SSC CGL 2022 Tier-I Official Paper (Held On : 13 Dec 2022 Shift 3) (Previous Year Paper)

The logic followed here is:-

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

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

Opposite pairs:

3 → 5

4 → 6

1 → 2

So, the opposite side of "1" will be side "2".

Hence, the correct answer is "2".

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

Conclusions:

I. All P are T → Does not follow (As some P are K and no K is T. So, some P's part comes in K which has direct negative or cross relation with T therefore it is definitely false)

II. All T are K → Does not follow (As no K is T. So, a direct negative or cross relation is given between K and T therefore it is definitely false)

III. Some P are not T → Follow (As some P are K and no K is T. So, some P's part comes in K which has direct negative or cross relation with T therefore it is definitely true)

∴ Here, Only conclusion III follows.​

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

The logic followed here is :- (2) is multiplied by the sum of the position value of the letters within the word according to English alphabetic series

​So,

• ‘FROST’ is written as ‘156’

And,

• ‘CANDLE’ is written as ‘78’

Similarly,

• ‘SCREAM’ is written as :

Hence, the correct answer is "118".

The logic followed here is : (5 × 1^st number) - (4 × 2^nd number) = 3^rd number

So,

• First row - 12, 7, 32

(5 × 12) - (4 × 7) = 32

60 - 28 = 32

32 = 32 (LHS = RHS)

And, 

• Second row - 17, 13, 33

(5 × 17) - (4 × 13) = 33

85 - 52 = 33

33 = 33 (LHS = RHS)

Similarly,

• Third row - 14, 8, ?

(5 × 14) - (4 × 8) = ?

70 - 32 = ?

38 = ? 

Hence, "38" is the correct answer.

Given :

Given statement : A - B % C * D + E

So,

• A - B → A is the mother of B.

• B % C → B is the brother of C.

• C * D → C is the sister of D.

• D + E → D is the father of E.

​​

Thus, according to the final family tree A is the paternal grandmother i.e father’s mother of E.

Hence, "Father’s mother" is the correct answer.

According to the question, after interchanging the number 9 and 6:

So,

• Option - (1) : 7 + 6 × 4 ÷ 9 – 8 = 5  ⇒  7 + 9 × 4 ÷ 6 – 8 = 5

7 + 9 × 4 ÷ 6 – 8 = 5

7 + 9 × 0.67 - 8 = 5

7 + 6 - 8 = 5

13 - 8 = 5

 

5 = 5 (LHS = RHS)

• Option - (2) : 6 × 8 – 9 ÷ 3 + 5 = 75  ⇒  9 × 8 – 6 ÷ 3 + 5 = 75

9 × 8 – 6 ÷ 3 + 5 = 75

9 × 8 – 2 + 5 = 75

72 + 5 - 2 = 75

77 - 2 = 75

75 = 75 (LHS = RHS)

• Option - (3) : 9 × 7 + 4 ÷ 1 – 6 = 38  ⇒  6 × 7 + 4 ÷ 1 – 9 = 38

6 × 7 + 4 ÷ 1 – 9 = 38

6 × 7 + 4 - 9 = 38

42 + 4 - 9 = 38

46 - 9 = 38

37  ≠Unknown node type: strong 38 (LHS ≠Unknown node type: strong RHS)

• Option - (4) : 7 × 6 ÷ 3 + 9 – 8 = 19  ⇒  7 × 9 ÷ 3 + 6 – 8 = 19

7 × 9 ÷ 3 + 6 – 8 = 19

7 × 3 + 6 – 8 = 19

21 + 6 – 8 = 19

27 - 8 = 19

19 = 19 (LHS = RHS)

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

Given : Year 2003 = (Leap year + 3)  = 2000 + 3

Explanation : 

In case of a repeating year, we add (11) to the given year :

So, 

2003 + 11 ⇒ 2014

Hence, "2014" is the correct answer.

Additional Information 

• Trick to remember:

Logic : ​

1. First letter → (2) is added to the position value according to the English alphabetic series.
2. Second letter → (2) is subtracted from the position value according to the English alphabetic series.​
3. Pair of the letters are opposite letters according to the English alphabetic series

​So,

​

Hence, the correct answer is "NM".

Given :

So,

• Option - (1) : Q - P + R → Q is the mother of P who is the sister of R.

​

Here, P is the sister of R.

• Option - (2) : P - Q + R → P is the mother of Q who is the sister of R.

​

Here, P is the mother of R.

• Option - (3) : P × Q + R → P is the father of Q who is the sister of R.

​

Here, P is the father of R.

• Option - (4) : R + Q - P → R is the sister of Q who is the mother of P.

​

Here, P is either niece or nephew of R.

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

The logic here followed is

Hence, the correct answer is "Option 1".

In the given analogy, "Flock" is related to "Birds" because a flock is a group of birds.

Similarly, "Swarm" is related to "Bees" because a swarm is a group of bees.

The relationship is based on the fact that both pairs represent groups of specific types of animals.

Hence, the correct answer is option 2 - Bees.

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

So,

• 8 : 48

​8 × (8 - 2) = 48

8 × 6 = 48

48 = 48 (LHS = RHS)

And,

• 15 : 195​

​15 × (15 - 2) = 195

15 × 13 = 195

195 = 195 (LHS = RHS)

Similarly,

• ? : 143​

​Let '?' be 'x'

​x × (x - 2) = 143

x2 - 2x = 143

x2 - 2x - 143 = 0 

(x - 13) (x + 11) = 0

x =  either 13 or (-11)

As, the answer cannot be negative, therefore value of x will be 13.

Hence, "13" is the correct answer.

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

Conclusions:

I. Some Lego are puzzles → Does not follow (As no block is lego and some puzzles are blocks. So, it is possible but not definitely true)

II. No Lego is a block → Follow (As no block is lego. So, a direct negative or cross relation is given between lego and block therefore it is definitely true)

III. Some toys are blocks → Does not follow (As all toys are lego and no block is lego. So, all toys comes in lego which has direct negative or cross relation with T therefore it is definitely false)

∴ Here, Only conclusion II follows.​

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

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

Given :

• (5, 2, 23)

$(5)^2$ - 2 = 23

25 - 2 = 23

23 = 23 (LHS = RHS)

• (6, 2, 34)

$(6)^2$ - 2 = 34

36 - 2 = 34

34 = 34 (LHS = RHS)

​So,

• Option - (1) : (3, 3, 3)

$(3)^2$ - 3 = 3

9 - 3 = 3

6 ≠ 6 (LHS ≠ RHS)

• Option - (2) : (3, 2, 9)​

$(3)^2$ - 2 = 9

9 + 2 = 9

7 ≠ 9 (LHS ≠ RHS)

• Option - (3) : (3, 5, 11)

$(3)^2$ - 5 = 11

9 - 5 = 11

4 ≠ 11 (LHS ≠ RHS)

• Option - (4) : (3, 2, 7)

$(3)^2$ - 2 = 7

9 - 2 = 7

7 = 7 (LHS = RHS)

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

In the given analogy, "Drama" is related to "Stage" because a drama is typically performed on a stage.

Similarly, "Trial" is related to "Court" because a trial takes place in a court.

The relationship is based on the fact that both pairs represent events or activities that occur in specific locations.

Hence, The correct answer is option 4 - Court.

Logic : Same difference of the position values between first letter and second letter and second letter and third letter according to English alphabetic series.

So,

• OQS​

​

• JLN​

• HJL​

• MOP

Here, Only 'MOP' is the odd one out as the difference is not same between the 1^st letter and 2^nd letter and 2^nd letter and 3^rd letter.

Hence, "MOP" is the correct answer.

