RRB JE CBT 1 - Full Test 1

•  Khan Abdul Ghaffar Khan was also known as Badshah Khan was a non-violent activist and close confidante of Mahatma Gandhi.
•  He was also known as Frontier Gandhi.
• He led his non-violent Khudai Khidmatgar movement against the British Raj in the 1930s and 1940s.

• Tinkathia System or Tinkathia Pratha was a system under which the native peasants of Champaran were forced by the European planters to use 3/20th of their land holding to cultivate Indigo.
• The European planters practiced illegal methods to grow indigo, however, with the help of Rajendra Prasad and Gandhiji the peasants of Champaran organised Satyagraha and abolished the system.

Lord Hardinge, the Viceroy of India from 1910 to 1916 ,had annulled the partition of Bengal in 1911.

Note: The partition of Bengal was done by Lord Curzon on 16th October 1905 and The annulment of Partition of Bengal was done by Lord Hardinge in 1911.

• Comrade is not related to Madan Mohan Malaviya who had been served as the president of Indian National Congress for four times.
• Comrade was published and edited by Maulana Mohammad Ali between 1911 and 1914.

The 960 kilometres (600 mi) long Chambal River originates from the Singar Chouri peak on the northern slopes of the Vindhyan escarpment, 15 kilometres (9.3 mi) West-South-West of Mhow in Indore District, Madhya Pradesh state.

• Chambal River is a tributary of Yamuna River.
• It flows through Madhya Pradesh, Rajasthan and Uttar Pradesh.
• Chambal and its tributaries drains Malwa region of Madhya Pradesh.
• Right Bank Tributaries - Parbati, Kali Sindh, Shipra.
• Left Bank Tributaries- Gandhi Sagar, Rana Pratap Sagar, Jawahar Sagar, Kota Barrage.

Andhra Pradesh is the largest producer of mica in India followed by Rajasthan and Jharkhand. Mica is used in paints.

• Uttar Pradesh has the largest railway network in the country. 
• However, it has the sixth-highest railway density among the states in India. 
• The state has the railway network of 9077.45 km connecting it with other parts of the country.

• Hindu Pilgrimage center Sabarimala is located at the Periyar Tiger Reserve in the Western Ghat mountain ranges of Pathanamthitta district, Perunad, Kerala.
• It is one of the world’s largest annual pilgrimages with over 40-50 million devotees visiting each year.

• Stratosphere layer of atmosphere has the maximum concentration of Ozone gas.
• Approximately 10 per cent of Ozone layer is present in Troposphere and rest of the 90 per cent found in Stratosphere layer of atmosphere..
• Ozone layer in Stratosphere atmosphere absorbs most of the ultraviolet radiation from the Sun.
• Stratosphere is the second layer of atmosphere whereas Troposphere is the lowest layer of the atmosphere.
• The Thermosphere is the layer of the Earth's atmosphere is above the Mesosphere.
• There are five layers of atmosphere namely- Troposphere, Stratosphere, Mesosphere, Thermosphere and Exosphere. 

• The gases which contribute to the greenhouse effect by absorbing infrared radiations are known as the greenhouse gases.
• The greenhouse gases are also termed as the radioactively active gases which include Carbon Dioxide (CO₂), Methane (CH₄), Nitrous Oxide (N₂O), etc.

N. Biren Singh is the incumbent Chief Minister of Manipur. He is a member of BJP. He won the 2017 Manipur Legislative Assembly Election from Heingang Assembly Constituency.

• The Ganga Gram Yojana was launched in January 2016 at Village Puth in Hapur district of Uttar Pradesh by the Ministry of Drinking Water and Sanitation.
• This scheme aims to develop 1600 villages of UP which are situated along the banks of river Ganga.

• "Brief Answers to the Big Questions" is a popular-science book written by Stephen Hawking.
• The book promotes the view that science is very important in helping to solve the problems on Earth.

