SSC CGL 2022 Tier-I Official Paper (Held On : 12 Dec 2022 Shift 1) (Previous Year Paper)

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

1) For ''

 element : Alternately rotating 45º and 90º in the anti-clockwise direction.

2) For '

' element : 

• Shifting in the anti-clockwise direction.
• Alternately number of '

' element is increasing and decreasing i.e 1-2-1-2-1-2.

• Singe '

' is positioned inside the ''

element and double '

' is positioned outside the ''

element.

​​

Final series is :

Hence, ‘option - (2)’ is the correct answer.

The least possible Venn diagram for the given statements is as shown below :

Conclusions:

I. Some fruits are apples → Follow (As all oranges are apples, some oranges are bananas and all bananas are fruits. So, as there is some common part between oranges and bananas which whole comes in apples and fruits respectively so some fruits are apples is definitely true) 

II. Some apples are bananas → Follow (As As all oranges are apples and some oranges are bananas. So, as bananas has some common part with oranges which whole comes in apples therefore some apples are bananas is definitely true)

III. Some oranges are fruits → Follow (As some oranges are bananas and all bananas are fruits. So, as there is some common part between oranges and bananas which whole comes in fruits so some oranges are fruits is definitely true) 

∴ Here, All conclusions I, II and III follows.

Hence, the correct answer is "All conclusions follow.".

According to the question, after interchanging the given signs "+ and ÷" :

So,

• Option - (1) : 18 + 6 – 6 ÷ 3 × 3 = 6

18 ÷ 6 – 6 + 3 × 3 = 6

3 – 6 + 3 × 3 = 6

3 + 9 - 6 = 6

12 - 6 = 6

6 = 6 (LHS = RHS)

• Option - (2) : 18 + 2 × 6 ÷ 3 – 7 = 50

18 ÷ 2 × 6 + 3 – 7 = 50

9 × 6 + 3 – 7 = 50

54 + 3 - 7 = 50

57 - 7 = 50

50 = 50 (LHS = RHS)

• Option - (3) : 7 × 8 ÷ 4 + 2 – 6 = 49

7 × 8 + 4 ÷ 2 – 6 = 49

7 × 8 + 2 - 6 = 49

56 + 2 - 6 = 49 

58 - 6 = 49

52 ≠ 49 (LHS ≠ RHS)

• Option - (4) : 6 × 9 + 3 – 24 ÷ 8 = 2

6 × 9 ÷ 3 – 24 + 8 = 2

6 × 3 - 24 + 8 = 2

18 + 8 - 24 = 2

26 - 24 = 2

2 = 2 (LHS = RHS)

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

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

1) For '

' element : Alternately shaded and non-shaded.

2) For '

'

 element : No change

​​

Final series is :

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

The logic followed here is :-

From the given three different cubes, figure 1 and figure 3 ,the adjacent sides are as shown below :

As 5 is common on both figure 1 and figure 3, it is clear that 1, 2, 3 and 4 are adjacent to it, and the remaining number i.e., 6 will be opposite to it.

Opposite pairs:

1 → 3

2 → 4

5 → 6

So, the opposite side of "6" will be side "5".

Hence, the correct answer is "5".

Logic : ​Sum of the position values of the first two letters according to the English alphabetic series is 28.

​So,

• CXA

​

• UGS

​

• JRH

​

• NNL

​

Thus, out of all options only 'CXA' sum of the position values of the first two letters according to English alphabetic series is 27 instead of 28.

Hence, "CXA" is the correct answer.

Logic : Letters are written in the reverse order within the word.

​So,

• ‘APPRECIATE’ is written as ‘ETAICERPPA’

 

​And,

• ‘MOTIVATION’ is written as ‘NOITAVITOM’

​Similarly,

• ‘FRIENDSHIP’ is written as :

​

Hence, "PIHSDNEIRF" is the correct answer.

The logic followed here is :

• A group of cattle is called herd.

Similarly,

• A group of sailors is called crew.

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

Additional Information

1. Soldiers ∶ Colony → A group of soldiers is called troop and a group of ants is called colony.
2. Pupils ∶ Team → A group of pupils is called class and a group of players is called team.
3. Player ∶ Class → A group of players is called team and a group of pupils is called class.

Given:

• The image must not to be rotated

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

The logic followed here is : 2^nd number - (1^st number × 2) = Square root of 3^rd number

Given :

• (17, 59, 625)

​59 - 17 × 2 = $\sqrt{625}$

59 - 34 = 25

25 = 25 (LHS = RHS)

• (8, 44, 784)​

​44 - 8 × 2 = $\sqrt{784}$

44 - 16 = 28

28 = 28 (LHS = RHS)

So,

• Option - (1) : (22, 78, 784)​

​78 - 22 × 2 = $\sqrt{784}$

78 - 44 = 28

38 ≠ 28 (LHS ≠ RHS)

• Option - (2) : (12, 69, 2025)​

​69 - 12 × 2 = $\sqrt{2025}$

69 - 24 = 45

45 = 45 (LHS = RHS)

• Option - (3) : (24, 70, 576)​

​70 - 24 × 2 = $\sqrt{576}$

70 - 48 = 24

22 ≠ 24 (LHS = RHS)

• Option - (4) : (18, 74, 1296)​

​74 - 18 × 2 = $\sqrt{1296}$

74 - 36 = 36

38 ≠ 36 (LHS ≠ RHS)

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

The logic followed here is :

• Freezing occurs when a liquid is cooled and turned into a solid.

Similarly,

• Evaporation happens when a liquid substance becomes a gas.

Hence, "Evaporates" is the correct answer.

Additional Information

1. Melts → Melting happens when a solid is heated and turned into liquid.
2. Smells → It occurs when an odor binds to a receptor within the nasal cavity.
3. Freezes → Freezing occurs when a liquid is cooled and turned to a solid.

Given :

So,

• Option - (1) : P ÷ R × Q → P is the mother of R who is the father of Q.

Here, P is the mother of R.

• Option - (2) : P ÷ Q × R → P is the mother of Q who is the father of R.

Here, P is the paternal grandmother of R.

• Option - (3) : P ÷ Q + R → P is the mother of Q who is the brother of R.

Here, P is the mother of R.

• Option - (4) : P × Q ÷ R → P is the father of Q who is the mother of Q.

​

Here, P is the maternal grandfather of R.

