RRB JE CBT 1 - Full Test 7

• In 1918, the British Government formed a committee under Justice Rowlatt to suggest ways to curb seditious activities in India. 
• The Viceroy of India at that time was Lord Chelmsford. 
• The Rowlatt Act 1919 gave unrestrained powers to the government to arrest and imprison suspected people without any trial. 
• Gandhi called for a Satyagraha against this draconian act and he was arrested soon after that. 

• Bengal Gazette or the Original Calcutta General Advertiser was an English language weekly newspaper published in Kolkata (then Calcutta), the capital of British India.
• It was the first newspaper printed in Asia and was published for two years before the East India Company seized the newspaper's types.

• The Nagarjuna Dam is the world’s largest and tallest masonry dam which is built across the Krishna River at NagarjunaSagar in the Nalgonda district of Telangana.
• It has an installed capacity of ‎about 816 MW (1,094,000 HP)

Bhagirathi and Alaknanda rivers meet at Devprayag. The two headstreams meet at Devprayag (Uttarakhand) to form the Ganges. Vishnuprayag, Nandaprayag, Karnaprayag, Rudraprayag and Devprayag are Panch Prayags (five prayags) where prayag refers to meeting point of two or more rivers.

Panchayati Raj generally refers to the system introduced by the constitutional amendment in the Constitutional 73rd Amendment Act 1992 came into force to provide constitutional status to the Panchayati Raj institutions.

• There are three All India Services in India.
• These include the Indian Administrative Service (IAS), the Indian Forest Service (IFS) and the Indian Police Service (IPS) which are all Civil services of India.
• While the members of these services are placed under various states, they are recruited by the Centre.
• Indian Foreign Services and Indian Engineering Service are under central civil services.

Born in 1723, Adam Smith is regarded as the Father of Economics due to his immense contribution to the subject. Amongst his many books, the most famous is Wealth of Nations (1776) which is regarded as the first work in modern economics. Smith influenced many later thinkers such as Karl Marx, Joseph Schumpeter, David Ricardo and many more.

The United Nations Environment Programme has been established by the United Nations General Assembly in pursuance of the Stockholm Conference. The UNEP worked as catalyst stimulator and coordinator among the member states on the environmental action.

Namdapha National Park is the largest protected area in the Eastern Himalaya biodiversity hotspot and is located in Arunachal Pradesh in Northeast India.

Project Tiger is a tiger conservation programme launched in 1973 by the Government of India during Prime Minister Indira Gandhi's tenure.

The project aims at ensuring

1) a viable population of Bengal Tigers in their natural habitats,

2) protecting them from extinction,

3) preserving areas of biological importance as a natural heritage

• Ustad Bismillah Khan used to play Shehnai.
• Ustad Bismillah Khan (1916 – 2006) (Real name is Qamaruddin Khan), was an Indian musician credited with popularizing the Shehnai.
• Shehnai is a musical instrument which is similar to the oboe (common in India, Pakistan, and Bangladesh.)
• He was honoured with India's highest civilian honour, the Bharat Ratna in 2001 thus becoming the third classical musician after M. S. Subbulakshmi and Ravi Shankar to be awarded this distinction.
• On his 102nd birth anniversary, he was honoured by Google with a Google doodle.

• “Lollapalooza Music festival” was held in August 2018 in Chicago.
• It started in the year 1991 and since then it is celebrated annually.
• It is a multi-genre (Alternative rock, punk rock, heavy metal, pop, hip hop, electronic ) delight which is celebrated every year in the USA.
• It includes music, dance, comedy and craft booths, etc.

• The Gandhi Peace Prize for the years 2015,2016,2017 and 2018 were announced on 16 January 2019.
• Vivekananda Kendra got the prize for 2015.
• Akshaya Patra Foundation and Sulabh International got the prize for 2016.
• EkalAbhiyan Trust got the prize for 2017.
• Yohei Sasakawa got the prize for 2018.
• The annual prize was instituted by the Government of India in 1995.

• The author of 'Feisty At Fifty' is Sudha Menon.
• 'Feisty at Fifty' is both, a moving personal story and the ultimate guide to make fifties, the most fabulous decade of your life.
• It is all about celebrating mid-life discoveries, and generally feeling great about ourselves.

