The pattern followed here is:

Similarly,

Hence, ‘KFRWFP’ is the correct answer.

The pattern followed here is:

11 → 1³ = 1

28 → 2³ = 8

327 → 3³ = 27

? → 4³ = 64

? = 464

5125 → 5³ = 125

Hence, ‘464’ is the correct answer.

The pattern followed here is:

1. 8-138 → 138 ÷ 8 = 17.25

2. 5-155 → 155 ÷ 5 = 31

3. 6-174 → 174 ÷ 6 = 29

4. 11-143 → 143 ÷ 11 = 13

All pairs except ‘8-138’ when divided gives an exact whole number while ‘8-138’ gives a decimal number.

Hence, ‘8-138’ is the correct answer.

In dice 2 and 3, ‘&’ symbol is common on the faces of the dice, so keeping it constant and moving in clockwise direction, we get the symbols opposite to other faces:

 

Hence, ‘#’ symbol will be on the face opposite to the one showing ‘@’.

The pattern followed here is:

6 : 252 → 6 : 6³ + 6²

Similarly,

5 : ? → 5 : 5³ +5² → 150

Hence, ‘150’ is the correct answer.

1. Jhalrapatan → Jhalrapatan is a town in Jhalawar district in the south of Rajasthan state in India.

2. Ahmedabad → Ahmedabad, in western India, is the largest city in the state of Gujarat. 

3. Rajkot → Rajkot is a city in the western Indian state of Gujarat. 

4. Surat → Surat is a large city beside the Tapi River in the West Indian state of Gujarat.

All options except ‘1’ are cities located in Gujarat while Jhalrapatan is a town in Rajasthan.

Hence, ‘Jhalrapatan’ is the odd one out.

The option figure which contains the given question figure embedded in it as its part is shown below: 

Hence, figure 4 is the correct answer.

1. 2 and 3

Given equation: 32 ÷ 6 + 26 – 13 × 6 = 54

After interchanging ‘2 and 3’, we get:

L.H.S = 23 ÷ 6 + 36 – 12 × 6

= 3.8 + 36 – 72

= 39.8 – 72

= -32.2 ≠ R.H.S

2. 3 and 6

Given equation: 32 ÷ 6 + 26 – 13 × 6 = 54

After interchanging ‘3 and 6’, we get:

L.H.S = 62 ÷ 3 + 23 – 16 × 3

= 20.6 + 23 – 48

= 43.6 – 48

= - 4.4 ≠ R.H.S

3. 3 and 1

Given equation: 32 ÷ 6 + 26 – 13 × 6 = 54

After interchanging ‘3 and 1’, we get:

L.H.S = 12 ÷ 6 + 26 – 31 × 6

= 2 + 26 – 186

= 28 – 186

= = 158 ≠ R.H.S

4. 6 and 2

Given equation: 32 ÷ 6 + 26 – 13 × 6 = 54

After interchanging ‘6 and 2’, we get:

L.H.S = 36 ÷ 2 + 62 – 13 × 2

= 18 + 62 – 26

= 80 – 26

= 54 = R.H.S

Hence, ‘6 and 2’ is the correct answer.

Given series: 4, 25, 121, ?, 529, 961

The pattern followed here is:

The series given above is squares of the alternate prime numbers.

Prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31

2² = 4;

5² = 25;

11² = 121;

17² = 289;

23² = 529;

31² = 961

Hence, ‘289’ is the correct answer.

Turmeric: Spices → Turmeric is a spice that comes from the turmeric plant. 

Or, in general we can say that turmeric is an example of spice.

1. Fig : Cashew Nuts → Fig (genus Ficus) is a soft, sweet fruit. Its skin is very thin and has many small seeds inside of it. 

The cashew seed is often considered a nut in the culinary sense; this cashew nut is eaten on its own, used in recipes, or processed into cashew cheese or cashew butter.

2. Dates : Dry Fruits → Dates are the fruit of the date palm tree, which is grown in many tropical regions of the world. Dates have become quite popular in recent years. Almost all dates sold in Western countries are dried. After it is dried, it is used as dry fruits.

Or, in general we can say that, dates is an example of dry fruits.

3. Nutmeg : Chilli Flakes → Nutmeg is the seed or ground spice of several species of the genus Myristica.

Chili flakes are nothing but coarse-grained red chilies.

4. Apricot : Pear → An apricot is a fruit, or the tree that bears the fruit, of several species in the genus Prunus.

The pear tree and shrub are a species of genus Pyrus, in the family Rosaceae, bearing the pomaceous fruit of the same name.

Hence, ‘Dates : Dry Fruits’ is the correct answer.

Persons who can speak exactly two languages lies in the intersection area of AB, BC and CA, as shown below:

Therefore, number of people who can speak exactly two languages = 11 + 5 + 2 = 18

Hence, ‘18’ is the correct answer.

The option that depicts how the given transparent sheet of paper will appear if it is folded at the dotted line is shown below:

Hence, figure 1 is the correct answer.

Given:

Product A is costlier than product B by Rs. 2.

A - B = 2

Or, A = 2 + B      ----(i)

If the price of product A is increased by two times the price of product B, the new price of product A become Rs. 17.

According to statement:

A + 2B = 17

2 + B + 2B = 17 [Substituting the value of A from (i)]

3B = 17 – 2

3B = 15

B = 5

Hence, the price of product B is Rs. 5.

According to the alphabetical positions of the letters,

 

Similarly,

 

Hence, ‘5291576’ is the correct answer.

 

Given: E ÷ F - H + J ÷ G × D → E is Wife of F, F is father of H, H is sister of J, J is wife of G, G is son of D.

 

Hence, E is mother-in-law of G.

The pattern followed here is:

W - 6 → Q;

Q - 5 → L;

L - 4 → H;

H - 3 → E;

E - 2 → C

Hence, ‘L’ is the correct answer.

According to the alphabetical positions of the letters,

The pattern followed here is:

Addition of the positional values of the first and last letter gives the middle number.

1. HEF

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2. DVR

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3. GMF

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4. OVG

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Hence, ‘HEF’ is the odd one out.

Given series:

The triangles at odd positions are water image of each other, while the triangle at even positions are mirror image of each other. So, the triangle at the ‘?’ position will be the water image of 3^rd image or similar to that of the 1^st image i.e, an equilateral triangle.

Only option 2 and 3 is an equilateral triangle.

Also the numbers given inside the triangles are the positional values of the vowels in the English alphabetical series i.e. A, E, I, O, and U.

A → 1; E → 5; I → 9; O → 15; U → 21

Hence, figure 2 is the correct answer.

