The logic is:

Hence, ‘M’ is the correct answer.

The logic is:

Letters are coded by their opposite alphabets.

Similarly,

Hence, ‘ZUPK’ is the correct answer.

The logic is:

North : South

North – the direction in which a compass needle normally points, towards the horizon on the left-hand side of a person facing east, or the part of the horizon lying in this direction.

South – the direction towards the point of the horizon 90° clockwise from east, or the point on the horizon itself.

They are opposite of each other. (Antonym)

1. Frown : Smile

Frown – a facial expression indicating disapproval, displeasure, or concentration, characterized by a furrowing of one's brows.

Smile – form one's features into a pleased, kind, or amused expression, typically with the corners of the mouth turned up and the front teeth exposed.

They are opposite of each other. (Antonym)

2. Whole : Total

Whole – a thing that is complete in itself.

Total – comprising the whole number or amount.

They are synonym of each other.

3. Ductile : Bendable

Ductile – able to be deformed without losing toughness; pliable, not brittle.

Bendable – capable of being bent or flexed or twisted without breaking.

They are synonym of each other.

4. Integrity : Honesty

Integrity – the quality of being honest and having strong moral principles.

Honesty – free of deceit; truthful and sincere.

They are synonym of each other.

Hence, ‘Frown : Smile’ is the correct answer.

The triangles are as shown below:

Hence, the figure has total 25 triangles.

The logic is:

Number – (Number)²

All number pairs except ‘15 : 250’ follows the logic.

Hence, ‘15 : 250’ is the correct answer.

The relation is:

‘Astronomy’ is related to ‘Stars’ → Astronomy is a natural science that studies celestial objects and phenomena.

Similarly,

‘Agronomy’ is relate to Crops' → Agronomy is the science and technology of producing and using plants in agriculture for food, fuel, fiber, and land restoration.

Hence, ‘crops’ is the correct answer.

‘+’ symbol is present in 3^rd dice, and ‘#’ is present on both 3^rd and 1^st dice, so keeping ‘#’ constant and then rotating in the clockwise direction, we get the faces opposite to each other.

So, ‘@’ symbol will be on the face opposite to the one showing ‘+’.

Hence, ‘@’ is the correct answer.

1. Quadrillion – a thousand raised to the power of five (10¹⁵)

2. Quintillion – a thousand raised to the power of six (10¹⁸)

3. Million – the number equivalent to the product of a thousand and a thousand; 1,000,000 or 10⁶

4. Octillion – a number equal to 1 followed by 27 zeros = 10²⁷

5. Trillion – a million million (1,000,000,000,000 or 10¹²)

Arranging them in ascending order, we get:

3. Million – the number equivalent to the product of a thousand and a thousand; 1,000,000 or 10⁶

4. Trillion – a million million (1,000,000,000,000 or 10¹²)

5. Quadrillion – a thousand raised to the power of five (10¹⁵)

6. Quintillion – a thousand raised to the power of six (10¹⁸)

7. Octillion – a number equal to 1 followed by 27 zeros = 10²⁷

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

The least possible venn diagram is:

I. Some machines are pigeons. → False (No machine is a pigeon)

II. All kites are pigeons. → False (Those kites which are machines are not pigeons)

III. Some kites are not pigeons. → True (Those kites which are machines are not pigeons)

Hence, only conclusion III follows.

The pattern followed here is:

First row:

23 + 5 = 28

Reverse it: 82

28 + 82 = 110

Second row:

56 + 9 = 65

Reverse it: 56

65 + 56 = 121

Similarly, third row:

49 + 3 = 52

Reverse it: 25

52 + 25 = 77

Hence, 77 is the correct answer.

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

Hence, option ‘2’ is the correct answer.

Given series: 5, 10, 26, ? 122, 170

The logic is:

(Prime number)² + 1

2² + 1 = 5

3² + 1 = 10

5² + 1 = 26

7² + 1 = 50

11² + 1 = 122

13² + 1 = 170

Hence, ‘50’ 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.

The number of traveller who like to travel either by train or plane but NOT by bus is represented by the region covered by triangle and rectangle which is not a circle, as shown below:

So, number of people = (11 + 6 + 13) = 30

Hence, ‘30’ is the correct answer.

The logic is:

Hence, ‘GMS’ is the correct answer.

1. × and –

Given equation: 12 + 81 – 27 × 9 ÷ 3 = 36

After replacing ‘× and –’, we get:

L.H.S = 12 + 81 × 27 – 9 ÷ 3

= 12 + 2187 – 3

= 2208 – 3

= 2205 ≠ R.H.S

2. ÷ and ×

Given equation: 12 + 81 – 27 × 9 ÷ 3 = 36

After replacing ‘÷ and ×’, we get:

L.H.S = 12 + 81 – 27 ÷ 9 × 3

= 12 + 81 – 9

= 93 – 9

= 84 ≠ R.H.S

3. • and ÷

Given equation: 12 + 81 – 27 × 9 ÷ 3 = 36

After replacing ‘- and ÷’, we get:

L.H.S = 12 + 81 ÷ 27 × 9 – 3

= 12 + 27 – 3

= 39 – 3

= 36 = R.H.S

4. • and ×

Given equation: 12 + 81 – 27 × 9 ÷ 3 = 36

After replacing ‘+ and ×’, we get:

L.H.S = 12 × 81 – 27 + 9 ÷ 3

= 972 – 27 + 3

= 975 – 27

= 948 ≠ R.H.S

Hence, ‘- and ÷’ is the correct answer.