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

1) For ''

 element : Corner triangles are shaded anti-clockwise subsequently.

​​

2) For ''

 element : No change

Final series is :

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

The logic followed here is :- the sum of the position value of the letters + 10

​So,

• 'YOU’ is written as '71'

And,

• 'TOO' is written as '60'

Similarly,

• 'SIT' is written as :

Hence, the correct answer is "58".

Logic : ​

• First letter → (2) is added to the position value according to the English alphabetic series.
• Second letter → (8) is subtracted from the position value according to the English alphabetic series.
• Third letter → (3) is added to the position value according to the English alphabetic series.
• Fourth letter → (4) is subtracted from the position value according to the English alphabetic series.

​So,

Hence, "IVON" is the correct answer.

The logic followed here is :Square of 1^st number = 2^nd number

• Option - (1) : 10 - 100

$(10)^2$ = 100

10 = 10 (LHS = RHS)

• Option - (2) : 8 - 62

$(8)^2$ = 62

64 ≠ 62 (LHS ≠ RHS)

• Option - (3) : 6 - 36

$(6)^2$ = 36

36 = 36 (LHS = RHS)

• Option - (4) : 4 - 16

$(4)^2$ = 16

16 = 16 (LHS = RHS)

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

The logic followed here is : Multiples of 3 are added subsequently.

Hence, "34" is the correct answer.

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

1) For '

' element : Rotating 90º in the clockwise direction subsequently.

2) For ''

 element : Shifting in the clockwise direction along with replacing the second succeeding letter according to the English alphabetical series.

3) For ''

 element : Shifting in the clockwise direction along with replacing the second succeeding letter according to the English alphabetical series.

​​Final series is :

Hence, ‘option - (1)’ is the correct answer.

The image embedded in given figure is as shown below :

∴ Here, Option figure -(2) is embedded in given figure.

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

According to the question, after interchanging the number 2 and 8:

So,

• Option - (1) : 8 ÷ 1 + 4 × 2 – 3 = 18  ⇒  2 ÷ 1 + 4 × 8 – 3 = 18

2 ÷ 1 + 4 × 8 – 3 = 18

2 + 4 × 8 – 3 = 18

2 + 32 - 3 = 18

34 - 3 = 18

31 ≠ 18 (LHS ≠ RHS)

• Option - (2) : 7 × 2 + 6 ÷ 3 – 8 = 60  ⇒  7 × 8 + 6 ÷ 3 – 2 = 60

7 × 8 + 6 ÷ 3 – 2 = 60

7 × 8 + 2 - 2 = 60

56 + 2 - 2 = 60

58 - 2 = 60 

56 ≠ 60 (LHS ≠ RHS)

• Option - (3) : 2 × 4 – 8 + 6 ÷ 3 = 33  ⇒  8 × 4 – 2 + 6 ÷ 3 = 33

8 × 4 – 2 + 6 ÷ 3 = 33

8 × 4 – 2 + 2 = 33

32 + 2 - 2 = 33

34 - 2 = 33

32 ≠Unknown node type: strong 33 (LHS ≠Unknown node type: strong RHS)

• Option - (4) : 8 × 4 + 6 – 2 ÷ 1 = 6  ⇒  2 × 4 + 6 – 8 ÷ 1 = 6

2 × 4 + 6 – 8 ÷ 1 = 6

2 × 4 + 6 – 8 = 6

8 + 6 - 8 = 6

14 - 8 = 6

6 = 6 (LHS = RHS)

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

Given statement : 95 * 5 + 19 ÷ 2 − 21 = 36

According to the question, after interchanging the signs:

So,

• Option - (1) : ÷ and *​

Given statement : 95 * 5 + 19 ÷ 2 − 21 = 36

95 ÷ 5 + 19 × 2 − 21 = 36

19 + 19 × 2 − 21 = 36

19 + 38 - 21 = 36

57 - 21 = 36

36 = 36 (LHS = RHS)

• Option - (2) : + and -

Given statement : 95 * 5 + 19 ÷ 2 − 21 = 36

After interchanging:

95 × 5 - 19 ÷ 2 + 21 = 36

95 × 5 - 9.5 + 21 = 36

475 + 21 - 9.5 = 36

496 - 9.5 = 36

486.5 ≠ 36 (LHS ≠ RHS)

• Option - (3) : ÷ and −

Given statement : 95 * 5 + 19 ÷ 2 − 21 = 36

After interchanging:

95 × 5 + 19 - 2 ÷ 21 = 36

95 × 5 + 19 - 0.095 = 36

475 + 19 - 0.095 = 36

494 - 0.095 = 36

493.9 ≠ 36 (LHS ≠ RHS)

• Option - (4) : + and *

Given statement : 95 * 5 + 19 ÷ 2 − 21 = 36

After interchanging:

95 + 5 × 19 ÷ 2 − 21 = 36

95 + 5 × 7.5 - 21 = 36

95 + 37.5 - 21 = 36

132.5 - 21 = 36

111.5 ≠ 36 (LHS ≠ RHS)

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

The correct answer is Africa.

Key Points

• Longitude and Latitude- Latitude and longitude are imaginary lines and are used to define any location on earth.
• Latitude is the angular distance of a point on the surface, from the central part of the Earth.
• While lines joining the North Pole to the South Pole are called longitude lines earth is divided into a total of 360 longitude lines.
• Longitude and latitude both measure in degrees.

Important Points

• Equator-Equator represents the zero degrees latitude line it is an imaginary line running on the globe divides it into two equal parts.
• The northern half of the earth is known as the Northern Hemisphere and the southern half is known as the Southern Hemisphere The Equator passes through South America, Asia, and Africa.
• Tropic of Cancer- It is a line of latitude 23½° N in the Northern Hemisphere.
• It passes through Africa, Asia, and North America.
• Tropic of Capricorn- It is a line of latitude 23½° S in the Southern Hemisphere.
• It passes through South America, Africa, and Australia.

The correct answer is It provides advisory opinion to the President of India.

 Key Points

• The High Courts of India are the highest courts of appellate jurisdiction in each State and Union Territory of India.
• Judges in a high court are appointed by the President of India in consultation with the chief justice of India and the governor of the state under Art 217 of the Constitution but through subsequent judicial interpretations, the primacy of the appointment process is in the hands of the Judicial Collegium.
• High courts are headed by a chief justice.
• The chief justices rank fourteenth (within their respective states) and seventeenth (outside their respective states) on the Indian order of precedence.
• The number of judges in a court is decided by dividing the average institution of main cases during the last five years by the national average, or the average rate of disposal of main cases per judge per year in that high court, whichever is higher.
• The judge of High court retires at the age of 62.
• According to Article 124(2) of the Constitution, the age of retirement for Supreme Court judges is 65.
• As per Article 217(1) of the Constitution, High Court judges retire at 62.
• Initially, the retirement age of High Court judges was 60, which was later in 1963 increased to 62 through the 15^th constitutional amendment Bill.
• The idea of increasing the age of retirement for judges has been mooted for decades as a solution for dealing with mounting pendency of cases and judicial vacancies.
• It has also been discussed in the context of ensuring serving judges do not look for post-retirement jobs from the executive.
• Attorney General for India K K Venugopal has been one of the vocal advocates of increasing tenure of the judges, and has consistently spoken about it at every farewell of Supreme Court judges since 2017.

The correct answer is Indira Gandhi.

