RRB JE CBT 1 - Full Test 8

Hence, the total number of triangles is 15.

The pattern followed here is,

Consecutive prime numbers are given,

13 and 17

Similarly,

19 and 23

Hence, 23 is the correct answer.

The game cricket is played with bat and ball.

Similarly, badminton is played with racket and shuttle cock.

Hence Badminton is related to Shuttle.

Let the age of A be “x” years, B be ‘y’ years and C be “z” years.

Three years ago,

Age of A = x – 3 years

Age of B = y – 3 years

Average of age of A and B = (A + B)/2 = 8 years

⇒ (x + y -6)/2 = 8

⇒ x + y – 6 = 16

⇒ x + y = 22

Now average of A,B and C = 15 years

⇒ (A + B + C)/3 = 15

⇒ x + y + z = 45

⇒ 22 + z = 45

⇒ z = 23 years 

Since the data about the age is not given.

The correct answer is Data inadequate.

Prime numbers before 19 = 17, 13, 11, 7, 5, 3, 2

We know, Average = sum of all the number/total number

∴ Average = (17 + 13 + 11 + 7 + 5 + 3 + 2)/7 = 58/7 = 8.28

• The hypothalamus is the processing center of the brain that controls body temperature.
• It does this by triggering changes to effectors, such as sweat glands and muscles controlling body hair.
• Heat stroke can happen when the body becomes too hot, and hypothermia when the body becomes too cold.

Time taken by 5 men to do a piece of work = 12 days

∴ Work done by 5 men in 1 day = 1/12

Time taken by 10 women to do the same work = 15 days

∴ Work done by 10 women in 1 day = 1/15

With the help of 15 children they finished the work = 5 days

∴ Work done by (5 men + 10 women + 15 children) in 1 day = 1/5

So, work by 15 children in 1 day = 1/5 - 1/12 - 1/15 = 1/20

Time taken by 15 children to do the same work = 20 days

The ratio of their time = 12 : 15 : 20

We know, the efficiency is inversely proportional to the time

So, ratio of their efficiency = 1/12 : 1/15 : 1/20 = 5 : 4 : 3

So, 5 + 4 + 3 = 12 unit = 36,000

⇒ 1 unit = 3,000

⇒ 3 unit = 9,000

∴ Share of 15 children is 9,000

So, share of 1 child = 9,000/15 = 600

So, share of 5 children = 600 × 5 = 3,000

The order of the increasing wavelength of the colors is:

• Violet
• Indigo
• Blue
• Green
• Yellow
• Orange
• Red

The visible light or visible spectrum is divided into these colors.

In all pairs except ‘LMNO – LMON’ 1^st & 2^nd and 3^rd & 4^th alphabets are interchanged while in ‘LMNO – LMON’ 1^st & 2^nd alphabets are not interchanged.

Hence, ‘LMNO – LMON’ is an odd letter pair.

Mycology is the branch of biology concerned with the study of fungi, including their genetic and biochemical properties, their taxonomy and their use to humans as a source for tinder, medicine, wine, cheese, (edible mushrooms), and entheogens, as well as their dangers, such as poisoning or infection.

In space craft freezing of fuel is prevented by the Usage of Glycol. It is an additive which lowers the freezing point of a water-based liquid and increases its boiling point. Thus ensuring performance of the engine or the space craft in situation of extreme temperature shifts.

• Chandragupta Maurya became a Jain and left for Sravanbelgola, Karnataka along with his Jain guru Bhadrabahu. 
• He died by slow starvation at Chandragiri Hill, Sravanbelgola .
• He lived as an ascetic for some years and died of voluntary starvation.
• He was the founder of the Maurya Dynasty in India. 

• 'Lippa Asrang' Wildlife Sanctuary is a part of district Kinnaur in Himachal Pradesh.
• It is situated in an area of 3089 hectares and is part of Moorang town.
• The sanctuary was established in the year 1974.