Croatia captain Luka Modric has won the FIFA Golden Ball for the best player at the World Cup 2018. England national football captain Harry Kane was awarded the Golden Boot for scoring most goals (6) in FIFA World Cup 2018. Belgium’s Thibaut Courtois won the Golden Glove as the best goalkeeper of FIFA World Cup 2018.

• Malabar Exercise was started as Indo-US bilateral naval war drill in 1992.
• Japan had formally joined the exercise as permanent participant in 2015, making it trilateral exercise.
• The primary aim of this multilateral exercise is to increase interoperability amongst navies of three countries and develop common understanding of procedures for Maritime Security Operations and deepen defence relations between them.

• A concave lens is a lens that possesses at least one surface that curves inwards.
• It is a diverging lens, meaning that it spreads out light rays that have been refracted through it.
•  A concave lens is thinner at its centre than at its edges and produces an erect and diminishing image.

• Impulse is defined as the integral of force over the time interval for which it acts.
• If a moving object is stopped by an impact, the change in momentum of the object occurs. This change in momentum is called the impulse.
• Impulse is a vector quantity and the impulse force on the body is measured in terms of its impulse force.

The momentum of a body, P = mv, where m is the mass of the particle, and v is the velocity of the particle.

Momentum is directly proportional to velocity.

The kinetic energy of a particle is given by the equation, KE = (1/2)mv^2.

KE = (1/2)mv²

When the momentum of a body is doubled, then the velocity will be doubled.

⇒ KE = (1/2) × m × (2v)² = 4 × (1/2)mv²

Hence, If the momentum of a body is doubled, the kinetic energy becomes 4 times.

To find the Power in this case, we must apply the following formula:

P= F_net . v

We first need to find out the net force applied on the car.

F_net = mass × acceleration + resistive force

       = 300 × 4/3 + 100

       = 400 + 100 = 500 N

Now, P= 500 × 10 = 5000 W = 5 kW

• The magnetic force acts perpendicular to the direction of motion of the proton, thus it does not change the speed but only its direction of motion
• This in turn means the velocity and momentum of the particle is changed.

A body is said to be in uniform motion if it travels equal distances in equal intervals of time. A body is said to have non-uniform motion if it travels unequal distances in equal intervals of time. These concepts are based on Newton’s three laws of motion.

• Conduction is the transfer of heat energy by direct contact.
• Convection is the movement of heat by actual motion of matter.
• Absorption is a physical or chemical phenomenon or a process in which atoms, molecules or ions enter some bulk phase, liquid or solid material.
• Advection is defined as the transfer of heat or matter by the flow of a fluid, especially horizontally in the atmosphere.

Hence, 4 is the correct option.

A scalar quantity is a one-dimensional quantity consisting of only magnitude and devoid of direction.

• Work is an example of scalar quantity as it has no precise direction attached to it making it a one-dimensional quantity.
• Other examples of scalar quantities include time, volume, speed, mass, temperature, distance, entropy, energy etc.

The residual volume is volume of air left inside the lungs after exhalation, this is the minimum volume of the lungs that remains even after air is pushed out of the lungs.

The mucus glands are located in the lining of the nasal cavity. They secrete mucus. Mucus is a fluid that keeps the lining of the respiratory system moist and traps dust and other foreign bodies in it. It is removed by small hair structures called cilia towards the mouth.

Kala Azar, also known as Visceral Leishmaniasis is a disease caused by protozoan parasites of the Leishmania genus. It is detected by the K-39 test. Typhoid is detected by the Widal test. ELISA test is done to detect AIDS. 

Soyabean has the highest source of protein content of 36 g, Grams contains 19 g protein content, sunflower protein content is 21 g and wheat‘s is 13.2 g.

Night Blindness results in loss of vision in the dark and is caused by the deficiency of Vitamin A

Lichens are best indicator of pollution because lichens are very sensitive to sulphur dioxide pollution in the air. If air is very badly polluted with sulphur dioxide there may be no lichens present, just green algae may be found. If the air is clean, shrubby, hairy and leafy lichens become abundant. A few lichen species can tolerate quite high levels of pollution and are commonly found on pavements, walls and tree bark in urban areas. Lichens have also shown sensitivity to some other pollutants, such as heavy metals and other toxic gases in air. 

