RRB JE CBT 1 - Full Test 9

• Michael Ondaatje was awarded the 2018 Golden Man Booker Prize for his novel “The English Patient”.
• Anna Burns received the 2018 Booker Prize for her novel, “Milkman”.
• George Saunders won the 2017 Man Booker Prize for the novel “Lincoln in the Bardo”.
• Paul Beatty won the 2016 Man Booker Prize for the novel “The Sellout”.

• Minister of External Affairs, Smt. Sushma Swaraj inaugurated the Mango Festival in Tashkent, Uzbekistan in August 2018.
• The festival was organized by the Government of Uttar Pradesh to promote Indian Mangoes business in Uzbekistan.
• The festival was organized with the participation of Mango exporters in Tashkent.

• India ranked 1^st in the 36^th Golden Glove of Vojvodina Youth Men and Women Boxing Tournament.
• The tournament took place in Serbia.
• India won total 7 gold medals (4 men, 3 women), 6 silver medals and 4 bronze medals.
• Kazakhstan secured the second position with 7 medals (including 5 gold) and Russia got the third position with total 11 medals (including 3 gold).

• Indu Bhushan is the CEO of the Ayushman Bharat Yojana.
• PMJAY was launched on 23^rd September 2018 in Ranchi, Jharkhand by Prime Minister Narendra Modi.
• Health insurance of worth Rs 5 lakh will be provided under this scheme to over 10 crore families.

• “Bebak Baat” authored by Vijay Goel, was released on 9 August 2018 by Vice President Shri M. Venkiah Naidu.
• Shri Naidu while addressing people at the gathering said that for the development of the nation, continuous communication between public representatives and the public is important.
• Books written by:

• Banihal Pass also known as Jawahar tunnel was named after Pandit Jawaharlal Nehru.

• It was inaugurated in the year 1956 and connects the Kashmir Valley to the hill areas of Jammu.
• It is situated at an elevation of 2835 meters above sea level.

• Volcanoes are known as the safety valves of nature because they periodically release the pressure that builds up because of tectonic activity in the Earth’s crust and even lower layers.
•  When pressure builds up, eruptions occur. Magma shoots up through the volcano and flows down its sides.

Warren Hastings was the Governor General during the period of First-Second Mysore war. Lord Cornwallis was the Governor General during the period of Third Anglo-Mysore war. Lord Wellesley was the Governor General during the period of Fourth Anglo-Mysore war.

• The first ever railway line was laid between Bombay and Thane in the year 1853. 
• Lord Dalhousie was known as the Father of Indian Railway since he launched the first ever railway carriage in the country. 
• He also established the telegraph line between Calcutta and Agra in 1853. 
• Lord Dalhousie was also known for the establishment of Public Works Department and Widow Remarriage Act 1856. 

• C.N. Annadurai in the year 1949 founded the Dravida Munnetra Kazhagam (DMK) party.
• It’s a state political party active in Tamil Nadu and Puducherry.
• The formation of the DMK party took place due to the breakdown of the Dravidar Kazhagam.
• It was the first party other than Indian National Congress to form government independently in a state.

Article 150: The accounts of the Union and of the States shall be kept in such form as the President may, on the advice of the Comptroller and Auditor General of India, prescribe

Article 124: Establishment and constitution of Supreme Court

Article 156: Term of office of Governor

Article 120: Language to be used in Parliament.

Jaldapara National Park is situated at the foothills of the Eastern Himalayas in Alipurduar District of northern West Bengal and on the banks of the Torsa River. It was declared a sanctuary in 1941 for protection of its great variety flora and fauna. Today, it has the largest population of the Indian one horned rhinoceros in the state, an animal threatened with extinction, and is a Habitat management area.

• According to the law of supply, if the price increases the quantity supplied will also increase.
• Law of supply states that other factors remaining constant, price and quantity supplied of a good are directly related to each other.
• It depicts the producer behavior at the time of changes in the prices of goods and services. When the price of a good rises, the supplier increases the supply in order to earn a profit because of higher prices.

• Uday Shankar is a famous Classical Indian dancer.
• He was an Indian dancer, choreographer, and pioneer of modern dance in India.
• He was awarded Padma Vibhushan in 1971, which is the second highest civilian award in India.

