SSC CPO Tier- I Previous Year Paper (Held On: 12 December 2019 Shift 2)

The given figure is embedded in,

Hence, option 1 is the correct answer.

The paper when unfolded looks like,

Hence, option 3 is the correct answer.

Arranging them in a clockwise manner starting from north on India’s Map,

Ladakh comes first in the order.

It is followed by Odisha.

Odisha is followed by Puducherry.

Puducherry is followed by Goa.

Goa is followed by Punjab.

The correct order is,

Ladakh (1) → Odisha (5) → Puducherry (3) → Goa (2) → Punjab (4)

Hence, option 3 is the correct answer.

NIZAM , MAINS and SAINT have two vowels in them, which are ‘A’ and ‘I’.

Whereas,

In STEIN, the two vowels are ‘E’ and ‘I’.

Hence, “STEIN” is the odd one.

According to the given information, codes for different letters are,

ABUNDANCE → GRATIGTUD

Hence, “GRATIGTUD” is the correct answer.

The number of straight line in the given figure are,

Hence, “17” is the correct answer.

The pattern followed here is,

Number of alphabets in word REASON = 6 → 6 × 2 + 1 = 13

Number of alphabets in word CHAIR = 5 → 5 × 2 + 1 = 11

Similarly,

Number of alpahbets in word EXAMINATION = 11 → 11 × 2 + 1 = 23

Hence, 23 is the correct answer.

Authentic, Genuine and Bona fide are synonyms which mean real.

Whereas,

Spurious  mean something which is fake.

Authentic, Genuine and Bona fide are synonyms and spurious is the antonym to these words.

Hence, “spurious” is the odd one.

Drawing diagram according to the given information,

He is facing West now.

Hence, “west” is the correct answer.

The pattern followed is,

(1^st term × 3^rd term ) + 4^th term = 2^nd term

For Column 1:

(6 × 7) + 55 = 97

42 + 55 = 97

And,

For Column 2:

(9 × 7) + 10 = 73

63 + 10 = 73

Similarly,

For Column 3:

(8 × 2) + 48 = 64

16 + 48 = 64

Hence, “2” is the correct number.

The pattern followed is,

The place value of M is 13 → 1 + 3 = 4

The place value of O is 15 → 1 + 5 = 6

The place value of U is 21 → 2 + 1 = 3

The place value of N is 14 → 1 + 4 = 5

The place value of T is 20 → 2 + 0 = 2

The place value of A is 1 → 1

The place value of I is 9 → 9

The place value of N is 14 → 1 + 4 = 5

So,

MOUNTAIN is written as ‘46352195’.

Similarly,

For UNIVERSE,

The place value of U is 21 → 2 + 1 = 3

The place value of N is 14 → 1 + 4 = 5

The place value of I is 9 → 9

The place value of V is 22 → 2 + 2 = 4

The place value of E is 5 → 5

The place value of R is 18 → 1 + 8 = 9

The place value of S is 19 → 1 + 9 = 10 = 1 + 0 = 1

The place value of E is 5 → 5

So,

UNIVERSE is written as ‘35945915’.

Hence, “35945915” is the correct answer.

The given figure is embedded in,

Hence, option 3 is the correct answer.

The pattern followed is,

O is moving in anti-clock wise direction by two positions in each step.

U is moving in clock wise direction by two positions in each step.

I is  moving in clock wise direction, +1 in first step, +2 in second step, +3 in third step.

e is moving in anti clock wise direction, 3 positions in each step.

Hence, option 1 is the correct answer.

Replacing the signs and using BODMAS rule,

Option 1 → × , −, ÷, + , =

1/6 × 1/24 – 2 ÷ 8 + 35 = 23

1/6 × 1/24 – 4 + 35 = 23

1 / 144 – 4 + 35 is not equal to 23

Option 2 → × , + , ÷, −, =

1/6 × 1/24 + 2 ÷ 8 – 35 = 23

1/ 6 × 1/ 24 + 1/ 4 – 35 = 23

1/ 144 + 1/ 4 – 35 = 23

37/ 144 – 35 is not equal to 23

Option 3 → + , −, ÷, × , =

1/6 + 1/24 – 2 ÷ 8 × 35 = 23

1/ 6 + 1/ 24 – 1/ 4 × 35 = 23

5 / 24 – 1/ 4 × 35 is not equal to 23

Option 4 → ÷, −, × , + , =

1/6 ÷ 1/24 – 2 × 8 + 35 = 23

4 – 2 × 8 + 35 = 23

4 – 16 + 35 = 23

39 – 16 = 23

23 = 23

Hence, option 4 is the correct answer.

The exact mirror image of the given figure when the mirror is held at the right side is,

Hence, option 4 is the correct answer.

Daemon comes first in the order.

It is followed by Dearth.

Dearth is followed by Demand.

Demand is followed by Dementia.

Dementia is followed by Demon.

The correct dictionary order is,

Daemon (5) → Dearth (3) → Demand (2) → Dementia (1) → Demon (4)

Hence, option 1 is the correct answer.

The exact mirror image of the given figure when the mirror is held at the right side,

Hence, option 2 is the correct answer.

The pattern followed is,

The symbols ‘ + ’ and ‘O’ are rotating anti – clockwise.

‘ + ’ is moving two places and ‘O’ is moving by one place anti – clockwise.

The image which will come next in the series is,

Hence, option 1 is the correct answer.

Women can be officers and stenographers.

The correct Venn diagram representation is,

Hence, option 1 is the correct answer.

Publisher is the one who publishes books or magazines.

Publications are periodical.

Periodical publications can be weekly or monthly.

The correct Venn diagram representation is,

Hence, option 2 is the correct answer.

Arranging the words in a meaningful order,

Option 1 → BARLEY

Option 2 → WHEAT

Option 3 → MAIZE

Option 4 → CASHEW

Wheat, Barley and Maize are grains.

Whereas,

Cashew is a nut.

Hence, “Cashew” is the different one.

The pattern followed is,

The symbols in the given image keeps on increasing by one.

Number of circles keeps on increasing by one, with square being constant.

The image which will come next in the series is,

Hence, option 4 is the correct answer.

According to the given diagram,

The shaded part represents people who have been called for the final interview = 7

Hence, “7” is the correct answer.

Conclusion 1: This does not follow, since it is given that that the importance of a person is not dependent only on one’s status and money, but not to acquire more money.

Conclusion 2: This follows because, it is given that there are other factors apart from status and money.

Hence, “only conclusion 2” follow.

According to the given figures,

‘5’ is opposite to ‘2’.

‘6’ is opposite to ‘1’.

And,

‘4’ is opposite to ‘3’.

‘3’ must be at the bottom face when the dice is in the position as shown in figure (a).

Hence, “3” is the correct answer.

By decoding given information,

50 - 10 + 25 ÷ 5 × 3 = ?

Using BODMAS rule,

50 – 10 + 5 × 3 = ?

50 – 10 + 15 = ?

65 – 10 = 55

Hence, “55” is the correct answer.

The pattern followed is,

72 : 14

7 × 2 = 14

Similarly,

Option 1 → 36 : 19 → 3 × 6 = 18, not 19

Option 2 → 92 : 17 → 9 × 2 = 18, not 17

Option 3 → 45 : 20 → 4 × 5 = 20

Option 4 → 81 : 80 → 8 × 1 = 8, not 80

’45: 20’ share the same relationship as that shared the given pair of numbers.