Bast fibre (also called phloem fibre or skin fibre) is plant fibre collected from the phloem (the "inner bark", sometimes called "skin"). In vascular plants, phloem is the living tissue that transports the soluble organic compounds made during photosynthesis in particular sugar sucrose, to parts of the plant where needed.

The small intestine is the part of the intestines where 90% of the digestion and absorption of the food occurs, the other 10% taking place in the stomach and large intestine.

• Graphite is widely used as a solid lubricant.
• Graphite is crystalline, low density, and soft allotrope of carbon.
• Graphite is composed of loosely bound sheets of carbon atoms, giving it lubricating texture which makes it an effective lubricating agent.

Optical glass, also known as flint glass, is softer than any other glass. It is clear and transparent. The main use of flint glass is in the manufacture of lenses, prisms and other optical instruments.

Silicon possess 4 valence electron (2, 8, 4). It has 2 electron in first shell,eight electrons in the second shell, and four electrons in the third shell.Since the electrons in the third shell are the outermost electrons, silicon has four valence electrons.​

Its electronic configuration is written as 1s²2s²2p⁶3s²3p².

• Calcination is a thermal treatment process in the absence or limited supply of air or oxygen. This process is applied to ores and other solid materials to bring about a thermal decomposition.
• Reduction: Reduction is a chemical reaction that involves the gaining of electrons by one of the atoms involved in the reaction
• Oxidation: Oxidation is the loss of electrons during a reaction
• Catalyst: Catalyst is a substance added to change the rate of reaction but it does not take part in the final products

Isomers are molecules that have the same molecular formula but different chemical structures. Therefore Butane and isobutane would be called as isomers.

Acetylene gas is used for artificial ripening of green fruits.

• It is produced when artificial ripening agent calcium carbide comes in contact with moisture.
• It has carcinogenic properties. Its compound formula is C₂H2.
• It is also used in the steel plants for the purpose of welding and cutting.

• Halite commonly known as rock salt, is a type of salt, the mineral (natural) form of sodium chloride (NaCl).
• Halite forms isometric crystals.

Commercial nitric acid has a brown color due to dissolved NO₂ (Nitrogen Dioxide), however pure nitric acid is colourless.

Kenya imposed the world's toughest law against plastic bags recently.

• If they sell or use any plastic bags it would become a risk of imprisonment of up to four years or fines of $40,000.
• Plastic is banned in more than 40 other countries including China, France, Rwanda, and Italy.

• An abiotic component is a non-living component in the environment.
•  These components have a major influence on a living organism.
•  Abiotic components are water, sunlight, temperature, fire, heat, sunlight, oxygen, climate.
•   Water is an only abiotic component from the above-mentioned components.

• Due to large quantities of nutrients in the water, excessive growth of planktonic algae occurs.
• Eutrophication is when a body of water becomes overly enriched with minerals and nutrients that induce excessive growth of plants and algae. 
• However, it reduces the amount of oxygen in any water body since these organisms consume a lot of oxygen. 

• British ecologist A.G. Tansley used the term ecosystem for the first time in 1935.
• According to him, an ecosystem is a special category of physical system, which consists of organic as well as inorganic components in a stable manner, of various sizes and kinds.

• China has built an 'artificial sun' that reaches temperature six times that of the core of the sun.
• The reactor named 'Experimental Advanced Superconducting Tokamak' (EAST) is designed to replicate the processes of the sun as part of a project to turn hydrogen into cost-effective green energy.
• It involves fusion of hydrogen atoms together to form heavier elements, such as helium.

Here Pisces, Gemini and Taurus are all Zodiac signs, while Arial is a name of font in MS office.

Thus, Arial is the odd word.

Let’s check each option,

1) 18 × 8 = 144

2) 16 × 8 = 128

3) 23 × 8 = 184

4) 15 × 7 = 105

Thus the odd number pair is (15, 105).