• The color of the skin is produced by the pigment Melanin. It is produced within the skin by cells called Melanocytes.
• Haemoglobin gives the red color to blood and helps in the transport of oxygen. Insulin controls the level of sugar in the blood.
• Adrenaline is a stress hormone released from the adrenal glands.

Beta cells are unique cells in the pancreas that produce, store and release the hormone insulin. The main function of a beta cell is to produce and secrete insulin-the hormone which is responsible for regulating levels of glucose in the blood.

• Sleeping sickness is caused by trypanosoma and that is why it is called African trypanosomiasis.
• Sleeping sickness is transmitted by tsetse fly.
• Sleeping sickness is sickness which happens in two stages.

Symptoms of the Sleeping Sickness:

1. First stage-Fever, headache and joint pain
2. Second stage- disturbance in sleeping pattern, personality changes and lethargy

• Lysosomes are called “Suicidal Bags” because whenever a cell is damaged the lysosome bursts releasing all the digestive enzymes and thus killing the cell as well as itself.
• The lysosome is a membrane-bound organelle that contains an array of enzymes, capable of breaking down all types of biomolecules like proteins, carbohydrates and lipids.
• The lysosomes also act as the waste disposal system of the cell by digesting unwanted materials.

The development of fruits without fertilization of the ovules is called parthenocarpy. The fruits which are formed by this process are seedless. Example- banana, pineapple, etc.

The edible part of coconut (Cocosnucifera) is endosperm.

Leprosy is a contagious disease that affects the skin, mucous membranes, and nerves, causing discoloration and lumps on the skin and, in severe cases, disfigurement and deformities. It is a long term infection caused by the bacteria Mycobacterium leprae andMycobacterium lepromatosis

• The pharynx is a part of the respiratory system and also a part of the digestive system.
• The pharynx has 3 parts: Nasopharynx, Oropharynx, and Laryngopharynx. The lower two part - the oropharynx and the laryngopharynx are involved in the digestive system. The Nasopharynx connects to the esophagus and it serves as a passageway for both air and food. 

Modern electric bulbs are usually filled with a mixture of argon and nitrogen. More rarely, some bulbs are filled with pure argon, krypton or xenon.

• Ohm’s law (V = IR) is applicable only to conductors and not to insulators. Even conductors like vacuum tubes, semiconductors, transistors, thermistors do not obey Ohm’s law. 
• Vacuum tubes are non ohmic conductors. Even though it is known that ohm's law is followed by conductors. There are some conductors that do not follow ohm's law and they are known as non ohmic conductor.

Nephometer:

• An instrument designed to measure the amount of cloudiness
• It consists of a convex hemispherical mirror mapped into six parts.
• the amount of cloud coverage on the mirror is noted by the observer and then cloudiness is measured

• Steam Engine is an example of an external heat engine. 
• An external heat engine is such that the engine heat is produced outside the engine. 
• In case of an internal heat engine, this heat is produced in the engine. 
• Petrol and diesel engines are examples of internal heat engines. 

At low pressure and high temperature, real gas can act as an ideal gas as the intermolecular force of attraction is negligible.

In total internal reflection, the light must travel from a denser medium to rarer medium (e.g. glass to air or water to air).

Capillary action is the ability of a liquid to flow in narrow spaces without the assistance of, or even in opposition to, external forces like gravity. The liquid of the oil is drawn up into the wick by capillary action and vapourised by the heat of the flame.

• Chemical energy is stored within the rechargeable cells.
• Chemical energy is a type of potential energy stored in the bonds of chemical compounds and is released in the form of heat when the bonds between the atoms are broken.
• A rechargeable cell is a type of cell which can be charged, discharged into a load, and recharged many times.
• Electrical energy is converted into Chemical Energy when these cells are recharged.

• Plaster of Paris is obtained by heating gypsum or calcium sulphate dihydrate to about 140-180 degree Celsius.
• When heated to such a temperature, gypsum formsPlaster of Paris.
• The name is derived from the large deposits of gypsum in the Montmartre hill in Paris.

Boron is a chemical element with symbol B and atomic number 5. It is a p-block element, produced entirely by cosmic ray spallation and supernovae and not by stellar nucleosynthesis. It is a low-abundance element in the Solar system and in the Earth's crust.

