According to the sequence in the dictionary:

The correct order of the given words is:

3. Petition
4. Petitionary
5. Petitioned
6. Petitioners
7. Petitioning

Hence, the correct answer is "3, 1, 5, 4, 2".

In first dice and second dice:

Given:

Logic: If two dice have the same face value in the given image then their clockwise or anticlockwise wise number are known as opposite numbers in dice.

In first dice and second dice. The symbol 'l' is common.

The left letter will be opposite each other writing them clockwise starting from I.

 

Hence, the face opposite the H is “@”.

Hence, the correct answer is “@”

The pattern followed here is:

(Previous number × 3) + (previous number – 2) = next number

Given: 5, 18, 70, 278, ?

1^st number → 5

2^nd number → (5 × 3) + (5 - 2) = 15 + 3 = 18

3^rd number → (18 × 3) + (18 - 2) = 54 + 16 = 70

4^th number → (70 × 3) + (70 - 2) = 210 + 68 = 278

5^th number → (278 × 3) + (278 - 2) = 834 + 276 = 1110

Hence, ''1110" is the correct answer.

Alternate MethodThe logic followed here is:

The Previous number × 4 - 2 = next number.

5, 18, 70, 278, ?

5 × 4 - 2 = 18

18 × 4 - 2 = 70

70 × 4 - 2 = 278

278 × 4 - 2 = 1110

Hence, the correct answer is "1110".

The logic here is,

• Consonants alphabet + 3 = next alphabet
• Vowel alphabet - 3 = previous alphabet

BACTERIA : EXFWBUFX

Similarly,

WOUNDS : ?

Hence, "ZLRQGV" is the correct answer..

Decoding the information, 

Given:

29 @ 128 $ 16 % 7 # 22

After replacing the signs from left to right and using the BODMAS rule,

= 29 + 128 ÷ 16 × 7 - 22

= 29 + 8 × 7 - 22

= 29 + 56 - 22

= 85 - 22

= 63

Hence, “63” is the correct answer.

The pattern followed here is:

Hence, '73' is the correct answer.

The table is alphabets place value:

The pattern followed here is:

CHHAPAK is coded as DJKEUGR.

​Similarly, 

'MALANGA' = ?

Hence, the correct answer is "NCOESMH".

The pattern followed here is,

Sum of digits of 1^st number + 1 = Sum of digits of 2^nd number.

Now follow the steps:

223 : 350

Sum of digits of 1st number + 1 = Sum of digits of 2nd number.

=> = (2 + 2 + 3) + 1 = 3 + 5 + 0

=> 7 + 1 = 8

=> 8 = 8

Similarly,

519:?

=> Sum of digits of 1^st number + 1 = (5 + 1 + 9) + 1 = 15 + 1 = 16

Check option all options:

Option (1): 736 → 7 + 3 + 6 = 16 

Option (2): 687 → 6 + 8 + 7 = 21 

Option (3): 654 → 6 + 5 + 4 = 15 

Option (4): 645 → 6 + 4 + 5 = 15 

Hence, "736" is correct answer.

Alternate Method

223 : 350 

⇒ 6³ + 7= 216 + 7 = 223; 73 + 7 = 343 + 7  = 350;

Similarly,

519 : ?

⇒ 83 + 7 = 512 + 7 = 519; 93 + 7 = 729 + 7  = 736;

Hence, "736" is correct answer.

The embedded part of this image is:

Hence, option (3) is the correct answer.

The image obtained when the paper is unfolded is,

Hence, option 3 is the correct answer.

The logic followed here is:

Top Number 48:

Top number 63:

Similarly,

Top number 56:

Middle number (?) = 21.

Hence, the correct answer is "21".

The logic followed here is:

The upper side three-figure rotates in a cyclic pattern in anticlockwise:

1)Triangle:

• 1st figure triangle position is upper right and the triangle in the rectangle.
• 1st to 2nd figure triangle shifted to upper left and triangle in the square.
• 2nd to 3rd figure triangle shifted to the middle and triangle in the hexagon.
• 3rd to 4th figure triangle shifted to the upper right side and in the rectangle.

2) Right angle triangle:

• 1st figure Right angle triangle position is upper left and the Right angle triangle in the square.
• 1st to 2nd figure Right angle triangle shifted to middle and Right angle triangle in the rectangle.
• 2nd to 3rd figure Right angle triangle shifted to the upper right side and Right angle triangle in the hexagon.
• 3rd to 4th figure right angle triangle shifted to the upper left side and in the square.

3) Arrow:

• 1st figure arrow position is middle and the arrow in the hexagon.
• 1st to 2nd figure arrow shifted to upper right side and Arrow in the square.
• 2nd to 3rd figure arrow shifted to upper left side and arrow in the rectangular.
• 3rd to 4th figure arrow shifted to the middle side and in the hexagon.

 

The lower right side figure and lower left side figure interchange their own position respectively.

Hence, ‘option 2’ is the correct answer.

Table show alphabet serial number –

The pattern followed is,

All follow the same pattern, except 'GTQ’.

Hence, “GTQ” is the odd one.

Let,

Price of one pen = x

Price of one notebook = y

Given:

1) Mohit bought 3 pens and 6 notebooks by paying an amount of Rs. 180

=> 3x + 6y = 180

=> 3x = 180 – 6y

=> x = (180 – 6y) ÷ 3

=> x = 60 – 2y --------------- (i)

2) Sudesh bought 5 pens and 2 notebooks by paying an amount of Rs. 116

=> 5x + 2y = 116

Putting the value of x from eq (i)

=> 5(60 – 2y) + 2y = 116

=> 300 – 10y + 2y = 116

=> 300 – 116 = 10y – 2y

=> 8y = 184

=> y = 23

Mohit spend on buying 6 notebooks

=> 6y = 6 × 23 = 138

Hence, Mohit spend **“**Rs. 138” on buying notebooks.

Table show alphabet serial number –

The pattern followed is,

Hence, “LGV” is the complete series.

Statements:

All flowers are beautiful.

Vaidehi is beautiful.

The least possible diagram for the given statements is as follows

Conclusions:

I. Vaidehi is a flower → False (No direct relationship given between Vaidehi and flower, so it may be possible but not defined)

II. Some beautiful are flowers → True (because all flowers are beautiful, so some beautiful are also flowers)

Hence, “Only conclusion II follows".

Preparing the family tree using the following symbols,

Given:

1. Nirupama is the mother of Deepak.

2. Yamini’s only son, Ankit, is married to Nirupama.

3. Kartik is the paternal grandfather of Deepak.

4. Saloni is the daughter of the only son of Kartik.

Hence, Kartik is the "Father" of Ankit.

Gaurav exits from the backdoor of his north-facing house means Gaurav starts to walk south side.

Drawing the diagram according to the given information,

1. Gaurav walks south 25 m straight
2. then he takes a left turn and walks 36 m
3. then he turns left and walks 47 m.
4. He turns left again and walks 36 m.

• So, Gaurav is 22 km far and the North direction is from his house now

Hence, “22 m, North” is the correct answer.

Option 1:

• The water image of N is incorrect.

Option 2:

• The water image of R is incorrect.

Option 3:

• The water image of D and F are incorrect.

Option 4:

• This is correct.

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

Check all the options

Option 1: Fathers, Brothers, Males

• All fathers and brothers are males

​

Option 2: Mothers, Aunts, Doctors

• Some mothers are Aunts and some mothers and aunties are doctors

Option 3: Literates, Engineers, Farmers

• All engineers are Literates and some farmers are Literates.

Option 4: Grandfathers, Fathers, Males

• All grandfathers are fathers
• All grandfathers and fathers are male.

Hence, ‘option4’ is the correct answer.

Given: _ Z _ C _ L Z _ C _ L _ X _ V L _ _ _ V 

By checking options and substituting accordingly.

1)  L, X, V, V, X, C, C, X, Z, Z → L Z X C V / L Z V C X / L C X C V / L X Z Z V 

2)  L, X, C, X, V, C, Z, C, Z, C → L Z X C C / L Z X C V / L C X Z V / L C Z C V 

3)  X, Z, L, X, V, Z, C, C, C, L → X Z Z C L / L Z X C V / L Z X C V / L C C L V 

4)  L, X, V, X, V, Z, C, Z, X, C → L Z X C V / L Z X C V / L Z X C V / L Z X C V 

Here "L Z X C V" is repeated itself.

• Option (4) gives a pattern of L Z X C V - L Z X C V - L Z X C V - L Z X C V

Hence, ‘L, X, V, X, V, Z, C, Z, X, C’ is the correct answer.

According to BODMAS rule:

Given equation 60 * 48 * 36 * 6 * 15 * 53

Option 1 : Using the combination +, ÷, ×, −, =

60 + 48 ÷ 36 × 6 - 15 = 53

60 + 1.34 × 6 - 15 = 53

60 + 8 - 15 = 53

68 - 15 = 53

53 = 53 (LHS = RHS)

Option 2 : Using combination +, ÷, −, ×, =

60 + 48 ÷ 36 - 6 × 15 = 53

60 + 1.34 - 6 × 15 = 53

60 + 1.34 – 90 = 53

61.34 – 90 = 53

-28.66 = 53 (LHS ≠ RHS)

Option 3 : Using the combination ÷, +, ×, −, =

60 ÷ 48 + 36 × 6 - 15 = 53

1.25 + 36 × 6 - 15 = 53

1.25 + 216 - 15 = 53

217.25 – 15 = 53

202.25 = 53 (LHS ≠ RHS)

Option 4 : Using the combination ×, ÷, +, −, =

60 × 48 ÷ 36 + 6 - 15 = 53

60 × 1.34 + 6 - 15 = 53

80 + 6 – 15 = 53

86 – 15 = 53

71 = 53 (LHS ≠ RHS)

Hence, the answer is “+, ÷, ×, −, =”.