Hans Christine Anderson Award also known as Anderson Award is an award given to honour the literary works of an author. Ruskin Bond was the first Indian to get this prestigious award which was established in 1956.

• Guava is the highest source of ascorbic acid and is also high in dietary fiber.
• Ascorbic acid or vitamin C is a multi-functional nutrient. It promotes a healthy immune system and protects the body from chemical damage.
• All the citrus fruits such as guava, oranges, kiwi, etc, are a good source of vitamin C.
• Apples and tomatoes are also rich in vitamin C.

• Cholera is caused because of a bacterium called Vibrio cholerae.

• The major component of honey is fructose.
• Honey is a food substance which is sweet and is produced by bees from the sugary secretions of plants.
• Honey gets its sweetness from glucose and monosaccharides fructose.
• Fructose, also known as fruit sugar is a ketonic monosaccharide found in many plants.
• Sucrose is the common table sugar and maltose is malt sugar.

• A nucleotide is an organic molecule which is the building block of RNA and DNA.
• Nucleotide base present in DNA and not RNA is thymine.
• Uracil is present in RNA instead of thymine.
• The 5 nucleobases include thymine, uracil, adenine, cytosine, and guanine.

• In a blast furnace, coke (C) reacts with oxygen to form carbon monoxide, which then reacts with iron oxide to form carbon dioxide and pig iron.
• Iron oxide must be reduced in order to obtain iron and this can be done only in a blast furnace.

• Silver is obtained by leaching it over with a dilute cyanide solution. It is also sometimes extracted from its ore by smelting.
• Titanium is obtained using the Kroll process.
• Vanadium is obtained through various ways such as passing the electric current through molten vanadium chloride or calcium with vanadium oxide.
• Zinc is obtained by roasting and smelting.

• Copper is extracted by the thermal reduction process. It is a group of processes based on the reduction of metal compounds by more active metals into corresponding metals and accompanied by the evolution of heat.
• Iron is extracted through the process of calcination roasting.
• Aluminium is extracted by the process of electrolysis.
• Magnesium is extracted through electrochemical processes.

• The S.I unit of “luminance” is candela per meter square, i.e., cd/m²
• Stilb is the CGS unit of “luminance”.
• For a light travelling in a given direction, the photometric measure of the luminous intensity per unit area, is termed as “luminance”.

Kinetic energy is given by the formula ½ × m × v², where m is the mass of the moving object and v is its velocity. Therefore, when speed is halved kinetic energy becomes ¼ of the original.

Eg. m = 2 kg, v₁ = 40, v₂ = 20(when speed of object is halved)

K.E₁ = 0.5 ×2× 40 ×40 = 1600

K.E₂ = 0.5 × 2 × 20 × 20 = 400

Oscillation is going back and forth repeatedly between two positions or states. Oscillation can be a periodic or aperiodic motion.

Simple harmonic motion is a type of periodic oscillation where the restoring force is directly proportional to the displacement.

The motion of a simple pendulum is an example of simple harmonic motion.

• It is the Charle’s Law that describes how gases tend to expand when heated. This law was formulated by Joseph Louis Gay-Lussac in 1802, but he credited it to the unpublished work of Jacques Charles.

• For a fixed mass of gas at constant pressure, the volume is directly proportional to the Kelvin temperature.

  V/T=Const

• The atmosphere of the earth is heated by the process of convection. 
• In cases of liquids and gases, the transfer of heat takes place through convection. It is a process by which heat travels through water, gas, air, or other liquids.
• In convection, the heat energy is transferred by the actual movement of the particles from one place to another. Whenever a liquid or a gas is heated, the molecules of these substances become lightened and move upwards and then cooler molecules settle downwards and heated. In this way, the atmosphere of our earth is heated by the process of Convection. 
• Radiation is the propagation or emission of energy in the form of waves or rays.
• Conduction is the process of movement of electricity or heat through a passage or medium.
• The discharge and production of radiations and gases is known as emission.

Note: Radiation and Conduction processes are also involved but Convection is dominant. 

• A person with hypermetropia cannot see nearby objects clearly.
• Hypermetropia, sometimes called hyperopia, is the term used to define being longsighted.
• If a person is hypermetropic, the image of a nearby object is formed behind the retina. This means that light is focused too far back in the eye, causing things which are close up to appear blurred.

