RRB NTPC CBT 2 (Level-5) Official Paper (Held On: 15 June 2022 Shift 3) (Previous Year Paper)

Given:

(y + z) = 8

(yz) = 6

(y - z)² = ?

Concept used:

(x - y)² = x² + y² - 2xy

(x + y)² = x² + y² + 2xy

Calculations:

According to the question,

(y + z) = 8

Squaring on both sides,

⇒ (y + z)² = (8)²

⇒ y² + 2yz + z² = 64

⇒ y² + 2(6) + z² = 64

⇒ y² + 12 + z² = 64

⇒ y² + z² = 64 - 12

⇒ y² + z² = 52

Now for (y - z)²

(y - z)2 = y² + z² - 2yz

⇒ (y - z)2 = 52 - 2(6)

⇒ (y - z)² = 52 - 12

⇒ (y - z)² = 40

∴ The value of (y - z)2 is 40.

Alternate Method(x - y)2 = (x + y)2 - 4xy

(y - z)2 = (y + z)2 - 4yz

(y - z)2 = (8)2 - 4 x 6

(y - z)2 = 40

The correct answer is Income Tax.

Key Points

• Income Tax is not a tax subsumed under GST in India.
• GST refers to Goods and Services Tax. It is an indirect tax which has replaced many indirect taxes in India such as the excise duty, VAT, services tax, etc.
• The Goods and Service Tax Act was passed in the Indian Parliament on 29^th March 2017 and came in result on 1^st July 2017.
• The notable dissimilarity among GST and Income Tax is that the GST is impose on the consumption of the goods and services, whereas income tax is impose on the income of a person. In a way, GST is an indirect tax, whereas income tax is a direct tax.

Additional Information

• Service tax is a tax imposed by the government on service providers on sure service transactions, but is actually support by the customers.
• Additional Customs Duty (CVD)This duty, commonly refers to as countervailing duty (CVD), is imposed on imported goods in terms of section 3 of the Customs Tariff Act, 1975 and is equal to the Central Excise duty imposable on the like goods if produced or manufactured in India.
• An excise or excise tax (sometimes called an excise duty) is a kind of tax charged on goods produced within the country**.**

The correct answer is Self Help Group.

Key Points

• Self-help groups are informal groups of people who come together to address their common problems.
• Some Villages face multiple problems related to poverty, illiteracy, lack of formal credit etc. These types of problems cannot go out at a particular level and require collective efforts
• It provides guarantee-free loans with terms finalized by the group at market-driven rates.

Additional Information

• The persons with disabilities are used to apply to all persons with disabilities including those who have long-period physical, mental, intellectual or sensory impairments which, in interaction with various Posture and environmental fencing obstruct their full and effective participation in society on an equal.
• Farmer who has more than 10 hectares of land are big farmers, the farmers who have 2 or less than 2 hectares of land are mentioned to as small farmers and those who range between 2 to 10 hectares are known as middle farmers.

Shortcut Trick

The empirical relationship between central tendencies is: (Mean − Mode) = 3 × (Mean − Median).

Given: Mean − Mode = 69

69 = 3 × (Mean − Median)

⇒ Mean − Median = 69 ÷ 3 = 23

∴ The correct answer is 23.

Alternate Method

Given: Difference between Mean and Mode (Mean − Mode) = 69.

Formula Used: Empirical relation: Mode = 3 Median − 2 Mean.

From the given condition: Mean − Mode = 69

⇒ Mode = Mean − 69

Substitute the value of Mode in the empirical formula:

⇒ Mean − 69 = 3 Median − 2 Mean

⇒ Mean + 2 Mean − 69 = 3 Median

⇒ 3 Mean − 3 Median = 69

⇒ 3(Mean − Median) = 69

⇒ Mean − Median = 69 ÷ 3

⇒ Mean − Median = 23

∴ The correct answer is 23.

Additional Information

Empirical Relationship

In a moderately skewed distribution, the relationship is Mode = 3 Median − 2 Mean or (Mean − Mode) = 3 (Mean − Median).

Symmetric Distribution

For a perfectly symmetrical distribution, the values of Mean, Median, and Mode are all equal (Mean = Median = Mode).

Karl Pearson Coefficient of Skewness

It is calculated as S_k = (Mean − Mode) ÷ Standard Deviation, or 3(Mean − Median) ÷ Standard Deviation.

Given:

Cost of painting at a rate of Rs. 2/cm² = Rs. 588

Formula used:

The surface area of the cube = 6a²

The volume of the cube = (a)³

Where 'a' is the side of the cube.

Calculations:

According to the question,

Cost of paintings = 2 × Surface area of a cube

588 =  2 ×  6a²

⇒ 12a² = 588

⇒ a² = 588/12

⇒ a = √49 = 7 cm

Now the volume of Cube

Volume = (7)³ = 343 cm³

∴ The volume of the cube is 343 cm3.

The correct answer is Kerala.

Key Points

• Malayalam is a Dravidian language vocalized in the Indian state of Kerala by the Malayali people.
• It is one of 22 scheduled languages of India and is vocalized by 2.88% of Indians.
• Malayalam was nominated as a "Classical Language of India" in 2013.
• Malayalam has official language status in Kerala, Lakshadweep, and, Puducherry also.
• It is also vocalized by the Malayali population worldwide, especially in the Persian gulf countries, due to the large populations of Malayali emigrants there.

Additional Information

• Urdu is the second official language of Telangana state, but English is used for all government documents and as a language of the courts.
• The Andhra Pradesh Official Language Act 1966  is the core legislation to refer to with regard to Telugu.
• Marathi shall, as from the appointed day, be the language which has to be used for all official purposes mentioned in article 345 of the Indian Constitution,

Given:

• Rajiv has scored the 14^th position from the top and Vatsala has scored the 32^nd position from the last.
• There are 12 students in between Rajiv and Vatsala.​

​Explanation:

• Position of Rajiv from top = 14
• Number of students in between Rajiv and Vatsala = 12
• So, position of Vatsala from top such that there are a maximum number of students in the class = 14 + 12 = 26
• maximum number of students in the class = Position of Vatsala from top + Position of Vatsala from last = 26 + 32 = 58

Hence, 58 is the correct answer.

The Correct answer is Orissa.

Key Points 

• Gotipua is a traditional dance from Odisha India, and the forerunner of Odissi classical dance.
• It has been performed in Orissa for centuries by young boys, who dress up like women to worship Lord Jagannath and Krishna.
• The dance is being implemented by a group of boys who performs acrobatics encouraged by the life of Radha and Krishna.
• **The dance of the Gotipuas goes along with traditional Odissi music **with the primary clash being the Mardala.

Additional Information​ 

• In Uttar Pradesh Kathak is one of the six leading classical dances of India developed. The word Katha, from which the name is obtained, means story.
• Jat-Jatin is the most famous folk dance of North Bihar, especially in the Mithila and Koshi domains.
• Lai Haraoba is the earliest form of dance in Manipur, and it forms the basis of all such dances. Lai Haraoba is a festival still celebrated in the state.

The correct answer is Indonesia.

Key Points

• The Census Bureau's International Data Base approximately July 1, 2021, the Inhabitants of Indonesia at 275.1M (4^th most populous).
• The number of inhabitants of Indonesia in 2021 was 273,753,191, a 0.7% increase from 2020.
• The Indonesia Inhabitants are projected to trend at around 275.40 Million in 2022, according to our econometric models.
• The inhabitant of Indonesia indicates 3.51% of the world´s total population which means that one person in every 29 people on the planet is a resident of Indonesia.

Additional Information

• The Inhabitant of Pakistan is expected at 225,199,937 or 225.200 million as of 1 July 2021.
• Pakistan stood number 5^th in the world by citizens in the list of 235 countries/territories.
• The Inhabitants of Brazil is expected at 213,993,437 or 214.00 million as of July 1, 2021.
• The Inhabitants of U.S. in 2021 was 336,997,624**, a 0.31%** increase from 2020.

The correct answer is Hematite.

