DSSSB Personal Assistant 27 November 2021 Shift 1 (Previous Year Paper)

The logic followed here is:

​Thus, CXX is the wrong term in the given series.

​Hence, the correct answer is "CXX".

The logic followed here is:

Thus, 'ZAX' will complete the given series.

Hence, the correct answer is "ZAX".

The logic followed here is:

• HIM ∶ SFK

​

Similarly,

• PAN ∶ ?

​

Thus, 'PAN' can be written as 'TXS'.

Hence, the correct answer is "TXS".

The logic followed here is:

(Total number of letters present in 1^st word) × (Total number of letters present in 2^nd word) = Number

• ‘PHONE × MEAN’ is written as ‘20

​

• ‘FACT × HARDEST’ is written as ‘28

​

Similarly,

• ‘ANY × TIME’

​

Thus, '‘ANY × TIME’' will be written as '12'.

Hence, the correct answer is "12".

Statements:

I. Some men are human.

II. No animal is human.

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

Conclusions:

I. Some men are not animal → True (Because ' No animal is human' and 'Some men are human'; which means the men that are human are not animal, so it is true)

II. No human is animal → True (Because 'No animal is human', so 'No human is animal' is definitely true)

Hence, the correct answer is "All conclusion follows".

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

According to the given information :

J is the mother of R. K is the only child of F and L. M is the brother of R and L.

Thus, the following family tree can be drawn :

On checking each

Statement:

I. L is the father of K

→ Here, the gender of L is not definite, so we can not conclude that L is father of K.

Thus, statement I is not correct.

II. J is the mother of L

→ Here, J is mother of M and M is brother of L, so J is also the mother of L.

Thus, statement II is correct.

III. L can be the daughter of J

→ Here, the gender of L is not definite, so it can be the daughter of J.

Thus, statement III is correct.

Clearly, Statement II and Statement III are correct.

Hence, the correct answer is "II and III".

,The logic followed here is:

• POEM ∶ RIRR

​

Similarly,

• TIRX ∶ CVLV

​

​Thus, TIRX ∶ CVLV is related to POEM ∶ RIRR.

Hence, the correct answer is "TIRX ∶ CVLV".

The logic followed here is:

1^st word is "the item" and 2^nd word is "collection of those items".

According to the given information:

Cup ∶ Crockery → Cup is a type of Crockery.

Similarly

​Sharpener ∶ Stationery → Sharpener is a type of Stationery.

Hence, the correct answer is "​Sharpener ∶ Stationery".

According to the given information: 

In a row at a bus stop, ‘A’ is 7^th from the left and ‘B’ is 9^th from the right.

If they both interchange their positions, A becomes 11^th from the left.

Total number of people in the row = Position of B before interchange + Position of A after interchange - 1

= 9 + 11 - 1

= 19

Thus, the total number of people in the row are '19'.

Hence, the correct answer is "19".

Alternate Method According to the given information: 

In a row at a bus stop, ‘A’ is 7^th from the left and ‘B’ is 9^th from the right.

If they both interchange their positions, A becomes 11^th from the left.

Total number of people in the row = (no.of people before B) + (no. of people after A) + (no. of People between B and A) + A +B

= 6 + 8 + 3 +1 + 1

= 19

Thus, the total number of people in the row are '19'.

Hence, the correct answer is "19".

The logic followed here is:

Thus, 'CQ23' will complete the given series.

Hence, the correct answer is "CQ23".

According to the given information:

A team of 5 or 6 members is to be formed from

6 boys ∶ B1, B2, B3, B4, B5 and B6 and 5 girls ∶ G1, G2, G3, G4 and G5.

Given :  Minimum two boys should be in the team.

1) B2 and G5 should be in the same team.

2) Either G1 or G2 should be in the team.

Possible cases:

3) G1 and G4 should not be in the same team. 

Possible cases:

4) Only one among G2, B3 and B6 should be selected.

Possible cases:

5) G4 can be selected with either B1 or B5.

Possible cases:

 

It is given that the team should have 5 or 6 members. So, after satisfying all the conditions, 

• B4 and G3 can be selected in Case I, Case II and Case III.
• B5 and G3 can be selected in Case IV.

​Thus we have,

On checking the given combinations of teams :

I. G4 B1 B2 G5 B6 B5

⇒ Here G4 is selected with both B1 and B5. Thus,it does no satisfy condition (5) i.e. G4 can be selected with either B1 or B5. So, it can not represent as a team.

II. B1 G1 B6 B4 G4

⇒ Here, G1 and G4 both are selected in one team. Thus it does no satisfy condition (3) i.e. G1 and G4 should not be in the same team. So, it can not represent as a team.

III. G3 G2 G5 B2 B5 G4

⇒ This team is same as the team in Case IV. Thus, these members can represent the members of the team.

IV. B4 B3 G1 G3 B2 G5

**⇒**This team is same as the team in Case I. Thus, these members can represent the members of the team.

Hence, the correct answer is "III and IV".

Table shows the positional values of letters :  

 

The logic followed here is:

Hence, the correct answer is "HFLM"

The logic followed here is:

The number is obtained by adding the digits of resultant number, obtained by adding the positional value of every letters.

• ‘JUDGE’ is written as ‘11’

Similarly,

• ‘MAJOR’ will be written as :

​

Thus, 'MAJOR' is written as '12'.

Hence, the correct answer is "12".

The logic followed here is :

   

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

The logic followed here is:

• PONG ∶ NPLH

​Similarly,

• HATE ∶ ?

​

Thus, 'HATE' can be written as 'FBRF'.

Hence, the correct answer is "FBRF".

The logic followed here is:

The number is obtained by multiplying the the sum of the positional value of first two letters and last two letters.

 ‘OKEY’ is written as ‘780’

 ‘WISE’ is written as ‘768’

Similarly,

‘COKE’ is written as :

Thus, 'COKE' will be written as '288'.

Hence, the correct answer is "288".

According to the given information :

8 boys A, B, C, D, E, F, G and H are sitting in a row facing towards north (not necessarily in the same order).

• E is the immediate neighbour of B and F.
• Only 4 boys are sitting between C and E. C is towards the right of E.
• A is second to the left of D.
• If H is not towards the right of E. Then, there are two possibilities:

Thus, the final arangemnet will be:

On checking each statement one by one :

I. 3 boys can sit between B and G

→ According to Case 1, it is true that  3 boys can sit between B and G.

Thus, statement I is correct.

II. H is fourth to the left of A

→ According to both the Cases, it is true that H is fourth to the left of A.

Thus, statement II is correct.

III. 2 boys can sit between C and A

→ According to both the Cases, it is true that 2 boys can sit between C and A.

Thus, statement III is correct.

IV. G is to the immediate left of A

→ According to both the Cases, G is to the immediate right of A

Thus, statement IV is not correct.

Hence, the correct answer is "Only IV".

Table shows the positional values of letters :

The logic followed here is that each alphabet is changing to it's opposite alphabet diagonally according to the English alphabet series.

Letters are replaced by Reverse letters.

• FOUGHT is written as "GSTFLU"

• JACKET is written as "GVPXZQ"

Similarly,

• NICELY is written as "BOVXRM"

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

Additional Information

Statements:

I. No Q is R.

II. No F is Q.

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

Conclusions:

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

II. Some Q are not F → True (Because 'No F is Q', so some Q are not F is definitely true)

III. No R is Q → True (Because  'No Q is R', no R is Q is definitely true)

Hence, the correct answer is "Both conclusion II and III follows".

The logic followed here is:

The number is obtained by adding the positional values of opposite letters of given word. 