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

According to the question, after interchanging the given two signs and numbers :

1. • and –
2. 3 and 5

So,

• Option - (1) : 5 × 4 + 3 – 6 ÷ 2 = 10

3 × 4 - 5 + 6 ÷ 2 = 10

3 × 4 - 5 + 3 = 10

12 + 3 - 5 = 10

15 - 5 = 10

10 = 10 (LHS = RHS)

• Option - (2) : 7 × 4 ÷ 2 – 5 + 3 = 12

 

According to the question, after interchanging the given two signs and numbers :

1. • and –
2. 3 and 5

So,

7 × 4 ÷ 2 + 3 - 5 = 12

7 × 2 + 3 - 5 = 12

14 + 3 - 5 = 12

17 - 5 = 12

12 = 12 (LHS = RHS)

• Option - (3) : 5 × 4 – 3 + 4 ÷ 2 = 15

According to the question, after interchanging the given two signs and numbers :

1. • and –
2. 3 and 5

So,

3 × 4 + 5 - 4 ÷ 2 = 15

3 × 4 + 5 - 2 = 15

12 + 5 - 2 = 15

17 - 2 = 15

15 = 15 (LHS = RHS)

• Option - (4) : 5 – 3 + 8 × 4 ÷ 2 = 10

According to the question, after interchanging the given two signs and numbers :

1. • and –
2. 3 and 5

So,

3 + 5 - 8 × 4 ÷ 2 = 10

3 + 5 - 8 × 2 = 10

3 + 5 - 16 = 10

8 - 16 = 10

-8 ≠ 10 (LHS ≠ RHS)

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

Given :

Given statement : F & G @ H # I @ J

So,

• F & G → F is the father of G.

• G @ H → G is the husband of H.

• H # I → I is the son of H.

• I @ J → I is the husband of J.

​

Thus, according to the final family tree G is the father-in-law of J.

Hence, "Father-in-law" is the correct answer.

Given statement : 13 − 65 ÷ 45 × 21 + 2 = 82

According to the question, after interchanging the given two signs and two numbers :

So,

• Option - (1) : 65 and 13, × and +

65 − 13 ÷ 45 + 21 × 2 = 82

65 - 0.28 + 21 × 2 = 82

65 + 42 - 0.28 = 82

107 - 0.28 = 82

106.72 ≠ 82 (LHS ≠ RHS)

• Option - (2) : 45 and 13, × and +

Given statement : 13 − 65 ÷ 45 × 21 + 2 = 82

45 − 65 ÷ 13 + 21 × 2 = 82

45 - 5 + 21 × 2 = 82

45 + 42 - 5 = 82

87 - 5 = 82

82 = 82 (LHS = RHS)

• Option - (3) : 45 and 21, × and +

Given statement : 13 − 65 ÷ 45 × 21 + 2 = 82

13 − 65 ÷ 21 + 45 × 2 = 82

13 - 3.09 + 45 × 2 = 82

13 + 90 - 3.09 = 82

103 - 3.09 = 82

99.91 ≠ 82 (LHS ≠ RHS)

• Option - (4) : 45 and 13, − and +

Given statement : 13 − 65 ÷ 45 × 21 + 2 = 82

45 + 65 ÷ 13 × 21 - 2 = 82

45 + 5 × 21 - 2 = 82

45 + 105 - 2 = 82

150 - 2 = 82

148 ≠ 82 (LHS ≠ RHS)

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

According to the sequence in the dictionary:

3. Aquarial
4. Aquarium
5. Aquatic
6. Aquatint
7. Aquavit

Hence, the correct option is "Aquatic".

The correct mirror image of the given combination when mirror is placed at AB is as shown below:

\

Detailed Explanation:

• The line AB is the mirror
• The figure "\

" the left corner up element is "\

". So, the mirror image should be ""

 ⇒ Option 1 is eliminated.

• The figure "

" the left corner down element is "

". So, the mirror image should be ""

 ⇒ Option 2 is eliminated..

• The figure " " the right corner down element is "

". So, the mirror image should be "

" ⇒ Option 4 is eliminated.

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

The logic followed here is :  (1^st number )³ - 3 = 2^nd number

So,

• 4 ∶ 61

​$(4)^3$ - 3 = 61

64 - 3 = 61

61 = 61 (LHS = RHS)

​And,

• 9 ∶ 726

​$(9)^3$ - 3 = 726

729 - 3 = 726

726 = 726 (LHS = RHS)

​Similarly,

• 6 ∶ ?

​$(6)^3$ - 3 = ?

216 - 3 = ?

213 = ?

​Hence, "213" is the correct answer.

The least possible Venn diagram for the given statements is as shown below :

Conclusions:

I.  All Z are L → Does not follow (As some L are Z. So, it is possible but not definitely true)

II. No T is Z → Does not follow (As some L are Z and some L are T. So, as no direct negative or cross relation between T and Z is given therefore it is definitely false)

∴ Here, Neither conclusions I nor II follow.

Hence, the correct answer is "Neither conclusion follows".

Logic : ​Number according to the position of letter within the word is added to the position value according to the English alphabetic series diagonally.

• First letter → (+1) is added
• Second letter → (+2) is added
• Third letter → (+3) is added
• Fourth letter → (+4) is added
• Fifth letter → (+5) is added
• Sixth letter → (+6) is added

​So,

• 'LABOUR' is written as 'XZSECM'

​And,

• ‘GAINED’ is written as ‘JJRLCH’

​Similarly,

• 'EARNED' is written as :

Hence, "JJRUCF" is the correct answer.

The logic followed here is : (1^st number + 3^rd number) × 7 = 2^nd number

Given :

• (5, 98, 9)

​(5 + 9) × 7 = 98

14 × 7 = 98

98 = 98 (LHS = RHS)

• (10, 168, 14)

​(10 + 14) × 7 = 168

24 × 7 = 168

168 = 168 (LHS = RHS)

​So,

• Option - (1) : (1, 28, 3)​

​(1 + 3) × 7 = 28

4 × 7 = 28

28 = 28 (LHS = RHS)

• Option - (2) : (7, 108, 23)​

​(7 + 23) × 7 = 98

30 × 7 = 108

210 ≠ 108 (LHS ≠ RHS)

• Option - (3) : (15, 248, 19)​

​(15 + 19) × 7 = 248

34 × 7 = 248

238 ≠ 248 (LHS ≠ RHS)

• Option - (4) : (3, 88, 17)​

​(3 + 17) × 7 = 88

20 × 7 = 88

140 ≠ 88 (LHS ≠ RHS)

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

The logic followed here is : Consecutive multiples of (7) are added subsequently.

Hence, "19.8" is the correct answer.

Logic : ​

• First letter → (2) is added to the position value according to the English alphabetic series.
• Second letter → (7) is subtracted from the position value according to the English alphabetic series.
• Third letter → (8) is added to the position value according to the English alphabetic series.
• Fourth letter → (3) is subtracted from the position value according to the English alphabetic series.

​So,

 

Hence, "IZIR" is the correct answer.

