The logic is:

Row 1: (11 + 2) = 13; (13 + 4) = 17

Row 2: (33 + 2) = 35; (35 + 4) = 39

Similarly,

Row 3: (189 + 2) = 191; (191 + 4) = 195

Hence, ‘195’ is the correct answer.

All options except ‘Russia’ are the name of Continents, while Russia is a Country.

Hence, ‘Russia’ is the odd one out.

Hence, ‘T’ is the correct answer.

Note: The letters are reversed first and then the sum of all the reverse letters is multiplied by the number of letters in each word.

Similarly,

 Hence, ‘528’ is the correct answer.

Given series: 45, 63, 101, 160, 241, ?

The logic is:

Hence, ‘345’ is the correct answer.

The paper when unfolded, will appear as shown below:

Hence, option 3 is the correct answer.

Similarly,

Hence, ‘LNNPBDJL’ is the correct answer.

The relation is:

‘Family’ is related to ‘Upbringing’ → A family is responsible for the good or bad upbringing of a child.

Similarly,

‘School’ is related to ‘______’ → A school is responsible for the education of a child.

Hence, ‘education’ is the correct answer.

The family tree diagram is shown below:

Rajeev said, “Her daughter’s father’s wife’s mother is my wife’s daughter’s mother’s mother-in-law.

Her daughter's father → Akansha's husband

Her daughter’s father’s wife → Akansha 

Her daughter’s father’s wife’s mother → Akansha's mother

my wife’s daughter’s → Rajeev's daughter

my wife’s daughter’s mother’s  → Rajeev's wife

my wife’s daughter’s mother’s mother-in-law.→ Rajeev's mother

Now, Rajeev's mother is Akansha's mother,

It means Rajeev and Akansha are siblings.

Hence, Rajiv is the brother of Akansha.

Note: Multiple of 400 years i.e. 800, 1200, 1600, 2000 have 0 odd days.

Calculating leap year: For Finding the number of leap year (1 - 99) years, divide the number of years by 4 and the quotient will be the number of leap years.

Code for weekdays:

Code for Month:

:2008 = we find out the odd days (the nearest leap century year + the nearest century year + completing year) = 2000 + 7 year + year 2008

• In 2000 year the odd days = 0 odd day
• In 7 years, odd days = 1 leap year & 6 normal year
• 1 leap year = 2 odd day
• 6 normal year = 6 odd day
• Odd days in 1 January to 5 February :
• In 2008, the number of days up to 5 February = 31 (Jan) + 5 (Feb) = 36 days = 1 odd day.
• Total = 0 + 2 + 6 + 1 = 9 days = 2 odd days
• 2 is the code for Tuesday.

​Hence, the correct answer is "Tuesday".

Alternate Method

5 February 2008 = (2007 years + Period from 1.1.2008 to 5.2.2008)

Odd days in 1600 years = 0

Odd days in 400 years = 0

7 years = (6 ordinary years + 1 leap year) = (6 × 1 + 1 × 2) = 8 odd days

31 jan + 5 feb = 36 days

=> 36 days = 5 weeks and 1 day = 1 odd day

Total number of odd days = 0 + 0 + 8 + 1 = 9 days

9 when divided by 7, we get 2 as remainder.

‘2’ is the code for Tuesday.

So, it was Tuesday on 5 February 2008.

Hence, ‘Tuesday’ is the correct answer.

The logic is:

23 : 527 → 23 : 23² – 2

Similarly,

19 : ?  → 19 : 19² – 2

=> ? = 361 – 2

=> ? = 359

Hence, ‘359’ is the correct answer.

The logic is:

(14, 17, 961) → 14, 17, (14 + 17)²

1. (13, 19, 1024) → 13, 19, (13 + 19)² = 1024

2. (12, 18, 851) → 12, 18, (12 + 18)² ≠ 851

3. (15, 14, 743) → 15, 14, (15 + 14)² ≠ 743

4. (11, 12, 729) → 11, 12, (11 + 12)² ≠ 729

Hence, ‘(13, 19, 1024)’ is the correct answer.

The venn diagram that best represents the relationship between the classes Utensils, Spoons, Steel items is shown below:

All spoons are utensils, and some spoons and utensils are steel items.

Hence, option 2 is the correct answer.

The logic is:

Hence, ‘QTRKWKSS’ is the correct answer.

Given expression: 43C 29B 3A 14B (5C4)C 11C (14A 3)A 64 D 8 B2

After interchanging the letters, we get:

43C 29B 3A 14B (5C4) C 11C (14A 3)A 64 D 8 B2

= 43 + 29 × 3 – 14 × (5 + 4) + 11 + (14 – 3) – 64 ÷ 8 × 2

= 43 + 87 – 14 × 9 + 11 + 11 – 8 × 2

= 43 + 87 – 126 + 22 – 16

= 152 – 142

= 10

Hence, ‘10’ is the correct answer.

The logic is:

The logic is here:

square of the place value of 1st letter → 2nd letter.

The place value of 1st letter + 3 → 3rd letter.

1. DPG

D = 4.

⇒ 4² = 16 = P = 2nd letter.

⇒ 4 + 3 = 7 = G = 3rd letter.

2. EYH

E = 5

⇒ 52 = 25 = Y = 2nd letter.

⇒ 5 + 3 = 8 = H = 3rd letter.

3. BFF
   

B = 2

⇒ 22 = 4 = D ≠ 2nd letter.

⇒ 2 + 3 = 5 = E ≠ 3rd letter.