Hence, “45 : 20” is the correct answer.

Drawing the Venn diagram,

Conclusion 1: All purses are pink → True (This is definitely true)

Conclusion 2: All pink are coins → False (Possible but not definite)

Conclusion 3: All rupees are purses → False (Possible but not definite)

Conclusion 4: All coins are pink → True (This is definitely true)

Hence, “only conclusion 1 and conclusion 4” follow.

The pattern followed is,

Hence, “55” is the correct answer.

The pattern followed here is,

Hence, “43” is the correct answer.

Logic: On adding the numbers, all options give one even number and one odd number, except "73 – 79".

The pattern followed is,

Option (1): 73 – 79, 

7 + 3 = 10 (Even number), 7 + 9 = 16(Even number)

Option (2): 31 – 41,

3 + 1 = 4(Even number), 4 + 1 = 5(Odd number)

Option (3): 61 – 71,

6 + 1 = 7(Odd number), 7 + 1 = 8(Even number)

Option (4): 83 – 97,

8 + 3 = 11(Odd number), 9 + 7 = 16(Even number)

Hence, the correct answer is "73 - 79".

Crocodile and snake both are reptiles.

Similarly,

Iguana and Chameleon, both are lizards.

‘Chameleon’ is similar to the given words and hence belongs to the same group.

Hence, “Chameleon” is the correct answer.

The pattern followed is,

Similarly,

‘WAGER’ is related to the third term in the same way as the second term is related to the first term.

Hence, “WAGER” is the correct answer.

The pattern followed is,

The numbers in the brackets should be ‘63’ and ‘342’.

Both the numbers are incorrect.

Hence, option 3 is the correct answer.

Gallop is the fastest pace of a horse.

Similarly,

Scamper is to run quickly in a hurry, which mouse do generally.

‘Scamper : Mouse’ share the same relationship as that shared by the given pair of words.

Hence, “scamper : mouse” is the correct answer.

Stable is a place where livestock are kept, especially horses.

Den is a place where wild animals are kept.

And,

Igloo is a place of shelter, which is made of snow, typically called as a snow house or a snow hut.

Whereas,

Court is a body of people presided by a judge or judges and acts as a tribunal in civil and criminal cases.

Stable, Den and Igloo are similar and Court is different.

Hence, “court” is the odd one.

The pattern followed is,

(90, 450, 810)

90 × 5 = 450

90 × 9 = 810

Similarly,

Option 1 → (5, 25, 45)

5 × 5 = 25

5 × 9 = 45

Option 2 → (21, 105, 189)

21 × 5 = 105

21 × 9 = 189

Option 3 → (7, 35, 56)

7 × 5 = 35

7 × 9 = 63, not 56

Option 4 → (17, 85, 153)

17 × 5 = 85

17 × 9 = 153

All follow the same pattern, except ‘(7, 35, 56)’.

Hence, “(7, 35, 56)” is the correct answer.

Prime number: A number that is divisible by ‘1’ and itself.

197, 193 and 191 are prime numbers.

Whereas,

195 is not a prime number.

Hence, “195” is a different number.

Watt is the SI unit of Power.

Similarly,

Pascal is the SI unit of pressure.

‘Pascal’ is related to the third word in the same way as the second word is related to the first word.

Hence, “Pascal” is the correct answer.

The pattern followed is,

Similarly,

PERCEIVE is written as ‘UHSCEHYL’.

Hence, “UHSCEHYL” is the correct answer.

Given:

Option 1 → 2 + 8 ÷ 4 = 2

After Interchanging operators ‘+’ and ‘÷’ and numbers ‘2’ and ‘8,

⇒ 8 ÷ 2 + 4 = 8

⇒ 4 + 4 = 8

⇒ 8 = 8

Option 2 → 8 + 4 ÷ 2 = 8

After Interchanging operators ‘+’ and ‘÷’ and numbers ‘2’ and ‘8,

⇒ 2 + 8 ÷ 4 = 2

⇒ 2 + 2 = 2

⇒ 4 ≠ 2.

Option 3 → 8 + 2 ÷ 4 = 6

After Interchanging operators ‘+’ and ‘÷’ and numbers ‘2’ and ‘8,

⇒ 2 ÷ 8 + 4 = 6

⇒ 0.25 + 4 = 6

⇒ 4.25 ≠ 6

Option 4 → 4 + 8 ÷ 2 = 4

After Interchanging operators ‘+’ and ‘÷’ and numbers ‘2’ and ‘8,

⇒ 4 ÷ 2 + 8 = 4

⇒ 2 + 8 = 4

⇒ 10 ≠ 4

Hence, the correct answer is "Option 1".

The pattern followed is,

For,

14 : 289

14 + 3 = 17

17² = 289

So,

14 : 289

And,

17 : 400

17 + 3 = 20

20² = 400

So,

17 : 400

Similarly,

21 : ?

21 + 3 = 24

24² = 576

So,

24 : 576

‘576’ is related to the fifth number in the same way as the second number is related to the first number and the fourth number is related to the third number.

Hence, “576” is the correct answer.

The pattern followed is,

Option 1 : 34 – 289 → 17 × 2 – 17²

Option 2 : 18 – 81 → 9 × 2 – 9²

Option 3 : 16 – 64→ 8 × 2 – 8²

Option 4 : 26 – 168 → 13 × 2 – (13² – 1)

All follow the same pattern, except ’26 – 168’.

Hence, “26 – 168’ is different.

The pattern followed is,

Option 1 → 13: 182 → 13 : 13² + 13

Option 2 → 25 : 650 → 25 : 25² + 25

Option 3 → 23 : 552 → 23 : 23² + 23

Option 4 → 18 : 306 → 18 : 18² – 18

All follow the same pattern, except ’18 : 306’.

Hence, “18 : 306” is different.

The pattern followed is,

6/ 34 : 8/62

6/ (6² – 2) : 8/ (8² – 2)

Similarly,

11/ 119: 13/ 167

11/ (11² – 2) : 13/ (13² – 2)

‘13/ 167’ is related to the third term in the same way as the second term is related to the first term.

Hence, “13/ 167” is the correct answer.

Joy is the synonym for Pleasure.

Similarly,

‘Industrious’ is the synonym for Diligent.

Hence, “Industrious” is the correct answer.

The pattern followed is,

Similarly,

‘TGUZNIL’ is related to the third term in the same way as the second term is related to the first term.

Hence, “TGUZNIL” is the correct answer.

The pattern followed is,

Hence, “NAP” is the correct answer.

The pattern followed is,

Hence, “F” is the correct answer.

Arranging them according to the given information,

Sapna is at the extreme end and her immediate neighbour is Megan.

Case 1:

Case 2:

Jenny is on the right of Megan.

Here, case 2 is eliminated.

Bhavna has Megan and Farhad on each side. Alka is to the immediate right of Jenny who is sitting third from the south end.

Case 1:

Jenny is sitting between Farhad and Alka.

Hence, “Farhad and Alka” is the correct answer.

Irwin's pact was done between Gandhi and Viceroy Irwin in 1931.

• Irwin Pact, 1931 had the following provisions-
• Removal of the salt tax.
• Return of all lands that were not yet sold to any third parties.
• Immediate release of all the political prisoners who were not convicted of violence.
• Indian National Congress would stop the civil disobedience movement.