• ‘BUNCH’ is written as ‘87’

​

• ‘CROWN’ is written as ‘62’

​

 

Similarly,

• ‘DRAWN’ is written as :

​

​Thus, ‘DRAWN’ is written as '75'.

Hence, the correct answer is "75".

As per the given information, 

the given venn diagram :

On checking each option one by one :

1) Number of cup which are not bottle are 17

→The shaded part represents the number of cup which are not bottle = 3 + 8 +6 = 17

Thus, this statement is correct.

2) Total number of cup are 11

→ The shaded part represent the total number of cup = (8 + 6 + 3 + 2 + 3) ≠ 11

Thus, this statement is not correct.

3) Total number of glass are 34

→ The shaded part represent the total number of glass = (11 + 8 +3 + 9) = 31 ≠ 34

Thus, this statement is not correct.

4) Number of bottle which are atleast glass are 5

→ The shaded part represent the number of bottle which are atleast glass = 3 ≠ 5

Thus, this statement is not correct.

Hence, the correct answer is "Number of cup which are not bottle are 17".

The logic followed here is :

1. Figure 1 has three symbols and all of them are arranged in a vertical line at the middle.

2. Figure 2 has the same three symbols, but the position of all the symbols get changed.

Let us first give numbering to the three symbols starting from 1 to 3 as :

Now,

In the first part of the question,

Figure (1) has three symbols and in Figure (2) the symbol at 1^st position goes to 3^rd, the symbol at 2^nd position goes to 1^st, and the symbol at 3^rd position goes to 1^st position respectively.

Figure 1 to Figure 2 →

Similarly,

​In the second part of the question,

Figure (3) has three symbols and in Figure (4) the symbol at 1^st position will go to 3^rd, the symbol at 2^nd position will go to 1^st, and the symbol at 3^rd position will go to 2^nd position respectively.

Figure 3 to Figure 4 →

​Thus, the final arrangement will be:

Hence, the correct answer is "option 1".

The logic followed here is :

Two figures are given i.e. a pentagon and a right angled triangle and both the figures are filled with the horizontal line.

The logic is followed by options (2) only.

 

Option(2) has a rectangle and it is filled with the horizontal lines. Thus, it follows the same logic that is being followed by the given two figures.

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

As per the information:

When the question figure is merged with the figure in option (3), the complete pattern can be seen as :

 

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

The logic followed here is:

In each column:

(1^st number + 3^rd number) ×  2^nd number = 4^th number

• Column 2:

(11 + 8) × 12 = 228 = 4^th number

• Column 3:

(19 + 15) × 3 = 102 = 4^th number

Similarly,

• Column 1:

(7 + 9) × 14 = 224 = 4^th number

Hence, the correct answer is "224".

The logic is here as:

Total number of pieces obtained with X cuts in x axis, Y cuts in y axis and Z cuts in z axis = (X+1) × (Y+1) × (Z+1)

If we cut 8 equal cube each axis of a big cube = 9 × 9 × 9 = 729

Hence, "729" is the correct answer.

Now check all the options:

Option 1 : 9 + 4 ÷ 1 × 8 – 7 = 2

After interchanging the 1 and 4,

=> 9 + 1 ÷ 4 × 8 – 7 = 2

=> 9 + 0.25 × 8 – 7 = 2

=> 9 + 2 – 7 = 2

=> 11 – 7 = 2

=> 4 = 2 (Incorrect)

Option 2 : 7 + 1 ÷ 2 × 4 – 3 = 7

After interchanging the 1 and 4,

=> 7 + 4 ÷ 2 × 1 – 3 = 7

=> 7 + 2 × 1 – 3 = 7

=> 7 + 2 – 3 = 7

=> 9 – 3 = 7

=> 6 = 7 (Incorrect)

Option 3 : 7 + 1 ÷ 4 × 8 – 2 = 33

After interchanging the 1 and 4,

=> 7 + 4 ÷ 1 × 8 – 2 = 33

=> 7 + 4 × 8 – 2 = 33

=> 7 + 32 – 2 = 33

=> 39 – 2 = 33

=> 37 = 33 (Incorrect)

Option 4 : 9 + 1 ÷ 4 × 8 – 2 = 39

After interchanging the 1 and 4,

=> 9 + 4 ÷ 1 × 8 – 2 = 39

=> 9 + 4 × 8 – 2 = 39

=> 9 + 32 – 2 = 39

=> 41 – 2 = 39

=> 39 = 39 (Correct)

Hence, the correct `answer is Option 4: “9 + 1 ÷ 4 × 8 – 2 = 39”.

Statements:

I. Some G are D.

II. No K is M.

III. No M is G.

The least possible diagram for the given statements is as follows

Conclusions:

I. Some M are not K → True (because statement given no K is M so definitely some M are not K)

II. Some G are not M → True (because statement given no M is G so definitely some G are not M)

III. Some D are not M → True (As it is given that some G is D and no G is M, Hence D which are G can never be M.)

Hence, “All conclusions follow".

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

• The left side row moves downward

• The Right side row moves upward

• Upper middle and Lower middle shape interchange their positions.

• dark shape become light and light shape become dark.

• Middle both arrows change their direction in each step.

The final series is:

Hence, ‘option 3’ is the correct answer.

Now check all the options:

Option (1)  Number of guava which are only grapes are 10 → Ture

Option (2)  Total number of tomato are 34 → True

=> 8 + 9 + 11 + 6 = 34

Option (3)  Number of grapes which are not tomato are 13 → True

Option (4)  Number of tomato which are neither grapes nor guava are 9 → False

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

Statements:

I. Some red are yellow.

II. Some pink are orange.

III. All red are orange.

The least possible diagram for the given statements is as follows

Conclusions:

I. Some red are pink → False (Because no direct relationship given between Red and Pink so it may be possible but not defined)

II. Some orange are pink → True (Because statement given some pink are orange so some orange are also pink)

III. Some yellow are red → True (Because statement given some red are yellow so some yellow are also red)

Hence, “Both conclusions II and III follow".

The pattern followed here is:

Here the prime numbers are alternatively subtracted and added in this series.

Here, 584 is the wrong term

Hence, '584' is the correct answer.

Note:  Prime number is a number that is divisible only by itself and 1. 

Here prime numbers are 23, 29, 31, 37 etc. 25, 27, 35  are not  prime numbers because they have more than 1 divisor.

The logic followed here is:

• All figures are in different directions.

​Option (1): 

→ All figures are in different directions.

Option (2): 

 → All figures are in different directions.

Option (3): 

 → All figures are in different directions.

Option (4): 

 → Two figures are in the same direction.

Hence, "option (4)" is the odd figure.

Statements:

I. No T is K.

II. No F is N.

III. No N is T.

The least possible diagram for the given statements is as follows

Conclusions:

I. No K is F → False (Because no direct relationship given between K and F so it may be possible but not defined)

II. All T are F → False (Because no direct relationship given between T and F so it may be possible but not defined)

III. No N is F → True (Because statement given No F is N so definitely no N is F)

Hence, “Only conclusion III follows".

I. Number of bike which are not green are 14. → True

The shaded part represents the total number of bike which are not green.

So, the total number of bike which are not green = 8 + 6 = 14

II. Number of yellow which are green are 15 → False

The shaded part represents the number of yellow which are green.

The number of yellow which are green = 15 + 3 = 18

Hence, the correct answer is 'Option 02' i.e. Only Statement II is incorrect.

The Venn diagrams best represent the relationship between - 

     ♦   Red, Colour, Lion

Red is a colour and a lion is a animal.

Hence, ‘option 1’ is the correct answer.

The correct water image of the given figure :

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

According to the given information :

The shaded part represents the number of brown are not white.

