SSC CGL 2020 Tier-I Official Paper (Held On : 17 Aug 2021 Shift 3) (Previous Year Paper)

The logic is here is:

Ratio of first number to second number is equal to 1/7.

Option (1): (16, 112)

16 / 112 = 1 / 7

Option (2): (15, 105)

15 / 105 = 1 / 7

Option (3): (18, 128)

18 / 128 = 9 / 64

Option (4): (17, 119)

17 / 119 = 1 / 7

The option (3) is ratio not equal to other option.

Hence, pair (18, 128) is an odd one.

Alternate MethodThe logic followed here is:

The second number is the completely divisible by the first number.

Option (1): (16, 112) → 112 is divisible by 16.

Option(2): (15, 105) → 105 is divisible by 15.

Option(3): (18, 128) → 128 is not divisible by 18.

Option(4): (17, 119) → 119 is divisible by 17.

In the above options, the 2nd number is completely divided by the 1st number.

In option (3), does not follow the pattern.

Hence, pair (18, 128) is an odd one.

Table show alphabet serial number –

The pattern for the code is as follows,

Similarly,

Hence, CANDLE is coded as OBDFME.

Given: 215, 231, 256, 292, ?

The pattern followed here is:

215 + 4² = 231

231 + 5² = 256

256 + 6² = 292

Similarly, 

292 + 7² = 341

Hence, “341” will complete the series.

Alternate Method

The logic followed here is:

Hence, the correct answer is "341".

The pattern followed here is,

Let (M : N)

Step 1 → N – 8 = A (A any number)

Step 2 → A × N = B

Step 3 → B + 12  = M

Now follow the steps:

396 : 24

Step 1 → 24 – 8 = 16

Step 2 → 16 × 24 = 384

Step 3 → 384 + 12 = 396

Similarly,

672 : 30

Step 1 → 30 – 8 = 22

Step 2 → 22 × 30 = 660

Step 3 → 660 + 12 = 672

Similarly,

? : 28

Step 1 → 28 – 8 = 20

Step 2 → 20 × 28 = 560

Step 3 → 560 + 12 = 572

Hence, 572 : 28 is correct answer.

Alternate MethodThe logic followed here is:

396 : 24

24 - 4 = (20)² - 4 = 396

672 : 30

30 - 4 = 26²- 4 = 672

Similarly, 

? : 28

28 - 4 = 24² - 4 = 576 - 4 = 572

Hence, 572 : 28 is the correct answer.

According to BODMAS rule:

Given equation 48 * 12 * 8 * 15 * 3 * 44

Option 1 : Using the combination ×, ÷, =, −, +

48 × 12 ÷ 8 = 15 - 3 + 44

By BODMAS rule

48 × 1.5 = 59 - 3

72 ≠ 56 (LHS ≠ RHS)

Option 2 : Using combination ÷, ×, +, −, =

48 ÷ 12 × 8 + 15 - 3 = 44

4 × 8 + 15 - 3 = 44

32 + 15 - 3 = 44

47 - 3 = 44

44 = 44 (LHS = RHS)

Option 3 : Using the combination =, ×, +, ÷, −

48 = 12 × 8 + 15 ÷ 3 - 44

48 = 12 × 8 + 5 - 44

48 = 96 + 5 - 44

48 = 101 - 44

48 = 57 (LHS ≠ RHS)

Option 4 : Using the combination +, ÷, −, =, ×

48 + 12 ÷ 8 - 15 = 3 × 44

48 + 1.5 - 15 = 132

49.5 - 15 = 132

34.5 = 132 (LHS ≠ RHS)

Hence, the answer is “÷, ×, +, −, =”.

The image obtained when the paper is unfolded is,

Hence, option 3 is the correct answer.

Confusion Points Here option 2 and option 3 seems to be same but there is a difference in the symbol on the top right.

The logic followed is:

Option (1) Guide → A guide is a person who leads travellers, sportsmen, or tourists through unknown or unfamiliar locations

Option (2) Mistress → A married man's mistress is a woman who is not his wife

Option (3) Instructor → An instructor is a teacher. One can be an instructor of just about anything

Option (4) Mentor → The meaning of mentor is someone who teaches or gives help and advice to a less experienced and often younger person.

Except for Mistress, All are play roles like teachers.

Hence, Option (2) is correct.