Key Points

• Hematite has 60-70% metallic content.
• It is Reddish and of the best quality.
• 80% of Hematite reserves are in Odisha, Jharkhand, Chattisgarh and Andhra Pradesh.
• Hematite ore is one of the most Important Industrial iron ores in terms of the Quantity used.

Additional Information

• **Limonite, a type of **major iron mineral, hydrated ferric oxide (FeO(OH)·_nH₂O). It was initially known as one of a series of such oxides.
• Siderite, also known as Chalybite, iron carbonate (FeCO₃), a universal mineral which is an ore of iron.
• Pyrite, also known as iron pyrite, a naturally occurring iron disulfide mineral

Shortcut Trick

Let total voters entitled to vote = 100 units

Voters who cast their ballot = 90% of 100 = 90 units

Valid votes = 80% of 90 = 72 units

Winner share = 60% of 72 = 43.2 units

Given: 43.2 units = 64800 ⇒ 1 unit = 1500

Total voters (100 units) = 100 × 1500 = 150,000

∴ The correct option is D.

Alternate Method

Given:

Winner's Votes = 64,800

Winner's share = 60% of Valid Votes

Valid Votes = 80% of Votes Cast

Votes Cast = 90% of Total Voters Entitled

Formula Used:

Total Voters × Cast % × Valid % × Winner % = Winner's Votes

Total Voters (100%)

Votes Cast (90%)

Valid Votes (80% of 90% = 72%)

Winner (60% of 72% = 43.2%) = 64,800

Calculations:

⇒ Let the number of people entitled to vote be V.

⇒ Votes cast = 0.90 × V

⇒ Valid votes = 0.80 × (0.90 × V) = 0.72V

⇒ Winner's votes = 0.60 × (0.72V) = 0.432V

⇒ 0.432V = 64800

⇒ V = 64800 ÷ 0.432

⇒ V = 64,800,000 ÷ 432

⇒ V = 150,000

∴ The correct option is D.

Additional Information

Successive Percentage Rule

When a value is changed by a%, b%, and c% successively, the final value = Initial × (a/100) × (b/100) × (c/100).

Election Terms

Valid Votes = Total Votes Cast − Invalid Votes. Winner's Share + Loser's Share = 100% of Valid Votes.

Base Value Identification

Always identify the base for each percentage. Here, 80% was based on votes cast, and 60% was based on valid votes.

Given:

30 ÷ (40 ÷ 2² × 10 ÷ 5) × 6 - 4

Concept used:

Calculations:

30 ÷ (40 ÷ 4 × 10 ÷ 5) × 6 - 4

⇒ 30 ÷ (10 × 2) × 6 - 4

⇒ 30 ÷ 20 × 6 - 4

⇒ 30/20 × 6 - 4

⇒ 3/2 × 6 - 4

⇒ 9 - 4 = 5

∴ The simplified value of the given equation is 5.

The positional values of English alphabet is as follows:

Let us deduce the relation between lett​er- clusters:

 JHQ does not follow the pattern.

Hence, "JHQ" is the correct answer.

The correct answer is Manpreet Singh.

Key Points

• Mangte Chungneijang Mary Kom, the 6-time world boxing champion, and Manpreet Singh who is the Indian men's hockey team skipper will be India's flag-bearers at the opening ceremony of the Tokyo Olympics 2020.
• Mangte Chungneijang Mary Kom OLY is an Indian amateur boxer, politician, and incumbent Member of Parliament, Rajya Sabha.
• Manpreet Singh Sandhu is an Indian field hockey player and the captain of India's men's national field hockey team since May 2017.
• The Olympic 2021 was held in Tokyo, Japan.

Additional Information

• Subedar Neeraj Chopra is an Indian athlete who is the Olympic champion in javelin throw.
• Ravi Kumar Dahiya is an Indian freestyle wrestler who won a silver medal at the 2020 Tokyo Olympics in the 57 kg category.
• Dutee Chand is an Indian sprinter and present national champion in the women's 100 metres event.

Shortcut Trick

Total sum of the first set = 67 × 5 = 335.

Value of variable x = 335 − (33 + 47 + 83 + 109) = 335 − 272 = 63.

Total sum of the second set = 50 + 64 + 100 + 126 + 63 = 403.

New arithmetic mean = 403 ÷ 5 = 80.6.

∴ The correct answer is 80.6.

Alternate Method

Given:

First set of numbers: 33, x, 47, 83, 109 with mean 67.

Second set of numbers: 50, 64, 100, 126, x.

Formula Used:

Arithmetic Mean = (Sum of all observations) ÷ (Total number of observations)

Calculations:

⇒ (33 + x + 47 + 83 + 109) ÷ 5 = 67

⇒ 272 + x = 67 × 5

⇒ 272 + x = 335

⇒ x = 335 − 272 = 63

Now, finding the mean of the second set:

⇒ New Set = 50, 64, 100, 126, 63

⇒ Sum = 50 + 64 + 100 + 126 + 63 = 403

⇒ New Mean = 403 ÷ 5

⇒ New Mean = 80.6

∴ The correct answer is 80.6.

Additional Information

Arithmetic Mean Properties

If every observation in a set is increased or decreased by a constant k, the mean also increases or decreases by k respectively.

Sum of Deviations

The algebraic sum of deviations of a set of observations from their arithmetic mean is always zero.

Combined Mean Formula

For two sets with means M₁ and M₂ and sizes n₁ and n₂, Combined Mean = (n₁M₁ + n₂M₂) ÷ (n₁ + n₂).

Friends: 5, namely A,B,C,D,E.

GIven:

• E is older than only two persons.

• | (Eldest) | | --- | | | | E | | | | (Youngest) |

• D is younger than only one person.

• | (Eldest) | | --- | | D | | E | | | | (Youngest) |

• A is the eldest among all.

• | A(Eldest) | | --- | | D | | E | | | | (Youngest) |

​Explanation: Using the given information, the following table can be drawn.

• | Case1 | Case2 | | --- | --- | | A**(eldest)** | A**(eldest)** | | D | D | | E | E | | C | B | | B | C |

So, C and B are the two youngest persons.

• Thus, only statement 4 of the question satisfies the given instructions.

Hence, "C and B are the two youngest persons" is the correct answer.

The Correct answer is Mahabharata.

Key Points

• Teejan Bai is a proponent of Pandavani, a traditional art form, from Chhattisgarh, in which she approves tales from the Mahabharata, with musical background.
• The Mahabharata is one of the two major Sanskrit Saga of ancient India the other being the Ramayana.
• It tells the struggle among two groups of cousins in the Kurukshetra war and the destiny of the Kaurava and the Pandava princes and their beneficiaries.
• It also contains Philosophical and devotional material, such as a discussion of the four "goals of life" or Purusartha.

Additional Information

• Possibly the greatest Sanskrit director, Mahakavi Kalidas wrote Abhigyan Shakuntalam nearly 2,500 years ago.
• The Ramayana is an ancient Sanskrit epic which follows Prince Rama's quest to save his beloved wife Sita from the grips of Ravana with the help of an army of monkeys. It is traditionally assigned to the authorship of the sage Valmiki and dated to around 500 BCE to 100 BCE.
• The Katha Sarit Sagar is a famous 11^th-century collection of Indian legends, fairy tales and folk epics as retold in Sanskrit by the Shaivite Somadeva.

Shortcut Trick

For a constant height (h), the speed of an aeroplane moving horizontally is given by:

Speed = [h × (cot θ₂ − cot θ₁)] ÷ Time

Given: h = 2400 m, θ₁ = 45°, θ₂ = 30°, Time = 12 s.

⇒ Speed = [2400 × (cot 30° − cot 45°)] ÷ 12

⇒ Speed = 200 × (√3 − 1)

∴ The correct answer is 200(√3 − 1) m/s.

Alternate Method

Given:

Initial angle of elevation (θ₁) = 45°

Final angle of elevation (θ₂) = 30°

Height (h) of the aeroplane = 2400 m

Time duration (t) = 12 seconds

Let x be the horizontal distance from point P to the initial position and y be the distance to the final position.