4. CIF
   

C = 3

⇒ 32 = 9 = I = 2nd letter.

⇒ 3 + 3 = 6 = F = 3rd letter.

Hence, ‘BFF’ is the odd one out.

The option figure in which the given figure is embedded is option ‘2’.

Hence, option ‘2’ is the correct answer.

The logic is:

1. 55 : 25 → 55 : (5 × 5) = 25

2. 44 : 16 → 44 : (4 × 4) = 16

3. 76 : 42 → 76 : (7 × 6) = 42

4. 28 : 56 → 28 : (2 × 8) ≠ 56

Hence, ‘28 : 56’ is the correct answer.

The number of triangles in the figure is shown below:

Hence, ‘22’ is the correct answer.

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

Hence, option 1 is the correct answer.

Part of a body from head to toe is arranged serially.

So the correct order is:

2. Forehead
3. Nose
4. Chin
5. Chest
6. Waist

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

The relation is:

Arteries : Circulatory system

Arteries – vessel that carries blood high in oxygen content away from the heart to the farthest reaches of the body. Since blood in arteries is usually full of oxygen, the haemoglobin in the red blood cells is oxygenated.

Circulatory system – The system that circulates blood and lymph through the body, consisting of the heart, blood vessels, blood, lymph, and the lymphatic vessels and glands. 

So, the relation is that arteries forms the Circulatory system of our body.

1. Kidney : Respiratory system

Kidney – The kidneys are two bean-shaped organs in the renal system. They help the body pass waste as urine. They also help filter blood before sending it back to the heart, creating hormones that help produce red blood cells, promote bone health, and regulate blood pressure.

Respiratory system – The human respiratory system is a series of organs responsible for taking in oxygen and expelling carbon dioxide. The primary organs of the respiratory system are the lungs, which carry out this exchange of gases as we breathe.

The kidneys forms the excretory system of our body and not the Respiratory system.

2. Eyes : Endocrine system  

Eyes – Eyes are organs of the visual system. They provide animals with vision, the ability to receive and process visual detail, as well as enabling several photo response functions that are independent of vision. Eyes detect light and convert it into electro-chemical impulses in neurons.

Endocrine system - The endocrine system is the collection of glands that produce hormones that regulate metabolism, growth and development, tissue function, sexual function, reproduction, sleep, and mood, among other things.

Eyes belong to the sensory system and not the endocrine system.

3. Lungs : Olfactory system

Lungs – The lungs are a pair of spongy, air-filled organs located on either side of the chest (thorax). The trachea (windpipe) conducts inhaled air into the lungs through its tubular branches, called bronchi. The lungs are covered by a thin tissue layer called the pleura.

Olfactory system – The olfactory system, or sense of smell, is the sensory system used for smelling (olfaction). Olfaction is one of the special senses, that have directly associated specific organs. Most mammals and reptiles have a main olfactory system and an accessory olfactory system.

Lungs are related to respiratory system, and not olfactory system.

4. Nerves : Nervous system

Nerves – Bundles of fibres or axons, in the peripheral nervous system are called nerves, and bundles of afferent fibers are known as sensory nerves. An efferent nerve fiber conducts signals from a motor neuron in the central nervous system to muscles.

Nervous system – The nervous system is a highly complex part of an animal that coordinates its actions and sensory information by transmitting signals to and from different parts of its body. The nervous system detects environmental changes that impact the body, then works in tandem with the endocrine system to respond to such events.

The nerves forms the nervous system.

Hence, ‘Nerves : Nervous system’ is the correct answer.

When the box will be constructed, the following symbols will be opposite to each other as shown below:

1. and @ → Yes

2. @ and % → No

3. & and % → No

4. $ and + → No

So, when the box will be constructed, the symbols ‘# and @’ will be opposite to each other.

Hence, ‘# and @’ is the correct answer.

Concept:

1. We have to check the conclusions are 100% match with the statement. If the conclusion is 100% match with the given statement then the conclusion is true. If there is a 1% chance of not following the statement then the conclusion is considered to be false.

2. The possibility case can be considered to be "false" in "definite case".

3. In Possibility case, either "can" or "possible" word must be present.

The least possible venn diagram is:

I. Some bowls are bottles. → False (It can be possible, but it is not definite)

II. Some glasses are bottles → True (It is definite)

III. No bowl is a bottle → False (It can be possible, but it is not definite)

Conclusion I and III forms a complementary pair.

Hence, only Conclusions II and either Conclusion I or III follow.

Note: 

Conditions of Either-or case:

1. The elements should be the same in both the statements.
2. Individually both the conclusions should be false.
3. One conclusion should be positive and one conclusion should be negative (Complementary pair)

The two complementary pairs are:

1. All + Some not

2. No + Some

Additional Information

Given series:

As we move one step forward in the series, we see that vertical lines are increasing by one and horizontal lines are decreasing by one.

So, in the ‘?’ figure, there will be 5 vertical lines and 1 horizontal line, as shown in option 1.

Hence, option 1 is the correct answer.

Sharad Arvind Bobde was appointed Chief Justice of India with effect from 18 November 2019.

• He is serving as the 47th Chief Justice of India.
• He is a former Chief Justice of the High Court of Madhya Pradesh.
• He was a member of the five-court Constitutional Court, which heard and issued a judgment dated 9 November 2019 on the land dispute case of Ram Janmabhoomi-Babri Masjid.
• Ranjan Gogoi was the 46th Chief Justice of India.
• Ashok Bhushan was the 31st Chief Justice of the Kerala High Court.
• Dipak Misra was the 45th Chief Justice of India.