Preparing the family tree using the following symbols,

1. Ram, Rajat and Ramesh are the three sons of Kavita.

2. Mukul is the son of Ram. Mukul’s paternal grandfather is Jay.

3. Jay has one daughter, Nikita.

4. Rajat’s son, Abhiram is married to Rani and their daughter is Ina.

5. Nirmala is the daughter of Nikita.

Hence, Jay is the “Great grandfather” of Ina

Given : Flower : Floriculture

The cultivation of flowering is called Floriculture.

Now check the option,

Option(1) → Mushroom : Viticulture

The cultivation of Mushroom is called Fungiculture not Viticulture.

So, this pair is wrong.

Option(2) → Silk : Silviculture

The cultivation of Silk is called Sericulture not Silviculture.

So, this pair is wrong.

Option(3) → Earthworm : Vermiculture

The cultivation of Earthworm is called Vermiculture.

So, this pair is correct.

Option(4) → Honey : Horticulture

The cultivation of Honey is called apiculture not Horticulture.

So, this pair is wrong.

Hence, “Earthworm : Vermiculture” is correct option.

Important Points

• Viticulture → Viticulture or winegrowing (wine growing) is the cultivation and harvesting of grapes.
• Silviculture → Silviculture is the science and art of growing and cultivating forest crops, based on a knowledge of silvics (the study of the life-history and general characteristics of forest trees and stands, with particular reference to local/regional factors).
• Horticulture → Horticulture is the art of cultivating plants in gardens to produce food and medicinal ingredients, or for comfort and ornamental purposes. Horticulturists are agriculturists who grow flowers, fruits and nuts, vegetables and herbs, as well as ornamental trees and lawns.

Table show alphabet serial number –

The logic is shown below –

So MANGO is coded as,

 

And,

So GRAPE is coded as,

 

Similarly,

So APPLE is coded as,

 

Hence, “APPLE” is coded as “1-32-48-48-25”.

The least possible diagram for the given statements is as follows

Conclusions:

I. Some tall are trained → False (It is possible but not definite)

II. Some employees are trained → True (because statement given ‘All trained are employees’ so definitely some employees are trained)

III. No tall is a guest → False (It is possible but not definite)

Hence, Only conclusion II follow.

Additional Information

The figure that will replace the question mark (?) in the following figure series is shown below:

1. The series is rotating in an Anti-clockwise direction and after rotating figure increase with one line.

2. In the first figure 'angle' with two sides, the second figure 'triangle' with three sides, the third figure 'square' with four sides and the last fourth figure 'pentagon' with five sides.

3) Circle are also rotating anti-clockwise direction but no shape change of the circle. 

Hence, ‘option 4’ is the correct answer.

The logic followed here is:

Sheep : Lamb → The young version one of a sheep is called a lamb.

Similarly,

Cockroach : ? → The young version of a cockroach is called a Nymph.

Hence, ‘Nymph’ is the correct answer.

For this question, the relation is given below -

Logic: If two dice have the same face value in the given image then their clockwise or anticlockwise wise number are known as opposite numbers in dice.

In first dice and second dice.

Number X is common.

The left letter will be opposite to each other writing them clockwise starting from X.

 

Hence, the correct answer is “XI”

The embedded part of this image is:

Hence, option (4) is the correct answer.

The number of rectangles in the given figure is:

 

So, there are a total of 14 rectangles in the figure.

Hence, ‘14’ is the correct answer.

The mirror image of this image is:

Hence, option 1 is the correct answer.

Table show alphabet serial number –

The logic is shown below –

Hence, “GKS” is complete the series.

According to the given information,

Total number of persons present at a press conference = 28.

7 of them refuse to shake hands

Total number of persons who shake hand n = 28 – 7 = 21

The number of handshakes exchanged is,

= n (n - 1) ÷ 2

= 21(21 – 1) ÷ 2

= 21 × 20 ÷ 2

= 21 × 10

= 210

Hence, total number of handshake is “210”

The Logic here is as follows:

First Number + √Third number = Second Number

In (4, 8, 16):

First Number + √Third number =

= 4 + √16

= 4 + 4

= 8 = Second Number

Similarly,

In (20, 24, 16):

 

First Number + √Third number =

= 20 + √16

= 20 + 4

= 24 = Second Number

Hence, the correct answer is "(20, 24, 16)".