 

• The number representing  the number of  brown are not white = 14 + 7 = 21

Hence, ‘21 ' is the correct answer.

The logic followed here is:

Hence the correct answer is "option(1)"

Opposite surface of the open dice can be found by the below method:-

• Alternate surfaces are opposite to each other.
• No two opposite surface are touched by side or by corners

So, by using the above rule we can find the opposite surface of open dice.

Below are the opposite surfaces:-

Note:

• Two opposite faces are never seen together or adjacent to each other.

Option (1): 

  X and  2 are opposite faces but here they are seen together which is wrong. Thus this cube cannot be made.

Option (2): 

  G and  9 are opposite faces but here they are seen together which is wrong. Thus this cube cannot be made.

Option (3): 

  A and 7 are opposite faces but here they are seen together which is wrong. Thus this cube cannot be made.

Option (4): 

None of the opposite faces are seen together nor they are adjacent to each other. Thus this cube can be made.

Hence, ‘Option (4)’ is the correct answer.

The correct answer is 'Only II'.

Key Points

Let's have a look at all options:

• Atomic Number
• ​The atomic number of an atom is equal to the number of protons in the nucleus of an atom or the number of electrons in an electrically neutral atom.
• Hence, Atomic Number = Number of Protons = Number of electrons. Therefore, the relation given in option 1 is incorrect.
• Mass Number
• ​The mass number is the sum of the number of protons and neutrons in an atom.
• Hence, Mass Number = Number of protons + Number of neutrons. Therefore, the relation given in option 2 is correct.

Additional InformationLet's see an example:

• The atom of Carbon (C) contains 6 protons, 6 neutrons, and 6 electrons.
• Therefore, the Atomic Number is 6. It can be denoted as ₆C.
• And the Mass Number is 12. It can be denoted as ¹²C.

The correct answer is 'Spread'.

Key PointsSpread:

• A bank earns money from the interest it receives on loans and other assets, and it pays out money to customers who make deposits into interest-bearing accounts.
• Bank spread is the difference between the interest rate that a bank charges a borrower and the interest rate a bank pays a depositor.
• The ratio of money a bank receives to money it pays out is called the bank spread.
• Thus, the difference between the borrowing rate and the lending rate in commercial banks is called Spread.
• Spread = Borrowing Rate - Lending Rate.
• The bank spread can indicate a bank’s profit margin.
• Let's see an example:
• Consider a bank that lends money to customers at an average rate of 8 percent.
• At the same time, the interest rate the bank pays on funds that customers deposit into their personal accounts is 1 percent.
• The net interest spread of that financial institution would be = 8 - 1 = 7, resulting in a bank spread of 7 percent.

Important PointsLet's have a look at other options:

• Profit
• ​It is the difference between Selling Price and Cost Price.
• Profit = Selling Price - Cost Price
• Here, the Selling Price is always greater than Cost Price.
• Loss
• ​It is the difference between Cost Price and Selling Price.
• Loss = Cost Price - Selling Price
• Here, the Cost Price is always greater than the Selling Price
• Float
• ​In financial terms, the float is money within the banking system that is briefly counted twice due to time gaps in registering a deposit or withdrawal.
• The float is essentially double-counted money: a paid sum which, due to delays in processing, appears simultaneously in the accounts of the payer and the payee.
• Float = Firm's available balance – Firm's book balance

The correct answer is 'Madurai'.

Key PointsPandya Dynasty:

• The Pandya dynasty was a dynasty of ancient India.
• It ruled India from 560 to 1300 AD.
• His kingdom was spread over the districts of Mriduraramnad (Madurai in present) and Trinevali.
• Their capital was Madura, which in the Tamil language refers to Mathura.
• It is also said on the basis of legend that the Pandya rulers were the children of Kuruvanshi and the Pandavas of Mahabharata.
• The first mention of the Pandyas was made by Megasthenes in his work Indika.
• According to him, women ruled in the Pandya country.

Additional Information

• Kaveripattinam, the chief port of the ancient Chola kingdom, was situated at the mouth of the Kaveri river.
• It is today identified with Puhar, a town in the Nagapattinam district of Tamil Nadu.
• King Karikala was the founder of Puhar.

The correct answer is 'Varanasi'.

Key PointsKashi Vishwanath Temple: 

• Kashi Vishwanath Temple is one of the 12 Jyotirlingas.
• This temple of Lord Shiva is one of the ancient Hindu temples,
• It is located in the city of Varanasi, Uttar Pradesh, and situated on the western bank of the river Ganges.
• Kashi Vishwanath Temple has a special place in Hinduism.
• The present temple was built by Maharani Ahilya Bai Holkar in the year 1780.

Thus, the correct answer is Varanasi.

Important PointsLet's have a look at other options:

The correct answer is 'Only I'.

Key Points Minimum Support Price (MSP)

• The MSP is the rate at which the government purchases crops from farmers to safeguard their interests. Thus, statement II is correct.
• It is based on a calculation of at least one-and-a-half times the cost of production incurred by the farmers.
• The Government of India announces MSP for 22 major agricultural commodities each year in both crop seasons after taking into account the recommendations of the Commission for Agricultural Costs and Prices (CACP).
• Thus, the statement I is incorrect.

Thus, the correct answer is Only I.

The correct answer is 'I, II and III'.

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

• Mahogany Tree
• Mahogany can be found throughout much of southern Mexico, Central America, and South America.
• It is chiefly a tropical rainforest tree found in Amazon Forests.
• It can be 200 feet tall and can live up to 350 years.
• With leaves that can reach lengths of 20 inches, it has earned its “big-leaf” name.
• This majestic tree is an integral part of the rainforest ecosystem and is an important resource for local communities.
• Ebony Tree
• Ebony is an evergreen tree that grows in tropical rainforests.
• The ebony trees can reach 65 to 98 feet in height.
• They can be found in Sri Lanka, India, West Africa and Indonesia.
• Dark heartwood of ebony trees has application in numerous industries because of its durability and strength.​
• Rosewood Tree
• ​Rosewood Tree is found in various tropical rain forests native to Brazil, Honduras, Jamaica, Africa, and India.
• Its height is up to 125 feet.
• Rosewood is a deep, ruddy brown to purplish-brown colour, richly streaked and grained with black resinous layers.

Additional InformationTropical Rain Forests:

• Tropical evergreen forest is the one type of forest, which is formed by evergreen forest.
• It occurs in a region where rainfall is more than 200 cm.
• The temperature of tropical evergreen forests is 15 - 30ºC.
• The Amazon is the world’s largest tropical evergreen forest.
• The tropical evergreen forest has a rich source of fauna (all animal life) and flora (all plant life).

The correct answer is 'Only I'.

Key PointsCharcteristics of Monopoly​

1. Same producer or seller-

• There should be only one producer, producer, or seller of a commodity.
• However, there may be more buyers of the item. Thus, statement II is incorrect.

2. Complete control over supply-

• The monopolist has complete control over the supply of the commodity.
• That is, monopolistic firms or industries can alter their supply as per their wish.

3. Complete control over the price-

• The monopolist has complete control over the price of the goods manufactured by him.
• It can be said that a monopoly firm is a price maker. Thus, statement I is correct.

4. Prohibition of entry of new firms-

• No new firm can enter the monopoly.
• The monopolist is absolutely sure that no new firm will be able to compete with him in the near future.
• Barriers to the entry of firms such as statutory barriers by patents, the ability to prevent new firms from flourishing, etc.

5. The elasticity of demand is zero-

• In a monopoly, the elasticity of demand for the monopoly commodity is zero.
• Because buyers have no other option than this.
• If it is an essential item, then they have to buy that item at any cost.