Key Points

• The Wheat Revolution stamp
• In the year 1968, as a result of the green revolution, wheat production in the country rose to 17 million tons from 12 million tons during the previous period.
• To signify the achievements of the green revolution, then Prime Minister Indira Gandhi released a special stamp titled 'Wheat Revolution' in July 1968.
• The Yellow Revolution is concerned with oilseed production.
• This revolution means the cultivation of mustard as a part of crop rotation.
• The Father of the Yellow Revolution is Sam Pit Roda.
• It was also called People Power Revolution.
• It was first launched in 1986-87 in India.
• To popularize the four major oilseeds- groundnut, mustard, soybean, and sunflower.

Additional Information

• Green Revolution
• The Green Revolution is referred to as the process of increasing agricultural production (especially wheat and rice) through the introduction of modern tools and technology.
• The green revolution marks the period when the agricultural sector of the country was transformed into a commercial sector with the adoption of modern methods and techniques like the use of a high-yielding variety of seeds, machinery, irrigation facilities, pesticides, and fertilizers.

The correct answer is Ghiyasuddin Balban.

Key Points

• Ghiyasuddin Balban:
• He ruled from 1266 AD-1287 AD.
• He was a member of Chahalgani Chalisa.
• He broke the power of Chahalgani and restored the prestige of the crown.
• He created a strong centralised army and established the military department Diwan-i-Arz.
• He took up the title of Zil-i-Ilahi (a shadow of God) and impressed upon the people that the king was the deputy of God (Niyabat-i-Khudai).
• He insisted on the Iranian ceremonies of Sijda and Paibos.
• Balban started the festival of Navroz.
• He adopted a policy of blood and iron.
• He was a patron of Persian literature and showed special favour to Amir Khusro.

Additional Information

• The list of Sultans belonging to the Slave Dynasty
• Qutb ud-Din Aibak (1206-1210 AD)
• Aram Shah (1210-1211 AD)
• Iltutmish (1211-1236 AD)
• Rukn-ud-din Feroze (1236 AD)
• Razia al-Din (1236-1240 AD)
• Muiz-ud-din Bahram Shah (1240-1242 AD)
• Ala-ud-din Masud Shah (1242-1246 AD)
• Nasiruddin Mahmud Shah (1246-1266 AD)
• Ghiyas-ud-din Balban (1266-1286 AD)
• Muiz-ud-din Muhammad Qaiqabad (1286-1290 AD)

The Correct answer is Legal right.

Key Points

• Right to Property:
• The right to property was deleted from the list of Fundamental Rights by the 44^th Amendment Act, of 1978.
• It is made a legal right under Article 300-A in Part XII of the Constitution. So at present, there are only six Fundamental Rights.
• Article 19 provided to all citizens the right to acquire, hold, and dispose of their property whereas Article 31 provides that "no person shall be deprived of his property save by authority of law."
• Later, in 44thAmendment of 1978 deleted the right to property from the list of fundamental rights.
• Hence, the right to property is no longer a fundamental right, however, it is still a constitutional right.​​

Additional Information 

• Fundamental Rights:
• Presently there are 6 fundamental rights.
• Supreme Court is the custodian or protector of fundamental rights.
• It was borrowed from U.S. Constitution.
• Articles:
• Right to equality (14 - 18)
• Right to freedom (19 - 22)
• Right against exploitation (23 - 24)
• Right to freedom of religion(25 - 28)
• Cultural and educational rights (29 - 30)
• Right to constitutional remedies (32)

The correct answer is Maharashtra.

Key Points

• Maharashtra ’s Health Minister Rajesh Tope had announced that "Hope Express" that was launched in the state to prevent cancer.
• He announced this at the launch of a state-of-the-art Mosaic-3D radiation machine at a private hospital in Kolhapur.
• This is the first such machine in India.
• He also inaugurated the Oncoprime Cancer Center online at the Hattarki Hospital in Gadhinglaj.

Important Points

• Hope Express started in every district of the state through district planning.
• The center will benefit patients in rural areas.

Additional Information 

• Maharashtra:
• Number of Districts - 36.
• Lok Sabha seats - 48.
• Rajya Sabha seats - 19.
• State Animal - Indian giant squirrel.
• State Bird - Yellow-footed green pigeon.
• National Parks - Chandoli National Park, Gugamal National Park, Nawegaon National Park, Sanjay Gandhi (Borivilli) National Park, Tadoba National Park.
• Dams - Koyna Dam (Koyna River), Jayakwadi Dam (Godavari River), Wilson Dam (Pravara River), Vaitarna Dam (Vaitarna River), Mula Dam (Mula River).

The correct answer is Aparna Satheesan

Key Points 

• National Nritya Shiromani Award is an annual award given to exceptional classical dancers and musicians of India for their contribution to art and culture.
• Aparna Satheesan, the international Kuchipudi dancer received the National Nritya Shiromani Award for 2022 at the 13^th Cuttak Mahotsav. Hence option 2 is correct.
• She is from Kerala, an expert in Bharatnatyam and a senior disciple of Guru Smt. Vyjayanthi Kashi.
• Kuchipudi is one of the 8 major Indian classical dances from Andhra Pradesh while Bharatnatyam originated from Tamil Nadu.

Additional Information 

• Radha Reddy is a renowned Indian classical dancer specialising in the Kuchipudi dance form.
• She has been awarded the Padma Shri and Padma Bhushan for her contributions to the field of dance.
• Usha Srinivasan is an accomplished Bharatanatyam dancer and teacher known for her unique style that seamlessly blends tradition and innovation.
• She has received several awards and accolades for her contributions to the field.
• Deepa Sashindran is a versatile contemporary dancer and choreographer from India who has trained in various dance forms.
• She has collaborated with many renowned artists and organizations around the world to create impactful performances that explore complex themes and issues.

The correct answer is Grass.

Key Points

• Grass contains a high amount of cellulose, which is a complex carbohydrate that is difficult to break down.
• To digest cellulose effectively, herbivores like cows, horses, and sheep have evolved a specialized digestive system that includes a longer small intestine.
• The small intestine is where most of the nutrients from food are absorbed into the body. In herbivores, the small intestine is longer than in carnivores or omnivores to allow for more time to break down and digest cellulose.
• Additionally, herbivores have a symbiotic relationship with microorganisms in their digestive tract, which help break down cellulose into simpler compounds that can be absorbed by the body.
• Overall, the longer small intestine and symbiotic relationship with microorganisms in the digestive tract are adaptations that have evolved to enable herbivores to efficiently digest cellulose and extract nutrients from plants, such as grass.

Important Points

• Digestion: 
• ​it is the complex process of turning the food we eat into nutrients, which the body uses for energy, growth and cell repair needed to survive.
• It also involves creating water to be excreted.
• Human Digestive System:​
• The Human Digestive system consists of the alimentary canal which can be further divided into various components.
• Buccal cavity
• Food pipe or oesophagus
• Stomach
• Small intestine
• Large intestine
• Rectum
• Anus

The correct answer is warning for misconduct.

Key Points

• Badminton
• ​Lawn, court, or badminton game played with a shuttlecock and lightweight rackets.
• The shuttlecock, commonly referred to as a "bird" or "birdie," was historically a little cork hemisphere with 16 goose feathers sewn on it that weighed about 0.17 ounces (5 grams).
• Modern play may still employ these shuttles, although the Badminton World Federation also permits the use of synthetic shuttles.
• The game is called after Badminton, which was initially played around 1873 at the Duke of Beaufort's country home in Gloucestershire, England.
• Poona, a game played by British army officers stationed in India in the 1860s, is directly related to badminton.
• In 1899, the first unofficial all-England men's badminton championships and the inaugural badminton competition for women were arranged the next year.
• Badminton made its Olympic debut in 1972 as a demonstration sport and in 1988 as an exhibition sport.
• It was made a full-medal Olympic sport for the 1992 Games, including competition in the men's and women's singles (one against one) and doubles events (two against two).
• The mixed pairs event debuted in the 1996 Olympics.
• The rectangular court is 44 feet (13.4 metres) long and 17 feet (5.2 metres) in width for singles and doubles, respectively.
• The 2022 BWF World Championships were a badminton competition that took place from August 22 to August 28 at Tokyo Metropolitan Gymnasium in Tokyo, Japan (formally known as the Total Energies BWF World Championships 2022 due to sponsorship considerations).
• 2022 BWF World Championships medalist table

Important Points 

The correct answer is 1891.

