DSSSB PA Grade II Official Paper (Held on:26 Feb 2022 Shift 3) (Previous Year Paper)

The logic followed here is:​

• The 1^st alphabet is increased by +4.
• The 2^nd alphabet is increased by +5.
• The 3^rd alphabet is increased by +6.
• The 4^th alphabet is increased by +7.

Hence, the correct answer is "QGPR".

The logic followed here is:

DNFGPB : EOGHQC

Similarly, 

TROLEX  is related to 

Hence, the correct answer is "USPMFY".

According to the given information:

From the above image, we can conclude that,

 

So the code for 'use your' is 'sf rn'.

Hence, the correct answer is "sf rn"

The logic followed here is:

Sum of the positional value of letters in a word - 3 = Number code.

'TANKA' is written as '44',

• T(20) +  A(1) + N(14) +  K(11) +  A(1) = 47 - 3 = 44

'MELBA' is written as '30'.

• M(13) +  E(5) + L(12) +  B(2) +  A(1) = 33 - 3 = 30

Similarly,

'BOHME = ? 

• B(2) +  O(15) + H(8) +  M(13) +  E(5) = 43 - 3 = 40

​Hence, the correct answer is "40".

According to the given information:

 

The possible answers are,

• "man-like" = 2   8, 2   9, 1  8, 1   9.
• As only 29 is present in the options it is correct.

Hence, the correct answer is "2   9".

Confusion Points

• There are more than 2 matches of code in the given question.
• Hence, tally the options with the outcomes.

According to the given information:

• Height of D is more than C and F but less than E and B.

​

• Height of F is not less than A.
• Height of C is more than H.

​

• Height of H is more than three persons.

​

• No sufficient information is provided for who is taller among E and B.
• Similarly, no sufficient information is provided for who is taller among A and G.

This is the final order of heights.

Conclusions:

I. If the height of A is 153 cm, then height of F can also be 153 cm.- True (F can be equal to or greater than A).

II. If the height of G is 132 cm, then the height of A can be 128 cm - True (There is no direct relation given between A and G, so there is a possibility that G can be taller than A)

III. If the height of B is 108 cm, then the height of E can be 103 cm - True (There is no direct relation given between E and B, so there is a possibility that B can be taller than E) 

IV. If the height of H is 100 cm, then the sum of the height of H and C can be 203 cm - True (As C is taller than H, there is a possibility)

​Hence, the correct answer is "I, II, III, and IV".

The logic followed here is:

 'FORTSE' is written as 'ESTROF'.

Similarly, 

'KNIGHT' will be written as,

Hence, the correct answer is "THGINK".

Given: 

• Five boys F, G, H, J and K.
• They like one cap among P, Q, R, S and T.
• They like one car among C1, C2, C3, C4 and C5.
• No two of them likes same car and same cap.

​1) F likes cap P and car C1.

 

2. One who likes cap S also likes car C5.

 

3. One who likes car C3 doesn't like cap T.

4. K likes car C3.

 

5. H likes cap Q.

 

6. J doesn't like car C5.

 

Arranging the final table,

 

I. C5 - G - S - True

II. C3 - K - R - True

III. C2 - H - Q - False

IV. C4 - F - T - False

Hence, the correct answer is "I and II only".

Given: A team of 5 members is to be selected from 5 boys: B1, B2, B3, B4, B5, and 5 girls: G1, G2, G3, G4, G5.

• Now check all given statements.

 

As only team 2 satisfies the given criteria,

Hence, the correct answer is "Only II".

The least possible diagram is as follows:

Conclusions:

I. Some Z are not R. → True (From the figure we can clearly see that no part of Z intersects with R).

II. Some P are not R → True (Since No R is P given so some P are not R, it is definitely true).

​Hence, the correct answer is "Both conclusion I and Il follow".

The logic followed here is :

It is clear from the above arrangement that, the first and second letter is increased by +2, and numbers are increased by +4.

Hence, the correct answer is "NR34".

The logic followed here is:

All the words Sofa, Table, and Chair are non-living things.

While,

'Doctor' is a person who treats patients.

Hence, the correct answer is "Doctor".

The pattern followed here is :

• CLOUD: XOLFW

From above arrangement, it is clear that each letter is written in its reverse letter.

Similarly,

• BREAK = ?

Thus, 'BREAK' can be written as 'YIVZP'.

Hence, the correct answer is "YIVPZ".

1. YWTP

2. ECZV

3) WUTR

4. LJCG

Clearly, 'WUTR' does not follow the same logic that is being followed by the other options thus it is different.

Hence, the correct answer is "WUTR".

According to the given information:

A team is to be selected from 9 girls: A, B, C, D, E, F, G, H, and I. 

Given: If C and G are selected in a team then the other players that can be selected in the same team under the given condition are as follows :

1) C cannot be selected with H.

2) G and F have to be selected together.

Possible cases:

3) Only one among D, H and B must be selected. 

Possible cases:

 

But, Case II will be eliminated as it contradicts with condition 1.

4) A and D have to be selected together.

Possible cases :

 

After satisfying all the conditions, we have two teams "C G F D A" and "C G F B".

Now, two girls are left  'E' and 'I', who are not mentioned in the above conditions.Thus, they can be selected in both the teams.

Thus we have,

 

Clearly, the maximum number of members in the team including C and G is in 'TEAM I' having '7 members'.

Hence, the correct answer is "7".

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

According to the given information :

1. J is the brother of B and B is the daughter of A.
2. If M is the son of B and K. R is the daughter of K.

Therefore, the following family tree can be drawn:

Thus, it is clear from the above diagram that 'J is Uncle of M'.

Hence, the correct answer is "Uncle".

Statements:

I. No S is T.

II. No T is Q.

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

Conclusions: 

I. Some Q are not S → False (Because there is no direct relation between Q and S, so it is possible but not definite)

II. No Q is T → True (Because there is a direct relation between T and Q as No T is Q, so No Q is T is also true)

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

The pattern followed here is:

1. KJHEA

2. VUSPL

3) POMHE

4. RQOLH

Thus, 'POMHE' does not follow the same logic that is being followed by the other options, so it is different from others.

Hence, the correct answer is "POMHE".

The arrangement of all the given words in the order in which they appear in an English dictionary is as shown below:

• The two letters E and X are common in all words, so we will start arranging the word from the third letter as per alphabetical order.

1. EXCEPT
2. EXISTS
3. EXPAND
4. EXPECT
5. EXPERT

Hence, the correct answer is "12354".

The logic followed here is:

1^st word is "the product" and 2^nd word is "the material by which the product is made".

Paper: Pulp → Paper is made from Pulp.

Similarly,

Wine: Grapes → Wine is made from Grapes.

Hence, the correct answer is "Wine : Grapes".

The logic followed here is:

• All the diagrams have different figure in the center compared to surrounding figures except for option 1.
• In option 1 all figures are triangles.

​Hence, the correct answer is "option 1".

According to the given information:

We can see that the shaded part denotes the number of sharpeners that are books = 3 + 2 = 5. 

That is given as "5".

​Hence, the correct answer is "5".

The logic followed here is,

The correct sequence should be,

• 14 × 3 = 42 + 1 = 43
• 43 × 3 = 129 + 1 = 130
• 130 × 3 = 390 + 1 = 391
• 391 × 3 = 1173 + 1 = 1174

​

• The number should be 391 instead of 390.

Hence, the correct answer is "390".

The number of triangles in given figure is,

So the total number of triangles become 7.

​Hence, the correct answer is "7".