A is to B

B is to A

P + R × T – Q ÷ S + U → P is husband of R, R is mother of T, Q is sister of T, S is son of Q, S is husband of U.

So, P is maternal grandfather of S.

Hence, ‘maternal grandfather’ is the correct answer.

Similarly,

Hence, ‘16132420’ is the correct answer.

Given series: 62, 66, 74, 90, ?

Hence, ‘122’ is the correct answer.

The logic is:

1.  GCV

2. DDP

3. BJT

4. FBL

Hence, ‘GCV’ is the odd one out.

The logic is:

Row 1: (15 – 3) × 2 = 24

Row 1: (21 – 6) × 2 = 30

Similarly,

Row 1: (49 – 5) × 2 = 88

Hence, ‘88’ is the correct answer.

The definition of the given terms is:

1. Saxophone – The saxophone is a woodwind instrument usually made of brass and played with a single-reed mouthpiece.

2. Trumpet – A trumpet is a woodwind instrument, a brass instrument commonly used in classical and jazz ensembles. 

3. Xylophone – The xylophone is a musical instrument in the percussion family that consists of wooden bars struck by mallets. 

4. Clarinet – The clarinet is a family of woodwind instruments. It has a single-reed mouthpiece, a straight, cylindrical tube with an almost cylindrical bore, and a flared bell.

All options except ‘xylophone’ belongs to the family of woodwind instruments.

Hence, ‘xylophone’ is the odd one out.

Let the number of men be m and that of horses be h.

Since, the no. of legs of men is 2 and that of horses is 4, total legs count of men is 2m and that of horse is 4h, and total number of heads is (m + h).

Given: The total number of legs is 14 more than twice the number of heads.

According to question:

(2m + 4h) – 2(m + h) = 14

⇒ 2m + 4h – 2m - 2h = 14

⇒ 2h = 14

⇒ h = 7

So, the number of horses in the group is 7.

Hence, ‘7’ is the correct answer.

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

Hence, option 1 is the correct answer.

Given series:

First of all, let us observe the pattern followed by the alphabets inside the figure:

Letters are: J, M, Q, V, ?

The logic is:

J + 3 = M; M + 4 = Q; Q + 5 = V; V + 6 = B

The letter ‘B’ is present only in option ‘3’.

Hence, option ‘3’ will be the next figure in the given series.

The correct answer is Water vapour.

Key Points

• Water Vapour- It is consistently seen to be the most abundant in a volcanic eruption.
• It occurs when lava and gas are discharged from the vent of the volcano.
• The eruption majorly emits water vapor into the atmosphere. But other gases like-Carbon dioxide, Sulphur Dioxide, Hydrogen Sulfide are also emitted.
• 'Glowing avalanche' is the most dangerous type of volcanic eruption.
• The magma which is freshly erupted forms a hot pyroclastic flow. This flow generally has a temperature of up to 1,200 degrees.
• The flow sometimes takes a speed of up to several hundred kilometers per hour. It can reach as far as 40 km from the original disaster site.

Mehrunnisa who was known as Nur Jahan was the wife of Jahangir.

• Jahangir was the son of Mughal emperor Akbar.
• He ruled from 1605 until his death in 1627, for 22 years.
• The popular Shalimar Bagh in Srinagar was built by Jahangir.
• It is in his time when paintings culture flourished in India.
• Jahangir died in Kashmir.

• DNA is a natural flame retardant.
• DNA-Deoxyribonucleic acid.
• It is made of an alternating phosphate-and-sugar backbone with nitrogen bases-A,T,G,C.
• The nitrogen-containing bases in DNA release ammonia, which in turn dilutes flammable gases and inhibits combustion reactions.
• This characteristic of DNA was known when a cotton cloth was coated with DNA extracted from herring sperm. It was found that the genetic material reduced the fabric’s flammability.
• RNA-Ribonucleic acid

• General K. M. Cariappa is the first General of the Indian Army, whose retirement day is celebrated as the 'Armed Forces Veterans Day' every year.
• He was the first Indian Commander-in-Chief of the Indian Army. He was appointed on 15 January 1949 and this day is celebrated as Army Day.
• He also led the force of the Indian Army on the Western Front during the Indo-Pakistan War of 1947.
• The Armed Forces Veterans Day is observed each year on 14th January.
• The Commemoration of this day acknowledges and honors the selfless devotion and sacrifice of our veterans in the service of the nation.

• D.C. Sircar publish Indian Epigraphy and Indian Epigraphical Glossary in 1965-66.
• Dineshchandra Sircar was an epigraphist and historian among his many talents. He is known for his work in deciphering inscriptions in India and Bangladesh.
• During 1949-1962, he was the Chief Epigraphist of the Archaeological Survey of India.
• Indian Epigraphy includes inscriptions and their evidence, languages in which the inscriptions are written, writing materials, the preparation and preservation of documents, systems of dating and the different eras, nomenclature, etc.
• Indian Epigraphical Glossary is a comprehensive dictionary of documents dating back to nearly 2000 years ago. Sircar has also given his interpretation of various cultural references and documents of this glossary.