Pyrex glass is a mixture of sodium and aluminium borosilicates. In ordinary glass, silica is the main constituent. In Pyrex glass some of the silica is replaced by boron oxide. Boron oxide expands very little when heated, thus, Pyrex glass does not crack on strong heating.

A Geiger counter (Geiger-Muller tube) is a device used for the detection and measurement of all types of radiation: alpha, beta and gamma radiation. Basically it consists of a pair of electrodes surrounded by a gas. The electrodes have a high voltage across them. The gas used is usually Helium or Argon.

• Bell metal is a hard alloy used for making bells and different musical instruments.
• It is made of 80% copper and 20% tin (Sn) with some amount of Zinc and Lead.
• Bell metal is known for its resonance and attractive sound.

• Van der Waal’s equation explains the behaviour of real gases with great accuracy and also the deviations of gas laws from ideal behaviour.
• The equation was proposed in the year 1873.
• It was a first step towards taking into account interaction forces which are acting between real gases molecules.

Cryogenic fuels are used in the rocket technology as the extremely low temperature is essential for lifting and placing of heavier objects in space.

GPRS stands for General packet radio service.

GPRS is a packet oriented mobile data service on the 2G and 3G cellular communication system.

GPRS is used for transmitting data in the GSM network in from of packets.

The unit of illuminance is lux (lx). It measures luminous flux per unit area. It is equal to one lumen per square metre.

• John Dalton, an English chemist, gave the theory of ‘Atom’.
• Dalton’s atomic theory states that all matter was composed of atoms.
• Atoms are the invisible and indestructible building blocks. All the atoms of the same elements are identical.

Gregor Mendel is usually considered to be the Father of modern genetics. Though farmers had known for centuries that crossbreeding of animals and plants could favor certain desirable traits, Mendel's pea plant experiments conducted between 1856 and 1863 established many of the rules of heredity.

Using BODMAS rule,

1) +, ×, ÷ ,- ⇒ 17 + 21 × 8 ÷ 13 – 52

→ 17 + 12.92 – 52 = -22.08 ≠ 36

2) -, +, ×, ÷ ⇒ 17 – 21 + 8 × 13 ÷ 52

→ 17 – 21 + 2 = -2 ≠ 36

3) +, -, ×, ÷ ⇒ 17 + 21 – 8 × 13 ÷ 52

→ 17 + 21 – 2 = 36

4) ÷, ×, +, - ⇒ 17 ÷ 21 × 8 + 13 – 52

→ 6.47 + 13 – 52 = -32.53 ≠ 36

Hence, correct answer is “+, -, ×, ÷”.

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

Conclusion I: No developer is CEO → False

Conclusion II: Some developers are CEO → False

But conclusion I and II forms a complementary pair.

Hence either conclusion I or II follows.

Let’s check each option,

1) 02, 44, 04, 96, 97 → CHAHP

2) 20, 66, 59, 42, 55 → CHAMC

3) 86, 79, 85, 89, 40 → CHAMP

4) 55, 66, 04, 34, 75 → CHAMC

Hence, the set which represent CHAMP is “86, 79, 85, 89, 40”.

On arranging given word as per dictionary order,

IV. Decibel
I. Decide
II. Decimal
III. Decisive
VI. Decode
V. Dedicate

Hence, “Decimal” comes third according to the dictionary.

All of them are specialist in the field of medical, whereas Epistemologistis someone who studies how we know things.

Hence, “Epistemologist” is the odd one.

1) 6² + 3² = 45; 45² = 2025

2) 5² + 4² = 41; 41² = 1681

3) 3² + 3² = 18; 18² = 324

4) 2² + 5² = 29; 29² = 841

Hence, “3, 3, 18, 330” is odd pair among the given option.

The logic here is as follows,

Similarly,

Thus NNNOL is coded as QRTQP.

The logic here is as follows,

8 – 2 = 6; 6³ = 216

1) 41 : 256,

4 – 1 = 3; 3³ = 27

2) 63 : 27

6 – 3 = 3; 3³ = 27

3) 52 : 64

5 – 2 = 3; 3³ = 27

4) 93 : 676

9 – 3 = 6; 6³ = 216

Hence, 63 : 27 is the correct pair.