CONCEPT:

• A satellite is an object that has been placed into the orbit. This is also known as artificial satellite.
• There are natural satellite also. eg. Moon
• The force of elasticity occurs as a deformed object (think spring) tries to return to its original shape. The force always acts in a direction that will return it to its original shape.
• Friction is the force which resist the relative motion between solid surfaces, fluid layers, etc. sliding against each other.
• Gravity is an universal force that acts over large distances between any two masses.
• Due to Gravity a planet or other body draws objects toward its center.

EXPLANATION:

• Satellites orbits around the planet because they have enough speed that is fast enough to defeat the downward pull of gravity.

• A satellite revolves in its orbit and balance two factors: its velocity (the speed it takes to travel in a straight line) and the gravity force that Earth has on it.
• So The correct answer is option 1 i.e**. gravity.**

• Due to no loss in energy of satellite while orbiting, fuel is not used for energy to the satellite. While fuel is required in the form of kinetic energy or speed of the satellite to put it in an orbit around the planet.

In 1948 the first Industrial Policy was presented in the parliament by then Industry Minister Dr. Shyama Prasad Mukherjee.

• The policy properly has a demarcation between the areas of operation vis-a-vis the private and public sectors in the country.
• Indian economy is called a mixed economy.
• When a system combines aspects of both capitalism and socialism it is called a mixed economy.

• Hiccups in humans generally occur due to the forceful downward shifting of the diaphragm.
• The diaphragm is located below the lungs and heart.
• The trachea is also called as the windpipe which connects the larynx  to the bronchi of the lungs.
• Larynx functions as the voice box.

Researchers from India and the United Kingdom have developed a hand-washing robot named Pepe.

• The robot was created to encourage children to wash their hands.
• The project comes under the ‘social robot’ research project.
• The project is the second ‘social robot’ research project conducted by the University of Glasgow and Amrita University.
• In 2018 they introduced a four-wheeled robot to help residents of Ayyampathy in southern India carry 20-liter bottles of water from a local well to their homes.
• According to the World Health Organization, hand-washing can help protect from diarrhea, cholera, and other such sanitary diseases.
• The government has recently launched the WASH scheme for the measures in lines with sanitation and hygiene.

According to the Demographic Transition Theory, the third stage in a demographic cycle is marked by low fertility low mortality

• Demographic transition theory is used to predict the future population of any area. The population of any region changes from high births and high deaths to lower births and lower deaths.
• The first stage has a high mortality and high fertility rate.
• Fertility remains high at the beginning of the second stage but then it starts to decline. This leads to a reduced mortality rate.
• In the last stage, which is the third stage in the cycle, both fertility and mortality decline considerably.

Jamuna Boro does not hold the distinction of reaching the final at the World Boxing Championships in her debut. She won a bronze in the 2019 Women’s boxing championship.

• Boxer Manju Rani entered the final of Women World Boxing Championships to become the first Indian in 18 years to do so in his/her maiden appearance at the event.
• Sonia Chahal into the final of the Women’s National Boxing Championships in 2019.
• Samjetsabam Sarjubala Devi won a silver at the Women's World Boxing Championship in 2014.

• Sundarbans is the largest protected wetland in India.
• There are a total of 75 wetlands in India.
• Wetlands are the small plant life habitats and species contained inside water sources that not only water bodies, but environments as a whole, bring about ecological health in abundance.
• The world’s first Ramsar Site was the Cobourg Peninsula in Australia.

Rotterdam Convention deals with Prior Informed Consent Procedure for Certain Hazardous Chemicals and Pesticides.

• Stockholm Convention deals with Persistent Organic Pollutants. It is a global treaty that focuses on health protection as well as environmental protection. Adopted on 22nd May 2001 and entered into force on 17th May 2004.
• The Basel Convention deals with the control of transboundary movements of hazardous wastes and their disposal. This convention was adopted on 22 March 1989.
• Nagoya Protocol is an international agreement focussing on shared benefits that arise from the utilization of genetic resources in a fair and equitable manner. Came into effect in October 2014.

• Munda language belongs to the Austro**-Asiatic** languages family.
• The Indo-Aryan languages are a major language family of South Asia.
• There are around 200 known Indo-Aryan languages.
• Sanskrit is one of the oldest Indo-Aryan classical literary languages.

• Rafael Nadal won the 2019 US Open - Men's Singles title defeating Daniil Medvedev.
• The US Open is played on DecoTurf which is a Hard court.
• Rafael Nadal belongs to Spain.
• Daniil Medvedev belongs to Russia.

The correct answer is Manganese

• Pyrolusite is an ore of Manganese.
• Pyrolusite consists of Manganese dioxide.
• Pyrolusite is used for the manufacture of steel and in dry cells.
• Bauxite and Cryolite are the ores of aluminium.
• Galena (PbS) is the ore of Lead. It is also an important source of Silver.

Concept:

• In a uniform circular motion, a body is experiencing a force in the inward direction

• Acceleration of the body is non-zero and has magnitude v2/r
• For a uniform circular motion, Speed of object remains constant.
• Whereas the velocity keeps on changing because the direction of velocity is changing continuously and it is perpendicular to radius of the circle.
• Distance:

• The length of the actual path covered by a moving object in a given time.
• It is a scalar quantity.
• It is always positive.
• The unit of distance is a meter (m).
• Displacement:

• It is the shortest distance covered by a body in a definite direction.
• It is a vector quantity.
• It can be positive, Negative or Zero.

Explanation:

• As explained above the distance is not always equal to the displacement in a uniform circular motion.
• In a uniform circular motion, an object moves along a circular path with uniform speed.
• Due to a circular path travelled the distance will be greater than zero but the displacement can or cannot be zero.
• The displacement is In UCM is called as angular displacement.
• Velocity is always perpendicular to the radius.

• Magnetic fields of the earth deflect most of the solar wind and have no effect on ocean currents.
• Ocean currents have influences of Coriolis force, frictional force, and heating effect of the sun.
• The sun heats water at the surface of the ocean which will evaporate and increase the concentration of salt and water will become dense and settle down hence whose place is taken by less dense water which leads to Ocean currents
• Wind forces also play a major role to influence ocean currents.

The correct answer is Banking.

Key Points

• The Concurrent List includes subjects that give powers to both the Union and state governments to make laws on subjects included in the list.
• The concurrent list includes subjects like Education, population control and family planning, protection of wildlife and animals, forests., criminal law, prevention of cruelty to animals.
• Banking comes under Union List.
• Other subjects in the Union list include defence, foreign affairs, railways.
• The legislative functions of union and states are discussed mainly in Articles 245 to 255 in Part XI of the constitution.

The process of the flow of genetic information from DNA to RNA is called Transcription.

• Enzymes called RNA polymerases performs transcription.
• Transcription is done mainly in three stages i.e. initiation, elongation, and termination.
• It is controlled separately for each gene in the genome.

The power to summon both the Houses of Parliament i.e. Rajya Sabha and Lok Sabha is vested with the President of India under Article 85(1) of the Indian Constitution.

• Article 85(1) empowers the President to summon each House of Parliament to meet at such time and place as he thinks fit.
• Budget, Monsoon, and Winter Sessions, are held in a calendar year.
• The President may also, from time to time
• Prorogue the houses
• dissolve the house of the people.
• Vice President is the Chairman of the Council of States/Rajya Sabha.