• International Energy Agency released the ‘World Energy Outlook 2019’ Report.
• This report provides critical analysis and insights on trends in energy demand and supply.
• It includes explanations on the impact of today’s decisions on tomorrow’s energy systems. The report describes a solution that would enable the world to meet climate, energy access and air quality goals and simultaneously maintaining a strong focus on the reliability and affordability of energy for a growing global population.
• The first World Energy Outlook Report was published in 1977.
• International Energy Agency HQ-Paris, Executive director: Fatih Birol.
• World Trade Organisation HQ-Geneva, Director-General: Roberto Azevêdo
• UNESCO HQ-Paris, Director-General: Audrey Azoulay

• Alyssa Healy who created a world record by becoming the highest scorer in women's T20I belongs to Australia.
• She had scored 148 in 61 balls at North Sydney Oval against Sri Lanka in October 2019.
• She reached her century in just 46 balls.
• She is also a wicket-keeper in the Australian cricket team (Women).
• Meg Lanning is the captain of the Australian cricket team (Women).

• C. Rajagopalachari gave us the C R Formula.
• This Formula is also known as Rajaji Formula.
• During the Second World War, the British government states that if the Indian National Congress and the Muslim League resolved their differences, Indian statehood would be possible.
• The Muslim League, however, was demanding a separate nation of Pakistan for the Muslims. Indian National Congress was against the partition of the country.
• C Rajagopalachari who was a member of INC  proposed a set of plans called the C R Formula or Rajaji Formula to break this deadlock between the two major political parties in India.
• To summarise the formula, the Congress was requested to hold the plebiscite in the regions where Muslims made a majority.
• Muslim league was supposed to support the congress’s demand for complete freedom from Britishers and then the majority provinces would go to a plebiscite.

• In the sequence of planets in the Solar system, Venus comes in between Mercury and Earth.
• The sequence of the planets going away from the sun is ----> Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune.
• Venus is also known as the evening star because it is visible when the sun is about to set.
• The orbit period of Venus is 225 days and its atmospheric pressure is 92 times greater than the Earth’s.
• The Earth and Venus have a 638 km difference in diameter and Venus have 81.5% of the Earth’s mass.
• It is also the hottest planet in our solar system.
• Venus does not tilt on its axis. Hence, there is no seasonal variation.
• Please note that Venus has no moons.

• Sri Lanka is the first South Asian country to call match-fixing a crime.
• It was passed in the Parliament of Srilanka under the "Prevention of Offences Related to Sports".
• If a person is found guilty of committing an offense related to corruption in sports, he may be jailed for a term up to 10 years and he would also be required to pay various fines.
• It covers all the sports in Srilanka.
• Sri Lanka's Sports Minister- Harin Fernando. He presented the bill.
• Sri Lankan former skipper- Arjuna Ranatunga, now a cabinet minister, supported the bill.
• The bill also criminalizes "acts of omission", which includes failure to report corrupt approaches.

• Madhavpur Mela takes place in Gujarat.
• Madhavpur Ghed is a culturally significant village. It is believed that it is the place where Lord Krishna married Rukmini
• This place lies on the seashore, very close to Porbandar.
• The event is commemorated by a cultural fair held every year, commencing on Ram Navami.
• It was supposed to start on 2nd April this year. But because of Pandemic COVID-19, it stands canceled.
• Assam, Sikkim, Manipur, Meghalaya, Mizoram, Tripura, Arunachal Pradesh, and Nagaland were also supposed to participate in this event.

• Deepak Punia has been named the Junior Freestyle Wrestler of the year (2019) by United World Wrestling (UWW).
• He played under the category of 86 Kg.
• The Junior World Championships were held in Tallinn, Estonia. He defeated Alik Shebzukov of Russia.
• Deepak Punia had also won a bronze medal at the 2016 Cadet World Championships in Tbilisi, Georgia
• He also won a silver medal on his debut at the Senior World Wrestling Championships.
• At the 2019 World Wrestling Championships which was held in Nur-Sultan, Kazakhstan in September.
• Deepak Punia defeated Colombia's Carlos Izquierdo in the quarterfinals and hence secured a berth for the Summer Olympics in Tokyo (which now stands postponed).

The correct answer is Copper.

Key Points

• Copper is the only metal that is antibacterial.
• It is also called "germ-killer" because its alloys show antibacterial, antiviral and anti-fungal properties.
• It is scientifically proven that copper continuously kills more than 99.9% of the microbes that have caused infections within two hours of contact. This is called ‘contact killing’.
• Copper is also proved to completely destroy the bacteria’s DNA which prevents bacteria from developing a resistance to copper.
• Copper is the only solid metal touch surface to have been approved by the US Environmental Protection Agency in recognition of these antimicrobial properties.
• The atomic number of Copper-29. Symbol- Cu

• Merchant discount rate refers to the rate charged to a merchant for payment processing services on debit and credit card transactions.
• The merchant are supposed to set up this service and has to agree with the rate before accepting debit and credit cards as payment.
• It is basically a fee that merchants should consider before managing the overall costs of their business.
• Most merchants can expect to pay a 1% to 3% fee for payment processing of each transaction.However, Local merchants and e-commerce merchants  typically have varying fees and service level agreements.
• It is generally referred in a short-form-MDR.

• Haemoglobin performs the task of capturing oxygen in the blood.
• They are basically the proteins inside RBCs and carry oxygen to cells. They also carry carbon dioxide to the lungs.
• It is made up of four symmetrical subunits and four heme groups.
• Irons which are associated with the heme actually bind oxygen.
• Please note that it is the same iron in haemoglobin that gives blood its red color.
• Red blood cells-The are made in the bone marrow and it helps in carrying oxygen and removing carbon dioxide.
• Chlorophyll- It is a green photosynthetic pigment that is found in plants, algae, and cyanobacteria.
• White blood cells- These are also called leukocytes. They are involved in providing immunity to the body or protecting the body against both infectious disease and foreign particles.