6. Price Differentiation-

• In some cases, a monopolist can sell his goods to different people, at different places, and at different prices.

The correct answer is '63 mm × 129 mm'.

Key PointsFeatures of 20 rupees note of the Mahatma Gandhi (new) series -

• Motif: Ellora Caves (Maharashtra)
• Colour: Greenish Yellow
• Size: 63 mm × 129 mm
• Signature: Governor, Reserve Bank of India.

Thus, the correct answer is 63 mm × 129 mm.

Important PointsLet's have a look at the size of all currencies:

The correct answer is 'Haryana'.

Key PointsSwang Dance:

• In northern India, this dance is popular mainly in the state of Haryana, also in Rajasthan, Uttar Pradesh and the Malwa region of Madhya Pradesh.
• The Swang is a type of musical drama, in which folktales are dramatized with folk songs, music and dance etc.
• Swang incorporates suitable theatrics and mimicry accompanied by song and dialogue.
• It is dialogue-oriented rather than movement-oriented.
• Religious stories and folk tales are enacted by a group of ten or twelve persons in an open area or an open-air theatre surrounded by the audience.
• In this dance form, the name of Pandit Lakhmi Chand is taken with great respect.
• He has written about 65 songs, hence he is called Suryakavi of Haryana.

Important PointsLet's have a look at other options:

The correct answer is 'Tamil Nadu'.

Key PointsAdiperukku Festival: 

• Aadi Perukku is a Hindu Tamil Festival.
• It is celebrated on the 18^th day of Tamil month in Tamil Nadu.
• It is a monsoon-based festival, mainly celebrated by the people associated with agriculture.
• This festival is celebrated on the banks of river Kaveri or any lake.
• During this time, due to the monsoon, there is enough water in the river, which brings happiness and prosperity to the local people.
• This festival is celebrated in many temples of Tamil Nadu.
• During the puja, people worship Varuna Devi for rain, so that the rains are good and yield good crops.
• On this day women worship Goddess Pachai Amma. She is considered a symbol of peace and harmony.

Important PointsLet's have a look at other options:

The correct answer is Option 4.

Key Points

• Epithelial tissue has a free surface, which faces either a body fluid or the outside environment and thus provides a covering or a lining for some part of the body
• On the basis of structural modification of the cells, the simple epithelium is further divided into three types.
• These are,
• Squamous
• Cuboidal
• Columnar
• Glandular

Additional Information 

• Squamous: The squamous epithelium is made of a single thin layer of flattened cells with irregular boundaries.
• Cuboidal: The cuboidal epithelium is composed of a single layer of cube-like cells.
• Columnar: The columnar epithelium is composed of a single layer of tall and slender cells.
• Glandular: Some of the columnar or cuboidal cells get specialised for secretion and are called the glandular epithelium. Glandular epithelial tissue covers glands of the body and is involved in secretion.

The correct answer is Option 2.

Key Points

• Most plants have roots, stems, and leaves. These are called the vegetative parts of a plant.
• The young plant grows vigorously and continues to grow till it attains a definite shape and size with its vegetative parts (roots, stem, leaves) well developed.
• This phase of the life cycle represents the young or the juvenile phase.

Additional Information 

• When we use the vegetative parts for propagating crops or ornamental plants it is termed artificial vegetative propagation.
• Stems, roots, leaves, and even buds are variously modified to suit this requirement. This is called natural vegetative reproduction.

The correct answer is Dekhni.

Key Points

• Deknni is a semi-classical Goan dance form.
• Dekhni in Konkani language means “bewitching beauty”.
• Dekhni dance associated with those people who converted to Christianity from Hinduism during Portuguese rule.
• It is a dance combined with graceful movements and peaceful remedies.
• Only two or three dekhni songs, composed and scored a long time ago, are extant.

Additional Information 

• Yakshagana: Yakshagana is a theatrical dance-art form famously performed in Coastal Karnataka.
• Chhau: Chhau is a major dance tradition of eastern India.
• Tharu: The Tharu people are an ethnic group indigenous to the Terai in southern Nepal and northern India.

The correct answer is Andhra Pradesh​.

Key Points

• This bifacial drum-like instrument is found in Andhra Pradesh.
• Raunza is a percussion instrument made of wood, leather, and cloth.
• A bifacial drum is held vertically away from the body at a particular angle.
• One drum-head is beaten with two sticks of different shapes and sizes for producing a variety of rhythmic patterns.

Additional Information 

The correct answer is I, II and III.

Key Points

• There are three components of Maps – distance, direction, and symbol.
• A map is a representation or a drawing of the earth’s surface or a part of it drawn on a flat surface according to a scale.
• When many maps are put together we get an Atlas.

Additional Information 

• DISTANCE: 
• ​Maps are drawings, which reduce the entire world or a part of it to fit on a sheet of paper. Or we can say maps are drawn to reduced scales.
• DIRECTION:
• Most maps contain an arrow marked with the letter ‘N’ at the upper right-hand corner.
• This arrow shows the north direction
• SYMBOLS: 
• It is not possible to draw on a map the actual shape and size of different features such as buildings, roads, bridges, trees, railway lines, or a well.
• So, they are shown by using certain letters, shades, colours, pictures, and lines.

The correct answer is Option 1.

Key PointsNational income:

• The national income of a country is defined as the sum total of factor incomes accruing to the residents of that country from the production activity performed by them both within and outside the economic territory in a year.
• The factor incomes are in the form of compensation for employees, rent, interest, and profits.
• There are three angles of looking at national income: 
• The value added angle
• The income distribution angle
• The final expenditure angle.
• The above definition is from the income distribution angle.

Additional Information 

• From the value added angle,
• National Income = Sum total of NVAfc by production units + Net factor income received from abroad
• From the final expenditure angle
• National Income = Final expenditure on goods and services produced in the economic territory - consumption of fixed capital - indirect taxes + subsidies + net factor income from abroad.

The correct answer is 1930.

Key Points

• Gandhi committed a technical breach of the Salt Law on 6^th April 1930, when he picked up the scattered sea salt from the coast to break this Law.
• In this movement farmers, traders and women took part in large numbers.
• The government arrested him in May 1930 and put him in Yervada jail at Poona.

Additional Information 

• The Civil Disobedience Movement, though a failure, was a vital phase in the struggle for freedom.
• It promoted unity among Indians of different regions under the Congress banner.
• It provided an opportunity to recruit younger people and educate them for positions of trust and responsibility in the organization as also in provincial administration, which was captured in the 1937 elections.
• It gave wide publicity to political ideas and methods throughout the country and generated political awareness even in remote villages.

The correct answer is I, II and III.

Key Points

• Exosphere: 
• ​The uppermost layer of the atmosphere is known as the exosphere.
• This layer has very thin air.
• Light gases like helium and hydrogen float into space from here.

Additional Information 

• Our atmosphere is divided into five layers starting from the earth’s surface.
• These are Troposphere, Stratosphere, Mesosphere, Thermosphere, and Exosphere
• Troposphere: Almost all the weather phenomena like rainfall, fog, and hailstorm occur in this layer
• Stratosphere: This layer is almost free from clouds and associated weather phenomena, making conditions most ideal for flying aeroplanes.
• Mesosphere: Meteorites burn up in this layer on entering from space.
• Thermosphere: This layer helps in radio transmission.

The correct answer is Alluvial​.

Key PointsNorthern Plains:

• The great Northern Plains have been formed by alluvium deposits brought by rivers flowing from the Himalayas and the Great Indian Plateau.
• This plain is dead flat, with almost negligible slope.
• The plain is of two types bangar and khadar.
• The Great Northern Plain can be divided into four parts - Western Plain, North Central Plain, Eastern Plain, and Brahmputra Plain.

