 48)]

Option 1 and 2 got eliminated as B = 7 and B = 0 is not possible.

Step 1:

Assume B = 4

\(\rm \begin{array}{l};;;;;;2\ ,,,,;;;A,4\ × ,;;,;;;6\ _______\ ;;;4;4,;4 \end{array}\)

(A × 6) + 2 = 44

6A = 42

or A = 7.

Step 2:

Assume B = 6

\(\rm \begin{array}{l};;;;;;3\ ,,,,;;;A,6\ × ,;;,;;;6\ _______\ ;;;6;6,;6 \end{array}\)

(A × 6) + 3 = 66

6A = 63

or A = 10.5 which is not possible.

Thus B = 4 and A = 7 is the correct option.

∴ The answer is B = 4 and A = 7.

Given:

A solid cylinder in which the height is 6 times the radius.

Is melted and cast into another cylinder with the height and radius interchanged.

The total surface area equal to 264 cm².

Formula used:

Total surface area of the cylinder = 2πr(h + r) [where, r is the radius and h is the height]

Calculations:

For the first case, let r = x and h = 6x.

For the second case, let h = x and r = 6x. (as, the radius and height are interchanged)

So, total surface area = 2πr(h + r)

264 = 2 × $\dfrac{22}{7}$ × 6x × (x + 6x)

264 = 2 × $\dfrac{22}{7}$ × 6x × 7x

264 = 2 × 22 × 6x × x

x² = $\dfrac{264}{2 × 22 × 6}$ = 1

x = 1.

Now, putting these value in the first case, r = 1 and h = 6 × 1 = 6.

Total surface area = 2 × $\dfrac{22}{7}$ × 1 × (6 + 1)

= 2 × 22 × 1 = 44 cm.²

∴ The answer is 44 cm².

Given:

$\sqrt[3]{\dfrac{4}{108}}$

Calculations:

$\sqrt[3]{\dfrac{4}{108}}$ = $\sqrt[3]{\dfrac{1}{27}}$ = $\sqrt[3]{\dfrac{1}{3× 3 × 3}}$ = $\dfrac{1}{3}$ [as, 27 = 3³]

∴ The answer is $\dfrac{1}{3}$.

Given:

$\sqrt[3]{?}+\frac{1}{2} \text { of } 42=\frac{27}{72} \times 216 \times \frac{1}{81} \times 20$

Formula used:

Using BODMAS rules, where B stands for Bracket, O stands for Of, D stands for Division, M stands for multiplication, A stands for Addition, S stands for substraction.

Calculations:

$\sqrt[3]{?}+\frac{1}{2} \text { of } 42=\frac{27}{72} \times 216 \times \frac{1}{81} \times 20$

= $\sqrt[3]{?}$ + 21 = 27 × 3 × $\frac{1}{81}$ × 20

= $\sqrt[3]{?}$ + 21 = 81 × $\frac{1}{81}$ × 20

= $\sqrt[3]{?}$ + 21 = 1 × 20

= $\sqrt[3]{?}$ = 20 - 21

= (-1)³ = -1

∴ The answer is -1.

Given:

The heights of a cylinder and a cone are in the ratio 2 ∶ 3, and the radii of their bases are in the ratio 3 ∶ 4.

Formula used:

Volume of the cylinder = πr₁²h₁

Volume of the cone = $\frac{1}{3}$πr₂²h₂ [where, r1 and r2 are the radius of the cylinder and cone, h1 and h2 are the heights of the cylinder and the cone.]

Calculations:

Let r₁ = 3x, r₂ = 4x and h₁ = 2y, h₂ = 3y.

Ratio of the volume of the cylinder and the volume of the cone.

πr₁²h₁ : $\frac{1}{3}$ πr₂²h₂

(3x)² × 2y : $\frac{1}{3}$ × (4x)² × 3y

9x² × 2y : $\frac{1}{3}$ × 16x² × 3y

18 : 16 = 9 : 8.

∴ The answer is 9 : 8.

Given condition: 

Numbers between 100 and 200 are divisible by 2 and 4 .

Concept:

Arithmetic Progression

an = a + (n - 1)d 

Calculation:

Here, 

Divisibility of 2:  All the even numbers between 100 and 200 are divisible by 2.102 , 104, 106 .............198

Divisibility of 4 : Last two digits are divisible by 4 that is in the number 104 the last two digits are 04 which is divisible by 4 so the number 104 is divisible by 4.