The least possible diagram is as follows:

Conclusions:

I. Some C are A. → False (There is no direct relation between C and A. It may be possible but not definite)

II. No W is A. → False (There is no direct relation between W and A. It may be possible but not definite)

III. No K is A. → True (As A is K given so no K is also A, it is definitely true)

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

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

Hence, ‘option 4’ is the correct answer.

The number of triangles in the given figure is:

So, there are a total of 8 triangles in the figure.

Hence, ‘8’ is the correct answer.

Mistake Points The question is asking for Which statement is not correct, so choose the not correct answer here.

Given:

I. Total number of bottles are 32 → False

The shaded part represents the total number of bottles.

 

The total number of bottles = 11 + 8 + 4 + 16 = 39

II. Number of towels which are bottle and red both are 4 → True

The shaded part represents the number of towels which are bottle and red both.

 

The numbers of towels which are bottle and red both = 4

Hence, 'Only I’ statement is not correct.

Statements:

I. All red are pen.

II. All rubber are pen.

The least possible diagram for the given statements is as follows

Conclusions:

I. Some red are rubber → False (because no direct relationship is given between red and rubber so it may be possible but not defined)

II. Some pen are rubber → True (because all rubber are pens so some pen are definitely rubber)

III. No red is rubber → False (because no direct relationship is given between red and rubber so it may be possible but not defined)

Hence, “Only conclusion II follows".

Statements:

I. No R is G.

II. No P is V.

III. Some R are V.

The least possible diagram for the given statements is as follows

Conclusions:

I. Some G are not P → False (Because direct relationship between P and G is not given so it may be possible but not defined)

II. Some V are not P → True (Because no P is V and Some V is R so definitely some V are not P)

III. Some V are R → True (Because some R are V so some V are also R)

Hence, “Both conclusion II and III follows".

Now check all the options:

Option 1 : 3 ÷ 8 - 16 × 8 + 5 = 3

After interchanging the × and –,

=> 3 ÷ 8 × 16 - 8 + 5 = 3

=> 0.375 × 16 - 8 + 5 = 3

=> 6 - 8 + 5 = 3

=> 11 – 8 = 3

=> 3 = 3 (Correct)

Option 2 : 21 - 4 ÷ 7 + 2 × 5 = 9

After interchanging the × and –,

=> 21 × 4 ÷ 7 + 2 - 5 = 9

=> 21 × 0.57 + 2 - 5 = 9

=> 12 + 2 - 5 = 9

=> 14 - 5 = 9

=> 9 = 9 (Correct)

Option 3 : 2 ÷ 5 - 10 + 7 × 8 = 3

After interchanging the × and –,

=> 2 ÷ 5 × 10 + 7 - 8 = 3

=> 0.4 × 10 + 7 - 8 = 3

=> 4 + 7 - 8 = 3

=> 11 – 8 = 3

=> 3 = 3 (Correct)

Option 4 : 91 ÷ 13 × 5 + 6 - 3 = 38

After interchanging the × and –,

=> 91 ÷ 13 - 5 + 6 × 3 = 38

=> 7 - 5 + 6 × 3 = 38

=> 7 - 5 + 18 = 38

=> 25 - 5 = 38

=> 20 = 38 (Incorrect)

Thus by interchanging the given two signs Option 4 equation will be incorrect.

 

Hence, the correct `answer is Option 4: “91 ÷ 13 × 5 + 6 - 3 = 38”.

Now check all the options:

Option 1 : 9 × 8 ÷ 6 + 7 - 3 = 24

After interchanging the 3 and 6,

=> 9 × 8 ÷ 3 + 7 - 6 = 24

=> 9 × 2.67 + 7 - 6 = 24

=> 24 + 7 - 6 = 24

=> 31 – 6 = 24

=> 25 = 24

= (Incorrect)

Option 2 : 6 - 4 + 1 ÷ 2 × 3 = 2

After interchanging the 3 and 6,

=> 3 - 4 + 1 ÷ 2 × 6 = 2

=> 3 - 4 + 0.5 × 6 = 2

=> 3 - 4 + 3 = 2

=> 6 – 4 = 2

=> 2 = 2 (Correct)

Option 3 : 3 + 6 × 8 ÷ 2 - 1 = 15

After interchanging the 3 and 6,

=> 6 + 3 × 8 ÷ 2 - 1 = 15

=> 6 + 3 × 4 - 1 = 15

=> 6 + 12 - 1 = 15

=> 18 – 1 = 15 (Incorrect)

Option 4 : 6 × 1 ÷ 3 + 5 - 2 = 5

After interchanging the 3 and 6,

=> 3 × 1 ÷ 6 + 5 - 2 = 5

=> 3 × 0.167 + 5 - 2 = 5

=> 0.5 + 5 - 2 = 5

=> 5.5 - 2 = 5

=> 3.5 = 5 (Incorrect)

Hence, the correct `answer is Option 2: “6 - 4 + 1 ÷ 2 × 3 = 2”.

The Venn diagrams best represent the relationship between - Sister, Female, Human figures are shown below:

• All sisters are female and all female are human

Hence, ‘Option 1’ is the correct answer.

Given:

I. Number of mango which are only fruit are 13 → True

The shaded part represents the number of mango which are only fruit.

So the number of mango which are only fruit are 13.

II. Number of potato which are neither fruit and nor mango are 5 → False

The shaded part represents the number of potato which are neither fruit and nor mango.

The number of potato which are neither fruit and nor mango are = 3

Hence, 'Only I’ statement is correct.

The logic followed here is:

2^nd Number – 1^st number = 11

Option (1) 165 – 176 → 176 – 165 = 11

Option (2) 125 – 136 → 136 – 125 = 11

Option (3) 204 – 216 → 216 – 204 = 12 ≠ 11

Option (4) 147 – 158 → 158 – 147 = 11

Hence, “204 – 216” is an odd one.

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

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

The logic followed here is:

• In the 3 side figure, one side is increased and becomes 4 side figure.
• 3 small same figures is in 3 side figure and 4 small same figures is in 4 side figure.

Similarly, 

• In the 5 side figure, one side is increased and becomes 6 side figure.
• 5 small same figures is in 5 side figure and 6 small same figures is in 6 side figure.

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

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

• The circle and the square rotate anticlockwise direction and every rotation its become dark and light respectively.

Final series is

Hence, ‘option 1’ is the correct answer.

The shaded part represents the number of banks are not office.

 

The number of banks are not office  = 11

Hence, ‘11’ is the correct answer.

The logic is here:

• There are cross lines inside the figure

Now check all the options:

Option (1): 

 Verticals lines inside the figures.

Option (2): 

 Horizontal and vertical lines inside the figures.

Option (3): 

Cross lines inside the figures.

Option (4): 

Horizontal lines inside the figures.

Hence, "Option 3" is the correct answer.

The correct answer is Both I and II.

Key Points

• The tropical rainforests always appear green as their trees never shed their leaves at any time of the year, the way tress of Deciduous forests do.
• Therefore they are called an evergreen forest.
• Tropical rainforests are found near the equator due to the amount of rainfall and the amount of sunshine these areas receive.
• Most tropical rainforests fall between the Tropic of Cancer and the Tropic of Capricorn.
• Thus, option 3 is the right answer.

Additional Information

• Tropical evergreen forests of India are found in
• the Andaman and Nicobar Islands
• the Western Ghats, which fringe the Arabian Sea
• the coastline of peninsular India
• the greater Assam region in the north-east.
• small remnants also found in Odisha state.

The correct answer is Goa.

Key PointsFugdi :

• Fugdi is a Maharashtra and Goan folk dance performed by women in the Konkan region.
• According to historical facts, this dance style is said to have been created from a few ancient Goan traditions.
• Women perform this dance form during Hindu religious festivals like Ganesh Chaturthi and Vrata or towards the end of other dances like Dhalo.
• Other popular folk dances in Goa are Deknni, Dhalo, Khol, Mussoll, etc.