Additional Information 

• Red Soil: Red soil develops on crystalline igneous rocks in areas of low rainfall in the eastern and southern parts of the Deccan Plateau.
• Laterite Soil: The laterite soils develop in areas with high temperatures and high rainfall.
• Black Soil: Black soil covers most of the Deccan Plateau which includes parts of Maharashtra, Madhya Pradesh, Gujarat, Andhra Pradesh and some parts of Tamil Nadu.

The correct answer is Nitrates​.

Key Points

• Organic impurities are often process-related or drug-related pharmaceutical impurities.
• These types of contaminants are most likely to arise during the synthesis, purification, and storage of the drug substance.
• A few examples include starting materials, by-products, intermediates, degradation products, reagents, ligands, and catalysts.

Additional Information 

• Inorganic impurities often derive from the manufacturing process.
• These impurities are often reagents, ligands, catalysts, heavy or residual metals, inorganic salts, filter aids, or charcoals.
• Inorganic contaminants can be detected and quantified using pharmacopeial standards.
• The third type of impurity in pharmaceuticals is residual solvents. These impurities are residuals of solvents present in the manufacturing process.

The correct answer is Neither I nor II.

Key Points

• Concacaf Gold Cup
• It is the main association football competition of the men's national football teams governed by CONCACAF.
• It determines the continental champion of North America, which includes Central America and the Caribbean.
• The Gold Cup is held every two years.
• Cooch Bihar Trophy
• ​The Cooch Behar Trophy is India's national cricket tournament for under-19 players.
• It has been held annually since the 1945–46 season.
• The trophy was donated by, and named after, the family of the Maharaja of Cooch Behar.

Additional Information

• Beighton Cup is the oldest hockey tournament in India.
• It was Instituted in 1895.
• It is organized by Hockey Bengal earlier called Bengal Hockey Association.
• All India Kumar Surendra Singh Memorial Shooting Championship was started in 2010 and is one of the largest tournaments held in India.
• Kumar Surendra Singh was the President of the NRAI (National Rifle Association Of India) in around 1992.

The correct answer is 76.

Key Points

• Article 76 says that the President shall appoint a person who is qualified to be appointed a Judge of the Supreme Court to be Attorney General for India.
• Duties of the Attorney General- as giving advice to the Government of India on legal matters and performing other duties of a legal character.
• In the performance of his duties, the Attorney General has the right to audience in all courts in the country.
• He/she holds office at the pleasure of the President.

Additional Information

• Article 54 decrees that the President shall be elected by the members of an electoral college consisting of the elected members of both Houses of Parliament and the Legislative Assemblies of the States.
• Article 63 provides for a Vice President of India.
• Article 70 deals with the discharge of functions of the President of India outside of what is mentioned in the constitution as per the Parliament.

The correct answer is 1130-1145.

Key Points

• Anangpal II, popularly known as Anangpal Tomar, was a ruler from the Tomar Rajput dyansty.
• He is known to have established and populated Delhi in the 11^th century.
• Much before the Lal Qila, there was another Red Fort in Delhi called Lal Kot, which was built by Anangpal Tomar in the eighth century.

Additional Information

• The Tomara dynasty ruled parts of present-day Delhi and Haryana in India during the 8^th-12^th centuries.
• They were displaced by the Chahamanas of Shakambhari in the 12^th century, who took over their capital in Delhi.
• Chahamanas were themselves soon displaced by the Ghurid ruler Muhammad of Ghor in 1192 CE.

The correct answer is Jnanpith Award.

Key Points

• The Jnanpith Award is the oldest and the highest Indian literary award.
• It is presented annually by the Bharatiya Jnanpith to an author for their "outstanding contribution towards literature".
• The award is bestowed only on Indian writers writing in Indian languages included in the Eighth Schedule to the Constitution of India and English, with no posthumous conferral.
• Eminent Konkani writer Damodar Mauzo was the latest to be conferred with the 57^th Jnanpith Award 2022 for his novel Karmelin(1991).

Additional Information

• The Vyas Samman is a Hindi language literary award in India, first awarded in 1991.
• It is awarded annually by the K.K. Birla Foundation and includes a cash payout of Rs 4,00,000.
• The Saraswati Samman is an annual award for outstanding prose or poetry literary works in any of the 22 languages of India listed in Schedule VIII of the Constitution of India.
• It was instituted in 1991 by the K. K. Birla Foundation.
• The Sahitya Akademi Award is an annual literary honour in India.
• The Sahitya Akademi, India's National Academy of Letters, confers on writers of the most outstanding books of literary merit.
• The works must be published in any of the 24 major Indian languages.

The correct answer is Discus Throw.

Key Points

• Vikas Shive Gowda is an Indian discus thrower and shot putter.
• He is a Padma Shri awardee in 2017.
• His father, Shive Gowda, coached the 1988 Indian Olympic track team.

Additional Information

• Sushil Kumar won a bronze medal in the men's 66 kg freestyle wrestling category at the 2008 Beijing Olympics. He followed this up with a silver medal at the 2012 London Olympics in the same weight category.
• Neeraj Chopra is the first Asian athlete to win an Olympic gold medal in the men's javelin throw.
• Abhinav Bindra remains the only Indian shooter to have won a gold in the Olympics.

The correct answer is Tony Joseph.

Key Points

• Tony Joseph is an Indian journalist and former editor of Businessworld magazine.
• He is also the author of the best-selling book Early Indians: The Story of Our Ancestors and Where We Came From.
• A hugely influential book, Early Indians authoritatively and bravely put to rest several ugly debates on the ancestry of modern Indians.

Additional Information

• Anna Burns is an author from Northern Ireland.
• Her novel Milkman won the 2018 Man Booker Prize, the 2019 Orwell Prize for political fiction, and the 2020 International Dublin Literary Award.
• Margaret Eleanor Atwood is a Canadian poet, and novelist.
• She is best known for The Handmaid's Tale (1985), a dystopian novel set in New England in the near future.
• George Saunders is an American writer of short stories, essays, novellas, children's books, and novels.
• He is the author of eleven books, including Lincoln in the Bardo, which won the 2017 Man Booker Prize for best work of fiction in English.

The correct answer is Wushu.

Key Points

• Wushu
• Wushu, or Kungfu, is a hard and soft and complete martial art and a full-contact sport.
• Wushu is all set to make its Youth Olympic debut in 2022.

Additional Information

• Water polo is a competitive team sport played in the water between two teams of seven players each.
• Sport climbing (or Bolted climbing), is a form of rock climbing that relies on permanent anchors (or bolts), permanently fixed into the rock for climber protection.
• The sport of sailing is racing other boats around a track or course, marked with floating buoys or other fixed marks.

The correct answer is Saudi Arabia.

Key Points

• The Net-Zero Producers Forum provides an innovative platform for energy-producing countries to work together to develop emission reduction strategies.
• Its members include Canada, Norway, Qatar, Saudi Arabia, and the United States.
• They collectively represent 40 percent of global oil and gas production.
• Saudi Arabia holds 15% of the world's proven oil reserves.

Additional Information

• Qatar holds 1.5% of the world's proven oil reserves.
• Iran holds 9% of the world's proven oil reserves.
• Oman holds 0.3% of the world's proven oil reserves.

The correct answer is Forty second.

Key Points

• One of the most significant amendments to the Indian Constitution is the 42^nd Amendment Act of 1976.
• This act is also known as the "Mini-Constitution" because of the enormous number of amendments it has made to the Indian Constitution.
• Changes to the Preamble-
• It changed the description of India from a "sovereign democratic republic" to a "sovereign, socialist secular democratic republic".
• It also changed the words "unity of the nation" to "unity and integrity of the nation".