Hence, 1 is the correct option.

• The phenomenon of electromagnetic induction is the current induced in a coil due to relative motion between a magnet and the coil.
• It was discovered by Michael Faraday.
• Electrical equipment like motor, generators, and transformer are based on the phenomena of electromagnetic induction.

Work done is given by the dot product of force and displacement vector i.e.,  = Fd cosq, where q is the angle between the force and displacement vector. Hence the work done depends on displacement d, force F, and q - angle between force and displacement.

• Dynamite is an explosive which is used in mining, quarrying, construction and demolition industries. 
• It is made of Nitroglycerin, sorbents and stabilizers. 
• It was invented by Swedish Chemist Sir Alfred Nobel on whose memory the Nobel Prize has been constituted. 
• Nitro Glycerin: C₃H₅N₃O₉

Antacids usually neutralize the acidity of the stomach which gives relief during indigestion.

Antibiotics prevent the growth of bacterial infections in the body.

Analgesic medicines are used to give relief from pain.

Antiseptics are used to cure infections or upper tissues of the body.

• Glycogen, starch and cellulose are polymers of Glucose.
• Polymers are materials made of long, repeating chains of molecules.
• Glycogen serves as a form of energy storage in humans, animals, fungi, and bacteria.
• Starch is a polymer made by plants to store energy.
• Cellulose is the main substance that makes up the cell walls and fibers of plants.

Ferrous Sulphate(FeSO₄) is also known as Green Vitriol. It is a bluish - green crystalline compound. It is used in sewage and water treatment and as a pigment and fertilizer. It also has usage in medicine to treat iron deficiency.

• Bituminous is the type of coal which is available in both caking and non-caking forms.
• Caking coal is a type of coal which when heated in anaerobic conditions leaves a solid residue whereas non-caking coal when heated in similar conditions leaves a powdery residue.
• Peat coal is the first stage of transformation and that is why it contains more impurities and less amount of carbon. 
• Lignite is lower grade coal and it contains 40-55 percent carbon. 
• Anthracite coal is the best quality coal and it contains around 90% carbon in it. 

The principal organic acids found in grapes are tartaric, malic, and to a small extent, citric.

Halophytes are plants that grow in salt water. The most common example of this is Mangroves which are quite ubiquitous across India’s coastal lines. Moreover it’s one of the type of Mangroves named Sundari, after which the forest of Sundarbans are based upon.

• Testa, also known as ‘seed coat’, is the tough outer covering of a seed which provides it protection. It develops from the integument.
• Hilum is a scar on the seed coat that indicates the region of detachment.
• Radicle is a part of the seedling that develops into the root of the plant.

The smallest blood vessels which are one-cell thick, are called Capillaries. Their main function is to enable the exchange of substances between the blood and surrounding tissues. They provide nutrients and oxygen to tissues and remove the byproducts of cellular reactions, such as carbon dioxide and water.

● An oil spill is the release of a liquid petroleum hydrocarbon in the environment, especially in the marine ecosystem because of human activity.

● It is a form of pollution which is caused because of release of crude oil from tankers, drilling rigs and wells, offshore platforms and more.

● It can have disastrous consequences for society; economically, environmentally, and socially.

Disclaimer: We have changed the statement and options of this question slightly as UPSC dismissed this question in the official answer key.

All of them are included in the National Air Quality Index

• Concentration of Air pollutants like PM₁₀, PM_2.5, NO₂, O₃, CO, SO₂, NH₃ and Pb in the air is computed to determine the Air Quality through National Air Quality Index.
• It is aimed at balancing environment, conservation and development.
• The Minister for Environment, Forests & Climate Change launched ‘The National Air Quality Index’ (AQI) in New Delhi
• There are six AQI categories, namely Good, Satisfactory, Moderately polluted, Poor, Very Poor, and Severe.  

Note: National Air Quality Index is ‘One Number- One Colour-One Description’ for the common man to judge the air quality within his vicinity.

The chemicals controlled by the Montreal Protocol at first included refrigerants such as Chlorofluorocarbons(CFCs) and halons, but the list of controlled chemicals under the Montreal Protocol today includes HCFCs, methyl bromide, and other ozone - depleting substances (ODS).