The logic followed here is :

1. 1^st number × 3 = 2^nd number  and,
2. 2^nd number × 3 = 3^rd number

So,

• Option - (1) : (17 –51 –147)

​17 × 3 = 51

51 = 51 (LHS = RHS) 

And,

51 × 3 = 147

153 ≠ 147 (LHS ≠ RHS)

• Option - (2) : (10 –30 –90)

​10 × 3 = 30

30 = 30 (LHS = RHS)

And,

30 × 3 = 90 

90 = 90 (LHS = RHS)

• Option - (3) : (15 –45 –135)

15 × 3 = 45

45 = 45 (LHS = RHS)

And,

45 × 3 = 135

135 = 135 (LHS = RHS)

• Option - (4) : (22 –66 –198)

22 × 3 = 66

66 = 66 (LHS = RHS)

And,

66 × 3 = 198

198 = 198 (LHS = RHS)

Thus, out of all the options only option - (1) doesn't follow the same pattern as others.

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

Logic : ​

1. First letter → (7) is subtracted from the position value according to the English alphabetic series.
2. Second letter → (7) is added to the position value according to the English alphabetic series.

​So,

​

Hence, "ZA" is the correct answer.

The correct answer is democratic.

Key Points

• A democratic country has a system of government in which the people have the power to participate in decision-making.
• A constitution is an aggregate of fundamental principles or established precedents that constitutethe legal basis of polity, organisation or other type of entity and commonly determine how that entity is to be governed.
• All democratic countries are most likely to have a constitution.
• However, there are exceptions as a democratic country may not have a constitution.
• For example, Britain does not have a codified constitution.
• All countries that have a constitution are not necessarily democractic.​

Additional Information

• Oligarchic - A government or system in which power is held by a select few individuals or a small class of powerful people.
• Communist - It is a political and economic doctrine that aims to replace private property and a profit-based economy with public ownership and communal control of at least the major means of production (e.g., mines, mills, and factories) and the natural resources of a society.
• Totalitarian - a country or a system of government in which there is only one political party that has absolute power and control over the people.

Correct Ladakh

Key Points

• "Tak Tok" or "Taktok" which is a Buddhist festival celebrated in the Taktok village of Ladakh, India.
• The festival is usually held in the month of July or August and is celebrated by the villagers and monks who perform traditional dances, chants, and prayers.
• During the festival, the monastery is decorated with colorful prayer flags, and the monks perform a traditional mask dance called "Cham."
• The festival is a celebration of the region's rich cultural heritage and Buddhist traditions and provides an opportunity for people to come together and celebrate with music, dance, and food.

Additional Information:

The correct answer is Shivkumar Sharma.

Key Points:

• Pandit Shivkumar Sharma (13 January 1938 – 10 May 2022) was an Indian classical musician and santoor player who is credited with adapting the santoor for Indian classical music.
• As a music composer, he collaborated with Indian flautist Hariprasad Chaurasia under the collaborative name Shiv–Hari and composed music for many Indian films.
• He was awarded the Sangeet Natak Akademi Award in 1986, the Padma Shri, India's fourth-highest civilian award in 1991, and the Padma Bhushan, India's third-highest civilian award in 2001.
• He is credited with introducing the santoor as a popular Indian classical music instrument.
• He co-produced a concept album, Call of the Valley (1967), 1967 with flautist Hariprasad Chaurasia and guitarist Brij Bhushan Kabra.

Additional InformationTarun Bhattacharya:

• He is an Indian classical musician who plays the santoor, a type of hammered dulcimer.
• He studied with Ravi Shankar.

Bhajan Sopori:

• He is an Indian instrumentalist.
• He is a player of the santoor, an ancient stringed musical instrument.
• On the occasion of the 67^th Indian Republic Day 2016, Pandit Bhajan Sopori was accorded Jammu and Kashmir State lifetime achievement award.

Satish Vyas:

• He is an Indian Santoor player.
• He is the son of Indian classical singer CR Vyas.
• He has been awarded the Tansen Award on 26 December 2020.

The correct answer is Goa.​

Key Points

• Dekhni dance represents an attractive mixture of folk culture and Western music, danced mostly by Christian girls in fully Indian dress.
• The gestures in the dance appear to have been borrowed from the Kathak and Bharata Natyam.
• Dekhni in Konkani language means bewitching beauty.
• Dekhni dance is one of the oldest dance forms of Goa.
• Dekhni dance can be associated with those people who converted into Christianity from Hinduism during Portuguese rule.
• Dekhni Dance is performed by a group of girls caring earthen oil lamps in their hands.
• These girls are represented as the servants of God in this dance form. It represents the life of a devadasi.
• Ghumat Drum is the main instrument used in this dance.

Additional Information

• Hanv Saiba Poltodi Vetam is one of the most famous songs of Dekni dance.
• It was written by Carlos Eugenio Ferreira.
• This song was first published in 1895 in Paris and then in Goa in 1926.
• This song talks about a dancer who wanted to cross the river but the boatman refused to take her because the river was very rough that day.

The correct answer is Buying and selling of bonds issued by the Government in the open market.

Key Points

• Open Market Operations (OMO) is conducted by the Reserve Bank of India (RBI) for the sale or purchase of government securities (g-secs), financial assets or bonds issued by the government to the banks in order to adjust the money supply.
• The RBI does this to regulate the liquidity from the system and to infuse liquidity into the system.
• There are two types of Open Market Operations: Outright Purchase and Repurchase Agreement. Hence option 1 is correct.
• Outright Purchase or PEMO is a permanent transaction which involves the RBI selling or purchasing securities in the open market to regulate the money supply.
• A Repurchase Agreement is a short-term agreement that involves the RBI buying and purchasing government securities after a specified date.​

Additional Information

• Open Market Operations are flexible and easily reversible thereby reducing the lags of monetary policy.
• In 1948, the RBI mentioned the OMO purchase for the first time in its Annual Report.
• Government securities or G-Secs are tradable instruments issued by central governments and state governments.
• They are risk-free instruments and can be short-term like Treasury bills (T-bills) with a maturity of less than a year or long-term like government bonds with a maturity of a year or more than a year.

The correct answer is Erich Huckel.

Key Points

• Erich Huckel was a German chemist and physicist.
• He proposed a theory in 1931 to help determine if a planar ring molecule would have aromatic properties.
• Erich Huckel recognized that an aromatic compound must have an odd number of pairs of electrons.
• His rule states that a cyclic, planar molecule is considered aromatic if it has 4n+2 pi electrons.
• This rule is known as Huckel's Rule.​

Additional Information

• Pi bond:- Bond formed by the same phase overlap of atomic orbitals along a direction perpendicular to the internuclear axis is called pi bond.
• Pi electrons:- An electron that resides in the pi bond (s) of a double bond or a triple bond or in a conjugated p orbital is called pi electron.
• ​System is divided into aromatic, anti-aromatic, and non-aromatic based on no. of pi electrons-
• ​​​Aromatic system - The number of pi electrons in an aromatic system is determined by N = 4n+2 (n is an integer)
• Anti-aromatic system - The number of pi electrons in an anti-aromatic system is determined by N = 4n (n is an integer)
• Non-aromatic - If a compound does not have a continuous ring of conjugated p orbitals in a planar module, then it is called non-aromatic.