LCM of 2 and 4 is 4. So, we have to calculate numbers divisible by 4.

The first number that is divisible by 4 (100 - 200) = 104 

104, 108, 112, ............................192 ,196

The above series makes an AP,

Where a = 104, Common Difference/d = 108 - 104 = 4 and Last term (an) = 196

⇒ an = a + (n - 1)d

⇒ 196 = 104 + (n - 1)4 

⇒ (196 - 104)/4 = n - 1 

⇒ 92/4 + 1 = n 

⇒ 23 + 1 = n 

⇒ n = 24 

∴ There are 24 numbers between 100 and 200 which are divisible by 2 and 4. 

Confusion Points The answer in answer key was 25. If the question had been How many numbers between 100 and 200 are divisible by 2 and not 4? In that case

Divisibility of 2:  All the even numbers between 100 and 200 are divisible by 2.102 , 104, 106 .............198

No of terms = 

⇒ an = a + (n - 1)d

⇒ 198 = 102 + (n - 1)2 

⇒ (198 - 102)/2 = n - 1 

⇒ 96/2 + 1 = n 

⇒ 48 + 1 = n

⇒ n = 49

Divisibility of 4 : Last two digits are divisible by 4 that is in the number 104 the last two digits are 04 which is divisible by 4 so the number 104 is divisible by 4.

LCM of 2 and 4 is 4. So, we have to calculate numbers divisible by 4.

The first number that is divisible by 4 (100 - 200) = 104 

104, 108, 112, ............................192 ,196

Where a = 104, Common Difference/d = 108 - 104 = 4 and Last term (an) = 196

⇒ an = a + (n - 1)d

⇒ 196 = 104 + (n - 1)4 

⇒ (196 - 104)/4 = n - 1 

⇒ 92/4 + 1 = n 

⇒ 23 + 1 = n 

⇒ n = 24 

The all the numbers that are divisible by 4 are divisible by 2 also. so, to get the numbers which are divisible by 2 but not 4 we will subtract numbers of terms divisible by 4 from numbers of terms divisible by 2.

i.e. 49 - 24 = 25.

Given:

L.C.M of 25, 30, 45.

Calculations:

Factors of 25 = 5 × 5 × 1

Factors of 30 = 2 × 3 × 5 × 1

Factors of 45 = 3 × 3 × 5 ×1

Now, the lowest common factor of the above numbers = 2 × 3 × 3 × 5 × 5 × 1 = 450.

∴ The answer is 450.

Given:

Radius of the cone = 7cm. and, slant height is 4 more than twice the radius.

Formula used:

Volume of the cone = $\dfrac{1}{3}$πr²h. [ where, r is the radius and h is the height]

l² = r² + h². [slant height be l]

Calculations:

Slant height(l) = 4 + 2r = 4 + 2 × 7 = 4 + 14 = 18.

l² = r² + h² = 18² = 7² + h² = 324 = 49 + h²

h² = 324 - 49 = 275.

Now, volume of the cone = $\dfrac{1}{3}$ × π × 49 × √275 = $\dfrac{1}{3}$ × π × 49 × 5√11 = $\dfrac{245}{3} \pi \sqrt{11}$ cm³[ √275 = √(5× 5 × 11)]

∴ The answer is $\dfrac{245}{3} \pi \sqrt{11}$.

Given:

Store announces a scheme of "Buy 1, Get 1.5 Free.

A woman buys a packet of 10 kg of sugar whose marked price is Rs.840. If the store has marked up 200% above the cost price.

Further gives a discount of 5% on the net payment.

Formula used:

Profit% = $\dfrac{selling \ price - cost \ price}{cost \ price}$ × 100

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

Calculations:

BUY 1 and GET 1.5 free = total number of items will be = 1 + 1.5 = 2.5 items.

Let cost price be 100 and marked price is 200% more than that of the cost price = 100 × 200% + 100 = 200 + 100 = 300.

Marked price of the article given as Rs. 840. So, the cost price = x × 200% + x = 840

Cost price = x × $\dfrac{200}{100}$ + x = 840

$\dfrac{200x + 100x}{100}$ = 840

300x = 840 × 100

Cost price of 1 item(x) = $\dfrac{840 × 100}{300}$ = Rs. 280.

Cost price of 2.5 items = 2.5 × 280 = Rs. 700.