Concept:

cos(90−θ)=sinθ
sin(90−θ)=cosθ

Tear gas also known as lachrymator agent is a chemical compound that is mostly used as a weapon as it causes severe eye, respiratory and skin irritation.

Chloropicrin is a constituent of tear gas and is responsible for causing irritation.

• Water in an electric kettle becomes hot by convection. It is the process of transfer of heat by mass motion of a fluid such as water when the heated fluid is caused to move away from the source of it and carrying energy with it.
• Conduction is the process of transmission of heat through the material of a substance.
• Radiation is the process of emission of energy in the form of moving subatomic particles or electromagnetic waves.

Rectangle represents Animators,

Circle represents Dancers,

Triangle represents Potters,

Square represents Mothers

Thus the letters inside the triangle but not in the intersection of square and triangle represent Potters who are not Mothers i.e. IH.

Hence, the correct answer is IH.

Lcm of (6, 5) = 30

Let’s assume the number be "30K + constant", where Constant is the remainder.

let that number be ‘M’

⇒ M/6 = 5 (remainder)

M could be 5, 11, 17, 23, 29, ...

⇒ M/5 = 3 (remainder) 

M could be 3, 8, 13, 18, 23, 28, ...

The very first number common in both term is 23.

⇒ M is 23 i.e. a constant term

⇒ 30K + constant = 30K + 23

The largest three digit number comes when K is 32

⇒ 30 (32) + 23 = 983

∴ When 983 is divided by 11, leaves the remainder 4.

• A radioactive element is that which breaks down over the time by turning into different elements and releasing energy.
• They are considered unstable since they have an unbalanced number of protons and neutrons in the nucleus. Germanium is not a radioactive element, while the rest of these are radioactive.

Harike Wetland is a manmade lake and wetland formed by the headworks built in 1953 on the confluence of the Beas and the Sutlej rivers. The wetland is characterized by the Harike freshwater lake and is a home to over 200 species of birds along with a rich marine flora and fauna.

Consider the horizontal relations,

In row 1, (7 × 5) – 2 = 35 – 2 = 33

In row 2, (8 × 6) – 2 = 48 – 2 = 46,

In row 3, (6 × 6) – 2 = 36 – 2 = 34,

Similarly in row 4, (8 × 7) – 2 = 56 – 2 = 54

Hence, 54 is the correct alternative.

sec²θ + tan²θ =53=53

[1 + tan²θ = sec²θ]

1 + tan²θ + tan²θ =53=53

2 tan²θ  = 5/3−1

tanθ =1/√3

∴ θ = 30°

Original weight of rice = 1 kg = 1000 gm

Let cost of 1 gm is Rs. 1

Cost price of 1000 gm = Rs. 1000

Selling price of 850 gm = Rs. 1000 (∵ giving only 850 gm instead of 1000 gm)

Profit = [error/ (true weight)] × 100

⇒ Profit = [(1000 - 850)/ 850] × 100 = (150/850) × 100 = 17.65%

∴ profit % on 5kg is equal to profit on 1 kg which is 17.65%

The pattern followed is:

95 + 65 + 23 = 81

9 × 5 + 6 × 5 + 2 × 3 → 45 + 30 + 6 = 81

Similarly;

56 + 23 + 62 = 48

5 × 6 + 2 × 3 + 6 × 2 → 30 + 6 + 12 = 48

Similarly;

56 + 26 + 32 = ?

5 × 6 + 2 × 6 + 3 × 2 → 30 + 12 + 6 = 48

Hence, 48 is the correct answer.

Let the first number be 5a.

So, the second number = 60% of 5a = 3/5 × 5a = 3a

HCF × LCM = 1^st no. × 2^nd no.