1. Micron → 1 micron = 1 × 10^-6 metres
2. Metre → 1 metre
3. Mile → 1 mile = 1609.34 m
4. Millimetre → 1 mm = 1 × 10^-3 metres
5. Kilometre → 1 km = 1 × 10³ m
6. Centimetre → 1 cm = 1 × 10^-2 m

The correct ascending order is:

Micron < Millimetre < Centimetre < Metre < Kilometre < Mile

1-4-6-2-5-3

Hence, ‘1-4-6-2-5-3’ is the correct answer.

The pattern followed here is:

Row 1: (10 - 3) × 2 = 14

Row 2: (49 - 15) × 2 = 68

Similarly,

Row 3: (33 - 19) × 2 = 28

Hence, ‘28’ is the correct answer.

‘Grapes’ is related to ‘Fruit’ → Grapes is an example of Fruit.

Similarly,

‘Pepper’ → is an example of spice.

Hence, ‘spices’ is the correct answer.

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

Hence, there are 11 triangles in the figure.

The pattern followed here is:

A + 2 → C; C + 2 → E; E + 2 → G; G + 2 → I

O + 2 → Q; Q + 2 → S; S + 2 → U; U + 2 → W

S + 2 → U; U + 2 → W; W + 2 → Y; Y + 2 → A

Hence, ‘ESW’ is the correct answer.

The correct mirror image of the given figure when a mirror is placed on the right of the figure is shown below:

Hence, figure 4 is the correct answer.

Mistake Points There is some difference between option 3 and option 4 (The Shape of the Hexagon is different in both of the options).

The least possible Venn diagram is as follows:

I. All cars are buses. → False, it is possible but not definite.

II. Some buses are trucks. → True, as all cars are trucks and some buses are cars.

III. All trucks are buses. → False, it is possible but not definite.

Hence, only conclusion II follows.

Option 4 is the correct answer: John Maynard Keynes hailed from England.

• John Maynard Keynes was born on June 5, 1883, in Cambridge.
• He completed his degree in Mathematics and had also joined Civil Services in Britain.
• He represented the Brish Treasury at the Conference of Versailles but resigned because he was against the heavy fine levied on Germany.
• He expressed his concerns about the fine imposed on Germany in his book 'The Economic Consequences of Peace'.

Keynesian Economics:

• In 1923, he published a book 'A Tract on Monetary Reform'.
• 'The General Theory of Employment, Interest and Money' published in1936 made a revolutionary change in economics as a subject.
• The book mainly focussed on two aspects employment and effective demand.
• According to him increasing employment will lead to more people buying more goods and hence demand will increase leading to economic progress.
• He also stated that without the government's intervention full employment cannot be achieved.

Option 3 is the correct answer: Hasan Minhaj topped the Forbes India's ‘20 people to watch in the 2020s’.

• Hasan Minhaj is an Indian origin US-born comedian and political commentator.
• He has been the critical of Indian elections and political system.
• Due to such a personality, he had been denied entry at Howdy Modi event in Texas.
• Mahua Moitra (Lok Saha member from TMC), Dushyant Chautala (Deputy CM of Haryana) and Prashant Kishor (poll strategist) have also featured in this list.
• Kanhaiya Kumar, Garima Arora and Aditya Mittal also got their names on the list.
• The international personalities like Gotabaya Rajapaksa, Mohammed bin Salman, Boris Johnson, Sanna Marina and Greta Thunberg also found a place on the list.

Option 4 is the correct answer. Union Home Minister Amit Shah chaired the 6^th meeting of Island Development Agency.

• This meeting was held in New Delhi in January 2020.
• The meeting was attended by Lt. Governor of Andaman & Nicobar, Administrator of Lakshadweep, the Cabinet Secretary, CEO of NITI Aayog and secretary and officials from various Ministries.
• Outcomes:
• Plans for tourism promotion, the export of seafood and coconut-based products have been taken up.
• Development of Land and Water-based tourism to be boosted.
• Digitally connecting will be improved in the islands of the two Archipelago through submarine Optical Fibre Cables.
• Improvement of air and sea connectivity has been proposed along with airports at Greater Nicobar and Minicoy Islands.
• Island Development Agency was established on June 1, 2017, to undertake island development.

Andaman and Nicobar islands: 

• These islands are a seaward extension of Arakan- Yoma Mountains of Myanmar.
• The Andaman group consists of North Andaman, Middle Andaman, South Andaman & Little Andaman and the Nicobar group consists of Car Nicobar, the Little Nicobar, and the Great Nicobar.
• The capital city Port Blair is situated in the South Andaman.
• 10º Channel separates the Andaman islands from Nicobar.
• The Barren Island, India's only active volcano is in the Middle Andaman and Narcondam is also a volcanic island.
• Saddle Peak is the highest point of this Archipelago.
• Indira Point, India's southernmost tip is part of Greater Nicobar.
• Andaman and Nicobar islands are one of the biodiversity hotspots of India.

Lakshadweep Islands:

• This archipelago consists of 36 islands and atolls that are of Coral origin.
• The capital of Lakshadweep is Kavaratti.
• These were earlier known as Laccadive, Minicoy and Amindivi Islands.
• Andrott is the largest island of this group.
• Lakshadweep islands are separated from the Maldives by 8º Channel.

The correct answer is option 4: Kristalina Georgieva was appointed as managing director of the International Monetary Fund (IMF).

• Before assuming the office of Managing Director of IMF Kristalina Georgieva held the office of Wolrd Bank CEO.
• On October 1, 2019, she succeeded Christine Lagarde to become the Managing Director of IMF.
• She is a Bulgarian lady who has chaired and worked with many International Platforms contributing in the fields of Climate Change and Other humanitarian crisis
• She has also played an important role in Economic Commission and has provided her services to Wolrd Bank before that.

 International Monetary Fund (IMF):

• IMF is an international organisation established in 1944 and headquartered at Washington DC, USA.
• It is one of the institutions of the World Bank Group, having 190 countries as its members.
• IMF aims to stabilize the global economy, Improve international trade and monitor financial policies of its member nations
• IMF provides loans to the countries which are suffering Balance of Payment crisis.
• Following reports/indices are published by IMF:
• World Economic Outlook.
• Global Financial Stability Report.

Option 3 is the correct answer: Achievements of Samudra Gupta have been engraved on the Allahabad Pillar inscription.

Allahabad Pillar:

• The Prayag Prashasti Pillar is considered to be erected during the time of the Mauryan empire.
• Harisena the poet in Samudraguta's Court inscribed the achievements of the ruler in this inscription.
• The inscription also applauds and praises the ruler for his conquests and is inscribed in Sanskrit.