Key Points

• National Archives of India 
• It was set up on 11 March 1891 in Kolkata.
• It is the custodian of the records of the enduring value of the Government of India.
• It is under the Ministry of Culture.
• It provides financial assistance to State/Union Territories.
• It has a regional office at Bhopal and records centres at Jaipur, Pondicherry, and Bhubaneswar.
• The National Archives of India (NAI) is located in New Delhi at the intersection of Janpath and Rajpath in Delhi.
• It is the Central Repository of non-current records of enduring value belonging to: 
• Ministries and Departments of the Government of India.
• Private papers of eminent Indians.
• Microfilm copies of records of Indian interests from abroad.

Additional Information

• Calcutta
• The National Archives was established on March 11^th, 1891.
• It is the keeper of the Government of India's enduringly valuable records.
• It is South Asia's largest repository for historical materials.
• Bombay
• According to the Court of Directors' directives in their letter dated November 21, 1787, this was founded in 1788, and its proceedings began on June 3, 1788. Up to 1805.
• It was a part of the Public Department.
• Uttar Pradesh
• In 1813, it was split off from the Commercial Department.
• The UP State Archives of UP's goals are to maintain and preserve government records and make them easier to use.
• To provide secure custody for non-current records that are dispersed throughout various departmental, divisional, district, and other public offices.

The correct answer is PI - Personal tax payments - Non-tax payments.

Key Points

• The part of National Income (NI) that is received by households is referred to as Personal Income (PI).
• First, let us note that out of NI, which is earned by the firms and government enterprises, a part of the profit is not distributed among the factors of production.
• This is called Undistributed Profits (UP).
• We have to deduct UP from NI to arrive at PI since UP does not accrue to households.
• Similarly, Corporate Tax, which is imposed on the earnings made by the firms, will also have to be deducted from the NI, since it does not accrue to the households.
• On the other hand, the households do receive interest payments from private firms or the government on past loans advanced by them.
• And households may have to pay interest to the firms and the government as well, in case they had borrowed money from either.
• So we have to deduct the net interests paid by the households to the firms and government.
• The households receive transfer payments from the government and firms (pensions, scholarships, prizes, for example) which have to be added to calculate the Personal Income of the households.
• Thus, Personal Income (PI) = NI – Undistributed profits – Net interest payments made by households – Corporate tax + Transfer payments to the households from the government and firms.
• However, even PI is not the income over which the households have a complete say.
• They have to pay taxes from PI. If we deduct the Personal Tax Payments (income tax, for example) and Non-tax Payments (such as fines) from PI, we obtain what is known as Personal Disposable Income.
• Thus Personal Disposable Income (PDI ) = PI – Personal tax payments – Non-tax payments.
• Personal Disposable Income is part of the aggregate income which belongs to the households.
• They may decide to consume a part of it and save the rest.

The correct answer is 1872.

Key Points

• A population census is a method by which demographic, social, cultural and economic data relating to each and every person in that country are compiled, collected, analysed and disseminated at a specific time over 10 years.
• The first census was conducted in India in 1872, but the regular census started in 1881.
• The first census in all of India was conducted by the British Raj authorities.

Additional Information

• The 15^th Census of India and the 7^th Census of Independent India-2011 were started on 1^st April 2010 with President being the first citizen to be enumerated, followed by the Vice President of India.
• The slogan of Census 2011 was ‘Our Census, Our future’.
• C. Chandramouli was the Census Commissioner of India in 2011.
• The population of the nation as per the provisional figures of Census 2011 is 1210.19 million of which 623.7 million (51.54%) are males and 586.46 million (48.46%) are females.
• Uttar Pradesh is the most populous state in India its population is more than the population of Brazil.
• Thus, the first census started in 1872.

Key Points

• Kunbi dance is a tribal folk dance of the Kunbi community of Goa that portrays social themes.
• The dance is simple in its presentation and is performed during various social occasions.
• Kunbi (alternatively Kanbi) is a generic term applied to castes of traditionally non-elite farmers in Western India.

Additional Information

The correct answer is a typhoon.

Key Points 

• A cyclone is known by different names in different parts of the world.
• It is called a 'typhoon’ in Japan and the Philippines.
• While they are called ‘cyclones’ in the Indian and South Pacific oceans.
• In the Atlantic Ocean, they are called ‘hurricanes’.

Additional Information 

• Cyclone: 
• A cyclone is a large air mass that rotates around a strong centre of low atmospheric pressure.
• Cyclones rotate clockwise in the Southern Hemisphere and anti-clockwise in the Northern Hemisphere.
• Cyclones are rapid inward air circulation around a low-pressure area.
• Factors like wind speed, wind direction, temperature and humidity contribute to the development of cyclones.
• Cyclone/Strom is termed by different names in different continents -

Important Points

• Cyclone is a chain of events that ends with the formation of a very low-pressure system with very high-speed winds revolving around it.
• The centre of a cyclone is a calm area.
• It is called the eye of the storm.
• A large cyclone is a violently rotating mass of air in the atmosphere, 10 to 15 km high.
• A cyclone is known by different names in different parts of the world.
• It is called a ‘hurricane’ on the American continent.
• In the Philippines and Japan, it is called a ‘typhoon’.
• In Australia it is known as willy - willy.

The correct answer is Sher Shah.

Key Points

• The Battle of Chausa took place in June 1539.
• Battle of Chausa
• This battle was fought between Humayun and Farid Khan (Sher Shah Suri) on 26^th June 1539.
• Chausa is located in Buxar, Bihar.
• Humayun was defeated in this battle.
• After this battle, Humayun flee to Iran, where he spent 12 years of his life in exile.
• After this battle, Farid Khan accepted the title of Sher Shah (Farīd al-Dīn Shēr Shah) as emperor.

Important Points

The correct answer is Gujarat.

Key Points

• Former Gujarat CM Vijay Rupani has approved the Rs.39 Cr Seema Darshan.
• This project is for developing more infrastructure facilities at Nadabet near Suigam in the Banaskantha district.
• Prime Minister Narendra Modi said, “Seema Darshan Project adds a new dimension to the tourism sector”.
• The project is being developed on the Wagah Border pattern & entails a parade ground with an amphitheatre.
• The project will encourage local economic activity in the Rann region & tourists can have a good view of the coastline.

Additional Information

• Gujarat:
• Chief Minister - Bhupendra Patel.
• Governor - Acharya Devvrat.
• State Animal - Asiatic lion.
• State Bird - Greater flamingo.
• National Parks - Vansda National Park, Blackbuck National Park, Gir Forest National Park, Marine National Park.
• Dams - Sardar Sarovar Dam(Narmada River), Ukai Dam (Tapti River), Dantiwada Dam (Banas River), Kadana Dam (Mahi River), Kamleshwar Dam (Hiran River).
• Registered GI: Agates of Cambay, Kutch Embroidery, Patan Patola, Tangaliya Shawl.

The correct answer is Surat.