The logic here is as follows,

Similarly,

Thus JAPAN is related to LDTFT.

MRF is the acronym for ‘Madras Rubber Factory’, similarly BMW is the acronym for ‘Bavarian Motor Works'.

Thus, BMW is related to Bavarian Motor Works.

The logic here is as follows,

27 × 7 = 189; 189 + 9 (i.e., 2 + 7) = 198

Similarly,

13 × 7 = 91; 91 + 4 (i.e., 1 + 3) = 95

Thus, 13 is related to 95.

2259 + 169 → 2259 + 13² = 2428;

2428 + 196 → 2428 + 14² = 2624;

2624 + 225 → 2624 + 15² = 2849;

2849 + 256 → 2849 + 16² = 3105;

3105 + 289 → 3105 + 17² = 3394

Hence, “2850” is the wrong term in the series, it should be 2849 in place of 2850.

The logic followed here is as follows,

The position of letter E in each term is moving forward by one place.

Thus, the next word in the series will be ‘Complete’.

The logic here is as follows,

Similarly,

Thus, DEBT is coded as YKUB.

Logic followed here is,

@ → even number of letter in a word

# → odd number of letter in a word

The number in each code is referred to as the number of letter in a word.

The last letter in each code is referred to as the second last letter of each word.

Financial can be written as → 9#A

Stability can be written as → 9#T

Hence, “9#T 9#A” is the correct answer.

The ball passed is shown as follows,

Thus it is clearly shown that E is in North-west direction with respect to A.

Thus it is clearly shown that D is in North direction with respect to H.

1) The rectangle represents Cars.

2) The circle represents Sedan.

3) Triangle represents SUV.

4) Square represents electric.

Cars which are electric, as well as sedan is represented by the letters which are inside the intersection of rectangle, circle and square.

Thus, letter ‘B’ represents cars which are electric as well as sedan.

1) Rectangle represents Hollywood

2) Circle represent Bollywood

3) Triangle represent Tollywood

4) Square represent Movies.

Bollywood which are neither Tollywood nor Movies is represented by the letters which are inside circle but not in triangle or square.

Thus letter ‘F’ represents Bollywood which are neither Tollywood nor Movies.

The logic here is as follows,

7 × 3 = 21;

8 × 4 = 32;

9 × 5 = 45;

10 × 6 = 60;

11 × 7 = 77;

12 × 8 = 96;

13 × 9 = 117;

14 × 10 = 140

Thus the missing number is 32.

Changing operators as per the given format:

Given expression: 42 + 36 – 6 ÷ 15 ×​ 8 ÷ 20 + 20 – 5 = ?

After changing the symbols: 42 – 36 ÷ 6 × 15 + 8 × 20 – 20 ÷ 5

= 42 – 6 × 15 + 160 – 4

= 42 – 90 + 160 – 4

= 108

Hence, “108” is the correct answer.

There are 7 darken circle in the innermost part of the diagram in the 1st diagram and there are 10 circle darken in the 2nd diagram. And in the 3rd diagram, there are 17 small circles and 1 big outer circle.

Total number of circle = 7 + 10 + 17 + 1 = 35

Hence, there are 35 circles in the given diagram.

If we look closely, figure(X) is hidden in option figure 1 as shown below.

Hence, the answer should be figure 1.

Assertion: Soft skills coaching centres are mushrooming all over India → True.

Reason (I): People are opting for soft skills training largely → True and is correct reason for the given assertion.

Reason (II): Other than soft skills, no other skills are useful these days → This statement itself is false. Soft skill is an important part of people’s life but these skills are not the only skills required.

Hence, only R (I) and not R (II) is the correct reason for the given assertion.

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

θ = 30 H – 11/2 M

Where H = hour hand

And M = minute hand

The hour hand is in between 3 and 4, 30 (3) = 90.

For minute hand

11/2 (24) = 132

The difference between our hand and minute hand will be 132 – 90 = 42 degree

Hence, 42 degree is the correct answer.

