RRB NTPC Mock Test - 10 (English)

• Indian National Army was founded by Rash Behari Bose in 1942.
• In July 1943 when Subhash Chandra Bose joined the INA, Rash Behari Bose handed over the leadership to him.
• INA had two headquarters at Rangoon and Singapore.
• INA had three fighting brigades named after Gandhi, Azad, Nehru. Rani Jhansi Brigade was an exclusively women force.

• The India Gate was designed by Sir Edwin Lutyens.
• It is a war memorial of the soldiers of the British Indian Army who died in the First World War.
• Edwin Lutyens designed various buildings like Viceroy's House which is now known as Rashtrapati Bhavan with Herbert Baker.
• Because of his marvellous work, an area in New Delhi is also known as Lutyens' Delhi.

• Impeachment of President is not the source from the constitution of Ireland.
• Impeachment of President is taken from the constitution of the USA. These are taken from the Constitution of Ireland.
• Principles of State Policy
• Method of Election of President
• Nomination of members of Rajya Sabha

• President of India can provide the sections out of Contingency Fund of India to meet the emergency expenditures of the country.
• Article 267 empowers the parliament to establish the Contingency Fund of India.
• In the year 2005, its limit was raised from Rs. 50 crore to Rs 500 crore.
• Before sanctioning of money by the President, a bill is introduced in the Parliament for the approval.

• Trisul peak is located in the Kumaon division in Bageshwar district of Uttarakhand.
• It is a combination of 3 peaks that form a trident shape, Trishul, a weapon of Lord Shiva.
• Trisul I: 7,120m
• Trisul II: 6,690
• Trisul III: 6,007

• Saddle Peak is located on the North Andaman.
• It is the highest peak on Andaman and Nicobar islands with an elevation of 731m.
• It is located near Diglipur, a town in North Andaman Island.

• Indian Standard Time is calculated on the basis of 82.5' E longitude, in Mirzapur Uttar Pradesh.
• This 82.5' E is termed as Indian Standard Meridian.
• This line pass through 5 Indian States namely: Madhya Pradesh, Uttar Pradesh, Chhattisgarh, Odisha, Andhra Pradesh.
• According to this IST, time has an offset of UTC + 05:30.

• B S Bhullar is the Director General of Civil Aviation of Airport Authority of India.
• The Civil Aviation training college is in Allahabad.
• Juhu Aerodrome is the first airport of India, Founded in 1928.
• Most beautiful Airport: Kushok Bakula Rimpochee Airport, Ladakh

• Paradip seaport is nearest to Rourkela Steel Plant.
• Rourkela Steel Plant is the first integrated steel plant in the public sector in India.
• Rourkela Steel Plant is in Odisha.
• It was founded in 1955.

• Palakkad gap connects Kerala and Tamil Nadu.
• The pass is located between the Nilgiri Hills to the North and Anaimalai Hills to the South.
• Palakkad Gap is also known as Palghat Gap.

• Lord Dalhousie is known as the father of Indian Railway
• Indian Railways was founded on 16 April 1853.
• The Headquarters of Indian Railway is in New Delhi.

• The blood pressure is highest in Arteries, beginning from Aorta.
• It loses pressure when it travels through the Capillaries, which are a bit leaky.
• It is the lowest at the superior vena cava before it enters the Heart.

• Riboflavin is another name of Vitamin B2.
• It is part of B-complex.
• All vitamins of B-complex helps the body to convert carbohydrate into food, which can be used by the body.

• The Centripetal force is required to maintain a body in Uniform Circular Motion.
• Centripetal Force acts when a body moves around the other body, the force that causes this acceleration and keeps the body moving along a circular path is acting towards the centre

• Total internal reflection cannot occur when light travels from Water to Glass because Total internal reflection can occur only when the light goes from a denser medium to rarer medium.
• Here water has refractive index 1.33 and glass has 1.5-1.8, water is less dense as compared to glass, so when the light goes from water to glass Total internal reflection cannot take place.