The 'Rectangle' represents 'Boys', the 'Triangle' stands for 'Players' and the 'Hexagon' stands for 'Indians'.

The shaded part represents the Indians are players but are NOT boys i.e = 10

Hence, "10" is the correct answer.

We put all the option in blank area and check who create particular pattern

1. P, R, Q, S, Q, S, P, R, S

_ Q _ S P _ R _ _ Q _ _ P _ R _

After filling the blanks with the letters/numbers in the option given above, we get:

P Q R S / P Q R S / Q Q S P / P R R S

No particular pattern is repeating itself when the sequence is divided into four equal parts.

2. S, P, R, S, P, R, Q, Q, S

_ Q _ S P _ R _ _ Q _ _ P _ R _

After filling the blanks with the letters/numbers in the option given above, we get:

S Q P S / P R R S / P Q R Q / P Q R S

No particular pattern is repeating itself when the sequence is divided into four equal parts.

3) P, R, Q, S, P, R, S, Q, S

_ Q _ S P _ R _ _ Q _ _ P _ R _

After filling the blanks with the letters/numbers in the option given above, we get:

P Q R S / P Q R S / P Q R S / P Q R S

A particular pattern is repeating itself when the sequence is divided into four equal parts.

4. P, R, Q, S, P, R, R, P, Q

_ Q _ S P _ R _ _ Q _ _ P _ R _

After filling the blanks with the letters/numbers in the option given above, we get:

P Q R S / P Q R S / P Q R R / P P R Q

No particular pattern is repeating itself when the sequence is divided into four equal parts.

Hence, ‘P, R, Q, S, P, R, S, Q, S’ is the correct answer

According to the sequence in the dictionary:

The correct order of the given words is:

3. Hydroelectric
4. Hydrology
5. Hydroplane
6. Hydroxide
7. Hygienic

Hence, the correct answer is "3, 5, 2, 4, 1".

The pattern followed is,

All follow the same pattern, except ‘QTV’.

Hence, “QTV” is the odd – cluster.

Mistake Points The question is asking for NOT related in the same way, please pick according to the statement.

The Logic here is as follows:

1^st number

2^nd number = (1^st number)² + 2

3^rd number = 1^st number + 15

Now follow these steps,

(7, 51, 22)

1^st number → 7

2^nd number = (1^st number)² + 2 → 7² + 2 = 49 + 2 = 51

3^rd number = 1^st number + 15 → 7 + 15 = 22

We get, (7, 51, 22)

Now we check all the options-

Option (1): (3, 11, 18)

1^st number → 3

2^nd number = (1^st number)² + 2 → 3² + 2 = 9 + 2 = 11

3^rd number = 1^st number + 15 → 3 + 15 = 18

We get, (3, 11, 18)

This option follows the pattern.

Option (2): (4, 18, 19)

1^st number → 4

2^nd number = (1^st number)² + 2 → 4² + 2 = 16 + 2 = 18

3^rd number = 1^st number + 15 → 4 + 15 = 19

We get, (4, 18, 19)

This option follows the pattern.

Option (3): (6, 38, 22)

1^st number → 6

2^nd number = (1^st number)² + 2 → 6² + 2 = 36 + 2 = 38

3^rd number = 1^st number + 15 → 6 + 15 = 21 ≠ 22

We get, (6, 38, 21)

But option (3) given (6, 38, 22) this option doesn’t follow the pattern.

Option (4): (11, 123, 26)

1^st number → 11

2^nd number = (1^st number)² + 2 → 11² + 2 = 121 + 2 = 123

3^rd number = 1^st number + 15 → 11 + 15 = 26

We get, (11, 123, 26)

This option follows the pattern.

Hence, option (3) is correct answer.

The correct answer is Mangifera indica.

Key Points

• Mangifera indica is the botanical name of mango.
• In this name, Mangifera represents the genus while indica is a particular species.
• Scientific name
• This system was given by Carolus Linnaeus.
• Each name has two components – the Generic name and the specific epithet.
• This system of providing a name with two components is called Binomial nomenclature.