Total 6 persons facing north:-  Amit, Gaurav, Hatim, Varun, Yukti and Zaid.

1. Hatim is fourth to the left of Yukti.

2. Yukti is sitting at one corner.

3. Gaurav is fourth to the left of Amit.

4. Zaid is third to the right of Gaurav.

5. Only Varun is left which is sitting in a blank place.

Hence, 'Hatim' is sitting in the second place to the left of Zaid.

Hence, the correct answer is "Hatim".

The table is alphabets place value:

The pattern followed here is:

Step 1: Vowels place values coded as numbers. 

Step 2: Consonants opposite alphabet place value code as numbers.

Step 3: Then this coded number is arranged in reverse order.

‘CROWD’ is coded as 23415924

And,

‘TRHICK’ is coded as 162491997

Similarly,

‘FRUGAL’ be coded

Hence, ‘FRUGAL’ is coded as "1512021921".

The pattern followed here is:

The word is coded as the total letter number of letters present in the word.

6219 means ‘Sachin is a cricketer’

And,

2646 means ‘He played from Mumbai’

Similarly,

‘Mumbai is very famous’ means ?

Hence, the correct answer is "6246".

The correct answer is 1761.

Key Points

• The British East India Company captured Pondicherry (Puducherry) from the French in the year 1761.
• Puducherry changed hands throughout the Anglo-French wars from 1742 to 1763, with the British "East India Company" capturing Puducherry from the French in 1761 and the French Company administration being restored by the Treaty of Paris in 1763.
• The British "East India Company" acquired control of the territory during the French Revolution in 1793, and it was returned to the French "East India Company" in 1814.
• When the British "East India Company" took control of India in the late 1850s, the French "East India Company" was allowed to keep their settlements in Pondicherry, Mahe, Yanam, Karaikal, and Chandernagore.​

Important Points

• The former French colonies of Puducherry, Karaikal, Mahe, and Yanam now make up the Union Territory of Puducherry.
• The states of Tamilnadu and Kerala surround the Puducherry and Karaikal regions, while Kerala surrounds Mahe, and Andra Pradesh surrounds Yanam.
• Pondicherry was founded in 1673 after the "La Compagnie française des Indes Orientales" was granted firman by the Qiladar of Valikondapurarm, who served under the Sultan of Bijapur.
• A French Company Official named Bellanger moved into the Danish Lodge at Pondicherry on February 4, 1673.

The correct answer is Prithviraj Chauhan.

Key Points

• The Rajput ruler Prithviraj Chauhan defeated Muhammad Ghori in the First Battle of Tarain in 1191 AD.
• Near Tarain, in 1191, the invading Ghurid army led by Muhammad of Ghor and the Rajput confederacy led by Prithviraj Chauhan fought the First Battle of Tarain, also known as the First Battle of Taroari (modern Taraori in Haryana, India).
• The Rajputs won the battle decisively, but Shihabuddin managed to flee and return to Ghor.
• After the Ghorid armies were routed, they retreated to the Ghazni, leaving a garrison of 2,000 soldiers under Zia ud-Din Tulaki to secure the fort of Tabarhind and delay the Rajput army for thirteen months, during this time Shahabuddin raised a stronger army of 120,000 men and invaded again, leading to the Second Battle of Tarain.

Important Points

• Prithviraj III, also known as Prithviraj Chauhan, was a monarch of the Chauhan (Chahamana) dynasty who controlled the Sapadalaksha region, with his capital in Ajmer, Rajasthan.
• He inherited an empire that stretched from Thanesar in the north to Jahazpur (Mewar) in the south, which he sought to expand through military campaigns against neighbouring kingdoms, particularly the Chandelas.
• Muhammad Ghori's initial raids were against Multan and the citadel of Uch in 1175, with the goal of reuniting the Muslim nations of India.

Additional Information

• Rao Maldeo Rathore was a Marwar monarch from the Rathore family who controlled the kingdom of Marwar, which is now part of the state of Rajasthan.
• Maharana Kumbha, also known as Kumbhakarna Singh, was the Maharana of the Mewar kingdom in India.
• Bappa Rawal was the monarch of Rajasthan, India's Mewar kingdom.

The correct answer is 137%.

Key Points

• The allocation towards health and well-being was increased by 137% over the previous year in Union Budget 2021-22.
• According to analysts, one of the sectors that have continually been neglected is "health."
• However, in her Budget 2021-22, Union Finance Minister Nirmala Sitharaman announced a 137 percent increase in the allocation for health from the previous year's budget estimate of over Rs. 94,000 crore (Rs. 94,452 crore) and a 118 percent increase from the previous year's revised budget of over Rs. 1.02 lakh crore (Rs. 1,02,873 crore).

Important Points

• The 2.23 lakh crore spending in Budget 2021 comprises allocations to the Ministry of Ayurveda, Yoga and Naturopathy, Unani, Siddha, and Homoeopathy, as well as the Ministry of Health and Family Welfare (MoHFW), which is the country's focal ministry for healthcare (AYUSH).
• To calculate the spending for health and wellness, the Finance Minister combined the amounts given under several categories of other ministries.

The correct answer is Dhaulagiri I.

Key Points

• Dhaulagiri I is also known as the ‘White Mountain’.
• Dhaulagiri, at 8,167 metres above sea level, is the world's seventh-tallest mountain and the highest mountain within a single country's borders (Nepal).
• A Swiss-Austrian-Nepali expedition climbed it for the first time on May 13, 1960.
• Dhaulagiri is 34 kilometres east of Annapurna I (8,091 metres).
• The Kali Gandaki River flows between them in the world's deepest gorge, the Kaligandaki Gorge.
• Pokhara is a major regional city and the gateway for climbers and trekkers exploring both ranges, as well as a tourist destination in its own right, located south of the Annapurnas.

Important Points

• Cho Oyu, at 8,188 metres above sea level, is the world's sixth tallest peak.
• Lhotse, at 8,516 metres, is the world's fourth-highest peak, behind Mount Everest, K2, and Kangchenjunga.
• At 8,485 metres, Makalu is the world's fifth-highest peak. It is 19 kilometres southeast of Mount Everest in the Mahalangur Himalayas, on the boundary between Nepal and China's Tibet Autonomous Region.

The correct answer is roots.

Key Points

• Pneumatophores are specialized root structures that grow out from the water surface and help hydrophytic plants, such as many mangrove species, get the aeration they need for root respiration.
• Pneumatophores are specialized roots that sprout vertically out of the water or mud to reach the air and get oxygen for the root systems of marshy or tidal trees.
• Pneumatophores include mangrove knees and bald cypress. It is also known as the air root.
• These unique aerial roots allow plants to breathe air in wet environments. The roots can grow up from the stem or down from traditional roots.
• If they emerge from the earth, some botanists define them as aerating roots rather than aerial roots.

The correct answer is Goods and Services Tax.

Key Points

• The Goods and Services Tax (GST) is a tax on goods and services.
• It is an indirect tax that was implemented to replace a variety of other indirect taxes such as VAT, service tax, purchase tax, excise duty, and so on.
• GST is a tax applied in India on the supply of certain goods and services.
• GST is a multi-stage, all-encompassing tax system that applies to the sale of goods and services.
• The fundamental goal of this taxing scheme, which is applicable throughout India, is to reduce the cascading effect of other indirect taxes.​

Important Points

• The tax on the consumption of goods and services is known as indirect tax. It isn't based on a person's earnings. Instead, he or she must pay the tax in addition to the cost of the products or services purchased from the seller.
• Corporation tax is a direct tax levied on corporations' net revenue or profit.
• An income tax is a type of tax that is levied on individuals or businesses based on their earnings or profits.
• If most investments are kept for at least one year**, capital gains** taxes must be paid on the earnings from their sale.

The correct answer is I, II and III.

Key Points

• The total monetary or market worth of all finished goods and services produced inside a country's borders in a certain time period is known as Gross Domestic Product(GDP).
• GDP includes the total value of final products that are produced and sold (and not resold) within the current year.
• It serves as a comprehensive scorecard of a country's economic health because it is a wide measure of entire domestic production.
• In a free market economy, GDP includes only those products that are sold through the market. That is, consumers are willing to pay prices for the products they consume. In principle, GDP does NOT include those products consumers do not pay for. Hence statement 1 is correct.
• Non-monetary goods and services (e.g. cooking by a housewife) are not included in GDP calculation. Hence statement 2 is correct.
• To avoid double-counting (adding the value of output to the GDP more than once), GDP only counts the ultimate output of commodities and services, not intermediary items or labour value in the supply chain. Hence statement 3 is correct.

Important Points

• GDP represents the monetary value of a country's final goods and services—those that are purchased by the end-user—produced over a specific period of time (say a quarter or a year).
• It counts all of the products produced within a country's borders. GDP is made up of commodities and services generated for market sale as well as certain nonmarket production, such as government-provided defence and education services.
• Gross national product, or GNP, is an alternative definition that counts all of a country's residents' productivity.