Samudragupta:

• Samudragupta is the successor of Chandragupta-I and ruled from 335 - 380 AD.
• According to Allahabad pillar inscription, he has never faced any defeat and hence called the Napolean of India.
• He also assumed the titles of Kaviraj and Vikramanka.
• Meghvarman, the ruler of Sri Lanka was also granted permission to build a Buddhist temple at Gaya by him.
• He defeated the kings of Ganga Yamuna plains, Eastern Himalayas, Vindhyan region, Eastern Deccan and southern kingdoms and tuned them into vassalage.

Option 2 is the correct answer: The development of a fruit without fertilization is called Parthenocarpy.

• During normal fruit development, the pollens from stamen reach the stigma and then travels down to ovary where pollen and ovule combine to form an embryo.
• The embryo then grows into a zygote and then into seed and then fruit development starts.
• But when the fruit production is brought about without fertilisation (naturally or artificially), it is called Parthenocarpy.

Option 2 is the correct answer: Dr Pattahbhi Sitaramayya was the first Governor of Madhya Pradesh.

• Dr Sitaramayya was born in 1880 in Andhra Pradesh.
• He had actively participated in the Indian freedom struggle and served in the Congress Working Committee.
• He also presided the Jaipur session of INC in 1948.
• Dr Sitaramayya was one of the members of the JVP committee constituted to examine the recommendations Dhar Commission in 1952.

Option 4 is the correct option: The city of Lucknow is famous for the Chikankari Embroidery style.

• It is very intricate and delicate threadwork done on the muslin clothe originally.
• Nowadays the work is being used to decorate a wide variety of fabric.
• There are many views regarding the origin of this embroidery style:
• Some believe that it originated in Persia and was taught to Indian by a Persian trader.
• Other sources state that the art has been **mentioned in accounts of Magasthenes which date back to 3^rd **century BC, hence it originated in India only.
• Meanwhile, Noor Jahan, the queen of Jahangir is also accredited with the introduction of Chikankari to India.

The correct answer is 1878 to 1887.

Key Points

• Victoria Terminus station, Mumbai, now known as Chhatrapati Shivaji Maharaj Terminus, was built from 1878 to 1887.
• The construction of Victoria terminus was started in 1878 to establish a new railway station in the place of old Bori Bunder railway station.
• The design was prepared by British born architectural engineer Frederick William Stevens in rich Italian Gothic Style.
• The terminus was named after Queen Victoria, who completed 50 years as a monarch in 1887.
• In 1996 the terminus was renamed as Chhatrapati Shivaji terminus to honour Maratha warrior king Shivaji.
• In May 2017, the word Maharaja was also added and hence known as Chhatrapati Shivaji Maharaj Terminus.
• The terminus is the headquarters of India's Central Railway.

Additional Information

• The railways were introduced in India in 1853 during the tenure of Lord Dalhousie.
• The first railway line was laid from Bombay (now Mumbai) to Thane.
• Mumbai is also known as The City of Seven Islands.
• Bombay  was gifted by the Portuguese to King Charles II of Britain as dowry after he married Princess Catherine in1661.

The correct answer is Phylum - Cnidaria.

Key Points

• Jellyfish are actually Invertebrates (without spinal cord) and not fish.
• These free-swimming sea creatures move in the direction of ocean currents and are found in almost all parts of the oceans.
• Some of the jellyfish are immobile also and are bound to seabeds.
• Mostly the Jellyfish have an umbrella or bell-shaped body and are clearly transparent (some of them can have fascinating colors).
• They have an opening inside through which they eat their prey and discard the waste through the same opening.
• Their fossils confirm their existence in pre-dinosaurs periods also.

Additional Information  

Option 1 is the correct answer: Jhanda Satyagrah was held in the city of Nagpur.

• The Satyagrah was started in Jabalpur and concluded in the city of Nagpur.
• The tricolor was first hoisted in the townhall of Bilaspur in March 1923, under the leadership of Sunderlal.
• But after the arrest of Sunderlal, the leadership was handed over to Mahatma Bhagwandin.
• He had a popular base in Nagpur, therefore the spark shifted from Jabalpur to Nagpur.
• On April 13, the anniversary of Jallianwala Bagh Massacre a flag March was organized which was opposed by the residents of civil lines.
• After this the Satyagraha was brutally suppressed, around 17,000 people were arrested, but a few volunteers kept the non-violent Satyagrah alive.
• Finally, Satyagrah was concluded on August 17, 1923, under the leadership of Sardar Patel.

Option 3 is the correct answer: Harsh Vardhan Shringla was chosen as foreign secretary of India in January 2020.

• On January 29, 2020, Harsh Vardhan Shringla became the Foreign Secretay of India succeeding Vijay Gokhale.
• He is a 1984 batch Indian Foreign Services (IFS) officer.
• His latest posting was in USA as Indian envoy to the country.
• This Time Government has bypassed the convention of appointing the seniormost official to the post and has chosen him over Ruchi Ghanshyam Indian High Commissioner to the UK.
• The foreign secretary is the administrative head of Ministry of External Affairs and is appointed for a term of two years.
• Ranjan Mathai was appointed as foreign secretary in 2011.
• Nirupama Rao is a 1973 batch IFS officer and served as foreign secretary from 2009 to 2011.

Additional Information Vinay Mohan Kwatra is an Indian diplomat and currently 34th Foreign Secretary of India from May 2022, succeeding Harsh Vardhan Shringla.

 Previously, he has served as ambassador to France and Nepal.

Option 1 is the correct answer: Sucheta Kripalani became the first woman chief minister of Uttar Pradesh.

• Sucheta Kriplani was born on June 25, 1908.
• She joined the freedom struggle after completing her graduation and became a disciple of Gandhiji.
• In 1936 She married JB Kriplani.
• She also laid the foundation of Women's wing of Congress in 1940.
• She handled underground non-violent political activities during the freedom struggle.
• She was appointed a member of the constituent assembly in 1946.
• She sang Vande Mataram on 14^th August 1947 in the opening session of parliament.
• But due to ideological differences with Nehru, she along with her husband left congress after Independence.
• She formed a new party of her called Kisan Majdoor Praja Party and served as MP from New Delhi.
• But in 1957 she rejoined the congress and in 1963 became the Chief Minister of Uttar Pradesh till 1967.

Uttar Pradesh:

• Uttar Pradesh was earlier known as United Provinces (till 1950).
• It is the largest state in terms of population and comprises of 16.50% of the total population of India
• It ranks **4^th **in terms of area.
• Lucknow is the capital city of Uttar Pradesh.
• Yogi Adityanath and Anandiben Patel are the current Chief Minister and Governor of the state.
• According to the census of 2011**, the Literacy rate** of Uttar Pradesh is 67.68% and the sex ratio is 912/1000.