Important Points

• Justice Uday Umesh Lalit is the current and 49th Chief Justice of India (CJI).
• He succeeded Justice N V Ramana, who retired on 26 August 2022.

Recently (in Oct 2022) D Y Chandrachud has been Appointed as the 50th Chief Justice Of India.

Muvendavelan was NOT a type of sacrifice performed by kings in ancient India to establish their position.

• Muvendavelan was a famous military officer of the Chola Empire, known for his generous donation to the numerous temples where he had been deployed by the king.
• The Rajasuya is connected with the consecration of the King and is prescribed as a way of maintaining the king's sovereignty.
• It involves a game of throwing dice, in which the king is enthroned and the world is regenerated.
• Vajapeya Yagna has been performed to preserve peace in the state. It's the highest form of Soma Yajna.
• Ashvamedha Yagna was performed by the King for fertility and strength in the kingdom.
• It is a rite of horse sacrifice accompanied by the practice of the Vedic religion of the Shrauta. This has been used by ancient Indian kings to assert their colonial supremacy.

As of January 2020, Uttar Pradesh has the maximum number of seats in the Rajya Sabha.

• The Legislative Assembly of Uttar Pradesh consists of 403 members elected and one nominated Anglo-Indian member for a term of five years.
• The State shall contribute 80 seats to the lower house of the Indian Parliament, Lok Sabha and 31 seats to the upper house of the Indian Parliament, Rajya Sabha.
• Maharashtra has 19 seats in the Rajya Sabha.
• Tamil Nadu has 18 seats in the Rajya Sabha.
• Karnataka has 12 seats in the Rajya Sabha.

In January 2020, China tested the world’s first high-speed driverless bullet train between Beijing and Zhangjiakou.

• It is capable of achieving a peak speed of up to 217 mph (350kph), making it the fastest autonomous train in service in the world.
• Launched in the context of the Beijing 2022 Winter Olympic and Paralympic Games, it will minimize travel time between the capital and Zhangjiakou.
• The first Beijing-Zhangjiakou line was opened in 1909 when the same journey lasted about eight hours.
• China's extensive high-speed rail network stretches nearly 22,000 miles and features the fastest train in commercial service, the Shanghai Maglev, capable of achieving a speed of 268 mph.

Article 244(1) of the Constitution of India deals with provisions related to the administration and control of Scheduled Areas and Scheduled Tribes.

• The provisions of the Fifth Schedule shall extend to the administration and control of the Scheduled Areas and of the Scheduled Tribes in every State other than Assam, Meghalaya, Tripura, and Mizoram.
• Article 244(2) provisions of the Sixth Schedule shall extend to the administration and control of tribal areas of Meghalaya, Tripura, Assam, and Mizoram.
• According to Article 222(1), The President can, after consulting the Chief Justice of India, move a Judge from one High Court to any other High Court.
• According to Article 222(2), When a judge has been or has been moved, he or she shall, for the time of which he or she serves, since the beginning of the Constitution Act (Fifteenth Amendment) of 1963.

The spice, cinnamon, is native to Sri Lanka.

• Cinnamon is a spice produced from the inner bark of many varieties of trees in the genus Cinnamomum.
• It is used primarily as an aromatic condiment and flavouring ingredient in a wide variety of desserts, sweet and savoury desserts, breakfast cereals, snack foods, tea, and traditional foods.
• Indonesia and China produced 75% of the world's cinnamon supply in 2016.
• Four countries accounted for 99% of the world as a whole in 2017: Indonesia, China, Vietnam and Sri Lanka.

Kartar Singh Sarabha was executed at Lahore in November 1915 for his role in the Ghadar Conspiracy in February 1915.

• He was a communist leader, one of the most prominent and reputed martyrs of Punjab.
• He was 15 years old when he became a member of the Ghadar Party, then he emerged as a leading luminary leader and started to struggle for independence.
• The Ghadar Party's goal was to get rid of British slavery through armed struggle.
• On 1 November 1913, the Ghadar Party started printing a paper called Ghadar.
• Bhagat Singh was influenced by him.

The correct answer is Blood.

Key Points

• It is an intense unreasonable fear of blood, a particular form of phobia.
• Serious cases of this fear can trigger physical reactions that are uncommon in most other fears, specifically vasovagal syncope (fainting).
• It is frequently triggered by direct or vicariate trauma in childhood or adolescence.

The Jungle Book is NOT authored by R.K. Narayan.

• It is a collection of stories written by Rudyard Kipling in 1894.
• In 2016, a film released "the jungle book" that based on this book.
• The Guide, Swami and Friends and Malgudi Days were written by R.K. Narayan.
• In 1964, R.K. Narayan was honoured by Padma Bhushan on the Republic Day.
• He was awarded the AC Benson Medal in 1980 by the Royal Society of Literature.

Crocodiles have a four-chambered heart.

• Adaptation to their maximum portion of the life cycle is done in water since they need to minimize the oxygen loss when submerged and the four-chambered hearts decrease the heartbeat by 2-3/minute and normalize this rate when the crocodile is above water.
• The crocodile may have the most complex circulatory vertebrate system.
• This has a four-chambered heart and two ventricles, an uncommon characteristic between the current reptiles, and both the left and the right aorta, which are connected by a hole called the Panizza Foramen.
• Crocodiles belong to Crocodylidae family.

