Given equation -

18 * 12 * 4 * 5 * 6 * 53

From option 1 -

×, ÷, =, +, −

18 × 12 ÷ 4 = 5 + 6 − 53

Applying BODMAS rule -

18 × 3 = 5 + 6 − 53

54 = 5 + 6 − 53

54 = 11 − 53

54 = − 42 It is not balanced equation.

From option 2 -

×, ÷, +, −, =

18 × 12 ÷ 4 + 5 − 6 = 53

Applying BODMAS rule -

18 × 3 + 5 − 6 = 53

54 + 5 − 6 = 53

59 − 6 = 53

53 = 53 It is balanced equation.

From option 3 -

×, ÷, −, +, =

18 × 12 ÷ 4 − 5 + 6 = 53

Applying BODMAS rule -

18 × 3 − 5 + 6 = 53

54 − 5 + 6 = 53

60 − 5 = 53

55 = 53 It is not balanced equation.

From option 4 -

×, ÷, +, =, −

18 × 12 ÷ 4 + 5 = 6 − 53

Applying BODMAS rule -

18 × 3 + 5 = 6 − 53

54 + 5 = 6 − 53

59 = 6 − 53

59 = − 47 It is not balanced equation.

Hence, "option 2" is the correct answer.

The logic followed here is:

From option 1-

From option 2-

From option 3 -

From option 4 -

From the above option 2 is different from others.

Hence, "option 2" is the correct answer.

The least possible Venn diagram is :

Conclusions:

I. Some bats are lions. → Ture (From the statement all camels are bats and some camels are lions. So due to this some bats are lions.) 

II. No parrot is a camel. → Ture (From the statement all camels are bats and no bat is a parrot. So due to this no parrot is a camel.)

III. No parrot is a lion. → False (From the above diagram there is no direct relation between parrot and lion with the definite condition.)

Hence, "option 3" is the correct answer.

The paper when unfolded appear as shown below-

Hence, "option 2" is the correct answer.

The logic followed here is:

From option 1 -

Stationary, Pencil, Stapler

From option 2 -

Girls, Intelligent, Boys

It follows the given figure because some boys are Intelligent and some girls are intelligent but no relation between boys and girls.

From option 3 -

Vegetarian, Woman, Sisters

From option 4 -

Yamuna, Rivers, Kaveri

Hence, "option 2" is the correct answer.

The logic followed here is:

Sympathy is the synonyms of Affinity.

Similarly,

Tranquil is the synonyms of Serene.

And Vivid is the antonyms of Dark, Tame is the antonyms of Harsh and Vain is the antonyms of Modest.

Hence, "option 1" is the correct answer.

The logic followed here is:

Hence, "497" is the correct answer.

The correct mirror image of the given combination when the mirror is placed at 'PQ' as shown below -

Hence, "option 3" is the correct answer.

For this question, the relation is given below -

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.

While moving in the clockwise direction from the common face $:

From both dices:

Hence, "#" is the correct answer$.

Let the father's present age be X years.

Father's age 15 years ago = (X - 15) years

Gautam's present age = 20% of (X - 15) = {\{(X - 15)} \over 5} years

Gaurav's present age = 60% of (X - 10) = {\{3(X - 10)} \over 5} years

{\{(X - 15)} \over 5} + {\{3(X - 10)} \over 5} = 31

X - 15 + 3X - 30 = 155

 4X - 45 = 155

4X = 200

X = 50 years

Fatehr's present age is 50 years.

Hence, "option 2" is the correct answer.

Given: 'PAYMENT' is coded as '6101814111520' and 'JUSTIFY' is coded as '11141519151620'. 

The logic followed here is:

1) Given letters in a word are arranged in alphabetical order i.e. A to Z.

2) then first 3 letters and last 3 letters are increased or decreased by +5, & -5 successively, and then we get number code.

3) Middle letter is the same.

PAYMENT is written as 6101814111520. 

1. PAYMENT → Alphabetical order → AEMNPTY.

2. 1^st 3 letter and last 3 letter +5, -5 successively so on.

3. Middle letter is the same.

And,

JUSTIFY' is coded as '11141519151620.

1) JUSTIFY → Alphabetical order → FIJSTUY.

2. 1^st 3 letter and last 3 letter +5, -5 successively so on.

3. Middle letter is the same.

Similarly, 

COMPARE = ?

1) COMPARE → Alphabetical order → ACEMOPR.

2) 1^st 3 letter and last 3 letter +5, -5 successively so on.

3) Middle letter is the same.

Hence, "681013101113" is the correct answer.

The logic followed here is:

The second number = 1^st number × 2 + 3 

The third number = 2^nd number × 6 - 2

(9, 21, 124)

9 × 2 + 3 = 18 + 3 = 21

21 × 6 - 2 = 126 - 2 = 124

Similarly, from option 1-

(5, 16, 220)

5 × 2 + 3 = 10 + 3 = 13 ≠ 16

16 × 6 - 2 = 96 - 2 = 94 ≠ 220, It is not follow.

From option 2-

(14, 58, 112)

14 × 2 + 3 = 28 + 3 = 31 ≠ 58

58 × 6 - 2 = 348 - 2 = 346 ≠ 112, It is not follow.

From option 3-

(17, 37, 220)

17 × 2 + 3 = 34 + 3 = 37

37 × 6 - 2 = 222 - 2 = 220, It is follow.

From option 4-

(11, 64, 131)

11 × 2 + 3 = 22 + 3 = 25 ≠ 64

64 × 6 - 2 = 384 - 2 = 382 ≠ 131, It is not follow.

Hence, "option 3" is the correct answer.

Alternate MethodThe logic followed here is:

(9, 21, 124)

= (9 + 21) × 4 + 4

= 30 × 4 + 4

= 120 + 4 = 124

Similarly,

From option 3-

(17, 37, 220)

= (17 + 37) × 4 + 4

= 54 × 4 + 4

= 216 = 4 = 220

Hence, "option 3" is the correct answer.

The logic followed here is:

Dermatologist is a doctor who studies and treats skin diseases.

So Dermatologist is related to Skin.

Similarly,

Neonatologist is a doctor who diagnose and treat newborns baby or Infants.

So Neonatologist is related to Infants.

Hence, "option 2" is the correct answer.

Key Points

• Neonatology is a subspecialty of pediatrics that consists of the medical care of newborn infants, especially the ill or premature newborns.
• It is a hospital-based specialty and is usually practiced in neonatal intensive care units.
• A neonatal intensive care unit (NICU), also known as an intensive care nursery (ICN), is an intensive care unit (ICU) specializing in the care of ill or premature newborn infants.
• Neonatal refers to the first 28 days of life.
• Neonatal care, as known as specialized nurseries or intensive care, has been around since the 1960s.
• The first American newborn intensive care unit, designed by Louis Gluck, was opened in October 1960 at Yale-New Haven Hospital.​

Additional Information 

The pattern followed is,

From option 1- pqmdh / pqmdq / phmdh / pqmdh -- No pattern or series can be formed.

From option 2- pqddh / hqmdm / pmmph / pqqdh -- No pattern or series can be formed.

From option 3- pqddh / mqmdm / ppmph / hqqdh -- No pattern or series can be formed.

From option 4- pqmdh / pqmdh / pqmdh / pqmdh -- Pattern or series can be formed.

(Repetition of pqmdh)

Hence, "option 4" is the correct answer.

Statement - Pointing to a player in a stadium, Sanjana said, "He is my paternal grandmother's only son's only son-in-law's son".

Here, my (Sanjana) paternal grandmother's only son's only son-in-law's means Sanjana will be the only daughter of Her father.

The final arrangement will be-

The Player's father is the husband of Sanjana.

Hence, "option 3" is the correct answer.