Option 1 is the correct answer: Kuldeep Yadav is the first Indian to bag two International hat-tricks in cricket.

• He made is the second Hatrick in ODIs against West Indies in December 2018.
• Kuldeep Bagged his first hattrick against Australia in 2017 at Eden Gardens.
• The other international cricketers to have double hattricks to their name are Wasim Akram, Saqlain Mushtaq, Chaminda Vaas and Trent Boult.
• Lasith Malinga is the only cricketer to have three hattricks to his name and he claimed these against Australia, Kenya and South Africa.
• Mohammad Shami, Kapil Dev and Chetan Sharma also have hattricks to their name.

The correct answer is the State Bank of India.

Key Points

• The nationalization of banks began on July 19, 1969, during the tenure of Indira Gandhi.
• The whole process took place in two phases.
• In 1969, 14 Private Sector Banks were nationalized that accounted for around 80% of the money deposited in banks.
• This major financial step was taken up to reform the lending sector and provide credit to some priority sectors like agriculture and small scale businesses.
• Then in 1980, another 6 banks were nationalized.

Key Points

 State Bank of India:

• The merger of Bank of Calcutta, Bank of Madras and Bank of Bombay in 1921 laid the foundation of Imperial Bank of India.
• In 1955 after the enactment of the State Bank of India Act Imperial Bank was renamed as State Bank of India (SBI).
• Its 60% stake was bought by RBI and SBI came under the control of the Government as Public Sector Undertaking.
• In 1969, SBI was already under the control of the government hence there was no need to nationalize it.
• Therefore, although SBI is a Public Sector Bank but is not included in the list of nationalized banks.
• Currently, SBI is headquartered in Mumbai.

*Industrial Development Bank of India (IDBI) is another Public Sector Bank that is not nationalized.

Option 2 is the correct answer: Thrissur and Thiruvalla are not the twin cities of India.

• Thrissur and Thiruvalla both cities are located in the state of Kerela.
• The word Thrissur is considered to be an anglicised form of the world Thrissivaperur which is the original name of the city.
• The word Thirisavepurar means 'Town of the Sacred Siva'.
• It was also known as 'Vrishabhadipuram' and 'Ten Kailasam'.
• Saktan Tanpuram is considered the architect of the city.
• The ancient name of Thiruvalla was 'Valla Vai' a town located on the Vallapuzha river (now Manimala).
• Cuttack-Bhubaneshwar twin city belongs to Odisha, Hubli-Dharwad to Karnataka and Ahmedabad-Gandhinagar to Gujarat.

*There is no official criteria of declaring twin cities, but the cities located close to each other that can be developed as one are called twin cities.

The correct answer is option 1: The famous physicist Georg Simon Ohm hailed from Germany.

• Ohm was born on March 16, 1789, in Erlangen, Bavaria.
• While teaching in Jesuits College he undertook the experiments on Newly discovered phenomenon of Electromagnetism.
• He observed the dependence of magnetic flux on the conductor material.
• Later in 1827, he gave a law establishing the relationship between Voltage, Electric Current and Resistance but he was severely criticized for this and was also thrown out of his job.
• But in 1841, the importance of his study was recognised and in 1849 he was offered a position of Experimental Physics Professor at the University of Munich.
• The unit of Resistance has been named after him as 'Ohm'.

 Ohm's Law:

It states that amount electric current through passing a conductor is directly proportional to the voltage across two ends of it. Following its the mathematical expression for Ohm's Law.

V = IR.

Option 3 is the correct answer: Jawara Dance from originated from Madhya Pradesh.

• Jawara Dance is also known as Harvest dance particularly practised in the Bundelkhand region of Madhya Pradesh.
• Men and women perform this dance to celebrate the wealth and happiness after the harvesting of their Jowar crop.
• Women keep the Jawara filled baskets on their heads and balance them while dancing.
• People perform this dance wearing colourful clothes and jewellery.

Madhya Pradesh:

• Madhya Pradesh is a central Indian state with its capital at Bhopal.
• It ranks 2^nd according to the area and 5^th on the basis of Population.
• Ujjain in Madhya Pradesh is known as the geographical centre of India.
• Block Mountain chains of Vindhya and Satpura flank the state.
• Madhya Pradesh is one of the 8 Indian states through which Tropic of Cancer passes.
• Narmada, Tapi and Son rivers originate from the mountain ranges of Madhya Pradesh.
• Panna National Park, Satpura Tiger Reserve, Bandhavgarh National Park and Kanha Tiger reserve are the major conservation areas in the state.

The Correct answer is option 4: Methane is commonly known as Marsh Gas.

• Methane is the hydrocarbon having the lowest molecular mass with chemical formula CH₄.
• It is called Marsh gas because it is released in huge amounts from marshes where anaerobic bacteria decompose matter.
• It was discovered by Alessandro Volta in 1776.
• It is the main constituent of Biogas and Compressed Natural Gas (CNG).
• It is a Greenhouse gas and its global warming potential is 28 - 36 times as that of CO₂.
• Paddy fields are also a huge source of Methane emissions.

Option 1 is the correct answer: The second phase of Intensified Mission Indradhanush 2.0 begins in the state of Uttar Pradesh.

Intensified Mission Indradhanush 2.0:

• This mission is based in the Intensified Mission Indradhanush which previously had its base in Mission Indradhanush.
• It aims to achieve full immunisation in all 272 identified districts in 27 states.
• This mission was to be carried out in 4 phases the first phase starting in December 2019, then continuing in January, February and March 2020.
• Salient features:
• Four rounds of activity will be conducted over 7 working days excluding holidays.
• Enhanced focus will be on the left-outs.
• Focus on the Urban and underserved tribal population will be laid.
• Interministerial coordination.
• Enhanced immunisation sessions.

Mission Indradhanush:

• It was launched in 2014 by the union government after realising the incompetence of the Universal Immunisation Programme which could achieve 65% immunisation only.
• This mission was launched to achieve full immunisation for the children up to 2 years of age and all pregnant ladies.
• 201 districts were identified in 28 states under this mission.

Intensified Mission Indradhanush:

• It was launched in October 2017 to reach out to all the children and Pregnant ladies who were left under Mission Indradhanush.
• This programme aimed to ensure full vaccination of more than 90% of the target population.
• It was also conducted in 4 rounds in 173 focus districts.

*Under the immunisation programmes in India Government provides the vaccine against Diphtheria, Pertussis, Tetanus, Polio, severe form of Tuberculosis, Hepatitis B, Meningitis and Measles free of cost. Vaccination against endemic disease like Japanese Encephalitis is also provided.