NBA is a social movement consisting of adivasis, farmers, environmentalists and human rights activists against a number of large dams being built across the Narmada River. Anna Hazare led the India against corruption movement whereas Sunderlal Bahuguna led the Chipko movement

The series of processes by which nitrogen and its compounds are interconverted in the environment and in living organisms is called nitrogen cycle. Important processes in the nitrogen cycle include fixation, ammonification, nitrification, and denitrification.

Sugary means containing much sugar.

Stinky means having a strong or unpleasant smell.

Cloying means to disgust or sicken (someone) with an excess of sweetness.

Saccharine means excessively sweet or sentimental.

Here all the words are related of sweet, while stinky is antonym of sweet.

Thus ‘stinky’ is the odd word.

1) Lao Kip → is a currency of Laos

2) Ngultrum → is a currency of Bhutan

3) Hryvnia → is a currency of Ukraine

4) Baku → is a capital of Azerbaijan

Here all the words are currencies of different countries, whereas Baku is the capital.

Thus ‘Baku’ is the odd word.

The logic here is as follows,

Considering the place value of letters as per English alphabetical series,

FD → 6² - 4² = 36 - 16 = 20

The alphabet whose place value is 20 is T.

Similarly,

DA → 4² - 1² = 16 - 1 = 15

The alphabet whose place value is 15 is O.

Hence, “O” is the correct answer.

Hepatitis, Measles and Tuberculosis are communicable diseases. Similarly from the options Cholera is also a communicable disease.

Hence, ‘Cholera’ belongs to the same group.

Here the pattern is as follows,

Thus the missing term is ‘N19 H’.

According to given coding language,

Now if numbers are written in reverse order we get, 19215816.

Similarly for HUMBLE,

Now writing the numbers in reverse order we get, 512213218.

Hence, “HUMBLE” is coded as “512213218”.

Cigarettes are injurious to health even if consumed in lower levels. It should be avoided completely since it will cause cancer leading to death finally. Argument I states this issue and strongly favours the statement of banning cigarettes. Argument II is also strong as the cigarette industry is a big one and closing it down completely will lead to many workers losing their jobs. Argument II also follows.

Either argument I or II is true. the statement.

If the letters A, E, G, H, N, O & N are numbered 1, 2, 3, 4, 5, 6, 7 & 8

1) 42871356 → HETPAGNO

2) 42781536 → HEPTANGO

3) 42781365 → HEPTAGON

4) 42783156 → HEPTGANO

Hence, “42781365” is the correct answer.

Rectangle represents Dutch, circle represents Indian, triangle represents African and square represents Chinese.

Letters representing Indians who are either African or Chinese i.e. circle which is either triangle or square are H and G.

Hence, “None of the above” is the correct answer.

Rectangle represents Cars, circle represents Ford, triangle represents Mercedes and square represents Truck.

Letters representing Truck who is either Ford or Mercedes i.e. square which is either circle or triangle are D and F.

Hence, “D and F” is the correct answer.

The least possible Venn diagram from the given statements is as follows,

Conclusion I: Some diets are healthy → False

Conclusion II: No diet is healthy → False

But these two forms a complementary pairs.

Hence, either conclusion I or II follows.

When the paper is unfolded it will appear as below:-

Hence option 3rd is the correct answer.

After a train derails, the first step would be to save the lives of people. Also, many coaches have caught fire. Therefore, sending medical help and fire brigade to the location of the accident would be necessary to stop more damage.

Hence, both I and II follow and option (4) is correct.

As face containing 2 is visible on all given cubes the other faces surrounding the face containing 2 are 5, 3, 6, and 4.

Face containing 6 is adjacent to face containing 4 and 3.

That means face containing 4 and 3 are opposite to each other.

According to the question,

1) No car gets it’s servicing done on Monday and Sunday.

2) Polo gets it’s servicing done on Saturday.

3) C is having Wagon R and visit service center on Friday.

4) A visits service center on Tuesday.

 

5) No person gets servicing done between A and D.

6) B don’t have Polo car or Jeep.

7) Car Alto gets serviced between Verna and Jeep.

Hence, from the above arrangement, Alto gets servicing done on Wednesday and A is having the Jeep.

Changing operations as given format:

Given expression: 18 - 9 ÷ 15 + 10 × 5 = ?