The logic followed here is:

We take the opposite letters of the alphabetical series.

Similarly,

Hence, "option 2" is the correct answer.

The logic followed here is:

Microphone, Keyboard and Joy stick are the input device and Projector is output device.

From option 1-

The microphone is a piece of electrical equipment that is used for making sounds louder or for recording them, which is an input device.

From option 2-

The keyboard is the set of keys on a piano, computer, etc., which is also an input device. 

From option 3-

The projector is a piece of equipment that projects pictures or films onto a screen or wall, which is an output device.

From option 4-

The joystick is a handle used for controlling movement on a computer, aircraft, etc., which is also an input device.

From the above option 3 is different from others.

Hence, "option 3" is the correct answer.

As per the dictionary, the given words can be arranged as:

5. Ecliptic
6. Ecology
7. Electric
8. Enormous
9. Exterior

The correct sequence is 5, 1, 3, 2, 4.

Hence, "option 4" is the correct answer.

The logic followed here is:

In a row:

1^st number × 5 - 3^rd number × 2 = second number.

For Row 1: 3, 11, 2

= 3 × 5 - 2 × 2

= 15 - 4 = 11

For row 2: 5, 11, 7

= 5 × 5 - 7 × 2

= 25 - 14 = 11

Similarly, 

For row 3: 13, ?, 18

= 13 × 5 - 18 × 2

= 65 - 36 = 29

Hence, the correct answer is "29"

Given series -

The pattern followed here is:

• If we point out the changes in figures 3 with respect to figure 1, and changes in figures 5 with respect to figure 3, we can easily find out how the sixth figure will be like.
• In the 1^st figure the equal (=) is at the upside left corner, in the 3^rd figure the equal is at the upside middle, in the 5^th figure the equal is at again upside left corner.
• In the 1^st figure, the triangle is at the middle, in the 3^rd figure the triangle is at the right side middle, in the 5^th figure the triangle is at again middle.
• In the 1^st figure, the star is at the right side middle, in the 3^rd figure the star is at the middle, in the 5^th figure the star is at again side middle.

Similarly,

• In the 2^nd figure, the equal is at the middle, in the 4^th figure the equal is at the left side middle, so in the 6^th figure, the equal is at again the middle.
• In the 2^nd figure, the triangle is at the upside right corner, in the 4^th figure the triangle is at the upside middle, so in the 6^th figure, the triangle is again at the upside right corner.
• In the 2^nd figure, the star is at the upside middle, in the 4^th figure the star is at the upside right corner, so in the 6^th figure, the star is again at the upside middle.

If we see each option, it is seen that option 1 satisfies the above conditions.

Hence, "option 1" is the correct answer.

The logic followed here is:

Hence, "option 1" is the correct answer.

The total number of triangles in the given figure is shown below:

Triangles are namely:

AKD, AIE, AIH, AKH, AKE, ADB, ACB, BKE, BFK, BKC, BKA, BDC, CGF, CDK, CFJ, CKF, CJG, CAD, DKG, DKH, EIK, EHA, EHK, FJK, FGK, GKJ, IHK and KCG.

So, the total number of triangles is 28.

Hence, "28" is the correct answer.

The logic followed here is:

Square of 1^st number - 8 = 2^nd number.

12 : 136 → 12² - 8 = 144 - 8 = 136

24 : 568 → 24² - 8 = 576 - 8 = 568

Similarly, 

? : 188 → 14² - 8 = 196 - 8 = 188

Hence, the correct answer is "14".

Alternate Method

The logic followed here is:

• First number multiply with (first number - 1) and add with subtraction between first number and 8 and so on.

12 : 136 : : ? : 188 : : 24 : 568

For 12 : 136;

• 12 × 11 + (12 - 8) = 132 + 4 = 136, and

For 24 : 568;

• 24 × 23 + (24 - 8) = 552 + 16 = 568

Similarly,

For ? : 188;

• ? × (? - 1) + (? - 8) = 188
• ?² - ? + ? - 8 = 188
• ?2 - 8 = 188
• ?2 = 196
• ? = 14

Hence, "option 3" is the correct answer.

The option in which the given figure is embedded when rotation is not allowed is shown below:

Hence, "option 4" is the correct answer. ​

The logic followed here is:

From option 1 -

136 - 56 = 80, It is not square of the number.

From option 2 -

89 - 25 = 64, It is square of the number 8.

From option 3 -

127 - 78 = 49, It is square of the number 7.

From option 4 -

97 - 61 = 36, It is square of the number 6.

Option 2, 3 and 4 are the square value but option 1 is not square value.

Option 1 is different from others.

Hence, "option 1" is the correct answer.

The correct answer is Chandi Prasad Mohanty.

• Lieutenant General Chandi Prasad Mohanty has taken over as the Vice Chief of the Army Staff.
• Lt Gen CP Mohanty was commissioned into the Rajput Regiment in 1982.
• An alumnus of Rashtriya Indian Military College (RIMC) Dehradun and National Defence Academy, Lt Gen Mohanty is a June 1982 batch Infantry Officer from the Rajput Regiment.

Additional Information

• Indian Army
• Army Day: 15 January
• Motto: Service Before Self
• Chief of the Army Staff: General Manoj Mukund Naravane
• Vice-Chief of the Army Chief: Lieutenant General Chandi Prasad Mohanty

The correct answer is Adille Sumariwalla.

Key Points

• Adille Sumariwalla was elected as Athletics Federation of India (AFI) president for a third term.
• While former Indian athlete Anju Bobby George was elected as the senior vice-president.
• Madhukant Pathak and Ravinder Chaudhary were elected as treasurer and general secretary of AFI respectively.

Additional Information

• The Athletics Federation of India is the apex body for running and managing athletics in India.
• Headquarters is located in New Delhi.
• The Athletics Federation of India nominated star javelin thrower Neeraj Chopra for the Rajiv Gandhi Khel Ratna Award, the country's highest sporting honor.

The correct answer is Kerala.

• Margomkali is a ritual folk art of the Syrian Christians of the Kottayam and Thrissur districts.
• A dozen dancers sing and dance around a lighted wick lamp (Nilavilakku), clad in the simple traditional white dhoti and sporting a peacock feather on the turban to add a touch of colour.

Additional Information

• Some Indian States and their folk Dances:

The correct answer is NG Ranga.

Key Points

• NG Ranga was the first General Secretary of All India Kisan Congress.
• Gogineni Ranga Nayukulu, also known as N. G. Ranga, was an Indian freedom fighter, farmers’ leader, and veteran Parliamentarian.
• N.G. Ranga brought peasants into our freedom struggle and fought for their cause.
• He was the founding president of the Swatantra Party.

Additional Information

• Acharya Narendra Deva:
• He was one of the leading theorists of the Congress Socialist Party in India.
• His democratic socialism renounced violent means as a matter of principle and embraced the satyagraha as a revolutionary tactic.
• Dev was first drawn to nationalism around 1915 under the influence of BG Tilak and Aurobindo Ghosh.
• Sardar Vallabhbhai Patel, popularly known as the Iron Man of India.
• He was the first Deputy Prime Minister and Home Minister of India.
• He was instrumental in India's independence struggle, and then for the integration of over 500 princely states into the Union of India.
• On the birth anniversary of Sardar Patel, on October 31, 2018, PM Modi unveiled the 'Statue of Unity' in Gujarat's Narmada district.
• Sahajanand Saraswati was considered a peasant leader of India.
• He along with other Hindi literary ran the Hindi weekly Hunkar from Patna.
• In 1929, He formed the Bihar Provincial Kisan Sabha to mobilize peasant grievances against the zamindari attacks on their occupancy rights.

The correct answer is Brad Pitt.