• The term 'wali' in sufi terminology means Saint.
• The Sufi doctrine was based on union with God.
• It was organised in different Silsilas (orders).
• Sufi doctrine was eager for Hindu-Muslim unity and cultural synthesis.

• The Aitchison Commission was appointed to make recommendations on Indian Civil services.
• Lord Dufferin appointed a "Public Service Commission"  which was known as the Aitchison Commission under Sir Charles Aitchison.
• The Aitchison Commission of 1886 was chaired by Sir Charles Aitchison.
• Lord Dufferin served as the Viceroy of India from 1884 to 1888.

• Archaeologists have recovered burial of five wild dogs and antler's horn at Burzahom.
• The Burzahom site is located in the Kashmir Valley.
• Utnur is known for the neolithic excavations.
• The Archaeological Survey of India was founded in 1861.

'Turi', 'Bungal' and 'Pava' are folk musical instruments from the state of Gujarat.

• The wind instruments like Turi, Bungal, Pava and string instruments like Ravan Hattho, Ektaro, and Jantar, and percussion instruments like Manjira and Zanz pot drum are omnipresent in the folk sounds of Gujarat.
• Gujarati folk music, known as Sugam Sangeet, is a hereditary profession of the Barot, Gadhvi and Charan communities.

The Purusharthas or the four aims of life are Dharma, Artha, Kama, and moksh.

• Dharma means duty or ethics, Artha is prosperity and wealth, Kama means pleasure or sensual gratification, Moksha is the pursuit of liberation.
• The pursharthas are the blueprint for the human fulfillment.

Pteridophytes reproduce with the help of spores.

• Pteridophytes don't produce flowers and seeds hence they reproduce using spores.
• Pteridophytes are also known as cryptogams.
• Ferns and Azolla are some examples of Pteridophytes.

Lakshya sen is a badminton player.

• The highest-ranking of Lakshya Sen till now is 28.
• He won the SaarLorLux Open in Saarbrücken, Germany.
• In 2019, he claimed his fourth title in Scottish Open.

CONCEPT:

• Displacement (X): The change in the position of an object is called displacement.
• Displacement is a one-dimensional quantity representing the smallest separation between two defined points.
• The standard unit of displacement in the International System of Units (SI) is the meter (m).
• Velocity (V): The rate of change of displacement is called velocity. It is a vector quantity. 
• The SI unit of velocity is called m/s and the CGS unit is cm/s.
• The slope of the displacement-time graph gives the velocity.

$Instantaneous;velocity;\left( V \right) = \frac{{dx}}{{dt}}$

$V = \frac{{dx}}{{dt}}$

Hence dx = V dt 

\(Displacement;\left( X \right) = \mathop \smallint \nolimits_{{x_1}}^{{x_2}} dx = \mathop \smallint \nolimits_{{t_1}}^{{t_2}} V;dt\)

• Thus the area under the velocity-time graph gives the displacement. Similarly, the area under-speed time graph gives the total distance travelled.

EXPLANATION:

• The area under a velocity-time graph is a representation of the displacement. So option 2 is correct.
• The rate of change of distance is called speed.
• The rate of change in velocity is called acceleration.

• The skull of a 'Homo erectus' was found at Hathnora near the banks of the Narmada river.
• Hathnora is in Madhya Pradesh.
• The fossil which is also known as Narmada Fossil brought India on Fossil Map of the world.
• Homo erectus was the species of humans from the Pleistocene period.

The Ninth Schedule was added to the Constitution by the First Amendment Act, 1951.

• Ninth Schedule of the Indian Constitution pertains to protect the state laws pertaining to land reforms from being challenged in the Judiciary.
• However, Judicial review was made a part of the Basic Structure of the Constitution after the Keshavananda Bharti Case.
• Further, the Coehlo case made a judgement where subjects from the ninth schedule couldn't be kept immune from judicial review.
• The eighth schedule contains provisions related to Scheduled Languages.
• The tenth Schedule contains provisions related to Anti defection Law.
• The seventh schedule contains the allocation of powers between the Union and States.

D. Gukesh became the youngest Indian Grandmaster at the age of 12 years and 7 months, 14 days.

• He became 2nd youngest Grandmaster in the world after Sergey Karjakin.
• D. Gukesh hails from Chennai, Tamil Nadu.
• Serjey Karjakin belongs to Russia.

Carbon tax can be classified as a Pigouvian tax.

• A Pigouvian tax can be defined as tax which is assessed against the private individuals or businesses for engaging in the activities that can create adverse side effects for the society.
• Its popular example is a tax on pollution. Pollution from an industrial plant can create a negative side effect.
• Pigouvian taxes were named after economist, Arthur Pigou.
• Long term capital gain tax is a tax levied on the sale of an asset that generates profit in the long term.
• Income Tax is levied on the income of an individual.

Hydrogen with atomic number 1 and atomic mass 1 comes first in the periodic table of elements.

• It is the lightest element in the periodic table.
• The last element in the periodic table is Ununoctium.
• The modern periodic table was made by Dimitri Mendeleev.
• It contains 118 elements.
• Oganesson is the heaviest element in the periodic table.

• The national 'total fertility rate' is expected to be below replacement rate by the year 2021.
• The states of Kerala, Tamil Nadu, Karnataka, Andhra Pradesh, Telangana, Maharashtra, West Bengal, Punjab and Himachal Pradesh have fertility rates well below the replacement rate.
• States like Bihar, Uttar Pradesh, Jharkhand, Chhattisgarh, Rajasthan and Madhya Pradesh is above replacement rate but it is declining.
• Replacement rate is the percentage of a person's annual employment income that is replaced by retirement income when the person retire.

• K.Siva Reddy composed the collection of poems titled 'Pakkaki Ottigilite'.
• K.Siva Reddy won the Saraswati Samman of 2018 for Pakkaki Ottigilite.
• K.Siva Reddy is a Telugu poet.
• Saraswati Samman Award is given by the KK Birla Foundation.

For the calculation of the 'wholesale price index' in 2019, 2011-2012 is taken as the base year.

• The Wholesale price index measures the changes in the prices of the goods sold and trade in the bulk or at the wholesale level. It is different from the “consumer price index” which tracks the prices at the consumer level.
• The numbers are released by the Office of Economic advisor in the ministry of commerce and industry.
• The official Wholesale Price Index for 'All Commodities' (Base: 2011-12=100) for the month of February 2020 declined by 0.6% to 122.2 (provisional) from 122.9 (provisional) for the previous month.

According to the United Nations, for a city to qualify as a Megacity it needs to have a minimum population of 10 million people.

• The UN takes into account urban sprawl and measure populations beyond official city limits.
• India has currently five megacities – New Delhi, Mumbai, Chennai, Bangalore, and Kolkata.
• China has the most urban agglomerations.
• Largest is the city of Tokyo, Jakarta, and Shanghai.

• Adam Harper was awarded the SASTRA Ramanujan Prize, 2019.
• Adam Harper is a  mathematician and an Assistant Professor at the University of Warwick, England.
• SASTRA stands for Shanmugha Arts, Science, Technology & Research Academy (SASTRA).
• The award was instituted in 2005 by Shanmugha Arts, Science, Technology & Research Academy located near Kumbakonam, India.

• Balban traced his descent to the ancient warrior Afrasiyab in order to fabricate a noble birth for himself.
• Balban belonged to Salve Dynasty.
• He introduced the practice of paibos and sajda.
• He established the military department Diwan-i-Arz.