Rupee is the currency of India. Similarly currency of Denmark is Krone.

Hence Denmark is related to Krone.

The logic here is as follows,

Similarly,

Thus SWIGGY is coded as VZMKJB.

The logic here is as follows,

So the wrong term in this series is OOYO. 

Hence, the correct answer is option 3.

From first to the second figure, the image is water image of mirror image of the first figure.

Similarly,

Hence above image will be the answer.

Here first the group of AB moves 1 place in forward direction.

A and B will always remain beside each other.

Hence set ‘GGABGDG’ will complete the series.

Most often than not, movies are a work of fiction and should be allowed to have any plot that would entertain the audience. Keeping a check on the plot of the movie would curb the right of creative freedom of its makers. People might end up getting offended but it is not the fault of the makers and not allowing them to freely make the movie is not a viable solution. Therefore, movies should be allowed to have any plot and option 1 is the right answer.

Here first you define the problem and the objectives, and then you measure it if any improvement is needed. Next step is to analyze the situation and the process follows to improve that, the next step is to improve the problem.

Thus the next term in the series is Improve.

Answer: Option 4 is correct.

Solution: The statement emphasizes on 2 potentially opposite forms of disasters, viz. drought and flood, Kerala is facing in a span of few months. So, we can assume that Kerala is prone to disasters. Hence assumption 3 is correct. The reason for the flood is not mentioned in the statement, so assumption 1 cannot be made. Similarly, no relation between the flood and the drought can be determined from the statement, so assumption 2 is also not true. Therefore, option 4 is the right answer.

Hence, “nothing” is coded as “%5”.

Argument I provides us with a valid reason in favour of the regular checking. Regular checks by the Income Tax department would help keep a check on the black money generated in the economy and would prevent people from hiding their real income. Argument II makes an assumption that people would not like this regular checking. We cannot consider this assumption as it is not concrete. Therefore, option 1 is the correct answer.

The distance between final destination and his home is 80 meters and the final destination is in North West direction with respect to the Bank.

Hence, “80 meters, North West” is the correct answer.

Hence, the correct answer is option 2.

According to the information given, from Mahesh's viewpoint,

1) No person sits to the left of E.

2) F sits exactly between D and H such that either D or H sits at extreme ends.

3) Number of people sitting to the left of G is equal to the number of people sitting to the right of H.

Here case 1 and case 4 are eliminated as H is sitting at extreme right end but G cannot be placed at extreme left end as E is already sitting there.

4) C is not the neighbor of E.

Thus case 3 also gets eliminated.

As while taking photograph the left and right hands of the person are in opposite direction to that of the viewer of photograph, E was sitting second to the right of C while taking the photograph.

Answer: 4. All of the above follow.

Solution: The air pollution index rises because of vehicles; hence controlling its number and improving its standard will be beneficial. So, action I follows. If there are better public transport systems available, people will use them instead of individual cars, which will reduce the overall traffic. Hence, action II follows. Promoting electric vehicles will also help in reducing the pollution index, therefore action III also follows. Hence, option 4 is the correct answer.

According to the question,

Thus T is the grandmother of G.

Hence, figure 4 is the correct answer.

Part filled by A in 1 hr. = 1/6

Part filled by B in 1 hr. = 1/8

Part filled by C in 1 hr. = 1/12

Now, pipes A and B are opened for 2 hrs.

⇒ Part filled by A and B together in 2 hrs. = 2(1/6 + 1/8) = 2 × 7/24 = 7/12

∵ Tank is initially 1/6 filled,

Remaining part of tank to be filled = 1 - 1/6 - 7/12 = 1 - 3/4 = 1/4

∴ Pipe C will fill the remaining part in = (1/4)/(1/12) = 3 hrs

sin x + sin² x = 1       ----(1)

cos² x + cos² x = ?        ----(2)

From equation (1)

sin x + sin² x = 1 (sin²x + cos²x = 1)

sin x + 1 – cos² x = 1

sin x = cos² x

sin² x = cos⁴ x

substituting value of cos² x and cos⁴ x in (2)

cos² x + cos⁴ x = sin x + sin² x = 1

Let the average weight of the 69 students be A.