• Brad Pitt won Oscar's award for Best Supporting Actor for the film 'Once Upon a Time in Hollywood'.
• Other important awards:

Additional Information

• The Academy Award for Best Picture is one of the Academy Awards.
• It is presented annually by the Academy of Motion Picture Arts and Sciences (AMPAS) since the awards debuted in 1929.
• It is considered the world’s prestigious annual award for the best directors, actors, writers, and technicians in the film business.
• The first time the Oscar award was held on May 14, 1929.

The correct answer is Article 109. 

Key Points

• Article 109 -  A Money Bill shall not be introduced in the Council of States.
• A money Bill is defined in Article 110 of the Indian Constitution.
• Money bills are concerned with financial matters like taxation, public expenditure, etc.
• The bill is significant for Indian Polity and governance as many important issues like Aadhar Bill, Insolvency, and Bankruptcy Bill are also related to it.

Additional Information

• Article 354: Application of provisions relating to the distribution of revenues while a proclamation of emergency is in operation.
• Article 193 speaks about the Penalty for sitting and voting before making an oath or affirmation under Article 188 or when not qualified or when disqualified.
• Article 298 of the Constitution deals with the power to carry on trade.

The correct answer is 1765.

Key Points

• In 1765 the Mughal emperor Shah Alam II appointed the Company as the Diwan of the provinces of Bengal.
• After the defeat at Plassey, Sirajuddaulah Nawab of Bengal was assassinated and installed the puppet Nawab of Bengal Mir Jafar.
• When the company interferes in the internal matter of administration Mir Jafar protested, the Company deposed him and installed Mir Qasim in his place.
• When Mir Qasim complained, he in turn was defeated in a battle fought at Buxar (1764), driven out of Bengal, and Mir Jafar was reinstalled.
• Nawab had to pay Rs 500,000 every month but the Company wanted more money to finance its wars, and meet the demands of trade and its other expenses.
• The Company wanted more territories and more revenue. By the time Mir Jafar died in 1765 the mood of the Company had changed.

The correct answer is Spinal cord.

Key Points

• Any animal having a backbone or Spinal cord is known as the vertebrae while invertebrates are animals that do not have a backbone.
• A total of 33 vertebrae are found in the vertebral column of humans.

Additional Information

• The Vertical column is divided into the following regions: Thoracic, Cervical, Sacral, Coccygeal, and Lumbar.
• Thoracic:
• These are 12 in number ranging from T1 to T12.
• The rib cage is held by the thoracic spine and thus helps in protecting the lungs and heart as well.
• Cervical:
• There are 7 cervical vertebrae present in the neck region ranging from C1 to C7.
• The weight of the head is supported by these cervical vertebrae.
• Sacral:
• There are 5 sacral vertebrae found in the body's infused form.
• They help majorly in connecting the spine to the bones of the hip.
• Coccygeal:
• Their function is to provide attachment for muscles and ligaments in the pelvic floor.
• A total of four coccyx bones is present in the fused form.
• Lumbar:
• There is a presence of 5 lumbar vertebrae in the body ranging from L1 to L5.
• They function primarily in bearing the weight of the body.

The correct answer is Bankim Chandra Chatterjee.

Key Points

• Vande Mataram is a Sanskrit poem written by Bankim Chandra Chatterjee.
• It was taken from Anand Math published in 1882.
• Vande Mataram was first sung by Rabindranath Tagore in 1896.
• It was adopted by the constituent assembly on 24^th January 1950.
• Jadhunath Bhattacharya composed the music of Vande Mataram.

Additional Information

• Bipin Chandra Pal was one of the influencers of the Swadeshi movement along with Sri Aurobindo. 
• He vehemently opposed the partition of Bengal by the British colonial government in December 1903.
• He was born in Habiganj on 7 Nov 1858 and completed his studies at the University of Calcutta.
• Rabindranath Tagore was a Bengali poet, writer, and painter.
• He was honoured with the Nobel Prize in Literature in 1913.
• He is the first non-European to receive the Nobel Prize for Literature.
• Rabindranath Tagore got the Nobel Prize for his work Gitanjali.
• Bhagat Singh was an Indian communist revolutionary whose two acts of spectacular brutality against the British in India and execution at the age of 23 made him a famous hero of the Indian independence movement.

The correct answer is Gravitational pull of the Sun and the Moon.

Key Points

• Tides refer to the cyclic rise and fall of the seawater.
• The tides are caused by the gravitational attraction of the moon and the sun on the earth.

Important Points 

• The gravitational pull of the Moon causes high tides and low tides in the sea.
• The gravitational pull of the moon pulls the seas towards it, causing the ocean tides.
• Due to the difference in the gravitational force of the moon across the earth, there is also a bulge on the opposite side of the earth.

The correct answer is **Udaipur.**​

• Pichola Lake is one of the oldest and largest lakes of Udaipur.
• In 1362 this lake was built by Pichu Banjara during the ruling period of Maharana Lakha.

Additional Information

Important lakes of India

The correct answer is Yeast.

• Yeast is single-celled microorganisms that are classified, along with moulds and mushrooms, as members of the Kingdom Fungi.
• It is also known as sugar eating fungus.
• Yeasts are evolutionarily diverse and are therefore classified into two separate phyla, Ascomycota or sac fungi and Basidiomycota or higher fungi, that together form the subkingdom Dikarya.

Additional Information

• Baking Powder - It is a dry chemical leavening agent, a mixture of a carbonate or bicarbonate, and a weak acid.
• These baking acids are tartrate, phosphate, and sodium aluminium sulfate used alone or in combination.
• It contains sodium bicarbonate.
• Vinegar is a sour liquid that is made by the fermentation of numerous dilute alcoholic liquids into a liquid containing acetic acid.
• Vinegar can be made from any liquid that is capable of being converted into alcohol in a two-step process.

The correct answer is Dara Shikoh.

Key Points

• Dara Shikoh translated 50 Upanishads from Sanskrit to Persian so they could be read by Muslim scholars.
• His translation is often called Sirr-i-Akbar.
• Dara Shikoh was the eldest son and heir apparent of the Mughal Emperor Shah Jahan.
• He devoted much effort towards finding a common mystical language between Islam and Hinduism.
• His spiritual quest for monotheistic strands in Hindu philosophy was a continuous process.
• This led him to study the Upanishads, with the help of some scholars of Benaras.
• This book was the greatest mystery and was completed in 1657.

Additional Information

• Other important translations:
• Ramayana and Singhasan Batisi were translated by Mulla Abdul Qadir Badayuni into Persian.
• Panchatantra was translated into Persian by Faizi.
• Rajataringini was translated by Maulana Shah Mohammad Shahabadi.
• Abul Fazl wrote the Ain-i-Akbari and Akbar Nama.

The correct answer is August.

• Val Vil Ori Festival (vizha) celebrated in a grand manner in Kollihills during the month of August (17^th and 18^th of Adi in Tamil Month) every year.
• School students from various parts will participate in archery competition held during Val Vil Ori Vizha.

Additional Information

Some important festivals of Northeastern states are:

The correct answer is Chemayungdung glacier of the Kailash range.

Key Points

• The Brahmaputra originates under the name of Siang or Dihang, from the Chemayungdung glacier of the Kailash range near the Mansarovar lake.
• It enters India west of Sadiya town in Arunachal Pradesh.
• Tributaries: Dibang, Lohit, Siang, Burhi Dihing, Tista, and Dhansari.
• It is known as Tsangpo in Tibet and Yarlung Zangbo in China.
• The river crosses Assam below Dhubri and enters Bangladesh where the river is known as Jamuna and it flows for 337 km.

Additional Information

The correct answer is Innovations for Sustainable Energy Transition.