The correct answer is potassium nitrate.

Key Points

• Potassium nitrate(KNO3) is also called Saltpetre or Nitre.
• It is widely used in Fertilizers, Gunpowder, Rocket Propellants, Firecrackers, food processing, etc. It has also certain pharmacological uses.

Additional Information

 Potassium manganite 

• Potassium Permanganate (KMnO4) is an inorganic chemical compound.
• It is also known as Condy's crystals or permanganate of potash.

Lead nitrate

• Lead(II) nitrate is an inorganic compound with the chemical formula Pb(NO3)2.
• It commonly occurs as a colourless crystal or white powder

The correct answer is Prashastis.

Key Points:

• Prashastis is a special kind of inscription, meaning “in praise of”.
• They were composed by learned Brahmans in praise of the rulers. (statement 1 is correct)
• They tell us how rulers of that time wanted to illustrate themselves.
• If the kings liked the prashastis, they gave land as a gift to the Brahmans, with records of it on copper plates. (statement 2 is correct)
• The prashastis generally contained ornate titles, links to mythical legends or comparisons to deities, and often fabricated stories about wars, victories, loot, and attributes.
• The earliest well-known example of an extensive prashasti is the Hathigumpha inscription of Kharavela inscribed in or about the 1^st century BCE in the Prakrit language and Brahmi script.
• The earliest prashastic inscription in the classical Sanskrit language is the Junagadh rock inscription of Rudradaman (circa 150 CE), which became a prototype for Gupta-era poetic prashastis in Sanskrit.

Examples of Prashasti

• Nashik prashasti (2^nd century CE), of the Satavahana dynasty.
• Prayaga prashasti (4^th century CE), Gupta Empire: Lists the rulers against whom the Gupta king Samudragupta fought.
• It also describes the policy that he followed toward each set of rulers.
• Velvikudi inscription (c. 8^th century CE), of Pandya dynasty.
• Deopara Prashasti (12^th century CE), of the Sena dynasty.

The correct answer is Kakrapar.

Key Points

• Kakrapar Atomic Power Station is located in Surat in the state of Gujarat.
• Kakrapar Atomic Power Station is a nuclear power station commissioned on 6 May 1993.

Additional Information

The correct answer is Advantage out.

Key Points

• Tennis is a game played on a rectangular-shaped court, which can be one of many surfaces.
• It is either played with two players (singles match), or four players (doubles match).
• Players stand on opposite sides of the net and use a stringed racquet to hit the ball back and forth to each other.
• Most tennis matches are played in a best-of-three format, which means that players need to win 2 sets to win the match.
• The score when the receiver wins the next point after deuce Advantage out.
• In Grand Slams, men play best-of-five sets while women play best-of-three sets.
• Doubles matches are best-of-3 with a 10-point tiebreak in lieu of the third set.
• USTA and club matches are usually best-of-3.
• There are two main ways of scoring a set.
• Advantage Set
• In an advantage set, a player or team needs to win six games, by two, to win the set.
• This means that there is no tiebreak game played at 6-6.
• The set continues until one player/team wins by two games.
• Tiebreak Set
• In a tiebreak set, a player or team needs to win six games wins a set.
• If the score gets to 5-5 (5-all), one player must win the next two games to win the set.
• If the score reaches 6-6 (6-all) in the set, a tiebreak game is played.

Additional Information

• Tennis is an Olympic sport and is played at all levels of society and at all ages.

The correct answer is 382.

Key Points

• As per the Census of India 2011, the population density of India was 382 per square km.
• The Indian Census is the most credible source of information on Demography (Population characteristics), Economic Activity, Literacy and Education, Housing Household Amenities, Urbanisation, Fertility and Mortality, etc.
• Census 2011 was the 15^th National Census of the Country.
• Census was introduced in India during the era of Lord Mayo in the year 1872. It came into force in 1881.
• This census was conducted under the guidance of Mr. C. Chandramouli.
• The slogan of census 2011 was ‘Our Census, Our future’.
• The population of the nation as per the provisional figures of Census 2011 was 1210.19 million of which 623.7 million (51.54%) were males and 586.46 million (48.46%) were females. Uttar Pradesh is the most populous state in India its population is more than the population of Brazil.​

Additional Information

• A census is official data on the population.
• Indian census includes demographic, social, and economic data.
• It is held periodically after every tenth year.
• The first census took place in 1872.

The correct answer is Vembanad lake – Maharashtra.

Key Points

• Vembanad Lake is also known as Vembanad Kayal, Vembanad Kol, Punnamada Lake and Kochi Lake (in Kochi).
• This is the largest lake in Kerala and the longest lake in India.
• This lake is Spanned in several districts of Kerala and covers a territory of more than 2033.02 km2.
• The lake has its source in four rivers, Meenachil, Achankovil, Pampa and Manimala.
• It is separated from the Arabian Sea by a narrow barrier island and is a popular backwater stretch in Kerala.
• The Government of India has identified the Vembanad wetland under the National Wetlands Conservation Programme.
• Vallam Kali (i.e Nehru Trophy Boat Race) is a Snake Boat Race held every year in August in Vembanad Lake
• It is not found in Maharashtra.

 Additional Information

Correct Answer Avogadro made a distinction between atoms and molecules.

Key PointsAvogadro is a term that refers to two related concepts in chemistry:

Avogadro's number:

• This is a fundamental constant in chemistry that represents the number of atoms or molecules in one mole of a substance. (Option 4 is correct)
• Its value is approximately 6.022 x 10^²³, and it is denoted by the symbol "N_A".
• Avogadro's number is a key concept in stoichiometry.
• The branch of chemistry deals with the quantitative relationships between reactants and products in chemical reactions.

Amedeo Avogadro:

• He is best known for his contributions to the development of the mole concept in chemistry.
• Avogadro proposed that equal volumes of gases at the same temperature and pressure contain the same number of particles, which led to the development of Avogadro's law.
• He also proposed the hypothesis that the same volume of different gases, at the same temperature and pressure, contains an equal number of molecules. This hypothesis became known as Avogadro's principle.
• Avogadro's contributions to the development of the mole concept and the understanding of the behavior of gases have had a profound impact on the field of chemistry.

The correct answer is Tropical evergreen forest.