The fact that Amit got grace marks in science doesn’t mean that he has not attempted all the questions in science. It’s possible that he attempted them but his answers were wrong. Also, the given statement doesn’t reflect anything about the syllabus.

Hence, none of the given conclusions follows.

Statement I) Number of friends taller than V is equal to the number of friends shorter than V.

_ > _ > V > _ > _

Statement I alone is not sufficient to answer the question.

Statement II) W is not the tallest one, but is taller than V and X is smaller than V.

_ > W > V > X > _  OR

_ > W > _ > V > X  OR

_ > _ > W > V > X

Statement II alone is also not sufficient to answer the question.

Combining statement I and II,

_ > W > V > X > _

Thus data even in both statement I and II together are not sufficient to answer the question.

I) None of them sits to the left of F and to the right of J.

Statement I alone is not sufficient to answer the question.

II) F sits to the immediate left of G, who is not a neighbor of H.

Statement II alone is not sufficient to answer the question.

Combining statement I and II,

On combining statement I and II we can say that J sits to the immediate right of H.

Thus, both the statement I and II are necessary to answer the question.

5 people: B, F, G, C and Q

Places: Shirdi, Goa, Wai, Leh, and Agra

Month: January, April, June, September and October of the same year.

1) C travel in the month having 31 days and visits Shirdi.

2) C is not the last one to visit any place in a calendar year.

3) Number of people travelled before B is equal to the number of people travelled after B.

 

4) Q travelled in the month having 31 days in it.

5) F visited Wai just after the month in which C visited.

6) The person who visited Goa travelled in the month of September.

Thus, G is the only person left and he must be travelling in the month of September.

Thus Q visits either Leh or Agra.

According to the question,

Thus Non-striker is the nephew of Pujara.

Given below are the stages of the process of blood flow in a human body.

II. Right atrium → VI. Right ventricle → V. Lungs → III. Left atrium → IV. Left ventricle → I. Body

Thus the correct sequence is II, VI, V, III, IV, I.

Given that, x = 
⇒ x = √(20 + x)

Squaring both sides,

⇒ x² = 20 + x

⇒ x² - x - 20 = 0

⇒ x² - 5x + 4x - 20 = 0

⇒ x (x - 5) + 4 (x - 5) = 0

x = 5 as x cannot be negative.

Trick

If the given expression is like this 
 

Then try to find its factors, and from the two factors which makes x the greater one will be the answer

Here,

x = 20 can be written as = 5 × 4

In this case, 5 is greater than 4 hence the answer will be 5

∴ Value of x = 5

Let the total no. of chairs = 8x + 13x + 4x = 25x

Cost of big chairs = 8x × 650 = 5200x

Cost of medium chairs = 13x × 500 = 6500x

Cost of small chairs = 4x × 400 = 1600x

∴ Average cost = (5200x + 6500x + 1600x)/25x = 13300/25 = 532

Let the total sum of ages of boys in class be x

Then, x/30 = 10 (Given Average)

⇒ x = 300

Now if Teacher’s age is y

⇒ (300 + y)/31 = 11

⇒ 300 + y = 341

⇒ y = 41 years

Given, ratio of number of boys and girls in a school is 2 : 3.

Let the number of boys and girls be 2a and 3a respectively. Where a is any constant

Given, 30% of the boys and 40% of the girls are scholarship holders.

Total number of boys who are not getting scholarship = 70% of 2a = 1.4a

Total number of girls who are not getting scholarship = 60% of 3a = 1.8a

Total number of students not getting scholarship = 1.4a + 1.8a = 3.2a

% of students not getting the scholarship =
∴ % of students not getting scholarship = 64%

Let the initial consumption of sugar be Y units and the initial price of sugar per kg be Rs. X. Thus,

The initial expenditure of household = X × Y

Given: the price of sugar increased by 25%. Thus,

⇒New price of sugar per kg = 
 

= 1.25X

Let the new consumption to keep the expenditure same be Y’ units. Hence,

New expenditure = 1.25X × Y’

Since the expenditures are same,

∴ XY = 1.25XY’

 ⇒ Y = 1.25Y’

Also, Reduction in consumption = Y – Y’

= 1.25Y’ – Y’

= 0.25Y’

⇒ Reduction percentage = 

= 20%

Let the incomes of X and Y be 7a and 8a

Let the expenditures of X and Y be 4b and 5b.