• UN Women proposes to partner with Kerala’s gender park with an aim to secure gender parity in South Asia.
• A Memorandum of Understanding was signed in the presence of Chief Minister of Kerala - Pinarayi Vijayan.
• This partnership aims to make the Gender Park- a gender equity and empowerment initiative as the South Asian hub of United Nations Women.
• UN Women has proposed to be an equal partner in the Gender Park initiatives. It has also extended support in setting up a Gender Data Centre within the International Institute for Gender and Development.
• It is believed that this collaboration would broaden and deepen various pioneering initiatives for gender equity.

• Cirrhosis is NOT transmitted from one person to another.
• It is a condition in which the liver of our body can not function properly, possibly because of long-term damage.
• The normal tissue is replaced by scar tissue in such conditions.
• However, it can have various reasons but alcohol consumption remains the second most common cause of liver cirrhosis after the hepatitis C virus.
• Hepatitis B-It is also a liver infection which is caused by the hepatitis B virus that's easily preventable by a vaccine, unlike Cirrhosis. It is spread by exposure to infected bodily fluids.
• Syphilis-It is a bacterial infection usually spread by sexual contact.
• AIDS-It interferes with the body's ability to fight against infections or in other words affect immunity. The virus can be transmitted through contact with infected blood, semen or vaginal fluids.

• If the inflation in an economy is rising steadily, the Central Bank might increase the repo rate.
• Repo Rate - It is the rate at which the Reserve Bank of India (RBI) lends short term money to banks.
• Reverse Repo Rate-As the name suggests, it is the reverse of the Repo Rate. It is the rate at which the Bank lends short term money to the Reserve Bank of India.
• In the event of inflation, the RBI increases the repo rate and this acts as a disincentive for banks to borrow from the RBI.
• This ultimately reduces the money supply in the economy and hence helps in handling inflation.

The Vikrama Era began in 57 BC.

• It is said (as per the Jain book Kālakācāryakathā) that Vikram Era was founded King Vikramāditya gained victory over the Śakas.
• However, V. A. Smith and D. R. Bhandarkar (Archaeologist) believed that Chandragupta II adopted the title of Vikramaditya. It was he who changed the era's name to "Vikrama Samvat".
• Vikram Samvat is also considered to be the official calendar of Nepal.
• The first day of the Vikram Samvat calendar is celebrated after Diwali in the states of Gujarat and Maharashtra.

• Mardani Khel, one of the famous martial art forms in India belongs to Maharashtra.
• Please note that it is a weapon-based martial art form.
• It is believed to emerge during the Maratha dynasty.
• Kolhapur was the center of this art and skilled people used to teach youngsters.
• The British, however, banned the use of weapons used by Indians after 1857 revolt.
• Now, Mardani Khel is kind of a folk game.
• The use of weapons such as swords, dagger, bamboo sticks, darts, javelin, etc is continued but the moves were restricted to make it less lethal.

• The SDG India index is developed by NITI Aayog.
• The NITI Aayog has released the Baseline Report of the Sustainable Development Goals (SDG) India Index.
• It comprehensively documents the progress made by India’s States and Union Territories so far towards implementing the 2030 SDG targets.
• There are 62 National Indicators which measure the progress on the outcomes of the interventions and schemes of the Government of India.
• The indexes are intended to provide a holistic view on the social, economic and environmental status of the country and its States and UTs.
• NITI Aayog CEO-Amitabh Kant

• The Supreme Court has declared access to the internet a fundamental right under Article 19 of the Indian Constitution.
• This ruling came on hearing of a plea in connection with Internet blockade in Jammu and Kashmir. when Article 370 was revoked.
• The ruling of the Supreme Court of India is also in sync with the United Nations recommendation that every country should make access to the Internet a fundamental right.
• Article 19 - Freedom of Speech
• Article 14 - Equality before the law or equal protection of the laws
• Article 21 - Liberty to live life
• Article 17 - Abolition of untouchability

• Kalli Puri was honoured with India's Most Powerful Woman in Media Award during the prestigious Confluence Excellence Award ceremony held in the British parliament on 27 September 2019.
• She is India Today's Group Vice-Chairperson.
• She was also honoured with the 'Outstanding Media & Entertainment Award' at the annual 21st Century Icon Awards in London.
• The Confluence Excellence Awards aims at recognizing the individuals for their innovative leadership and the success they have achieved while revolutionizing in their field of work.
• Smita Srivastav is Chairperson and Founder of the Confluence Foundation.

• The Jayakwadi dam is situated at Godavari river - Maharashtra.
• It is in Paithan taluka of Aurangabad district.
• This dam is primarily used for storing water for the purpose of irrigation. But it is a multipurpose dam.
• Please note that the foundation of the dam was laid by the former Prime minister of India Lal Bahadur Shastri.

• Ovary is the primary sex organ in females.
• Ovaries produce female gametes (ova).
• It also secretes female sex hormones.
• Estrogens and Progesterone are female sex hormones.
• The vagina is a thin-walled tube lying between the bladder and the rectum.
• The uterus is where offsprings are conceived and in which they gestate before birth.
• A fallopian tube receives the ovulated oocyte and provide a site for fertilization.