Doreen Lawrence is not a recipient of the '2019 Right Livelihood Award'. She is a social campaigner based in London, England.

• Aminatou Haidar for his actions for self-determination of the people of Western Sahara.
• Guo Jianmei won for her work in securing women's rights in China.
• Greta Thunberg for her inspiring political demands for action on climate change.
• The Right Livelihood Award was established in 1980 to “honor and support courageous people solving global problems”.
• It has become widely known as the 'Alternative Nobel Prize' and there are now 178 Laureates from 70 countries.

CONCEPT:

Nuclear reactor:

• It is a device in which a nuclear reaction is initiated, maintained, and controlled.
• It works on the principle of controlled chain reaction and provides energy at a constant rate.

EXPLANATION:

• The function of the moderator and coolant in the Canada Deuterium Uranium (CANDU) reactor is performed by heavy water
• The moderator's function is to slow down the fast-moving secondary neutrons produced during the fission. T
• The material of the moderator should be light and it should not absorb neutrons.
• Usually, heavy water, graphite, deuterium, and paraffin, etc. can act as moderators.
• The heat released by fission in nuclear reactors must be captured and transferred for use in electricity generation.
• To this end, reactors use coolants that remove heat from the core where the fuel is processed and carry it to electrical generators.
• Coolants also serve to maintain manageable pressures within the core.

The Netravati River flows through Mangaluru. The river has its origins at Gangamoola and flows through the Mangalore city after which it joins the Kumaradhara River and flows into the Arabian Sea.

• The river flows through the Dharamsthala which is a famous pilgrimage.
• The origin of the river lies in the Western Ghats in Banagrabalike forest valley in the Karnataka state.
• Netravati River is also known as the Bantwal River.

• Natarajan Chandrasekaran co-authored the book titled 'Bridgital Nation: Solving Technology’s People Problem'.
• Natarajan Chandrasekaran is chairman of the Board of Tata Sons.
• Nandan Nilekani is the co-founder of Infosys.
• Sundar Pichai is the CEO of ‎Google‎ and ‎Alphabet.

• The Bill and Melinda Gates Foundation confers the Global Goalkeepers Award.
• Bill Gates is the founder of The Microsoft Corporation.
• Prime Minister Narendra Modi received the 2019 ‘Global Goalkeeper Award’
• PM Narendra Modi was awarded this award for his leadership of Swachh Bharat Abhiyaan.

The Fundamental Rights have been described in Articles 12-35, Part III of the Indian Constitution.

• Right to Life and Personal Liberty is a right enshrined in Article 21 of the Indian Constitution.
• This right cannot be curtailed even during the National Emergency (Article 359).
• Other rights within the ambit of Article 21 includes the recently upheld Right to Privacy by the Supreme Court in the Puttuswamy Case.
• Prohibition of traffic in human beings is enshrined in Article 23 of the Indian Constitution.
• Right to education is enshrined in Article 21A which was a result of the 86th Amendment 2002 of the Indian Constitution.
• It provides for free and compulsory education until the age of 14 for all children.
• Prohibition of employment of any child below fourteen years of age in any factory or mine is enshrined in Article 24 of the Indian Constitution.

• The IRDAI (Insurance Regulatory and Development Authority of India) does not regulate capital markets in India.
• It functions to regulate and promote the insurance industries in India.
• The SEBI (Securities and Exchange Board of India) is the main regulator of capital markets in India.
• It was formed in 1988 and it became a statutory body in 1992.
• Headquarters of SEBI is in ‎Mumbai, Maharashtra.

The Ionosphere is the ionized part of Earth's upper atmosphere, which extends from about 60 km to 1,000 km altitude.

• The ionosphere is a very active part of the atmosphere, and it grows and shrinks depending on the energy it absorbs from the Sun.
• It contains charged particles and is ionized by solar radiation.
• The ionosphere is a region that includes the thermosphere and parts of the mesosphere and exosphere.

Article 61 of the Indian constitution gives the procedure for the impeachment of the President of India.

• According to Article 61, the President can be impeached for the violation of the constitution and in that case charge shall be preferred by either house of the parliament.
• The President can be removed by an absolute majority.
• A resolution for the impeachment of the President can either be accepted or rejected by the speaker/chairman.
• Article 63 deals with Vice-President.
• Article 62 deals with the time of holding an election to fill the vacancy in the office of President.
• Article 60 deals with the oath and affirmation of the President.

Chief Election Commissioner, Shri Sunil Arora assumed Chairmanship of Association of World Election Bodies (A-WEB) in September 2019 for the term 2019-21 as India takes over the Chair from Romania.

• India was unanimously nominated to be the Chair of A-WEB at the last General Assembly held at Bucharest in 2017.
• The Association of World Election Bodies (A-WEB) is the largest association of Election Management Bodies (EMBs) worldwide.
• A-WEB was established on October 14, 2013, in Song-do, South Korea.
• The permanent secretariat of A-WEB is located in Seoul.

The correct answer is Agriculture.

Key Points

• The 'Sitadhyaksha' was the officer in charge of agriculture.
• Akaradhyaksha was the Superintendent of mines.
• Samsthadhyaksha was the  Superintendent of the market.
• With the help of Chanakya (Vishnugupta/ Kautilya), Chandragupta Maurya defeated Dhana Nanda (322 BCE) and founded the Mauryan Dynasty.
• Chanakya encouraged Chandragupta Maurya and his army to take over the throne of Magadha.
• His vast empire included Bihar, Bengal, Deccan (except modern Kerala, Tamilnadu, and parts of Northeast India), Eastern Afghanistan, Baluchistan, and the area west of the Indus river.
• 

Important Points

bindusara

• Chandragupta was succeeded by his son Bindusara.
• Bindusara ruled for approximately 25-26 years and his succession was disputed which ultimately gave India a great king called Asoka.
• Ashoka
• Asoka was the third and the greatest of the Mauryan rulers.
• Ashoka is referred to as Ashokavardhana.
• Kunala
• Kunala was the son of Emperor Ashoka and Queen Padmavati and the presumptive heir to Ashoka.

Additional Information

• With the help of Chanakya (Vishnugupta/ Kautilya), Chandragupta Maurya defeated Dhana Nanda (322 BCE) and founded the Mauryan Dynasty.
• Chanakya encouraged Chandragupta Maurya and his army to take over the throne of Magadha.
• His vast empire included Bihar, Bengal, Deccan (except modern Kerala, Tamilnadu, and parts of Northeast India), Eastern Afghanistan, Baluchistan, and the area west of the Indus river.

The Government of India has granted multiple entry visas for an indefinite period to Overseas Citizens of India (OCI).

• The government of India launched the ‘Overseas Citizenship of India (OCI) Scheme’ by amending the Citizenship Act, 1955 in 2005.
• The Government of India discontinued the Person of Indian Origin (PIO) card and merged it with the OCI card.
• They do not have the Right to Vote.
• An OCI is an immigration status given to a foreign citizen of Indian origin to live and work in India indefinitely.
• Anyone who is applying for OCI card should hold a valid Passport of another country.
• Benefits for OCI cardholders include lifelong Visa to visit India multiple times, but special permission needed for research work in India.
• However, Individuals having parents/grandparents with Pakistani citizenship OR Bangladeshi citizenship cannot apply for OCI.

Kailpodh is the festival of Karnataka.