Additional Information

• Monoon longifolium is an Asian small tree species in the family Annonaceae. Common names include false Ashoka, the Buddha tree, the Indian mast tree, and the Indian fir tree.
• Cocos nucifera is a Coconut tree. It is a tall tree that is native to tropical islands in the western Pacific.
• Casuarina is a nitrogen-fixing tree through symbiotic relationship with an actinomycete called Frankia. Common names include coast sheoak, beach casuarina, beach oak, beach sheoak, beach pine, whistling tree, etc.

The correct answer is HH Gossen.

Key Points

• HH Gossen formulated the Law of Diminishing Marginal Utility (DMU).
• He formulated this law in 1854.

Important Points

• Marginal Utility is the change in total utility due to a one-unit change in the level of consumption.
• Law of Diminishing Marginal Utility
• It states that as a person consumes an item or a product, the satisfaction or utility that they derive from the product declines as they consume more and more of that product.
• In other words, the additional utility gained from an increase in consumption decreases with each subsequent increase in the level of consumption.
• Demand curves are downward-sloping in microeconomic models since each additional unit of a good or service is put toward a less valuable use.
• Marketers use the law of diminishing marginal utility because they want to keep marginal utility high for products that they sell.

The correct answer is Bhimsen.

Key Points

• Bhimsen is the author of the book ‘Tarikh-i Dilkusha'.
• ‘Tarikh-i Dilkusha' is a memoir of Aurangzeb.
• It was written in 1707.
• It was written in the Persian language. Jadunath Sarkar translated it into the English language.
• Bhimsen was a soldier and news-writer for Aurangzeb’s campaigns into the Deccan.
• Bhimsen begins the Tarikh-i Dilkusha by telling his readers that he is facing difficult times.
• Aurangzeb first appears in the Tarikh-i Dilkusha as a young prince who was made the governor of the Deccan by his father Shah Jahan in 1636.

Additional Information

• Charaka
• He was the court physician of Kaniska.
• Charaka was one of the principal contributors to Ayurveda medicine in ancient India.
• He is best known for his work Charaka Samhita.
• Sushruta was a physician in ancient India known today as the “Father of Indian Surgery” and “Father of Plastic Surgery” for inventing and developing surgical procedures.
• Panini
• He was a Sanskrit grammarian and gave a comprehensive and scientific theory of phonetics, phonology, and morphology.
• He is considered the founder of the language and literature of Sanskrit.
• His major work involves a treatise called Astadhyayi (or Astaka). It consists of eight chapters, each subdivided into quarter chapters.

The correct answer is Galileo Galilei.

Key Points

• Galileo Galilei was the first to conclude that in vacuum all objects fall with the same acceleration g and reach the ground at the same time.
• The acceleration of the object equals the gravitational acceleration.
• The mass, size, and shape of the object are not a factor in describing the motion of the object.
• So all objects, regardless of size or shape, or weight, free fall with the same acceleration.
• In a vacuum, a feather falls at the same rate as a ball.
• The remarkable observation that all free-falling objects fall with the same acceleration was first proposed by Galileo Galilei.

Important Points

• Galileo conducted experiments using a ball on an inclined plane to determine the relationship between the time and distance traveled.
• He found that the distance depended on the square of the time and that the velocity increased as the ball moved down the incline.
• The relationship was the same regardless of the mass of the ball used in the experiment.
• The experiment was successful because he was using a ball for the falling object and the friction between the ball and the plane was much smaller than the gravitational force.

The correct answer is Prasoon Joshi.

Key Points

• As of January 2021, Prasoon Joshi was the Chairperson of the Central Board of Film Certification.
• He became its 28th chairperson on 11 August 2017 after Pahlaj Nihalani.
• He is also the CEO of McCann World group India and Chairman APAC (Asia Pacific), a subsidiary of the global marketing firm McCann Erickson.

Important Points

• Central Board of Film Certification (CBFC)
• It is a statutory body under the Ministry of Information and Broadcasting, regulating the public exhibition of films under the provisions of the Cinematograph Act 1952.
• Films can be publicly exhibited in India only after they have been certified by the Central Board of Film Certification.
• The Board consists of non-official members and a Chairman (all of whom are appointed by Central Government) and functions with headquarters at Mumbai.
• It has nine Regional offices, one each at Mumbai, Kolkata, Chennai, Bangalore, Thiruvananthapuram, Hyderabad, New Delhi, Cuttack and Guwahati.
• The Regional Offices are assisted in the examination of films by Advisory Panels.
• The members of the panels are nominated by Central Government by drawing people from different walks of life for a period of 2 years.