⇒ 2535 = 5a × 3a

⇒ 2535 = 15a²

⇒ a² = 169

⇒ a = 13

∴ Difference between the numbers = 5a - 3a = 2a = 2 × 13 = 26

• Water comes out of leaves in the form of vapour by the process of transpiration.
• Evaporation occurs on the surface of a liquid when it changes into gaseous phase before reaching its boiling point.
• Condensation is the change of the physical state of matter from gas to liquid.
• Sublimation is the direct transition of a substance from solid to the gas phase.

• Dysentery is a disease which affect the small intestine of a human being.
• It includes the severe diarrhea and abdominal pain.
• It is caused by a parasite which is known as Entamoeba histolytica.
• It is an inflammatory disease which causes inflammation in the small intestine.

Linux is an operating system, not a programming language. It is a free & open-source operating system.

Converting fractions to decimals,

⇒ 3/4 = 0.75

⇒ 5/12 = 0.4167

⇒ 13/16 = 0.8125

⇒ 16/29 = 0.5517

⇒ 3/8 = 0.375

∵ 0.375 < 0.4167 < 0.5517 < 0.75 < 0.8125

∴ 3/8 < 5/12 < 16/29 < 3/4 < 13/16

Hence, option 3) is the correct mirror image of the question figure.

I) Shifa is the daughter of Taimur.

We can’t determine relation between Shifa with Azad as Azad is not mentioned here.

II) Azad is the child of Amreen, who is the wife of Taimur.

We can’t determine relation between Shifa with Azad as Shifa is not mentioned here.

But, when combined together, we get

As the gender of Azad is not determined, we cannot say whether he is the sister or brother of Shifa.

Hence, the data even in the both statements I and II together are not sufficient to answer the question.

• Union Minister for Minority Affairs Mukhtar Abbas Naqvi announced that the GST on Haj has been reduced from 18 per cent to 5 per cent. 
• The move will save Haj pilgrims’ Rs 113 crore this year by lowering the airfare.
• He also inaugurated a new conference hall and passport section at the Haj House in Mumbai. 

• Under the command of Francois Curan, the French East India Company established the first French factory in India at Surat in 1668.

• The second factory was established by Marcara in 1669 at Masulipatnam

Work done by P in 1 day = 1/20

Work done by Q in 1 day = 1/60

Work done P and Q in 1 day = 1/20 + 1/60 = 1/15

Work done by P and Q in 5 days = 5 ⨯ 1/15 = 1/3

∴ P and Q finished 1/3^rd of the work in 5 days.

R finished 2/3^rd of the work in 10 days

2/3 work = 10 days

1 work = 10 × (3/2) = 15 days

∴ R will finish the whole work in 15 days.

The patter followed is,

1) (2, 3, 4): 2 + 1 = 3; 3 + 1 = 4;

2) (4, 5, 6): 4 + 1 = 5; 5 + 1 = 6;

3) (6, 7, 8): 6 + 1 = 7; 7 + 1 = 8;

4) (4, 6, 8): 4 + 2 = 6; 6 + 2 = 8

Hence, (4, 6, 8) is the correct answer.

On arranging in reverse word as per dictionary order,

i) Grieve

ii) Grief

iii) Graze

iv) Grass

Hence, “Graze” comes third after arranging in reverse word as per dictionary order.

• Ant bite injects formic acid that will irritate our nerves and triggers an inflammatory response.
• So, the sharp pain caused by the sting of an ant is due to formic acid.

Let the cost price of the article be 100 unit

So, SP of the article = 100 × 110/100 = 110 unit

If he had bought it at 10% less, then new CP of the article = 100 × 90/100 = 90 unit

If he had paid for the article Rs. 11 less, he would have gained 10%

According to the question

⇒ (90 × 110/100) unit = 110 unit – 11

⇒ (110 – 99) unit = 11

⇒ 11 unit = 11

⇒ 100 unit = 100

∴ Cost price of the article Rs. 100

The correct answer is option 1. Both A and R are true and R is the correct explanation for A. 