Selling price = marked price - discount% on marked price (after allowing 5% discount on marked price)

Selling price = 840 - 840 × 5%

= 840 - 840 × $\dfrac{5}{100}$

= 840 - 42 = Rs. 798.

Now, profit% = $\dfrac{798 - 700}{700}$ × 100

Profit% = $\dfrac{98}{700}$ × 100 = 14%.

∴ The answer is 14%.

Given:

Average of eleven values is 69. Average of first five and last five are 68 and 61.

Formula used:

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

Middle term = S - (S1 + S2)

Calculations:

Let the sum of eleven values = S, and, sum of first five values = S1, sum of last five values = S2.

S = 11 × 69 = 759.

S1 = 5 × 68 = 340 and S2 = 5 × 61 = 305.

The middle term = 759 - (340+ 305) = 759 - 645 = 114.

∴ The answer is 114.

Given:

A shopkeeper gives the discount of 10% on the listed price against 20% gain.

Formula used:

Selling price = marked price - discount on marked price.

Profit = selling price - cost price

Profit% = $\dfrac{profit}{cost \ price}$ × 100

Calculations:

Let the marked price be 100x.

10% discount on marked price = selling price = 100x - 10% on 100x = 90x.

At 90x, profit is 20%, so, cost price = $\dfrac{100}{120}$ × 90x = 75x.

At 13% discount, selling price = 100x -13% on 100x = 87x.

Profit = 87x - 75x = 12x.

Profit% = $\dfrac{12x}{75x}$ × 100 = 16%.

∴ The answer is 16%.

Given:

4 litres are required to paint the surface of a solid sphere.

Formula used:

Surface area of the solid sphere = 4πr² [ where, r is the radius]

Surface area of the hemisphere = 2πr²

Calculations:

The solid sphere is cut into 4 identical parts. After making the first cut two hemisphere will be formed and two surfaces with area πr²(total 2πr²). Similarly, after second cut surfaces equal to 2π² will be added to the solid figure.

Now, after cutting the total surface area will be = 4πr² + 2πr² + 2πr² = 8πr².

4 lts of paint will be required to paint an area of 4πr².

Therefore, 8 lts of paint will be required to paint an area of 8πr².

∴ The answer is 8 litres.

Given:

$\sqrt[3]{0.000216}$

Calculations:

$\sqrt[3]{0.000216}$ = $\sqrt[3]{0.06 × 0.06 × 0.06}$ [as, 216 = 6³]

= 0.06

∴ The answer is 0.06.

Given:

₹10,000 is borrowed for two years at the rate of 15% per annum and the interest compounded annually.

Formula used:

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

Calculations:

Amount = 10000 × (1 + $\frac{15}{100}$)²

= 10000 × (1 + $\frac{3}{20}$)²

= 10000 × ($\frac{23}{20}$)² = 10000 × $\frac{529}{400}$ = 13225.

∴ The answer is Rs. 13225.

Given:

20% more than x is 30% less than 360.

Calculations:

20% more than x is 30% less than 360.

20% more than x = 20% of x + x = $\dfrac{20}{100}$ of x + x = $\dfrac{1}{5}$x + x = $\dfrac{x + 5x}{5}$ = $\dfrac{6x}{5}$ [ eqn1]

30% less than 360 = 360 - $\dfrac{30}{100}$ × 360 = 360 - 108 = 252. [eqn2]

Equating both the equations,

$\dfrac{6x}{5}$ = 252

x = $\dfrac{252 × 5}{6}$ = 210.

∴ The answer is 210.

Given:

A park has an average of 630 visitors on Sundays and 360 on other days.

Formula used:

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

Average number of visitors per day = $\dfrac{total \ sum}{number \ of \ days \ in \ one \ month}$

Concept used:

If a month starts with Sunday then the number of Sundays in that month is 5 and the remaining days is 30 - 5 is 25.

Calculations:

First case for sundays, Sum of visitors on sundays = 5 × 630 = 3150.

Similarly, for rest of the days, sum of visitors on other days = 25 × 360 = 9000.

Average of visitors in one day = $\dfrac{3150 + 9000}{30}$ = $\dfrac{12150}{30}$ = 405.

∴ The answer is 405

Given:

Numbers is divisible by 8.

Concept used:

If the last three digits of a number are divisible by 8 then the number is completely divisible by 8.