Interest rate for 1 year when interest compounded yearly = 8%

Interest rate for 1 year when interest compounded half-yearly = 8/2 = 4%

Total interest rate for at the end of the year when interest compounded half-yearly

4 + 4 + (4 × 4)/100

⇒ 8 + 0.16

⇒ 8.16%

Hence, Difference of rate = 8.16 - 8 = 0.16%

Now, 0.16% of 7800

⇒ 7800 × 16/10000

⇒ 12.48

Average marks of 30 boys = 88

Sum of marks of 30 boys = 88 × 30 = 2640

Average marks of 28 boys = 87.5

Sum of marks of 28 boys = 87.5 × 28 = 2450

Sum of marks of 2 boys = 2640 - 2450 = 190

Let higher marks be x, then lower marks be x - 2

⇒ x + x - 2 = 190

⇒ 2x = 192

⇒ x = 96

Average marks of 30 boys = 88

Deviation of marks on 28 boys = 0.5 × 30 = 15

Sum of marks of 2 boys = 87.5 + 87.5 + 15 = 190

Let higher marks be x, then lower marks be x - 2

x + x - 2 = 190

⇒ 2x = 192

⇒ x = 96

Given:

Diameter of bigger sphere = 40 cm

Radius of smaller sphere = 0.5 cm

Formula used:

Volume of sphere = (4/3) πr³

where r = radius of the sphere

Calculation:

Let the radius of the bigger and smaller sphere be R and r respectively.

The radius of bigger sphere R = 40/2

⇒ 20 cm

Radius of smaller sphere r = 0.5 cm

Let the number of the smaller sphere be x, then

According to the question,

x × (4/3) πr³ = (4/3) πR³

⇒ x × (4/3) × π × (0.5)³ = (4/3) π × (20)³

⇒ x = 8,000/0.125

⇒ x = 64,000

∴ The total numbers of the smaller sphere are 64,000.

Number of smaller sphere = (radius of bigger sphere/radius of smaller sphere)³ = (20/0.5)³

= 40³

= 64,000

∴ The total numbers of the smaller sphere are 64,000.

Marked price of the article = Rs. 888

SP of the article = 888 × (78/100)

∴ CP of the article = 888 × (78/100) × (100/111) = 624

Formula used

sin (90 - θ) = cos θ and cos (90 - θ) = sin θ

cosec (90 - θ) = sec θ and sec (90 - θ) = cosec θ

cos θ sec θ = 1

Solution

sin 40°/cos50° + cosec50°/sec40° - 4 cos50°cosec40°

⇒ cos50°/cos50° + sec 40°/sec40° - 4 cos 50° sec50°

⇒ 1 + 1 - 4

⇒ -2

Total work = 360

Work done by B and C in 6 days = (18 + 20) × 6 = 228

Remaining work = 360 - 228 = 132

Remaining work, A complete in = 132/15 = $8\frac{4}{5};days;$

Let cost price of the article be Rs. x, then according to the question

125x/100 - 118x/100 = 49

⇒ (125x - 118x)/100 = 49

⇒ 7x = 4900

⇒ x = 700

Cost price of the article is Rs. 700

Short Trick:

Let cost of article be Rs. 100%

25% - 18% = 49

⇒ 7% = 49

⇒ 1% = 7

⇒ 100% = 700

As we know,

Area of circle = πr² and circumference of circle = 2 πr

Area of disc = 0.64 π m²

⇒ πr² = 0.64 π

⇒ r = √0.64

⇒ r = 0.8 m

Circumference of disc = 2 × 22/7 × 0.8 = 35.2/7 m

And, 1.408 km = 1408 m

Number of revolutions disc makes = 1408/(35.2/7) = (1408 × 7)/35.2 = 280

As we know,

Area of equilateral triangle = √3/4 × a²

⇒ √3/4 × a² = 36√3

⇒ a² = 36 × 4

⇒ a = 6 × 2

⇒ a = 12

∴ Perimeter of the triangle = 3a = 3 × 12 = 36 cm

Side of triangle a = 8 cm

Area of triangle = √3/4 × a²

⇒ Area of triangle ABC = √3/4 × 8 × 8 = 16√3

As we know, If P,Q and R are the mid points of sides AB, BC and CA, then

Area of ΔPQR = 1/4 × Area of ABC

⇒ Area of ΔPQR = 1/4 × 16√3 = 4√3

$\frac{{\left[ {\left( {30 \times 5} \right) + \left( {84; \times ;6} \right)} \right] \div 5}}{{\left[ {\frac{2}{3} \div 18} \right] - \left[ {4 \div 2} \right]}}$

If ‘+’ means ‘-', '-' means ‘+’, ‘×’ means ‘÷’ and ‘÷’ means ‘×’ then

⇒ $\frac{{\left[ {\left( {30 \div 5} \right) - \left( {84 \div ;6} \right)} \right] \times 5}}{{\left[ {\frac{2}{3} \times 18} \right] + \left[ {4 \times 2} \right]}}$

$\Rightarrow \frac{{\left[ {6 - 14} \right] \times 5}}{{12 + 8}}$

$\Rightarrow \frac{{ - 8 \times 5}}{{20}}$

⇒ -2

(2 sin A + cosec A) = 2√2

Put, A = 45

⇒ 2 sin 45 + cosec 45 = 2√2

⇒ 2 × 1/√2 + √2 = 2 √2

⇒ √2 + √2 = 2 √2

⇒ 2√2 = 2√2 (satisfied)

Now,

2 (sin⁴ A + cos⁴ A)

⇒ 2 (sin⁴ 45 + cos⁴ 45)

⇒ 2 [(1/√2)⁴ + (1/√2)⁴]

⇒ 2 [1/4 + 1/4]

⇒ 2 × 1/2

⇒ 1

Given,

∠OAB = ∠OBA = 30° [OA = OB (radius)]