• The 3^rd Global RE-INVEST Renewable Energy Investors Meet & Expo, organised by the Ministry of New and Renewable Energy (MNRE).
• The theme is ‘Innovations for Sustainable Energy Transition’.
• Prime Minister Narendra Modi inaugurated the virtual 3^rd Global Renewable Energy Investment Meeting and Expo (RE-INVEST 2020) on 26 November 2020.

Additional Information

• International Renewable Energy Agency (IRENA):
• It is the first international organization to focus exclusively on renewable energy, addressing needs in both industrialized and developing countries.
• It was founded in 2009 and its statute entered into force on 8 July 2010.
• It is headquartered in Masdar City, Abu Dhabi.

The correct answer is Gujarat.

Key Points

• Gujarat has topped the Niti Aayog's Export Preparedness Index 2020 with a score of 75.19 followed by Maharashtra and Tamil Nadu in the second and third places respectively.
• NITI Aayog in partnership with the Institute of Competitiveness released the Export Preparedness Index (EPI) on 26 August 2020.

Important Points

• Among the landlocked states, 
• Rajasthan has performed the best, followed by Telangana and Haryana.
• Among the Himalayan states, 
• Uttrakhand has performed the best, followed by Tripura and Himachal.
• Among theUnion Territories, 
• Delhi has performed the best, followed by Goa and Chandigarh.

Additional InformationInformation about NITI Aayog:

• Stands for National Institution for Transforming India. It was a replacement for the Planning Commission of India instituted in 1950. NITI Aayog is the premier policy Think Tank of the Government of India.
• Founded: January 1, 2015.
• Chairperson: Hon'ble Prime Minister  Shri Narendra Modi.
• Vice-Chairperson: Suman K Bery.
• Chief Executive Officer:  BVR Subrahmanyam.

The correct answer is Scotland.

• Scotland has become the first country to allow free and universal access to menstrual products, including tampons and pads, in public facilities.
• Scotland has passed a bill that has made everyone who wants them free of period items such as tampons and pads.
• Local authorities are required by the Period Product(Free Provision) (Scotland) Bill passed unanimously, to ensure that period products are usually obtainable free of charge.

Additional Information

• Scotland:
• Capital - Edinburgh.
• Currency - Pound sterling.

The correct answer is Yamuna.

• Giri River is also famous as Giri Ganga” and is an important tributary of the Yamuna river.
• Giri River originates from the hills of Kotkhai and drains at the parts of Himachal in the southeastern areas.
• It flows through the district of Sirmaur and further merges with the Yamuna River.

Additional Information

• ​The Yamuna River is the largest tributary of the Ganga River.
• It originates from the Yamunotri glacier, at the Bandarpoonch peak in Uttarakhand.
• The main tributaries joining the river include the Sin, Hindon, Betwa Ken, and Chambal.
• The Chambal is the largest tributary of the Yamuna.

The correct answer is explicit cost.

Key Points

• Explicit costs are expenses that are easily quantifiable and identifiable.
• Payment made to others for the purchase of factors of production is known as explicit cost.
• It includes direct payments/expenses in business like wages, rent, raw materials, etc.
• The explicit cost of capital can be referred to as the "discount rate" which equates the present value of cash inflow that is incremental of financing opportunity with the present value of cash outflows.

Important Points

• Factors of production:
• Land: 
• The land has a broad definition as a factor of production and can take on various forms, from agricultural land to commercial real estate to the resources available from a particular piece of land.
• Labor: 
• Labor refers to the effort expended by an individual to bring a product or service to the market. Again, it can take on various forms.
• Capital: 
• In economics, capital typically refers to money.
• Organization:
• A business organization is defined as a firm established and run to earn profit by producing and selling commodities.

The correct answer is Article 161.

• Article 161 of the Indian constitution deals with the Pardoning Power of the Governor.
• The Power of the Governor to grant pardons, etc., and to suspend, remit or commute sentences in certain cases.
• The governor does not have the power to pardon the sentence inflicted by the court-martial on the convict.

Additional Information

• Types of Pardoning Powers of the President -
• Pardon - It removes both the sentence and the conviction of the convict and completely absolves the convict from all sentences, punishments and disqualifications.
• Commutation - It substitutes one form of punishment for a lighter form.
• Remission - It reduces the period of the sentence but the character of the sentence remains the same.
• Respite - It denotes awarding a lesser sentence in place of one originally awarded due to some special fact such as the physical disability of a convict or the pregnancy of a woman offender, the President can use this power.
• Reprieve - It implies a stay of the execution of a sentence (especially that of death) for a temporary period. Its purpose is to enable the convict to have time to seek pardon or commutation from the President.

The correct answer is P. V. Sindhu.

• PV Sindhu becomes the first Indian Badminton player to win a gold medal in the World Badminton Championship in 2019.
• PV Sindhu became the first Indian woman to claim two Olympic medals after she won a badminton bronze medal in Tokyo2020.
• Other medals of Sindhu:
• Rio Olympic silver medal in 2016.
• A silver at the Gold Coast Commonwealth Games.
• An Asian Games silver at Jakarta.
• The BWF World Tour Finals last year.

Additional Information

• Saina Nehwal is an Indian professional badminton singles player.
• A former world no. 1, she has won over 24 international titles, which includes eleven Superseries titles.
• She has represented India three times in the Olympics, winning a bronze medal in her second appearance.
• She was awarded Padma Bhushan, Rajiv Gandhi Khel Ratna, and Arjuna Award.
• Jwala Gutta is an Indian professional badminton player.
• Jwala Gutta was the first badminton player of Indian to qualify for two events in the Olympics–women's doubles with Ponnappa and mixed doubles with V. Diju at London.
• She was awarded the Arjuna Award, India's second-highest sporting award for her achievements.
• KidambiSrikanth is a famous badminton player in India.
• In 2018, he has been awarded with the Padma Shri Award.
• In April 2018, Srikanth became the top-ranked player in the world in badminton.

The correct answer is virus.

Key Points

• Melatonin encodes proteins in cells to prevent virus entry.
• Melatonin synthesised in the lungs acts as a barrier against Covid-19 infection.
• This also prevents the expression of genes that are entry points for the virus.

Additional Information

• Melatonin hormone is released by the Pineal gland
• The pineal gland is present on the dorsal side of the forebrain. It produces an enzyme called melatonin which is responsible for maintaining the diurnal rhythm (24-hour) of the body like the sleep-wake cycle, body temperature, etc.
• In addition, melatonin also influences metabolism, pigmentation, the menstrual cycle as well as our defence capability.

The correct answer is Jairam Ramesh.

• Jairam Ramesh is the author of the book The Light of Asia: The Poem that Defined the Buddha.

Mistake Points

• The Light of Asia is an epic on the life of Lord Buddha by Edwin Arnold.

Additional Information

• Books by Chetan Bhagat - Five Point Someone, Two States, What Young India Wants
• Books by Shashi Tharoor - Inglorious Empire, Why I am a Hindu, Pax Indica, Bookless in Baghdad
• Books by Salman Rushdie - Midnight’s Children, The Sellout - Paul Beaty, The Satanic Verses 

The correct answer is India and Singapore.

Key Points

• Indian Navy hosted the 27^th edition of India - Singapore Bilateral Maritime Exercise SIMBEX-20.
• The SIMBEX series of exercises between the Indian Navy and Republic of Singapore Navy, being conducted annually since 1994, are aimed at enhancing mutual inter-operability and imbibing best practices from each other.

Additional Information

• The joint military exercise between India and Sri Lanka is Mitra Shakti.
• The joint military exercise between India and Thailand is SITMEX.
• India-US Joint Exercises:
• Vajra Prahar (Army).
• Yudh Abhyas (Army).
• Cope India (Air Force).
• Red Flag (USA’s multilateral air exercise).