Marie Curie won two Nobel prizes. One for chemistry and the other for physics. One doesn't win Nobel prize easily. Her contribution was remarkable which is why she won.

• The outer coating of a capsule is made up of gelatin.
• The traditional capsules are made from gelatin, while the soft-shelled capsules are made of liquids or oils.
• Gelatin is an animal protein which is flavorless, colorless, brittle, and translucent food ingredient derived from collagen.
• It is commonly used in medications, vitamin capsules, medications, drugs, cosmetics, gelling agent in food, etc.

Alphabets are coded as per their place value

98 → IH

35 → CE

Similarly,

165 → AFE

Hence, '165' is coded as 'AFE'

• According to Newton’s second law, Force acting on a body is equal to the product of the mass and acceleration of that body, assuming a constant mass.
• This law also states that Force is equal to the change in momentum per change in time.

Let the principal be P

⇒ P(1 + r/100)² = 1800

⇒ 1 + r/100 = √(1800/P)      ----(i)

Also, P(1 + r/100)³ = 1926

⇒ 1 + r/100 = (1926/P)^1/3      ----(ii)

⇒ √(1800/P) = (1926/P)^1/3

⇒ P = 1572

Putting the value of P in (i), we get

⇒ 1 + r/100 = √(1800/1572)

⇒ 1 + r/100 = 1.07

⇒ r/100 = 0.07

∴ r = 7%

In organic chemistry, an alkene is an unsaturated hydrocarbon that contains at least one carbon-carbon double bond. The words alkene and olefin are often used interchangeably.

The formula of Alkane - C_nH_(2n+2)

The formula of Alkene - C_nH_(2n) 

The formula of Alkyne - C_nH_(2n-2)

Let the three numbers be a/r, a, ar. As the numbers form an increasing GP. So, r > 1. It is given that a/r, 2a, ar are in A.P.

From the arithmetic mean concept

• Henry is the unit of inductance, represented with a symbol H or L.
• Inductance, in electronics and electromagnetism, is the property of an electric conductor which causes an electromotive force to be generated with a change in the flowing current.

Since, the total no. of persons or the position of G from any of the sides is not given, the answer to the question cannot be determined.

Hence, answer is ‘Cannot be determined’.

The statement asserts that books should contain the knowledge of life. It cannot be inferred whether it is true for all books. Thus inference I does not follow. Inference II also does not follow because the statement does not relate to people in any way.

Given Series: A5H, F15J, K25L, P35N, ?

Logic Followed here is,

⇒ A + 5 = F; F + 5 = K; K + 5 = P; P + 5 = U

⇒ 5; 5 + 10 = 15; 15 + 10 = 25; 25 + 10 = 35; 35 + 10 = 45

⇒ H + 2 = J; J + 2 = L; L + 2 = N; N + 2 = P

Hence, U45P will be the next term.

• World Wetlands Day is celebrated every year on 2 February.
• It marks the anniversary of the signing of the Convention on Wetlands of International Importance (Ramsar Convention) in Ramsar, Iran, on 2 February 1971.
• The international theme for World Wetlands Day 2019 is 'Wetlands and climate change'
• World Wetlands Day was first celebrated in 1997.

Given,

A and B together have six times the sum what B and C together have

∴ A + B = 6(B + C)…..(1)

A, B and C together have Rs. 30 more than the sum that A has

∴ A + B + C = A + 30

⇒ B + C = 30…..(2)

B has four times the sum than that of C.

∴ B = 4C…..(3)

Using (2) and (3)

4C + C = 30

⇒ 5C = 30

⇒ C = Rs. 6

Putting this in (2)

B + 6 = 30

⇒ B = Rs. 24

Putting value of B and C in (1)

A + 24 = 6(24 + 6)

⇒ A = 180 – 24 = Rs. 156

• The oil used in the flotation method for the purification of ores is pine oil.
• It is used in froth flotation process since it attracts impurities which can be washed away and it does not have any affinity towards water.
• it is an essential oil which is obtained by steam distillation of twigs, cones, and needles from different species of pines.
• The process of selectively separating hydrophobic materials from hydrophilic is known as froth flotation.