Rabindranath Tagore was awarded the Nobel Prize in 1913 and a knighthood in 1915.

• He became the first non-European to win the Nobel Prize in Literature in 1913.
• After Theodore Roosevelt, he was the second non-European to win a Nobel Prize.
• King George V was awarded the Knighthood in 1915 of Birthday Honours, but Tagore renounced it after the 1919 massacre of Jallianwala Bagh.
• Jana Gana Mana is an Indian national anthem.
• It was originally written by the poet Rabindranath Tagore as Bharoto Bhagyo Bidhata in Bengali.

Palolem is a beach in Goa.

• This beach is located in Canacona in southern Goa.
• It is considered to be one of the most beautiful beaches in India.
• It was ranked the 20th best beach in Asia by TripAdvisor in 2018.​​

The Government of India launched the Start-up India Initiative on 16 January 2016, with the objective of supporting entrepreneurs, building a robust start-up ecosystem, and transforming India into a country of job creators instead of job seekers.

• The Government of India launched the "Start-up India" campaign in New Delhi on 16 January 2016.
• The aim of this event was at celebrating the entrepreneurial spirit of the youth of the country and attended by CEOs and founders of the biggest start-ups (over 1500) from across the world.
• The Department of Industrial Policy and Promotion (DIPP) coordinated this event along with Invest India and Start-up ecosystem players iSpirt, YourStory, NASSCOM, SheThePeople.tv and the Kairos Society and the FICCI and CII Youth wings.
• The closing session addressed by the Honorable Prime Minister of India, Shri Narendra Modi, who officially launched the project and unveil the Start-up Action Plan.

Kandhamal Haldi, a variety of turmeric indigenous to Odisha earned the Geographical Indication (GI) tag from Intellectual Property India(IPI) in April 2019.

• IPI is an organization that operates under the auspices of the Union ministry of commerce & industry.
• Kandhamal Haldi is so well known for its strong medicinal properties.
• 'Kandhamal Haldi' has been put under class-30 type.
• The Geographical Indication (GI) tag is used to classify agricultural, natural or manufactured products originating in a region.

The Kyaik Htee Yoe pagoda(It's also known as Golden Rock) is located in Myanmar(Burma).

• It's a well known Buddhist pilgrimage site in Mon Province.
• It is a 24 ft pilgrimage built on the top of a granite boulder covered with gold leaf pasted by its male devotees.
• Precariously perched on a strand of Buddha's hair.
• The rock and the pagoda are situated at the top of Mt. Kyaiktiyo.
• This is the third-largest Buddhist pilgrimage site in Burma after the Mahamuni Pagoda and Shwedagon Pagoda.

The correct answer is  India Gate.

Key Points 

• In the question, India Gate is described.
• The India Gate is located at the heart of India’s capital city, New Delhi.
• It is about 2.3 km from the Rashtrapati Bhavan, located on the eastern extremity of the ceremonial boulevard, Kartavya Path (Rajpath).
• India Gate is a war memorial dedicated to honouring the soldiers of the Undivided Indian Army who died during World War I between 1914 and 1921.
• The India Gate, originally named All India War Memorial, was built to pay homage to the 82,000 soldiers of the Undivided Indian Army who lost their lives fighting for the British Empire in World War I (1914-1918) and the Third Anglo-Afghan War (1919).

India Gate

France's Arc- de-Triomphe

Additional Information

• Charminar:
• Sultan Mohammed Quli Qutb Shah built Charminar in 1591.
• It is said that this square-shaped structure with four pillars and intricate carvings was built in honour of his wife, Bhagmati.
• Gateway of India:
• The Gateway of India, with its regal arches, stand guard facing the Arabian Sea at Apollo Bunder in the bustling Colaba area of Mumbai.
• The ‘Elephanta Festival of music and dance’ which was earlier held at the Elephanta caves, is now held in front of the Gateway in March every year.
• Red Fort entry gate:
• A Delhi Tour is synonymous with a Red Fort trip, famously called Lal Kila of Delhi.
• Originally Red Fort was known as 'Qila-I-Mubarak', meaning a residence for the royal family.
• It was Emperor Shah Jahan who built Red Fort; he also created another famous piece of architecture of India the Taj Mahal of Agra.

The correct answer is option 3 i.e., performing the world's first human heart transplant.

• Christiaan Barnard is famous for performing the world's first human heart transplant.
• He was a cardiac surgeon in South Africa who underwent the first heart transplant in which the patient regained consciousness.
• He moved the heart of the death survivor, Denise Darvall, to the chest of 54-year-old Louis Washkansky on 3 December 1967.
• Henry Briggs has introduced the first table of logarithms.
• Louise Joy Brown is the first test-tube baby via IVF(in vitro fertilization).
• Dolly Sheep is the first cloned mammal.

The correct answer is Mollusca.

Key Points 

• Mollusca is the second-largest invertebrate animal phylum after Arthropoda.
• They are the largest marine phylum, accounting for about 23% of all marine species.
• Snails and slugs belong to a broad taxonomic class of invertebrates within the phylum of Mollusca called the Gastropoda.
• They are a large part of the phylum Mollusca and the most widely diversified class in the phylum, with between 65,000 and 80,000 live snail and slug species.
• The Gastropoda class comprises a vast majority of named animals, second only to the total number of insects.

The first Wimbledon Championship was held in 1877.