Shortcut Trick

Use the direct ratio formula between Cost Price (CP) and Marked Price (MP):

CP : MP = (100 − Discount%) : (100 − Loss%)

CP : 2720 = (100 − 25) : (100 − 15) = 75 : 85 = 15 : 17

Since 17 units = 2720, then 1 unit = 2720 ÷ 17 = 160

Cost Price (CP) = 15 × 160 = 2400

∴ The correct answer is Rs. 2400.

Alternate Method

Given:

Marked Price (MP) = Rs. 2720

Discount = 25%

Loss = 15%

Step 1: Calculate the Selling Price (SP)

⇒ SP = MP × (100 − Discount%) / 100

⇒ SP = 2720 × (100 − 25) / 100

⇒ SP = 2720 × (75 / 100)

⇒ SP = 2720 × (3 / 4)

⇒ SP = 680 × 3 = Rs. 2040

Step 2: Calculate the Cost Price (CP)

⇒ CP = SP × 100 / (100 − Loss%)

⇒ CP = 2040 × 100 / (100 − 15)

⇒ CP = 2040 × 100 / 85

⇒ CP = 2040 × 20 / 17

⇒ CP = 120 × 20 = Rs. 2400

∴ The correct answer is Rs. 2400.

Additional Information

Relation between CP and MP

The relationship is given by CP / MP = (100 − D%) / (100 ± P/L%), where D is discount, P is profit, and L is loss.

Markup Percentage

Markup % = (Marked Price − Cost Price) ÷ Cost Price × 100.

Effective Discount

For successive discounts d₁ and d₂, the single equivalent discount is d₁ + d₂ − (d₁ × d₂) / 100.

Given:

ABCD is a cyclic quadrilateral with AB is the diameter of the circle

∠ADC = 145° 

Calculation:

∠ADC + ∠ABC = 180° ...(since the sum of the opposite angles of a quadrilateral is 180°)

⇒ ∠ABC = 180° – 145° 

⇒ ∠ABC = 35° 

Also, ∠ACB = 90°..... (since the angle subtended by diameter at the circumference of the circle, is 90°)

In ΔABC, we have

∠ACB = 90° and ∠ABC = 35° 

So, ∠CAB = 180° – (∠ACB + ∠ABC)

⇒ 180° – (90° + 35°)

⇒ 180° – 125° 

⇒ 55° 

∴ The measure of ∠BAC is 55°

Shortcut Trick

Compare the expression with a³ + b³ = (a + b)(a² − ab + b²) where a = (x + y) and b = 3(x − y).

First factor: (a + b) = (x + y) + 3(x − y) = 4x − 2y ⇒ Comparing with (Ax − 2y), A = 4.

Second factor: (a² − ab + b²) = (x + y)² − 3(x² − y²) + 9(x − y)².

Coefficient of x²: 1 − 3 + 9 = 7 (B) | Coefficient of xy: 2 + 0 − 18 = −16 (C).

Calculate: A − B − C = 4 − 7 − (−16) = −3 + 16 = 13.

∴ The correct answer is 13.

Alternate Method

Given: (x + y)³ + 27(x − y)³ = (Ax − 2y)(Bx² + Cxy + 13y²)

Formula Used: a³ + b³ = (a + b)(a² − ab + b²)

Rewrite the left-hand side:

⇒ (x + y)³ + [3(x − y)]³

⇒ [(x + y) + 3(x − y)] [(x + y)² − (x + y)(3(x − y)) + (3(x − y))²]

⇒ [x + y + 3x − 3y] [(x² + 2xy + y²) − 3(x² − y²) + 9(x² − 2xy + y²)]

⇒ [4x − 2y] [x² + 2xy + y² − 3x² + 3y² + 9x² − 18xy + 9y²]

⇒ (4x − 2y) [7x² − 16xy + 13y²]

Comparing this with (Ax − 2y)(Bx² + Cxy + 13y²):

⇒ A = 4, B = 7, C = −16

Calculating the required value:

⇒ A − B − C = 4 − 7 − (−16)

⇒ −3 + 16

⇒ 13

∴ The correct answer is 13.

Additional Information

Algebraic Identities

Standard factorization of sum and difference of cubes: a³ ± b³ = (a ± b)(a² ∓ ab + b²).

Expansion Formulas

(a + b)² = a² + 2ab + b² and (a − b)² = a² − 2ab + b².

Comparison of Coefficients

If two polynomials are equal for all values of variables, the coefficients of their corresponding terms must be identical.

Given:

$x^2-√{11}x+1=0$

Formula used:

(x + 1/x)³ = x³ + 1/x³ + 3(x + 1/x)

Calculation:

$x^2-√{11}x+1=0$

⇒ x² + 1= √11x

⇒ x + 1/x = √11

(x + 1/x)3 = x3 + 1/x3 + 3(x + 1/x)

⇒ (√11)³ = x3 + 1/x³ + 3(√11)

⇒ (x3 + x-3) = 11√11 – 3√11

⇒ (x3 + x-3) = 8√11

∴ Required value is $8\sqrt{11}$

Given:

Rate of sugar of quantity 1 = Rs. 45

Quantity = 20 kg

Rate of sugar of quantity 2 = Rs. 50

Quantity = 25 kg

Rate of sugar of quantity 3 = Rs. 40

Quantity = 35 kg

Money spent on transportation and other expenses = Rs. 450

Selling price of mixed sugar = Rs. 52.50

Formula used:

Profit = SP – CP

Profit%= (Profit/CP) × 100

Calculation:

CP of sugar of quantity 1 = 45 × 20

⇒ 900

CP of sugar of quantity 2 = 50 × 25

⇒ 1250

CP of sugar of quantity 3 = 40 × 35

⇒ 1400

Total quantity of mixes sugar = (20 + 25 + 35)

⇒ 80

Final CP including transportation and other expenses = (900 + 1250 + 1400 + 450)

⇒ 4000

CP of 1 kg of mixed sugar = 4000/80

⇒ 50

SP of 1 kg of mixed sugar = 52.50

Profit = (52.50 – 50)

⇒ 2.50

Profit% = (2.50/50 × 100)

⇒ 5%

∴ His profit percentage in the entire transaction is 5%

Calculation:

Sale in 2015 = 1000

Sale in 2016 = 1290

Sale increase = [(1290 – 1000)/1000 × 100]

⇒ (290/1000 × 100)

⇒ 29000/1000

⇒ 29%

Sale in 2017 = 1100

Sale in 2018 = 1450

Sale increase by more than 25% of the previous year = [(1450 – 1100)/1100 × 100]

⇒ (350/1100 × 100)

⇒ 35000/1100

⇒ 31.81%

∴  The sale increases by more than 25% of the previous year is 2016 and 2018

Given:

If x8 - 433x4 + 16 = 0

Calculation:

Divided by x⁴

⇒ x8 - 433x4 + 16 = 0

⇒ (x8 - 433x4 + 16)/x⁴ = 0

Now, adding 8 on both sides

⇒ x⁴ + 16/x⁴ + 8 = 433 + 8

⇒ (x² + 4/x²)² = (441)

⇒ (x² + 4/x²) = √441

⇒ (x² + 4/x²) = 21

Now, adding 4 on both sides

⇒ (x2 + 4/x2) + 4 = 21 + 4

⇒ (x + 2/x)² = 25

⇒ (x + 2/x) = √25

⇒ (x + 2/x) = 5

∴ The required value is 5

Given:

Points P, Q, R, S and T lie in this order on a circle with centre O

chord TS is parallel to diameter PR

∠RQT = 58° 

Calculation:

PR is a diameter

∠PTR = 90° .....(angle inscribe in a semicircle)

also ∠TPR = 58°   .....(angle formed on same chord)

so, ∠PRT = 180° - ∠PTR – ∠TPR

⇒ ∠PRT = 180° - 90° - 58°

⇒ ∠PRT = 32° 

∠PRT = ∠RTS = 32°   (Alternate interior angle as chord TS is parallel to diameter PR)

 

∴ The measure of ∠RTS is 32.