After changing the symbols: 18 ÷ 9 × 15 - 10 + 5

= 2 × 15 - 10 + 5

= 30 - 10 + 5

= 25

Hence, “25” is the correct answer.

Using the formula to find the angle between hour hand and minute hand

Θ = 30 H - 11/2 M

Where H = hour hand

And M = minute hand

Hour hand is in between 2 and 3, 30 (2) = 60.

For minute hand

11/2 (22) = 121

The difference between our hand and minute hand will be 121 – 60 = 61 degree

Hence, 61 degree is the correct answer.

The pattern followed here is,

5² = 25; 25 – (5 × 2) = 25 – 10 = 15; 15 + 5² = 40

4² = 16; 16 – (4 × 2) = 16 – 8 = 8; 8 + 4² = 24

Similarly,

6² = 36; 36 – (6 × 2) = 36 – 12 = 24; 24 + 6² = 60

Thus the missing number is 60.

According to the question,

1) Eight people A, B, C, D, E, F, G, and H are sitting around a circular table facing outside.

2) A and E sits opposite to each other.

3) C is not the immediate neighbor of either A or E.

4) D sits second to the left of A.

5) H is the immediate neighbor of A.

6) F who is not an immediate neighbor of C sits opposite to that of H.

7) G is not an immediate neighbor of A.

Hence, from the above arrangement, B is sitting third the left of C and there are 2 people sitting between E and B counting clockwise from E.

Hence “B, 2” is the correct answer.

Answer: Option 4 is correct.
Solution: The statement does say that some of the victim’s allegations were not true, but that does not mean that all of the victim’s allegations were fake. So, inference I does not follow. The third suspect is taken for misprision but that does not imply that the other two guilty ones made him conceal their crime. So, inference II is also not true. Therefore, option 4 is the correct answer.

Harshita gets more marks than only Sakshi and Shweta.

_ > _ > Harshita > Shweta/Sakshi > Shweta/Sakshi

Shweta scored less marks than Deepti, who did not scored the highest marks.

Fatima > Deepti > Harshita > Shweta/Sakshi > Shweta/Sakshi

Hence Fatima scored the highest.

Hence, from the above arrangement, K is the grandson of A.

I am child of her father’s wife’s mother-in-law’s grandchild but none of my parents are teacher: Means teacher is a female as her is used here. And none of C's parents are teacher means Teacher cannot be the mother of C.

Hence, from the above arrangement Teacher is Aunt of C.

On close observation, we find that the problem figure in embedded in figure (3) as shown below.

Hence, the answer is figure 3.

Answer: Option (4) is correct.
Solution: Labour laws and excessive regulations assumed to protect the labor are the cause of slow employment growth in high paying, organized sector. Companies find it difficult to pay the minimum wages and ask them to work only up to some time limit fixed by the respective country’s government. As a result, there is less foreign investment leading to a downturn of the economy. Therefore, assertion is completely false by definition only and reason, as stated above, is true. Therefore A is false but R is true.

[(289 + 87) ÷ 2 - 7 × 18 ÷ 2 + {(9 + 5) × 19} + 3 × 7 - 9] × 19 + 9 = ?

[376 ÷ 2 - 7 × 18 ÷ 2 + {(9 + 5) × 19} + 3 × 7 - 9] × 19 + 9 = ?

? = [188 - 7 × 18 ÷ 2 + 266 + 3 × 7 - 9] × 19 + 9

? = [188 - 7 × 9 + 266 + 3 × 7 - 9] × 19 + 9

? = [188 - 63 + 266 + 3 × 7 - 9] × 19 + 9

? = [188 - 63 + 266 + 21 - 9] × 19 + 9

? = 7657 + 9

? = 7666.

Cost of 10 shirts on 1^st day = 10 × 150 = 1500 Rs.

Cost price of shirt on 2^nd day = 150 – 30 = 120 Rs.