Additional Information

• Folk dances of Meghalaya - Behdiengkhlam, Nоngkrem, Shad Suk Mynsiem, Wangala, Dоrsegata, Lahoo, etc.
• Folk dances of Chhattisgarh - Saila, Karma, Sua Nacha, Pandawani, Raut Nacha, Panthi, Jhirliti, Gendi, etc.
• Folk dances of Haryana - Saang, Ragini, Chaupaiya, Phaag, Teej, Been, Dhamal, Loor, etc.

The correct answer is Deposits.

Key Points

• Bank deposits are assets for the depositor because deposits represent money that's owed to them.
• The deposits are liabilities to the bank because they represent money the bank must return.

Additional Information

• By the same logic -
• Cash, government securities, and interest-earning loan accounts are all a part of a bank's assets.
• Loans are assets as it is money owed to the banks.

The correct answer is Maharashtra.

Key Points

• The Aga Khan Palace was built by Sultan Muhammed Shah Aga Khan III in the city of Pune, Maharashtra in 1892.
• The palace was an act of charity by the spiritual leader of the Nizari Ismaili Muslims, who wanted to help the poor in the neighbouring areas of Pune, who were drastically hit by famine.

Additional Information

• Sir Sultan Mahomed Shah, Aga Khan III was the 48^th Imam of the Nizari Ismaili sect of Islam.
• He played a very important role in giving the Muslims a political stance to express their opinions to the British.
• In 1906, the Aga Khan was a founding member and first president of the All India Muslim League.

The correct answer is Only I.

Key Points

• The main role of the phloem tissue is to transport carbohydrates from sources to sinks through the sieve elements.
• Xylem is the tissue of vascular plants that transports water and nutrients from the soil to the stems and leaves.
• Thus, option 3 is correct.

Additional Information

• The plant vascular system is a complicated network of conducting tissues that interconnects all organs and transports water, minerals, nutrients, organic compounds, and various signaling molecules throughout the plant body.
• The vascular system is comprised of two main types of tissue - the xylem and the phloem.
• The xylem distributes water and dissolved minerals upward through the plant, from the roots to the leaves.
• The phloem carries food downward from the leaves to the roots.

The correct answer is Both I and II.

Key Points

• The five factors that control soil formation are-
• Parent material
• Relief or topography
• Organisms (including humans)
• Climate
• Time.
• Thus, option 3 is the correct answer.

Additional Information

• Types of soil found in India -
• alluvial soil
• black soil
• red soil
• laterite soil
• desert or arid soil
• forest and mountainous soil
• peaty or marsh soil
• saline or alkaline soil.

The correct answer is 1764.

Key Points

• The Battle of Buxar was fought between 22 and 23 October 1764.
• It resulted in the treaty of Allahabad in 1765, in which the sovereignty of Bengal was surrendered to the British by the Mughal emperor.

Additional Information

• The war was between
• the forces under the command of the British East India Company, led by Hector Munro.
• the combined armies of  Nawab of Bengal - Mir Qasim, the Nawab of Awadh - Shuja-ud-Daula, and the Mughal Emperor - Shah Alam II.
• The main cause behind this battle was the misuse of privileges in trade granted by the Nawab of Bengal and also the colonialist ambitions of the British.

The correct answer is Only I.

Key Points

• Sirius, also called Alpha Canis Majoris or the Dog Star, brightest star in the night sky.
• It is a binary star in the constellation Canis Major.
• Thus, option 3 is the correct answer.
• Its name is derived from the Greek word Seirios, meaning lit. 'glowing' or 'scorching'.

Additional Information

• Cassiopeia A is a supernova remnant.
• It is notable for being the brightest astronomical radio source in the sky.
• It is the strongest radio source in the sky outside the solar system and was one of the first radio sources to be discovered, in 1947.
• The five brightest stars of Cassiopeia – Alpha, Beta, Gamma, Delta, and Epsilon Cassiopeiae – form the characteristic W-shaped asterism.
• Its brightest star is Alpha Cassiopeiae or Shedar (Arabic for “breast”).

The correct answer is GDP + Net factor income from abroad.

Key Points

• Gross Domestic Product + Net factor income from abroad = Gross National Product.
• Net factor income from abroad = Factor income earned by our residents from the rest of the world - Factor income earned by non- residents in our domestic territory.

Additional Information

• Net national product refers to gross national product, i.e. the total market value of all final goods and services produced by the factors of production of a country or other polity during a given time period, minus depreciation.

The correct answer is Ellora Caves.

Key Points

• The Ellora Caves, Maharashtra are printed on the reverse side of Rs. 20 banknotes.
• In the year 1983, Ellora Caves were declared as World Heritage Site by UNESCO.
• It is one of the largest rock-cut Hindu temple cave complexes in the world, with artwork dating from the period 600–1000 CE.

Additional Information

• The Rs 10 note has a picture of Konark Sun Temple of Odisha on the rear side.
• Konark Sun Temple is a 13^th-century CE Sun temple at Konark, Odisha.
• The temple is attributed to king Narasimhadeva I of the Eastern Ganga dynasty about 1250 CE.
• It was declared a World Heritage Site by UNESCO in 1984.
• The Rs 100 note has a picture of Rani ki Vav, Gujarat on its back.
• Rani Ki Vav is a stepwell situated in the town of Patan in Gujarat state of India.
• Its construction is attributed to Udayamati, daughter of Khengara of Saurashtra, queen and spouse of the 11^th-century Chaulukya king Bhima I.
• It was declared a World Heritage Site by UNESCO in 2014.
• The Rs 50 note has a picture of the Chariot of Hampi, Karnataka on its back.
• ​The stone Chariot is a shrine dedicated to Garuda, the official vehicle of Lord Vishnu.
• The chariot was built by King Krishnadevaraya of the Vijayanagara Empire during the 16^th century.
• Hampi was declared a World Heritage Site by UNESCO in 1986.

The correct answer is Drum.

Key Points

• Alingya drums have the animal hide fixed to a wooden round frame and are embraced or held close to the body with one hand while the other hand is used for playing the instrument.
• Under this category, the Duff, Dufflies, etc. are very popular.
• It comes under Avanaddha Vadya which are percussion instruments. Such instruments are made by stretching the animal skin across a metal or earthen pot, wooden barrel, or frame.
• The sound is produced by striking the animal skin that has been stretched across the body.

Additional Information

Tabla:

• A tabla is a pair of twin hand drums from the Indian subcontinent.
• Tabla has been the principal percussion instrument in Hindustani classical music.

Kamcha (Kamancheh):

• Kamancheh is a Persian bowed string instrument used in Persian, Azerbaijani, Armenian, and Kurdish music.
• The strings are played with a variable-tension bow.

Flute:

• The flute is a family of classical music instruments in the woodwind group.
• A flute is an aerophone or reedless wind instrument that produces its sound from the flow of air across an opening.

The correct answer is Chilika Lake

Key Points

• Chilika Lake is a brackish water lagoon, spread over the Puri, Khurda and Ganjam districts of Odisha state on the east coast of India, at the mouth of the Daya River, flowing into the Bay of Bengal.
• It is the biggest lake in India after Vembanad Lake.
• This lake is the largest coastal lagoon in India and the largest brackish water lagoon in the world. It is the largest Salt Water lake in India.