⇒ In the first case: tan 45° = height ÷ x

⇒ 1 = 2400 ÷ x ⇒ x = 2400 m

⇒ In the second case: tan 30° = height ÷ y

⇒ 1/√3 = 2400 ÷ y ⇒ y = 2400√3 m

⇒ Distance covered (d) = y − x = 2400√3 − 2400 = 2400(√3 − 1) m

⇒ Speed = Distance ÷ Time = 2400(√3 − 1) ÷ 12

⇒ Speed = 200(√3 − 1) m/s

∴ The correct answer is 200(√3 − 1) m/s.

Additional Information

Trigonometric Ratios

The basic ratio used in height and distance is tan θ = Perpendicular ÷ Base. For these problems, cot θ = Base ÷ Perpendicular is also useful for horizontal distance.

Angle of Elevation and Distance

As an object moves away from the observer at a constant height, the angle of elevation decreases. If it moves toward the observer, the angle increases.

Speed-Distance Relation

Speed = Distance ÷ Time. In problems involving horizontal flight, the distance is the difference between horizontal components at two different time intervals.

The correct answer is Etienne Glichitch Award.

Key Points

• Etienne Glichitch Award, 2021
• On May 21 (Friday), 2021, Hockey India received the esteemed Etienne Glichitch Award in honour of its contribution to the expansion and improvement of the sport in the nation.
• During the HockeyInvites virtual conference, the awards were presented by the International Hockey Federation (FIH), the organisation that oversees the sport.
• It was a component of the 47^th FIH Congress, which ended with the FIH Honorary Awards.
• According to a Friday press release from the FIH, "Hockey India was announced as the recipients of the Etienne Glichitch Award in appreciation of its exceptional commitment to the growth and development of Hockey."

Additional Information

• The honour carries Etienne Glichitch's name, who served as the FIH's Hon. Secretary from 1966 until 1984, when he was elected its President, a position he held until 1996.
• His innovative methods and great dedication to the sport helped to lay the foundation for the FIH as it is recognised today.
• Gyanendro Ningombam, the president of Hockey India, thanked the FIH for recognising Hockey India's efforts to develop the sport in India.

Given:

Number of friends = 6

Name of friends = A, B, C, D, E and F

Solution:

• B is sitting second to the right of A

• Only two people sit between D and A.

• C is not an immediate neighbour A.

​

• B and E are not immediate neighbours of each other. So, B and F are neighbours of each other.

​

So, F is third to the right to C.

Hence, "Third to the right of C" is the correct answer.

The correct answer is Battle of Chinhat.

Key Points

• The famous battle of Chinhat in Ismailganj of Lucknow(Uttar Pradesh) on  30 June 1857, opposed British forces' guidance by Henry Lawrence.
• Henry Lawrence died as an out-turn of an aggressive Battle.
• Barkat shah guides one of the most powerful armies with Ahmadullah Shah as his leader

Additional Information

• The Third Battle of Panipat took place on 14 January 1761 between the Maratha Empire and the captured army of the Durrani Afghan Empire. The battle took place in and around the city of Panipat, in the north of Delhi.
• The Battle of Plassey was a conclusive success of the British East India Company on the Nawab of Bengal and his French merge on 23 June 1757, under the lead under the guidance of Robert Clive.
• The Battle of Buxar was fought between 22 and 23 October 1764, between the forces under the order of the British East India Company, headed by Hector Munro, and the integrated armies of Mir Qasim, Nawab of Bengal 1764.

The correct answer is MM Naravane.

Key Points

• Indian Army Memorial
• From July 5 to July 8, 2021, General MM Naravane, the Chief of Army Staff (COAS), traveled to Italy and the United Kingdom (UK).
• The Army Chief inaugurated the Indian Army Memorial in the well-known Italian village of Cassino and will also receive training at the Counter IED Center of Excellence for the Italian Army in Cecchingola, Rome.
• According to the Ministry of Defence, he will meet with his counterparts and top military officers during his four-day tour to Italy and the UK, , with the goal of expanding India's defence cooperation.
• Over 5,000 Indian soldiers who lost their lives battling the Japanese and German forces during World War II (1939 to 1945) are remembered by the Indian Army Memorial that was built in Cassino town.

Additional Information

• In order to fight for Italy's liberation between 1943 and 1945, about 50,000 Indian soldiers were sent there.
• According to former Italian Army Chief General Fabrizio Castagnetti, the fourth, eighth, and tenth Indian Infantry Divisions participated in both the brutal fight to take Mount Cassino and the subsequent difficult operation to breach the Gothic Line.
• Indian soldiers who served in Italy during World War II are buried in other cemeteries throughout the country, in addition to Cassino.
• During the Second World War, the Indian soldiers assisted in the liberation of several Italian cities, including Luca, Perugia, San Marino, Florence, Forli, Cesena, Ferrara, and Bologna.
• Six Indian soldiers who were fighting alongside other allied forces in Italy's liberation had also been awarded the renowned Victoria Cross.

The correct answer is Chitra Pournami.

Key Points

• Poompuhar Beach
• The natural and historic Poompuhar Beach is situated along the Bay of Bengal in Poompuhar, Tamil Nadu, India.
• The beach begins at the Kaveri River and stretches 3 kilometres northward toward Neithavasal.
• South Indian history is very important to this beach and the city of Poompuhar.
• A significant celebration for this beach is called Chitra Pournami, and it takes place in the Tamil month of Chittrai at the full moon.
• During the new moon in the Tamil months of Thai and Adi, a holy dip is also observed near the mouth of the Kaveri River.

Additional Information

• This beach's sand extends for around three kilometres.
• To avoid erosion, granite stones have just been added to the shore.
• The closest town, Mayiladuthurai, is about 24 kilometres away from this beach and is situated on the bank of the Kaveri River.
• An engraved monument is another attraction near Poompuhar Beach in addition to Chitra Pournami.
• The Silappathikara Art Gallery is another one, and it provides information about the area's past.
• The Zion Church and the Thiruppallavaneeswaram Temple, both of which are close to Poompuhar Beach, should also be visited.

The correct answer is Mahanadi.

Key Points

• The Western Ghats,  also called Sahyadri, north-south running range of mountains or hills in western India that for the crest of the western edge of the Deccan plateau parallel to the Malabar coast of the Arabian sea.
• The major rivers originating in the western ghat are the following
• The Godavari is India's second longest river after the Ganga and the third largest in India,  drains about 10% of India's total geographical area. Its source is in Trimbakeswar, Nashik, Maharashtra.
• Cauvery is one of the major Indian rivers flowing through Karnataka and Tamil Nadu states. In ancient Tamil Literature, the river was also called Ponni.
• The Tungabhadra River is a river that starts flowing through the state of Karnataka during most of its course. before flowing along the border between Telangana, and Andhra Pradesh and ultimately joining the Krishna River near Gundimalla village in Jolumba Godwal district of Telangana.

Additional Information 

• The Mahanadi is a major river in East Central India. it drains an area of around 132,100 kilometres and has a total length of 900 kilometres.
• Mahanadi is also known for the Hirakud dam. The river flows through the states of Chattisgarh and Odisha and finally merged with the Bay of Bengal.

Given:

$\sqrt[3]{16384}$ /$\sqrt[3]{256}$

Calculation:

(16384)^1/3 /(256)^1/3

⇒ (16 × 16 × 16 × 4)^1/3 /(8 × 8 × 4)^1/3

⇒ 16(4)^1/3 /4(4)^1/3

⇒ 16/4 = 4

∴ The simplified value is 4.

Given:

Number of friends=8 

Name:Janak, Kuldeep, Punit, Kavita, Naveen, Azad, Vikas and Anil.

Explanation:

• Four of them are sitting at the four corners and the rest four are sitting at the middle of each of the four sides of the table.
• The ones who sit at the corners face the center, while those who are sitting in the middle of the sides face away opposite to the center of the table.
• So, the representation will be as follows:

 

• Janak faces the centre and is third to the right of Azad.

• Naveen faces the center but is not an immediate neighbour of Azad.

​

• Kavita is sitting second to the right of Kuldeep. Kuldeep faces the centre.

​

• Punit is not an immediate neighbour of Janak.