• It is the oldest tennis tournament in the world.
• It was held at the All England Club in Wimbledon, it is played on the outer grass-court till 1877.
• Since 2009, it plays roof over centre court.
• Wimbledon is one of the four Grand Slam tennis tournaments, the other being the US Open, Australian Open and the French Open.
• The first Wimbledon Championship player Spencer Gore, an old Harrovian racket player, won from field 22.

The amalgamation of Vijaya Bank and Dena Bank with Bank of Baroda (BoB) came into effect from 1 April 2019.

• With amalgamation with BOB to create India's third largest bank.
• According to the Amalgamation Scheme, Vijaya Bank shareholders would earn 402 BoB equity shares for every 1,000 shares owned.
• In Dena Bank's case its shareholders will receive 110 BoB shares per 1,000 shares.
• The three-way merger announcement was among many reform initiatives undertaken by Financial Services Secretary Rajiv Kumar to make public-sector banks (PSBs) stable, robust and competitive globally.

Argon is an inert gas most commonly found in light bulbs.

• Argon improves bulb life by avoiding too rapid a degradation of the tungsten filaments.
• Nitrogen also added in incandescent light bulbs at the rate of 7%.
• Argon has a comparable low breakdown voltage, applying a small amount of nitrogen to avoid arcing between the supports of the filaments.
• Other gasses like hydrogen, neon, nitrogen and krypton are also used for illumination purposes.
• High-brightness "halogen" bulbs use argon mixture and a limited quantity of halogen, usually bromine or iodine.

Itanagar is the capital of Arunachal Pradesh, located 530 meters above sea level between 93 East longitude and 27 North latitude.

• Itanagar has a humid subtropical climate with warm and wet summers and mild winters.
• It is inhabited by various tribes, namely, Nyishi, Tagin, Galo, Adi, Apatani.
• It had a population of 59,490 as of the 2011 census of India. Males make up 53% of the population and 47% of females**.**

The Mission Indradhanush(an initiative of Govt. of India) is associated with immunisation.

• In December 2014, the Government of India initiated "Mission Indradhanush" to improve and reinvigorate the system and achieve full immunization coverage for both children and pregnant women at a rapid pace.
• On 8 October 2017, Prime Minister Shri Narendra Modi launched the Enhanced Mission Indradhanush.
• ​In 1978, the Indian Ministry of Health and Family Welfare, Government of India, launched the immunization system in India as 'Expanded Immunization Programme' (EPI).
• The program was updated in 1985 as the 'Universal Immunization Programme' (UIP) to be introduced in a staggered manner by 1989-90 to include all districts in the country with one of the world's largest health programs.
• In the first year of their existence, UIP was able to completely immunize only 65% of Children.

Uruguay was the first host country of the FIFA (Federation Internationale de Football Association) World Cup.

Key Points

• The FIFA World Cup was first organized in 1930, when FIFA, the governing body for football in the world, agreed to stage an international men's football competition under FIFA president Jules Rimet's reign, who put this idea into effect.
• The inaugural competition, which took place in 1930, was challenged as a final tournament with just 13 teams invited by the organisation.
• The first official international football match between Scotland and England was played at Glasgow in 1872.
• Uruguay also became the first champion of the FIFA World Cup.
• France got the FIFA World Cup title 2nd times in 2018.

Pallichchhandam – land donated to Jaina institutions is the only correct pair as described by Chola inscriptions.

• The inscriptions issued by the Kings of Chola are known from different parts of the old Madras City.
• They provide evidence for an attack on Kerala by the Cholas.
• The inscriptions discovered from the temples at Cholapuram, Kanyakumari, Darsanam Koppu, Thirunanthikarai and Sucheendram list attacks on southern Kerala regions.

Income from overtime of employee D = 2,500

Total income of employee D = 40,000

Required percentage = (2500/40000) × 100 = 6.25%

Number of girls studying Arts = 45

Total number of girls studying in science, commerce and vocational = 18 + 42 + 30 = 90

Required ratio = 45 : 90 = 1 : 2

Mistake PointsThe ratio of the number of girls studying Arts to the number of girls studying in all other streams 

Here all other streams mean all the streams other than Arts. 

So, while calculating for other streams, Arts will not be considered.

PC = PD + CD = 15.3 + 11.9 = 27.2

AP × PB = PD × PC

⇒ 30.6 × PB = 15.3 × 27.2

⇒ PB = (15.3 × 27.2)/30.6

⇒ PB = 13.6

Now, AB = AP - PB = 30.6 - 13.6 = 17 cm

Radius of the circle = 17/2 = 8.5 cm

As we know,

∠OQP = 90° [tangent]

OP² = PQ² + OQ²

⇒ 13² = 12² + OQ²

⇒ OQ² = 169 - 144

⇒ OQ = √25

⇒ OQ = 5 cm

As we know,

If a + b + c = 0, then

a³ + b³ + c³ = 3abc

Similarly,

x + 3y + 2 = 0, then

⇒ x³ + 27y³ + 8 - 18xy

⇒ x³ + (3y)³ + 2³ - 3 × x × 3y × 2 = 0

Ratio of A : B : C = 3 : 4 : 2

⇒ 3 + 4 + 2 = 9 unit

⇒ 9 unit = 990

⇒ 1 unit = 990/9 = 110

⇒ 4 unit = 4 × 110 = Rs. 440

Given:

Total work = 8 × 20 = 160 units

Concept used:

(M₁ × D₁)/w₁ = (M2 × D2)/w₂

Calculation:

As we know,

M₁ × D₁ = M₂ × D₂

⇒ 8 × 15 = M₂ × 8

⇒ M₂ = 15

∴ Number of extra persons = 15 - 8 = 7

Let CP of cell phone was be Rs. 100

MP of the cell phone = 100 × 120/100 = 120

SP of the cell phone = 120 × 90/100 = 108

∴ Profit = 108 - 100 = 8

Profit % = 8/100 × 100 = 8%

Short Trick :

Profit % = 20 - 10 - (20 × 10)/100 = 10 - 2 = 8%

a, o and u vowels occur less than 80 times.