∴ total weight of the 69 of them will be 69A.

As question states, the total weight of the class = 69A + 38

When this student is also included, the average weight decreases by 0.2 kg;

⇒ (69A + 38)/70 = A - 0.2

⇒ 69A + 38 = 70A - 14

⇒ 70A - 69A = 38 + 14

⇒ A = 52

∴ Average weight of the remaining 69 students = 52 kg

x² + 1 / x² = 2

⇒ x² + 1 / x² - 2 = 0

⇒ (x - 1 / x)² = 0

⇒ x - 1 / x = 0

⇒ x = 1 / x

⇒ x² = 1

∴ x = 1, -1

Hence, x⁶ = 1

For the given A.P.,

First term, a = 3 and common difference, d = 2

The nth term = a + (n – 1) d

5^th term = 3 + 4 × 2 = 11

16^th term = 3 + 15 × 2 = 33

49^th term = 3 + 48 × 2 = 99

Hence, the G.P. is 11, 33, 99

Since, G.P. is of the form a, ar, ar²

Hence the common ratio, r = 33/11 = 3

a : b : c : d

2/9 : 1/3 : 1/3 : 1/3

3/7 : 3/7 : 5/14 : 5/14

7/10 : 7/10 : 7/10 : 3/5

42/630 : 21/210 : 35/420 : 15/210

⇒ 42/3 : 21/1 : 35/2 : 15/1

⇒ 28 : 42 : 35 : 30

We know if ax² + bx + c = 0 is a quadratic equation, product of the roots = (c/a)

⇒ In the given problem a = 7, b = -14, c = a

If the roots of the equation are reciprocal to each other, then the product of the roots = 1

⇒ (a/7) = 1

⇒ a = 7

On putting ‘a’ = 7 in the original equation, the equation will now be 7m² – 14m + 7 = 0

⇒ m² – 2m + 1 = 0 (Dividing the previous equation with 7 on both sides)

⇒ m² – m – m + 1 = 0

⇒ m (m – 1) – (m -1) = 0

⇒ (m - 1) (m – 1) = 0

⇒ (m - 1)² = 0

⇒ m = 1

∴ So, the roots of the quadratic equation are 1, 1

Let the five subjects are a, b, c, d and e

Marks in third subject c = 65 given

Average marks in first three subjects = 81

⇒ (a + b + c)/3 = 81

⇒ a + b + c = 243

Average marks in last three subjects = 74

⇒ (c + d + e)/3 = 74

⇒ c + d + e = 222

⇒ 65 + d + e = 222

⇒ d + e = 222 – 65 = 157

Average marks of suman in all sub. = (a + b + c + d + e)/5 = (243 + 157)/5

∴ Average marks = 400/5 = 80

5 × 2 = 10

⇒ The number of 2’s and 5’s in the product determines the number of zeroes in it.

4⁸ × 35¹²

= (2²)⁸ × (7 × 5)¹²

= 2¹⁶ × 7¹² × 5¹² (∵ (a^m)ⁿ = a^mn & (a × b)^m = a^m × b^m)

=7¹² × 2⁴ × (2 × 5)¹²

∴ Number of zeroes in the product 4⁸ × 35¹² are 12.

Let CD be the pole and A and B be positions of two persons

⇒ Then CD = 100 cm and ∠DAC = 30⁰ and ∠DBC = 45⁰

⇒ AB = 273 cm

∴ The distance between two persons = 273 cm

Let P₁ = x and P₂ = 3100 - x

Simple Interest =(P × R × T)/100

Where P is Principle amount, R is rate of interest, T is time in years.

Total annual interest = I₁ + I₂ = (8 × x × 1)/100 + [(3100 - x) × 6 × 1]/100

x = Rs. 1300

Let the speed of boat = x km/hr

& the speed of stream = y km/hr

According to the question

⇒ 12/(x - y) = 4

⇒ x - y = 3      ----(1)

⇒ 12/(x + y) = 3

⇒ x + y = 4     ----(2)

From equation (1) and equation (2)

⇒ x = 3.5 and y = 0.5

So, speed of boat in still water is 3.5 km/h

Let the number of questions attempted correctly be X and those attempted wrong be Y.