Additional Information

• The 44^th Amendment of 1978 removed the right to property from the list of fundamental rights.
• A new provision, Article 300-A, was added to the constitution, which provided that “no person shall be deprived of his property save by authority of law”.
• The First Amendment Act, of 1951 made several changes to the Fundamental Rights provisions of the Indian constitution.
• It provided means to restrict freedom of speech and expression, and validation of zamindari abolition laws.
• it also clarified that the right to equality does not bar the enactment of laws that provide "special consideration" for weaker sections of society.
• The Eleventh Amendment  Act of 1961 provided that the Vice-President shall be elected by the members of an electoral college.
• This electoral college will consist of the members of both Houses of Parliament.
• It dispensed with the earlier requirement of a joint meeting of members of both Houses of Parliament for this.

The correct answer is I, II and III.

Key Points

• Both Assamese and Bengali were part of the original list of scheduled languages in 1950.
• Bengali, generally known by its endonym Bangla, is an Indo-Aryan language native to the Bengal region of South Asia.
• Assamese, also Asamiya, is an Indo-Aryan language spoken mainly in the northeast Indian state of Assam.
• Nepali was added to the eighth schedule in 1992.
• Nepali also known as ‘Gorkhali’ is an Indo-Aryan language of the sub-branch of Eastern Pahari.

Additional Information

• 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 correct answer is Nashik.

Key Points

• In December 2019, an 'Oxygen Parlour' was opened at Nashik railway station.
• The aim is to provide an experience of breathing clean air to the commuters.
• The initiative is the efforts of the Airo Guard in collaboration with the Indian Railways.

Additional Information

• Howrah station in Kolkata is the oldest and largest existing railway complex in India.
• It was completed in 1905.
• It is the busiest railway station in India in terms of train frequency.
• The Royapuram railway station in Chennai is India's oldest surviving railway station.
• The first train left the station in 1856.

The correct answer is The Vice President.

Key Points

• In India, Vice-President has the second-highest office in the country.
• Vice President holds the position for five years.
• He acts as the ex-officio Chairman of Rajya Sabha.
• Article 63 to Article 71 of the Indian Constitution deals with the election, qualification, and removal of Vice Presidents of India.
• The vice president also acts as the chancellor of the central universities of India.
• The current 14^th Vice-President is Jagdeep Dhankhar (August 2022).

Additional Information

• The Prime Minister is the real executive authority or the de facto executive.
• They are the leader of the Lower House i.e. the Lok Sabha.
• The current Prime Minister is Narendra Modi.
• The President of India is the head of the state and the nominal executive authority or de jure executive.
• They are the first citizen of India and a symbol of solidarity, unity, and integrity of the nation.
• The current president is Draupadi Murmu.
• The Attorney General of India (Article 76^th)  is the highest law officer in India.
• As a chief legal advisor to the government of India, he/she advises the union government on all legal matters.
• He/she is also the primary lawyer representing the Union Government in the Supreme Court of India.

The correct answer is Saba Naqvi.

Key Points

• ‘Politics of Jugaad: The Coalition Handbook’ examines the history of coalition governments to project the possibilities of one, as the countdown to the 2019 Lok Sabha election begins.
• It is written by Saba Naqvi, an Indian Journalist, Author, Commentator, and well-popular Political Analyst from New Delhi.
• She has written and published 3 books previously, namely In Good Faith (2012), Capital Conquest (2015), and Shades of Saffron (2018).

Additional Information

• Gurcharan Das is an Indian author, who wrote a trilogy based on the classical Indian goals of the ideal life.
• The books are India Unbound (2002) about artha, The Difficulty of Being Good (2009) about dharma, and Kama: The Riddle of Desire (2018) about desire.
• Vikram Seth is an Indian poet, novelist, and travel writer.
• He is known for his verse novel The Golden Gate (1986) and his epic novel A Suitable Boy (1993).
• Anita Desai née Mazumdar is an English-language Indian novelist and author of children's books.
• She received a Sahitya Akademi Award in 1978 for her novel Fire on the Mountain and the British Guardian Prize for The Village by the Sea.

The correct answer is China.

Key Points

• The Supply Chain Resilience Initiative (SCRI) is a trilateral agreement between India, Japan and Australia.
• It was launched on 27 April 2021 during the COVID-19 pandemic.
• Significance
• Vulnerabilities in the global supply chain were revealed as a piece to the puzzle in light of reliance on China.
• For this reason, Japan, Australia and India are seeking to reduce their dependency on China.
• Thus, China is not a part of it and option 3 is the right answer.

Additional Information

• India's major import partners are -
• China (16 percent of total imports)
• the United States (6 percent)
• United Arab Emirates (6 percent)
• Saudi Arabia (5 percent)
• Switzerland (5 percent).
• The most common destination for the exports of India are -
• United States ($49.7B)
• China ($18.5B)
• United Arab Emirates ($18.1B)
• Hong Kong ($9.18B)
• Germany ($8.8B)$.

The correct answer is II.

Key Points

• Part II of the Indian Constitution deals with Citizenship.
• It includes articles 5 to 11 -
• Art. 5 - Citizenship at the commencement of the Constitution.
• Art. 6 - Rights of citizenship of certain persons who have migrated to India from Pakistan.
• Art. 7 - Rights of citizenship of certain migrants to Pakistan.
• Art. 8 - Rights of citizenship of certain persons of Indian origin residing outside India.
• Art. 9 - Persons voluntarily acquiring citizenship of a foreign State are not to be citizens.
• Art. 10 - Continuance of the rights of citizenship.
• Art. 11 - Parliament to regulate the right of citizenship by law.

Additional Information

• Part I of the Indian Constitution - The Union and Its Territories; Art. 1-4
• Part III of the Indian Constitution - Fundamental Rights; Art. 12-35
• Part IV of the Indian Constitution - Directive Principles of State Policy; Art. 36-51

The correct answer is Lichchhavis.

Key Points

• Licchavi 
• Vardhamana Mahavira was born in Kundagrama, which was a part of the Lichchhavi kingdom.
• The Lichchhavis were a powerful clan of Kshatriyas who ruled over a large territory in what is now Bihar, India.
• Mahavira's father, Siddhartha, was the ruler of the Jnatrika clan, which was one of the most important clans in the Lichchhavi kingdom.
• Vajji Gana Parishad
• Vajji Sangha was an alliance of neighbouring clans including Licchavis and one of the principal Mahajanpadas.
• They ruled the Mithila region in Northern Bihar and had Vaishali as their capital.

Additional Information

• Kusinari or Kushinagar is an important Buddhist pilgrimage site.
• Buddhists believe Gautama Buddha attained Parinirvana after his death.
• Sarnath is a small village in Uttar Pradesh.
• Formerly known as Isipatana.
• It is famous as the site where Buddha preached his first sermon.
• It is also the place where the original Sangha was formed.
• Vaishali is the earliest known example of a stupa.
• The Buddha relic stupa which is said to contain the ashes of the Buddha.
• It contains one of the best-preserved of the Pillars of Ashoka, topped by a single Asiatic lion.

The correct answer is Human Development Report.

Key Points

• Human Development Report
• The Human Development Report (HDR) is an annual Human Development Index report.
• It is published by the Human Development Report Office of the United Nations Development Programme (UNDP).
• India has been positioned at 131 out of 189 countries and territories, according to Human Development Index report 2020.
• Norway ranked 1^st(2020).