No. of shirt purchased on 2^nd day = 1800/120 = 15

Total expenditure = 1500 + 1800 = 3300

Total shirts = 10 + 15 = 25

∴ Average cost of shirt = 3300/25 = Rs. 132

Given,

⇒ Percent votes gained by Suresh = 34%

⇒ Percent votes gained by Ramesh = 36%

⇒ Percent difference between their votes = 2%

⇒ Number of Vote difference between them = 40

∴ 2% = 40

⇒ 100% = (40/2) × 100 = 2000

Let the four students be a, b, c, d

Sum of age of the last three students (b + c + d) = 20 × 3 = 60      ----(1)

Sum of age of the first three students (a + b + c) = 21 × 3 = 63     ----(2)

Subtraction Equation 2 with Equation 1, we get (a - d) = 3

Given age of the first student ‘a’ = 26

Age of the last student ‘d’ = a – 3 = 26 – 3 = 23

∴ Required answer = 23

Let Length and breadth of rectangle be a and b respectively

Initial area = length × Breadth = ab

New length = a + 40% of a = 1.4a

New breadth = b + 70% of b = 1.7b

New area = (1.4a) × (1.7b) = 2.38ab

∴ Required % = {(2.38ab – ab/ab} × 100 = 138%

Let the amounts of silver, gold and platinum in the first alloy be 4x, 7x and 3x.

Total amount used = 14x.

Let the amounts of iron, gold and platinum in the second alloy be 8y, 9y and 11y.

Total amount used = 28y

Since equal amounts are mixed, 14x = 28y ⇒ x = 2y

Total alloy = 28y + 28y = 56y = 1 Kg. ⇒ y = 1/56 Kg

Amount of gold = 7x + 9y = 14y + 9y = 23y = 23/56 Kg.

Follow these BODMAS rules to solve the question

Step-1∶ The part of the equation containing 'Brackets' must be solved first, and in the bracket,

Step-2∶ Any mathematical 'Of' or 'Exponent' must be solved next,

Step-3∶ Next, the parts of the equation that contain 'Division' and 'Multiplication' are solved

Step-4∶ At last, the part of the equation that contains 'Addition' and 'Subtraction' should be solved.

⇒ (1/64)⁰ + (-32)^4/5 + (64)^-1/2 + (32)^2/5 = ?

Anything raise to power 0 is 1, ∴ (1/64)⁰ is = 1

⇒ ? = 1 + (-2^{5 × 4/5}) + (1/8) + (2^{5 × 2/5})

⇒ ? = 1 + 16 + 1/8 + 4

⇒ ? = 21 + 1/8

⇒ ? = 169/8

There is a rice for 150 children

100 children have taken the meal.

Remaining rice is to be catered to 50 children.

150 children = 75 men.

50 children = (75 × 50)/150 = 25 men.

Given that,

Ratio of the wages of Sunny and Mickey = 2 : 3

Ratio of the wages of Mickey & Vicky = 7 : 8

Ratio of the wages of Sunny, Mickey and Vicky are 14 : 21 : 24

Let the wages of Mickey be 21x and that of Vicky be 24x

According to the question,

21x × 24x = 50400

⇒ 504x² = 50400

⇒ x² = 100

⇒ x = 10

So, the wages of Mickey = Rs. 210 and the wage of the Vicky is Rs. 240

So, the wage of Sunny = 210 × (2/3) = Rs. 140

Hence the required difference = (210)² – (140)² = 44100 – 19600 = 24500

∴ The required answer is 24500

We can write, 2⁵⁵ = (2⁴)¹³ × 2³

⇒ Unit digit (2⁵⁵) = Unit digit (6¹³ × 8)

⇒ Unit digit (2⁵⁵) = Unit digit (6 × 8) = 8

Similarly,

We can write, 3²³ = (3⁴)⁵ × 3³

⇒ Unit digit (3²³) = Unit digit (1⁵ × 7)

⇒ Unit digit (3²³) = 7

Now,

Unit digit (2⁵⁵ + 3²³) = Unit digit (8 + 7) = 5

∵ When 5 is divided by 5, the remainder is 0

∴ When (2⁵⁵ + 3²³) is divided by 5, the remainder is 0

When a number is divisible by both 4 and 7, then the number is also divisible by 4 × 7 = 28.

The numbers from 33 to 143 which are divisible by 28 are 56, 84, 112 and 140

Hence, there are 4 numbers between 33 and 143 which are divisible by 4 and 7.