Key Points

• Surat in Gujarat has become the first city in the country to get a processed steel slag (industrial waste) road.
• The first 6-lane highway made using Steel Slag was inaugurated in Surat by Union Steel Minister Ram Chandra Prasad Singh on 15 June 2022.
• The road has been jointly made by the Central Road Research Institute & ArcelorMittal Nippon Steel India.

Additional Information

• ​Gujarat is a state along the western coast of India.
• Its coastline of about 1,600 km is the longest in the country, most of which lies on the Kathiawar peninsula.
• Gujarat:
• Capital: Gandhinagar
• Formation: 1 May 1960
• Governor: Acharya Devvrat
• Chief Minister: Bhupendrabhai Patel

The Correct Answer is Canada.

Key Points

• Commonwealth Games:
• Commonwealth Games were previously called the 'British Empire Game'.
• The Commonwealth Games take place every four years.
• The first Commonwealth Games were held in 1930 in Hamilton, Canada.
• The last country to join the Commonwealth was Rwanda in 2009.
• UK, Birmingham is to host the 2022 Commonwealth Games.

Additional Information

• Olympic Games:
• The first modern Olympics were held in Athens, Greece, in 1896.
• The Olympic Games were held every four years.
• Paris is to host the 2024 Olympics.
• Asian Games:
• The Asian Games, also known as Asiad.
• The Asian Games is a multi-disciplinary sports event held once every four years.
• It is the second-largest multi-sport event after the Olympics.
• It is held every four years among athletes from all over Asia.
• The first-ever Asian Games were held at New Delhi in 1951.
• China is to host the 2022 Asian Games.
• Pan American Games:
• It is an American summer sports event.
• The competition is held among athletes from nations of the Americas.
• It is held every four years.

The correct answer is 7.

Key Points

• The theory of plate tectonics proposes that the earth's lithosphere is divided into 7 major and 8 minor plates.
• The theory of plate tectonics is the modern update of Continental drift proposed by Alfred Wegener in 1912.
• The theory of plate tectonics explains the features and movement of the Earth's surface.
• In Plate tectonics, Earth’s outermost layer i.e. the lithosphere is broken into large rocky plates.
• Plate tectonics explains many events such as volcanoes, earthquakes, and the formation of mountains which are a result of Earth’s subterranean movements.
• The Lithosphere is made of the crust and upper mantle of the Earth and is 100km thick.

Additional Information

• The Largest plates are the Antarctic, Eurasian, and North American plates.
• Continental plates (up to 200km) are thicker than oceanic plates (50-100km).
• The Seven major plates are:

1. African,
2. Antarctic,
3. Eurasian,
4. North American,
5. South American,
6. India-Australian, and
7. The Pacific plates

​The Some of minor plates are:

• Arabian,
• Caribbean,
• Nazca, and
• Scotia plates.​

The correct answer is The build-up of lactic acid in our muscles during sudden activity causes cramps.

Key Points

• Anaerobic respiration:
• During heavy physical exercise, most of the energy in our muscles is provided by oxygen breakdown.
• Anaerobic respiration in muscles provides only some extra energy which is needed under the conditions of heavy physical activities.
• The anaerobic respiration by muscles brings about a partial breakdown of glucose to form lactic acid.
• The accumulation of lactic acid in the muscles causes muscle cramps.
• Thus, muscle cramps occur due to the accumulation of lactic acid in muscles when the muscles respire anaerobically while doing hard physical exercise.
• We can get relief from cramps in muscles caused by heavy exercise by taking a hot water bath or massage.
• A hot water bath improves the circulation of blood in the muscles.
• Due to improved blood flow, the supply of oxygen to the muscles increases.
• This oxygen breaks down lactic acid accumulated in muscles into carbon dioxide and water, and hence gives us relief from cramps.

The correct answer is (i) - (a), (ii) - (c), (iii) - (b), (iv) - (d).

Key Points

• Alkali metal:
• Group 1 elements in the periodic table, consist of lithium, sodium, potassium, rubidium, cesium, and francium.
• They are highly reactive, easily losing an electron to form a positive ion, and are stored under oil or inert gas to prevent reactions with air and moisture.
• Alkali metals have low densities, and low melting points, and are good conductors of heat and electricity.
• They have various uses, including in batteries, alloys, and as a coolant in nuclear reactors.
• Alkaline earth metal:
• Group 2 elements in the periodic table, including beryllium, magnesium, calcium, strontium, barium, and radium.
• They are also reactive and easily lose two electrons to form a positive ion but are less reactive than alkali metals.
• Alkaline earth metals have higher densities and melting points than alkali metals and are also good conductors of heat and electricity.
• They have many practical applications, such as in construction materials, alloys, and fireworks.
• Transition metal:
• Elements in the d-block of the periodic table, consisting of groups 3-12, including iron, copper, silver, and gold.
• They have multiple valence electrons and can form various oxidation states, giving them the ability to form complex compounds and exhibit colourful properties.
• Transition metals have high densities, and melting points, and are good conductors of heat and electricity.
• They have numerous applications in technology, such as in catalysts, electronic devices, and construction materials.
• • Group 18 elements in the periodic table, consisting of helium, neon, argon, krypton, xenon, and radon.
• They are characterized by their extremely low reactivity and are usually found as monatomic gases in the atmosphere.
• Noble gases have complete valence electron shells, making them chemically stable and unreactive with other elements.
• They have applications in lighting, cryogenics, and as a shielding gas in welding.

The correct answer is Kirana.

Key Points

• Kirana Gharana is one of Hindustan's most prolific Khayal Gharana.
• The name of this music school stems from Kirana or Kairana in Uttar Pradesh's Shamli region, which is also the hometown of stalwarts like Ustad Abdul Karim Khan and Ustad Abdul Waheed Khan who founded this Gharana.
• The Kirana style is primarily concerned with Swara, or individual notes, specifically precision tuning and note expression.
• Individual notes of the raga are regarded as autonomous domains of music capable of horizontal growth in the Kirana Gayaki, not merely random positions in the scale.
• It is regarded as the best in terms of a note or Swara intonation
• The major emphasis of the Kirana style is Swara, namely exact tuning and note expression.
• There were four schools or vanis of singing the dhrupad.

Additional Information

The correct answer is Dr Padma Subrahmanyam.

Key Points

• Padma Subrahmanyam:
• Dr Padma Subrahmanyam entered her training in Bharatanatyam under the education of Vazhuvoor Ramaiah Pillai and Mylapore Gouri Amma.
• An exponent of Bharatanatyam, Dr Padma Subrahmanyam has presented her art across the world, sharing in prestigious public and transnational carnivals of dance.
• She has won multitudinous accolades including the Padma Shri, the Padma Bhushan (2003), the Sangeet Natak Akademi Award( 1983), the Kalaimamani, and the Kalidas Samman.

Additional Information

• Mungara Yamini Krishnamurthy, an Indian dancer who specialises in Kuchipudi and Bharatanatyam, was born on December 20, 1940.
• In Madras, Yamini Krishnamurthy made his debut in 1957.
• She is honoured to serve as the Tirumala Tirupati Devasthanam's Asthana Nartaki (resident dancer).
• She was also referred to as the "torch bearer" of the Kuchipudi dancing style.
• The Padma Shree (1968), Padma Bhushan (2001), and Padma Vibhushan (2016), three of the highest civilian honours bestowed by the Republic of India, were among the many honours she received for her dancing career.
• Rukmini Devi Arundale, the first woman in Indian history to be nominated as a member of the Rajya Sabha. is associated with Bharatanatyam.
• Also an activist for animal rights and welfare.
• Rukmini Devi features in India Today's list of '100 People Who Shaped India'.
• Kalakshetra Foundation at Adyar, Chennai was established by Rukmini Devi.
• Rukmini Devi was nominated as a member of the Rajya Sabha in April 1952 and re-nominated in 1956.
• Google Doodle paid tribute to Rukmini Devi Arundale on her 112^th birth anniversary.
• Awarded the Padma Bhushan in 1956.
• Chinta Ravi Bala Krishna is a winner of the Sangeet Natak Akademi’s Ustad Bismillah Khan Yuva Puraskar for 2009, a recipient of the singular honour of Yuva Sutradhari at the Siddhendra Yogi Nrityotsav in 2007, a Gold Medallist M.A Kuchipudi, as well as being a winner of a host of other awards.