Option 2 is the correct option: Amit Shah released the book titled Karmyodha Granth.

• The book was released on January 7, 2020.
• The book is based on the life story of Honourable Prime Minister Narendra Modi.
• On the launch of this book Amit Shah while addressing the people he discussed various phases of the life of the Prime Minister.
• Mr Shah also described a man with a beating heart for people, a statesman, a hard taskmaster, an able administrator and an ideal leader as qualities of a Karmyodha.
• He also talked about the hardships that Mr Modi had to face while living in poverty.
• The achievements and the developmental activities taken up by the Prime Minister were also applauded by Amit Shah.
• He mentioned about the 13 crores free LPG connections, construction of household and public toilets, universal healthcare (Ayushman Yojana) provided to the people under the leadership of Narendra Modi.

The correct answer is option 3: Roger Federer will have a Swiss coin minted to his honour.

• The Swissmint announced to mint 20 Franc coins in honour of Roger Federer in December 2019.
• With this, he will become the only Swiss personality to have a coin minted to his honour while alive.
• Roger Federer is a Swiss Tennis Player.
• He has  20 Grandslam Titles to his name highest in the men's category.
• Serena Williams is an American Tennis player with 23 Grand slams to her name, the highest for any player of the modern era.
• Rafael Nadal a Tennis Player from Spain has won the Grandslam 20 times.
• After winning the 2021 Wimbledon title Novak Djokovic is now level with Roger Federer and Rafael Nadal in the list of most singles Grand Slam titles in men’s history.

The correct answer is Option 2: Planet Jupiter comes in between Mars and Saturn.

Option 2 is the correct answer: Red Blood Cells are produced in Bone Marrow.

Bone Marrow:

• Bone Marrow is the soft tissue present inside the Medullary cavities of a bone.
• It is mainly present in the hip and thigh bones.
• Bone marrow produces immature cells called Stem cells that can transform into various kinds of cells later on.
• Mesenchymal and Hematopoietic are the two types of stem cells produced by Bone Marrow.
• Mesenchymal transform into fat cartilage and bones whereas Hematopoietic turn into Blood cells (RBC, WBC and Platelets).

Red Blood Cells (RBC):

• ​These are also known as Erythrocytes.
• These disc-shaped cells contain Haemoglobin and have no nucleus.
• RBCs are produced in Bone Marrow and Spleen & Liver (in the foetus).
• The average lifetime of RBCs is 120 days.
• RBCs, when produced in more amount, leads to Polycythemia and if produced in lesser amount leads to Anaemia.

The correct answer is Madurai.

Key Points

• The city of Madurai is located in Tamil Nadu on the banks of River Vaigai.
• It has found mentions in the texts of Kautilya and Megasthenes dating back to the 3rd century BC.
• The ancient city has served as the capital of the Kingdom of Pandyas.
• The city was initially developed in the shape of Lotus.
• The magnificent Hindu temples are the major attractions of Madurai like Meenakshi Amman Temple, Koodal Azhagar Temple, and many more.

Additional Information

• The resemblance to Athens: Madurai is known as the Athens of East due to two features mentioned as follows:
• In Athens, there is the Greek Pantheon an elevated top that is visible from anywhere in the city. Similarly, the Gopurams of the Meenakshi Sundareswarar temple are visible from anywhere.
• Another feature is the walkways that favor pedestrians inside the city. The two-way lanes for vehicular traffic are mostly located on the outskirts of the city.
• But with time, the visibility of gopurams has been affected by the high-rising buildings and the pedestrian walkways by increased traffic.

Shortcut Trick

Put θ = 0° as the expression is independent of θ.

tan 0° = 0 and sec 0° = 1

Expression = 3(1)²(0)² + (0)⁶ − (1)⁶

⇒ 0 + 0 − 1 = −1

∴ The correct answer is −1.

Alternate Method

Given: 3 sec² θ tan² θ + tan⁶ θ − sec⁶ θ

Formula Used: (a − b)³ = a³ − b³ − 3a²b + 3ab² = a³ − b³ − 3ab(a − b)

⇒ We know that sec² θ − tan² θ = 1

⇒ Cubing both sides: (sec² θ − tan² θ)³ = 1³

⇒ (sec² θ)³ − (tan² θ)³ − 3 sec² θ tan² θ (sec² θ − tan² θ) = 1

⇒ sec⁶ θ − tan⁶ θ − 3 sec² θ tan² θ (1) = 1

⇒ sec⁶ θ − tan⁶ θ − 3 sec² θ tan² θ = 1

⇒ Multiply the entire equation by −1:

⇒ −sec⁶ θ + tan⁶ θ + 3 sec² θ tan² θ = −1

∴ The correct answer is −1.

Additional Information

Trigonometric Identities

Standard Pythagorean identities: sin²θ + cos²θ = 1; 1 + tan²θ = sec²θ; 1 + cot²θ = cosec²θ.

Value Substitution Method

For expressions independent of the angle, substituting standard angles like 0°, 45°, or 90° (where defined) provides the fastest solution.

Algebraic Expansion

Expansion of (x − y)³ as x³ − y³ − 3xy(x − y) is frequently used in higher-power trigonometric simplifications.

As we know,

a³ + b³ + c³ – 3abc = (a + b + c) [(a + b + c)² – 3 (ab + bc + ca)]

⇒ a³ + b³ + c³ – 3abc = 7 [7² – 3 (–6)] = 7 [49 + 18] = 7 × 67 = 469

Given,

PB = 4.2 cm and AB = 7 cm

AP = 4.2 + 7 = 11.2

PD = 2.8 cm and Let CD = x.