Then the income of both will be,

⇒ 7a = 4b + 960     ----(1)

⇒ 8a = 5b + 960     ----(2)

By solving the above equation, we get

a = 320 and b = 320

The income of X = 7a = 7 × 320 = 2240.

a : b = 2 : 3

⇒ a/b = 2/3

⇒ b = 3a/2

b : c = 4 : 5

⇒ b/c = 4/5

⇒ 3a/2 : c = 4 : 5

⇒ c = 15a/8

c : d = 6 : 7

⇒c/d = 6/7

⇒ a/d = 16/35

⇒ a : d = 16 : 35

A jar contains a blend of a fruit juice and water in the ratio 5 : x

Quantity of fruit juice in 4 litres of blend = 4[5/(5 + x)] = 20/(5 + x)

⇒ Quantity of water in 4 litres of blend = 4[x/(5 + x)] = 4x/(5 + x)

According to questions

20/(5 + x) : {4x/(5 + x) + 1} = 1 : 1

⇒ 20 - 4x = 5 + x

∴ x = 3

As, 5! = 1 × 2 × 3 × 4 × 5 will have 0 as its unit digit because of the presence of (2 × 5). Hence all factorials above it will have 0 as their unit digit

⇒ 1! + 2! + 3! + 4! = 1 + 2 + 6 + 24 = 33

∴ Unit digit of (1! + 2! + 3! + 4! + ....... + 20!) = Unit digit of (1! + 2! + 3! + 4!) = 3

LCM of 3, 4, 5 and 6 = 2 × 3 × 2 × 5 × 1 × 1 = 60

On dividing 60 with 3105, we get remainder 45

∴ Number to be added = 60 - 45 = 15

Find the least number required to be added to 3105 so that it is exactly divisible by 3, 4, 5 and 6.

Given x³ + y³ = 20 and x + y = 5

 = 4 ⇒ x² + y² − xy = 4
⇒ (x+y)² − 3xy = 4 ⇒ 3xy = 5² − 4 = 25 − 4 = 21
xy = 21/3 = 7

x = √5 + 2

On rationalizing


 

= 5/8

= .625

x⁶ + y⁶ = (x²)³ + (y²)³
x⁶+y⁶=(x²+y²)(x⁴+y⁴−x²y²)

x6+y6=(x2+y2)(x2y2−x2y2)x6+y6=(x2+y2)(x2y2−x2y2)

x⁶ + y⁶ = 0

SP of 1 orange is 1/36 and it suffers 4% loss.

Let CP be x.

⇒ (96/100)x = 1/36

⇒ x = 100/(36 × 96)

To make profit of 8%

He should sell = 108/(36 × 96) = 1/32

∴ 32 oranges per rupee

Jay’s total investment = 80000 × 4 + 70000 × 8 = 320000 + 560000 = 880000

Jatin’s total investment = 60000 × 4 + 70000 × 8 = 240000 + 560000 = 800000

∵ Ratio of their profits = ratio of their total investment

∴ Ratio of their profits = 880000 ∶ 800000 = 11 ∶ 10

We know the formula for compound interest –

CI = [P{1 + r/100}^t – 1]

Where,

CI = Compound interest

P = Principal

R = Rate of interest

T = Time period

According to the question,

⇒ kP – P = [P {1 + r/100}⁶ – 1]

⇒ kP = P {1 + r/100}⁶          ----- (1)

∴ Total sum becomes after 24 year

⇒ P {1 + r/100}²⁴ = P [{1 + r/100}⁶]⁴

Using equation (1)

= Pk⁴

Note : Compound Interest for 1 year is equal to the Simple Interest for 1 year 

Interest on Rs. 5618 in 1 year = Rs. (5786.54 - 5618) = Rs. 168.54

Rate =

Let the sum be Rs. y.