• K₂CO₃ or potassium carbonate is known as pearl ash.
• Pearl ash, in ancient times, was created by baking potash in a kiln in order to remove impurities. The remaining fine, white powder was pearl ash.
• Potassium carbonate is an inorganic compound and a white salt which is soluble in water.
• It is mainly used in the production of glass and soap.

We know that,

Third proportional to a and b = b²/a

∴ Third proportional to 12 and 30 = (30)²/12 = 900/12 = 75

We also know that,

Fourth proportional to a, b, c is given by = (b × c)/a

∴ Fourth proportional to 11, 15, 33 = (33 × 15)/11 = 45

∴ Ratio of Third proportional to 12 and 30 and Fourth proportional to 11, 15 and 33 = 75 : 45 = 5 : 3

The pattern followed here is,

All the given numbers are squares of the consecutive prime numbers,

For e.g.

4 = 2²; 9 = 3²; 25 = 5²; 49 = 7²…. so on.

But 64 = 8², and 8 is not a prime number.

Hence, 64 is the odd one out.

Given: 22 P 4 P 9 S (6 P 7 S 8 R 4) Q 3 P 1 S 2

Substituting the symbols:

22 + 4 + 9 - (6 + 7 - 8 ÷ 4) × 3 + 1 - 2

Solution through BODMAS:

22 + 4 + 9 - (6 + 7 - 8 ÷ 4) × 3 + 1 - 2

22 + 4 + 9 - (6 + 7 - 2) × 3 + 1 - 2

22 + 4 + 9 - 11 × 3 + 1 - 2

22 + 4 + 9 - 33 + 1 - 2

22 + 4 + 9 + 1 - 33 - 2

36 - 35 = 1

Hence, the correct answer is 1

The Kyoto Protocol is an international treaty which extends the 1992 United Nations Framework Convention on Climate Change (UNFCCC) that commits State Parties to reduce greenhouse gas emissions.

Let the principal = Rs. 100

Now, S.I. on Rs. 100 = PTR/100

Thus, S.I. on Rs. 100 = Rs. 15

⇒ C.I. on Rs. 100 = Rs. 15.7625

Now, the difference of C.I. and S.I. = 15.7625 – 15 = 0.7625

⇒ For Rs. 100 the difference in C.I. and S.I. is Rs. 0.7625

⇒ For Rs. X the difference in C.I. and S.I. is Rs. 366

∴ On Rs. 48000, the difference of compound and simple interest, shall come out to be Rs. 366

Xylem is one of the two types of transport tissue in vascular plants, phloem being the other. The basic function of xylem is to transport water from roots to shoots and leaves, but it also transports some nutrients.

Given,

A number is increased by 18%

Let number be n.

New number =

= n + n × (18/100)

= 59n/50

To obtain old number,

Let percentage number should be decreased to obtain new number be a.

n = 59n/50 - (59n/50) × (a/100)

n = (5900n - 59na)/5000

5000n = 5900n - 59na

59na = 900n

a = 900n/59n

a = 15.25

By 15.25% new number should be decreased to obtain new number.

From I, we get the order: S, - , - , - , Q.

From II, we get the order: R, T

Combining I and II, we get two possible orders:

S, R, T, P, Q or S, P, R, T, Q.

Thus, either P or T is at the penultimate position.

Let the length of the train be D metres and speed of the train be S m/s

Now As per the basic formula of speed,

S = D/T

Where S = Speed, D = Distance, T = Time

As the train passes an electric pole in 30 seconds

S = D/30  ........eq(i)

As train passes a platform 240 m long in 120 seconds

S = (D + 240)/120  .....eq(ii)

from eq(i) and (ii) we get

D/30 = (D + 240)/120

∴ 4D = D + 240

∴ 3D = 240

∴ D = 80 m

Uniforms were made to maintain equality and motivate discipline. Therefore City Y imposing this rule shows that they believe that uniforms will instill discipline and that their students need more discipline. Consequently, option 3 is the correct answer.