• Pyrolusite is the ore of Manganese.
• Manganese Symbol Mn .
• Atomic number 25.
• The metal is obtained by reduction of the oxide with sodium, magnesium, aluminium, or by electrolysis.
• Pyrolusite is extensively used for the manufacture of spiegeleisen and ferromanganese.
• Colour: Darkish, black to a lighter grey, sometimes bluish

Let the weight of the players ‘P’, ‘Q’ and ‘T’ (coach) be ‘p’, ‘q’, ‘t’ respectively

Given the average weight of both the players P and Q = 38 kg

⇒ (p + q)/2 = 38

⇒ (p + q) = 76     ----(1)

Also given the average weight of the players ‘P’, ‘Q’ and ‘T’ is 49

⇒ (p + q + t)/3 = 49

⇒ (p + q + t) = 147      ----(2)

Subtracting Equation 2 with Equation 1, we get the weight of the coach, t = (147 – 76) = 71

∴ Weight of the coach = 71 kg

7cos²θ + 3 sin²θ = 4

3 sin²θ + 3 cos²θ + 4 cos²θ = 4

4 cos²θ = 4 - 3

Let, the distance = x km

Time taken to go at 6 km/hr = x/6 hr.

Time taken to come back at 4 km/hr = x/4 hr.

∴ Average speed,

⇒ 24/5

⇒ 4.8 km/hr

given ; Ratio = 1:2:3

Earning of A =  x

Earning  of B = 2x

Earning of  C =  3x

According to question;

Earning of C = earning of A + 1200 

=> 3x =  1200+ x

=>  2x =  1200

But ( 2x ) is earning of B 

So, monthly income of ( B) = 1200

=> Annual income of B :-

1200 * 12 => 14400₹

Therefore, annual income of B is = ₹14400

LIOVTE → VIOLET

REGEN→ GREEN

LOWLEY → YELLOW

NATMEAG → MAGENTA

All colours are present in the rainbow except MAGENTA.

Only potato is grown underground, but not others.

Let a and b are constants.

Given,

⇒ 1300 = 200A + B

⇒ 1600 = 250A + B

Solving equations,

⇒ 50A = 300

⇒ A = 6

Then,

⇒ B = 1300 - 1200 = 100

For 300 inmates,

Expenses = 300 × 6 + 100 = 1900

∴ Expenses for 300 inmates is Rs. 1900

From the given graph,

⇒ Number of voters participating in the election campaign from city N in the year 2017 = 30 lakhs

⇒ Number of voters participating in the election campaign from city O in the year 2017 = 22.5 lakhs

Applying formula to find x is what % of y = (x/y) × 100%

⇒ (30/22.5) × 100%

⇒ 1.333 × 100% = 133.3%

∴ Required percentage = 133% (approximately)

From the given graph,

⇒ Average number of voters in the year 2016 = Sum of all the voters in all the cities in 2016/Total number of cities

⇒ (27.5 + 27.5 + 30 + 32.5 + 22.5 + 35)/6

⇒ (175/6) Lakhs

⇒ 29.1666 Lakhs (approximately)

⇒ 29.17 Lakhs (approximately)

∴ Required Average = 2917000

Given, ∠AOB = 120° & AB = 10 cm

Draw OD ⊥ AB

So, ∠DOB = 1/2 × ∠AOB = 1/2 × 120 = 60°

⇒ DB = 1/2 × 10 = 5 cm

Now, In ΔODB

⇒ cot 60° = OD/DB

⇒ 1/(√3) = OD/5

⇒ OD = 5/(√3)

Therefore, distance of the chord from the centre is 5/(√3)

AB = is building with height h, b is height of chimney

In ΔABC
tanx = h/a
a = h cot x        ----(I)

H cot x = h + b

b = h (cot x - 1)   

Their relative speed = 30 + 45 = 75 km/hr.