• Only one person is sitting between Azad and Vikas.

The above representation is the final arrangement.

• So, Kuldeep sits third right to Punit. Option 1 is false.
• Punit is an immediate neighbour of Naveen and Kavita. Options 2 and 3 are discarded.
• Punit faces away from the centre of the table

Hence, "Punit faces away from the centre of the table" is the correct answer.

LOGIC: The difference between the numbers is Prime numbers from 11 to 29.

Hence, 117 is the correct answer.

Given :

The train takes 8 hours less if its speed is increased by 12 km/h.

The train takes 12 hours more if its speed decreased by 12 km/h.

Formula used :

Speed × time = distance

Calculations : 

Let the speed of the train be x km/h and the time taken be y h.

The total distance is then xy km.

Case 1:

Speed increases by 12 km/h and the time taken is reduced by 8 hours. 

The distance traveled remains xy km.

(x + 12) (y − 8) = xy

⇒ xy − 8x + 12y − 96 = xy

⇒ − 8x + 12y − 96 = 0

⇒ − 2x + 3y = 24      ----(1)

Case 2:

Speed decreases by 12 km/h, then the time taken increases by 12 hours. 

However, the distance remains xy km.

(x − 12) (y + 12) = xy

\()⇒ xy + 12x − 12y − 144 =xy

⇒ 12x − 12y − 144 = 0

⇒ x − y = 12      ----(2)

From equation (1) & (2) : 

⇒ x = 60 km/h

Using this in (2), we get

⇒ 60 − y = 12

⇒ y = 48

∴ The distance is 60 × 48 = 2880 km.

The correct answer is The currency issued by the Central Bank that can be held by the public or by the commercial banks.

Key Points

• High-powered money is the liability of the monetary authority of the country.
• This is also called the monetary base and is created by the RBI.
• High-powered money includes currency (notes and coins), deposits with the government, and reserves of commercial banks with RBI. So, to sum up, high-powered money is. H = C + R
• The other name of the Reserve Money is “High Powered Money” and also “Monetary Base”.

Additional Information

• There are 4 major types of Money :
• Commodity Money
• Fiat Money.
• Fiduciary Money.
• Commercial Bank Money.

The positional value of English alphabet is as follows:

 'GREEN' is written as '209222213'

​ 'BLUE' is written as '2515622'

Similarly,

Hence,"41918722" is the correct answer.

The correct answer is Article 17.

Key Points

• Article 17 of the Indian constitution mainly deals with the account of untouchability. This article puts restrictions and prohibits the practice of untouchability. It ensures that untouchability is eradicated in all forms. Any kind of disability that is arising out of untouchability is considered an offence.
• Article 17 of the Indian Constitution eliminates the practice of untouchability.
• This Act was passed in the Indian Parliament for the eradication of all sorts of untouchability from the country
• The punishment imposed in this act is a 6-month-imprisonment or a fine of Rs.500 for any person convicted of carrying out the disabilities of untouchability on anyone else in case of his first offence.
• In the case of subsequent and repeated offences, the convicted person will be sentenced to a jail term along with a fine. There is a provision for increasing the punishment also if needed.
• The Act was introduced in the Lok Sabha on 8^th May 1955 and passed in both houses and came into force on 1^st June 1955.
• The Act was revised on September 2^nd, 1976, and renamed Protection of the Civil Rights Act. This Act had even severe measures to eradicate untouchability.

Additional Information

• Article 19 says Everyone has the right to freedom of opinion and expression; this right includes the freedom to hold opinions without interference and to seek, receive and impart information and ideas through any media and regardless of frontiers.
• Article 16 in The Constitution Of India 1949. Equality of opportunity in matters of public employment.
• Article 18(1) abolishes all titles. It prohibits the State to confer titles on anybody whether a citizen or a non-citizen. Military and academic distinctions are, however, exempted from the prohibition.

Given:

2.98 of 5 + 1.96 of 5 - 4 ÷ 2 + 0.98 = ?

Concept:

In approx value:

2.98 = 3

1.96 = 2

0.98 = 1

Calculation:

Now, according to the question,

3 × 5 + 2 × 5 - 4 ÷ 2 + 1 

⇒ 3 × 5 + 2 × 5 - 4 × $1\over2$ + 1 

⇒ 15 + 10 - 2 + 1 

⇒ 25 - 2 + 1

⇒ 23 + 1 = 24

∴ The simplified value of the given equation is 24.

The correct answer is UNCTAD.

Key Points

• Its full name is United Nations Conference on Trade and Development.
• It was established in 1964.
• It is an intergovernmental organization intended to promote the interests of developing states in world trade.
• UNCTAD is part of the United Nations Secretariat dealing with trade, investment, and development issues.
• The General Assembly in the sphere of trade and development.
• Its purpose is the promotion of trade and development, particularly in developing countries.

Additional Information

• UNISDR stands for United Nations International Strategy for Disaster Reduction.
• UNICEF, in full originally called the United Nations International Children's Emergency Fund.
• UNHRC stands for United Nations Human Rights Council.

According to the given information:

1) Guava is the only brother of Grape's father.

2) Mango is the mother of Apple.

3) Apple is the brother of Kiwi.

4) The wife of Apple's maternal grandfather is also the paternal grandmother of Grape. 

Clearly, we can see that Mango is the sister of Gauva.

Hence, the correct answer is "Sister".

Given: 

• Number of boxes = 5, namely A, B, C, D and E.
• Boxes are kept in vertical arrangement.
• The topmmost box is numbered 1 and the bottommost is 5.

Explanation:

• Only one box is kept below box C.

• There are two boxes kept between boxes D and C.

 

• Box E is kept at the second place from the top.

• | Sr. No. | Name of the box | | --- | --- | | 1(topmost) | D | | 2 | E | | 3 | | | 4 | C | | 5(bottom) | |

• Only two boxes are kept above box A.

• | Sr. No. | Name of the box | | --- | --- | | 1(topmost) | D | | 2 | E | | 3 | A | | 4 | C | | 5(bottom) | B |

• So, Box B is placed at the bottom.

Hence, Box B is the correct answer.

The correct answer is Alt + Tab.

Key Points

• A popular Windows shortcut key is Alt + Tab, which allows you to switch between all of your open programs.
• While continuing to hold down the Alt key, choose the program you want to open by clicking Tab until the correct application is highlighted, then release both keys.
• You can also Select the Task View icon on the taskbar.

Additional Information

• Ctrl+N is a keyboard shortcut most often used to create a new document, window, workbook, or another type of file.
• Ctrl+Tab is a keyboard shortcut most often used to switch between open tabs in a browser.
• In Microsoft PowerPoint, the Alt + N keyboard shortcut opens the Insert tab in the Ribbon.

Given: 

Speed (S) of the train = 95 km/h 

Time (T) taken to cross the post = 18 s 

Formula used: 

S = D/T  

Concept used:

Convert the speed of the train from km/h to m/s

S = 95 × 1000/3600 = 95 × 5/18 = 475/18 m/s​

Calculation: 

According to the question, 

475/18 = D/18

⇒ D = 475/18 × 18 

⇒ D = 475 m

∴ The length of the train is 475 m.

• Assume the train is stationary and the post is moving at a speed of 95 km/h and the length of the train is the distance travelled by the post.

Now,

• 'NEWTON' is written as 'LUCFKL'.
• 'PASCAL' is written as 'JYGWYN'.
• Similarly, for TESLA:

So, TESLA is written as FUGNY.

Hence, FUGNY is the correct answer.

Given: SLU_ _ INGS _ _ ICING _ UICIN LUICI _

Explanation:

Lets check each option.

1) S,L,I,C,L,U,G,N,G,L → SLUSLING - SICICING - LUUICING - NLUICIGL

No pattern is followed.

2) I,C,L,U,S,L,G,S,N,G → SLUICING - SLUICING - SLUICING - SLUICING

​SLUICING is repeating itself.

3) L,I,C,U,S,L,G,L,G,N → SLULIING - SCUICING - SLUICING - LLUICIGN

No pattern is followed.