Given,

Total question attempted= 75

⇒ X + Y = 75       …………………(1)

Also total score is 125. Since 4 marks is awarded for every correct answer and 1 marks is lost for every wrong answer. Thus

 ⇒(X × 4) +(Y × (-1)) = 125

⇒ 4X – Y = 125       ………………….(2)

Adding (1) and (2) both sides, we get

⇒ 5X = 200

⇒ X = 40

Hence total number of questions attempted correctly is 40. 

In Vessel B, the proportion of milk in 4/((4 + 5) ) = 4/9.

In vessel A, the proportion of milk is 5/(5 + 1) = 5/6.

The amount of milk in the mixture = 5/((5 + 4)) = 5/9

X = (5/6) - (5/9) = 5/18

Y = (5/9) - (4/9) = 1/9

The ratio is (5/18) ∶ (1/9) = 5 ∶ 2

Formula:

a² – b² = (a + b)(a – b)

Given,

x¹⁶ + x⁸ + 1

= x¹⁶ + 2x⁸ + 1 – x⁸

= (x⁸ + 1)² – (x⁴)²

= (x⁸ + 1 – x⁴)(x⁸ + 1 + x⁴)

= (x⁸ + 1 – x⁴)((x⁴ + 1)² – (x²)²)

= (x⁸ + 1 – x⁴)(x⁴ + 1 – x²)(x⁴ + 1 + x²)

= (x⁸ + 1 – x⁴)(x⁴ + 1 – x²)((x² + 1)² - x²)

= (x⁸ + 1 – x⁴),(x⁴ + 1 - x²)(x² + 1 + x)(x² + 1 - x)

Thus the factors are:

(x⁸ + 1 – x⁴), (x⁴ + 1 - x²) , (x² + 1 + x), (x² + 1 - x)

Suppose the speeds of train are 5x and 7x km/hr;

∴ Length of 1^st train = 60x

Length of 2^nd train = 105x

∴ Time in which they will cross each other = (60x + 105x) / (5x + 7x) = 165/12 = 13.75 seconds

Let the initial price of a jeans and a watch be Rs. ‘x’ and Rs. ‘y’ respectively

Hence, we have, 20x = 2y

⇒ x = y/10      ----(1)

New price of a jeans = (100 + 20)% of x = 1.2x

New price of 45 jeans = 45 × 1.2x = 54x

Substituting from (1),

New price of 45 jeans = 54 × (y/10) = 5.4y

New price of a watch = (100 – 10)% of y = 0.9y

No. of watches costing equal to 45 jeans = 5.4y/0.9y = 6

∴ The new price of 45 jeans is equal to that of 6 watches

Since 3 women would as much work as 2 men;

Ratio of efficiencies of Man and Woman = 3 ∶ 2 Or 2M = 3W

15 men take 21 days of 8 hours each to do a piece of work, let suppose 21 women take x days of 6 hours each to do that work;

∴ (15M × 21 × 8) = (21W × 6 × x)

Putting 2M = 3W;

⇒ (15M × 21 × 8) = (14M × 6 × x)

⇒ x = 30

∴ 21 women will take 30 days of 6 hours each to do the work.

Let ‘x’ kg of rice at Rs. 54 per kg be mixed

Total weight of mixture = (x + 30) kg

Cost price of (x + 30) kg mixture = 54x + 30 × 40 = 54x + 1200

⇒ Cost price of 1 kg mixture = (54x + 1200)/(x + 30)

Now, when selling price is Rs. 48.4 per kg, profit is 10%

⇒ Cost price of 1 kg mixture + 10% of Cost price = Selling price

⇒ 110% of Cost price of 1 kg mixture = Selling price

⇒ Cost price of 1 kg mixture = 48.4/1.1 = Rs. 44

Hence, we get,

⇒ (54x + 1200)/(x + 30) = 44

⇒ 54x + 1200 = 44x + 1320

⇒ 10x = 120

⇒ x = 120/10 = 12

∴ 12 kg of rice must be added

Let time taken by Rajdhani be y hrs

Let the speed of Express train be x km/hr

Time taken by Express train = 660/x

660/x = y + 10      ----(1)

New speed of Express train be 2x km/hr

Time taken by Express train = 2x/660

660/2x = y - 7      ----(2)