To convert it into m/s multiply it with 5/18

⇒ 75 × 5/18 = 20.833 m/s

Now the total distance to be travelled = 450 + 550 = 1000m

Time required by slower train to cross faster is = 1000/20.833 = 48s

∴ The time required by small train to cross the faster train is 48s

Value of 

⇒ 0.04 + 0.4 + 4

⇒ 4.44

∴ Ans = 4.44

17^34.5 × 17^68.9 ÷ 17^27.4 = 17^x

⇒ 17^x = 17^{(34.5 + 68.9)} ÷ 17^27.4

⇒ 17^x = 17^{(103.4 - 27.4)}

⇒ 17^x = 17⁷⁶

⇒ x = 76

Given,

⇒ 11a + 11b = 29282

⇒ 11(a + b) = 29282

⇒ a + b = 29282/11

⇒ a + b = 2662

⇒ (a + b)/4 = 2662/4 = 665.5

Given,

Marked price of a table = Rs. 900

Discount percentage = 16%

Selling price of a table = 900 - 900 × 16/100 = 756

Given,

Profit percentage = 5%

⇒ 5 = [(756 - C.P)/C.P] × 100

⇒ C.P = 15120 - 20C.P

⇒ 21C.P = 15120

⇒ C.P = 720

∴ Cost price of a table is Rs. 720.

Given,

Pipe P 1 hour's work = 1/3

Pipe Q 1 hour’s work = 1/4

Pipe Q is opened for 2 hours then = 2 × 1/4 = 1/2

Remaining part of tank remain unfilled = 1 - 1/2 = 1/2

1/2 part will be filled by P in = (1/2) / (1/3) = 1.5

Pipe P should be closed after 1 hr 30 min.

Let the number be x.

When this number is multiplied by 2/3, then we get = 2x/3

And when this number is multiplied by 7/11, then we get = 7x/11

Required Percentage = 

Let the number be x

81% of x = 0.81x

49% of x = 0.49x

Difference between 81% of x and 49% of x = 768

⇒ 0.81x - 0.49x = 768

⇒ 0.32x = 768

⇒ x = 2400

48% of x = 0.48x = 0.48 × 2400 = 1152

• Catalysis was discovered by Berzelius.
• It is a term used for the reactions which occur in the presence of certain substances that increases the rate of the reaction without being consumed.

Catalysis is called:

• Homogeneous when reactant and catalysis are in the same phase
• Heterogeneous when reactant and catalysis are in a different phase
• Autocatalysis when one of the product increases the rate of reaction.

• Intel 4004 was the first microprocessor.
• It was conceived by Ted Hoff and Stanley Mazor.
• A microprocessor is the controlling element in a computer system.
• They are classified into five types. That is as follows:

• CISC-Complex Instruction Set Microprocessors
• RISC-Reduced Instruction Set Microprocessor
• ASIC-Application Specific Integrated Circuit
• Superscalar Processors
• DSP's-Digital Signal Microprocessors.

• Botnet  is also known as ‘Zombie Army’
• A botnet is a number of Internet computers that have been set-up to forward transmissions including spam and viruses to the computer without the knowledge of their owners.
• It is a type of Security Threat.

Building is made up of bricks and Book is made up of pages.

USA is a country in North America but Africa, Asia, Australia are the Continents.

Chandra Shekhar was the Prime Minister of India for 1990 - 1991 but others are names of the former President of India.

Except courage all others are the synonyms of fear.

All the options except 2 suggest the problems caused by pain. These strengthen the people's argument. Only 2 explains that bad posture causes pain. Posture is something which can be corrected in a second. If the posture is okay, the pain will be bearable.

So 2 weakens the argument.

Sandeep, even after being shot, wants to come back to the world of hockey. So obviously he has a lot of passion for it. Also, one does not get shot just while walking on the road. Whenever there are guns involved, the situation is very tense and troublesome. Sandeep must have in such a situation if he was shot. So we see that both the inferences follow.

Day on 7^th August 2017 = Monday

Number of odd days in 2017 = 1

Day on 7^th August 2018 = Tuesday

Day on 6^th August 2018 = Monday.

Hence, Ram’s internship ends on 6^th August 2018.

The mirror image of the question will be:


Hence, we can say that option 4 is the correct mirror image of the given question.

• India’s first semi-high speed train, the Vande Bharat Express, was flagged off by Prime Minister Narendra Modi from the New Delhi Railway Station.
• The train travels from Delhi to Varanasi in nine hours and forty-five minutes. This includes stoppage time of 40 minutes each at Kanpur and Allahabad.
• The train had been produced indigenously at the Integral Coach Factory, Chennai.
• The train has begun and it is running commercially from February 17 from Delhi to Varanasi.