Calculations:

So, as per rule, if we consider last 3 digits of 28353 that is, 353 ÷ 8 = 44.1 does not satisfy the rule.

if we consider last 3 digits of 28354 that is, 354 ÷ 8 = 44.25 does not satisfy the rule.

if we consider last 3 digits of 28350 that is, 350 ÷ 8 = 43.75 does not satisfy the rule.

Similarly, as per the rule, if we consider the last 3 digits of 28352 that is, 352 ÷ 8 = 44 is completely divisible by 8. So the number is divisible by 8.

∴ The answer is 28352.

Given:

Formula used:

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

Calculations:

Let the initial average marks = x, which increased by 4 makes the average marks = x + 4.

Let the new sum of marks be y. And z being sum of marks scored by those boys who were added.

4 boys having marks 30 in which the sum = 4 × 30 = 120 which were removed.

Now, the corresponding average(x) = $\dfrac{y}{10}$ (as, 10 being the total number of boys)

y = 10x

So, according to the problem,

x + 4 = $\dfrac{y - 120 + z}{10}$

10x + 40 = 10x - 120 + z (putting the values y = 10x)

z = 120 + 40 = 160

Now, the average of those 4 boys will be $\dfrac{160}{4}$ = 40.

∴ The answer is 40.

Given:

The population of a species is decreasing at a rate of 5% per annum. Their current population is 19,855.

Formula used:

Future population = present population(1 ±  $\dfrac{rate}{100}$)ⁿ [where, n is the time]

Calculations:

Two years ago : 

Population after 2 years  = 19,855

Present population be x

Future  population = x (1 - $\dfrac{5}{100}$)² = 

⇒ 19855 = x × (1 - $\dfrac{1}{20}$)2

= 19855 = x × ($\dfrac{19}{20}$)²

= 19855 × $\dfrac{400}{361}$ = 22000

∴ The answer is 22000.

Given:

$\dfrac{63}{x}$ = $\dfrac{49}{21}$

Calculations:

$\dfrac{63}{x}$ = $\dfrac{49}{21}$

x = $\dfrac{63 × 21}{49}$ = 3 × 9 = 27.

∴ The answer is 27.

Given:

A works twice as fast as B.

To finish a work, A worked twice as many hours every day as B.

The wages for the entire work are Rs. 5,000.

Formula used:

Work done = time taken × rate of work(efficiency)

If A and B can do a piece of work in X and Y days respectively.

The ratio of their wages will be Y : X then the wages on by A and B will be A's wages = $\dfrac{Y}{X + Y}$ × total wages and B's wages = $\dfrac{X}{X + Y}$ × total wages

Calculations:

Let, B work for = y hours and A work for = 2y.

Let, efficiency of B = x and efficiency of A = 2x.

For A, work done = 2x × 2y = 4xy

For B, work done = x × y = xy

Now, ratio of A : B = 4xy : xy = 4 : 1

A's wages = $\dfrac{4}{4 + 1}$ × 5000

A's wages = $\dfrac{4}{5}$ × 5000 = Rs. 4 × 1000 = Rs. 4000.

∴ The answer is Rs. 4000.

Given:

Vandana made an item for Rs. 120 and sold it to Shama at a 25% profit.

Shama sold it to Mangesh, who sold it for Rs. 198, thereby making 10% profit.

Formula used:

Profit% = $\dfrac{selling \ price - cost \ price}{cost \ price}$ × 100

Calculations:

Let x be the amount of Mangesh.

Vandana made an item for Rs. 120 and sold it to Shama at a 25% profit.

25 = $\dfrac{selling \ price - 120}{120}$ × 100

25 × 120 = (selling price - 120) × 100

3000 + 12000 = 100 selling price

Selling price = $\dfrac{15000}{100}$ = Rs. 150.

Shama sold it to Mangesh who sold it for Rs. 198 making 10% profit.

x × 10% + x = 198

x × $\dfrac{10}{100}$ + x = 198

x × $\dfrac{1}{10}$ + x = 198

$\dfrac{10x + x}{10}$ = 198

$\dfrac{11x}{10}$ = 198

x = $\dfrac{198 × 10}{11}$ = 180.

So, now, Shama had an amount of Rs. 150 which may be considered as the cost price and Mangesh had an amount of Rs. 180 which can be considered as the selling price.

Profit% of Shama = $\dfrac{180 -150}{150}$ × 100

= $\dfrac{30}{150}$ × 100 = 20%.

∴ The answer is 20%.