Amount in 2 years = 

y(1+3/100)² = 5618

By solving, we get

Sum, y = Rs. 5295.50

⇒ Speed of Train 1 = 45 kmph = 45 × 1000 meters per hour = 45000 meters / hour

= 45000 / 3600 meters per second

= 12.5 meters a second

According to Question the Speed of Train 2 = 10 meters a second

⇒ Ratio = Speed Of Train 1 : Speed of Train 2

⇒ Ratio = 12.5/10 = 5 : 4

Speed of the man in still water = 10 km/h

Speed of the current = 2 km/h

Speed of the man along the current = (10 + 2) km/h = 12 km/h

Speed of the man against the current = (10 – 2) km/h = 8 km/h

Given,

He takes 3 hours more in upstream than in the downstream

Let, The distance is x km = x/8 – x/12 = 3

⇒ x = 72 km

Length of train = 450 m

Length of bridge = 650 m

To cross a bridge train has to cover a distance which is sum of the length of the train and length of the bridge.

∴ Distance covered to cross the bridge

= 450 m + 650 m

= 1100 m

Time required = 36 seconds

∴ Speed = Distance covered/Required time = 1100/36 = (1100/1000)/(36/3600)

= 110 km/hr

A can fill the tank in = 9 hours

∴ In 1 hour A can fill = 1/9

B can fill the tank in = 6 hours

∴ In 1 hour B can fill = 1/6

C can empty the tank in = 4 hours

∴ In 1 hour C can empty = 1/4

∴ In 6 hours they together can fill ,

 

160 men can last for 40 days

1 man can last for = 40 × 160 days

Total number of men = 160 + 40 = 200

200 soldiers can last for = (30 × 160/200) = 24 days

Let the altitude of the triangle be ‘h’ centimeters.

We know that, Area of a triangle = ½ × base × height

And, area of a square = side²

According to question, Area of the given triangle = Area of the given square

⇒1/2 × 15 × h = 15²

⇒ h = 30 cm

Hence, the height of the triangle is 30 centimeters.

Let radius of cylinder be r and radius of sphere be R

Volume of a right circular cylinder = πr²h

Volume of a sphere = (4/3)πR³

Given,

R = 2r

Ratio of the volumes of a right circular cylinder and a sphere is 3 : 2

⇒ h = 16r

Curved Surface area of a right circular cylinder = 2πrh

Surface area of the sphere = 4πR²

∴ Ratio of the surface areas of the cylinder and the sphere = = 2 : 1

Let ∠ABC be x then ∠BAC = 2x

Using Exterior angle property

⇒ ∠CAB + ∠ABC = ∠ ACD

⇒ 2x + x = 114

⇒ x = 38

⇒ ∠BAC = 2x = 2 × 38 = 76

∴ ∠BAC is 76

If a, b, and c are the three sides of a triangle, then the circum-radius ‘R’ is given as,

R = abc/4A

Where A = area of triangle = (base × height)/2

Given, height = 8 cm

Let base = QR = x cm

⇒ Area of triangle = A = 8x/2 = 4x

The other two sides of triangle are of lengths 24 cm and 12 cm,

∴ Circum-radius of triangle = (24 × 12 × x)/(4 × 4x) = 18 cm

x = cos²θ + sec² θ

For a cos²θ + b sec²θ

Min value = 

So x 
 

∴ x ≥ 2

Alternate Solution:

Arithmetic mean ≥ Geometric mean

(cos²θ + sec² θ)/2 ≥ 
 

cos²θ + sec² θ ≥ 2√1

∴ x ≥ 2

∴ tanx =1

∴ x = π/4

Let the regular polygon has n sides. We also know that the sum of all the interior angles of a regualr polygon with n sides is (n - 2) × 180°

According to the question,

⇒ (n - 2) × 180° = 540°

⇒ n - 2 = 3

∴ n = 5

Required percentage = 57.6/360 × 100 = 16%