• Krav Maga is a form of hybrid martial arts developed in Israel by Israel Defense Forces.
• It is combined techniques developed from boxing, wrestling, Aikido, judo and karate.
• The ranking system in this technique is based on the coloured belt grading system which is originated from the judo ranking system.

Hence, answer is option ‘4’.

• The book “Eleven Minute Late” was written by author Matthew Engel describing a story on railway.
• Eleven Minutes Late: A Train Journey to the Soul of Britain was written in 2009.
• It provides the backdrop to a history of Great Britain’s railways, focusing on the political environment rather than the technology.

• Shyam Saran wrote the book “How India Sees the World: Kautilya to the 21^st Century” in 2017.
• The book shows part memoir and part thesis on India’s International relations since Independence.
• Shyam Saran is a career diplomat born on September 4, 1946.
• He has been India’s Ambassador to Myanmar, Indonesia and the Nepal and High Commissioner to Mauritius.

• Raghubar Das is the Chief Minister of Jharkhand.
• Constituency : Jamshedhpur East.
• Jharkhand shares its border with Bihar, Uttar Pradesh, Chhattisgarh, Odisha and West Bengal.

Some facts about Jharkhand:

• Capital : Ranchi
• Number of Districts : 24
• Governor : Draupadi Murmu
• Rajya Sabha seats : 6
• Lok Sabha seats : 14

• Anandiben Patel is the governor of Madhya Pradesh.
• Constituency : Ghatlodiya
• MP shares its boundary with Uttar Pradesh, Chhattisgarh, Maharashtra, Gujarat and Rajasthan

Some facts about Madhya Pradesh:

• Capital : Bhopal
• Chief Minister : Kamal Nath
• State Animal : Barasingha
• State Bird : Asian Paradise-flycatcher

• Addis Ababa is the capital of Ethiopia
• Official languages: Amharic
• Currency : Birr
• Ethiopia shares its boundary with Eritrea, Djibouti, Somalia, Sudan and South Sudan, and Kenya.

A = 01

LION = L (1 + 2 = 3) + I (0 + 9 = 9) + O (1 + 5 = 6) + N (1 + 4 = 5) = 23

CAMEL = C (0 + 3) + A (0 + 1 = 1) + M (1 + 3 = 4) + E (0 + 5 = 5) + L (1 + 2 = 3) = 16

Similary,

TIGER = T (2 + 0 = 2) + I (0 + 9 = 9) + G (0 + 7 = 7) + E (0 + 5 = 5) + R (1 + 8 = 9) = 32

Hence, the correct answer is 32.

Using BODMAS

20 + 40 - 10 % 5 * 14

= 20 + 40 - 2 * 14

= 20 + 40 - 28 = 60 - 28 = 32.

Hence, 32 is the correct answer.

The logic followed is:

7 → 2³ - 1 = 8 - 1.

124 → 5³ - 1 = 125 - 1

63 → 4³ - 1 = 64 - 1

342 → 7³ - 1 = 343 - 1

Hence, the correct answer is 342.

SREIRBE → BERRIES

EALIPPPEN → PINEAPPLE

UAGAV → GUAVA

DONMAL → ALMOND

All except ALMOND are fruits.

LETNARIG → TRIANGLE

RHESPE → SPHERE

RSEQUA → SQUARE

GCERALENT → RECTANGLE

All except sphere are two dimensional figures. Only sphere is a three dimensional figure.

Except oxygen all the others are greenhouse gases.

The pattern followed is:

Hence, the correct answer is G16R.

Similarly,

Hence, the correct answer is 478692.

Similarly,

Hence, the correct answer is AZLG.

The least possible Venn diagram is as follows,

Conclusion:
I) All rats are dogs → False (it is possible but not definite)
II) At least some cats being rat is a possibility → False.

Hence, neither conclusions I and II follows.