As we know,

∠OAP = ∠OBP = 90° [tangents]

⇒ ∠OAB + ∠BAP = 90°

⇒ 30 + ∠BAP = 90°

⇒ ∠BAP = 60°

Similarly,

∠OBA + ∠ABP = 90°

⇒ 30° + ∠ABP = 90°

⇒ ∠ABP = 60°

In ΔABP

∠BAP + ∠ABP + ∠APB = 180°

⇒ 60° + 60° + ∠APB = 180°

⇒ ∠APB = 180° - 120° = 60°

3^a = 27^b = 81^c

⇒ 3^a = 3^3b = 3^4c

Comparing on powers

a = 3b = 4c

Let a = 3b = 4c = k

a = k

⇒ 3b = k

⇒ b = k/3

⇒ 4c = k

⇒ c = k/4

abc = 144

k × k/3 × k/4 = 12 × 12

k³ = 12 × 12 × 12

⇒ k = 12

a = 12

b = 12/3 = 4

c = 12/4 = 3

Now,

12 (1/a + 1/2b + 1/5c)

⇒ 12 (1/12 + 1/8 + 1/15)

⇒ 12 × (10 + 15 + 8)/120

⇒ 33/10

Shortcut Trick3^a = 27^b = 81^c

3^a = 3^3b = 3^4c

If we put a = 12, b = 4 and c = 3, then

3¹² = 3¹² = 3¹² [condition satisfied]

Now,

12 (1/a + 1/2b + 1/5c)

⇒ 12 (1/12 + 1/8 + 1/15)

⇒ 12 × (10 + 15 + 8)/120

⇒ 33/10

Shortcut Trick

Let the original population be 100%.

Successive percentage change: 1.30 × 0.85 = 1.105.

Equating with present population: 1.105 units = 11,050.

1 unit = 11,050 ÷ 1.105 = 10,000.

∴ The correct answer is 10,000.

Alternate Method

Given:

Present Population = 11,050

Increase in 1^st year = 30%

Decrease in 2^nd year = 15%

Let the population 2 years ago be P.

⇒ P × (1 + 30/100) × (1 − 15/100) = 11,050

⇒ P × (130/100) × (85/100) = 11,050

⇒ P × (13/10) × (17/20) = 11,050

⇒ P × (221/200) = 11,050

⇒ P = (11,050 × 200) ÷ 221

⇒ P = 50 × 200

⇒ P = 10,000

∴ The correct answer is 10,000.

Additional Information

Successive Percentage Change Formula

Net change = [a + b + (ab/100)]%, where a and b are the percentage changes (use negative sign for decrease).

Population Growth Formula

Final Population = P × (1 ± r₁/100) × (1 ± r₂/100), where P is the initial population and r is the rate of change.

Effective Ratio Method

Convert percentages to fractions: 30% increase = 13/10 and 15% decrease = 17/20. Multiply ratios to find the total change factor.

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

If the number 687x29 is divisible by 9, then

6 + 8 + 7 + x + 2 + 9

⇒ 32 + x

If we put x = 4, so that number become divided by 9.

32 + 4

⇒ 36

Now,

2x

⇒ 2 × 4

⇒ 8

According to the question

2A = 5B = 7C

Let

2A = 5B = 7C = k

2A = k

⇒ A = k/2

5B = k

⇒ B = k/5

7C = k

⇒ C = k/7

Ratio of A, B and C = k/2 : k/5 : k/7 = 70/2 : 70/5 : 70/7 = 35 : 14 : 10

35 + 14 + 10 = 59 unit

59 unit = 1180

⇒ 1 unit = 20

∴ 35 unit = 35 × 20 = 700

Short Trick:

If 2A = 5B = 7C, then

Ratio of A : B : C = 1/2 : 1/5 : 1/7 = 35 : 14 : 10

35 + 14 + 10 = 59 unit

⇒ 59 unit = 1180

⇒ 1 unit = 20

∴ 35 unit = 35 × 20 = 700

Speed of the student = 4 km/hr

Distance between home and school = 4 × 1.25 = 5 km

New time = 1.25 × (3/4) = 15/16 hr

New speed = 5/(15/16) = (5 × 16)/15 = 16/3

For savings time take ratio

Ratio of original speed to new speed = 4 : 16/3 = 3 : 4

Let original speed = 3 and New speed = 4

Speed increased by = 4 - 3 = 1

∴ Speed increased by (in %) = 1/3 × 100 = $33\frac{1}{3}\%$

Short Trick:

Let time taking in the starting be 4 unit

New time = 4 × 3/4 = 3 unit

Ratio of original to new = 4 : 3

As we know,

Speed is inversely proportional to time, then

Speed ratio original to new = 3 : 4

∴ Required speed = 1/3 × 100 = $33\frac{1}{3}\%$

a + b + c = 9 and ab + bc + ca = -22

As we know,

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

⇒ a³ + b³ + c³ - 3abc = 9 [9² - 3 × (-22)]

⇒ a³ + b³ + c³ - 3abc = 9 [81 + 66] = 9 × 147 = 1323

As we know,

If (a - b)² + (x - y)² = 0, then a - b = 0 and x - y = 0,

(a + b - 2)² + (b + c - 5)² + (c + a - 5)² = 0

So,

(a + b - 2) = 0

⇒ a + b = 2     ---- (1)

(b + c - 5) = 0

⇒ b + c = 5     ---- (2)

(c + a - 5) = 0

⇒ c + a = 5     ---- (3)