Key Points

Tropical evergreen forests:

• Tropical evergreen forests have trees that always have leaves and have a shade look.
• They always receive heavy rainfall i.e greater than 200 cm.
• The temperature that is maintained is between 20-27o C.
• The trees reach great heights up to 60 metres or even above.
• These are generally found in the Western Ghats, Andaman, and Nicobar, North East Area.
• Examples of tropical evergreen are Rubber, Beetle Nut, Jamun, Mango, Roseberry, and Bamboo.
• These forests have a multilayered structure with trees, shrubs and creepers.
• There is no definite time for trees to shed their leaves.
• As such, these forests appear green all year round.
• Anacondas can be seen in the Amazon River.
• Anacondas are a group of large snakes found in the tropical evergreen forest of South America.
• Only four species of Anacondas are currently recognized.

Additional Information

​Semi-evergreen forests:

• Semi-evergreen forests are found in the Western Ghats, Andaman and Nicobar Islands, and the Eastern Himalayas.
• Such forests have a mixture of wet evergreen trees and moist deciduous trees.
• The forest is dense and is filled with a large variety of trees of both types.

Important Points 

The correct answer is England.

Key Points

• The 2022 Commonwealth Games will be held in Birmingham, England.
• It is officially known as the XXII Commonwealth Games and is commonly known as Birmingham 2022.
• This is the 3^rd time England has hosted the Games, after London in 1934 and Manchester in 2002.
• 'Games for Everyone' is the motto of the 2022 Commonwealth Games.
• The venues being used for the Games are mostly located in Birmingham and a few in Coventry, Royal Leamington Spa, Sandwell, and London.

Additional Information

• The first Commonwealth Game in 1930 was hosted in Hamilton, Canada.
• Delhi hosted Commonwealth Games in 2010.
• List of Commonwealth Games and their venue

Correct Answer Bihar

Key Points

• Bihar state government is set to conduct a caste-based census in the state.
• The decision was taken at an all-party meeting chaired by Chief Minister Nitish Kumar.
• The exercise would be called Jaati Aadharit Ganana and the state government will publish the data related to the census through advertisements in newspapers.
• The aim of this exercise is to carry out developmental work for people who are deprived.
• A caste-based census means that the census exercise would not just include religion of a person but also have a caste-wise tabulation.
• It would help in knowing the population under different castes.
• Usually the census is conducted by the central government every ten years.
• But now the Bihar government has decided to conduct its own census.

Additional Information:

• As per details from Census 2011, Bihar has a population of 10.41 Crores, an increase from the figure of 8.30 Crore in the 2001 census.
• The total population of Bihar as per the 2011 census is 104,099,452 of which males and females are 54,278,157 and 49,821,295 respectively.
• In 2001, total population was 82,998,509 in which males were 43,243,795 while females were 39,754,714.
• The total population growth in this decade was 25.42% while in the previous decade it was 28.43%.
• The population of Bihar forms 8.60% of India in 2011.
• In 2001 the population of Bihar forms 8.70% of India.

The correct answer is 1764. 

Key Points

• The Battle of Buxar was fought between the English Forces (Hector Munro – British Army Major), and a joint army of the Nawab of Oudh, Nawab of Bengal, and the Mughal Emperor.
• The Battle of Buxar was fought on 22 October 1764. Hence the correct answer is 1764. ​

Additional Information

The reasons for battle were:

• Mir Qasim wanted to be independent and shifted his capital to Munger Fort from Calcutta.
• These factors fuelled the English to overthrow him and war broke out between Mir Kasim and the Company in 1763.
• Participants of the Battle of Buxar were:
• Mir Qasim – (Administering Bengal in place of Mir Jafar – Nawab of Bengal)
• Shuja-Ud-Daulah – Nawab of Awadh (Oudh)
• Shah Alam II – Mughal Emperor

Result of Battle of Buxar:

• Mir Jafar (Nawab of Bengal) handed over districts of Midnapore, Burdwan, and Chittagong to the English for the maintenance of their army.
• The English were also permitted duty-free trade in Bengal, except for a duty of two per cent on salt.
• Clive made political settlements with Emperor Shah Alam II and Shuja-Ud-Daula of Awadh in the Treaty of Allahabad.

The correct answer is Recruitment of youth in the Armed Forces.

Key Points

• The Centre has cleared the AGNIPATH Scheme for recruitment of youth in the armed forces.
• The youth selected under this scheme will be known as Agniveers.
• They will be getting an attractive monthly package with risk and hardship allowances as applicable in the three services.
• They will be also paid a one-time Seva Nidhi Package upon completion of the engagement period of four years.

Additional Information 

• ​‘Agniveers’will form a distinct rank in the three services, and will also wear a distinct insignia as part of their uniform.
• The ‘Agnipath’ model envisages the recruitment of personnel below officer rank (PBOR) in the army, air force and navy for four years, including six months of training.
• The soldiers recruited under ‘Agnipath’ will be released from service after four years, though the new system will have a provision for retaining around 25% of them after another round of screening.

The correct answer is Union Carbide.

Key Points

• Bhopal Gas Tragedy:
• It was a gas leak incident that happened in  India on 3^rd December 1984.
• The leakage of toxic methyl isocyanate gas at a Union Carbide plant was the cause of the Bhopal Gas Tragedy.
• Union Carbide plant was owned by the Indian subsidiary of the American firm Union Carbide Corporation.
• About 45 tons of the dangerous gas methyl isocyanate leaked from an insecticide plant.
• Methyl isocyanate is an extremely toxic gas and its concentration in the air touches 21ppm (parts per million).
• It can cause death within minutes of inhaling the gas.
• The final death toll was estimated to be between 15,000 and 20,000.
• Some half a million survivors suffered respiratory problems, eye irritation or blindness, and other maladies.

Additional Information Bhopal:

• Due to various natural and artificial lakes, it is known as the City of Lakes.
• It is also one of the greenest cities in India.
• It is the 16^th largest city in India and 131^st in the world.
• Bhojtaal is also known as Bada Talab is the oldest man-made lake in India.

The correct answer is Padma Bhushan.

Key Points

• Vempati Chinna Satyam, who lived from 15 October 1929 to 29 July 2012, was a legend in the Kuchipudi dancing style.
• He is credited with spreading the dancing style's popularity all over the world.
• He has received numerous honours, including the Raja Lakshmi Award from Madras and the Sangeet Peeth of Bombay.
• He received Padma Bhushan award in 1998.​

Additional Information

• Kathak Dance
• One of the primary categories of ancient Indian classical dance, known as Kathak, is thought to have started with the wandering storytellers known as Kathakars in North India.
• Similar to the early Greek theatre, these wandering Kathakars used music, dance, and songs to convey legendary tales.
• The Bhakti movement, a tendency of theistic devotion that emerged in mediaeval Hinduism, is when the genre first came into being.
• Manipuri Dance
• Manipuri dance is one of India's most well-known classical dance genres and is particularly renowned for its Vaishnavist themes and spectacular performances of dance dramas centred on the love between Radha and Krishna known as "Ras Lila."
• Additional subjects in this kind of art related to Shaktism, Shaivism, and the sylvan gods known as Umang Lai during the Manipuri festival "Lai Haraoba."
• Although this dance style has its roots in the ancient Sanskrit Hindu literature "Natya Shastra," it is named after the north-eastern Indian state of Manipur, where it first appeared.
• Kathakali Dance
• An essential subgenre of Indian classical dance known as "Kathakali" is linked to this kind of storytelling.
• It is a dance drama from Kerala in southern India. Like other Indian traditional dance forms, "Kathakali" uses spectacular facial and hand movements along with music and vocal performance to effectively convey the story to the audience.