Additional Information

Pulicat lake

• Pulicat Lagoon is the second largest brackish water lagoon in India.
• Major part of the lagoon comes under Tirupati district of Andhra Pradesh. The barrier island of Sriharikota separates the lagoon from the Bay of Bengal and is home to the Satish Dhawan Space Centre.

Loktak Lake

• Loktak Lake is the largest freshwater lake in India.
• The lake is located at Moirang in Manipur state, India.

Dal Lake

• Dal is a lake in Srinagar, the summer capital of Jammu and Kashmir.
• It is integral to tourism and recreation in the Kashmir valley and is variously known as the "Lake of Flowers","Jewel in the crown of Kashmir"or "Srinagar's Jewel".

The correct answer is Repo rate

Key Points

• Repo rate refers to the rate at which commercial banks borrow money by selling their securities to the Central bank of the country i.e Reserve Bank of India.
• It is to maintain liquidity, in case of a shortage of funds or due to some statutory measures.
• It is one of the main tools of RBI to keep inflation under control.

Additional Information

• The reverse Repo Rate is defined as the rate at which the Reserve Bank of India (RBI) borrows money from banks for the short term.
• The Reverse Repo Rate helps the RBI get money from the banks when it needs it.
• A liquidity adjustment facility (LAF) is a tool used in monetary policy, primarily by the Reserve Bank of India (RBI) that allows banks to borrow money through repurchase agreements (repos) or to make loans to the RBI through reverse repo agreements.
• A bank rate is the interest rate a nation's central bank charges to its domestic banks to borrow money.
• The rates central banks charge are set to stabilize the economy.

The correct answer is Trade Surplus

Key Points

• Trade surpluses occur when a country exports more products than it imports.
• A trade surplus is an economic measure of a positive balance of trade.
• Trade Balance = Total Value of Exports - Total Value of Imports.
• A trade surplus represents a net inflow of domestic currency from foreign markets.

Additional Information

Trade deficit

• A trade deficit occurs when a country imports more than it exports.
• A trade deficit reduces the incomes of domestic workers, pushing many into lower income brackets.

Current Account Deficit (CAD)

• The current account deficit is the shortfall between the money received by selling products to other countries and the money spent to buy goods and services from other nations.
• It is called the current account because goods and services are generally consumed in the current period.

Fiscal deficit

• The difference between total revenue and total expenditure of the government is termed a fiscal deficit.
• It is an indication of the total borrowings needed by the government.

The correct answer is Kushinagar

Key Points

• Kushinagar is a town in the Kushinagar district in Uttar Pradesh.
• is an important Buddhist pilgrimage site, where Buddhists believe Gautam Buddha posthumously attained Mahaparinirvana.
• Ashoka built a stupa and pilgrimage site to mark Buddha's parinirvana in Kushinagar.

Additional Information

Sarnath:

• Sarnath is a place located northeast of Varanasi near the confluence of the Ganges and the Varuna rivers in Uttar Pradesh.
• The Deer Park in Sarnath is where Gautama Buddha first taught the Dharma, and where the Buddhist Sangha came into existence through the enlightenment of Kondanna.

Vaishali:

• Vaishali district is a district in the Indian state of Bihar.
• Vaishali is popularly known as the birthplace of Lord Mahavir of the Jain religion.

Magadha:

• Magadha was a region and one of the sixteen Mahajanapadas.
• Magadha played an important role in the development of Jainism and Buddhism.

The correct answer is Both I and II.

Key Points

• India has a land boundary of about 15,200 km.
• India shares borders with several sovereign countries; it shares land borders with China, Bhutan, Nepal, Pakistan, Bangladesh, Afghanistan, and Myanmar.
• Bangladesh and Pakistan share both land borders as well as maritime borders, while Sri Lanka shares only a maritime border through Ram Setu.

Additional Information

• India's Andaman and Nicobar Islands share a maritime border with Thailand, Myanmar, and Indonesia.
• India and Bangladesh share one of the longest borders in the world and it covers an area of 1,43,998 sq km.
• Afghanistan has the shortest boundary with India.
• India, with its claim to a 12-nautical-mile territorial maritime zone and 200-nautical-mile exclusive economic zone, has a more than 7,000-kilometre maritime border shared with seven nations.

The correct answer is Kerala.

Key Points

• Onam is an annual Malayali harvest festival celebrated in the Indian state of Kerala.
• It is the official festival of the state.
• Onam commemorates King Mahabali and Vamana.
• Few events are performed during Onam celebrations: Vallam Kali (boat races), Pulikali (tiger dances), Pookkalam (flower rangoli), Onathappan (worship), Onam Kali, Tug of War, Thumbi Thullal (women's dance), Kummattikali (mask dance), etc.

Additional Information

Pongal - Tamilnadu

• The harvest festival of Tamilnadu is popularly known as Pongal.
• Pongal signifies the celebration of flourishing crops in the fields.

Jallikattu - Tamil Nadu 

• Jallikattu is typically practised in the Indian state of Tamil Nadu as a part of Pongal celebrations on Mattu Pongal day, which occurs annually in January.
• It is a traditional event in which a bull is released into a crowd of people, and multiple human participants attempt to grab the large hump on the bull's back with both arms and hang on to it while the bull attempts to escape.

Bihu - Assam

• Bihu is a set of three important Assamese festivals in the Indian state of Assam.
• 'Rongali' or 'Bohag Bihu' is observed in April, 'Kongali' or 'Kati Bihu' is observed in October, and 'Bhogali' or 'Magh Bihu' is observed in January.

The correct answer is Image at infinity and highly enlarged.

Key Points

• When an object is at the focus of the concave mirror the image is formed at infinity and it is real, inverted and highly magnified.
• A concave mirror has a reflective surface that is curved inward and away from the light source.
• Light converges at a point when it strikes and reflects back from the reflecting surface of the concave mirror. Hence, it is also known as a converging mirror.

 

     

Additional Information

• Image is formed behind the mirror when the object is placed between Pole and Focus.
• The image formed is enlarged.
• When the object is at the Centre of Curvature, the image formed is at the Centre of Curvature.
• When the object is at Focus, the image formed is at infinity.

The correct answer is Poles > equator

Key Points

• The force of earth's gravity on the body at the equator is 9.798 m/s² times the mass of the body, whereas at the poles it is 9.863 m/s² times the mass of the body.
• Thus, the force of gravity at Poles is greater than the force of gravity at the Equator.
• The distance from the poles to the centre of the earth is lesser than the distance from the equator to the centre of the earth. Therefore the acceleration due to gravity is greater at the poles than at the equator.

 Additional Information

• The value of g on earth is maximum at the poles and goes on decreasing as we go towards the equator.
• The value of 'g' is minimum at the equator because the earth is not a perfect sphere. Its radius is maximum at the equator. Hence, according to the equation g = GM/R², the equator is the place where g will be minimum.
• Even on the surface of the Earth, there are local variations in the value of g. These variations are due to latitude (the Earth isn't a perfect sphere; it buldges in the middle), altitude and the local geological structure of the region.

The correct answer is Bromeliad.

Key Points

• The Bromeliaceae (the bromeliads) is a family of monocot flowering plants of 75 genera and around 3590 known species native mainly to tropical America.
• The family includes both epiphytes, such as Spanish moss, and terrestrial species, such as the pineapple.
• Many bromeliads are able to store water in a structure formed by their tightly overlapping leaf bases.

Additional Information

• Majestic palm: Ravenea rivularis, the majestic palm, or majesty palm, is a species of tree in the family Arecaceae.
• They generally grow to 10 to 12 feet tall and are often marketed in stores as a "houseplant" in a pot.
• Anthurium: Anthurium is a genus of about 1,000 species of flowering plants, the largest genus of the arum family, Araceae.
• General common names include anthurium, tailflower, flamingo flower,and laceleaf.
• Croton: Croton is a diverse and complex taxonomic group of plants ranging from herbs and shrubs to trees.