The correct answer is Tamralipti.

Key Points

• Tamralipti was an ancient Bengal port city and the capital of the Suhma Kingdom, located on the Bay of Bengal's shore.
• It is typically attributed to the Tamluk town in modern-day Purba Medinipur, West Bengal. It was close to the river Rupnarayan.
• Its name comes from the Sanskrit term "tmra," which refers to copper, which was mined nearby at Ghatsila in the Chota Nagpur Plateau's Singbhum region and traded through this port.
• Tamralipta was the principal emporium under the Gupta era, acting as a point of departure for trade with Ceylon, Java, and China, as well as the west.​

Important Points

• The ancient capital of Northern Panchala, a northern Indian kingdom mentioned in the Mahabharata, was Ahichchhatra, located near the contemporary Ramnagar hamlet in Aonla tehsil, Bareilly district in Uttar Pradesh.
• Champa was the capital of the Anga empire in ancient India (a region corresponding with the eastern part of present-day Bihar state).
• Shravasti was the capital of the Kosala kingdom in ancient India, and it was here that the Buddha spent the most of his time after enlightenment.

The correct answer is Pacific.

Key Points

• Many volcanic eruptions and earthquakes occur in the Ring of Fire, which runs along much of the Pacific Ocean's rim.
• The Ring of Fire is a 40,000 km long and up to 500 km broad horseshoe-shaped ring.
• The Pacific coasts of South America, North America, and Kamchatka, as well as certain islands in the western Pacific Ocean, make up the Ring of Fire.
• Although geologists agree on almost all of the locations that make up the Ring of Fire, the dispute on the inclusion or exclusion of a few areas, such as the Antarctic Peninsula and western Indonesia.
• Plate tectonics, specifically the movement, collision, and destruction of lithospheric plates beneath and around the Pacific Ocean, has created the Ring of Fire.
• There is no single geological feature that makes up the Ring of Fire. Each segment of the Ring of Fire experiences volcanic eruptions and earthquakes independently of eruptions and earthquakes in other parts of the Ring.

Important Points

• The Pacific Ocean is the world's largest and deepest oceanic division.
• It stretches from the Arctic Ocean to the Southern Ocean in the south and is bordered on the west by Asia and Australia, and on the east by the Americas.
• With a surface area of 70,560,000 km², the Indian Ocean is the third largest of the world's five oceanic divisions. Asia to the north, Africa to the west, and Australia to the east define its borders.
• The Atlantic Ocean is the world's second-largest ocean, covering approximately 106,460,000 km².
• Of the world's five major oceans, the Arctic Ocean is the smallest and shallowest. It is the coldest of all the seas, covering an area of approximately 14,060,000 km².

The correct answer is Tirath Singh Rawat.

Key Points

• Tirath Singh Rawat became the Chief Minister of Uttarakhand in March 2021.
• He is a former Chief Minister of Uttarakhand and a serving Member of Parliament in India.
• In the 2019 Indian general election, he was elected to the 17th Lok Sabha from the Garhwal constituency as a member of the Bharatiya Janata Party.
• From 9 February 2013 until 31 December 2015, he was the party head of the Bharatiya Janata Party Uttarakhand and a former member of the Uttarakhand Legislative Assembly from the Chaubattakhal constituency from 2012 to 2017.
• He was also Uttarakhand's first Education Minister.

Important Points

• Madan Kaushik is the state president of the BJP in Uttarakhand and a four-time MLA from Haridwar.
• Dhan Singh Rawat is a member of the Bharatiya Janata Party and the Cabinet Minister of Uttarakhand.
• From 2007 to 2009, and again from 2011 to 2012, Indian politician Major General Bhuwan Chandra Khanduri served as Chief Minister of Uttarakhand.

Additional Information

• The chief minister of Uttarakhand is the state's chief executive.
• The governor is a state's de jure head, while the chief minister has de facto executive authority, according to the Indian Constitution.
• First Chief Minister: Nityanand Swami

The correct answer is Bihar.

Key Points

• The election was NOT held in Bihar during March-April 2021.
• Members of the Seventeenth Bihar Legislative Assembly were elected in three parts from October to November.
• The previous Bihar Sixteenth Legislative Assembly's tenure concluded on November 29, 2020.
• Following the elections, incumbent Chief Minister Nitish Kumar was re-sworn in as Chief Minister after being chosen as the leader of the National Democratic Alliance in Bihar, and two new deputy Chief Ministers, Tarkishore Prasad, and Renu Devi were recruited into the new administration.

Important Points

• The election for 292 of the 294 constituencies of West Bengal's Legislative Assembly in 2021 was held in eight phases between March 27 and April 29, 2021.
• The election for the remaining two seats had been postponed until September 30, 2021.
• Despite opinion surveys generally expecting a close fight against the Bharatiya Janata Party, which formed the formal opposition with 77 seats, the incumbent All India Trinamool Congress administration led by Mamata Banerjee won the election by a substantial margin.
• On April 6, 2021, the Sixteenth Tamil Nadu Legislative Assembly Election was conducted to elect representatives from the state's 234 constituencies. The Dravida Munnetra Kazhagam (DMK) won the election, ending the All India Anna Dravida Munnetra Kazhagam's decade-long reign (AIADMK).
• M. K. Stalin, the leader of the DMK, was elected as the eighth Chief Minister of Tamil Nadu, and the 12th since the 1956 reorganization. He took the place of AIADMK leader Edappadi K. Palaniswami.
• The fifteenth legislative assembly election was held on April 6, 2021, in the union territory of Puducherry, India, to elect members to the Legislative Assembly from 30 constituencies.

The correct answer is Sri Aurobindo.

Key Points

• The book ‘The Secret of the Veda' was written by Sri Aurobindo.
• This volume comprises Sri Aurobindo’s writings on and translations of the Rig Veda that were published in the monthly review 'Arya' between 1914 and 1920.
• Most of this material appeared under three headings:
• The Secret of the Veda, August 1914 – July 1916.
• Selected Hymns, August 1914 – July 1915.
• Hymns of the Atris, August 1915 – December 1917.
• Sri Aurobindo was an Indian nationalist and freedom fighter, a major Indian English poet, philosopher, and yogi.
• He joined the movement for India's freedom from British rule and for a duration (1905–10), became one of its most important leaders, before turning to develop his own vision and philosophy of human progress and spiritual evolution.

Additional Information

• Swami Vivekananda, born Narendranath Datta, was an Indian Hindu monk, philosopher, and author. He was a chief disciple of the 19th-century Indian mystic Ramakrishna.
• Annie Besant was a British socialist, theosophist, women's rights activist, writer, orator, political party member, educationist, and philanthropist. Regarded as a champion of human freedom, she was an ardent supporter of both Irish and Indian self-rule. In 1916 she established the Indian Home Rule League, of which she became president. She became the first woman President of the Indian National Congress to head the Calcutta session of the Indian National Congress in 1917.
• Jiddu Krishnamurti was a philosopher, speaker, and writer. In his early life, he was groomed to be the new World Teacher, an advanced spiritual position in the theosophical tradition, but later rejected this mantle and withdrew from the organization behind it. He was the adopted son of Annie Besant.

The correct answer is Mumbai City FC.

Key Points

• At the GMC Stadium in Goa, Mumbai City FC defeated ATK Mohun Bagan (ATKMB) 2-0 to win the Indian Super League Winners Shield and the coveted AFC Champions League slot that comes with it.
• Mumbai and ATKMB tied for the first position with 40 points, but the former won due to a stronger head-to-head record.
• Mumbai City FC became the second Indian team to qualify for the AFC Champions League group stages. Mumbai City Football Team is an Indian professional football club based in Mumbai, Maharashtra, that participates in India's top flight, the Indian Super League.
• The club was created in August 2014, during the Indian Super League's debut season.​

Important Points

• Kerala Blasters Football Team is an Indian professional football club headquartered in Kochi, Kerala, that competes in the Indian Super League, India's highest level of football.
• ATK Mohun Bagan FC is a West Bengal-based Indian professional football team. The club competes in the Indian Super League, one of the country's premier football leagues.
• NorthEast United FC is an Indian professional football team headquartered in Guwahati, Assam, that participates in India's top division, the Indian Super League.

Additional Information

• In the Indian football system, the Indian Super League is the men's professional top-flight football league.
• All India Football Federation and their commercial partners Football Sports Development Limited are putting up the event.
• It is officially known as the Hero Indian Super League because of its sponsorship links with Hero MotoCorp.

The correct answer is Restore our Earth.

Key Points

• The theme for International Mother Earth Day, 2021 was 'Restore our Earth'.
• Every year on April 22nd, the world celebrates Earth Day, also known as International Mother Earth Day.
• The Earth Day 2022 Theme is Invest In Our Planet.
• The day will be commemorated around the world to raise awareness about the environment and encourage people to support environmental protection.
• The 51st anniversary of World Earth Day, which began in 1970, celebrated in 2021.
• In 2009, the United Nations renamed Earth Day International Mother Earth Day.

Important Points

• Earth Day was established in 1970 when around 20 million Americans felt that maintaining Mother Earth was a critical need.
• As a result, Earth Day was observed for the first time this year.
• Every year, billions of people throughout the world participate in various activities such as tree planting, cleanliness campaigns, and other activities to help Mother Nature.

The correct answer is Eighty-Sixth Amendment Act, 2002.