PC = 2.8 + x

As we know,

AP × PB = PC × PD

11.2 × 4.2 = 2.8 × (x + 2.8)

⇒ x + 2.8 = (11.2 × 4.2)/2.8

⇒ x + 2.8 = 16.8

⇒ x = 16.8 – 2.8

⇒ x = 14 cm

Radius of cylindrical vessel r = 30 cm

Height of cylindrical vessel h = 42 cm

Length of rectangular tub L = 75 cm

Breadth of rectangular tub B = 44 cm

Le the height of the rectangular tub be H cm

As we know,

Volume of cylindrical vessel = πr²h

The volume of rectangular tub = L × B × H

According to the question

75 × 44 × H = (22/7) × 30 × 30 × 42

⇒ H = (22 × 30 × 30 × 6)/(75 × 44)

⇒ H = 36

P × Q ÷ R

$\frac{{{x^4} - 8x}}{{{x^3} - {x^2} - 2x}} \times \frac{{{x^2} + 2x + 1}}{{{x^2} - 4x - 5}} \div \frac{{2{x^2} + 4x + 8}}{{x - 5}}$

$\Rightarrow \frac{{x({x^3} - {2^3})}}{{x({x^2} - x - 2)}} \times \frac{{{x^2} + 2x + 1}}{{{x^2} - 4x - 5}} \times \frac{{\left( {x - 5} \right)}}{{2({x^2} + 2x + 4)}}$

$\Rightarrow \frac{{x\left( {x - 2} \right)\left( {{x^2} + 4 + 2x} \right)}}{{x({x^2} - 2x + x - 2)}} \times \frac{{{x^2} + 2 \times {\rm{x}} \times 1 + {1^2}}}{{{x^2} - 5x + x - 5}} \times \frac{{\left( {x - 5} \right)}}{{2({x^2} + 2x + 4)}}$

$\Rightarrow \frac{{\left( {x - 2} \right)\left( {{x^2} + 4 + 2x} \right)}}{{x\left( {x - 2} \right) + 1\left( {x - 2} \right)}} \times \frac{{{{\left( {x + 1} \right)}^2}}}{{x\left( {x - 5} \right) + 1\left( {x - 5} \right)}} \times \frac{{\left( {x - 5} \right)}}{{2({x^2} + 2x + 4)}}$

$\Rightarrow \frac{{\left( {x - 2} \right)}}{{\left( {x - 2} \right)\left( {x + 1} \right)}} \times \frac{{{{\left( {x + 1} \right)}^2}}}{{\left( {x - 5} \right)\left( {x + 1} \right)}} \times \frac{{\left( {x - 5} \right)}}{2}$

⇒ 1/2

Let the income of B be Rs. 5x

income of A is 60% less than that of B

(100 - 60)/100 = 2/5

Income of A = 5x × (2/5) = Rs. 2x  

Let the expenditure of B be Rs. 5y

expenditure of A is equal to 60% of B’s expenditure

60/100 = 3/5

Expenditure of A = 5y × (3/5) = 3y

According to the question

2x = 5y × (70/100)

⇒ 2x = y × (7/2)

⇒ 4x = 7y

⇒ x : y = 7 : 4

Savings of A = 2x – 3y = 2 × 7 – 3 × 4 = 14 – 12 = 2

Savings of B = 5x – 5y = 5 (7 – 4) = 5 × 3 = 15

∴ Ratio of savings A to B = 2 : 15

Given:

QR : ST = 9 : 5, PQ = 21.6 cm,

∠Q = 85°, ∠R = 65 and ∠STR = 95°

Concept Used:

Two triangles are similar if the measure of two angles is the same and vice-versa.

Calculation:

From the following figure

ΔPTS ∼ PQR

⇒ QR/TS = PQ/PT

⇒ 9/5 = 21.6/PT

⇒ PT = (21.6 × 5)/9

⇒ PT = 12 cm

∴ The length of PT is 12 cm.

MP of the article = Rs. 740

After getting 15% discount the first SP of the article = 740 × (85/100) = 629

Second SP of the article = Rs. 566.10

Second discount = 629 – 566.10 = 62.9

∴ Second discount percentage = (62.9/629) × 100 = 10%

30x² – 15 x + 1 = 0

Divide by 6x

5x – 15/6 + 1/6x = 0

⇒ 5x + 1/6x = 5/2

Squaring on both sides

(5x + 1/6x)² = (5/2)²

⇒ 25x² + 1/36x² + 2 × 5x × 1/6x = 25/4

⇒ 25x² + 1/36x² + 5/3 = 25/4

⇒ 25x² + 1/36x² = 25/4 – 5/3

⇒ 25x² + 1/36x² = 55/12

The ratio of boys and girls in a group is = 7x : 6x

According to the question

(7x + 4)/(6x – 3) = 4/3

⇒ 3 (7x + 4) = 4 (6x – 3)

⇒ 21x + 12 = 24x – 12

⇒ 24x – 21x = 12 + 12

⇒ 3x = 24

⇒ x = 24/3 = 8

∴ Number of boys and girls in the group were = 7x + 6x = 13x = 13 × 8 = 104

In ΔCAE

CF/CE = CD/AC

CD/AC = 2.5/6 = 25/60

⇒ CD/AC = 5/12      ------ 1)

Let CF = 5x and CE = 12x

In ΔCAB,

CE/BC = CD/AC

CD/AC = 6/BC      ------ 2)

From equation (1) and equation (2)

6/BC = 5/12

⇒ BC = (12 × 6)/5

⇒ BC = 72/5

⇒ BC = 14.4

Total revenue from the sale of products A, B and D in 2012 and 2013 = 98 + 74 + 74 + 94 + 96 + 102 = 538

Total revenue from the sale of products B in 2013 to 2016 = 96 + 92 + 84 + 98 = 370

Required percentage = (538 – 370)/370 × 100 = 45.4%

Total revenue of the company in 2014 from the sale of all the four products = 80 + 92 + 96 + 92 = 360

Total revenue from the sale of product C in 2014 to 2017 = 96 + 88 + 93 + 103 = 380

∴ Required ratio = 360 : 380 = 18 : 19

According to the question

1/(8 + d) + 1/(18 + d) = 1/d

⇒ (18 + d + 8 + d)/(144 + 26d + d²) = 1/d

⇒ 144 + 26d + d² = 26d + 2d²

⇒ d² = 144

⇒ d = √144

⇒ d = 12 days

A and B together, can complete the whole work = 12 days

A alone can complete the whole work in = 12 + 8 = 20 days

B alone can complete the whole work in = 12 + 18 = 30 days.

Let the remaining work B complete in x days, then

According to the question

4/20 + x/30 = 1

⇒ x/30 = 1 – 1/5

⇒ x/30 = 4/5

⇒ x = 24 days

Shortcut Trick

D = √(8 × 18)

⇒ D = 12

A and B together, can complete the whole work = 12 days

A alone can complete the whole work in = 12 + 8 = 20 days

B alone can complete the whole work in = 12 + 18 = 30 days.

Total work = 60

Work done by A in 4 days = 4 × 3 = 12

Remaining work = 60 – 12 = 48

∴ Remaining work, B complete in = 48/2 = 24 days

Concept used:

Divisibility law of 11: If the difference of the alternating sum of digits of the number is a multiple of 11 (e.g. 2343 is divisible by 11 because 2 – 3 + 4 – 3 = 0, which is a multiple of 11).

Divisibility law of 8 ⇒ A number is divisible by 8 if the number formed by its last three digits is divisible by 8

Divisibility law of 9 ⇒ A number is divisible by 9 if the sum of its digits is divisible by 9.