• 'Roma' won the award for Best Foreign Language Picture.
• Spider-Man: Into the Spider-Verse won the award for the Best animated picture.
• Mahershala Ali won the award for the Best Supporting Actor.
• Regina King won the award for the Best Supporting Actress.
• Christian Bale won the award for the Best Actor – Musical or Comedy
• Olivia Colman won the award for the Best Actress – Musical or Comedy

• Plaster of Paris is made from gypsum.
• The common name for plaster is calcium sulphate hemi hydrate which is made by heating gypsum or sulphate of lime.
• PoP gets its name from a huge amount of gypsum deposited on Montmartre Hill in Paris.

It is true that Mahatma Gandhi is the Father of the Nation of India and hence, A is true. It is also true that Gandhi’s picture is printed on the Indian currency notes, so R is also true. But Gandhi is the Father of the Nation because of his contribution to the freedom struggle and only after that was his picture printed on the currency notes. Therefore, R is not the correct explanation of A and option 2 is the correct solution.

We know, two angles whose sum is 90° are called complementary angles and two angles whose sum is 180° are called supplementary angles

Let the angle be x

According to the question,

⇒ (180° – x) = 5/2 (90° – x)

⇒ 360° – 2x = 450° – 5x

⇒ 3x = 90°

⇒ x = 30°

∴ The angle is 30°

Let, 11 consecutive numbers are,

⇒ (x - 5), (x - 4), (x - 3), (x - 2), (x - 1), x, (x + 1), (x + 2), (x + 3), (x + 4), (x + 5)

According to problem,

⇒ (x - 5) + (x - 4) + (x - 3) + (x - 2) + (x - 1) + x + (x + 1) + (x + 2) + (x + 3) + (x + 4) + (x + 5) = 11

⇒ 11x = 11

⇒ x = 1

∴ The lowest number = 1 - 5 = -4

⇒ c = 1 – 1/a

⇒ c + 1/a = 1

• Radio waves have lower frequencies and longer wavelengths as compared to the visible light waves.
• These are the kind of electromagnetic radiations having wavelengths in the electromagnetic spectrum longer than infrared light.
• They travel at the speed of light.

• The Vice President can be removed from his office by a resolution of the Rajya Sabha passed by a majority of its members and agreed to by the Lok Sabha. (Article 67)
• No formal impeachment is required for the removal of the Vice President from his or her post. 
• Generally, the term of the office of the Vice President is five years. 

• A genetic disorder which is caused by the presence of a part or all of the third copy of chromosome 21 is known as the Down's Syndrome.
• It is associated with delays in physical growth, characteristic facial features, and moderate to mild intellectual disability.
• A person affected with it is mentally retarded and has a furrowed tongue.
• The parents are typically genetically normal of the affected individual.

Applying componendo - dividendo,
Again applying componendo - dividendo,

The side mirrors of vehicles are convex mirrors. Because the image is smaller, more space can be covered by this mirror, so a convex mirror provides for a larger field of view than a plane mirror. This is why they are used whenever a mirror with a large field of view is needed. For example, the passenger-side rear view mirror on a car is convex.

• Plasma is the largest component of blood, comprising about 55% of its overall content.
•  Along with water, plasma carries salts, hormones and enzymes.
• The main purpose of plasma is to transport nutrients, hormones, and proteins to the parts of the body that need it.