Key Points

• Eighty-Sixth Amendment Act, 2002 added a new fundamental duty under Article 51-A.
• The Constitution of India's Eighty-sixth Amendment guarantees the right to education for children aged six to fourteen and early childhood care for children under the age of six.
• It has replaced Article 45 (Early Childhood Education) of directive principles of State policy with Article 21A (Right to Education as a Fundamental Right) and altered Article 51A (Fundamental Duties) to establish a new duty of parents to provide education to their children aged six to fourteen years.
• In part III of the constitution, the 86th Amendment Act of 2002 established the right to education as a fundamental right. "Who is a parent or guardian to provide chances for education to his child or, as the case may be, ward between the ages of six and fourteen years," was added after clause (J).

Important Points

• The Constitution (88th Amendment) Act, 2003: The Union and States collect and appropriate service taxes, which are levied by the Union. Articles 268, 270, and the VIIth Schedule are amended by the Act.
• The main goal of the 85th Amendment Act of 2001 was to extend the advantage of the reservation to SC/STs in areas of promotion and subsequent seniority.

The correct answer is a half.

Key Points

• Algae photosynthesis accounts for at least half of all carbon dioxide fixing on the planet.
• They enhance the amount of dissolved oxygen in their immediate environment because they are photosynthetic.
• The conversion of inorganic carbon to organic carbon by living organisms is known as carbon dioxide fixation.

Important Points

• Biological carbon fixation, also known as carbon assimilation, is the process by which living organisms transform inorganic carbon (most commonly in the form of carbon dioxide) into organic compounds.
• After that, the compounds are employed to store energy and provide structure for other biomolecules.
• Carbon is typically fixed through photosynthesis, however, in the absence of sunshine, some organisms use a process called chemosynthesis.
• Photosynthesis is the process through which plants produce oxygen and energy in the form of sugar from sunlight, water, and carbon dioxide.
• Plants, algae, and some bacteria are involved in the process, which gathers energy from the sun to produce oxygen (O2) and chemical energy stored in glucose (a sugar). Herbivores get their energy from plants, while predators get theirs from herbivores.

The correct answer is large, narrow-mouthed earthenware pot used as a percussion instrument.

Key Points

• A Ghatam is a large, narrow-mouthed earthenware pot used as a percussion instrument.
• The ghatam is a percussion instrument that is utilized in several Indian repertoires.
• The ghatam is an Indian percussion instrument that dates back thousands of years. It's a narrow-mouthed clay pot.
• A small amount of plasticine clay or water can be used to change the pitch significantly.

Important Points

• The Kanjira is a South Indian frame drum that belongs to the tambourine family of instruments. It has been used in India for generations as a folk and bhajan instrument.
• Mridangam is a leather and jackwood percussion instrument. This traditional instrument can be found throughout South India.
• The saxophone is a single-reed woodwind instrument with a conical, brass body. Sound is produced when a reed on a mouthpiece vibrates, producing a sound wave inside the instrument's body, as it is with all single-reed instruments.

The correct answer is Ossuary Feast.

Key Points

• Tribes of the Nicobar Islands pay their respects to the departed soul of the head of the family during the Ossuary Feast.
• The Andaman and Nicobar Islands' Nicobar dance is a captivating indigenous circle dance.
• It is typically performed in or around the houses on the island of Car Nicobar during the Ossuary Festival or the Pig Festival.
• This dance is devoted to the house's deceased head. Long night dances under the swaying palms in total moonlight are witnessed.
• The performers began sweetly in time with traditional music, dressed in coconut fronds.

Important Points

• In West Bengal, Goddess Jagaddhatri Puja is celebrated.
• Kalpataru Utsav is an annual Hindu religious holiday celebrated by monks and lay members of the Ramakrishna Math monastic order, as well as the worldwide Vedanta Societies.
• Gajan, also known as Shivagajan, is a Hindu festival held mostly in West Bengal, India.

The correct answer is 22 March.

Key Points

• World Water Day is an annual United Nations (UN) commemoration held on March 22 that emphasises the importance of clean water.
• The day is used to advocate for sustainable freshwater resource management.
• Each day's subject focuses on topics related to clean water, sanitation, and hygiene (WASH), which aligns with the Sustainable Development Goal 6 aims.
• World Water Day is organized by UN-Water, which chooses the theme each year in conjunction with UN institutions with a stake in the topic.
• The subject for 2021 was "Valuing Water," and the public campaign encouraged individuals to "give us their tales, opinions, and feelings about water" in a worldwide debate on social media.
• World Water Day is observed with a variety of activities all across the world.
• The day could also feature fundraising initiatives for water projects. In 1993, the United Nations declared the inaugural World Water Day.

The correct answer is 1998.

Key Points

• The Lotteries Regulation Act of 1998 is a significant piece of law that establishes detailed standards for the central government's handling of Indian lotteries.
• It also permits state governments to conduct and regulate lotteries under certain conditions.
• This legislation was passed on the 7th of July, 1998, and went into effect on the 2nd of October, 1998. The Lotteries (Regulation) Ordinance of 1998 is repealed.
• Furthermore, the phrase "bumper draw of the lottery" is defined in Section 2 (a) of the Act as a special lottery drawn on any festival or a special occasion where the offered prize money is greater than the prize money offered in a regular draw of lotteries.
• According to Section 2 (b) of the Lotteries Regulation Act, a lottery is "a programme in which prizes are distributed by choosing the fate of ticket purchasers by lot or chance."​

Important Points

• Lotteries have long been a popular kind of gambling around the world.
• They were typically sold during the medieval period to collect funds for the town's defences and to assist the area's poor.
• While many Indian gambling laws apply to all forms of gambling in India**, the Lotteries Regulation Act of 1998** is separate legislation that governs the Indian lottery system.
• The legislation was written with the intention of regulating the buying and selling of lotteries in the country and, as a result, bringing the entire lottery selling industry under the control of the government.

The correct answer is All observable characteristics.

Key Points

• Numerical taxonomy is a biological systematics classification system that deals with the numerical grouping of taxonomic units based on their character states.
• Its goal is to establish a taxonomy utilizing numerical algorithms such as cluster analysis rather than subjective property evaluation.
• Robert R. Sokal and Peter H. A. Sneath first proposed the idea in 1963, and the same authors later expanded on it.
• They divided the field into phenetics, which classifies organisms based on overall similarity patterns, and cladistics, which classifies organisms based on the branching patterns of the taxa's estimated evolutionary history.
• The relationships between organisms are mathematically established, usually with the help of a computer, and their characteristics are given equal weight.
• Thus, the numerical taxonomy of plants is based on all observable characteristics.

The correct answer is 2nd February.

Key Points

• World Wetlands Day is an environmental celebration that began in 1971 when a group of environmentalists gathered to reaffirm the protection and love for wetlands, which are small ecosystems of plant life and organisms found within water bodies that provide abundant ecological health to not only water bodies but entire environments.
• The World Wetlands Secretary Department is based in Gland, Switzerland, and according to the Ramsar Convention, the first acknowledgment of World Wetlands Day was given to "the Iranian city of Ramsar on the Caspian Sea's banks."
• Every year on the second of February, World Wetlands Day is commemorated, but it was not established until 1997.
• This day honours the good impact that wetlands have had on the world, as well as the importance of bringing people together for the benefit of Mother Nature.
• This day also increases global awareness about the importance of wetlands to people and the environment.
• On this day, community guardians and environmentalists join together to celebrate their love for nature via a festival that recognizes what wetlands have done for not only humans but all living things.

Important Points

• The Ramsar Convention on Internationally Significant Wetlands Waterfowl Habitat is an international treaty for the conservation and sustainable use of wetlands, which is particularly important.
• It's also known as the Wetlands Convention. It takes its name from the Iranian city of Ramsar, where the treaty was signed in 1971.
• Representatives of the contracting parties gather every three years at the Conference of the Contracting Parties (COP), the convention's policy-making organ, to adopt decisions (resolutions and recommendations) to administer the convention's activities and strengthen the parties' ability to achieve its goals.

The correct answer is ATK Mohun Bagan.

Key Points

• The former Spanish footballer, Antonio Lopez Habas, was the coach at the Hero ISL 2020-21 of ATK Mohun Bagan.
• He is a former defender and manager in the Spanish professional football league.
• On March 15, 2020, he signed with the newly created ATK Mohun Bagan.
• His team finished level with Mumbai City in the first stage of his debut season, but was pushed down to second place on head-to-head points and lost the final 2–1.
• He agreed to a one-year contract extension on April 3, 2021. After a string of bad outcomes, López resigned on December 18, 2021.

Important Points

• ATK Mohun Bagan FC is a West Bengal-based Indian professional football team.
• The club competes in the Indian Super League, one of the country's premier football leagues.
• ATK Mohun Bagan FC was founded as a result of a merger between the football section of multi-sport club Mohun Bagan AC and the ATK FC in the 2020–21 season.

Additional Information

• Football Club Goa is an Indian professional football club based in Goa, that competes in the Indian Super League, the top flight of Indian football. The club was established on 26 August 2014.
• Kerala Blasters Football Team, also known as The Blasters, is an Indian professional football club headquartered in Kochi, Kerala, that competes in the Indian Super League, the country's highest level of football.
• The East Bengal Club is a professional football club situated in Kolkata, West Bengal, India. The club was founded in 1920 and competes in the Indian Super Competition, India's top flight, as well as the Calcutta Premier Division A, Asia's oldest football league.