The correct answer is Cholas.

Key Points

• The Chola king Karikala founded Puhar and constructed 160 km of the embankment along the Kaveri River.
• This was built with the labour of 12000 slaves from Sri Lanka.
• Puhar is a place identical to Kaveripattanam.
• It was the capital of Chola.
• Excavations show that it had a large dock and was a centre of trade and commerce.
• The port city of Puhar became an emporium of foreign trade, as big ships entered this port with precious goods.
• Other ports of commercial activity include Tondi, Musiri, Korkai, Arikkamedu, and Marakkanam.

Important Points

• Chola dynasty:
• Vijayalaya was the founder of the Chola dynasty. His reign was from 850-870 CE.
• Vijayalaya established the dynasty by taking advantage of the war between the Pandyas and Pallavas.
• He conquered Thanjavur from Elango Mutharaiyar who was the final ruler of the Mutharaiyar dynasty.
• With the help of the Muttaraiyar king, Sattan Paliyilli he established the dynasty in Tanjavur.
• He was succeeded by his son Aditya I.
• The Tiruvalangadu plates or the Tamil copper-plate inscriptions mention Vijayalaya's capture of Tanjavur city.

The correct answer is Karnal

Key Points

• ICAR-National Dairy Research Institute (NDRI) at Karnal, Haryana is one of the premier institutes in the dairy sector
• It has contributed a lot to the growth of the dairy industry
• NDRI played a crucial role in India's development of milk production with its continuous research.
• National Dairy Research Institute (NDRI), Karnal was originally started as the Imperial Institute of Animal Husbandry and Dairying in 1923 in Bangalore.
• It was expanded and renamed Imperial Dairy Institute in 1936
• It was known as National Dairy Research Institute after India's independence in 1947.
• In 1970, NDRI was brought under the Indian Council of Agricultural Research.
• The institute has the distinction of being a Deemed University for implementing its academic programs since 1989.

Additional Information

• Anand:
• Amul Dairy (Headquarters of Gujarat Cooperative Milk Marketing Federation Ltd.)
• Anand Agricultural University.
• Institute of Rural Management Anand (IRMA).
• Lucknow:
• Dr. Ram Manohar Lohia National Law University
• Indian Institute of Management Lucknow
• King George's Medical University
• National Botanical Research Institute
• National Institute of Pharmaceutical Education and Research
• Sanjay Gandhi Post Graduate Institute of Medical Sciences
• Palampur:
• CSK Himachal Pradesh Agricultural University
• Institute of Himalayan Bioresource Technology
• Sardar Vallabhbhai Patel Cluster University, Mandi

Calculation:

The prime factors of the numbers are:

72 = 2 × 2 × 2 × 3 × 3

108 = 2 × 2 × 3 × 3 × 3

2010 = 2 × 3 × 5 × 67

So,

HCF of 72, 108, 2010 = 2 × 3 = 6

∴ The correct answer is 6.

Shortcut Trick

Using the reciprocal identity, we know that 1/cos θ = sec θ.

Thus, the equation becomes 2 sec θ = 2, which gives sec θ = 1.

For any power n, 1ⁿ is always 1, so sec⁵⁵ θ + (1/sec⁵⁵ θ) = 1 + 1 = 2.

∴ The correct answer is 2.

Alternate Method

Given:

sec θ + (1/cos θ) = 2

Formula Used:

Reciprocal relation: sec θ = 1/cos θ

Algebraic relation: If x + 1/x = 2, then x = 1.

Calculations:

Given equation:

⇒ sec θ + (1/cos θ) = 2

Using the identity 1/cos θ = sec θ, we can substitute it into the given equation:

⇒ sec θ + sec θ = 2

⇒ 2 sec θ = 2

⇒ sec θ = 1

Now, we need to find the value of the target expression:

⇒ sec⁵⁵ θ + (1/sec⁵⁵ θ)

Substitute sec θ = 1 into this expression:

⇒ (1)⁵⁵ + (1 / (1)⁵⁵)

Since 1 raised to any power remains 1:

⇒ 1 + (1 / 1)

⇒ 1 + 1 = 2

∴ The correct answer is 2.

Additional Information

Reciprocal Relations in Trigonometry

Reciprocal pairs include sin θ × cosec θ = 1, cos θ × sec θ = 1, and tan θ × cot θ = 1.

Properties of x + 1/x = 2

If x + 1/x = 2 (for real x), then x = 1. Consequently, the value of xⁿ + 1/xⁿ = 2 for any positive integer power n.

Properties of x + 1/x = −2

If x + 1/x = −2, then x = −1. For any integer power n, the expression xⁿ + 1/xⁿ is equal to 2 if n is even, and −2 if n is odd.

Concept used:

Average = (sum of the observations)/(number of observations)

Calculation:

Average export of commodity P:

⇒ (300 + 650 + 1300 + 1200 + 800 + 1400 + 1250)/7

⇒ 6900/7 = 985.71

So, there are 3 less exports of P than the average export of P.

∴ The correct option is 4.

Given:

C.P of article = Rs.800

Discount given = 10%

Profit = 12.5%

Formula used:

C.P/M.P = (100 - discount %)/(100 ± profit/loss %)

Calculation:

By applying the formula 

C.P/M.P = (100 - discount %)/(100 + profit%)

⇒ 800/M.P = (100 - 10)/(100 + 12.5)

⇒ M.P = (800 × 112.5)/90

⇒ M.P = 1000

∴ The correct answer is Rs.1000.

Given:

Side of the equilateral triangle = 9 cm

Concept used:

Circumradius (R) = (a × b × c)/4 × area

Calculation:

Circumradius (R) = (a × b × c)/4 × area of equilateral triangle

⇒ (9 × 9 × 9)/{4 × (√3/4) × 9 × 9}

⇒ 9/√3 = 3√3 cm

∴ The correct answer is 3√3 cm.

Alternate MethodConcept used:

Circumradius of equilateral triangle = side/√3

Calculation:

Circumradius (R) = side/√3

⇒ 9/√3 = 3√3 cm

∴ The correct answer is 3√3 cm.

Given:

Shiva’s monthly salary = Rs.75,000

Shiva’s savings = Rs.21,000

Calculation:

Shiva’s total expenditure = (12,000 + 14,000 + 15,000 + 10,000) = Rs.51,000

The amount Shiva donated to the orphanage 

⇒ 75,000 - (51,000 + 21,000)

⇒ 75,000 - 72,000 = Rs.3,000

So

Required percentage = (3,000/75,000) × 100

⇒ 100/25 = 4%

∴ The correct answer is 4%.

Calculation:

Ratio of export to import in 2010 = E : I = 9 : 10

Ratio of export to import in 2011 = E : I = 12 : 10

Ratio of export to import in 2012 = E : I = 7 : 10

Ratio of export to import in 2013 = E : I = 24 : 10

Ratio of export to import in 2014 = E : I = 35 : 10

Ratio of export to import in 2015 = E : I = 24 : 10

Hence, there are four observations in which the export of company A was more than the company A import

∴ The correct answer is four.