From (1) and (2) we get x = (660/34) km/hr and y = 24 hr

Speed of Rajdhani = 660/24 = 27.5 km/hr

Alternate:
Put θ = 0,

⇒ [(cos³2θ + 3cos2θ) ÷ (cos⁶θ - sin⁶θ)] = [(cos³(0) + 3cos(0)] ÷ (cos⁶(0) - sin6(0)]

⇒ [(1 + 3) ÷ (1 - 0)] = 4

∴ [(cos³2θ + 3cos2θ) ÷ (cos⁶θ - sin⁶θ)] = 4

Given,

First shirt is sold at a profit of 30%

We write 30% = 3/10

Let CP of the first shirt be 10 and profit be 3

So, SP of the first shirt = 10 + 3 = 13

(CP)₁/(SP)₁ = 10/13      ----(1)

Similarly second shirt is sold at a loss of 30%

We write 30% = 3/10

Let CP of the second shirt be 10 and loss be 3

So, SP of the second shirt be = 10 – 3 = 7

(CP)₂/(SP)₂ = 10/7      ----(2)

Given, CP of the first shirt is equal to the SP of the second shirt.

Multiply by 7 in equation (1) and multiply by 10 in equation (2) we get

CP)₁/(SP)₁ = 70/91

(CP)₂/(SP)₂ = 100/70

∴ ratio of the selling price of the first shirt to the cost price of the second shirt is 91 : 100

⇒ given: Radius of cone, r = 16 cm, Height, h = 12 cm

⇒ Radius of cylindrical jar, r₁ = 8 cm, height, h₁ = x

⇒ Volume remains the same in this case

⇒ Volume of cone = Volume of Cylinder

⇒ (1/3) × (π × r² × h) = (π × r₁² × h₁)

⇒ (1/3) × (π × 16² × 12) = (π × 8² × x)

⇒ 16 × 16 × 4 = 8 × 8 × x

∴ x = 16 cm

Total decrease = 3000 - 120 = 2880

C’s share = 5/12 × 2880 = 5 × 240 = 1200

Share of C out of 3000 = 1200 + 60 = 1260

Work done by 2 men in 1 day = 1/12

Work done by 3 women in 1 day = 1/15

Work done by (2 men + 3 women + 5 children) in 1 day = 1/5

∴ Work done by 5 children in 1 day = 1/5 – 1/12 – 1/15 = 1/20

⇒ 5 children alone can do the work in 20 days

Ratio of their time (2 Men ∶ 3 Women ∶ 5 Children) = 12 ∶ 15 ∶ 20

We know, efficiency is inversely proportional to the time

∴ Ratio of their efficiency (2 Men ∶ 3 Women ∶ 5 Children) = 1/12 ∶ 1/15 ∶ 1/20 = 5 ∶ 4 ∶ 3

So, 5 + 4 + 3 = 12 unit = 12000

⇒ 3 unit = 3000

⇒ Share of 5 children is 3000

∴ Share of 1 child = 3000/5 = 600

Simple interest = (P × r × t)/100

P = Principal

t = Time period

r = Rate of interest

Given,

t = 2 years

r = 10%

Simple Interest = Rs. 600

600 = (P × 2 × 10)/100

⇒ P = 3000

Compound Interest = [P(1 + r/100)^t - 1]

Where,

CI = Compound interest

P = Principal

r = Rate of interest

t = Time period

Given,

t = 2 years

r = 10%

Compound Interest = Rs. 660

630 = [P(1 + 10/100)² - 1]

630 = 21P/100

P = 3000

Previous

Expenditure = Total salary - Savings

So, 100 % salary will be = [12000 × 100]/ [100/3] = 36,000

So, his monthly expenses are = 36000 – 12000 = Rs. 24,000

According to the question,

Expense for Home & Food = 3/4 × 24000 = Rs. 18000

So, expense on transport = 24000 – 18000 = Rs. 6000

∴ So Rahul spend Rs. 6000 in transportation

If x be the number, then 54 - x, 71 - x, 75 - x and 99 - x are in proportion.

(54 - x) (99 - x) = (71 - x) (75 - x)

5346 - 153x + x² = x² - 146x + 5325

X = 3