Solving, (1), (2) and (3), we get

a = 1, b = 1 and c = 4

Now, $\sqrt {{{\left( {b + c} \right)}^a} + {{\left( {c + a} \right)}^b} - 1} = \sqrt {{{\left( {1 + 4} \right)}^1} + {{\left( {4 + 1} \right)}^1} - 1} = \sqrt 9 = 3$

x cos A - y sin A = 1          ---(1)

x sin A + y cos A = 4         ---(2)

Add equation (1) and (2) after squaring

x² cos² A + y² sin² A - 2xysinAcosA + x² sin² A + y² cos² A + 2xysinAcosA = 1² + 4²

⇒ x² (sin² A + cos² A) + y² (sin²A + cos² A) = 1 + 16

⇒ x² + y² = 17

Multiply by 17 on both sides

17x² + 17y² = 289

Total production of maize in 2015 = 490

Total production of maize in 2019 = 840

∴ Required percentage = (840 - 490)/490 × 100 = 71.43%

Production of sugarcane in 2015 = 1000

Production of sugarcane in 2016 = 1120

Growth percentage in 2016 compare to previous year = (1120 - 1000)/1000 × 100 = 12%

Production of sugarcane in 2017 = 1250

Growth percentage in 2017 compare to previous year = (1250 - 1120)/1120 × 100 = 11.6%

Production of sugarcane in 2018 = 1325

Growth percentage in 2018 compare to previous year = (1325 - 1250)/1250 × 100 = 6%

Production of sugarcane in 2019 = 1250

Growth percentage in 2019 compare to previous year = (1450 - 1325)/1325 × 100 = 9.43%

Total production of wheat over five years = 2500 + 4218 + 3482 + 4500 + 3300 = 18000

Average production of wheat over five years = 18000/5 = 3600

Total production of barley over five years = 975 + 825 + 700 + 625 + 775 = 3900

Average production of barley over five years = 3900/5 = 780

Total production of rice over five years = 415 + 520 + 585 + 625 + 600 = 2745

Average production of rice over five years = 2745/5 = 549

Required difference = 780 - 549 = 231

The correct answer is option 2 i.e. they will not be allowed

The sentence uses a pronoun 'those' as a term to refer to people, thus another pronoun - they - is unnecessary and should be removed from the sentence.

The correct answer is option 2.

The correct answer is ambivalent

Key Points

• Ambivalent: Refers to someone who has opposing or contradictory feelings about something
• Let's look at the meaning of the other words:
• Coinciding: Refers to 2 things that happen together, and they are unplanned
• Equivalent: Refers to 2 or more things that are equal
• Contemporary: Refers to something that is living and occurring at the same time
• Thus the correct answer is option 2.

The correct answer is we had run

Key Points

• Here the past perfect tense is used, and we know that with 'had' we should use the third form of the verb. Here the verb used is 'ran' which is the past form but we need past participle (V₃). So 'ran' must be replaced with 'run'.
• If you run out of something, you have no more of it left.
  

 Examples:     

• They have run out of ideas.
• We're running out of time.
• By now the plane was running out of fuel.
• We had lots before but now we've run out.

Thus, the correct sentence is: We came back because we had run out of money.

The correct answer is option 3 i.e. cease

Persist: Refers to someone who does not give up

Cease: Refers to someone who stops

Thus, it is clear that persist and cease are opposite words

Let's look at the meaning of the other words:

Insist: Refers to someone who demands something forcefully

Remain: Refers to someone who stays back

Continues: Refers to someone who goes on

Thus, the correct answer is option 3.

The correct answer is The fields are being ploughed by the farmer.

Key Points  

• In Active Voice, a sentence emphasizes the subject, performing an action.
• In Passive Voice, a sentence emphasizes the action or the object of the sentence.
• The given sentence is in the active voice and 'The farmer' is the subject and 'the fields' is the object.
• When we convert this sentence into passive voice, the subject 'The farmer' of the active voice becomes the object, the object 'the fields' becomes the subject.
• The passive format "are + being + V3 (ploughed)" should be used.
• This is the active and passive voice rule for the present continuous tense.
  

Hence, the correct answer is option 2.

Additional Information

• Verbs of passive format have a different set of tenses (*V3 - Past participle or Third form of the Verb) as given below in the table:
  

The correct answer is option 1 i.e. She exclaimed that it was a very rare flower.

The original sentence contains an exclamation point, thus the reported speech should incorporate this. Thus, option 2 and 4 cannot be used here as they use the verbs told and asked respectively. Option 3 uses present tense and reported speech should be in the past tense, option 3 uses the verb 'is' in the present tense and thus cannot be the answer.

Thus, the correct answer is option 1.

The correct answer is option 3 i.e. offered

The passage talks about Atlas holding up the world on his shoulders. One cannot 'afford' to hold something for someone, thus option 1 is wrong. One cannot 'order' themselves to do something, they can order someone else to do something, thus option 2 is incorrect. Option 4 is incorrect because one cannot extend 'to' something.

Thus, the correct answer is option 3.

The correct answer is option 1 i.e. for

Look for is a phrasal verb which means attempt to find someone or something.

Thus, the work that fits in blank 2 in the sentence is 'for'- the latter went looking (2)______ golden apples. 

The sentence mentions looking for apples, things cannot be looked 'on', thus option 2 is incorrect. One cannot 'went looking at' something, thus option 3 is incorrect. Option 4 is incorrect because one cannot 'went looking after' apples.

Thus, the correct answer is option 1.