Given:

tan 40° = α 

Formula used:

Tan (A - B) = (tan A - tan B)/1 + tan A × tan B

tan (90° - θ) = cot θ 

cot θ × tan θ = 1

Calculation:

⇒ $\frac{tan320^0 - tan 310^0}{1 + tan320^0.tan 310^0}$ = tan (320° - 310°)

⇒ tan 10° 

Now, we can write:

Tan 10° = tan (50° - 40°)

⇒ [(tan 50° - tan 40°)/1 + (tan 50° × tan 40°)]

⇒ [tan (90° - 40°) - tan 40°/1 + tan (90° - 40°) × tan 40°]

⇒ cot 40° - tan 40°/1 + cot 40° × tan 40°

⇒ (1/α - α)/1 + 1

⇒ (1/α - α)/2

⇒ (1 - α²)/2α 

∴ The correct answer is (1 - α2)/2α.

Calculation:

Total foreign trade by country M in 5 years = 125 + 185 + 275 + 255 + 170 = 1010

∴ The correct answer is 1010.

Shortcut Trick

Convert first part to km: 18 m/s × (18/5) = 64.8 km/h. Distance = 64.8 × (5/60) = 5.4 km.

Total Distance = 5.4 + 7.5 + 12 = 24.9 km.

Total Time = 5 + 10 + 10 = 25 minutes = (25/60) hours.

Average Speed = 24.9 ÷ (25/60) = 24.9 × 2.4 = 59.76 ≈ 59.8 km/h.

∴ The correct answer is 59.8 km/h.

Alternate Method

Given:

Speed₁ = 18 m/s, Time₁ = 5 min, Distance₂ = 7.5 km, Time₂ = 10 min, Distance₃ = 12 km, Time₃ = 10 min.

Formula Used:

Average Speed = Total Distance ÷ Total Time

Distance = Speed × Time | 1 m/s = 18/5 km/h

Calculations:

⇒ Distance₁ = (18 × 5 × 60) / 1000 = 5.4 km

⇒ Total Distance = 5.4 + 7.5 + 12 = 24.9 km

⇒ Total Time = 5 + 10 + 10 = 25 minutes

⇒ Total Time in hours = 25 / 60 = 5 / 12 hours

⇒ Average Speed = 24.9 / (5 / 12) = (24.9 × 12) / 5

⇒ Average Speed = 298.8 / 5 = 59.76 km/h

⇒ Rounded to 1 decimal place = 59.8 km/h

∴ The correct answer is 59.8 km/h.

Additional Information

Average Speed for Equal Distances

If two equal distances are covered at speeds x and y, the average speed is given by the harmonic mean: 2xy / (x + y).

Conversion Factors

To convert m/s to km/h, multiply by 18/5. To convert km/h to m/s, multiply by 5/18.

Relative Speed

For objects moving in the same direction, relative speed is |s₁ − s₂|. For opposite directions, it is (s₁ + s₂).

Given:

$\frac{r}{13} + \frac{13}{r} = 1$

Concept used:

If x + (1/x) = 1

then x³ = - 1

Calculation:

Let (r/13) = x

According to the question:

⇒ $\frac{r}{13} + \frac{13}{r} = 1$

⇒ x + 1/x = 1

then x3 = - 1

Now, putting the value of x

⇒ (r/13)3 = - 1

⇒ r³ = - 2197

∴ The correct answer is -2197.

Additional InformationGiven - x + 1/x = 1

Formula Used - a³ + b³ = (a + b)(a² – ab + b²)

Calculation:

x + 1/x = 1

⇒ x² + 1 = x

⇒ x² - x + 1 = 0      ---(1)

Multiply (x + 1) into both side of eq (1)

⇒ (x + 1)( x² – x + 1) = 0

⇒ x³ + 1 = 0

⇒ x³ = -1

Given:

$\frac{a}{b} + \frac{b}{a} = -1$

Concept used:

if x + 1/x = - 1

then x³ = 1

Calculation:

Let (a/b) = x

Now the equation is:-

x + 1/x = - 1

So, x³ = 1------- (1)

Putting the value of x in eq.(1)

⇒ x3 = 1

⇒ (a/b)³ = 1

⇒ a³ = b³ ------- (2)

Putting the value of eq. (2) in the given equation:

⇒ a3 - b3

⇒ a3 - a3 = 0

∴ The correct answer is 0.

Alternate Method

Here, $\frac{a}{b} + \frac{b}{a} = -1$ 

⇒ $\frac{a^2 + b^2}{ab} = -1$ 

⇒ a2 + b2 + ab = 0

Now, a3 - b3 = (a - b) (a2 + ab + b2) = 2 × 0 = 0

Given:

Principal = Rs.2000 

Rate = 5 % and time = 3 years

Formula used:

Installment = $\frac{A\times 100}{N \times 100 + (N_{n-1} + N_{n-2} + ..+ 1)\times R}$

Where A = Amount, R = rate, and N = number of years

Calculation:

S.I = (P × R × T)/100

⇒ (2000 × 5 × 3)/100 = 300

Amount (A) = 2000 + 300 = Rs.2300

Installment = $\frac{A\times 100}{N \times 100 + (N_{n-1} + N_{n-2} + ..+ 1)\times R}$

⇒ 2300 × 100/[3 × 100 + (2 + 1) × 5]

⇒ 230000/315 = 46000/63

⇒ 730$\frac{10}{63}$

∴ The correct answer is ₹730$\frac{10}{63}$.

Mistake Points We calculate installment on Amount, 

Here, Principal is 2,000. 

Hence first we need to find the Amount, using the Simple Interest formula, 

and then solve the question.

Given:

Person A can sanitize a building = 6 h

Person B can sanitize a building = 10 h

Concept used:

Efficiency × Time = Total work

Calculation:

Now, according to the question:

⇒ (5 + 3) = 8 units = 2 hours

⇒  2 hours = 8 units 

so

⇒ 6 hours = 8 × 3 = 24 units

till 7^th hours, work completed = 24 + 5 = 29 units

Remaining work = 30 - 29 = 1 unit 

1 unit of work is completed by B in 1/3 hour.

Total time is taken to complete the total work = 7$1\over3$ hours

∴ The correct answer is 7$1\over3$ h.

Shortcut Trick

For similar triangles, the ratio of their areas is equal to the square of the ratio of their corresponding altitudes.

Ratio of Altitudes = √(Ratio of Areas)

Ratio = √(324 / 289)

Ratio = 18 / 17

∴ The correct answer is 18/17.

Alternate Method

Given:

Area of the first triangle (A₁) = 324 cm²

Area of the second triangle (A₂) = 289 cm²

Formula Used:

If two triangles are similar, the ratio of their areas is the square of the ratio of their corresponding altitudes (h₁ and h₂):

A₁ / A₂ = (h₁ / h₂)²

Calculations:

⇒ A₁ / A₂ = (h₁ / h₂)²

⇒ 324 / 289 = (h₁ / h₂)²

⇒ h₁ / h₂ = √(324 / 289)

⇒ h₁ / h₂ = 18 / 17

∴ The correct answer is 18/17.

Additional Information

Ratio of Corresponding Parts

For two similar triangles, the ratio of their corresponding sides, altitudes, medians, and perimeters are all equal.

Area Ratio Theorem

The ratio of the areas of two similar triangles is equal to the square of the ratio of any of their corresponding linear dimensions (sides, altitudes, etc.).

Calculation:

The marks scored in Hindi and mathematics = 70 + 90 = 160

The marks scored in English and Science = 55 + 80 = 135

The marks scored in Hindi and Mathematics is more than the marks scored in English and Science

⇒ 160 - 135 = 25

∴ The correct answer is 25.