Alternate Method

 

In this figure ∠PQR = 90° 

And ∠PQT = 90° - 58° = 32° 

Now we know angle formed on same chord are equal.

∴ ∠PQT = ∠PRT

And ∠PRT = ∠RTS (Alternate angle) 

∠RTS = 32°

Given:

The ratio of rural to urban students = 4 : 7

The average percentage marks of rural and urban students = 65 and 63

Formula used:

Average = sum of observations/Number of observations

Calculation:

The average percentage marks of rural students = 4/11 × 65

⇒ 23.63

The average percentage marks of urban students = 7/11 × 63

⇒ 40.1

The overall percentage marks of the class = (23.63 + 40.1)

⇒ 63.73

∴ Required overall percentage marks of the class is 63.73%

Shortcut Trick

Mean Proportional (M) = √(1.8 × 3.2) = √(5.76) = 2.4

Third Proportional (T) = 3² ÷ 5 = 9 ÷ 5 = 1.8

Difference = 2.4 − 1.8 = 0.6

∴ The correct answer is 0.6.

Alternate Method

Given: First set (1.8, 3.2) for Mean Proportional; Second set (5, 3) for Third Proportional.

Formula Used:

1. Mean Proportional of a and b = √(a × b)
2. Third Proportional of a and b = b² / a

Calculations:

⇒ Mean proportional (M) = √(1.8 × 3.2)

⇒ M = √(18/10 × 32/10) = √(576/100) = 24/10 = 2.4

⇒ Third proportional (T) = (3 × 3) / 5

⇒ T = 9 / 5 = 1.8

⇒ Difference = M − T = 2.4 − 1.8 = 0.6

∴ The correct answer is 0.6.

Additional Information

Mean Proportional

It is the middle term of a geometric progression. If x is the mean proportional between a and b, then a:x = x:b, which gives x = √(ab).

Third Proportional

If c is the third proportional to a and b, then the ratio a:b = b:c, which simplifies to c = b²/a.

Fourth Proportional

If d is the fourth proportional to a, b, and c, then a:b = c:d, implying d = (b × c)/a.

Calculation:

Total income of family = Rs. 43200

Degree of amount spent on food = 105

Amount spent on food = (43200 × 105/360)

⇒ 12600

Degree of amount on saving = 80

Amount spent on saving = (43200 × 80/360)

⇒ 9600

Degree spent on miscellaneous expenses = 45

Amount spent on miscellaneous expenses = (43200 × 45/360)

⇒ 5400

Total amount on saving and miscellaneous expenses = (9600 + 5400)

⇒ 15000

Required percentage on food to saving and miscellaneous expenses = (12600/15000 × 100)

⇒ (1260000/15000)

⇒ 84

∴ Required percentage is 84%

Given:

The given value = 42a48b

Concept used:

Divisibility rule of 11 - The sum of the digits at odd places and the sum of its digits at even places is either 0 or divisible by 11, then the number is divisible by 11.

Calculation:

As per the question

⇒ (4 + a + 8) – (2 + 4 + b) = 0 or multiple of 11

⇒ (12 + a) – (6 + b) = 0 or multiple of 11

⇒ 6 + a – b = 0 or multiple of 11

⇒ (a – b) = 11 – 6

⇒ (a – b) = 5

∴ The smallest value is 5

Given:

∠B = 62° 

∠C = 36° 

Calculation:

According to the question

⇒ ∠A = 180° – 62° – 36° 

⇒ 82° 

∠BAE is the bisector of ∠A

⇒ ∠BAE = 82/2

⇒ ∠BAE = 41° 

∠BAD = 180° – 62° – 90° 

⇒ 28° 

∠DAE = 41° – 28° 

⇒ 13° 

∴ The measure of ∠DAE is 13° 

Shortcut Trick

When angle bisector and perpendicular bisector are given for a triangle and the angle made by them is asked then in that case,

Angle made = Difference of angles/2 

⇒ ∠DAE = (62° - 36°)/2 

⇒ ∠DAE = 26°/2

⇒ ∠DAE = 13° 

∴ The correct answer is 13°.

Given:

Time taken by first water tap to fill the empty tank = 12 hours

Time taken by second water tap to fill the empty tank = 18 hours

Time taken by leakage to empty the filled tank = 36 hours

Formula used:

Work = Efficiency × Time

Calculation:

LCM of 12, 18 and 36 is 36

Efficiency of first water tap = 36/12 = 3 units/hr

Efficiency of second water tap = 36/18 = 2 units/hr

Efficiency of leakage = 36/36 = 1 unit/hr

Efficiency of these 2 taps and leakage together = (3 + 2 – 1) = 4 units/hr

Remaining units = (36 – 4) = 32 units

Work done by two tap water together to fill the empty tank = 32/(3 + 2) hr

⇒ 32/5 hr

⇒ 6.4 hours = 6 hours + 0.4 hours (0.4 hours = 24 minutes)

⇒ 6 hr 24 min

Total time taken to fill the empty tank = (6 hr 24 min + 1 hr)

⇒ 7 hr 24 min

∴ The empty tank will completely filled in 7 hr 24 minutes

Shortcut Trick

For the first one hour = (3 + 2 - 1) × 1 = 4 units

Time to fill remaning tank = (36 - 4) ÷ (3 + 2) = 6.4 hours

Total time taken = (6.4 + 1) = 7.4 hours = 7 hr 24 min

∴ The empty tank will completely filled in 7 hr 24 minutes

Given:

Principal = Rs. 160000

Rate = 10%

Time = 2 years

Formula used:

SI = (P × R × T)/100

Amount = P × (1 + r/100)^t

CI = Amount –  Principal

When compound semi-annually, r' = r/2 and t' = 2 × t

Calculation:

According to the question

SI = (160000 × 10 × 2)/100

⇒ Rs. 32000

Now,

Compounded amount when compounded semi annually = P(1 + r/200)^{2 × t}

Compounded amount = 160000[1 + 10/200)^{2 × 2}

⇒ 160000(21/20)⁴

⇒ Rs. (160000 × 21/20 × 21/20 × 21/20 × 21/20)

⇒ Rs. 194481

CI = Amount – Principal = (194481 – 160000)

⇒ Rs. 34481

Now, the amount earned by A in the whole transaction = CI – SI

⇒ (34481 – 32000)

⇒ Rs. 2481

∴ Required amount earned by A in the whole transaction is 2481

Calculation:

Total number of students = 1400

Number of students in B. Sc Maths = (1400 × 20/100)

⇒ 280

Number of boys in B. Sc Maths = (280 × 40/100)

⇒ 112

Number of girls in B. Sc Maths = (280 – 112) = 168

Number of students in B. Sc. Sci = (1400 × 25/100)

⇒ 350

Number of boys in B. Sc. Sci = (350 × 80/100)

⇒ 280

The ratio of number of girls in B. Sc. Maths to number of boys in B. Sc. Sci = (168 : 280)

⇒ 3 : 5

∴ Required ratio is 3 : 5

Alternate MethodLet the total salary of Rajan be Rs. x.