The least possible Venn diagram is as follows,

I. All books are pens → False (It is possible but not definite)

II. All chairs are pens → False (It is possible but not definite)

Hence, neither conclusion I nor II follows.

We should drink plenty of water as water regulates a lot of metabolic activities in our body and helps in elimination of waste product from the from the body.

Milk is definitely rich in nutrients like calcium, protein etc.

MILK is rich in nutrients but not the reason for drinking water.

Reason given is supporting the assertion.

The Archaeological Survey of India (ASI) declared 6 monuments as ‘protected and of national importance’ in January 2019.

These sites are:

• 125-year-old Old High Court Building in Nagpur, Maharashtra.
• The Group of Temples in Ranipur Jharail in Bolangir district of Odisha.
• 2 Mughal era monuments in Agra- Haveli of Agha Khan and Hathi Khana.
• The Neemrana Baori in Alwar district of Rajasthan.
• The Vishnu Temple in Kotali, Pithoragarh district in Uttarakhand.

• Rishabh Pant was named the International Cricket Council’s (ICC) Emerging Player of the Year.
• He had an impressive show in India’s first-ever Test series win in Australia in December 2018.
• The 21-year-old wicketkeeper-batsman scored 350 runs in the four-match Test series that India won 2-1 to script history in 71 years and 11 attempts.
• He became the first Indian wicketkeeper to score a Test century in Australia.

Using the symbols above we draw the family tree diagram of the above expression: T * S % R # U + P: S is the brother of T, R is the sister of S, U is the son of R, P is the father of U.

Hence, U is the nephew of S.

Using the symbols above we draw the family tree diagram of the above expression: T * S % R # U + P: S is the brother of T, R is the sister of S, U is the son of R, P is the father of U.

Insufficient data is provided in this question as we don’t know the gender of T. We are unable to define the relation between T and S.

• The 4^th edition of annual “Aadi Mahotsav” was organized by the Ministry of Tribal Affairs in at Dilli Haat, New Delhi.
• It is a National Tribal Festival festival that is organised every year.
• This year, more than 600 tribal artisans from 23 states, 80 tribal chefs hailing from 20 States took part in the Mahotsav.

• The National Green Tribunal (NGT) ordered automobile giant Volkswagen to pay Rs. 500 crore as fine for “intentionally programming its diesel engines with cheat devices”.
• A bench headed by NGT chairperson Justice Adarsh Kumar Goel directed the carmaker to deposit the amount within two months.
• According to the expert panel report filed on December 24, 2018, estimated that Volkswagen cars released approximately 48.678 tonnes of NOx in 2016.

The 1983 batch IPS officer of Madhya Pradesh Cadre Rishi Kumar Shukla has been appointed as the new Director of Central Bureau of Investigation, CBI.
He will serve the post for a period of two years.
Rishi Kumar Shukla has already served as the DGP of Madhya Pradesh.

Krishna Sobti was a famous Hindi writer and essayist.
She had won the Sahitya Akademi Award in 1980 for her novel Zindaginama.
She was awarded the Jnanpith in 2017 for her contribution to Indian literature.
Some of her celebrated works include Daar Se Bichhudi, Mitro Marjani, Zindaginama, Dil-o-Danish etc.

• The Centre Government designated Dera Baba Nanak land check post in Gurdaspur district of Punjab as an authorised immigration checkpoint to exit and entry for visiting Kartarpur Sahib Gurdwara in Pakistan.
• All classes of passengers with valid travel documents can exit or enter through the post.
• The government also appointed the Chief Immigration Officer as the Civil Authority for the purpose.

• Union Minister Smt Harsimrat Kaur Badal commissioned Godavari Mega Aqua Food Park at Tundurru Village in West Godavari District, Andhra Pradesh.
• The park is promoted by M/s Godavari Mega Aqua Food Park Pvt. Ltd.
• This is the 1^st Mega Aqua Food Park operationalised and exclusively established for fish and marine products processing in the State of Andhra Pradesh.
• Another Mega Food Park sanctioned by the Ministry in Chittoor District of Andhra Pradesh has already been inaugurated on 9^th of July 2012.
• The 3^rd Mega Food Park sanctioned by the Ministry in Andhra Pradesh is under implementation at Krishna District.