The correct answer is Salman Rushdie

Key Points

• Quichotte is a 2019 novel by Salman Rushdie.
• Quichotte is the story of Ismail Smile — a traveling salesman of pharmaceutical products ,who falls in love with a woman on TV and sets out on a quest to win her heart.
• Sir Ahmed Salman Rushdie is an Indian-born British-American novelist and essayist. His work, combining magical realism with historical fiction, is primarily concerned with the many connections, disruptions, and migrations between Eastern and Western civilizations.

Additional Information

Elif Shafak:

• Elif Shafak is a Turkish-British novelist, essayist, public speaker, political scientist and activist.
• She is best known for her novels, which include The Bastard of Istanbul, The Forty Rules of Love, Three Daughters of Eve and 10 Minutes 38 Seconds in This Strange World.

Lucy Ellmann:

• Lucy Ellmann is an American-born British novelist based in Edinburgh, Scotland.
• Her first book, Sweet Desserts, won the Guardian Fiction Prize.

Arundhati Roy:

• Arundhati Roy is an Indian author best known for her novel The God of Small Things, which won the Man Booker Prize for Fiction in 1997 and became the best-selling book by a non-expatriate Indian author.
• She is also a political activist involved in human rights and environmental causes.

The correct answer is Both I and II

Key Points

• Bombay Spinning and Weaving Company was the first cotton mill to be established in Bombay, India, on 7 July 1854.
• This mill began production on 7 February 1856.
• The Ahmedabad Spinning and Weaving Company Ltd. was the first textile mill and garments company established in Ahmedabad and one of the first textile mills of India.
• It was opened on 30 May 1861, and started by entrepreneur, Ranchhodlal Chhotalal.

Additional Information

• A cotton mill is a building that houses spinning or weaving machinery for the production of yarn or cloth from cotton,an important product during the Industrial Revolution in the development of the factory system.
• The first Indian cotton cloth mill was established in 1818 at Fort Gloaster near Kolkata, but this mill was a failure.
• The second mill which was established by KGN Daber in 1854 is called the true foundation of modern cotton industry in India. Its name was Bombay Spinning and weaving Company, Bombay.

The correct answer is Neither I nor II

Key Points

• The 2019 FIFA Women's World Cup Final was a football match that determined the winner of the 2019 FIFA Women's World Cup. It was the eighth final of the FIFA Women's World Cup.
• The final was contested by the United States, the defending champion, and the Netherlands, in their first final.
• The United States won 2–0, earning their second consecutive and fourth overall Women's World Cup title.
• Team combination for the semi-final of the 2019 FIFA Women's World Cup:
• United States of America vs**. England** and Netherlands vs. Sweden.

Additional Information

• The FIFA Women's World Cup is an international association football competition contested by the senior women's national teams of the members of Fédération Internationale de Football Association (FIFA), the sport's international governing body.
• The competition has been held every four years and one year after the men’s FIFA World Cup since 1991.

The correct answer is West Indies

Key Points

• The 2022 ICC Under-19 Cricket World Cup was an international limited-overs cricket tournament that was held in the West Indies in January and February 2022 with sixteen teams taking part.
• It was the fourteenth edition of the Under-19 Cricket World Cup, and the first that was held in the West Indies.
• Bangladesh was the defending champions.

Additional Information

• The ICC Under-19 Cricket World Cup is an international cricket tournament organised by the International Cricket Council (ICC) contested by national under-19 teams.
• First contested in 1988, as the Youth World Cup.
• India have won the World Cup on a record five occasions,while Australia have won three times, Pakistan twice, and Bangladesh, England, South Africa and the West Indies once each.

The correct answer is Swami Dayanand Saraswati

Key Points

• The Samaj was founded by Dayanand Saraswati on 7 April 1875.
• It promoted values and practices based on the beliefs of the Vedas.
• People of this community believed in one god and rejected worshipping idols.
• It was probably the first Hindu Organization to introduce proselytization in Hinduism, which means converting to Hinduism.

Additional Information

• Ishwar Chandra Vidyasagar: Ishwar Chandra Vidyasagar born as Ishwar Chandra Bandyopadhyay, was an Indian educator and social reformer of the nineteenth century. 
• He is considered the "Father of Bengali prose.
• Swami Vivekananda: Swami Vivekananda, born Narendranath Datta, was an Indian Hindu monk, philosopher and author.
• Vivekananda founded the Ramakrishna Math and the Ramakrishna Mission.
• Pandita Ramabai Sarasvati: Pandita Ramabai Sarasvati was an Indian social reformer. 
• She was the first woman to be awarded the title of Pandita as a Sanskrit scholar. She founded Mukti Mission at Kedgaon village, Pune.

The correct answer is Only I

 Key Points

Jitender Yadav:

• Jitender Yadav is the Coach of the Women's Wrestling team.
• Yadav is a former national-level wrestler from Services who has had a long coaching stint with the Air Force and junior India teams and in Pro League Wrestling.

Yogeshwar Dutt:

• Yogeshwar Dutt is an Indian freestyle wrestler.
• At the 2012 Summer Olympics, he won the bronze medal in the 60 kg category.
• He was awarded the Padma Shri by the Government of India in 2013.
• He won gold medals at the 2010 and the 2014 Commonwealth Games.
• He is one of only 5 male wrestlers in India to win an Olympic medal.

The correct answer is China

Key Points

• India, Nepal, and Bhutan have drafted a memorandum of understanding(MoU) to create a transboundary wildlife conservation 'Peace Park'.
• The proposed Park will include biodiversity-rich landscapes in adjoining areas of the three countries.
• The transboundary parks present a fundamental shift in which wildlife conservation is done. From a species-focused approach, it is a landscape-based approach.

Additional Information

• This project will maintain the natural connectivity of wildlife species, undisturbed by political boundaries.
• The project will also help the local communities through ecotourism.
• It will also maintain the traditional and cultural continuity of villages that share similar traditions from time immemorial but have been separated by the political boundary. In this sense, this park will be a harbinger of peace in the area.

The correct answer is Manpreet Singh.

Key Points

• Manpreet Singh Sandhu is an Indian field hockey player and the captain of Indian men's national field hockey team.
• He led the Indian field hockey team to the bronze medal at the Tokyo 2020 Olympics.
• In 2021, He was awarded the Khel Ratna Award, the highest sporting honour of India.

Additional Information

• Neeraj Chopra: Neeraj Chopra is an Indian track and field athlete who is the reigning Olympic champion and world championship silver medalist in the javelin throw.
• He is the first Asian athlete to win an Olympic gold medal in the men's javelin throw.
• Sumit Antil: Sumit Antil is an Indian Paralympian and javelin thrower.
• He won a gold medal in the men's javelin throw F64 category at the 2020 Summer Paralympics.
• Faisal Ali Dar: Faisal Ali Dar is an Indian sports enthusiast, and the first person to receive the Padma Shri Award in sports from Jammu and Kashmir.
• He was conferred with the national award for his contributions to promoting sports through martial arts and his works for keeping the youth away from drugs.

The correct answer is World Trade Organisation.

Key Points

• The World Trade Organization (WTO) is an intergovernmental organization that regulates and facilitates international trade.
• It officially commenced operations on 1 January 1995, pursuant to the 1994 Marrakesh Agreement, thus replacing the General Agreement on Tariffs and Trade (GATT) that had been established in 1948.
• The WTO is the world's largest international economic organization, with 164 member states representing over 98% of global trade and global GDP.