4) S,G,C,L,U,S,N,G,S,L → SLUSGING - SCLICING - USUICINN - GLUICISL

No pattern is followed.

Hence, "ICLUSLGSNG" is the correct answer.

Given: It is Wednesday on 5^th August 1994.

To find: which day of the week will be on 2^nd September 1995.

Explanation:

Neither 1994 nor 1995 is a leap year.

∴ 5^th August 1995 will be a Thursday because 5^th August 1994 + 365 days or 1 odd day = 5^th August 1995.

No. of odd days from 5^th August 1995 to 2^nd September 1995 = 26 days (Aug 1995) + 2 days (Sep 1995) = 28 days = 0 odd day

∴ 5^th August 1994 + 1 odd day + 0 odd day = 2^nd September 1995

∴ Wednesday + 1 odd day = 2^nd September 1995.

∴ Thursday = 2^nd September 1995.

​Hence, Thursday is the correct answer.

Given:× stands for subtraction, ÷ stands for addition, + stands for division, and - stands for multiplication.

 

Explanation:

• Option1:
• 45 - 15 ÷ 15 × 60 + 16 = 42 will be written as
• 45 × 15 + 15 - 60 ÷ 16 = 42
• 675 + 15 -15/4 = 42
• As this contains a fractional value, so the option is discarded.
• Option 2:
• 25 + 5 × 20 ÷ 5 - 16 = 6 will be written as
• 25 ÷ 5 - 20 + 5 × 16 = 6
• 5 - 20 + 80 = 16
• 65 = 16 (false)
• Option 3:
• 9 ÷ 28 - 10 × 15 + 9 = 10 will be written as
• 9 + 28 × 10 - 15 ÷ 9 = 10
• 9 + 280 - 5/3 = 10
• As this contains a fractional value, so the option is discarded.
• Option 4:
• 16 ÷ 20 - 6 + 10 × 12 = 16
• 16 + 20 × 6 ÷ 10 - 12 = 16
• 16 + 12 - 12 = 16
• 16 = 16 (both sides are equal)

Hence, 16 ÷ 20 - 6 + 10 × 12 = 16 is the correct answer.

The correct answer is Ohm.

Key Points 

• Electrical Resistance
• A measurement of an object's resistance to the flow of electrical current is called its electrical resistance.
• An object's resistance is mostly determined by the substance from which it is formed; for example, rubber-manufactured items typically have very high resistance and low conductivity.
• The ratio of the voltage (V) applied across an object to the current (I) flowing through it is known as its resistance (R).
• Ohm (Ω) is the SI unit of electrical resistance.
• A conductor's electrical resistance depends on the following factors:
• Size of the conductor
• The cross-sectional area of the wire
• Composition of the conductor and
• Temperature

Additional Information 

The correct answer is Isoquant,

Key Points

• An isoquant in economics is a curve that, when plotted on a graph, shows all the combinations of two factors that produce a given output.
• Often used in manufacturing, with capital and labour as the two factors, isoquants can show the optimal combination of inputs that will produce the maximum output at minimum cost.
• An isoquant is also called an equal product curve or production indifference curve or constant product curve.
• Isoquant curve shows combinations of inputs employable to produce a certain output.

Additional Information

• Elasticity is an economic concept used to measure the change in the aggregate quantity demanded of a good or service in relation to price movements of that good or service.
• A product is considered to be elastic if the quantity demand of the product changes more than proportionally when its price increases or decreases.
• The long run refers to a period of time where all factors of production and costs are variable.
• Over the long run, a firm will search for the production technology that allows it to produce the desired level of output at the lowest cost.
• A duopoly exists when two companies dominate a market for a given product or service.
• A duopoly can have the same impact on the market as a monopoly if the two players collude on prices or output.

The correct answer is Greek.

Key Points

• Megasthenes 
• Greek historian, diplomat, and explorer Megasthenes lived in the Hellenistic era (350–290 B.C.).
• Megasthenes has been sent as an ambassador to Chandragupta Maurya's court by Seleucus I Nicator, the Greek conqueror of West Asia.
• India is described in the book "Indica" by Megasthenes.
• The term "father of Indian history" refers to Megasthenes because he was the first to depict ancient India.
• The two main rivers Sindhu and Ganga are also described by him.
• The Mauryan capital Pataliputra was visited by Megasthenes.
• He gives a thorough description of the rivers of the Punjab region in northwest India.

Additional Information

• Chandragupta Maurya
• Chandragupta Maurya became king when he was 25 years old.
• He defeated the Nandas and established the Mauryan Empire.
• In 322 BC, he defeated the final Nanda emperor Dhanananda and took control of Pataliputra.
• A wise man by the name of Chanakya/Kautilya supported Chandragupta Maurya.
• Seleucus Nicator was defeated by Chandragupta Maurya in 305 BC.
• During Chandragupta Maurya's rule, all of northern India was united.

The correct answer is Formula bar.

Key Points

• Formula Bar
• In an Excel worksheet, the content of the active cell is displayed in the formula bar.
• Excel's formula bar is a unique toolbar located at the top of the worksheet window that is marked with a function symbol (fx).
• It can be used to display numerous lines for a single formula and is used to edit the content of any cell.
• When working with a lengthy formula, the formula bar is really helpful since it allows us to examine the whole formula without covering the contents of the adjacent cells.
• The equal sign in any cell or a click anywhere in the formula bar activates the bar.

Additional Information

• Name Box
• The Name Box in Excel refers to the input box located immediately to the left of the formula bar.
• The address of the worksheet's "active cell" is often shown in the Name Box.
• Title Bar
• The title bar is located above or next to the quick access toolbar in the excel window.
• It includes the close, minimise, and maximise buttons as well as the window's title.
• Status Bar
• The lower edge of the worksheet window, which shows different data about an Excel worksheet, is known as the status bar.
• The sum, count, and average of the currently selected cells can be displayed in the status bar.

Given:

AB = 16 cm.

RC = 3 cm 

DS = 10 cm 

Formula used:

The perimeter of a quadrilateral = (Sum of all the sides)

Concept used:

Tangent to a point from a circle are equal then AS = AP and BP = BQ

Calculations:

According to the question,

⇒ AB = AP + BP,

AS = BQ  then, AS + BQ = 16 ( 8 + 8)

⇒ RC = CQ then, RC = 3 & CQ = 3

⇒ DS = RD then, DS = 10 & RD = 10 

∴ Perimeter of the quadrilateral

⇒  AB + ( AS + BQ ) + QC + RC + RD + DS 

⇒ 16 + 16 + 3 + 3 + 10 + 10 = 58.

∴ The perimeter of the quadrilateral is 58 cm.

Given: The starting point of Aditya is given and directions in which he moves to reach an ATM are given. We have to find the shortest distance to the ATM.

Condition applied: All the turns are 90° only.

Explanation:

• The starting point is a juice corner.
• Aditya, looking for ATM, walked 20 m due North from the starting point.
• He turned right and walked 18 m. He again turned right and walked 20 m.
• Then he finally turned left and walked 12 m to reach the ATM.

​

Therefore, the shortest distance between ATM and juice corner is 30m (18m +12m) and ATM is in East direction from his starting point.

Hence, 30m due East is the correct answer.

Shortcut Trick

Let the radius of the large sphere be R and the small sphere be r.

Volume is proportional to r³. Since 27 spheres are made: R³ = 27 × r³ ⇒ R = 3r.

Surface area is proportional to r². Ratio of SA_large to SA_small = R² : r² = 9 : 1.

Total Surface Area of 27 spheres = 27 × SA_small = 27 × (SA_large ÷ 9) = 3 × SA_large.

From Volume = 972π = (4/3)πR³ ⇒ R = 9 cm. SA_large = 4π(9)² = 324π. Total SA = 3 × 324π = 972π cm².

∴ The correct answer is 972π cm².

Alternate Method

Given: Volume of large sphere = 972π cm³, Number of small spheres = 27.

Formula Used: Volume of sphere = (4/3)πr³; Surface Area = 4πr².