Shortcut Trick

Ratio of Time taken (Same direction : Opposite direction) = 72 : 36 = 2 : 1.

Ratio of Relative Speed (Same : Opposite) = 1 : 2 (since Distance is same).

Let speeds be V_A and V_B. ⇒ (V_A − V_B) / (V_A + V_B) = 1 / 2.

By Componendo and Dividendo, V_A / V_B = (2+1) / (2−1) = 3 / 1.

Given V_A = 81 km/h ⇒ V_B = 27 km/h. Total Distance (L_A + L_B) = Relative speed (Opposite) × Time = (81 + 27) × (5/18) × 36 = 1080 m.

L_A = 1080 − 600 = 480 m.

∴ The correct answer is 480 m.

Alternate Method

Given: Speed of Train A (V_A) = 81 km/h, Length of Train B (L_B) = 600 m.

Formula: Distance = Relative Speed × Time; 1 km/h = 5/18 m/s.

⇒ Let L_A be length of Train A and V_B be speed of Train B.

⇒ Case 1 (Same direction): L_A + 600 = (81 − V_B) × (5/18) × 72

⇒ L_A + 600 = (81 − V_B) × 20 ... (i)

⇒ Case 2 (Opposite direction): L_A + 600 = (81 + V_B) × (5/18) × 36

⇒ L_A + 600 = (81 + V_B) × 10 ... (ii)

⇒ Equating (i) and (ii): (81 − V_B) × 20 = (81 + V_B) × 10

⇒ 162 − 2V_B = 81 + V_B ⇒ 3V_B = 81 ⇒ V_B = 27 km/h

⇒ L_A + 600 = (81 + 27) × 10 = 1080

⇒ L_A = 1080 − 600 = 480 m

∴ The correct answer is 480 m.

Additional Information

Relative Speed Concept

When two objects move in the same direction, relative speed is |V₁ − V₂|. When moving in the opposite direction, it is V₁ + V₂.

Crossing Distance

To fully cross or overtake each other, two trains must cover a distance equal to the sum of their lengths (L₁ + L₂).

Speed Conversion

To convert speed from km/h to m/s, multiply by 5/18. To convert from m/s to km/h, multiply by 18/5.

Given:

Distance covered by airplane in the east = 14 km

Distance covered by airplane in the north = 48 km

Concept used:

By Pythagorean theorem

(Hypotenuse)² = (perpendicular)² + (base)²

Calculation:

By Pythagorean theorem

⇒ (Hypotenuse)2 = (perpendicular)2 + (base)2

⇒ (AC)² = (BC)² + (AB)²

⇒ AC = √{(48)² + (14)2}

⇒ AC = √{2304 + 196}

⇒ AC = √2500 = 50 km

∴ The correct answer is 50 km.

Given:

∠ABC = (x + 60)°

∠PQR = (85 - 4x)°

∠RPQ = (3x + 65)°

Calculation:

If ΔABC ≅ ΔPQR 

then ∠ABC = ∠PQR 

⇒ (x + 60) = (85 - 4x)

⇒ 5x = 85 - 60 

⇒ x = 25/5 = 5 units

So,

∠ABC = (x + 60)°

⇒ (5 + 60)° = 65°

∴ The correct answer is 65°.

Concept used:

If the difference in the sum of alternative digits of a number is divisible by 11, then that number is divisible by 11.

Calculation:

According to the question:

⇒ (6 + 8 + 9 + 4 + 4) - (7 + 8 + 3 + a) = 11

⇒ 31 - (18 + a) = 11

⇒ a = 2

∴ The correct answer is 2.

Given:

C.P of an item = Rs.1250

Concept used:

S.P = (100 ± profit/loss %)

Calculation:

The selling price for Ram = 1250 × 118% = Rs.1475

The selling price for Ramesh = 1475 × 90% = Rs.1327.5

∴ The correct answer is Rs.1327.5.

Given:

The ratio of the present age of the father to that of his son = F : S =  7 : 2.

Calculation:

Let the present age of the father (F) = 7x

the present age of son (S) = 2x

According to the question:

⇒ (7x + 10)/(2x + 10) = 9/4

⇒ 28x + 40 = 18x + 90

⇒ 28x - 18x = 90 - 40

⇒ 10x = 50 

⇒ x = 5

So, the present age of the father (F) = 7x = 7 × 5 = 35 years.

∴ The correct answer is 35 years.

Given:

tan² θ + tan⁴ θ = 1

Concept used:

tan2 θ + 1 = sec² θ

Calculation:

⇒ tan2 θ + tan4 θ = 1

⇒ tan2 θ (1 + tan2 θ) = 1

⇒ tan2 θ × sec² θ = 1

⇒ tan2 θ = 1/sec² θ = cos² θ 

Now put the value of tan2 θ in the equation:

⇒ tan2 θ + tan4 θ = 1

⇒ tan2 θ + (tan²)² θ = 1

⇒ cos2 θ + (cos²)² θ = 1

⇒ cos² θ + cos⁴ θ = 1

∴ The correct option is 2.

Given:

Diameter of a solid hemisphere = 12.6 cm

Formula used:

Volume of solid hemisphere = (2/3) × π × r³ 

Calculation:

Diameter of a solid hemisphere = 12.6 cm

Radius of a solid hemisphere = 12.6/2 = 6.3 cm

Now,

Volume of solid hemisphere = (2/3) × π × r3 

⇒ (2/3) × (22/7) × (6.3)3

⇒ 523.908 cm³

∴ The correct answer is 523.908 cm3.

Concept used:

a² - b² = (a + b) × (a - b)

Tn = a + (n - 1) × d

Where, Tn = last term

a = first term, d = common difference and n = number of terms

Calculation:

if we take the first statement:

1002 - 992 + 982 - 972 + 962 - 952 + 942 - 932 + ......  + 222  - 212 is 4840.

⇒ (100 + 99) × (100 - 99) + (98 + 97) × (98 - 97) ........ + (22 + 21) × (22 - 21)

⇒ 100 + 99 + 98 + 97 ........... + 22 + 21

Now, the series is in A.P

⇒ a + (n - 1) × d = Tn 

⇒ 100 + (n - 1) × (- 1) = 21

⇒ 100 - n + 1 = 21

⇒ - n = (21 - 101) = - 80

⇒ n = 80

Sum of the series : 100 + 99 + 98 + 97 ........... + 22 + 21

⇒ {(100 + 21)/2} × 80

⇒ 60.5 × 80 = 4,840

∴ The first statement is correct.

if we take the second statement:​​​​

$\left(k^2+ \frac{1}{k^2} \right) \left(k- \frac{1}{k} \right) \left(k^4+ \frac{1}{k^4} \right)$ $\left(k+ \frac{1}{k} \right)\left(k^4- \frac{1}{k^4} \right)$ is $k^{16}- \frac{1}{k^{16}}$

⇒ $\left(k^2+ \frac{1}{k^2} \right) \left(k^2- \frac{1}{k^2} \right) \left(k^4+ \frac{1}{k^4} \right)$(\left(k^4- \frac{1}{k^4} \right)\)

⇒ $\left(k^4- \frac{1}{k^4} \right) \left(k^4+ \frac{1}{k^4} \right)$(\left(k^4- \frac{1}{k^4} \right)\)

⇒ $\left(k^8- \frac{1}{k^8} \right) \left(k^4- \frac{1}{k^4} \right)$ ≠ $k^{16}- \frac{1}{k^{16}}$

∴ The second statement is wrong.

∴ The correct option is 4.