Total saving of Rajan = 1480 + 5000 = Rs. 6480

Now,

x × (100 - 10/100) × (100 - 20)/100 × (100 - 40)/100 × (100 - 80)/100 = 6480

⇒ x × (90/100) × (80/100) × (60/100) × (20/100) = 6480

⇒ x × 0.0864 = 6480

⇒ x = 64800000/864

⇒ x = Rs. 75000

Traditional method:

Given:

Salary spent on rent = 10%

Salary spent on transport of the balance = 20%

Salary spent on food of the balance = 40%

Salary spent on various bills of the balance = 80%

Money deposited in bank = Rs. 5000

Money kept for his own petty expenditure = Rs. 1480

Calculation:

Let total salary be Rs. 100x

Salary spent on rent = 10% of Rs. 100x

⇒ (100x × 10/100)

⇒ 10x

Remaining salary spent on transport = 20% of 90x

⇒ (20/100 × 90x)

⇒ 18x

Remaining salary spent on food = 40% of 72x

⇒ (40/100 × 72x)

⇒ 28.8x

Remaining salary spent on various bills = 80% of 43.2x

⇒ (80/100 × 43.2x)

⇒ 34.56x

Remaining salary = 100x – (10 + 18 + 28.8 + 34.56)x

⇒ (100 – 91.36)x

⇒ 8.64x

Money deposited in the bank and saved for his own petty expenditure = Rs. (5000 + 1480)

⇒ Rs. 6480

Now, as per the question,

⇒ 8.64x = Rs. 6480

⇒ 100x = (6480/8.64 × 100)

⇒ Rs. 75,000

∴ His monthly salary is Rs. 75,000

Given:

Speed = 72 km/h

Time = 12 sec

Distance = 360 m

Formula used:

Time = Distance/Speed

Calculation:

Speed = 72 × 5/18

⇒ 20 m/s

Distance = Length = (20 × 12) m

⇒ 240 m

Now,

Time = Distance/Speed

⇒ (360 + 240)/20

⇒ 600/20

⇒ 30 sec

∴ Required time is 30 sec

Given:

cos θ - sin θ = √3cos(90° - θ)

Formula used:

cos(90° – θ ) = Sinθ 

cotθ = cosθ/sinθ 

tanθ = 1/cotθ 

Calculation:

cos θ - sin θ = √3cos(90° - θ)

⇒ cosθ – sinθ = √3Sinθ 

⇒ cosθ = (√3 + 1)Sinθ 

cotθ = √3 + 1       -----(1)

tanθ = 1/(√3 + 1)    ----(2)

Now, 

tanθ – cotθ = 1/(√3 + 1) – (√3 + 1)

⇒ tanθ – cotθ =  [1- (√3 + 1)²]/(√3 + 1)

⇒ tanθ – cotθ = [1 - (3 + 1 + 2√3)]/(√3 + 1)

⇒ tanθ – cotθ = [-3 - 2√3]/(√3 + 1)

⇒ tanθ – cotθ = - (3 + 2√3)/(√3 + 1)

∴ Required value is $-\frac{3+2√3}{(1+√3)}$

Concept Used:

Follow the BODMAS rule according to the table given below:

Calculation:

$5\frac{1}{5}÷ \left[3\frac{1}{2}-\lbrace{\frac{5}{6}-\left(\frac{3}{5}+\frac{1}{10}-\frac{4}{15}\right)\rbrace}\right]$

⇒26/5 ÷ [7/2 – {5/6 – (3/5 + 1/10 – 4/15)}]

⇒ 26/5 ÷ [7/2 – {5/6 – (18 + 3 – 8)/30}]

⇒ 26/5 ÷ [7/2 – {5/6 – 13/30}]

⇒ 26/5 ÷ [7/2 – {(25 – 13)/30}]

⇒ 26/5 ÷ [7/2 – 2/5]

⇒ 26/5 ÷ [(35 – 4)/10]

⇒ 26/5 ÷ 31/10

⇒ 26/5 × 10/31

⇒ 52/31

∴ The required value is 52/31

Given:

Sin A = 1/2

Formula used:

Sin 30° = 1/2

tan 30° = 1/√3

Cot 30° = √3

Cosec 30° = 2

Calculation:

Sin A = 1/2

⇒ A = 30° 

Now put the value of A in given equation we get,

$\frac{tan A-cot A}{√ 3(1+cosecA)}$

⇒ tan 30° – cot 30°/√3(1 + cosec 30°)

⇒ (1/√3 – √3)/√3(1 + 2)

⇒ [(1 – 3)/√3]/3√3

⇒ (-2/√3)/3√3

⇒ -2/9

∴ Required value is $-\frac{2}{9}$

Calculation:

The total number of female teachers in the five districts = (2375 + 2651 + 1520 + 1085 + 859)

⇒ 8490

The average number of female teachers in the five districts = (8490/5)

⇒ 1698

∴ Required average is 1698

Given:

$\frac{1}{cos θ}+\frac{1}{tan θ -sec θ}$

Formula used:

1/cosθ = secθ 

tan²θ – sec²θ = -1

Calculation:

$\frac{1}{cos θ}+\frac{1}{tan θ -sec θ}$

⇒ secθ + 1/tanθ – secθ 

Rationalizing the value we get,

⇒ secθ + [1(tanθ + secθ )/tanθ – secθ × (tanθ + secθ)]

⇒ secθ + (tanθ + secθ)/(tan²θ – sec²θ)

⇒ secθ + (tanθ + secθ)/-1

⇒ secθ + [-(tanθ + secθ)]

⇒ secθ – tanθ – secθ 

⇒ -tanθ 

∴ Required value is -tanθ

Given:

Inner radius (r) = 2 cm

Outer radius (R) = 3 cm

Formula used:

Volume of a hollow sphere of outer radius R and inner radius r = 4/3π(R³ – r³)

Calculation:

According to the question

Volume of a hollow sphere of outer radius R and inner radius r = 4/3π(R3 – r3)

⇒ 4/3 × π × (3³ – 2³)

⇒ 4/3 × π × (27 – 8)

⇒ 4/3 × π × 19

⇒ 76π/3

∴ Volume of spherical shell is 76π/3

Given:

AC = 21 cm

BC = 11 cm

The length of BD is 3 cm less than DC

AD is the bisector of ∠A meeting BC at D

Concept used:

AD is the angle bisector of ∠BAC

And AB/BD = AC/CD

Calculation:

Let the length of CD be x

⇒ x + x – 3 = 11

⇒ 2x – 3 = 11

⇒ 2x = 14

⇒ x = 7

Length of BD = 7 – 3 = 4

From angle bisector property

AB/4 = 21/7

⇒ AB = 4 × 3

⇒ 12 cm

∴ The length of side AB is 12

The correct answer is Sprawling.

Key Points

• Let's look at the meaning of the words given in options:-
• Sprawling: built over a wide area in an ugly way. (बदसूरत तरीके से विस्तृत क्षेत्र में बनाया गया)
• ​For example, The fire is sprawling in all directions.
• Stroking: to move your hand gently over somebody/something. (किसी व्यक्ति या वस्तु पर अपना हाथ धीरे से हिलाना)
• ​For example, Peter stroked his nose.
• Stretching: to pull something so that it becomes wider. (किसी चीज को खींचना जिससे वह चौड़ी हो जाए)
• ​For example, Yoga involves breathing exercises, stretching, and meditation.
• Slouching: to have a droop or downward bend. (झुकना)
• ​For example, Several students were slouching against the wall.
• The given sentence is trying to express that some patches of the garden that has been built over a wide area have a rich cover of grass. (दिया गया वाक्य यह व्यक्त करने का प्रयास कर रहा है कि एक विस्तृत क्षेत्र में बने बगीचे के कुछ हिस्सों में घास का एक समृद्ध आवरण है)
• From the given meanings of the words given above, it is clear that the correct option suitable for the sentence is Sprawling.
• Therefore, the correct option is 1.

The correct answer is Diminish.

Key Points 

• The meaning of the words:
• Augment: to make it larger, more effective by adding something to it. (इसमें कुछ जोड़कर इसे बड़ा, अधिक प्रभावी बनाना)
• For example, Reading regularly will augment your vocabulary skills.
• Diminish: to become less in size. (घटाना)
• For example, I don't want to diminish her achievements.
• It is clear from the above-meaning words that the correct answer is Diminish.
• Therefore, the correct answer is Option 2.