Additional Information

• The World Development Report is an annual report published since 1978 by the International Bank for Reconstruction and Development or World Bank.
• Each WDR provides an in-depth analysis of a specific aspect of economic development.
• The Ease of Doing Business (EoDB) index is a ranking system established by the World Bank Group.
• In the EODB index, 'higher rankings' (a lower numerical value) indicate better, usually simpler, regulations for businesses and stronger protections of property rights.
• Global Economic Prospects is a World Bank Group flagship report that examines global economic developments and prospects.
• It is issued twice a year - in January and then in June.

The correct answer is Praveen Sinha.

Key PointsPraveen Sinha:

• In February 2021, Praveen Sinha succeeded RK Shukla as the new interim CBI director.
• In June 2021, he succeeded Rakesh Asthana as the new Special Director of CBI.
• Praveen Sinha is a Gujarat-cadre IPS officer of the 1988 batch.

Additional Information

• Aditya Mishra is a 1989 batch IPS officer of the Uttar Pradesh cadre.
• He was appointed as the Chairman of the Land Ports Authority of India (LPAI) in 2019.
• Ranjit Sinha was an Indian Police Service (IPS) officer of the 1974 batch of the Bihar cadre.
• He was the former Director of the Central Bureau of Investigation for a 2-year tenure from December 2012.
• He was the Director General of Police of the Indo-Tibetan Border Police and the Director General of the Railway Protection Force.
• Rishi Kumar Shukla is a 1983 batch Indian Police Service (IPS) officer of the Madhya Pradesh cadre.
• He served as the former director of the Central Bureau of Investigation (CBI), from February 2019 to February 2021.

The correct answer is 1757.

Key Points

• The Battle of Plassey is regarded as a historic turning point for the British in India.
• It established the political and military supremacy of the British in Bengal.
• Battle of Plassey
• The Battle of Plassey was fought in 1757 in the Plassey (or Palashi) region of West Bengal, on the east of the Bhagirathi river.
• British East India Company, led by Robert Clive, won against the forces of Siraj-ud-Daulah, the last independent Nawab of Bengal, and his French allies.
• In the aftermath, Mir Jafar was installed as the Nawab of Bengal, on the throne of Murshidabad.

Additional Information

• Reasons behind the Battle of Plassey
• The British victory in the Carnatic made the Nawab of Bengal apprehensive of the rising power of the British.
• The East India Company kept misusing its power, including fortifying Calcutta without the Nawab’s permission.
• The Nawab marched to Fort Williams and captured it, leading to the infamous ‘Black Hole of Calcutta’ incident.
• Robert Clive was sent to overthrow the Nawab leading to the battle.

The correct answer is Homi Jehangir Bhabha.

Key Points

• Homi Jehangir Bhabha was an Indian nuclear physicist, founding director, and professor of physics at the Tata Institute of Fundamental Research.
• Father of the Indian Nuclear Programme
• ​In 1954, Bhabha founded a nuclear research centre at Trombay which was later renamed the Bhabha Atomic Research Centre (BARC).
• He was the principal architect of India's nuclear energy program and headed it until his death.
• Awards and Accolades
• ​Homi Bhabha was awarded the Adams Prize (1942) and Padma Bhushan (1954).
• He was also nominated for the Nobel Prize for Physics in 1951 and 1953-1956.

Additional Information

• C.N.R. Rao is a Linus Pauling Research Professor and Honorary President of the Jawaharlal Nehru Centre for Advanced Scientific Research (JNCASR), Bangalore.
• He is known for his research into superconductivity and the chemical properties of superconductive materials.
• M.S. Swaminathan is an Indian agronomist, agricultural scientist, and plant geneticist.
• He is known as the father of India's Green Revolution, for his contributions to the development of high-yielding varieties of wheat.
• He founded the MS Swaminathan Research Foundation, the pioneer organization behind the ”evergreen revolution”.
• Vikram Sarabhai was an Indian physicist and astronomer who initiated space research and helped develop nuclear power in India.
• He was honored with Padma Bhushan in 1966 and the Padma Vibhushan in 1972.
• He is internationally regarded as the Father of the Indian Space Program.

Given:

Capital invested by A (C₁) = Rs. 6000

Capital invested by B (C₂) = Rs. 18000.

Time for which A invested (t₁) = 12 months

Time for which B invested (t₂) =  t₂ months

Ratio of profits of A and B = C₁t₁ : C₂t₂ = 2 : 3

Formula used:

In a partnership, profit is divided in the ratio of investment multiplied by their time in the business, for two persons A and B we write,

Profit of A : Profit of B = Investment of A × time period of A : Investment of B × time period of B.

Calculation:

The ratio of profits of A and B,

Profit of A : Profit of B = (Investment of A × Time period of A) : (Investment of B × Time period of B)

C₁t₁ : C₂t₂ = (6000 × 12) : (18000 × t₂)

2 : 3 = 72 : 18 × t₂

\(\dfrac{2}{3} = \dfrac{4}{t_2}\)

t₂ = 12 / 2

t₂ = 6 months

∴ B joined after 6 months.

Shortcut Trick 

The ratio of profits of A and B,

Profit of A : Profit of B = (Investment of A × Time period of A) : (Investment of B × Time period of B)

C1t1 : C2t2 = (6000 × 12) : (18000 × t2) ⇒ 2 : 3 = 72 : 18 × t2

\(\dfrac{2}{3} = \dfrac{4}{t_2}\) ⇒ t2 = 12/2 ⇒ t2 = 6 months

∴ B joined after 6 months.

Given:

1^st number = (1 / 2) of 2^nd number

Average = 126.

Formula used:

Average = Sum of quantities / number of quantities

Calculation:

Let the first number be x then the second number will be 2x.

Average = Sum of quantities / number of quantities

126 = (x + 2x) / 2

252 = 3x

x = 252 / 3

x = 84

∴ The first number is 84.

Given:

K = \(\frac{\sqrt{6}+\sqrt{5}}{\sqrt{6}−\sqrt{5}}\)

P = \(\frac{\sqrt{6}−\sqrt{5}}{\sqrt{6}+\sqrt{5}}\)

Concept used:

In such questions we first rationalize the terms having roots in the denominator.

Calculation:

Rationalizing K,

\(K = \dfrac{\sqrt6 + \sqrt 5}{\sqrt 6 - \sqrt 5} \times \dfrac{\sqrt6 + \sqrt5}{\sqrt6 + \sqrt5}\)

\(K = \dfrac{(\sqrt6 + \sqrt 5)^2}{(\sqrt 6)^2 - (\sqrt 5)^2}\)

\(K = \dfrac{6 + 5 + 2\sqrt{6}\sqrt{5}}{6 - 5}\)

\(K = 11 + 2\sqrt{30}\)

Rationalizing P,

\(P = \dfrac{\sqrt6 - \sqrt 5}{\sqrt 6 + \sqrt 5} \times \dfrac{\sqrt6 - \sqrt5}{\sqrt6 - \sqrt5}\)

\(P = \dfrac{(\sqrt6 - \sqrt 5)^2}{(\sqrt 6)^2 - (\sqrt 5)^2}\)

\(P = \dfrac{6 + 5 - 2\sqrt{6}\sqrt{5}}{6 - 5}\)

\(P = 11 - 2\sqrt{30}\)

Now,

K² + P² + KP

= \((11 + 2\sqrt{30})^2 + (11 - 2\sqrt{30})^2 + (11 + 2\sqrt{30})(11 - 2\sqrt{30})\)

= \(11^2 + (2\sqrt{30})^2 + 2 \times 11 \times 2\sqrt{30} + 11^2 + (2\sqrt{30})^2 - 2 \times 11 \times 2\sqrt{30} + ((11)^2 - (2\sqrt{30})^2)\)

= \(121 + 120 + 121 + 120 + 121 - 120\)

= 482 + 1

= 483.