Let the fraction be y

According to the problem statement

⇒ 4y + 7/y = 16

⇒ 4y² – 16y + 7 = 0

⇒ (y – 1/2)(y – 7/2) = 0

⇒ y = ½ or y = 7/2

the required fraction is 7/2 which satisfies the above given condition

∴ the value of required fraction is 7/2

∵ (a + 1/a)² = (a² + 1/a²) + 2

⇒ (a + 1/a)² = 17/4 + 2 = 25/4

⇒ (a + 1/a) = 5/2

Also,

∵ (a - 1/a)² = (a² + 1/a²) - 2

⇒ (a - 1/a)² = 17/4 - 2 = 9/4

⇒ (a - 1/a) = 3/2

∴ (a² - 1/a²) = (a + 1/a)(a - 1/a) = 5/2 × 3/2 = 15/4

Let the roots be t and t²

⇒ Sum of roots = -b/a

⇒ t + t² = -p

⇒ Product of roots = c/a

⇒ t³ = q

p³ + q² = -(t + t²)³ + t⁶

⇒ -[t³ + t⁶ + 3t³(t + t²)] + t⁶ [∵ (a + b)³ = a³ + b³ + 3ab(a + b)]

⇒ -[t³ + 3t³(t + t²)]

⇒ -[q - 3qp] [∵ t³ = q, t + t² = -p]

⇒ p³ + q² = -q + 3pq

∴ p³ + q + q² = 3pq

Applying the operation of a*b with 12 and 4 we have

= 12 + 4 + (12/4)

= 16 + 3

= 19

Let Kunal and Karan’s share be Rs. ‘x’ and Rs. ‘y’ respectively

Amount of money = x + y

⇒ 5x + 2y = 4(x + y)

⇒ 5x – 4x = 4y – 2y

⇒ x = 2y

Also, (1/5)x + (1/4)y = 325

⇒ 4x + 5y = 325 × 20

Substituting for x,

⇒ 4(2y) + 5y = 6500

⇒ 13y = 6500

⇒ y = 6500/13 = 500

⇒ x = 2y = 2(500) = 1000

∴ The amount of money is = x + y = 1000 + 500 = Rs. 1500

Given,

A man gains 70% by selling an article for a certain price.

Let the cost price of an article be Rs.100.

Profit percentage = [(S.P - C.P) / C.P] × 100

⇒ 70 = [(S.P - 100) / 100] × 100

⇒ 70 = S.P - 100

⇒ S.P = Rs.170

Given,

If he sells it at half the price, then

New S.P = Rs.85

Loss percentage =

= [(C.P - S.P) / C.P] × 100

= [(100 - 85) / 100] × 100

= 15

∴ Loss percentage is 15%.

X invested Rs. 12000 for 4 months

⇒ X’s total capital investment = 12000 × 4 = 48000

Y invested Rs. 9000 for 12 months

⇒ Y’s total capital investment = 9000 × 12 = 108000

Z invested Rs. 18000 for 12 - 4 = 8 months

⇒ Z’s total capital investment = 18000 × 8 = 144000

∵ Ratio of profit share = Ratio of total capital investment

⇒ Ratio of profit share = 48000 ∶ 108000 ∶ 144000 = 4 ∶ 9 ∶ 12

Sum of ratios = 4 + 9 + 12 = 25

Now, total profit = Rs. 12500

∴ Z’s profit share = 12/25 × 12500 = Rs. 6000

⇒ a + a² + a³ - 1 = 0

⇒ a + a² + a³ = 1      ---- (1)

Dividing the equation by a, we get

⇒ 1 + a + a² = 1/a

⇒ a³ + (1/a) = a³ + 1 + a + a² = a + a² + a³ + 1

Substituting the value from equation 1, we get

⇒ a³ + (1/a) = 1 + 1 = 2

Total cost price = 10 × 180 = Rs. 1800

Total selling price = 10 × 12 × 19.5 = Rs. 2340

∴ Profit % = {(S.P - C.P)/C.P} × 100 = {(2340 - 1800)/1800) × 100 = 30%

Let rate of interest be r

C.I = Principal × [(1 + r/100)^Time - 1]

⇒ 1881 = 10000 × [(1 + r/100)² - 1]

⇒ 1881/10000 = [(1 + r/100)² - 1]