Additional Information

New Development Bank: 

• The New Development Bank, formerly referred to as the BRICS Development Bank, is a multilateral development bank established by the BRICS states.
• The bank is headquartered in Shanghai, China.

 World Economic Forum (WEF):

• The World Economic Forum (WEF) is an international non-governmental and lobbying organisation based in Geneva, Switzerland.
• It was founded on 24 January 1971.

Organisation for Economic Cooperation and Development: 

• The Organisation for Economic Co-operation and Development is an intergovernmental organization with 38 member countries, founded in 1961 to stimulate economic progress and world trade.
• It is headquartered in France.

The correct answer is Both I and II.

Key Points

• The Eighth Schedule to the Constitution of India lists the official languages of the Republic of India.
• As per Articles 344(1) and 351 of the Indian Constitution, the eighth schedule includes the recognition of the 22 languages.
• The Eighth Schedule to the Constitution comprises the following 22 languages:

           (1) Assamese, (2) Bengali, (3) Gujarati, (4) Hindi, (5) Kannada, (6) Kashmiri, (7)Konkani, (8) Malayalam, (9) Manipuri, (10) Marathi, (11) Nepali, (12)                 Oriya, (13) Punjabi, (14) Sanskrit, (15) Sindhi, (16) Tamil, (17) Telugu, (18) Urdu (19) Bodo, (20) Santhali, (21) Maithili and (22) Dogri.

• Of these languages, 14 were initially added to the Constitution.
• The Sindhi language was added in 1967.
• Konkani, Manipuri, and Nepali were included in 1992.
• Bodo, Dogri, Maithili, and Santhali were added in 2004.
• Currently, there are six languages that enjoy the ‘Classical’ status in India:
• Tamil (declared in 2004), Sanskrit (2005), Kannada (2008), Telugu (2008), Malayalam (2013), and Odia (2014).
• All the Classical Languages are listed in the Eighth Schedule of the Constitution.

The correct answer is P. T. Usha.

Key Points

• P. T Usha is a retired Indian track and field athlete.
• She has won 4 Asian gold medals and 7 Silver medals.
• She is often called the "Queen of Indian track and field".
• On 6 July 2022, she was nominated to the Rajya Sabha by President Ram Nath Kovind.
• She is also nicknamed Golden Girl.

Additional Information

Pradip Kumar Banerjee ​

• Pradip Kumar Banerjee was an Indian professional footballer who played as a striker for the Indian national football team.
• He was one of the first recipients of the Arjuna Award when the awards were instituted in 1961.

Milkha Singh ​

• Milkha Singh also known as The Flying Sikh, was an Indian track and field sprinter.
• He is the only athlete to win gold in 400 meters at the Asian Games as well as the Commonwealth Games.

Hima Das

• Hima Das, nicknamed Dhing Express, is an Indian sprinter from the state of Assam.
• She is the first Indian athlete to win a gold medal in a track event at the IAAF World U20 Championships.

The correct answer is Narmadapuram

Key Points

• Hoshangabad, officially Narmadapuram, is a city and municipality in the Indian state of Madhya Pradesh.
• It is located in central India, on the south bank of the Narmada River.
• The city is famous for its beautiful ghats along the banks of the Narmada river, Sethani ghat is a major attraction.

Additional Information

• The city was earlier called Narmadapur after the Narmada river. Later the name was changed to Hoshangabad after Hoshang Shah Gori, the first ruler of the Malwa Sultanate.
• Hoshangabad district was part of the Nerbudda (Narmada) Division of the Central Provinces and Berar, which became the state of Madhya Bharat (later Madhya Pradesh) after India's independence in 1947.
• Tawa Reservoir is a large reservoir on the Tawa River in the Hoshangabad district.

The correct answer is I and II

Key Points

• 42^nd Amendment Act, 1976 is one of the most important amendments to the Indian Constitution.
• It was enacted by the Indian National Congress headed by Indira Gandhi.
• It is also known as ‘Mini-Constitution.
• By this amendment Act Terms- Socialist, Secular and Integrity were added to the Preamble.

Additional Information

42^nd Amendment Act, 1976:

• It laid down Fundamental Duties for citizens.
• Through the amendment  five subjects were transferred from the state list to the concurrent list:

1. Education
2. Forests
3. Weights & Measures
4. Protection of Wild Animals and Birds
5. Administration of Justice

The correct answer is Barbados

Key Points

• Barbados is an island country in the Lesser Antilles of the West Indies, in the Caribbean region of the Americas, and the most easterly of the Caribbean Islands.
• Its capital and largest city is Bridgetown.
• On 30 November 2021, Barbados transitioned to a republic within the Commonwealth of Nations.

Additional Information

Antigua and Barbuda

• Antigua and Barbuda is an independent Commonwealth country comprising its 2 namesake islands and several smaller ones.
• Antigua and Barbuda became an independent state within the Commonwealth of Nations on 1 November 1981.

Trinidad and Tobago

• Trinidad and Tobago is a dual-island Caribbean nation near Venezuela.

Dominica

• Dominica is a mountainous Caribbean island nation with natural hot springs and tropical rainforests.
• The capital, Roseau, is located on the western side of the island.

The correct answer is Bhubaneswar.

Key Points

• The 2018 Men's Hockey World Cup was the 14^th edition of the Hockey World Cup.
• It was held from 28 November to 16 December 2018, at the Kalinga Stadium in Bhubaneswar, India.
• Belgium won the tournament for the first time after defeating the Netherlands 3–2 in the final.

Additional Information

• The Men's FIH Hockey World Cup is an international field hockey competition organised by the International Hockey Federation (FIH).
• The tournament was started in 1971.
• It is held every four years, bridging the four years between the Summer Olympics.
• Pakistan is the most successful team, having won the tournament four times.
• The Netherlands and Australia have each won three titles, and Germany has won two titles. Belgium and India have both won the tournament once.

The correct answer is Nagaland

Key Points

• An Act has been passed to enable certain special powers to be conferred upon members of the armed forces in disturbed areas in the states of Arunachal Pradesh, Assam, Manipur, Meghalaya, Mizoram, Nagaland and Tripura.
• Nagaland is a mountainous state in northeast India, bordering Myanmar.
• Its capital city is Kohima and its largest city is Dimapur.
• Nagaland with a population of 1,980,602 per the 2011 Census of India, making it one of India's smallest states.
• Disturbed area: in any area within a State extensive disturbance of the public peace and tranquillity, by reason of differences or disputes between members of different religious, racial, language or regional groups or castes or communities, it may, by notification in the Official Gazette, declare such area to be a disturbed area.

Additional Information

Manipur

• Manipur is a state in Northeast India, with the city of Imphal as its capital.
• Meitei language (officially known as Manipuri language) is the most widely spoken language and is also the official language of the state.

Jharkhand

• Jharkhand is a state in eastern India. It's known for its waterfalls, the elegant Jain temples of Parasnath Hill and the elephants and tigers of Betla National Park.
• The state capital of Ranchi is a gateway to the park. It features the 17^th-century Jagannath Temple, a Hindu shrine and the Jharkhand War Memorial.

Chhattisgarh

• Chhattisgarh is a landlocked state in Central India. It is the ninth largest state by area.
• Formerly a part of Madhya Pradesh, it was granted statehood on 1 November 2000 with Raipur as the designated state capital.

The correct answer is The President.

Key Points

• Article 76 of the constitution mentions that he/she is the highest law officer of India.
• As a chief legal advisor to the government of India, he advises the union government on all legal matters.
• The President of India appoints a person who is qualified for the post of Supreme Court Judge.
• Attorney General is appointed by the President on the advice of the government.
• There is no fixed term for the Attorney General of India.