∴ The value of K2 + P2 + KP is 483.

Alternate Method

Please note that

K = 1/P

So,

K2 + P2 + KP = K2 + 1/K2 + 1

So,

K2 + P2 + KP = K2 + 1/K2 + 2 - 1 = [K + 1/K]2 - 1

and

K + 1/K = 2[(√6)2 + (√5)2] = 22

So,

[K + 1/K]2 - 1 = 222 - 1 = 483

Concept used:

In such questions we first simplify the expression using rationalizing the denominator.

Calculation:

Let us first rationalize the first term,

= \(\dfrac{1}{\sqrt2 + 1} \times \dfrac{\sqrt2 - 1}{\sqrt 2 - 1}\)

= \(\dfrac{\sqrt 2 - 1}{(\sqrt2)^2 - (1)^2} \)

= \(\sqrt 2 - 1\)

Now we rationalize the second term,

= \(\dfrac{1}{\sqrt3 + \sqrt2} \times \dfrac{\sqrt3 - \sqrt2}{\sqrt 3 - \sqrt 2}\)

= \(\dfrac{\sqrt 3 - \sqrt 2}{(\sqrt3)^2 - (\sqrt2)^2} \)

= \(\sqrt 3 - \sqrt 2 \)

Adding the first and second term

= \(\sqrt 2 - 1 + \sqrt 3 - \sqrt 2\)

= \(\sqrt 3 - 1\)

Similarly rationalizing the 3^rd term,

= \(\dfrac{1}{\sqrt4 + \sqrt3} \times \dfrac{\sqrt4 - \sqrt3}{\sqrt 4 - \sqrt 3}\)

= \(\dfrac{\sqrt 4 - \sqrt 3}{(\sqrt4)^2 - (\sqrt3)^2} \)

= \(\sqrt 4 - \sqrt 3\)

Adding the first 3 terms

= \(\sqrt 3 - 1 + \sqrt 4 - \sqrt 3\)

= \(\sqrt 4 - 1\)

This way rationalizing and adding all the terms we will get

\(= \sqrt 2 - 1 + \sqrt 3 -\sqrt 2 + \sqrt 4 - \sqrt 3 ......+\sqrt {99} + \sqrt {100} - \sqrt {99}\)

= \(\sqrt {100} - 1\)

= 10 - 1

= 9.

Squaring this we will get the answer,

= 9² 

= 81.

∴ The value of \(\left(\frac{1}{\sqrt{2}+1}+\frac{1}{\sqrt{3}+\sqrt{2}}+\ldots+\frac{1}{\sqrt{100}+\sqrt{99}}\right)^{2}\) is 81.

Given:

Ratio of cost price to selling price of article = 5 : 8.

Formula used:

Profit% = [(S.P. - C.P.) / C.P.] × 100

where 

S.P. = Selling price

C.P. = Cost price

Calculation:

Let the cost price be 5x and selling price be 8x.

Profit%

= [(S.P. - C.P.) / C.P.] × 100

= [(8x - 5x) / 5x] × 100

= 300 / 5

= 60%.

∴ The profit percentage is 60%.

Formula used:

a³ + b³ = (a + b)(a² - ab + b²)

Calculation:

We have

\(\frac{(0.88)^{3}+(0.12)^{3}}{(0.88)^{2}−0.1056+(0.12)^{2}}\)

Using the formula,

= \(\dfrac{[0.88 + 0.12][(0.88)^2 - 0.1056 + (0.12)^2]}{(0.88)^2 - 0.1056 + (0.12)^2}\)

= 0.88 + 0.12

= 1.

∴ The value of \(\frac{(0.88)^{3}+(0.12)^{3}}{(0.88)^{2}−0.1056+(0.12)^{2}}\) is 1.

Mistake Points It is a previous year paper QuestionIn the original answer key the answer was given as 3. In our calculation we found the answer should be 1. So, the answer was changed.

Concept used:

For two positive numbers if a>b then a² > b² .

Follow VBODMAS rule to solve this question, as per the order given below.

Step - 1: Parts of an equation enclosed in 'Vinculum Bar' must be solved first.

Step - 2: Parts of an equation enclosed in 'Brackets' must be solved second, and following BODMAS rule in the bracket

Step - 3: Any mathematical 'Of' or 'Exponent' must be solved next.

Step - 4: Next, the parts of the equation that contain 'Division' and 'Multiplication' are calculated.

Step - 5: Last but not the least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

Calculation:

For statement I,

Squaring LHS,

= \((\sqrt 7 + \sqrt3)^2\)

= \(7 + 3 + 2\sqrt7\sqrt3\)

= \(10 + 2\sqrt{21}\) ....

(1) Squaring RHS,

= \((\sqrt 6 + 2)^2\)

= \(6 + 4 + 2 \times 2 \sqrt6\)

= \(10 + 2\sqrt{24}\) ..... (2) Comparing (1) and (2)

\(10 + 2\sqrt{21}\) < \(10 + 2\sqrt{24}\)

or

\(\sqrt{7} + \sqrt{3} < \sqrt{6} + 2\)

Statement I is false.

For statement II,

\(1035 \div \left[\dfrac{3}{4} \times (65 + 59) - 90\right] \)

= \(1035 \div \left[\dfrac{3}{4} \times 124 - 90\right] \)

= \(1035 \div \left[3 \times 31 - 90\right] \)

= \(1035 \div \left[93 - 90\right] \)

= \(1035 \div 3\)

= 345.

Statement II is true.

∴ Only statement II is true.

Given:

Price of an article = Rs. 20000. Formula used:

Given value of an entity is p, for x% increase in an entity we use

p' = p + x% of p

where p' is the new value of entity.

Calculation:

When it is increased by 20%

= 20000 + 20% of 20000

= 20000 + (20 / 100) × 20000 

= 20000 + 20 × 200

= 20000 + 4000

= 24000.

When it is decreased by x percent

= 24000 - x% of 24000

= 24000 - (x / 100) × 24000 

= 24000 - 240x.

When it is increased by 50%

= (24000 - 240x) + 50% of (24000 - 240x)

= \((24000 - 240x) + \dfrac{50}{100} \times (24000 - 240x)\)

= \((24000 - 240x) + \dfrac{1}{2} \times (24000 - 240x)\)

= (24000 - 240x) + (12000 - 120x)

= 36000 - 360x

This is equal to 27000,

36000 - 360x = 27000

9000 = 360x

x = 9000 / 360

x = 25%

∴ The value of x is 25 percent.

Shortcut Trick

Ratio of Alcohol : Water = 3 : 7

Difference in ratio = 7 − 3 = 4 units

According to the question, 4 units = 4 litres ⇒ 1 unit = 1 litre

Quantity of Water = 7 units = 7 × 1 = 7 litres

∴ The correct answer is 7 litres.

Alternate Method

Given Ratio of Alcohol and Water = 3 : 7

Difference in quantity = 4 litres

Let the quantity of Alcohol and Water be 3x and 7x respectively.

⇒ Water − Alcohol = 4

⇒ 7x − 3x = 4

⇒ 4x = 4

⇒ x = 1

⇒ Quantity of Water = 7x = 7 × 1 = 7 litres.

∴ The correct answer is 7 litres.

Additional Information

Ratio Difference Rule

If two quantities are in the ratio a : b and their difference is 'D', then the value of 1 part = D ÷ (b − a).

Total Mixture Quantity

The total quantity of the mixture is calculated by (a + b) × value of 1 part. In this case, (3 + 7) × 1 = 10 litres.

Percentage Composition

Percentage of a component in a mixture = [Component Part ÷ Total Parts] × 100. For water, it is (7 ÷ 10) × 100 = 70%.