The correct answer is 26th January 1950.

Key Points

• The National Emblem of India was adopted on 26^th January 1950.
• It is a representational seal of the Republic of India, based on Ashoka Pillar's Lion Capital (based in Sarnath, Uttar Pradesh.)
• The Indian National Emblem's motto is 'Satyamev Jayate,' which means 'Truth Alone Triumphs.'
• The National Emblem is a symbol of power that appears in all official government communications.
• "A heraldic instrument or symbolic object as a unique insignia of a nation, organization, or family," according to the definition.
• A nation's National Emblem is a seal that is used for official purposes and commands the highest respect and allegiance.
• The National Emblem of India may only be used in accordance with the provisions of the State Emblem of India (Prohibition of Improper Use) Act-2005, and any unauthorized use is illegal.

Important Points

• The National Emblem can be displayed in the following public buildings:
• Rashtrapati Bhawan
• Parliament House
• Supreme Court
• Central Secretariat buildings
• Raj Bhawan or Raj Niwas
• State Legislature
• High Courts
• Secretariat buildings of the States or the Union territories
• Premises of India’s Diplomatic Mission abroad
• Heads of Missions' residences in the countries where they are accredited.
• At the front doors of buildings where India's consulates are located.

The correct answer is Abatement.

Key Points

• Abatement is reducing the degree or intensity of or eliminating, pollution.
• Restoration, reclamation, or recovery of natural resources are examples of abatement methods for reducing the degree or intensity of pollution.
• Only until the causes of pollution have been thoroughly identified can pollution abatement strategies be successfully implemented.
• Because it is intimately linked to urban planning, urban greenery and its role in pollution abatement is an interesting and emerging topic that demands joint work from specialists from other fields.

Important Points

• Aeration is the circulation of air through, mixing with, or dissolving in a liquid or other fluid-like substance.
• In air or another gas, an aerosol is a suspension of small solid particles or liquid droplets. Natural or anthropogenic aerosols can exist.
• Absorption is a physical or chemical phenomenon in which atoms, molecules, or ions enter a bulk phase, such as a liquid or solid material.

Shortcut Trick

Total weight of P and his 3 friends = 4 × 55 = 220 kg.

Let P's weight be P. The average of the 3 friends is (P − 4) kg.

Total weight = P + 3 × (P − 4) = 220

⇒ 4P − 12 = 220

⇒ 4P = 232 ⇒ P = 58 kg.

∴ The correct answer is 58 kg.

Alternate Method

Given:

Average weight of P and his 3 friends = 55 kg

P's weight is 4 kg more than the average weight of his 3 friends.

Formula Used:

Sum of values = Average × Number of values

Average of 4 persons = 55 kg

3 Friends Total Weight = 3x

Person P Weight = x + 4

Total Weight = 4 × 55 = 220 kg

Calculations:

⇒ Let the average weight of the 3 friends be x kg.

⇒ Total weight of the 3 friends = 3x kg

⇒ Weight of P = (x + 4) kg

⇒ Total weight of all 4 persons = 4 × 55 = 220 kg

⇒ 3x + (x + 4) = 220

⇒ 4x + 4 = 220

⇒ 4x = 216

⇒ x = 216 ÷ 4 = 54 kg

⇒ P's weight = x + 4 = 54 + 4 = 58 kg

∴ The correct answer is 58 kg.

Additional Information

Basic Average

Average = Sum of all observations ÷ Total number of observations.

Weighted Average

If two groups have sizes n₁ and n₂ with averages A₁ and A₂, Combined Average = (n₁ × A₁ + n₂ × A₂) ÷ (n₁ + n₂).

Net Deviation Method

The sum of deviations of all individual values from their average is always zero. This property helps in finding an unknown observation quickly.

Given:

A sold a mobile phone to B at a gain of 25%

B sold the mobile to C at a loss of 10%

Total money paid by C = Rs. 5625

Calculation:

Let, the A paid for the mobile phone = x

So, x × (125/100) × (90/100) = 5625

⇒ x = 5625 × (100/125) × (100/90)

⇒ x = 5000

∴ A paid Rs. 5000 (in Rs.) for the phone

Given:

The angle of elevation of the top of an unfinished tower at a point = 30°

The angle of elevation of the top of the finished tower at the point = 60°

The distance from the tower to the point = 78 m

Calculation:

Here, OC = Height of the unfinished tower

AC = The height will be the finished tower's height

In ΔOBC, tan 30° = OC/BC

⇒ 1/√3 = OC/78  [∵ tan 30° = 1/√3]

⇒ OC = 78/√3

⇒ OC = (78 × √3)/(√3 × √3) = 26√3   .....(1)

Let, the height of the tower will be raised (AO) = x

In ΔABC, tan 60° = AC/BC

⇒ √3 = (OC + x)/78  [∵ tan 60° = √3]

⇒ x + OC = 78√3

⇒ x + 26√3 = 78√3

⇒ x = 78√3 - 26√3 = 52√3

∴ The tower will be raised (in m) 52√3 meters

Given:

The speed of the motorboat in still water = 20 km/h

Concept used:

If the speed of a boat in still water is x km/h and the speed of the stream is y km/h, then

Downstream speed = (x + y) km/h

Upstream speed = (x - y) km/h

Time = Distance/Speed

Calculation:

According to the question, the motorboat takes 30 minutes more to go 24 km upstream than to cover the same distance downstream.

Let, the speed of the water = x km/h

So, 24/(20 - x) = 24/(20 + x) + (1/2)  [∵ 30 minutes = 1/2 hour]

⇒ 24/(20 - x) - 24/(20 + x) = (1/2)

⇒ $\frac{24(20+x)-24(20-x)}{400-x^2}=\frac{1}{2}$

⇒ $\frac{24(20+x-20+x)}{400-x^2}=\frac{1}{2}$

⇒ $\frac{24×2x}{400-x^2}=\frac{1}{2}$

⇒ 400 - x² = 96x

⇒ x² + 96x - 400 = 0

⇒ x2 + 100x - 4x - 400 = 0

⇒ x (x + 100) - 4 (x + 100) = 0

⇒ (x + 100) (x - 4) = 0

⇒ x + 100 = 0 ⇒ x = -100 ["-" is neglacted]

⇒ x - 4 = 0 ⇒ x = 4

∴ The speed of the water = 4 km/h

The speed of the motorboat in still water increased 2 km/h = 20 + 2 = 22 km/h

The time for 39 km downstream and 30 km upstream = 39/(22 + 4) + 30/(22 - 4) hours

= (39/26) + (30/18) hours

= 3/2 + 5/3 hours

= 19/6 hours

= (19/6) × 60 minutes

= 190 minutes

= 3 hours 10 minutes

∴ The motorboat will take 3 hours 10 minutes to go 39 km downstream and 30 km upstream

Shortcut TrickValue putting method, 

According to the question, 

30 min = 1/2 hr

x = 20 (Speed in still water)

⇒ 24/(20 - y) - 24/(20 + y) = 1/2

Here the R.H.S is 1/2, so the value of 20 - y must be more than 12

Hence take y = 4 (so that right bracket will become 1 as 20 + 4 = 24) and (left bracket will be more than half)

⇒ 24/(20 - 4) - 24(20 + 4) = 3/2 - 1 = 1/2

Hence the value of Y = 4

Now according to the question, 

⇒ 39/(22 + 4) + 30/(22 - 4) = 39/26 + 30/18

⇒ 19/6 = 3(1/6) = 3 hours and 10 min

∴ The motorboat will take 3 hours 10 minutes to go 39 km downstream and 30 km upstream

Given:

4sin2 θ = 3(1+ cos θ), 0° < θ < 90°

Calculation:

4 (1 - cos2 θ) = 3 + 3cos θ

⇒ 4 - 4cos2 θ = 3 + 3cos θ

⇒ 4cos2 θ + 3cos θ - 1 = 0

⇒ 4cos2 θ + 4cos θ - cos θ - 1 = 0

⇒ 4cos θ (cos θ + 1) - 1 (cos θ + 1) = 0

⇒ (4cos θ - 1) (cos θ + 1) = 0

⇒ cos θ + 1 = 0 ⇒ cos θ = - 1 [Not possible because 0° < θ < 90]

⇒ 4cos θ - 1 = 0 ⇒ cos θ = 1/4

We can get all value by using the image below,

The height will be = √(4² - 1²) = √(16 - 1) = √15

So, (2tan θ + 4sin θ - sec θ) = (2 × √15) + (4 × √15/4) - 4

= 2√15 + √15 - 4

= 3√15 - 4

∴ The value of (2tan θ + 4sin θ - sec θ) is 3√15 - 4

Shortcut Trick

Check the sum of digits for each option to verify divisibility by 3 and 9.

Sum of 239685 = 2 + 3 + 9 + 6 + 8 + 5 = 33 (Divisible by 3, but not by 9).

Sum of 237687 = 2 + 3 + 7 + 6 + 8 + 7 = 33 (Valid but smaller than 239685).

Sums of 238689 and 239688 are 36, which is divisible by 9 (Invalid).

∴ The correct answer is 239685.

Alternate Method

Given: A number in the form 23a68b that is divisible by 3 but not divisible by 9.

Formula Used: Sum of digits rule for divisibility.