• It is also known as the festival of weapons and harvest.
• It is celebrated by the Kodava community of Kodagu district, Karnataka.
• This festival is celebrated after Putthari the harvest festival.
• Kail means Armory/weapon and Podh means festivals.
• Kailpodh is celebrated in the month of September and marks the end of the sowing season.

• Ganymede is the largest moon amongst 53 known moons of Jupiter.
• It is 8% larger than the planet Mercury.
• It is the largest natural satellite.
• Jupiter has overall 79 satellites out of which 26 are yet to be named.

Given: 

Two times of A’s salary is five times of B’s salary and four times of B’s salary is twice C’s salary

Calculation∶

According to the question

⇒ 2A = 5B

A : B = 5 : 2     ---(1)

⇒ 4B = 2C

B : C = 2 : 4     ---(2)

From equation (1) and Equation (2)

A : B : C = 5 : 2 : 4

∵ 4 unit = 1600

⇒ 1 unit = 1600/4 = 400

 5 unit = 400 × 5 = 2000

∴ The correct answer is Rs.2000

Shortcut Trick

B’s salary = 2 × 1600/4 = Rs. 800

∴ A’s salary = 5 × 800/2 = Rs. 2,000

Given:

Total spent on sports = 2,40,00,000

Calculation:

Total spent on cricket and football together

⇒ 2,40,00,000 × [(80 + 52)/360]

⇒ 2,40,00,000 × 132/360 = 88,00,000

Given:

The diameter of a cycle wheel is 126 cm. A cyclist takes $16\frac{1}{2}$ minutes to reach the destination at a speed of 72 km/hr.

Formula used:

Circumference of circle = 2πr

Calculation:

Distance covered by Cyclist in 16.5 minutes with speed of 72 km/hr

⇒ 72 × $100000\over60$ × $33\over2$ = 1980000 cm

Distance covered by wheel in 1 revolution = 2πr = 126 × $22\over7$ = 396

Number of revolutions = $1980000\over396$ = 5000

Shortcut Trick

Ratio of two number = 2x : 3x

HCF of 2x and 3x is x.

According to the question, x = 8

So, the larger number = 3 × 8 = 24

Alternate Method

Given:

The HCF of the two numbers = 8

The LCM of the two numbers = 48

The ratio of two numbers = 2x : 3x

Formula used:

Product of both the number = HCF × LCM

Calculation:

According to the question,

2x × 3x = 8 × 48

⇒ x² = (8 × 48) / (2 × 3)

⇒ x² = 4 × 16 

∴ x = √64 = 8

The largest number = 3x

⇒ 3 × 8

⇒ 24 

∴ The largest number is 24.

Given:

Amount after 2 years = Rs 8928

Amount after 3(1/2) years = Rs 10,224

Concept used:

SI = PRT/100

A = P + SI

P → princiapl R → rate of interest T → time

Calculation:

SI for 3/2 years = amount after 3(1/2) years - amount after 2 years =10224 – 8928 = 1296

SI for 3/2 years  = 1296

SI for 2 years = 1296 × (2/3) × 2 = 1728

Principal = 8928 – 1728 = 7200

R= (100 × SI) / (P × T)

R = (100 × 1728) / (7200 × 2) = 12%

∴ The rate of interest is 12%.

Alternate Method

Amount after 2 years = Rs 8928

Amount after 3(1/2) years = Rs 10,224

⇒ A  = P +2 SI  ------------(1)

⇒ A = P + 7/2SI  -------------(2)

⇒ 3/2 SI = 10224 - 8928

⇒ 3/2 SI = 1296

⇒ SI = (1296 × 2)/3

⇒ SI = Rs. 864

Now,putting value of SI in eq(2) we get.

⇒ P = 10224 - 7/2 × 864

⇒ P = 7200

Rate = Interest(1 year)/Principal 

Rate = 864/7200 × 100

= 12

Rate % = 12 %

Given:

A capital usage = 5 months

B capital usage = 7 months

C capital = Rs, 4600

A profit = 1/7

B profit = 1/5

C time = 9 months

Formula used:

Capital × Time = Profit

Calculation:

Let the total profit be 35 unit.

Profit of A = 1/7 × 35 = 5 unit

Profit of B = 1/5 × 35 = 7 unit

Profit of C = 35 – 5 – 7 = 23 unit

Let the capital of A and B are x and y, respectively.

As we know,

Capital × Time = Profit

⇒ 5x : 7y ∶ 4600 × 9 = 5 : 7 : 23

According to the question

⇒ 23 unit = 4600 × 9

⇒ 1 unit = (4600 × 9)/23

⇒ 5 unit = 5x

⇒ [(4600 × 9)/23] × 5 = 5x

⇒ x = [(4600 × 9)/23] × 5/5 = 1800

∴The correct answer is Rs.1800.

Given:

x⁴ + x^-4 = 2599

Calculation:

As we know,

(x² + 1/x²)² = x⁴ + 1/x⁴ + 2

⇒ (x² + 1/x)² = 2599 + 2 = 2601

⇒ (x² + 1/x²) = √2601 = 51

Again, (x – 1/x)² = x² + 1/x² – 2

⇒ (x – 1/x)² = 51 – 2 = 49

⇒ x – x^-1 = √49 = 7

∴ The correct answer is 7.

Ratio of income of Raju and Peter = 3x : 5x

According to the question

(3x + 2500) / (5x + 2500) = 11/15

⇒ 15(3x + 2500) = 11(5x + 2500)

⇒ 45x + 37500 = 55x + 27500

⇒ 55x – 45x = 37500 – 27500

⇒ 10x = 10000

⇒ x = 10000/10 = 1000

∴ Income of Peter = 5 × 1000 = 5000

Short Trick:

5 unit = 2500

1 unit = 500

10 unit = 10 × 500 = 5000

∴ Income of Peter = 5000

Concept used:

Area of Rectangle = length × breadth

Calculation:

Diameter of circle(2r) = 77 cm

Circumference of circle = 2r(π)  = 77 × 22/7 = 242

Given that 142% = 71/50

Let the breadth of the rectangle be 50x.

⇒ Length of the rectangle = 71x

According to the question

Perimeter of the rectangle = 2(l + b)

⇒ 2(l + b) = 242

⇒ 2(71x + 50x) = 242

⇒ 121x = 242/2 = 121

⇒ x = 1

∴ Area of rectangle = 71x × 50x = 71 × 1 × 50 × 1 = 3550 cm²

Given:

Speed of Ranjeet = 50 km/hr

Calculation:

Total distance covered by Ranjeet in 8 hrs = 50 × 8 = 400 km

Speed of Rahman = 400/5 = 80 km/hr

New speed of Ranjeet = 50 + 10 = 60 km/hr

New speed of Rahman = 80 + 20 = 100 km/hr

Time taken by Ranjeet to cover 400 km distance = 400/60 = 6 hr 40 min

Time taken by Rahman to cover 400 km distance = 400/100 = 4 hr

Required difference = 6 hr + 40 min – 4 hr = 2 hours 40 minutes

Let the average of score in 14 innings be x.