The correct answer is Chola.

Key Points

The lost-wax technique (Cire Perdue):

• Used for making the bronze statues.
• In this technique, wax figures are first coated with wet clay and allowed to dry.
• The clay coated figures are then heated, allowing the wax inside to melt.
• The wax is then poured out through a tiny hole and liquid metal is poured inside the hollow mould.
• After the metal has cooled down and solidified, the clay coat is removed and a metal figure of the same shape as the wax figure is obtained.
• Chola Dynasty also used this technique to make bronze statues.

Additional Information

• Example: The Dancing Girl
• It is the world’s oldest bronze sculpture.
• Found in Mohenjo-Daro.
• It is a 4-inch figure that depicts a naked girl wearing only ornaments, which include bangles in the left arm, and an amulet and bracelet on the right arm.
• She stands in a ‘Tribhanga’ dancing posture with the right hand on her hip.

The correct answer is Andhra Pradesh.

Key Points

• Kolleru Lake is one of the largest freshwater lakes in India located in the state of Andhra Pradesh, 15 km from the city of Eluru.
• Kolleru is situated between the Krishna and Godavari deltas. Kolleru is spread over two districts - Krishna and West Godavari.
• The lake serves as a natural flood-balancing reservoir for these two rivers.
• The RAMSAR site of Kolleru Sanctuary is facing pollution and degradation due to large-scale shrimp cultivation for export.

Additional Information

The correct answer is Bhagwant Mann

Key Points

• In March 2022 Bhagwant Singh Mann became the Chief Minister of Punjab.
• He is the Punjab cabinet minister and a member of the Aam Aadmi Party.
• On 20 February 2022, elections for the 117 members of the 16^th Assembly of the Punjab Legislative Assembly were conducted in Punjab through which he gained a majority,

Additional Information

• AAP Punjab convener and MP Bhagwant Mann were sworn in as Chief Minister on 16 March 2022.
• Mann's ministry was formed with 10 cabinet ministers on 19 March 2022.

Correct Answer Right to be forgotten

Key Points

• The Supreme Court's decision to remove the personal details of individuals involved in matrimonial litigation is a recognition of the right to privacy.
• This right is a fundamental right that is protected under Article 21 of the Indian Constitution.
• The court's decision is in line with the landmark judgment in the Puttaswamy case (2017).
• Supreme Court declared that the right to privacy is a fundamental right that is essential to the dignity and autonomy of individuals.
• The court recognized that the right to privacy includes the right to control the dissemination of personal information.
• This decision is a step towards protecting that right for individuals involved in matrimonial disputes.
• Article 21 is one of the prime Articles comprising Part III of the Constitution of India dealing with fundamental rights.
• Article 21 is the protection of life and personal liberty.
• No person shall be deprived of his life or personal liberty except according to the procedure established by law.
• It guarantees life and personal liberty to all persons irrespective of caste or gender.
• It guarantees the right of persons to live with human dignity.
• All the aspects of life go to make a person's life meaningful, complete, and worth living.

Additional Information:

• The right to be forgotten is a relatively new concept that has emerged in the digital age.
• It refers to the right of an individual to request the removal of personal information from the internet.
• .In India, the Supreme Court has recognized the right to privacy as a fundamental right under the Constitution.
• There have been calls for the recognition of the right to be forgotten in Indian law.
• Fundamental rights are the rights that are essential for the survival of people with dignity.
• The Indian Constitution accommodates fundamental rights that are Justiciable subject to reasonable restrictions.

There are six fundamental rights namely

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

The correct answer is Sindhu.

Key Points

• The word Hindu is derived from the Sanskrit word Sindhu which is the local name for the Indus River. Hence option 3 is correct.
• Indus flows through the north-western part of the Indian subcontinent.
• Sindhu also means sea.

Additional Information

• The Indus River is historically famous in Asia.
• It is originated from the Tibetan Plateau and then flows through the Ladakh then entered into Pakistan and finally merge into the Arabian Sea after travelling a distance of 3180 km.

Important Points

Calculation:

The number of persons who have taken the insurance policy, excluding the year 2012 = 54 + 65 + 72 + 84 + 85

⇒ 360

Average = 360/5

⇒ 72

∴ The required answer is 72.

Given:

The HCF of the two numbers is 8 and their LCM is 2520.

Formula used:

Product of the two numbers = LCM × HCF

Calculation:

Let the other number be x

56 × x = 2520 × 8

⇒ x = 2520/7

⇒ x = 360

So, the other number is 360

∴ The other number is 360.

Calculation:

Scheme - I:

15 + 25 - (15 × 25)/100

⇒ 40 - 3.75

⇒ 36.25%

Scheme - II:

So, for buying 5 customers will get a total of 8

So, Discount = (3/8) × 100

⇒ 37.5%

Scheme - III:

So, for buying 4 customers will get a total of 6

So, Discount = (2/6) × 100

⇒ 33.33%

So, Scheme - II is the best for customers

∴ The required answer is Option 3.

Mistake PointsScheme - II: Buy 5, get 3 free

It means, on purchasing 5 items, the buyer will get three more items for free

Scheme - III: Buy 4, get 6

It means, on purchasing 4 items, the buyer will get total of 6 items i.e. two more items for free

Given:

The ratio of the cost price and selling price of an article is 10 ∶ 11.

Concept used:

Profit % = (Profit/Cost price) × 100

Calculation:

Let the cost price and selling price be 10a and 11a

Now,

Profit = 1a

Profit% = (1a/10a) × 100

⇒ 10%

∴ The gain percent is 10%.

Given:

Anju is 30% more efficient than Bitt

Anju can complete the task in 23 days.

Concept used:

Total work = Efficiency of the worker × time taken by the worker

Calculation:

Let the efficiency of Bitt be 10a

So, efficiency of Anju = 10a × 130%

⇒ 13a

So, total work = 13a × 23

⇒ 299a

Now,

If they both work then time = 299a/(13a + 10a)

⇒ 299a/23a

⇒ 299/23

⇒ 13

∴ The required answer is 13 days.

Shortcut Trick

Let Upstream speed be U and Downstream speed be D.

Case 1: 25/U + 39/D = 8 | Case 2: 35/U + 52/D = 11

Using HCF of downstream distances (39, 52) = 13. Let D = 13 km/h.