Calculation:

The 6–digit numbers x35624 is divisible by 11, then

⇒ x – 3 + 5 – 6 + 2 – 4 = 0

⇒ x + 7 – 13 = 0

⇒ x = 6

The 6–digit number 1257y4 is divisible by 72, so we can say that the number is also divisible by 8 and 9, then

⇒ 1 + 2 + 5 + 7 + y + 4

⇒ 19 + y

If we put y = 8, then the number becomes 27 which is divisible by 9.

⇒ 5x – 2y

⇒ 5 × 6 – 2 × 8

⇒ 30 – 16

⇒ 14

The answer is 14.

$\frac{{5\frac{1}{2} \div 3\frac{2}{3};of\frac{1}{4} + \left( {5\frac{1}{9} - 7\frac{7}{8} \div 9\frac{9}{{20}}} \right) \times \frac{9}{{11}}}}{{5 \div 5;of;\frac{1}{{10}} - 10 \times 10 \div 20}}$

$\Rightarrow \frac{{\frac{{11}}{2} \div \frac{{11}}{3}; \times \frac{1}{4} + \left( {\frac{{46}}{9} - \frac{{63}}{8} \div \frac{{189}}{{20}}} \right) \times \frac{9}{{11}}}}{{5 \div 5; \times ;\frac{1}{{10}} - 10 \times \frac{1}{2}}}$

$\Rightarrow \frac{{\frac{{11}}{2} \div \frac{{11}}{{12}} + \left( {\frac{{46}}{9} - \frac{{63}}{8} \times \frac{{20}}{{189}}} \right) \times \frac{9}{{11}}}}{{5 \div \frac{1}{2} - 5}}$

$\Rightarrow \frac{{\frac{{11}}{2} \times \frac{{12}}{{11}} + \left( {\frac{{46}}{9} - \frac{5}{6}} \right) \times \frac{9}{{11}}}}{{5 \times 2 - 5}}$

$\Rightarrow \frac{{6 + \left( {\frac{{92 - 15}}{{18}}} \right) \times \frac{9}{{11}}}}{{10 - 5}}$

$\Rightarrow \frac{{6 + \frac{{77}}{{18}} \times \frac{9}{{11}}}}{5}$

$\Rightarrow \frac{{6 + \frac{7}{2}}}{5}$

$\Rightarrow \frac{{\frac{{19}}{2}}}{5}$

$\Rightarrow \frac{{19}}{{10}}$

$\Rightarrow 1\frac{9}{{10}}$

∠QRP = 28°

As we know,

∠ORP = 90° [tangents at R]

⇒ ∠ORQ = ∠ORP – ∠QRP = 90° – 28° = 62°

⇒ ∠OQR = ∠ORQ = 62° [OQ = OR = radius]

As we know,

∠OQR = ∠ QRP + ∠QPR

⇒ 62 = 28 + ∠QPR

⇒ ∠QPR = 62 – 28 = 34

⇒ ∠SPR = ∠QPR = 34

Total revenue of the company from the sale of products B, C and D in 2014 = 92 + 96 + 92 = 280

Total revenue of the company from the sale of products C and D in 6 years = 82 + 98 + 96 + 88 + 93 + 103 + 74 + 102 + 92 + 93 + 97 + 102 = 1120

There are 2 years in which the revenue of the company from the sale of product D is more than the average revenue from the sale of product A over six years.

∴ Required Percentage = (280/1120) × 100 = 25%

Given:

One–third of goods are sold at a 15% profit

25% of the goods are sold at a 20% profit

The rest at a 20% loss

Concept used:

Profit from each part = quantity × profit percentage

Calculation:

Let the total number of articles be 120.

Let the cost price of 120 articles be 120 unit

1/3^rd of 120 = 40 and 1/4^th of 120 = 30 and Rest = 120 – 40 – 30 = 50

Total profit = 40 × (15/100) + 30 × (20/100) – 50 × (20/100) = 6 + 6 – 10 = 2 unit

2 unit = 138.50

⇒ 1 unit = 69.25

⇒ 120 unit = 69.25 × 120 = Rs. 8310

Shortcut Trick

Difference in effective interest rate for 1 year = (5 × 5) / 100 = 0.25%.

0.25% of Sum = Rs. 88.80 ⇒ 100% of Sum (Principal) = 88.80 × 400 = Rs. 35,520.

Simple Interest for 1²/₃ (or 5/3) years = (35,520 × 10 × 5/3) / 100.

Required SI = 35,520 ÷ 6 = Rs. 5,920.

∴ The correct answer is Rs. 5,920.

Alternate Method

Given: Rate (R) = 10% p.a., Time (T) = 1 year, Difference in CI = Rs. 88.80.

Formula Used: CI = P[(1 + r/n)^nt − 1]; SI = (P × R × T) / 100.

⇒ Case 1 (Yearly): CI₁ = P × 10% = 0.10P

⇒ Case 2 (Half-yearly): Rate = 5%, Periods = 2; CI₂ = P[(1 + 0.05)² − 1] = 0.1025P

⇒ Difference = 0.1025P − 0.10P = 0.0025P

⇒ 0.0025P = 88.80 ⇒ P = 88.80 / 0.0025 = 35,520

⇒ For SI: T = 5/3 years, R = 10%

⇒ SI = (35,520 × 10 × 5/3) ÷ 100 = 35,520 × 50 ÷ 300

⇒ SI = 35,520 ÷ 6 = 5,920

∴ The correct answer is Rs. 5,920.

Additional Information

Half-Yearly Compounding

When interest is compounded half-yearly, the annual rate is divided by 2 (R' = R/2) and the time is multiplied by 2 (n = 2T).

Difference for Two Periods

The difference between CI and SI for two periods is given by P × (R/100)², where R is the rate per period.

Effective Rate Method

For two successive changes of a% and b%, the effective change is (a + b + ab/100)%. This is useful for Compound Interest calculations.