Sum of runs in 14 innings = 14x

According to the question,

14x + 92 = (x + 4) × 15

⇒ 14x + 92 = 15x + 60

⇒ 15x – 14x = 92 – 60

⇒ x = 32

So, new average is 32 + 4 = 36

Short Trick:

Average scores of 14 inning is = 92 – 15 × 4 = 92 – 60 = 32

Average scores of 15 innings is = 32 + 4 = 36

√2 sin(60° – α) = 1

sin(60° – α) = 1/√2 = sin45°

60° – α = 45°

∴ α = 60° – 45° = 15°

Given:

Rebate on TV price = 40%

Rebate wanted = Rs. 26,400

Price of each TV = Rs. 6000

Calculation:

Let the total price of all TV sets be Rs x.

According to the question

x × 40/100 = 26400

x = 26400 × 100/40 = 66000

Number of TV sets = 66000/6000 = 11

∴ The correct answer is 11.

Given:

Vaibhav can do a piece of work = 60 days

Number of days Vaibhav works = 15 days

Sandeep alone finish the remaining work = 30 days

Formula used:

Work = Efficiency × Time

Calculation:

Total work = 60

Let efficiency of Sandeep be x, then

15 + 30x = 60

30x = 60 – 15 = 45

x = 45/30 = 1.5

Vaibhav and Sandeep together can complete the whole work in = 60/(1 + 1.5) = 60/2.5 = 24 days

Alternate Method

Suppose Sandeep can complete the whole work in x days. 

According to the question,

15/60 + 30/x = 1

⇒ 30/x = 1 – 1/4

⇒ 30/x = 3/4

⇒ x = 40 days

Vaibhav and Sandeep together can complete the work in 1 day = 1/60 + 1/40

⇒ (2 + 3)/120 = 5/120 = 1/24

∴ Vaibhav and Sandeep together can complete the whole work in 24 days.

Alternate MethodCalculation:

Time taken by Vaibhav to complete the work = (60/15) = 4 days

Number of days Sandeep works = (1 – 1/4) = 3/4 days

Time taken by Sandeep to complete the work = (4/3 × 30) = 40 days

Now,

LCM of 60 and 40 is 120

Efficiency of Vaibhav = (120/60) = 2 units/day

Efficiency of Sandeep = (120/40) = 3 units/day

Time taken by Vaibhav and Sandeep together to complete a work = [120/(2 + 3)]

⇒ 120/5 days

⇒ 24 days

∴ The required days is 24 days.

Given:

OQ = OR = r = 6 cm

OP = 10 cm

Calculation:

In △OQP

(OP)² = (OQ)² + (QP)²

⇒ 10² = 6² + (QP)²

⇒ (QP)² = 100 – 36 = 64

⇒ QP = √64 = 8

Area of △OPQ = 1/2 × Base × Height = (1/2) × 6 × 8 = 24 cm

Area of quadrilateral PQOR = 2 × Area of △OPQ = 2 × 24 = 48 cm

sin θ – cos θ = 0

sin θ = cos θ

So, the value of θ = 45°

⇒ sin⁴θ + cos⁴θ

⇒ sin⁴45 + cos⁴45

⇒ (1/√2)⁴ + (1/√2)⁴

⇒ 1/4 + 1/4 = 1/2

Given:

$\sqrt {0.00576; \times ;y} ; = ;2.4$

Calculation:

$\sqrt {0.00576; \times ;y} ; = ;2.4,$

Squaring both sides

⇒ 0.00576y = 5.76

⇒ y = $5.76\over0.00576$ = 1000

∴ y = 1000

Calculation:

The sum invested in company Q in the year 2000 = 4,00,000

The interest rate in the year 2000 for investors in company Q = 9%

The interest rate in the year 2001 for investors in company P = 6.5%

Amount after 2001 = 4,00,000 × $109\over100$ × $106.5\over100$ = 4,64,340

Calculation:

Expenditure on Hockey = 65

Expenditure on basketball = 50

Expenditure on Hockey is more than that on basketball by

⇒ [(65 – 50)/50] × 100 = 30%

As we know,

∠PAQ = 90° [PQ is a diameter]

∠BAQ = 105° (Given)

⇒ ∠BAP + ∠PAQ = 105°

⇒ ∠BAP = 105° – 90° = 15°

As we know,

∠BAP = ∠AQP = 15°

In △APQ

∠APQ + ∠PAQ + ∠AQP = 180°

⇒ ∠APQ + 90° + 15° = 180°

∴ ∠APQ = 180° – 90° – 15° = 75°

Calculation:

As we know,

Total expenditure = 100%

Expenditure on salary = 20%

20% = 2.8 cores

Difference between the expenditure on advertisements and taxes

⇒ 15% - 10% = 5%

∴ 5% represents = $2.8\over20$ × 5

= 70 lakhs

Calculation:

As we know,

(a – b)² = a² + b² – 2ab

⇒ 5² = 45 - 2ab

⇒ 25 = 45 – 2ab

⇒ 2ab = 45 – 25 = 20

⇒ ab = 20/2 = 10

∴ The correct answer is 10

As we know,

Perimeter of isosceles right triangle is = (2a + √2a)

(2a + √2a) = (16√2 + 16)

√2a(√2 + 1) = 16(√2 + 1)

a = 8√2

∴ Area of triangle = 1/2 × Base × Height = 1/2 × 8√2 × 8√2 = 64

**Calculation:**­­­

The difference of interest rate in 2000 between company P and Company Q

⇒ 9% - 7.5% = 1.5%

⇒ 1.5% of 3,50,000

⇒ 3,50,000 × $1.5\over100$ = 5,250

$\frac{{{{\left( {2.8} \right)}^3}; + ;{{\left( {2.2} \right)}^3}}}{{{{\left( {28} \right)}^2} - 28; \times ;22; + ;484}}$

$\Rightarrow \frac{{\left[ {{{\left( {28} \right)}^3}; + ;{{\left( {22} \right)}^3}} \right]; \times ;{{10}^{ - 3}}}}{{{{\left( {28} \right)}^2} - 28; \times ;22; + ;{{22}^2}}}$

As we know, a³ + b³ = (a + b) (a² – ab + b²)

$\Rightarrow \frac{{\left( {28; + ;22} \right)[{{\left( {28} \right)}^2} - 28; \times ;22; + ;{{22}^2}]; \times ;{{10}^{ - 3}}}}{{{{\left( {28} \right)}^2} - 28; \times ;22; + ;{{22}^2}}}$

⇒ 50 × 10^-3 = 0.05

Short Trick:

Work done by pipe A in 12 min = 4 × 12 = 48

Remaining work = 72 – 48 = 24

Time taken by pipe B = 24/3 = 8 min

So, Pipe should be closed after 8 min.

Detailed solution

Let the Pipe B opened for x min, then

According to the question

12/18 + x/24 = 1

x/24 = 1 – 2/3 = 1/3

x = 8 min

∴ Pipe B is opened for 8 min.

Alternate Method

Let

Total capacity = 72

Total time = 12 min

A efficiency = 4

B efficiency = 3

Let Pipe B opened for x minutes and then closed

So, for the remaining time pipe A was operated alone

∴ (A + B)x + A(12 - x) = 72

⇒ 7x + 4(12 - x) = 72

⇒ 3x = 24

⇒ x = 8 

∴ The correct answer is 8 min.

Given:

a + b + c = 9

ab + bc + ca = 18

Formula used:

a3 + b3 + c3 – 3abc = (a + b + c) [(a + b + c)2 – 3(ab + bc + ca)]

Calculation:

We know that,

a3 + b3 + c3 – 3abc = (a + b + c) [(a + b + c)2 – 3(ab + bc + ca)]

⇒ 9[92 – 3 × 18]

⇒ 9 × 27

⇒ 243

∴ The Required answer is 243.