From Case 1: 25/U + 39/13 = 8 ⇒ 25/U + 3 = 8 ⇒ 25/U = 5 ⇒ U = 5 km/h.

Speed of stream = (D − U) ÷ 2 = (13 − 5) ÷ 2 = 8 ÷ 2 = 4 km/h.

∴ The correct answer is 4 km/h.

Alternate Method

Given:

Upstream distance₁ = 25 km, Downstream distance₁ = 39 km, Time₁ = 8 hours

Upstream distance₂ = 35 km, Downstream distance₂ = 52 km, Time₂ = 11 hours

Formula Used:

Time = Distance ÷ Speed | Speed of Stream = (Downstream Speed − Upstream Speed) ÷ 2

Calculations:

Let Upstream speed be U and Downstream speed be D.

⇒ 25/U + 39/D = 8 --- (Equation 1)

⇒ 35/U + 52/D = 11 --- (Equation 2)

⇒ Multiply (1) by 4 and (2) by 3 to eliminate D:

⇒ (100/U + 156/D = 32) − (105/U + 156/D = 33)

⇒ −5/U = −1 ⇒ U = 5 km/h

⇒ Substitute U = 5 in (1): 25/5 + 39/D = 8 ⇒ 5 + 39/D = 8 ⇒ 39/D = 3 ⇒ D = 13 km/h

⇒ Speed of stream = (13 − 5) ÷ 2 = 8 ÷ 2 = 4 km/h

∴ The correct answer is 4 km/h.

Additional Information

Upstream and Downstream Speeds

Downstream speed (D) = x + y and Upstream speed (U) = x − y, where x is speed in still water and y is stream speed.

Speed of Boat in Still Water

Speed in still water (x) = (D + U) ÷ 2. This is the arithmetic mean of the two speeds.

Average Speed of Boat

If a boat travels a certain distance downstream and returns upstream, Average speed = (D × U) ÷ x = (x² − y²) ÷ x.

Given:

cosec θ + cot θ = p

Concept used:

cosec2 θ - cot2 θ = 1

Calculation: 

cosec² θ - cot² θ = 1

⇒ (cosec θ + cot θ)(cosec θ - cot θ) = 1

⇒ p(cosec θ - cot θ) = 1

⇒ (cosec θ - cot θ) = 1/p

Now,

cosec θ + cot θ + cosec θ - cot θ = p + 1/p

⇒ 2cosec θ = ${{p^2 \ +\ 1} \over p}$

⇒ cosec θ = ${{p^2 \ +\ 1} \over 2p}$

⇒ ${{H} \over P}$ = ${{p^2 \ +\ 1} \over 2p}$

So, H² = P² + B²

⇒ (p² + 1)² = (2p)² + B²

⇒ p4 + 1 + 2p² = 4p2 + B2

⇒ p4 + 1 - 2p2 = B2

⇒ (p2 - 1)2 = B²

⇒ (p2 - 1) = B

Now,

${{p^2 \ - \ 1} \over p^2 \ + \ 1}$ = ${{B} \over H}$ = cosθ

∴ The required answer is cos θ.

Given:

A machine takes 10 h to cut 240 tools.

Calculation:

In 10 h the machine can cut 240 tools

So, in 1 h the machine can cut 24 tools

Now in 25 h the machine will cut 24 × 25

⇒ 600

∴ The required answer is 600.

Given:

m + ${{1} \over m \ - \ 2}$ = 4

Concept used:

(a + b)² = a² + b² + 2ab

Calculation:

m + ${{1} \over m \ - \ 2}$ = 4

⇒ (m - 2) + ${{1} \over (m \ - \ 2)}$ = 2

⇒ (m - 2)2 + ${{1} \over (m \ - \ 2)^2}$ + 2 × (m - 2) × ${{1} \over (m \ - \ 2)}$ = 4

⇒ (m - 2)2 + ${{1} \over (m \ - \ 2)^2}$ = 4 - 2

⇒ (m - 2)2 + ${{1} \over (m \ - \ 2)^2}$ = 2

∴ The required answer is 2.

Given:

cos 2A cos 2B + sin2(A - B) - sin2(A + B)

Concept used:

cos (a + b) = cos a cos b - sin a sin b

sin²a - sin²b = sin(a + b) sin(a - b)

Calculation:

cos 2A cos 2B + sin2(A - B) - sin2(A + B)

⇒ cos 2A cos 2B - [sin2(A + B) - sin2(A - B)] 

{sin2a - sin2b = sin(a + b) sin(a - b)}

⇒ cos 2A cos 2B - [sin(A + B + A - B) sin(A + B - A + B)]

⇒ cos 2A cos 2B - [sin(A + A) sin(B + B)]

⇒ cos 2A cos 2B - sin 2A sin 2B

⇒ cos (2A + 2B)

∴ The required answer is cos (2A + 2B).

Given:

5x - ${{5} \over x}$ + 6 = 0

Concept used:

(a - b)² = a² + b² - 2ab

Calculation:

5x - ${{5} \over x}$ + 6 = 0

⇒ x - ${{1} \over x}$ + ${{6} \over5}$ = 0    [By dividing 5 from both sides]

⇒ x - ${{1} \over x}$ = - ${{6} \over5}$ 

⇒ x2 + ${{1} \over x^{2}}$ - 2 = ${{36} \over25}$

⇒ x2 + ${{1} \over x^{2}}$ = ${{36} \over25}$ + 2

⇒ x2 + ${{1} \over x^{2}}$ = ${{86} \over 25}$

∴ The required answer is ${{86} \over 25}$.

Given:

The number are 3, 4, 5 and 7

Concept used:

The least number which is exactly divisible by a, b, and c is the L.C.M of a, b and c

Calculation:

LCM of 3, 4, 5, and 7 is 420

Now,

By dividing 420 from 35460 we get 180 as the remainder

So,

The required number should be added to the next multiple of 420 = 420 - 180

⇒ 240

∴ The required number is 240.

Given:

AD = x + 3, DB = 2x − 3, AE = x + 1 and EC = 2x − 2

Concept used:

When two triangles are similar, their corresponding angles are equal and their corresponding sides are proportional.

Calculation:

 

 

As DE ΙΙ BC, and ∠A is common in both triangle ABC and triangle ADE

So, ABC ∼ ADE

So,

AB/AD = AC/AE

⇒ (x + 3 + 2x - 3)/(x + 3) = (x + 1 + 2x - 2)/(x + 1)

⇒ (3x)/(x + 3) = (3x - 1)/(x + 1)

⇒ 3x² + 3x = 3x² - x + 9x - 3

⇒ 3x = 8x - 3

⇒ 5x = 3

⇒ x = 3/5

∴ The value of x is ${{3} \over 5}$.