The correct answer is option 2 i.e. struggling

One cannot be 'tackling' hard, thus option 3 is incorrect. Option 1 is incorrect because does not 'cope' hard to hold up the sky. Option 4 is incorrect because one cannot 'seek' hard to hold up the sky.

Thus, the correct answer is option 2.

The correct answer is option 1 i.e. was making

The sentence is in the past tense as it is in reported speech. Thus, option 2 and 4 cannot be correct as they are in the present tense. Option 3 is incorrect as there is only one sky - singular - thus the verb should also be singular and 'were' is a plural verb and so cannot be in the answer.

Thus, the correct answer is option 1.

The correct answer is option 1 i.e. take back

The passage shows that Atlas holds up the sky, and Hercules offers to hold it up for a while and he is groaning and sweating meaning that it is not a pleasant job. Thus, this is not a job Atlas would want to 'take back' thus option 3 is incorrect. A job is not an entity that can be 'taken out' and neither can it be taken 'in'. 

Thus, the correct answer is option 1.

The correct answer is option 4 i.e. collapsed

Key Points

• Option 1 is incorrect because a roof is not an entity that can 'destroy'.
• Option 2 is incorrect because 'scratched' needs to have the verb 'be' before it.
• Option 3 is incorrect because it is missing the verb 'was'.
• Option 4 is correct because 'collapsed' means fell down/broke apart, which fits in here as per the grammatical context.

Thus, the correct answer is option 4.

The correct answer is option 4 i.e. the nearest house

The sentence refers to only one house, the term 'nearer' is a comparative term which is used only where there are 2 entities to compare. Thus, the sentence needs to replace 'nearer' with a superlative term 'nearest'.

Thus, the correct answer is option 4.

The correct answer is sieze

Key Points

• The correct spelling is 'seize'. When a group of people seize a place or seize control of it, they take control of it quickly and suddenly, using force.
• Example: Troops have seized the airport and railroad terminals.
• ​Fierce: A fierce animal or person is very aggressive or angry.
• Example: They look like the teeth of some fierce animal.
• ​Piece: A piece of something is an amount of it that has been broken off, torn off, or cut off.
• Example: a piece of cake.
• ​Grief: Grief is a feeling of extreme sadness.
• Example: Their grief soon gave way to anger.

The correct answer is she have

Key Points

• If the subjects are joined by 'as well as', 'with', 'along with', 'together with', 'and not', 'besides', 'except' etc, the verb will agree with the first subject. As 'Everyone' is an indefinite singular pronoun, so singular verb will be used.
• Except is a preposition here and it will be followed by the objective case of pronoun, so 'her' should be there in place of 'she'.

Thus, the correct answer is option 3. 

The correct sentence is: Everyone except her has travelled by air.

The correct answer is fleet

Key Points

• Fleet: A collective term for a group of ships
• Let's look at the meaning of the other words:
• Colony: Refers to territory under the control of people that are not from there
• Swarm: A collective term for a group of bees
• Squad: A collective term for a group with a common goal
• Thus, the correct answer is option 1.

The correct answer is "Woe". 

Key Points

• Glee refers to great delight or joy. ("आनंद" or "खुशी".)
• Example: The child's face was filled with glee when he saw the pile of presents.
• Woe is the correct antonym, which refers to great sorrow or distress. ("दुःख" or "संताप".)
• Example: After learning about the tragedy, her heart was filled with woe.
• Therefore, the correct answer is "Option 1".

Additional Information

• Bliss is a state of perfect happiness or joy, which is similar in meaning to glee. ("परम सुख" or "आनंद".)
• Joy refers to a feeling of great pleasure and happiness. ("आनंद" or "खुशी"), making it synonymous with glee.
• Fun denotes enjoyment, amusement, or light-hearted pleasure. ("मज़ा".)

**The correct answer is '**Applause'.

Key Points

• Ovation: Refers to a sustained show of appreciation through applause (विशेष रूप से उत्साही तालियों द्वारा लोकप्रिय प्रशंसा की अभिव्यक्ति या प्रदर्शन)
• Applause: Approval or praise through clapping (ताली बजाकर व्यक्त की गई स्वीकृति या प्रशंसा)

Thus, it is clear that ovation and applause are similar words

Let's look at the meaning of the other words:

• Preparation: The process of being prepared for something (किसी चीज के लिए तैयार होने की प्रक्रिया)
• Censure: Refers to severe disapproval by someone (कड़ी आलोचना या अस्वीकृति व्यक्त करने के लिए)
• Creation: Refers to the act of producing something (कुछ नया बनाने या की क्रिया या प्रक्रिया)

The correct answer is option 3 i.e. DACB

The passage begins with statement D which introduces the topic at hand - Andre Maginot's fight against the Germans. This is followed by statement A which talks about the war in detail - the Western Front as the location, the comes statement C which talks about the Western Front in further detail and finally comes statement B which talks about how the men on either side dealt with the terrain.

Thus, the correct answer is option 3.

The correct answer is option 1 i.e. cowardly

The idiom 'chicken-hearted' refers to someone who is scared easily or is a coward

Thus, the correct answer is option 1.

The correct answer is option 2 i.e. gradually

The idiom 'by and by' refers to something that happens slowly and eventually.

Thus, the correct answer is option 2.

The correct answer is wondered

Key Points

• Meaning of the words given in the options are:
• Suspected: believed guilty of an offense
• Wondered: to have curiosity or doubt about; want to know
• Bewildered: If you are bewildered, you are very confused and cannot understand something or decide what you should do.
• Puzzled: Someone who is puzzled is confused because they do not understand something.
• Thus, the correct answer is option 2.