Checking each option systematically:

⇒ For 238689: Sum = 2 + 3 + 8 + 6 + 8 + 9 = 36. Since 36 ÷ 9 = 4, it is divisible by 9. (Invalid)

⇒ For 239685: Sum = 2 + 3 + 9 + 6 + 8 + 5 = 33. Since 33 ÷ 3 = 11 and 33 is not divisible by 9. (Valid)

⇒ For 239688: Sum = 2 + 3 + 9 + 6 + 8 + 8 = 36. Since 36 ÷ 9 = 4, it is divisible by 9. (Invalid)

⇒ For 237687: Sum = 2 + 3 + 7 + 6 + 8 + 7 = 33. Since 33 ÷ 3 = 11 and 33 is not divisible by 9. (Valid)

⇒ Comparing valid options 239685 and 237687, we find that 239685 is the greatest.

∴ The correct answer is 239685.

Additional Information

Divisibility by 3

A number is divisible by 3 if the sum of its digits is a multiple of 3.

Divisibility by 9

A number is divisible by 9 if the sum of its digits is a multiple of 9. Note that all numbers divisible by 9 are also divisible by 3.

Relationship between 3 and 9

To be divisible by 3 but NOT by 9, the sum of the digits must be in the set {3, 6, 12, 15, 21, 24, 30, 33, 39, ...} excluding multiples of 9.

Given:

20% of the boys and 15% of the girls failed the exam.

Total number of students who failed = 90

Calculation:

The percentage of boys who passed = (100 - 20)% = 80%

The percentage of girls who passed = (100 - 15)% = 85%

Let, the number of appeared boys = x

The number of appeared girls = y

So, 80x/100 - 85y/100 = 70

⇒ 5 (16x - 17y) = 7000

⇒ 16x - 17y = 1400   .....(1)

Also, 20x/100 + 15y/100 = 90

⇒ 5 (4x + 3y) = 9000

⇒ 4x + 3y = 1800   .....(2)

Multiplying 4 to equation (2),

16x + 12y = 7200   .....(3)

Subtracting equation (2) from equation (3),

16x + 12y - 16x + 17y = 7200 - 1400

⇒ 29y = 5800

⇒ y = 5800/29 = 200

∴ The number of girls appeared = 200

Putting y = 200 in equation (2),

4x + 3 × 200 = 1800

⇒ 4x = 1800 - 600 = 1200

⇒ x = 1200/4 = 300

∴ The number of boys who appeared = 300

The total number of students who appeared = 300 + 200 = 500

∴ The number of students that appeared for the exam is 500

Alternate Method Calculation:-

Let the Number of boys and Girls who appeared in exam be x and y respectively,

So, according to question-

Number of boys passed in exam = [(100 - 20) × x]/100 = 0.80x

Number of girls passed in exam = [(100 - 15) × y]/100 = 0.85y

Condition (1) -  

⇒ 0.80x = 0.85y + 70

⇒ 0.80x - 0.85y = 70    ...(i)

Condition (2) -

Total failed students = 90

⇒ 0.20x + 0.15y = 90    ...(ii)

From eqⁿ (1) - [4 × eqⁿ (ii)]

⇒ (-0.85y) - 0.60y = 70 - 360 

⇒ 1.45y = 290

⇒ y = 200

Put this value in eqⁿ (i)

⇒ 0.80x = 0.85 × 200 + 70

⇒ 0.80x = 170 + 70 = 240

⇒ x = 300

So, total number of students appeared in exam = 300 + 200 = 500.

Given:

(x + 6y) = 8

xy = 2

Formula used:

(a + b)³ = a³ + b³ + 3ab (a + b)

Calculation:

xy = 2

⇒ y = 2/x   .....(1)

Also, (x + 6y) = 8

⇒ x + (6 × 2/x) = 8

⇒ x + 12/x = 8   .....(2)

⇒ (x + 12/x)³ = 8³  [Taking cube of both sides]

⇒ x³ + (12/x)³ + 3 × x × (12/x) (x + 12/x) = 512

⇒ x3 + (12/x)3 + 3 × 12 × 8 = 512  [∵ We get from equation (2), x + 12/x = 8]

⇒ x3 + (12/x)3 + 288 = 512

⇒ x3 + (12/x)3 = 512 - 288

⇒ x3 + [(2 × 6)/x]³ = 224

⇒ x3 + (6y)³ = 224  [∵ y = 2/x]

⇒ x3 + 216y³ = 224

∴ The value of x3 + 216y3 is 224

Alternate MethodUsing Formula - (a + b)3 = a3 + b3 + 3ab (a + b)

(x + 6y)³ = x³ + 216y³ + 3 × x × 6y(x + 6y)

Put  (x + 6y) = 8, xy = 2

⇒ 8³ = x3 + 216y3 + 3 × 6 × 2 × 8

⇒ x3 + 216y3 = 512 - 288

⇒ x3 + 216y3 = 224

∴ The value of x3 + 216y3 is 224.

Shortcut Trick

∠BAC = 75º

∠ABC + ∠ACB + ∠BAC = 180°

∠ABC + ∠ACB + 75° = 180°

∠ABC + ∠ACB = 180° - 75° = 105°

Let, ∠ABC = ∠PBQ = 70° and ∠ACB = ∠RCQ = 35°

So, ∠PQR = 180° - (∠PQB + ∠RQC)

= 180° - [(180° - 2∠PBQ) + (180° - 2∠RCQ)  [∵ BQ = PQ; QC = QR]

= 180° - [(180° - 2 × 70°) + (180° - 2 × 35°)]

= 180° - (40° + 110°)

= 180° - 150°

= 30°

Alternate Method

Given:

In a ΔABC, ∠BAC = 75º

BQ = PQ and QC = QR

Concept used:

The sum of all three angles of a triangle = 180°

The sum of all angles on a straight line = 180°

Calculation:

Let, ∠ABC = x and ∠ACB = y

So, ∠ABC = ∠PBQ = ∠QPB = x  [∵ BQ = PQ]

∠ACB = ∠RCQ = ∠QRC = y  [QC = QR]

In ΔABC, ∠ABC + ∠ACB + ∠BAC = 180°

⇒ x + y + 75° = 180°

⇒ x + y = 180° - 75° = 105°   .....(1)

For ΔBPQ and ΔCRQ,

(∠PBQ + ∠QPB + ∠PQB) + (∠RCQ + ∠QRC + ∠RQC) = 180° + 180° = 360°

⇒ (x + x + ∠PQB) + (y + y + ∠RQC) = 360°

⇒ 2x + 2y + ∠PQB + ∠RQC = 360°

⇒ 2 (x + y) + ∠PQB + ∠RQC = 360°

⇒ (2 × 105°) + ∠PQB + ∠RQC = 360°  [∵ x + y = 105°]

⇒ ∠PQB + ∠RQC = 360° - 210° = 150°   .....(2)

Also, ∠PQB + ∠RQC + ∠PQR = 180°

⇒ 150° + ∠PQR = 180°  [∵ ∠PQB + ∠RQC = 150°]

⇒ ∠PQR = 180° - 150° = 30°

∴ The measure of ∠PQR (in degrees) is 30°

Shortcut Trick

Total work = 48 (LCM of 16 and 12)

Efficiency = Work/Time

Total efficiency = 3 + 4 = 7 units

Remaining work after 4 days = 48 - (7 × 4) = 48 - 28 = 20 units

Time is taken by B to finish the remaining work = 20/4 = 5 days

Total number of days B work = 4 + 5 = 9 days

∴ B work the total number 9 days to finish the work completely.

Alternate Method

Given:

A can finish a piece of the work in 16 days

B can finish the same work in 12 days

Calculation:

A can finish in 1 day = 1/16 work

A can finish in 4 days = 4/16 = 1/4 work

B can finish in 1 day = 1/12 work

B can finish in 4 days = 4/12 = 1/3 work

The remaining work = 1 - [(1/4) + (1/3)]

= 1 - (7/12)

= 5/12

Time taken by B to finish the work = (5/12) ÷ (1/12) = (5/12) × 12 = 5 days

Total number of days B work = 4 + 5 = 9 days

∴ B work the total number 9 days to finish the work completely.

Given:

The given expression = $\frac{{\sin 23^\circ \cos 67^\circ + \sec52^\circ \sin38^\circ + \cos 23^\circ \sin 67^\circ + \rm cosec52^\circ \cos 38^\circ }}{{\rm cose{c^2}20^\circ - {{\tan }^2}70^\circ }}$

Formula used:

cos 67° = sin (90° - 67°) = sin 23°

sin 67° = cos (90° - 67°) = cos 23°

sin² θ + cos² θ = 1

sec² θ - tan² θ = 1

Calculation:

$\frac{{\sin 23^\circ \cos 67^\circ + \sec52^\circ \sin38^\circ + \cos 23^\circ \sin 67^\circ + \rm cosec52^\circ \cos 38^\circ }}{{\rm cose{c^2}20^\circ - {{\tan }^2}70^\circ }}$

= $\frac{{\sin 23^\circ \sin 23^\circ +\frac{1}{cos,52^\circ} \sin38^\circ + cos 23^\circ cos 23^\circ + \frac{1}{sin,52^\circ} \cos 38^\circ }}{sec^2,70^\circ-tan^2,70^\circ}$

= $\frac{sin^2,23^\circ+\frac{sin,38^\circ}{sin,38^\circ}+cos^2,23^\circ+\frac{cos,38^\circ}{cos,38^\circ}}{1}$

= sin2 23° + 1 + cos2 23° + 1

= 1 + 1 + 1

= 3

∴ The value of the given expression is 3

Shortcut Trick

Given LCM = 56 × HCF and LCM + HCF = 1710.