⇒ (4/3) × π × R³ = 972π

⇒ R³ = (972 × 3) ÷ 4 = 243 × 3 = 729

⇒ R = 9 cm

⇒ Volume of one small sphere = 972π ÷ 27 = 36π cm³

⇒ (4/3) × π × r³ = 36π ⇒ r³ = 27 ⇒ r = 3 cm

⇒ Total Surface Area = 27 × (4 × π × r²)

⇒ Total Surface Area = 27 × 4 × π × 3² = 27 × 36π = 972π cm²

∴ The correct answer is 972π cm².

Additional Information

Volume and Radius Relation

When a solid is melted and recast into n smaller identical solids, Total Volume remains constant: V_large = n × V_small.

Surface Area of Sphere

The surface area of a sphere with radius r is 4πr². For a hemisphere, curved surface area is 2πr² and total surface area is 3πr².

Scale Factor Property

If the ratio of radii is 1:k, the ratio of their surface areas is 1:k² and the ratio of their volumes is 1:k³.

Given:  

Simple Interest (SI) = 13/8 ×  Principle

Time period (T) = 10 years 

Formula used: 

SI = (P × R × T)/100 

Calculation: 

According to the question, 

Let the sum of money that's principal be x 

Amount after 10 years becomes  = 13x/8 

⇒ SI = Amount - P = 13x/8 − x = 5x/8 

⇒ Rate per annum = (SI × 100)/(P × T) 

⇒ R = (5x/8 × 100)/( x × 10) 

⇒ R = 500/80 = 6.25% per annum.

∴ The rating percentage of the interest will be 6.25%.

The correct answer is wooden.

Key Points

• Kanjira 
• The frame drum known as the kanjira (Khanjari) originates from South India and belongs to the tambourine family.
• It consists of a skin (usually iguana) stretched and pasted on a circular wooden frame.
• In the side of the frame, there are frequently three or four slots where bell-metal jingle discs are hung from metal crossbars.
• The khanjari and kanjani of North and East India and Nepal are related to the term kanjira.
• Wetting the skin allows the kanjira to be tuned to different pitches.
• The right hand's fingers are used to beat it while it is being held at the bottom of the frame by the left hand, which also adjusts the skin's tension.

​

Additional Information

• This instrument has a monitor lizard skin drumhead covering one side and is left open on the other.
• It has been used for many years in India as a folk and bhajan instrument.
• Manpoondia Pillai is credited with the invention of the modern form of the kanjira as well as the instrument's introduction into South Indian Carnatic music.
• Kanjira is known as Khaijadi in Nepal.
• In addition to the Khaijadi, the Daanf, Damphu, and Hring tambourines are also played in Nepal.

The correct answer is the Pacific Ocean.

Key Points

• El Niño is a climate pattern that describes the unusual warming of surface waters in the eastern equatorial Pacific Ocean.
• Trade winds and the atmosphere are also impacted by El Niño.
• El Niño is a climate pattern that describes the unusual warming of surface waters in the eastern tropical Pacific Ocean.
• El Nino, meaning "Child Christ'' is a warm ocean current appearing along the Peru coast, generally in December.
• It normally happens once every 4-5 years though it is not fixed.
• It replaces the cold Peru Ocean current flowing along the Peru coast in normal years.

Additional Information

• East Greenland current and the Labrador current flow from the Arctic Ocean into the Atlantic Ocean.
• The Labrador current flows along part of the east coast of Canada and meets the warm Gulf Stream.
• The Indian Ocean gyre is composed of two major currents: the South Equatorial Current, and the West Australian Current.

Friends: K, L, M, N, O, P, Q, R and S (South facing)

Important Points

• Because the friends are facing South, when we say that L is to the left of M, it will be placed at the right in the diagram.

1) K is sitting at one end of the row. 

Case 1:

Case 2:

2) O is sitting at the third place to the left of K. (So case 1 is eliminated)

3) There are only five people sitting to the right of M.

4) L is sitting to the immediate right of M.

5. M at the second place to the right of N.

6. Only Q is seated between P and O. 

7. S is sitting to the immediate left of N.

Hence, R is sitting to the immediate left of M.

Given:

• Number of floors: 7 such that  The floors were numbered 1 to 7 from bottom to top, floor 1 being the ground floor.
• Number of men: 7; A, B, C, D, E, F, and G

Explanation:

• G occupied floor number 4.
• C was exactly below G.
• F occupied the topmost floor.

• Only one person lived below the floor occupied by E.

• B was exactly above A.

Thus D lives on floor number 1.

Hence, D is the correct answer.

Given:

Area of rectangle = 180 cm²

Ratio of length (l) and breadth (b) = 9/5

Formula used:

Perimeter of a Rectangle (P) = 2 × (l + b)

Area of a Rectangle = l × b.

Calculations:

According to the question,

l/b = 9/5

⇒ l = 9b/5

Area of rectangle = l × b

⇒ 180 = (9b/5) × b

⇒ 900 = 9b²

⇒ b = √100 = 10 cm

Then, length = (9 × 10)/5 = 18 cm

The perimeter of the rectangle:

⇒ P = 2 × (l + b) = 2 × (18 + 10)

⇒ P = 2 × (28) = 56 cm

∴The Perimeter of the Rectangle is 56 cm.

Given:

The HCF of two different numbers is always 1

Concept Used:

The HCF of two consecutive numbers is always one because the two consecutive numbers do not have any common factor other than 1.

Prime numbers only divide by themselves, the only common factor that can be obtained is 1.

∴ The HCF of two different numbers is always 1 when both numbers are prime numbers.

Given:  

Simple Interest (SI) = 2 × Principle (P)  

Time period (T) = 8 years 

Formula used: 

⇒ SI = (P × R × T)/100 

SI = Amount - P 

Calculation: 

According to the question, 

Let the sum of money that's principal be x 

Amount after 8 years becomes double = 2x 

⇒ SI = Amount - P = 2x − x = x 

⇒ Rate per annum = (SI × 100)/(P × T) 

⇒ R = (x × 100)/(x × 8) 

⇒ R = 100/8 = 12.5% per annum.

∴ The rating percentage of the interest will be 12.5%.

Given:

Spheres of radius r₁ = 6 cm, r₂ = 8 cm, r₃ = 10 cm molten in single one. 

Formula used:

The volume of Sphere = 4/3π r³

Calculations:

Let the Radius of the larger bead be 'R' 

According to the question,

The volume of smaller beads = Volume of the larger bead

⇒ 4/3π [(6)³ + (8)³ + (10)³] = 4/3π R³

⇒ R³ = [(216) + (512) + (1000)]

⇒ R³ = 1728 = 12 cm.

∴ The radius (in cm) of the larger bead will be 12 cm.

The correct answer is the International Federation of Film Archives (FIAF) award.

Key Points

• Bollywood actor Amitabh Bachchan was honoured with the International Federation of Film Archives (FIAF) Award 2021.
• The virtual ceremony was held on March 19. Bachchan shared a heartwarming message after he received the award.
• In the lengthy message, the 'Chehre' actor also, as they conferred the award.
• Amitabh is the first Indian to receive the award for his contribution to the preservation of and access to the world`s film heritage for the benefit of present and future generations.

Additional InformationFIAF Award

• Once a year, FIAF celebrates a film personality whose experience and personal commitment in the field of cinema underlines the missions of the Federation, by presenting them with a FIAF Award.
• The FIAF Award recognizes in particular, their dedication and contribution to the preservation of, and access to, the world film heritage, for the pleasure of today’s audiences, as well as for the benefit of future generations.
• The FIAF Award is usually presented at an official ceremony organized during one of the major film festivals or, if relevant, a FIAF Congress.
• The trophy itself is a silver film can be made by Talleres de los Ballesteros in Mexico, with the help of the Filmoteca de la UNAM.

Given:

x(x + y + z) = 30      -----(1)

y(x + y + z) = 64      -----(2)

z(x + y + z) = 50      -----(3)

Where x, y, z > 0.

Calculation:

By adding the equations (1), (2), and (3) we get

[x (x + y + z)] + [y (x + y + z)] + [z (x + y + z)] = 144

Taking (x + y + z) common,

⇒ (x + y + z) (x + y + z) = 144

⇒ (x + y + z)² = 144

⇒ (x + y + z) = 12

Multiplying 2 on both sides,

⇒ 2 (x + y + z) = 24

∴ The value of 2(x + y + z) is 24.