Additional Information

Here Frequency is the number of occurrences of a repeating event per unit of time. 

frequency of a = 75 which is less than 80

frequency of o = 70 which is less than 80

frequency of u = 75 which is less than 80

Given:

cos 10° cos 30°cos 50° cos 70° cos 90°

Formula used:

cos(90° - θ) = sinθ 

cos90° = 0

Calculation:

cos 10° cos 30°cos 50° cos 70° cos 90°

cos 90° = 0

⇒ cos10° × cos 30° × cos 50° × cos 70° × 0

⇒ 0

∴ cos 10° cos 30°cos 50° cos 70° cos 90° = 0

p + q = 7 and pq = 5

As we know,

(p + q)³ = p³ + q³ + 3pq (p + q)

⇒ 7³ = p³ + q³ + 3 × 5 × 7

⇒ p³ + q³ = 343 - 105

⇒ p³ + q³ = 238

∠ABC = 72°

∠ABC = ∠ACB = 72° [AB = AC]

In ΔABC

∠ABC + ∠ACB + ∠BAC = 180°

⇒ 72° + 72° + ∠BAC = 180°

⇒ ∠BAC = 180° - 144° = 36°

Concept used:

Calculation:

(cosec 30° - tan 45°) cot 60° tan 30°

⇒ (2 - 1) × 1/√3 × 1/√3

⇒ 1/3

∠ABO = 32°, ∠BAQ = X and ∠ACB = Y

∠ABO = ∠BAO = 32° [OA = OB]

∠OAQ = 90° [tangent]

∠OAQ = ∠BAO + ∠BAQ

⇒ 90° = 32° + x

⇒ x = 90° - 32° = 58°

∠BAQ = X and ∠ACB = Y are on same arc, hence

⇒ ∠BAQ = ∠ACB 

⇒ x = y = 58°

⇒ x + y = 58° + 58°

⇒ x + y = 116°

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

The number 1190*6 is divisible by 9 if

1 + 1 + 9 + 0 + * + 6

⇒ 17 + *

If put * = 1, then number become 18 which is divisible by 9.

CP of the car = 1,08,500

Let the amount spent on car maintenance be Rs. x, then

SP of the car = 1,56,250

Price of the car after maintenance = 1,56250 × 100/125

Price of the car after maintenance = 1,25,000

x = 1,25,000 - 1,08,500

⇒ x = 16,500

SI for 2 years = 400

SI for 1 year = 400/2 = 200

Difference between CI and SI = 408 - 400 = 8

∴ Rate of interest = (8/200) × 100 = 4%

As we know

Perimter of the square = 4a

Perimeter of the rectangle = 2 (l + b)

Sides of rectangular plot are 35 m and 15 m

Perimeter of the rectangular plot = 2 (35 + 15) = 2 × 50 = 100 m

Perimeter of square plot = perimeter of rectangular plot = 100 m

4a = 100

⇒ a = 100/4

⇒ a = 25 m

Shortcut Trick

Net deviation in total score = Correct score − Incorrect score = 58 − 88 = −30.

Deviation in average = Net deviation ÷ Total students = −30 ÷ 30 = −1.

Actual Average = Initial Average + Deviation = 69 − 1 = 68.

∴ The correct answer is 68.

Alternate Method

Given:

Total number of students (n) = 30

Initial average score = 69

Wrongly marked score = 88

Correct score = 58

Formula Used:

Average = Sum of observations ÷ Number of observations

Calculations:

⇒ Incorrect Sum of scores = Average × Total students

⇒ Incorrect Sum = 69 × 30 = 2070

⇒ Correct Sum = Incorrect Sum − Incorrect score + Correct score

⇒ Correct Sum = 2070 − 88 + 58 = 2040

⇒ Actual Average = 2040 ÷ 30

⇒ Actual Average = 68

∴ The correct answer is 68.

Additional Information

Net Change Property

If each observation in a data set is increased or decreased by a constant value 'k', the new average will also increase or decrease by 'k'.

Weighted Average

When two groups with averages A₁ and A₂ and sizes n₁ and n₂ are combined, the resultant average is (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Correction Method

For any error in recording data, Correct Average = Original Average + [(Correct Value − Incorrect Value) ÷ n].

Let price of the cooking oil be Rs. 4

Price of the cooking oil after increment = 4 × (5/4) = Rs. 5

Ratio of oil price before and after = 4 : 5

Ratio of consumption before and after = 5 : 4

Required percentage = (5 - 4)/5 × 100 = 20%

The distance between two stations, A and B = 575 km,

Speed of first train = 50 km/hr

Speed of second train = 60 km/hr

Distance covered by first train in 30 min (1/2 hr) = 50 × 1/2 = 25 km

Remaining distance = 575 - 25 = 550 km

Relative speed, if opposite direction = 50 + 60 = 110 km/hr

As we know,

Time = Distance/speed

Both train meet each other in = 550/110 = 5 hrs

Distance covered in 5 hrs by first train = 5 × 50 = 250 km

Total distance covered by first train = 25 + 250 = 275 km

Both trains meet each other 275 km far from station A.