• The country's second-largest IT services firm Infosys launched the 'InfyTQ' app.
• It is a digital platform to offer learning and engagement experiences to engineering students in the country.
• InfyTQ is a free platform open to all engineering students in their third and fourth years across India.
• The platform encourages holistic development by imparting technical as well as professional skills, helping them become industry-ready.

• Indian Institute of Technology-Hyderabad (IIT-H) has announced the launch of a full-fledged bachelor’s programme in Artificial Intelligence (AI) technology from the new academic session, a first for the country and only the third globally.
• IIT-H is already offering a Masters in Technology programme in AI-Machine Learning (ML).
• Besides IIT, Carnegie Mellon University and Massachusetts Institute of Technology (MIT), both of which are in the US, offer full-fledged B.Tech programmes in AI.

• Scientists have developed the first walking robot that can explore its environment and find its way home without GPS or mapping.
• It is equipped with an optical compass used to determine its heading by means of polarised light.
• With the help of an optical movement sensor directed to the Sun, it measures the distance covered.
• Researchers from the French National Center for Scientific Research (CNRS) took inspiration from desert ants to design the AntBot.

• Australian spinner, Shane Warne has been named the brand ambassador of Rajasthan Royals for the upcoming edition of IPL.
• He led Rajasthan Royals to its first and only IPL title in 2008.
• Also, Rajasthan Royals has decided to change its jersey colour from blue to pink this year.
• Ajinkya Rahane is the captain of Rajasthan Royals.

• Novak Djokovic defeated Rafael Nadal to win his 7^th Australian Open Men’s Singles title at Melbourn.
• The resurgent world No. 1 outplayed the second-ranked Nadal 6-3, 6-2, 6-3 in a largely one-sided match.
• In Women’s Singles, Japan’s Naomi Osaka clinched her maiden Australian Open Grand Slam Singles title in Melbourne.

No. of people who owns dogs only = 66

No. of people who owns dogs and cats = 25

No. of people who owns all = 30

No. of people who owns parrots and cats = 52

No. of people who owns parrots alone = 12

Total no. of people who owns pets = 314

No. of people that have cats only = total no. of people - no. of people owns dogs - no. of people owns parrots alone - no. of people owns parrots and cats both.

= 314 - 130 - 12 - 52 = 120

No. of people who owns dogs only = 66

No. of people who owns dogs and cats = 25

No. of people who owns all = 30

No. of people who owns parrots and cats = 52

No. of people who owns parrots alone = 12

Total no. of people who owns pets = 314

No. of people owns parrots = total no. of people owns pet - people owns dogs only - people cats only - people owns both cats and dogs.

= 314 - 66 - 120 - 25 = 103

No. of people who owns dogs only = 66

No. of people who owns dogs and cats = 25

No. of people who owns all = 30

No. of people who owns parrots and cats = 52

No. of people who owns parrots alone = 12

Total no. of people who owns pets = 314

Hence, 66 people own dogs only.

No. of people who owns dogs only = 66

No. of people who owns dogs and cats = 25

No. of people who owns all = 30

No. of people who owns parrots and cats = 52

No. of people who owns parrots alone = 12

Total no. of people who owns pets = 314

No. of people have at least two pets = no. of people owns both dogs and cats + no. of people owns both cats and parrots + no. of people owns both dogs and parrots + no. of people owns all = 25 + 52 +9 + 30 = 116

Interest = PRT/100

Amount = Principal + Interest

Let the rate be r%

Interest = (2100 × r × 2)/100

2352 - 2100 = (2100 × r × 2)/100

252 = 42r ⇒ r = 6%

New rate of interest = r - 1 = 5%

Interest when r% is 5% = (P × (5) × 2)/100 = (2100 × 5 × 2)/100 = Rs. 210

Downstream speed = distance/time = 12/(40/60) = 18 km/hr

∵ Downstream speed = Speed in still water + Speed of stream

∴ Speed of boat in still water = Downstream speed – Speed of stream = 18 – 8 = 10 km/hr