Shortcut Trick

Given equation: sin²β − sin 30° = 0

⇒ sin²β = sin 30°

Using standard value sin 30° = 1/2:

⇒ sin²β = 1/2 ⇒ sin β = 1/√2

For an acute angle, sin β = 1/√2 implies β = 45°.

∴ The correct answer is 45°.

Alternate Method

Given: sin²β − sin 30° = 0 where β is an acute angle.

Formula Used: sin 30° = 1/2; sin 45° = 1/√2

Calculations:

⇒ sin²β − sin 30° = 0

⇒ sin²β = sin 30°

⇒ sin²β = 1/2

⇒ sin β = √(1/2)

⇒ sin β = 1/√2

⇒ β = sin⁻¹(1/√2)

⇒ β = 45°

∴ The correct answer is 45°.

Additional Information

Trigonometric Values of Sine

sin 0° = 0, sin 30° = 1/2, sin 45° = 1/√2, sin 60° = √3/2, sin 90° = 1.

Acute Angle

An acute angle is an angle that is greater than 0° and less than 90°.

Fundamental Identity

For any angle θ, sin²θ + cos²θ = 1.

Shortcut Trick

Ratio of sides = 4 : 3

Ratio of areas = 4² : 3² = 16 : 9

Sum of area units = 16 + 9 = 25 units → 225 cm²

1 unit = 9 cm² ⇒ Side unit = √9 = 3 cm

Side of smaller square = 3 × 3 = 9 cm

Perimeter = 4 × 9 = 36 cm

∴ The correct answer is 36 cm.

Alternate Method

Given: Ratio of sides = 4 : 3, Sum of areas = 225 cm²

Formula Used: Area of square = (side)²; Perimeter = 4 × side

⇒ Let the sides be 4x and 3x.

⇒ (4x)² + (3x)² = 225

⇒ 16x² + 9x² = 225

⇒ 25x² = 225

⇒ x² = 9

⇒ x = 3

⇒ Side of smaller square = 3x = 3 × 3 = 9 cm

⇒ Perimeter = 4 × 9 = 36 cm

∴ The correct answer is 36 cm.

Additional Information

Square Properties

A square has all sides equal. Area = a², Perimeter = 4a, and Diagonal = a√2.

Ratio of Areas

If the ratio of sides of two similar figures is a : b, then the ratio of their areas is a² : b².

Diagonal Relation

Area of a square can also be calculated using the diagonal (d) as Area = d² ÷ 2.

The correct answer is Sun God.

Key PointsPongal

• Pongal is a harvest festival celebrated by the Tamil community.
• It is a celebration to thank the Sun, Mother Nature and the various farm animals that help to contribute to a bountiful harvest.
• Celebrated over four days, Pongal also marks the beginning of the Tamil month called Thai, which is considered an auspicious month.
• It usually falls on the 14^th or 15^th of January each year.
• Pongal is also the name of the dish made and eaten during this festival. It is a mixture of boiled sweet rice.
• It is derived from the Tamil word pongu, which means “to boil over”.

Additional Information

• Vasant Panchami, also called Saraswati Puja in honor of the Hindu goddess Saraswati.
• It is a festival that marks the preparation for the arrival of spring.
• The festival is celebrated by people of Dharmic religions in the Indian subcontinent and Nepal in different ways depending on the region.
• A festival essentially dedicated to the fire and the sun God, Lohri is associated with the concept of life and health in the Hindu religion.
• Ganga Dussehra is one of the major festivals observed in India in the honor of Goddess Ganga.
• It is celebrated on the tenth day of the Shukla Paksha (waxing Moon) of the Jyestha month, as per the Hindu calendar

Statements:

1. Some professors are doctors.
2. No doctor is a researcher.

Possible Venn Diagram:

Conclusions:

I. Some professors are not researchers → True (Since some professors are doctors and no doctor is a researcher)

II. All professors are researchers → False (It is not possible)

Hence, only conclusion I follows.

Option 2 is the correct answer.

Given: XY_XY_ ZXYX XYXY _ _

Lets check each option.

1) Y,X,Y,Y,Z,Z,X,Y → XYYXY - XYZXY - XYZXY - XYZXY

• No pattern followed.

2) Z,X,Y,Y,Z,Z,X,Y → XYZXY - XYZXY - XYZXY - XYZXY

• XYZXY is repeating itself.

3) Z,X,Y,Y,Z,Z,X,Z  → XYZXY - XYZXY - XYZXY - XYZXZ

• No pattern followed.

4) Z,Y,Y,Y,Z,Z,X,Y → XYZXY - YYZXY - XYZXY - XYZXY

• No pattern followed.

Hence, "ZXYYZZXY" is the correct answer.

Given:

Distance traveled by Train (D₁) = (5/12)x km

Distance traveled by Bus (D₂) = (1/3)x km

Distance traveled by Bicycle (D₃) = 36 km

Calculations:

According to the question,

Let the total distance traveled be 'x'.

⇒ x = (D₁) + (D₂) + (D₃)

⇒ x = (5/12)x + (1/3)x + 36

⇒ x = (5x + 4x)/12 + 36

⇒ x = 9x/12 + 36

⇒ x = 3x/4 + 36

⇒ x - (3x/4) = 36

⇒ 1x/4 = 36

⇒ x = 36 × 4 = 144 km

∴ The total distance traveled is 144 km.

Given:

$\frac{7}{18}$of the balls in the drum were red 

$\frac{8}{15}$ of the balls in the drum were blue 

Concept:

No. of red balls = No. of yellow balls + 84

Calculations: 

Let the number of the balls be X .

Now, No. of red balls = ($\frac{7}{18}$X)

And, No. of blue balls = ($\frac{8}{15}$X)

 Therefore, No. of yellow balls

 = X - { $\frac{7}{18}$X + $\frac{8}{15}$X }

 = $\frac{7}{90}$X

According to question, 

    No. of red balls = No. of yellow balls + 84

$\Rightarrow$ $\frac{7}{18}$X = $\frac{7}{90}$X + 84

$\Rightarrow$ $\frac{28}{90}$X = 84

$\Rightarrow$ X = 270

Hence, total no. of balls = X = 270.

Given:

0.002 + 5.025 - 35.08 - 5.058

Calculations:

0.002 + 5.025 - 35.08 - 5.058

⇒ 5.027 - 35.08 - 5.058

⇒ (- 0.031) - 35.08 = - 35.111

∴ The simplified value is - 35.111

The correct answer is 1236 CE.

Key Points

• Sultan Raziyyat-Ud-Dunya Wa Ud-Din, popularly known as Razia Sultana, was a ruler of the Delhi Sultanate in the northern part of the Indian subcontinent.
• She was the first female Muslim ruler of the subcontinent and the only female Muslim ruler of Delhi.
• In 1236 CE, the daughter of Sultan Iltutmish became the sultan of Delhi.
• The writer Minhaj-i-Siraj recognized that she was capable. But he could not accept a woman as his ruler.

Additional Information

• Razia Sultan was very wise, an excellent administrator, brave and a warrior like her father.
• In spite of the fact that her rule was only for the time of three years, her deeds have been saved in the pages of history.
• Razia Sultan's Tomb in Delhi is one of those spots, which recollects the memory of this courageous woman.
• She dressed like a man and sat in an open durbar.
• She was an effective ruler and had the characteristics of a monarch.

The correct answer is 10 January 1942.

Key Points

• The WPI indices are used for the purpose of escalation clauses in the supply of raw materials, machinery and construction work.
• The Office of the Economic Adviser in the Department of Industrial Policy and Promotion, Ministry of Commerce & Industry is responsible for compiling WPI and releasing it.
• The first index number of wholesale prices commenced in India for the week of January 10, 1942.