Total parts = 56 + 1 = 57 parts = 1710 ⇒ 1 part (HCF) = 30.

LCM = 56 × 30 = 1680.

Using the property: First Number × Second Number = HCF × LCM

Other number = (30 × 1680) ÷ 240 = 210.

∴ The correct answer is 210.

Alternate Method

Given:

LCM = 56 × HCF

LCM + HCF = 1710

One number (N₁) = 240

Formula Used:

LCM × HCF = N₁ × N₂

Number 1 × Number 2 240 × ?

HCF × LCM 30 × 1680

Calculations:

⇒ Let HCF = H

⇒ LCM = 56H

⇒ 56H + H = 1710

⇒ 57H = 1710

⇒ H = 1710 ÷ 57 = 30

⇒ HCF = 30

⇒ LCM = 56 × 30 = 1680

⇒ N₁ × N₂ = HCF × LCM

⇒ 240 × N₂ = 30 × 1680

⇒ N₂ = (30 × 1680) ÷ 240

⇒ N₂ = 30 × 7

⇒ N₂ = 210

∴ The correct answer is 210.

Additional Information

Product of Two Numbers

For any two positive integers a and b, the product of the numbers is equal to the product of their HCF and LCM: a × b = HCF × LCM.

Co-prime Factors

If two numbers are expressed as H × x and H × y (where H is the HCF), then x and y are always co-prime to each other. Their LCM is formed by H × x × y.

LCM Divisibility

The LCM of a given set of numbers is always perfectly divisible by their HCF. Dividing the LCM by the HCF will always leave a remainder of 0.

Given:

The total exports of cars of type A and B (in Rs. millions) from 2014 to 2018 are shown in the bar graph.

Calculation:

Total exports of cars of type A in 2014 and 2017 = 200 + 175 = 375

The total exports of cars of type B in 2015 and 2016 = 250 + 200 = 450

The ratio = 375 : 450 = 5 : 6

∴ The ratio of the total exports of cars of type A in 2014 and 2017 to the total exports of cars of type B in 2015 and 2016 is 5 : 6

Shortcut Trick

Effective rate of Compound Interest for 2 years at 10% = 10 + 10 + (10 × 10)/100 = 21%

Effective rate for 4 years (combining 21% and 21%) = 21 + 21 + (21 × 21)/100 = 46.41%

Difference in interest rates = 46.41% − 21% = 25.41%

As per the question: 25.41% of Sum = ₹5,082

Sum = (5082 ÷ 25.41) × 100 = ₹20,000

∴ The correct answer is ₹20,000.

Alternate Method

Given:

Rate of Interest (R) = 10% per annum

Time (T₁) = 2 years, Time (T₂) = 4 years

Difference in Interest = ₹5,082

Formula Used:

Compound Interest (CI) = P[(1 + R/100)^T − 1]

Calculations:

⇒ CI₂ = P[(1 + 10/100)² − 1] = P[(1.1)² − 1] = P[1.21 − 1] = 0.21P

⇒ CI₄ = P[(1 + 10/100)⁴ − 1] = P[(1.1)⁴ − 1] = P[1.4641 − 1] = 0.4641P

⇒ Difference = CI₄ − CI₂ = 0.4641P − 0.21P = 0.2541P

⇒ 0.2541P = 5082

⇒ P = 5082 ÷ 0.2541

⇒ P = (5082 × 10000) ÷ 2541

⇒ P = 2 × 10000 = 20000

∴ The correct answer is ₹20,000.

Additional Information

Effective Rate for Compound Interest

For a rate R% for 2 years, the effective rate is calculated using the successive percentage formula: R + R + (R × R)/100.

CI vs SI for 2 Years

The difference between CI and SI for 2 years is given by the formula: Difference = P(R/100)².

Amount in Compound Interest

The total amount A after T years is A = P(1 + R/100)^T, where P is the Principal sum.

Given:

An equilateral triangle ABC is inscribed in a circle with centre O

∠CBD = 40º

Concept used:

The sum of the opposite angles of a cyclic quadrilateral = 180°

The sum of all three angles of a triangle = 180°

Calculation:

∠ABC = ∠ACB = ∠BAC = 60°  [∵ ΔABC is an equilateral triangle]

Also, ∠BAC + ∠BDC = 180°

⇒ 60° + ∠BDC = 180°

⇒ ∠BDC = 180° - 60° = 120°

Also, ∠CBD + ∠BDC + ∠BCD = 180°

⇒ 40° + 120° + ∠BCD = 180°

⇒ ∠BCD = 180° - 40° - 120° = 20°

∴ The value of ∠BCD is 20°

Given:

The lengths of the three sides of a right-angled triangle are (x - 1) cm, (x + 1) cm and (x + 3) cm

Formula used:

In a right-angled triangle,

Hypotenuse² = Perpendicular² + Base²

Calculation:

Here, (x + 3) is greater than other sides for each value of x

We can take (x + 3) as the hypotenuse

So, (x + 3)² = (x + 1)² + (x - 1)²

⇒ x² + 6x + 9 = 2 (x² + 1)  [By using (a + b)2 + (a - b)2 = 2 (a² + b²) formula]

⇒ x² + 6x + 9 = 2x2 + 2

⇒ 2x2 - x2 - 6x + 2 - 9 = 0

⇒ x2 - 6x - 7 = 0

⇒ x2 - 7x + x - 7 = 0

⇒ x (x - 7) + 1 (x - 7) = 0

⇒ (x + 1) (x - 7) = 0

⇒ x + 1 = 0 ⇒ x = - 1 ["-" will be neglacted]

⇒ x - 7 = 0 ⇒ x = 7

Then, the value of (x + 3) = (7 + 3) cm = 10 cm

∴ The hypotenuse of the right-angled triangle (in cm) is 10 cm

Given:

The total number of students = 350

Calculation:

The total number of students who scored 140 marks and above = 55 + 40 + 15 = 110

The total number of students who scored marks between 60 to 120 = 32 + 45 + 60 = 137

The ratio = 110 : 137

∴ The ratio of the total number of students who scored 140 marks and above to the total number of students who scored marks between 60 to 120 is 110 : 137

Shortcut Trick

Income ratio of A and B = 11 : 13

Expenditure ratio of A and B = 9 : 11

Since the difference between the ratio parts for both A and B is equal (11 − 9 = 2 and 13 − 11 = 2), these 2 units represent the savings directly.

2 units = ₹4,000

Difference in their incomes = 13 units − 11 units = 2 units

∴ The correct answer is ₹4,000.

Alternate Method

Given:

Income ratio of A and B = 11 : 13

Expenditure ratio of A and B = 9 : 11

Savings of both A and B = ₹4,000 each

Income A = 11 units

Income B = 13 units

Exp. A = 9 units

Exp. B = 11 units

-2 units = ₹4000

-2 units = ₹4000

Formula Used:

Income − Expenditure = Savings

Calculations:

Let the incomes of A and B be 11x and 13x respectively.

Let their expenditures be 9y and 11y respectively.

⇒ 11x − 9y = 4000 .... (i)

⇒ 13x − 11y = 4000 .... (ii)

Since both equal ₹4,000, we can equate equations (i) and (ii):

⇒ 11x − 9y = 13x − 11y

⇒ 11y − 9y = 13x − 11x

⇒ 2y = 2x

⇒ x = y

Substitute x = y in equation (i):

⇒ 11x − 9x = 4000

⇒ 2x = 4000

⇒ x = 2000

Now, to find the difference in their incomes:

⇒ Difference = 13x − 11x = 2x

⇒ Difference = 2 × 2000 = 4000

∴ The correct answer is ₹4,000.

Additional Information

Income, Expenditure & Savings Relation

The foundational rule for all such problems is: Income = Expenditure + Savings. Any two known variables can be used to find the third.

Ratio Balancing Method

When the difference in ratio parts is not inherently equal across quantities, we balance the ratio gaps by multiplying the first ratio by the difference of the second ratio's terms, and vice versa.

Cross-Multiplication Trick

If an initial ratio a:b changes by quantities x and y to become c:d, then the value of 1 ratio unit can be evaluated instantly using |ad − bc| = |dx − cy|.

Given:

Each side of the cube = 8 cm

The rectangular container has a length of 16 cm, breadth of 8 cm, and height of 15 cm

Formula used:

The volume of cube = (Edge)3

The volume of a cuboid = Length × Breadth × Height

Calculation:

The volume of cube = The volume of the rectangular container with a length of 16 cm, breadth of 8 cm, and height of the water level rise

Let, the height of the water level will rise = x cm

So, 8³ = 16 × 8 × x

⇒ 512 = 128 × x

⇒ x = 512/128 = 4

∴ The rise of water level (in cm) is 4 cm

Given:

There are the number of cars passing the road near a colony from 6 am to 12 noon has been shown in the following histogram.

Calculation:

The number of cars passed between 6 am and 8 am = 70 + 105 = 175

The number of cars passed between 9 am and 11 am = 115 + 95 = 210

The ratio = 175 : 210 = 5 : 6

∴ The ratio of the number of cars passed between 6 am and 8 am to the number of cars passed between 9 am and 11 am is 5 : 6

Given:

The cost price of an item = Rs. 400

The selling price of the item = Rs. 216

Sale discount = x%

Coupon discount = 10%

Formula used:

The successive discount of a% and b% = (a + b - ab/100)%

Discount% = (Discount/M.P.) × 100

Where, M.P. = Marked price

Calculation:

Here, Marked price = The cost price of an item = Rs. 400

(Because discount is given on this price.)