Given:

AB = 6 cm, DF = 16 cm and DE = 8 cm

Concept used:

When two triangles are similar, their corresponding angles are equal and their corresponding sides are proportional.

Calculation:

As ΔABC ~ ΔEDF

So, AB/DE = BC/DF = AC/FE

Now,

AB/DE = BC/DF

⇒ 6/8 = BC/16

⇒ BC = (6 × 16)/8

⇒ BC = 96/8

⇒ BC = 12 cm

∴ The length of BC is 12 cm.

Given:

The diameter of the base as 14 m and slant height as 9 m

Formula used:

Curved surface area of cone = πrl

Here,

r = radius

l = slant height

Calculation:

Let the length of the cloth be a meter.

Area of cloth = a × 2 = 2a m²

Diameter of tent = 14 m

Radius of tent = 14/2 = 7 m

Slant height = 9 m

Curved surface area of cloth = 22/7 × 7 × 9

⇒ 198 m² Then,

2a = 198

⇒ a = 99 m

∴ The length of the cloth is 99 m.

Given:

a = 26 and b = 22

Concept used:

(a² - b²) = (a + b)(a - b)

(a - b)² = a² + b² - 2ab

(a3 - b3) = (a - b)(a² + b² + ab)

Calculation:

${{a^3 \ - \ b^{3}} \over a^2 \ - \ b^{2}}-{{3ab} \over a \ + \ b}$

⇒ ${{a^3 \ - \ b^{3}} \over (a \ + \ b)(a,-,b)}-{{3ab} \over a \ + \ b}$

⇒ ${{(a \ - \ b)(a^2+b^2+ab)} \over (a \ + \ b)(a,-,b)}-{{3ab} \over a \ + \ b}$

⇒ ${{(a^2+b^2+ab)} \over a \ + \ b}-{{3ab} \over a \ + \ b}$

⇒ ${{a^2+b^2+ab-3ab} \over a \ + \ b}$

⇒ ${{a^2+b^2-2ab} \over a \ + \ b}$

⇒ ${{(a-b)^2} \over a \ + \ b}$

⇒ ${{(26-22)^2} \over 26 \ + \ 22}$

⇒ ${{4^2} \over 48}$

⇒ ${{16} \over 48}$

⇒ ${{1} \over 3}$

∴ The required answer is ${{1} \over 3}$.

Calculation:

The total budget allocation for education in all the states = 225 + 75 + 250 + 425 + 535

⇒ 1510

∴ The required answer is 1510.

Given:

Radius of a circle is 5 cm.

Length of chord AB in this circle is 6 cm.

Calculation:

Let OB be the radius of the circle and OD be the distance from the center to the chord AB

Now, We know altitude from the center of a circle to its chord bisect the chord

OB² = BD² + OD²

⇒ 52 = 32 + OD2

⇒ 25 = 9 + OD2

⇒ OD2 = 16

⇒ OD = 4

∴ The distance of this chord from the centre of the circle is 4 cm.

Calculation:

Total GDP of country A in all the 5 years = 175 + 200 + 150 + 75 + 50

⇒ 650

Average = 650/5

⇒ 130 i.e K1

Total GDP of country B in all the 5 years = 285 + 300 + 125 + 85 + 95

⇒ 890

Average = 890/5

⇒ 178 i.e K2

So,

(K1 + K2) = 130 + 178

⇒ 308

∴ The required answer is 308.

Given:

tan 27° tan 34° + tan 34° tan 29° + tan 29° tan 27°

Concept used:

If A + B + C = 90°

Then, tanA.tanB + tanB.tanC + tanC.tanA = 1

Calculation:

27 + 34 + 29

⇒ 90°

Now,

According to the concept,

tan 27° tan 34° + tan 34° tan 29° + tan 29° tan 27° = 1

∴ The required answer is 1.

Given:

The minute hand of a clock is 20 cm long.

Concept used:

Area of a sector = πr² × ${{\theta} \over 360}$

Calculation:

As we know in the 1-minute angle made by the minute hand = 6°

So, in 45 min the minute hand will make 45 × 6 = 270°

Area = π × 20² × ${{270} \over 360}$

⇒ ${{22} \over 7}$ × 400 × ${{270} \over 360}$

⇒ ${{6600} \over 7}$

∴ The required answer is ${{6600} \over 7}$ cm2

Calculation:

No. of students who scored less than 20 = 5

No. of students who scored less than 30 = 6

So, the number of students who scored marks between 20 and 30 = 6 - 5

⇒ 1

∴ The required answer is 1.

Given:

A person borrows Rs. 1,00,000 from a bank at 10% per annum simple interest and clears the debt in five years.

The installment paid at the end of the first, second, third, and fourth years to clear the debt are Rs. 10,000, Rs. 20,000, Rs. 30,000, and Rs. 40,000

Concept used:

S.I = (P × T × R)/100

Here,

P = Principle

T = Time

R = Rate

Calculation:

1^st year interest = 100000 × 10% = 10000

Principal amount after 1^st year = 100000 - 10000 = 90000

2^nd year interest = 90000 × 10% = 9000

Principal amount after 2^nd year = 90000 - 20000 = 70000

3^rd year interest = 70000 × 10% = 7000

Principal amount after 3^rd year = 70000 - 30000 = 40000

4^th year interest = 40000 × 10% = 4000

Principal amount after 4^th year = 40000 - 40000 = 0

At the end of the fifth year, the person has to pay the total interest remaining:

Total Interest = 10000 + 9000 + 7000 + 4000 = 30000

So, the person should pay Rs. 30,000 at the end of the fifth year to clear the debt.

Given:

Average of six numbers = 3.52

Average of two numbers = 3.7

Average of the other two = 2.5

Formula used:

Average = Total sum of numbers/Number of numbers

Calculation:

Total sum of six numbers = 3.52 × 6

⇒ 21.12 

Total sum of two numbers = 3.7 × 2

⇒ 7.4

The total sum of the other two numbers = 2.5 × 2

⇒ 5 

Total sum of remaining two numbers = 21.12 - 7.4 - 5

8.72

Average of remaining two numbers = 8.72/2 = 4.36

∴ The average of the remaining two is 4.36.

Given:

A Microwave oven is sold in Hyderabad for Rs. M.

A retailer, Elahi from Hyderabad went to Madras and bought it for 25% less (when compared to the price in Hyderabad).

Calculation:

Price at Madras = M × 75%

⇒ 3M/4

According to the question,

(3M/4 + 1000) × 110% = M

⇒ (3M/4 + 1000) × 110/100 = M

⇒ (3M/4 + 1000) × 110 = 100M

⇒ 82.5M + 110000 = 100M

⇒ 17.5M = 110000

⇒ M = 110000/17.5

⇒ M = 6285.71 ≈ 6285.7

∴ The value of M is 6285.7.