Additional InformationWholesale price index

• A wholesale price index (WPI) measures changes in the overall price of goods before they are sold at retail.
• This includes the prices charged by manufacturers and, often outside the U.S., wholesalers.
• Usually expressed in terms of the percentage change from the prior month or a year earlier, the WPI is an inflation indicator.
• In the U.S., the WPI has been reported as the Producer Price Index (PPI) since 1978.

The correct answer is Director General of the National Investigation Agency.

Key Points

• CRPF Chief Kuldiep Singh has been given the additional charge of the Director General of the National Investigation Agency (NIA) to replace Y C Modi.
• Modi was a 1984-batch IPS officer of the Assam-Meghalaya cadre.
• He was appointed as the chief of the federal anti-terror probe agency in September 2017.
• Consequent to the superannuation of Y C Modi, DG, NIA, on May 31, 2021, the competent authority has approved that Kuldiep Singh shall hold additional charge of the post of DG, NIA.
• He should hold the charge till the appointment and joining of the successor or until further orders.

Additional Information

• Currently, Dinkar Gupta serves as the Director-General of the National Investigation Agency since 28 June 2022.
• The NIA (National Investigation Agency) can investigate terror cases across the country without having to get permission from the states.
• The agency investigates terror offenses, waging war against the country, offenses on nuclear facilities, etc.
• It came into force after Parliament passed the National Investigation Agency Act 2008.

The correct answer is Narmada.

Key Points

• Ahilya Fort is in the central Indian town of Maheshwar.
• It sits high above the sacred river Narmada.
• Maharani Ahilyabai Holkar ruled here from 1765 to 1796 and built Ahilya Wada. Later its name became the "Ahilya fort".
• Inside this fort was her personal residences, offices, and barbara audience hall.

Additional Information

• Ahilya Fort or palace sits on top of the 16^th CE ramparts that were potentially built by the Mughals.
• The palace is now a heritage hotel which means the residential part is open only to the guests staying here.
• The Ahilya Fort Hotel has 19 rooms of character, set in six buildings of the 18^th century, with modern amenities and comforts.
• Guests stroll through 3 acres of courtyards, fountains, and gardens that link areas within the Wada.

The correct answer is Lieutenant Shivangi Singh.

Key PointsLieutenant Shivangi Singh

• India's first woman Rafale fighter jet pilot Shivangi Singh was a part of the Indian Air Force (IAF) tableau at the Republic Day parade 2022.
• Shivangi Singh is only the second woman fighter pilot to be a part of the IAF's Republic Day tableau.
• Last year Flight Lieutenant Bhawna Kanth was a part of the IAF Republic Day tableau.
• She became the first female fighter pilot to feature on the IAF Republic Day tableau.

Additional InformationIAF's Republic Day tableau on 26^th January 2022

• The Indian Air Force (IAF) tableau participated in the Republic Day Parde 2022.
• The theme of the tableau was 'Indian Air Force Transforming For The Future'.
• It showcased scaled-down models of MiG-21, Gnat, Light Combat Helicopter (LCH), Aslesha radar and Rafale aircraft.

Date: June 10, 1992

Steps to find the day of the week:

Total = (92 + 23 + 5 + 10) = 130

And 130 ÷ 7, we get 4 as the remainder.

 

Hence, "Wednesday" is the correct answer.

Given: 

The total surface area of the hemisphere = 108π cm² 

Formula used: 

The total surface area of the hemisphere = 3πr² 

The volume of hemisphere = (2/3)πг³ 

Where r is the radius of the hemisphere! 

Calculation: 

According to the question, 

The total surface area of the hemisphere = 108π 

⇒ 3πr² = 108π 

⇒ r² = 36 

⇒ r = 6  

Volume of the hemisphere (V) = (2/3) × πг³ 

V = (2/3) × π × (6)³ 

⇒ V = (2/3) × π × 216 

⇒ V = 432/3 × π = 144π cm³.

∴ The volume of the hemisphere is 144π cm3.

Explanation:

• Option1: (19)² + 14 = 361 + 14 = 375
• Option 2: (17)² + 14 = 289 + 14 = 303
• Option 3: (8)² + 14 = 64 + 14 = 78, and not 82
• Option 4: (24)² ​+ 14 = 576 + 14 = 590

So, (8, 82) does not belong to the group.

Hence, 8, 82 is the correct answer.

Given: If you do not work hard, I will fire you."- A statement by the Head of Department to a junior.

Implicit means that understood though not put clearly into words

Explanation: Assumption II talks about all juniors but information about other juniors is not implicit in the statement.

Assumption I directly follows the statement and so it is implicit.  The statement issued by the Head must be with the belief that the junior will work hard after the warning given by him.

Hence, Only assumption I is implicit is the correct answer.

Shortcut Trick

To check divisibility by 8, we only need to verify if the last three digits of the number are divisible by 8.

Checking options: 792 ÷ 8 = 99; 552 ÷ 8 = 69; 112 ÷ 8 = 14; 412 ÷ 8 = 51.5.

Since 412 is not divisible by 8, the entire number 35412 is not divisible by 8.

∴ The correct answer is 35412.

Alternate Method

Given: Four numbers: 35792, 35552, 35112, and 35412.

Formula Used: A number is divisible by 8 if and only if the number formed by its hundreds, tens, and units digits is divisible by 8.

Step-by-step verification:

⇒ For 35792: Last 3 digits 792; 792 ÷ 8 = 99 (No remainder).

⇒ For 35552: Last 3 digits 552; 552 ÷ 8 = 69 (No remainder).

⇒ For 35112: Last 3 digits 112; 112 ÷ 8 = 14 (No remainder).

⇒ For 35412: Last 3 digits 412; 412 ÷ 8 = 51 with a remainder of 4.

∴ The correct answer is 35412.

Additional Information

Divisibility Rule of 2 and 4

A number is divisible by 2 if its units digit is even. For 4, the last two digits must be divisible by 4.

Divisibility Rule of 16

A number is divisible by 16 if the number formed by its last four digits is divisible by 16.

Divisibility Rule of 3 and 9

A number is divisible by 3 (or 9) if the sum of its digits is divisible by 3 (or 9).

The correct answer is A mixed economy is one in which the public sector (consisting of government enterprises) and the private sector (consisting of private enterprises) coexist with each other.

Key Points

• A market system of resource allocation, commerce, and trade in which free markets coexist with government intervention.
• Mixed economies have public, private, legislative, judicial, and regulatory components.
• The main feature of a mixed economy is the co-existence of both public and private enterprises.
• They work together. The industries in the private sector are managed and operated completely by private entrepreneurs.
• It allows the free market and the laws of supply and demand to determine prices.

Additional Information

• An economy is a system whereby goods are produced and exchanged. Without a viable economy, a state will collapse.
• There are three main types of Economy:
• ​Free market.
• Command
• Mixed economy.
• ​Capitalism is the greatest economic system because it has numerous benefits and creates multiple opportunities for individuals in society.
• Some of these benefits include producing wealth and innovation, improving the lives of individuals, and giving power to the people.

Explanation:

• D likes Mango.
• E likes Orange.
• A likes Apple.

 

• F neither likes Grapes nor does he like Guava. so, F likes kiwi.
• C neither likes Guava nor does he like Kiwi. so, C likes Grapes.

 

 Hence, C is the correct answer.

Given:

Time taken by 12 men to build a wall = 24.5 days

Calculation:

Let total work be 'W'

Let work done by 1 man in 1 day be 'w'

⇒ W = 12 × w × 24.5     .........(1)

Work done by x man in 10 days,

Where x is the number of men required to build the wall in 10 days,

⇒ W = x × w × 10      ........(2)

Equating both equations (1) and (2),

⇒ x × w × 10 = 12 × w × 24.5

⇒ x = (12 × 24.5)/10

⇒ x = 294/10 ​= 29.4 ~ 30 men.

∴ The number of men needed to build five such walls in 49 days is 30 men.

Given: "pu ma kas' means 'we eat mangoes'.

Statements: 

I. 'la ti kas' means 'we are graduate'.

II. 'hum tup pu' means 'they eat bananas'.

From I and II statements we conclude that both are sufficient to answer the question. So 'ma' is the code of 'mangoes'.

Hence, Statements I and II together are sufficient to answer the question.