Given:

$\frac{{3\left( {1 - 2si{n^2}x} \right)}}{{co{s^2}x - si{n^2}x}}$

Formula used:

cos2A = cos2A - sin2A

cos2A = 2cos2A - 1 = 1 - 2 sin2A

Calculation:

$\frac{{3\left( {1 - 2si{n^2}x} \right)}}{{co{s^2}x - si{n^2}x}}$

⇒ ${{3cos2x}}\over{{cos2x}}$ = 3

∴ $\frac{{3\left( {1 - 2si{n^2}x} \right)}}{{co{s^2}x - si{n^2}x}}$ = 3

Alternate Method $\frac{{3\left( {1 - 2si{n^2}x} \right)}}{{co{s^2}x - si{n^2}x}}$

Put x = 0°, then 

$⇒ \frac{{3\left( {1 - 2si{n^2}0} \right)}}{{co{s^2}0 - si{n^2}0}}$ (sin0° = 0)

$⇒ \frac{{3\left( {1 - 0} \right)}}{{1 - 0}}$ = 3

As we know,

a² - b² = (a - b) (a + b)

Hence, 515 × 485

⇒ (500 + 15) (500 - 15)

⇒ 500² - 15²

⇒ 250000 - 225

⇒ 249775

Total number of students = 5 + 11 + 18 + 38 + 39 + 24 + 15 = 150

Number of students who got less than 50 marks = 5 + 11 + 18 + 38 = 72

∴ Required percentage = 72/150 × 100 = 48%

(26 - 13 × 2) ÷ 2 + 1

⇒ (26 - 26) ÷ 2 + 1

⇒ 0 ÷ 2 + 1

⇒ 0 + 1

⇒ 1

The correct answer is option 2, i.e., had finished.

• The sentence talks about an activity that has already happened in the past.
• This is also suggested by the second sentence, which uses the simple past tense.
• In this case, the most appropriate tense is the past perfect tense form, viz, had finished.

Thus, the completed sentence is: Long after those five horses had finished drinking water from the trough, an old horse appeared over the brow of the hill.

The correct answer is option 1, i.e., shows.

• The sentence uses the main verb 'is', which reflects simple present tense.
• This suggests that the blank must contain a verb that also reflects the same tense.
• Out of the options, only shows can make the sentence meaningful.

Thus, the completed sentence is: The popular leader is remarkable for the way in which he shows the qualities of a good politician and a world-class thinker.

The correct answer is Aid.

Key Points

• Relief means a feeling of reassurance and relaxation following release from anxiety or distress.
• Aid refers to help, typically of a practical nature.
• Thus, only Aid can be an appropriate synonym for Relief.

Additional Information

Meanings of the given words:

• Stress- pressure or tension exerted on a material object.
• Anger- a strong feeling of annoyance, displeasure, or hostility.
• Emotion- a strong feeling deriving from one's circumstances, mood, or relationships with others.

The correct answer is option 2, i.e., Granary.

Meanings of the given words:

Greenery- green foliage, growing plants, or vegetation.

Granary- a storehouse for threshed grain.

Grate- reduce (food) to small shreds by rubbing it on a grater.

Grandstand- the main stand, usually roofed, commanding the best view for spectators at racecourses or sports grounds.

Out of these, only Granary is an appropriate word for the given group of words.

The correct answer is option 2, i.e., Cruel.

Key Points

• "Humane" refers to being compassionate, kind, and considerate towards others. Its antonym, "cruel," represents the opposite behavior of being unkind, harsh, and lacking compassion.
• Therefore, option 2, "cruel," is the correct antonym in this context.
• So, its opposite must mean something that is unkind or cruel.

Additional Information

Meanings of the given words:

• Sympathetic- feeling, showing, or expressing sympathy.
• Cruel- wilfully causing pain or suffering to others, or feeling no concern about it.
• Living- the pursuit of a lifestyle of the specified type.
• Kind- a group of people or things having similar characteristics.

Out of these options, only Cruel is an appropriate antonym for Human.

The correct answer is option 4, i.e., CADB.

• The first sentence of a paragraph is independent and introduces a topic. Here, only C is independent in meaning. So, C must be the first sentence.
• It is easier to find the first sentence and then eliminate the options accordingly, as it saves time.
• Here, only option 4 begins with C.

So, the correct order must be: CADB.

The correct answer is option 2, i.e., seat.

• The sentence talks about sitting in a restaurant.
• So, seat is the most appropriate option for the blank in the given options.

Thus, the complete sentence is: When you enter a restaurant, you take your seat and you are served a glass of water.

The correct answer is option 4, i.e., time.

• The sentence talks about taking something to decide what to order.
• Given the options, the most appropriate option is time.

Thus, the complete sentence is: You take your time to decide what you should order.

The correct answer is option 3, i.e., waiter.

• The sentence talks about someone appearing to take your order.
• Given the options, the most appropriate word here is waiter.

Thus, the complete sentence is: When a waiter appears, you ask him the routine question

The correct answer is option 4, i.e., What.

• The sentence talks about asking a question regarding the restaurant having something special.
• In this case, the most appropriate wh-question here is 'what'.

Thus, the complete sentence is: “What do you have?”

The correct answer is option 1, i.e., the.

Key Points

• The sentence suggests that the blank should contain an article, as it is used before the noun 'day's menus'.
• Given the context, the most appropriate article here is 'the'.
  