Vikram Ambalal Sarabhai (12 August 1919 – 30 December 1971) was an Indian scientist and innovator widely regarded as the father of India's space programme. Sarabhai received the Shanti Swarup Bhatnagar Medal in 1962. The nation honoured him awarding Padma Bhushan in 1966 and Padma Vibhushan (posthumously) in 1972

• Uber cup associated with Badminton.
• It is named after a former British women's badminton player, Betty Uber.
• It is often called World Team Championships for Women.
• It is a major international badminton competition contested by women's national badminton teams.
• Thomas Cup is the World Team Championship for Men in Badminton.

A wide area network is a telecommunications network or computer network that extends over a large geographical distance/place. Wide area networks are often established with leased telecommunication circuits.

Names: Jyoti, Vipul, Disha, Ramki, Ralston, Abha, Kiran and Anjali

1. Disha sits two places away to the right of Ramki. (Two places away mean one person in between).

2. Only one person sits between Ramki and Abha.

3. Anjali does not sit adjacent to Ramki.

4. Vipul does not sit adjacent to Ramki.

5. Vipul sits exactly between Ramki and Disha.

Note: exactly between doesn't mean persons should be the neighbors. Count from the left of Ramki and right of Disha.

B exactly between A and C means the number of persons between A and B is equal to the number of persons between B and C

6. Ralston sits exactly between Vipul and Kiran.

7. Ralston sits opposite to Anjali.

Hence, Jyoti sits opposite to Ramki.

Names: Jyoti, Vipul, Disha, Ramki, Ralston, Abha, Kiran and Anjali

1. Disha sits two places away to the right of Ramki. (Two places away mean one person in between).

2. Only one person sits between Ramki and Abha.

3. Anjali does not sit adjacent to Ramki.

4. Vipul does not sit adjacent to Ramki.

5. Vipul sits exactly between Ramki and Disha.

Note: exactly between doesn't mean persons should be the neighbors. Count from the left of Ramki and right of Disha.

B exactly between A and C means the number of persons between A and B is equal to the number of persons between B and C

6. Ralston sits exactly between Vipul and Kiran.

7. Ralston sits opposite to Anjali.

Thus, Kiran and Vipul is the correct answer.

• Filament of an electric bulb is generally made of Tungsten.
• These bulbs create light by passing a current through a tungsten filament to heat it to 2700⁰ C.
• The inert gas filled in the bulb prevents the filament from oxidizing and evaporating.
• Argon is filled in electric bulbs 

Given, a + b + c = 8, a2 + b2 + c2 = 30 and a3 + b3 + c3 = 134

∵ (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)

⇒ 8² = 30 + 2(ab + bc + ca)

⇒ 2(ab + bc + ca) = 64 - 30

⇒ (ab + bc + ca) = 34/2 = 17

We know that, 

∵ a³ + b³ + c³ – 3abc = (a + b + c) (a² + b² + c² – (ab + bc + ca))

⇒ 134 – 3abc = 8 × (30 – 17) = 104

⇒ 3abc = 134 - 104 = 30

⇒ abc = 30/3 = 10

∴ (abc)^-1 = 1/10

• The force acting between two electric charges is related to Coulomb's law.
• Coulomb's law states that the electrostatic force of repulsion or attraction between two point charges is directly proportional to the product of charges.
• Ampere's law-  The magnetic field created by an electric current is proportional to the size of that electric current with a constant of proportionality equal to the permeability of free space.
• Faraday's laws-

         1. Emf is induced whenever a conductor is rotated in the magnetic field.
         2. The induced emf equals the rate of change of flux

• Ohm's law- The direct current flowing in a conductor is directly proportional to the potential difference between its ends.