The discount = 400 - 216 = Rs. 184

The total discount = (184/400) × 100 = 46%

So, x + 10 - (10x/100) = 46

⇒ x + 10 - x/10 = 46

⇒ 9x/10 + 10 = 46

⇒ 9x/10 = 46 - 10

⇒ 9x/10 = 36

⇒ x = 36 × (10/9) = 40

∴ The value of x is 40

Given:

x + y + 3 = 0

Formula used:

(a + b)3 = a3 + b3 + 3ab (a + b)

Calculation:

x + y + 3 = 0

⇒ x + y = - 3   .....(1)

⇒ (x + y)³ = (- 3)³  [Taking cube of both sides]

⇒ x3 + y3 + 3xy (x + y) = - 27

⇒ x3 + y3 + 3xy × (- 3) = - 27  [∵ x + y = - 3]

⇒ x3 + y3 - 9xy = - 27

⇒ x3 + y3 - 9xy + 9 = - 27 + 9  [Adding 9 in both sides]

⇒ x3 + y3 - 9xy + 9 = - 18

∴ The value of x3 + y3 - 9xy + 9 is (- 18)

Given:

AB is a diameter of a circle with a center O

∠APC = 62º

Concept used:

The radius/diameter of a circle is always perpendicular to the tangent line.

Sum of all three angles of a triangle = 180°

Calculation:

 

Minor arc AC will create angle CBA

∠APC = 62º = ∠APB

∠BAP = 90° (diameter perpendicular to tangent)

In Δ APB,

∠APB + ∠BAP + ∠PBA = 180° 

⇒ ∠PBA = 180° - (90° + 62°)

⇒ ∠PBA = 28° 

∴ The measure of minor arc AC is 28° 

Mistake PointsMeasure of the minor arc AC is asked,

∠ABC marks arc AC, 

∴ ∠ABC is the correct angle to show a measure of arc AC

This is a previous year's question, and according to the commission, this is the correct answer.

Given:

There is the monthly expenditure of a family on different heads is shown in the following pie chart.

Calculation:

The total angle of all expenditures = 75° + 60° + 70° + 65° + 50° + 40° = 360°

The total angle of the amount spent on Children Education, Transport and Rent = 70° + 50° + 60° = 180°

The percentage = (180/360) × 100 = 50%

∴ The amount spent on Children Education, Transport and Rent is 50% of the total earnings.

Given:

The given expression = 372 ÷ 56 × 7 - 5 + 2

Calculation:

372 ÷ 56 × 7 - 5 + 2

= (93/14) × 7 - 5 + 2

= (93/2) - 5 + 2

= (93/2) - 3

= 87/2

= 43$\frac{1}{2}$

∴ The value of the given expression is 43$\frac{1}{2}$

The correct answer is 'Have very little money'.

Key Points

• The most appropriate meaning of the given idiom 'Be hard up' is 'Have very little money'.
• Be hard up: having very little money. (बहुत कम पैसा होना)
• Example: We're a bit hard up at the moment so we're not thinking about holidays.
  

Correct Answer: Have very little money.

The erroneous part is 'the very well-directed film'.

Key Points

• The given sentence is grammatically incorrect.
• Here, 'a very well-directed film' should be used instead of 'the very well-directed film'.
• The rule for the usage of "an" or "a" is, that if the word following has a vowel sound, "an" is used (e.g. An honor, A house).
• If there's a consonant sound, "a" is used.
• There are many examples of this in relation to "very".
• Example: That was a very nice house!
• Thus, the correct answer is Option 3.
  

Correct Sentence: It was a very well-directed film and we enjoyed it.

The correct answer is 'want to'.

Key Points

• The given sentence is grammatically incorrect.
• Here, 'wants to' should be used instead of 'want to'.
• We know that after 'each, every, everyone, someone, nobody, one' a singular verb, singular noun, singular adjective, and a singular pronoun is used.
• Example: Each student has come.
• Thus, the correct answer is Option 2.
  

Correct Sentence: Every curious child wants to rip open a toy.

The correct answer is 'Prevent'.

Key Points

• The most appropriate synonym of the given word 'Avert' is 'Prevent'.
• Avert: to prevent something unpleasant. (अप्रिय घटना को घटने से रोक लेना; अप्रिय स्थिति का निवारण करना, टालना)
• Example: The accident could have been averted.
• Synonyms: forestall, head off, help, obviate, preclude, prevent, stave off
• Near Antonyms: nurture, promote, allow, leave, let, permit
• Prevent: to stop something from happening or to stop somebody from doing something. (किसी बात को होने न देना या किसी को कोई काम करने से रोक देना)
• Example: This accident could have been prevented.
• Synonyms: avert, forestall, head off, help, obviate, preclude, stave off
• Antonyms: advance, cultivate, encourage, forward, foster, further
  

Correct Answer: Prevent.

Additional Information

• Let's look at the meaning of other words:
• Face: the front part of your head; the expression that is shown on it. (चेहरा; चेहरे का भाव)
• Confront: come face to face with (someone) with hostile or argumentative intent. (किसी मुसीबत का या अप्रिय स्थिति का सामना करना या सामना करवाना; के आमने-सामने होना, मुक़ाबला करना)
• Permit: to allow somebody to do something or to allow something to happen. (किसी बात की अनुमति देना या कोई बात होने देना)

The correct answer is He said to me, “When did you book the flight tickets?”

Key Points

• The given sentence is in Indirect Speech. As per the question we have to change it into Direct Speech.
• The process of transformation is as follows:
• 'Asked' will be changed into 'said to' because the given question is an example of an interrogative sentence with a question word.
• Commas and inverted commas will be added.
• 'had booked' will be changed into 'did book'.
• 'I' will be changed into 'you' because we know that in 'direct to indirect' transformation second-person pronouns are changed according to the object of the reporting verb.
• Thus, the correct answer is Option 1.
  

​Correct Sentence: He said to me, “When did you book the flight tickets?”

The correct answer is 'have assured'.

Key Points

• The given sentence is grammatically incorrect.
• Here, 'have assured' should be used instead of 'are assured'.
• The given sentence is in the active voice hence the use of 'are assured' is completely out of context
• The present perfect tense is used to discuss something that happened at a non-specific time before now.
• It may have been moments ago, already, several times, or so far.
• This verb form is made with has/have + past participle. 
• Example: The teacher has helped the class understand geometry.
• Thus, the correct answer is Option 4.
  

Correct Sentence: The authorities have assured the people that they will look into the matter.

The erroneous part is 'this year it reflect badly'.

Key Points

• The given sentence is grammatically incorrect.
• Here, 'this year it will reflect badly' should be used instead of 'this year it reflect badly'.
• The given sentence is an example of a conditional sentence.
• The type 1 conditional is used to refer to the present or future where the situation is real.
• Type 1 conditional refers to a possible condition and its probable result.
• Let's look at the structure of these kinds of sentences: If + simple present, simple future
• Example: If you don't hurry, you will miss the train.
• Thus, the correct answer is Option 3.
  

Correct Sentence: If the economy fails this year it will reflect badly on the government.

The erroneous part is 'No one were'.

Key Points

• The given sentence is grammatically incorrect.
• Here, 'No one was' should be used instead of 'No one were'.
• ">The indefinite pronouns  ">anyone, everyone, someone, no one, nobody "> are always singular and, therefore, require singular verbs.
• ">​E.X.- No one is interested in the game.
• Thus, the correct answer is Option 2.

​Note- We use no one, nobody, nothing and nowhere to refer to an absence of people, things or places. We use them with a singular verb

Correct Sentence: No one was present when I entered the hall.

The correct answer is 'Seismology'.

Key Points

• The most appropriate word for the given group of words is 'Seismology'.
• It means 'the scientific study of movements in the earth’s surface(earthquakes)'. [भूकंप-विज्ञान]
• Example: Large scale global seismology has helped to identify areas at risk from earthquakes and tsunami.
  

Correct Answer: Seismology.

Additional Information

• Let's look at the meaning of other words:
• Geography: the study of the world’s surface, physical qualities, climate, population, products, etc. [विश्‍व भूगोल की सतह, भौतिक लक्षण, मौसम, जनसंख्‍या आदि का अध्‍ययन]
• Topography: the physical characteristics of an area of land, especially the position of its rivers, mountains, etc. [किसी क्षेत्र की प्राकृतिक विशेषताएँ (विशेषतः नदियों, पर्वतों आदि की स्थिति); स्‍थलाकृति]
• Geology: is the scientific study of the Earth, its structure, composition, and the processes that shape it over time. the study of rocks, and of the way they are formed. (चट्टानों और उनके निर्माण-प्रकार का अध्‍ययन; भूविज्ञान)

The correct answer is 'achieving'.

Key Points

• The most appropriate word for the given blank is 'achieving'.
• In the given sentence 'towards' is a preposition.
• If we want to follow a preposition by a verb, we must use the "-ing" form which is really a gerund or verb in noun form.
• Example: I will call you after arriving at the office.
• Thus, the correct answer is Option 4.
  

Correct Sentence: The increasing concerns about climate change point to the need for enhanced efforts towards achieving sustained growth.