Additional Information

• Let's look at the meaning of the other words given in options:-
• Extend - cause to cover a wider area; make larger. (विस्तार)
• Expand - become or make larger or more extensive. (विस्तार)
• Spread - extend over a large or increasing area. (फैलाना)

The correct answer is 'No improvement is required.'

Key Points

• In the underlined segment of the sentence, no improvement or correction is required.
• The given sentence is talking about preparing children to face challenges.
• Here, 'preparing' is used as a participle and the doer of the action expressed by the participle is usually the subject of the sentence or the main clause.
• 'Preparing' is singular in form and therefore the use of singular verb 'keeps' is correct.
• The pronoun 'them' that is used as the object of a verb or preposition to refer to two or more people or things previously mentioned or easily identified is correctly used to refer to the noun 'children'.
• The preposition 'in' is correct as it is used for showing the condition or state of somebody or something.
• The noun 'readiness' is correctly used as it means the state of being ready or prepared.
• Here, the subject of the sentence is preparing not children. Because if we try to convey the meaning by "children" be taken as subject then it means children keep them in readiness but we want to convey the meaning that preparing something will keep them in readiness hence, we need to take a subject 'preparing' in focus.

Hence, the correct answer is option 3.

Correct sentence: Preparing children for uncertainties keeps them in readiness to face challenges.

Hinglish

• वाक्य के रेखांकित खंड में किसी सुधार या प्रतिस्थापन की आवश्यकता नहीं है।
• दिया गया वाक्य बच्चों को चुनौतियों का सामना करने के लिए तैयार करने की बात कर रहा है।
• रेखांकित खण्ड में एकवचन विषय के साथ क्रिया 'keeps' के एकवचन रूप का प्रयोग सही है।
• Pronoun 'them' जिसका प्रयोग verb or preposition की वस्तु के रूप में दो या दो से अधिक लोगों या पहले बताई गई या आसानी से पहचानी जाने वाली चीजों को संदर्भित करने के लिए किया जाता है, संज्ञा 'बच्चों' को संदर्भित करने के लिए सही ढंग से उपयोग किया गया है।
• Preposition 'in' का सही उपयोग किया गया है क्योंकि इसका उपयोग किसी चीज़ की स्थिति या स्थिति को दिखाने के लिए किया जाता है।
• Noun 'readiness' का सही प्रयोग किया गया है क्योंकि इसका अर्थ है तैयार या तैयार होने की अवस्था।

अत: सही उत्तर विकल्प 3 है।

सही वाक्य: Preparing children for uncertainties keeps them in readiness to face challenges.

The correct answer is Fluctuate.

Key Points 

• In the given sentence, 'fluctuate' will be used.
• Let's look at the meaning of the correct answer:-
• Fluctuate: change frequently from one thing to another (prices or numbers). (उतार चढ़ाव)
• For example, School enrollment has fluctuated from year to year.
• The given sentence is trying to express that sales change frequently from day to day.
• Hence, the appropriate word for the blank is Fluctuate.

Additional Information

• Let's look at the meaning of the other words given in options:-
• Swing - move or cause to move back and forth or from side to side while suspended or on an axis. (घूम जाना)
• Rotates - move or cause to move in a circle round an axis or centre. (घूमता है)
• Revolves - move in a circle on a central axis. (एक केंद्रीय अक्ष पर एक सर्कल में चलना)

The correct answer is You are requested to do your work properly.

Key Points 

• 'Please do your work properly' is an Imperative sentence. As per the given question we have to change it to passive voice.
• Imperative sentences are sentences that express advice, request, or command.
• Passive voice sentences containing requests start with 'You are requested to'.
• The structure of passive voice would be: You are requested to + verb + ...
• For example, Please bring me some water. (Active Voice)

                     You are requested to bring me some water. (Passive Voice)

• Therefore, the correct answer is Option 1.

Hinglish 

• 'Please do your work properly' एक अनिवार्य वाक्य है। दिए गए प्रश्न के अनुसार हमें इसे पैसिव वॉयस में बदलना होगा।
• अनिवार्य वाक्य ऐसे वाक्य होते हैं जो सलाह, अनुरोध या आदेश व्यक्त करते हैं।
• अनुरोध वाले निष्क्रिय ध्वनि वाक्य 'You are requested to' से शुरू होते हैं।
• निष्क्रिय आवाज की संरचना होगी: You are requested to + verb + ...
• उदाहरण के लिए, Please bring me some water. (सक्रिय आवाज)

                                           You are requested to bring me some water. (कर्मवाच्य)

• अतः सही उत्तर विकल्प 1 है।

The correct answer is CDBA.

Key Points 

• Sentence C depicts the main idea of the paragraph. Therefore, it is the first sentence.
• Followed by sentence C, sentence D is the second sentence.
• ​Sentence B will be the third sentence as it is further describing how the cat hopes that her idea would work because the mice would no longer be afraid to come near her.
• The paragraph ends with sentence A, as it concludes with the mice saying, "Many a bag have I seen in my day, but never one with a cat's head”.
• Therefore, the correct option is 2.

Hinglish 

• वाक्य C अनुच्छेद के मुख्य विचार को दर्शाता है। अतः यह प्रथम वाक्य है।
• वाक्य C के बाद वाक्य D दूसरा वाक्य है।
• सेंटेंस बी तीसरा वाक्य होगा क्योंकि यह आगे वर्णन कर रहा है कि बिल्ली कैसे उम्मीद करती है कि उसका विचार काम करेगा क्योंकि चूहे अब उसके पास आने से नहीं डरेंगे।
• पैराग्राफ वाक्य A के साथ समाप्त होता है, क्यूंकि यह चूहे के इस कथन के साथ समाप्त होता है, "मैंने अपने दिन में कई बैग देखे हैं, लेकिन बिल्ली के सिर के साथ कभी नहीं"।
• अतः सही विकल्प 2 है।

The correct answer is 'No substitution.'

Key Points

• In the underlined segment of the sentence, no substitution is required or needed.
• The given sentence is talking about the fully prepared furniture.
• In the given sentence, the word 'furniture' is an uncountable noun and is not used in the plural. Furniture is always followed by a singular verb.
• Therefore, the singular verb 'is' after the singular subject 'The furniture' is correct.
• The adjective 'ready' is correctly used as it means prepared and able to do something or to be used.
• The given sentence is in the present simple tense passive voice. Therefore, the to be + past participle (here, delivered) construction in the given sentence is correct.

Hence, the correct answer is option 3.

Correct sentence: The furniture is ready to be delivered.

Hinglish

• वाक्य के रेखांकित खंड में किसी सुधार या प्रतिस्थापन की आवश्यकता नहीं है।
• दिया गया वाक्य पूरी तरह से तैयार फर्नीचर के बारे में बात कर रहा है।
• दिए गए वाक्य में 'furniture' शब्द एक uncountable संज्ञा है और बहुवचन में इसका प्रयोग नहीं किया गया है। Furniture के बाद हमेशा एकवचन क्रिया होती है।
• इसलिए, एकवचन क्रिया 'is' एकवचन विषय 'The furniture' के बाद सही है।
• Adjective 'ready' का सही प्रयोग किया गया है क्योंकि इसका अर्थ है तैयार और कुछ करने में सक्षम या इस्तेमाल किया जाना।
• दिया गया वाक्य present simple tense passive voice में है। इसलिए, दिए गए वाक्य में to be + past participle (यहां, delivered) की रचना सही है।

अत: सही उत्तर विकल्प 3 है।

सही वाक्य: The furniture is ready to be delivered.