Initial income = Rs. 45000

Initial Expenditure = Rs. 33000

Savings = Rs. 45000 - Rs. 33000 = Rs. 12000

New Income = 45000 + 22% of 45000 = Rs. 54900

New Expenditure = 33000 + 11% of 33000 = Rs. 36630

New savings = 18270

∴ Percentage increase in savings = [(18270 - 12000)/12000] × 100 = 52.25%

Let the rate of upstream be x kmph and rate of downstream be y kmph

Adding eq (1) and eq(2), we get

⇒ 52(1/x + 1/y) = 33/2

Subtracting eq (1) from eq(2), we get

⇒ 12(1/x – 1/y) = 1/2

Adding eq (3) and eq (4), we get

⇒ 2/x = 14/39

⇒ x = 5.57 kmph

⇒ Substitute x in eq (3), we get

⇒ 1/(5.57) – 1/y = 1/24

⇒ y = 7.25 kmph

Upstreamrate is 5.57 kmph and rate downstream is 7.25 kmph

∴ Rate of current =  = 0.84 kmph

In the figure, H is the height of the other tree.

In triangle AEB, AB = 200/tan45°

⇒ AB = 200 mtr

⇒ BC = 400 - 200 = 200 mtr

In triangle DCB, tan 60° = H/BC

⇒ H = 200√3 mtr

∴ Height (in metres) of the other tree = 200√3 mtr

• The mirage is formed because of Total Internal Reflection and refraction. It is a naturally occurring optical illusion in which light rays bend to produce a displaced image of distant objects or the sky.
• Refraction-  the change in direction of a wave passing from one medium to another or from a gradual change in the medium
• Dispersion- the separation of white light into colors or of any radiation according to the wavelength

Let, marked price = Rs. x

Discount = 40%

∴ Cost price = x - x × 40/100 = Rs. 0.6x

Profit = 40%

∴ Selling price,

⇒ 0.6x + 0.6x × 40/100

⇒ 0.84x

∴ Required Ratio,

⇒x ∶ 0.84x

⇒ 100 ∶ 84

⇒ 25 ∶ 21

• Carolina Marin won the BWF World Championship 2018 women’s singles title.
• She belongs to Spain.
• After being defeated in the finals, P.V. Sindhu settled with the silver medal.
• In the Men's Singles, Kento Momota of Japan defeated Shi Yuqi of China to win the gold medal.
• The championship was held in China.

Let his average before the 21^st match be x and average after the 21^st match will be x + 2

His total runs before the 21^st match can be given as 20x.

From the problem statement

⇒ x + 2 = (87 + 20x)/21

⇒ x = 45

∴ His average before the 21^st match is 45.

• Combines dance, music, dialogue, costume, make-up, and stage techniques with a unique style and form. This theatre style is mainly found in all parts of Karnataka.
• Yakshagana is traditionally presented from dusk to dawn.

Perimeter of the circle = Perimeter of the rectangle

Perimeter of the circle = 2 × (length + breadth)

Perimeter of the circle = 2 × (18 + 34) = 104 cm

2πr = 104

r = 16.5 cm

Area of the circle = π × r² = π × 16.5² = 856 cm²

∴ The area of the circle is 856 sq.cm

There are five types of Writs -Habeas Corpus, Mandamus, Prohibition, Certiorari and Quo warranto. The writ of prohibition is meant to direct a subordinate to stop doing something that the law prohibits. It is issued by a higher court to a lower court.

We know that if α and β are roots of a quadratic equation then the quadratic equation is of the form

x² – (α + β) x + αβ = 0

So in the question, α + β = 3 and αβ = 2

Sum of the reciprocals of roots =  

Pampas grasslands are fertile South American lowlands, covering more than 750, 000 km2 that include the Argentine provinces of Buenos Aires, La Pampa, Santa Fe, most of Uruguay; and the southernmost BrazilianState, Rio Grande do Sul.

The given information can be represented as follows,

Thus Rupam is the daughter of Pariksha.

• A True Fish is one which goes by the strict definition of a fish having gills for respiration, fins and tail for propulsion and inner skeletal system of bones.
• Dogfish is the true fish.

• Russian author Leo Tolstoy is the author of the novel “War and Peace”.
• It is regarded as one of his finest works and is also a major work in the field of literature.