Additional Information

• The Attorney General (AG) of India is a part of the Union Executive.
• He is the highest law officer in the country. He can be part of any court in the Indian Territory.
• He got the right to speak and to take part in the proceedings of both the Houses of Parliament (Read about the difference between Lok Sabha and Rajya Sabha here) or their joint sitting and any committee of the Parliament of which he may be named a member
• He has no right to vote when he participates in the proceedings of the Indian Parliament
• Similar to a Member of Parliament, he also enjoys all powers related to immunities and privileges
• He is NOT considered a government servant.
• He can practise privately too as he is not debarred from private legal practice.

The correct answer is China

Key Points

• Asian Games, 2022 will be a multi-sport event celebrated in Hangzhou, Zhejiang, China.
• Hangzhou will be the third Chinese city to host the Asian Games, after Beijing in 1990 and Guangzhou in 2010.
• On 8 April 2019, the Olympic Council of Asia initially announced that the Games would feature 37 sports, including the 28 mandatory Olympic sports to be contested at the 2024 Summer Olympics in Paris.

Additional Information

• The Asian Games, also known as Asiad, is a continental multi-sport event held every four years among athletes from all over Asia.
• Since the 1982 Games, they have been organized by the Olympic Council of Asia (OCA).
• First Games were organized in 1951 in New Delhi.
• The Games are recognized by the International Olympic Committee (IOC) and are described as the second largest multi-sport event after the Olympic Games.
• The Games were originally scheduled to take place from 10^th to 25^th September, 2022, but the event was postponed due to the Covid-19 pandemic on 6^he May 2022.On 19^th July, 2022, the new dates were announced to be from 23^rd September to 8^th, 2023.

The correct answer is II and III.

Key Points

• 6 out of 28 states have bicameral legislatures, namely Andhra Pradesh, Bihar, Karnataka, Maharashtra, Telangana, and Uttar Pradesh, with the remaining states having a unicameral one.
• The Vidhan Sabha is the lower house and corresponds to the Lok Sabha while the Vidhan Parishad is the upper house and corresponds to the Rajya Sabha of the Parliament of India.
• Article 168 mentions about the Legislative Council in some of the States of our country.

Additional Information

• The State Legislative Assembly, or Vidhan Sabha, is a legislative body in the states and union territories of India.
• 5 union territories are governed directly by the Union Government of India and have no legislative body.
• Each Member of the Legislative Assembly (MLA) is directly elected to serve 5-year terms by single-member constituencies.

The correct answer is Charles Cornwallis.

Key Points

• The Permanent Settlement of Bengal was brought into effect by the East India Company headed by Governor-General Lord Cornwallis in 1793.
• This was basically an agreement between the company and the Zamindars to fix the land revenue.
• He envisaged the creation of a hereditary class of landlords in India. This system was also called the Zamindari System.

Additional Information

Warren Hastings:

• Warren Hastings served as the first Governor of the Presidency of Fort William (Bengal), the head of the Supreme Council of Bengal, and so the first Governor-General of Bengal in 1772–1785.
• He and Robert Clive are credited with laying the foundation of the British Empire in India.

Lord Ripon:

• Lord Ripon was a British politician and Viceroy and Governor General of India who served in every Liberal cabinet between 1861 and 1908.
• Lord Ripon is known for the Resolution of 1882, which would give Indians the right to local self-government.

Lord Dalhousie:

• Lord Dalhousie served as Governor-General of India from 1848 to 1856.
• He introduced the Doctrine of Lapse policy which turned out to be one of the major causes of the Revolt of 1857.

Given:

Number of Girls = 400

Number of boys = 800

Calculation:

Total Number of students = 400 + 800

= 1200

If 60 percent of girls passed in an exam,

then 40% of girls failed in the exam = 40% × 400

= \(\frac{40}{100}\) × 400

= 160

If 30 percent of boys passed in an exam,

then 70% of boys failed in the exam = 70% × 800

= \(\frac{70}{100}\) × 800

= 560

Percentage of students failed in the exam = \(\frac{160+560}{1200}\) × 100

=  \(\frac{720}{12}\) 

= 60%

Answer is 60 percent.

Given:

three lengths 1 m 12 cm, 1 m 8 cm and 3 m 24 cm

Concept used:

HCF - Highest Common Factor

Calculation:

1m = 100cm

Length 1 = 1m 12cm

= 100 + 12

= 112cm

Length 2 = 1m 8cm

= 100 + 8

= 108cm

Length 3 = 3m 24cm

= 300 + 24

= 324cm

HCF ( length 1 , length 2 , length 3 )

= HCF ( 112 , 108, 324 )

= 4cm

Answer is 4cm.

Given:

The ratio of the volumes of the three vessels is 4 : 3 : 1 respectively

The ratio of water to milk in the three vessels is 2 : 3, 3 : 7 and 2 : 5 respectively

Calculation:

The ratio of the volumes of the three vessels is 4 : 3 : 1 

V1 : V2 : V3 = 4 : 3 : 1

Multiply the ratio by 70 and let us assume the Volume be ,

V1 : V2 : V3 = 280 : 210 : 70

Step 1: First mixture

V1 = 280

Ratio of the water to milk is 2 : 3

Quantity of water = \(\frac{2}{5}\) × 280

= 2 × 56

= 112

Quantity of Milk = 280 - 112

= 168

Step 2: Second mixture

V2 = 210

Ratio of the water to milk is 3 : 7

Quantity of water = \(\frac{3}{10}\) × 210

= 3 × 21

= 63

Quantity of Milk = 210 - 63

= 147

Step 3: Third mixture

V3 = 70

Ratio of the water to milk is 2 : 5

Quantity of water = \(\frac{2}{7}\) × 70

= 2 × 10

= 20

Quantity of Milk = 70 - 20

= 50

Step 4: Total Mixture

Mixture of all the three containers are poured into a large container

Total Quantity of water = 112 + 63 + 20 = 195

Total Quantity of milk = 168 + 147 + 50 = 365

The ratio of milk to water in the large container = 365 : 195

= 73 : 39

Answer is 73 : 39.

Given:

The initial ratio of income and expenditure of Vinay is 6 : 5

new savings are Rs. 38000

Formula used:

Income = Expenditure + Savings

Calculation:

Initial ratio of income, expenditure and savings is 6 : 5 : 1

Increased ratio of income and expenditure = 6 × 140% : 5 × 130%

= 6 × 14 : 5 × 13

= 84 : 65

Increased ratio of income, expenditure and savings is 84 : 65 : 84 - 65

= 84 : 65 : 19

Increased Savings 19x = 38000

x = 2000

then, Increased Income 84x = 168000

Initial income × 140% = Increased Income

Initial income × 140% = 168000

Initial income = \(\frac{168000×100}{140}\)

= 120000

Answer is Rs. 120000.

Shortcut Trick

Interest for 3 years (5 − 2) = Rs. 1080 − Rs. 900 = Rs. 180.

Interest for 1 year = Rs. 180 ÷ 3 = Rs. 60.

Principal (P) = Amount after 2 years − (2 × Interest per year) = 900 − 120 = Rs. 780.

Rate (R) = (Interest per year ÷ Principal) × 100 = (60 ÷ 780) × 100 = 7.69%.

∴ The correct answer is 7.69 percent.

Alternate Method

Given: Amount after 2 years (A₂) = Rs. 900, Amount after 5 years (A₅) = Rs. 1080.

Formula Used: Simple Interest (SI) = (P × R × T) ÷ 100; Amount (A) = Principal (P) + SI.