Let the total students in the class be x, then

Average weight of x students in the class = 58.4

Sum of weight of x students in the class = 58.4x

Average weight of 5 students = 62.8 kg

Sum of weight of 5 students = 62.8 × 5 = 314

According to the question

58.4x + 314 = (x + 5) (58.4 + 0.55)

⇒ 58.4x + 314 = (x + 5) 58.95

⇒ 58.4x + 314 = 58.95x + 294.75

⇒ 58.95x – 58.4x = 314 – 294.75

⇒ 0.55x = 19.25

⇒ x = 19.25/0.55

⇒ x = 35

Short Trick:

Let total number of students be x after joining 5 students, then

0.55x = 5 (62.8 – 58.4)

⇒ x = (5 × 4.4)/0.55

⇒ x = 40

∴ Number of students in the class were = 40 – 5 = 35

Speed of the stream = 3 km/hr

Let speed of the boat be x km/hr

As we know,

Time = Distance/Speed

According to the question

13/(x + 3) = 7/(x – 3)

⇒ 13 (x – 3) = 7 (x + 3)

⇒ 13x – 39 = 7x + 21

⇒ 13x – 7x = 21 + 39

⇒ 6x = 60

⇒ x = 60/6 = 10

So, speed of boat = 10 km/hr

∴ Time taken to cover 44.8 km distance in still water = 44.8/10 = $4\frac{{12}}{{25}}$

Total revenue of sale from product A over six year = 98 + 94 + 80 + 95 + 110 + 115 = 592

Average revenue of sale from product A over six year = 592/6 = 98.66

There are 2 years 2013 and 2017 in which the revenue of the company from the sale of product D is more than the average revenue from the sale of product A over six years.

Short Trick:

$\frac{{{{\tan }^2}\theta - {{\sin }^2}\theta }}{{2 + {{\tan }^2}\theta + {{\cot }^2}\theta }}$

⇒ Put θ = 45

$\Rightarrow \frac{{{{\tan }^2}45 - {{\sin }^2}45}}{{2 + {{\tan }^2}45 + {{\cot }^2}45}}$

$\Rightarrow \frac{{1 - \frac{1}{2}}}{{2 + 1 + 1}}$

⇒ (1/2)/4

⇒ 1/8

From option 2.

sin⁶ θ

⇒ sin⁶ 45

⇒ (1/√2)²

⇒ 1/8

Detailed Method:

$\frac{{{{\tan }^2}\theta - {{\sin }^2}\theta }}{{2 + {{\tan }^2}\theta + {{\cot }^2}\theta }}$

$\Rightarrow \frac{{\frac{{{{\sin }^2}{\rm{\theta }}}}{{{{\cos }^2}{\rm{\theta }}}} - {{\sin }^2}\theta }}{{2 + \frac{{{{\sin }^2}{\rm{\theta }}}}{{{{\cos }^2}{\rm{\theta }}}} + \frac{{{{\cos }^2}{\rm{\theta }}}}{{{{\sin }^2}{\rm{\theta }}}}}}$

$\Rightarrow \frac{{si{n^2}{\rm{\theta }}\left[ {\frac{1}{{{\rm{co}}{{\rm{s}}^2}{\rm{\theta }}}} - {\rm{;}}1} \right]}}{{2 + \frac{{si{n^4}{\rm{\theta }} + {\rm{co}}{{\rm{s}}^4}{\rm{\theta }}}}{{si{n^2}{\rm{\theta }}co{s^2}{\rm{\theta }}}}}}$

$\Rightarrow \frac{{si{n^2}{\rm{\theta }}\left[ {\frac{{1 - {\rm{co}}{{\rm{s}}^2}{\rm{\theta }}}}{{{\rm{co}}{{\rm{s}}^2}{\rm{\theta }}}}} \right]}}{{\frac{{2si{n^2}{\rm{\theta }}co{s^2}{\rm{\theta }} + si{n^4}{\rm{\theta }} + {\rm{co}}{{\rm{s}}^4}{\rm{\theta }}}}{{si{n^2}{\rm{\theta }}co{s^2}{\rm{\theta }}}}}}$

$\Rightarrow \frac{{si{n^2}{\rm{\theta si}}{{\rm{n}}^2}{\rm{\theta }} \times \frac{1}{{{\rm{co}}{{\rm{s}}^2}{\rm{\theta }}}}}}{{\frac{{{{\left( {si{n^2}{\rm{\theta }} + {\rm{co}}{{\rm{s}}^2}{\rm{\theta }}} \right)}^2}}}{{si{n^2}{\rm{\theta }}co{s^2}{\rm{\theta }}}}}}$

$\Rightarrow \frac{{si{n^4}{\rm{\theta }} \times \frac{1}{{{\rm{co}}{{\rm{s}}^2}{\rm{\theta }}}}}}{{\frac{1}{{si{n^2}{\rm{\theta }}co{s^2}{\rm{\theta }}}}}}$

⇒ sin⁴θ × (1/cos²θ) × sin²θ cos²θ

⇒ sin⁶ θ

7 sin² θ – cos² θ + 2 sin θ = 2

⇒ 7 sin² θ – (1 – sin² θ) + 2 sin θ = 2

⇒ 7 sin² θ – 1 + sin² θ + 2 sin θ = 2

⇒ 8 sin² θ + 2 sin θ – 3 = 0

⇒ 8 sin² θ + 6 sin θ – 4 sin θ – 3 =0

⇒ 2sin θ (4sin θ + 3) – 1 (4sin θ – 3) = 0

⇒ (2sin θ – 1) (4sin θ + 3) = 0

Taking,

2 sin θ – 1 = 0

⇒ sin θ = 1/2

⇒ sin θ = sin 30

⇒ θ = 30

Now,

$\frac{{\sec 2\theta + \cot 2\theta }}{{cosec;2;\theta + \tan 2\theta }}$

$\Rightarrow \frac{{\sec 60 + \cot 60}}{{cosec;60 + \tan 60}}$

$\Rightarrow \frac{{2 + \frac{1}{{\sqrt 3 }}}}{{\frac{2}{{\sqrt 3 }} + \sqrt 3 {\rm{;}}}}$

$\Rightarrow \frac{{\frac{{2\sqrt 3 {\rm{;}} + {\rm{;}}1}}{{\sqrt 3 }}}}{{\frac{{2 + 3}}{{\sqrt 3 }}{\rm{;}}}}$

$\Rightarrow \frac{{2\sqrt 3 {\rm{;}} + {\rm{;}}1}}{5}$

Short Trick:

7 sin² θ – cos² θ + 2 sin θ = 2

Put θ = 30 and satisfied, then

$\Rightarrow \frac{{\sec 60 + \cot 60}}{{cosec;60 + \tan 60}}$

$\Rightarrow \frac{{2 + \frac{1}{{\sqrt 3 }}}}{{\frac{2}{{\sqrt 3 }} + \sqrt 3 {\rm{;}}}}$

$\Rightarrow \frac{{\frac{{2\sqrt 3 {\rm{;}} + {\rm{;}}1}}{{\sqrt 3 }}}}{{\frac{{2 + 3}}{{\sqrt 3 }}{\rm{;}}}}$

$\Rightarrow \frac{{2\sqrt 3 {\rm{;}} + {\rm{;}}1}}{5}$