Thus, the complete sentence is: The waiter will begin to recite the day’s menus, generally with nothing new in it, but you like to hear it all over again.

The correct answer is option 4, i.e., Fasineting.

The correct spelling of the word is: Fascinating.

Meanings of the given words:

Grammatical- relating to grammar.

Occurrence- an incident or event.

Professional- relating to or belonging to a profession.

Fascinating- extremely interesting.

The correct answer is option 1, i.e., Johnny’s mother asked him to run down to the grocer’s and get a loaf of French bread and a pound of cheddar cheese.

Key Points

• The sentence seems like  a command given by the mother to Johnny; but it is, in fact, an errand or task that Johnny's mother has 'asked him to do'.
• So, when turning the sentence into indirect, the verb 'asked' is more appropriate here than 'commanded' or 'pleaded'..
• In the indirect form, the reporting verb "said" changes to "asked," and the noun "Johnny" changes to "him" as the subject becomes the object.
• Also, the imperative verb "run" is changed to its infinitive forms "to run".
• The tense of the reported verb remains the same as in the original sentence.
• Option 2 is incorrect because it changes the meaning of the sentence by making Johnny the subject who is commanding his mother to go down to the grocer and buy the items, which is the opposite of what is intended.
• Option 3 is incorrect because it changes the reporting verb to "pleaded," which implies a request made with desperation or urgency. The original sentence does not convey any such urgency or desperation.
• Option 4 is incorrect because it changes the roles of the speaker and the listener. In the original sentence, Johnny’s mother is the speaker who is making the request, while Johnny is the listener. However, in option 4, Johnny becomes the speaker, asking his mother to go to the grocer, which is the opposite of the intended meaning.
  

So, the indirect sentence becomes: Johnny’s mother asked him to run down to the grocer’s and get a loaf of French bread and a pound of cheddar cheese.

The correct answer is- Labarotary

Key Points  

• Let's explore the meaning of the correct word:
• Laboratory(noun): A room or building with scientific equipment for doing scientific tests or for teaching science, or a place where chemicals or medicines are produced. (वैज्ञानिक परीक्षण करने के लिए या विज्ञान पढ़ाने के लिए वैज्ञानिक उपकरणों के साथ एक कमरा या इमारत, या एक जगह जहां रसायन या दवाएं पैदा होती हैं।)
• Example: Laboratory tests suggest that the new drug may be used to treat cancer.
  

From the above line, we can say that: Labarotary is the correct answer.

Additional Information 

• Let's explore the meaning of the other words:
• Presence(noun): The fact that someone or something is in a place. (तथ्य यह है कि कोई या कुछ जगह पर है।)
• Definite(adjective): Fixed, certain, or clear. (निश्चित, निश्चित या स्पष्ट।)
• Absence(noun): The fact of not being where you are usually expected to be. (वह नहीं होने का तथ्य जहां आप आमतौर पर होने की उम्मीद करते हैं।)

The correct answer is option 3, i.e., To do something that will not get the result you want.

Key Points:- 

• The idiom To bark up the wrong tree means to mistakenly give emphasis to something that will not solve the problem. (गलती से किसी ऐसी चीज पर जोर देना है जो समस्या को हल नहीं करेगी।)
• e.g. I think he is barking up the wrong tree by going to the committee.

Out of the given options, only option 3 reflects this meaning.

The correct answer is option 4, i.e., but you will get wet.

• The sentence uses the incorrect conjunction 'but'.
• Given the context, the correct conjunction here should be 'or' or 'else'.

Thus, the rectified sentence is: It’s raining heavily, so you should take an umbrella, or/else you will get wet.

The correct answer is option 2, i.e.,To become less important or to give up control over things.

• The idiom 'To take a back seat' means to let go of control and let someone else be in charge.
• e.g. After his retirement, Alan took a back seat and let his son run the company.

Out of the options, only option 2 reflects this meaning.

The correct answer is option 4, i.e., CABD.

• The first sentence in a paragraph is independent and introduces a topic. Here, only C is independent. So, C must be the first sentence.
• In order to save time, it is easier to find the first sentence and then eliminate the options.
• Out of the given options, only option 4 begins with C.

So, the correct order must be: CABD.

The correct answer is option 3, i.e., Diligent.

Meanings of the given words:

Indigent- poor; needy.

Dilatory- slow to act.

Diligent- having or showing care and conscientiousness in one's work or duties.

Indulgent- having or indicating a readiness or over-readiness to be generous to or lenient with someone.

Out of these, only Diligent is the most appropriate word for the given set of words.

The correct answer is option 3, i.e., Let all the exams be conducted in a fair and proper manner.

• When changing an authoritative sentence or a command into passive voice, 'let' is used.

So, here, the sentence becomes, Let+ all the exams+ be + conducted +in a fair and proper manner.

The most appropriate option to substitute the underlined segment is - whether you like it

Key Points

• The sentence uses the incorrect present progressive verb form 'liking it.
• We use whether … or not or whether or not to give an opposite alternative:
• Given that the sentence uses the modal verb 'must', it indicates that going to the book fair is a compulsion and opposite alternatives are there.
  

Thus, the rectified sentence is: You must go to the book fair whether you like it or not.

The correct answer is option 1, i.e., abroad drowned.

• The part uses the incorrect noun/adverb abroad, which means in or to a foreign country or countries.
• Given the context of the ship, the correct adverb here must be aboard, which means on or into (a ship, aircraft, train, or another vehicle).

 Thus, the rectified sentence is: The big ship sank and everyone aboard drowned.