⇒ Simple Interest for 3 years = Rs. 1080 − Rs. 900 = Rs. 180

⇒ Simple Interest for 1 year = 180 ÷ 3 = Rs. 60

⇒ Simple Interest for 2 years = 60 × 2 = Rs. 120

⇒ Principal (P) = Amount₂ − SI₂ = 900 − 120 = Rs. 780

⇒ Annual Rate (R) = (SI × 100) ÷ (P × T)

⇒ R = (60 × 100) ÷ (780 × 1) = 100 ÷ 13

⇒ R ≈ 7.6923%

∴ The correct answer is 7.69 percent.

Additional Information

Calculation of Rate

Rate (R) can be calculated using 100 × Interest ÷ (Principal × Time). Always ensure the interest and time period correspond to each other.

Nature of Simple Interest

In Simple Interest, the interest amount remains constant for every equal time interval, as it is always calculated on the original Principal.

Amount Relation

Amount (A) = P(1 + RT/100). If you have two different amounts for two time periods, the difference in amounts gives the interest for the difference in time.

Given:

The length, breadth and height of a room are in the ratio 6 : 3 : 2 respectively

Formula used:

Curved surface area of a cuboid = 2(length + breadth) × height

Calculation:

Step 1:

The length, breadth and height of a room are in the ratio 6 : 3 : 2

let length, breadth and height be 6cm , 3cm , 2cm

Initial Curved surface area of the room = 2(length + breadth) × height

= 2 ( 6 + 3 ) × 2

= 18 × 2

= 36cm²

Step 2:

The length and height of the room are halved and its breadth is doubled

length = 6/2 = 3cm

height = 2/2 = 1cm

breadth = 3 × 2 = 6cm

Latter Curved surface area of the room = 2(length + breadth) × height

= 2 ( 3 + 6 ) × 1

= 18

= 18cm2

Step 3:

Percentage decrease = \(\frac{36-18}{36}\) × 100

= 100/2

= 50

Percentage decrease in the area of the four walls of the room is 50

Answer is 50.

Additional InformationVolume of a cuboid = length × breadth × height

Total surface area of a cuboid = 2(length × breadth + breadth × height + length × height)

Given:

Cost price of a article = Rs. 2000

he gains 30 percent on one article and looses 50 percent on the other article

Formula used:

Selling Price = Cost Price × ( 100 ± profit or loss )%

Loss% = \(\frac{Cost\ Price - Selling\ Price}{Cost\ Price}\) × 100

Calculation:

Selling Price of the article at 30% gain,

Selling Price = 2000 × ( 100 + 30 )%

= 2000 ×  \(\frac{130}{100}\)

= 2000 × 1.3

= 2600

Selling Price of the article at 50% loss,

Selling Price = 2000 × ( 100 - 50 )%

= 2000 ×  \(\frac{50}{100}\)

= 2000 × 0.5

= 1000

Selling Price of both articles = 2600 + 1000 = 3600

Cost Price of both articles = 2000 + 2000 = 4000

Loss% = \(\frac{Cost\ Price - Selling\ Price}{Cost\ Price}\) × 100

= \(\frac{4000-3600}{4000}\) × 100

= \(\frac{400}{4000}\) × 100

= 10%

Overall loss is 10%.

Answer is 10 percent.

Alternate Method

Given:

Cost price of a article = Rs. 2000

he gains 30 percent on one article and looses 50 percent on the other article

Formula used:

Loss% = \(\frac{Cost\ Price - Selling\ Price}{Cost\ Price}\) × 100

Calculation:

Percentage is asked in the question so don't take amount in consideration

Let Cost Price be 100

Selling Price of the article at 30% gain,

Selling Price of first article = 130

Selling Price of the article at 50% loss,

Selling Price of second article = 50

Total Cost Price = 200

Total Selling Price = 130 + 50 = 180

Loss% = \(\frac{200 - 180}{200}\) × 100

= \(\frac{20}{200}\) × 100

= 10%

Overall loss is 10%.

Answer is 10 percent.

Shortcut Trick

Total CP = 2000 + 2000 = 4000

Total SP = (2000 + 0.3 × 2000) + (2000 - 0.5 × 2000)

⇒ Total SP = 2600 + 1000 = 3600

∴ Overall Loss % = \(\frac{{4000 - 3600}}{{4000}} \times 100 \) = 10%

Given:

\(K = \sqrt 3 + \sqrt 2 \)

Calculation:

\(K = \sqrt 3 + \sqrt 2 \)

\(K^2 = 3 + 2 + 2\sqrt6\)

\(\frac{1}{K} =\frac{1}{ \sqrt 3 + \sqrt 2 }\)

Taking conjugate,

\(\frac{1}{K} =\frac{1}{ \sqrt 3 + \sqrt 2 }\)  ​×  \(\frac{\sqrt 3 - \sqrt 2 }{ \sqrt 3 - \sqrt 2 }\)

\(\frac{1}{K} =\frac{\sqrt 3 - \sqrt 2}{ 3^2 - 2^2 }\)

\(\frac{1}{K} =\frac{\sqrt 3 - \sqrt 2}{1}\)

\(\frac{1}{K^2} = 3 + 2 - 2\sqrt6\)

\({K^2} + \frac{1}{{{K^2}}}\) = \(3 + 2 + 2\sqrt6 + 3 + 2 - 2\sqrt6\)

= 10

Answer is 10.

Shortcut Trick

When Selling Prices are equal, the ratio of Cost Prices is inversely proportional to their respective Selling Price percentages.

CP₁ (at 25% loss) : CP₂ (at 25% profit) = (100 + 25) : (100 − 25)

CP₁ : CP₂ = 125 : 75 = 5 : 3

Total ratio parts = 5 + 3 = 8 parts → Rs. 1056

CP of watch sold at loss (CP₁) = (1056 ÷ 8) × 5 = 132 × 5 = 660

∴ The correct answer is Rs. 660.

Alternate Method

Given:

Total Cost Price = Rs. 1056

Loss percentage on the first watch = 25%

Profit percentage on the second watch = 25%

Selling Price of both watches is the same.

Formula Used:

Selling Price (SP) = CP × (100 ± Profit/Loss)%

Calculation:

⇒ Let the cost price of the first watch be CP₁ and the second watch be CP₂.

⇒ Selling price of the first watch (SP₁) = CP₁ × (100 − 25)% = 0.75 × CP₁

⇒ Selling price of the second watch (SP₂) = CP₂ × (100 + 25)% = 1.25 × CP₂

⇒ Since SP₁ = SP₂

⇒ 0.75 × CP₁ = 1.25 × CP₂

⇒ CP₁ ÷ CP₂ = 1.25 ÷ 0.75 = 125 ÷ 75 = 5 ÷ 3

⇒ Let CP₁ = 5x and CP₂ = 3x

⇒ Total CP = 5x + 3x = 8x

⇒ 8x = 1056

⇒ x = 1056 ÷ 8 = 132

⇒ Cost price of the watch sold at a loss = 5x = 5 × 132 = 660

∴ The correct answer is Rs. 660.

Additional Information

Overall Loss Concept (Equal SP)

If two items are sold at the same price, one at a profit of x% and the other at a loss of x%, there is always an overall loss. Loss % = (x ÷ 10)² %.

Ratio of Cost Prices (Equal SP)

When Selling Prices are equal, the Cost Prices are inversely proportional to their respective Selling Price percentage values: CP₁ : CP₂ = (100 ± x₂) : (100 ± x₁).

No Profit No Loss Concept (Equal CP)

If two articles are bought for the same Cost Price and sold at x% profit and x% loss respectively, there is neither profit nor loss in the overall transaction.