Actual money with the person = 0.5((6/9) × 45) + 1((2/9) × 45) + 2((1/9) × 45) = 15 + 10 + 10 = Rs. 35

Total money in First case:

Total value of coins = 0.25((6/9) × 45) + 0.50((2/9) × 45) + 1((2/9) × 45) = 7.5 + 5 + 10 = Rs. 22.50

Total money in Second case:

Total value of coins = 0.25((6/9) × 90) + 0.50((2/9) × 90) + 1((2/9) × 90) = Rs. 45

Total money in Third case:

Total value of coins = 0.25((6/14) × 70) + 0.50((5/14) × 70) + 1((3/14) × 70) = Rs. 35

In third case, the amount is same

Let the sum of money be Rs. ‘P’

Given, CI – SI = 10

⇒ P[(1 + Rate/100)^Time – 1] – [(P × Rate × Time)/100] = 10

⇒ P[(1 + 5/100)²) – 1] – [(P × 5 × 2)/100] = 10

⇒ P[(1.05)² – 1] – 0.1P = 10

⇒ 0.1025P – 0.1P = 10

⇒ 0.0025P = 10

⇒ P = 10/0.0025 = 4000

∴ Required sum = Rs. 4000

Given profit % = 16

Selling price of each watch = Rs. 1454.64

Cost price of the watch × 1.16 = 1454.64

∴ Cost price of each watch = Rs. 1254

 Cost price of dozen watches = 1254 × 12 = Rs. 15048.00

Given,

Speed of train = 56 km/hr and Time = 8 hrs

We know that,

Distance = Speed × Time

⇒ Distance = 56 × 8 = 448 km

To cover the same distance in 7 hrs,

Speed = 448/7 = 64 km/hrs

Let cost price of an article be Rs. A

Profit percentage = 10% = loss percentage

Then,

⇒ 10 = [(A - S.P)/A] × 100

⇒ A = 10A - 10S.P

⇒ S.P = 9A/10

Selling price of an article = Rs. 270

Given,

⇒ 9A/10 = 270

⇒ A = 300

∴ Cost price of an article is Rs. 300.

The numbers are 1, 3, 5, 7…., 49

Sum of n terms of an AP = n/2 × {2a + (n - 1)d}

Where a is the first term, n is the number of terms and d is the common difference

First term of the series (a) is 1

Common difference (d) = 3 - 1 = 2 and n is 25

Sum = 25/2 × (2 + 24 × 2) = 625

When a number x is divided by y and it leaves a remainder z,

the number (x + z) is always divisible by y

When number is divided by 192 and a remainder of 54 is obtained, the number can be written as

(192x + 54) where x is a natural number.

Now this number is divided by 16, both the sum of numbers can be individually divided by 16.

192x is divisible by 16 as 192 is divisible by 16

54 = (16 × 3) + 6

54 when divided by 16 leaves a remainder of 6 and quotient of 3 so when the sum is divided by

16, a remainder of 6 is obtained 

According to question,

Curved surface area of cylinder/Total surface area of cylinder = 2/3

⇒ 2πRh/2πR(R + h) = 2/3

⇒ h/ (R + h) = 2/3

⇒ 3h = 2R + 2h

⇒ h = 2R       ---- (1)

∵ Volume of cylinder = Volume of solid hemisphere

⇒ πR²h = 2/3πr³ (where, R = radius of cylinder and r = radius of solid hemisphere)

Putting value of ‘h’ from equation (1),

⇒ R² × 2R = (2/3) × 14 × 14 × 14

⇒ R³ = (14 × 14 × 14)/3

⇒ R = 14/∛3

∴ Radius of its base = 14/∛3 cm

Let the fraction be x.

Reciprocal = 1/x

Then,

x + 3/x = 73/20

⇒ x² + 3 = 73x/20

⇒ 20x² – 73x + 60 = 0

⇒ x = {- (-73) + √ (5329 – 4800)}/40     or        x = {- (-73) - √ (5329 – 4800)}/40

⇒ x = 96/40 = 12/5                                or        x = 50/40 = 5/4

∴ the required fraction is 5/4 or 12/5.

For finding the LCM of 2 fractions.