Given:

Discounts = 10%, 16%, 25%

Formula used:

Discount = [(MP - SP)/MP] × 100

Calculation:

Let the number be 100.

Number after discount = 100 × 90/100 × 84/100 × 75/100 = 56.7

∴ Single equivalent discount = [(100 – 56.7)/100] × 100 = 43.3%

∴ The correct answer is 43.3%.

Shortcut Trick

10% = 1/10, 16% = 4/25 & 25% = 1/4

∴ Required discount = (1000 – 567)/1000 × 100 = 43.3%

Given:

Right circular cylinder

Diameter = 7 cm

Height = 28 cm

Formula used:

The volume of a hemisphere = $2\over3$πr3

The volume of a cylinder = πR2h 

Calculation:

Let the radius of the hemisphere be r cm.

Radius of the cylinder = 7/2 cm

Height of the cylinder = h = 28 cm

According to the question,

12 × The volume of a hemisphere = The volume of a cylinder 

⇒ 12 × (2/3) × π × r³ = π × R² × h

⇒ r³ = (7 × 7 × 7)/8 = (7/2)³

⇒ r = 7/2 = 3.5 cm

Given:

Total spent on sports = 1,80,00,000

Calculation:

The amount spent on tennis is more than the expenditure on golf by

⇒ [(48° – 35°)/360°] × 1,80,00,000

⇒ [13/360] × 18,00,000 = 6,50,000

As we know, height of triangle and height of quadrilateral will be same,

∴ Height of the triangle = Height of the quadrilateral = √3/2 × a = √3/2 × 10√3 = 15 cm

Let the remaining mangoes sold at Rs. x, then,

According to the question

[10,000/3] × [96/100] + x = 10,000 × [130/100]

⇒ 3200 + x = 13000

⇒ x = 13000 – 3200

⇒ x = 9800

As we know,

Price of [2/3] ton of mangoes is Rs. 9800

∴ Price of 1-ton mango = 9800 × [3/2] = 14700

Given:

Length = 88 cm

Width = 11 cm

Height of cylinder  = Width of the paper

Formula used:

Circumference of circles  = 2 × π × r

Vomule of cylinder = π × r² × h

Calculation:

Height of cylinder = 11 cm

2πr = 88

⇒ 2 × 22/7 × r = 88

⇒ r = 88 × 7/ 22 × 2

⇒ r = 14 cm

Volume of cylinder = πr²h

⇒ 22/7 × 14 × 14 × 11 = 6776 cm³

∴ The correct answer is 6776 cm³.

Calculation:

Given, BC = 6.5 m

In △ABC

cos60° = AB/AC

1/2 = 6.5/AC

AC = 2 × 6.5 = 13 m

Shortcut Trick

1 unit = 6.5 m

2 unit = 6.5 × 2 = 13 m

Shortcut Trick

Ratio of Efficiency (Vishal : Vivek) = 175% : 100% = 7 : 4.

Since Time is inversely proportional to efficiency, Time Ratio (Vishal : Vivek) = 4 : 7.

Given Vivek takes 14 days, so 7 units = 14 days ⇒ 1 unit = 2 days.

Vishal takes 4 units = 4 × 2 = 8 days.

∴ The correct answer is 8 days.

Alternate Method

Given: Time taken by Vivek = 14 days. Vishal is 75% more efficient than Vivek.

Formula: Total Work = Efficiency × Time | Time = Total Work ÷ Efficiency

⇒ Let Efficiency of Vivek = 4 units/day

⇒ Efficiency of Vishal = 175% of 4 = 7 units/day

⇒ Total Work = 14 × 4 = 56 units

⇒ Time taken by Vishal = 56 ÷ 7 = 8 days

∴ The correct answer is 8 days.

Additional Information

Inverse Proportion Rule

For a constant amount of work, efficiency and time are inversely proportional: E₁ × T₁ = E₂ × T₂.

Work and Wages

Wages are generally distributed in the ratio of the efficiency of the workers or the actual work done by them.

Combined Efficiency

When two or more people work together, their individual efficiencies are added to find the total rate of work (E_total = E₁ + E₂).

Given, BC = 300 m

In ΔCDB

tan30° = DB/BC

1/√3 = DB/300

DB = 300/√3 = 100√3

In △ABC

tan60° = AB/BC

√3 = AB/300

AB = 300√3

AD = AB – DB

AD = 300√3 – 100√3 = 200√3

AD = 200 × 1.732 = 346.4 cm

Short Trick:

√3 unit = 300

1 unit = 100√3

2 unit = 200√3 = 200 × 1.732 = 346.4

As we know,

Divisibility law of 6: A number is divisible by 6 if it is also divisible by 2 and 3.

Divisibility law of 9∶ A number is divisible by 3 if sum of its digit is divisible by 3.

Divisibility law of 2: A number is divisible by 2 it its last digit is 2, 4, 6, 8 or 0.

With the option (b)

5643252 number is divisible by 2 because its unit digit is 2.

Sum of digits = 5 + 6 + 4 + 3 + 2 + 5 + 2 = 27

27 is divisible by 3, so the number is divisible by 3.

∵ The number is divisible by 2 and 3 both, the number will also be divisible by 6.

Calculation:

Total expenditure = 100%

According to the question

12.5% × x = 100%

x = 8

Given:

Volume of tank = 25000 litres

Depth of cuboid = 1/5 of length

Breadth of cuboid = 1/8 of length

Formula∶ 

Volume of a cuboid = lbh

Calculation:

As we know,

1000 litres = 1 m³

25000 litres = 25 m³

Let the length of the tank be x m.

Depth of tank = x × 1/5 = x/5

Breadth of tank = x × 1/8 = x/8

Formula∶ Volume of a cuboid = lbh

x × x/5 × x/8 = 25

⇒ x³ = 5³ × 2³

⇒ x = 5 × 2 = 10 m

∴ The correct answer is 10 m.

Distance = 486 and time = 9 hours

Speed of the car = 486/9 = 54 km/hr

Speed of the train = 54 × (13/6) = 117 km/hr

Distance covered by train in 6 hrs = 117 × 6 = 702 km

Given:

A + B total money per week = Rs. 2040

B's money = 140% of A's Money

Calculation:

Total paid of A and B = 2040

∵ 140% = 7/5

Let the sum paid to A be 5x.

Sum paid of B = 5x × (7/5) = 7x

7x + 5x = 2040

⇒ 12x = 2040

⇒ x = 170

Sum paid to A = 5 × 170 = 850

∴The correct answer is Rs. 850. 

Alternate Method

According to the question,

B = 140% of A

⇒ B = 1.4A

Again, A + B = 2040

⇒ A + 1.4A = 2040

⇒ A = 850

Follow BODMAS rule to solve this question, as per the order given below :

Step-1: Parts of an equation enclosed in 'Brackets' must be solved first, and in the bracket,

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

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

Step-4: Last but not least, the parts of the equation that contain 'Addition' and 'Subtraction' should be calculated.

$\frac{{17.35; + ;\frac{7}{5};of;55 - 7}}{{\left( {42 \div 6; \times ;8.35} \right) - \frac{3}{7};of;\left( {\frac{2}{3} - \frac{1}{5}} \right); + ;\left[ {291 \div \left( {80 \div 8} \right)} \right]}}$