⇒ 0.1881 + 1 = (1 + r/100)²

⇒ 1.1881 = (1 + r/100)²

⇒ 1.09 = 1 + r/100

⇒ r = 9%

Simple interest = (Principle × Time × r)/100

⇒ S.I = (10000 × 9 × 3)/100 = 2700

∴ Simple interest = Rs. 2700

Alternative Method :

Given, Principal = Rs. 10000   

Amount = 10000 + 1881 = Rs. 11881 (After 2 years)

for calculating the rate for 2 years. we have to take square root of both the values

then we get

P = 100 and A = 109

R = 109 - 100/100 × 100 = 9%

Now,

Simple interest = (Principle × Time × r)/100

⇒ S.I = (10000 × 9 × 3)/100 = 2700

∴ Simple interest = Rs. 2700

The relative speed of driver of the goods train with respect to the passenger train

⇒ 32 + 40 = 72 kmph

⇒ The relative speed of driver of the goods train with respect to the passenger train in m/s

∴ Time taken by the driver of the goods train to pass the passenger train = 1200/20 = 60 s

Let each installment be Rs. x

Hence, (Amount of Rs. x due 1 year hence) + (Amount of Rs. x due 2 years hence) + (Amount of Rs. x due 3 years hence) = 7620

⇒ 6x/7 + 36x/49 + 216x/343 = 7620

⇒ 294x + 252x + 216x = 7620 × 343

⇒ x = (7620 × 343) /762 = 3430

∴ Amount of each installment = Rs. 3430

⇒ Let the total distance covered by the train ‘S’ be ‘d’, Then the distance covered by train ‘R’ be (90 + d)

⇒ When they meet for the first time, they both have travelled for the same time, so the Speed is directly proportional to Distance

⇒ S₁/S₂ = D₁/D₂

⇒ (35/42) = d/(d + 90)

⇒ (35/42) = d/(d + 90)

⇒

⇒ 5× (d + 90) = 6d

⇒ 5d+ 450 =6d

⇒ d = 450

⇒ Distance between S and R =  450 + (450 + 90)

∴ Required Distance = 990

Alternative:

Difference in speed between 2 trains = 42 - 35 = 7 km/hr

Since train 2 has covered 90 kms more before they meet.

So, total time taken to cover 90 km = 90/7 = 12.857 hours

Distance covered by train 1 before they meet = 12.857 × 35 = 450 km

Distance covered by train 2 before they meet = 450 + 90 = 540 km

So total distance between S and R = 450 + 540 = 990 km

Given,

L’s 1 hour’s work = 1/100

M’s 1 hour’s work = 1/150

Let N can complete work in n days.

N’s 1 hour’s work = 1/n

Given,

(L + M + N)’s 1 hour’s work = 1/30

⇒ 1/30 = (1/100) + (1/150) + (1/n)

⇒ 1/30 = 1/60 + 1/n

⇒ 1/n = 1/30 - 1/60

⇒ 1/n = 1/60

∴ N can complete work in 60 days.

Let the radii be a and b respectively

⇒ a + b = 91     ---- (1)

⇒ Difference in area = (22/7) × (a² – b²) = 2002

⇒ a² – b² = 91 × 7     ---- (2)

Dividing equation 2 by equation 1 and using [a² – b² = (a + b) (a – b)], we get

⇒ a – b = 7     ---- (3)

By Adding equation 1 and 3, we get

⇒ 2a = 98

⇒ a = 49 cm

⇒ b = 42 cm

∴ Radii of larger circle is 49 cm

IN ΔABC

When cube of maximum volume is cut from sphere, the diagonal of the cube = Diameter of the sphere

∴ √3 a = 2r

a/r = 2/√3

Volume of cube/Volume of sphere = a³/ (4/3 π r³)

⇒ 3/(4π) × (a/r)³

⇒ 3/(4π) × (2/√3)³

⇒ 2/(√3π)

∴ The required ratio = 2 ∶ √3π

We know, a₁, a₂, a₃…..a_n are said to be H.P, then 1/a₁, 1/a₂, 1/a₃….. 1/a_n are in A.P

Given, 6^th term of HP is 8,

In A.P, a + 5d = 1/8                 ….. (1)

5^th term of HP is 11,

In A.P, a + 4d = 1/11                     ….(2)

Solving equation (1) and (2) we get