The correct answer is Gold.

Key Points

• Gold is a Monatomic unit.
• Monatomic elements are elements that are stable as single atoms.
• For an element to be stable by itself, it must have a stable byte of valence electrons.
• The atomic number of a monoatomic element is equal to the number of protons in the element.
• Under standard temperature and pressure conditions, the monatomic elements are the noble gases helium, neon, argon, krypton, xenon, and radon.

Important Points

• Gold is the most malleable and ductile metal.
• Symbol: Au
• Atomic no.: 79
• It is a soft metal and is usually alloyed to give it more strength.
• It is a good conductor of heat and electricity and is unaffected by air and most reagents.
• The most common gold compounds are auric chloride (AuCl₃) and chloroauric acid (HAuCl₄).

The correct answer is Ministry of Tribal Affairs.

Key Points

• The Ministry of Tribal Affairs received the SKOCH Challenger Award for ‘Best Performance in e-Governance’ in January 2021.
• The Award was received by the Union Minister for Tribal Affairs- Shri Arjun Munda.
• The award has been given to the Ministry for its IT-led initiatives and other transformational initiatives leading to outcome-based performance improvement.
• It has digitalized all the processes leading to a paperless office.
• The Ministry has partnered with reputed organizations to develop innovative models with various Non-Governmental and private sectors as partners.
• The objective is to dismantle inefficient and burdensome practices and encourage best practices.

Additional Information

• Ministry of Tribal Affairs is not only implementing its own schemes but also monitoring Central and State Schedule Tribe Component (earlier known as Tribal Sub plan) which has a budget of more than 2 lakh crore per annum.
• The Ministry also received 3 Gold Awards for its initiatives namely-
• “Eco-Rehabilitation of tribal villages through Innovative design in water management using Ice-stupa”
• Swasthya: Tribal Health and Nutritional Portal
• Performance Dashboard “Empowering Tribals Transforming India

The correct answer is Supply of food to plant parts.

• The supply of food to plant parts is not the main function of the root system of a plant.

Key Points

• Plants have specialized organs that help them survive and reproduce in a great diversity of habitats. The major organs of most plants include roots, stems, and leaves.
• Roots are important organs in all vascular plants.
• Most vascular plants have two types of roots: primary roots that grow downward and secondary roots that branch out to the side.
• Together, all the roots of a plant make up a root system.
• A root is a complex organ consisting of several types of tissue. The structure of roots helps them perform their primary functions, which are-
• Absorbing water and minerals
• Thin-walled epidermal cells and root hairs are well suited to absorb water and dissolved minerals from the soil. The roots of many plants also have a mycorrhizal relationship with fungi for greater absorption.
• Anchoring and supporting the plant
• Root systems help anchor plants to the ground, allowing plants to grow tall without toppling over. A tough covering may replace the epidermis in older roots, making them ropelike and even stronger.
• Storing food
• In many plants, ground tissues in roots store food produced by the leaves during photosynthesis. The bloodroot stores food in its roots over the winter.

The correct answer is Greater Vishakhapatnam Municipal Corporation.

Key Points

• Greater Vishakhapatnam Municipal Corporation was declared as the ‘Best Performing Municipal Corporation’ in India in December 2020 for implementing the Pradhan Mantri Awas Yojana Urban Mission.
• Satraboina Durga, a housing beneficiary of Ward No. 50 of Gajuwaka, was selected under the ‘best house construction’ category.

Additional Information

• Reason for GVMC winning the award-
• Ms. Durga used to reside in a thatched house and used to spend at least ₹6,000 replacing thatched roof every year.
• The GVMC had allocated a pucca house to the family under PMAY- Urban Housing Programme. While the unit cost of the house is ₹3.5 lakh, the Union government offered a subsidy of ₹1.5 lakh, and the State government ₹1 lakh.
• The GVMV provided all the civic amenities such as water supply, underground drainage, C.C roads, street-lighting, etc.
• Pradhan Mantri Awas Yojana – Urban (PMAY-U), a flagship Mission of the Government of India being implemented by the Ministry of Housing and Urban Affairs (MoHUA), was launched on the 25th June 2015.
• The Mission addresses urban housing shortage among the EWS/LIG and MIG categories including the slum dwellers by ensuring a pucca house to all eligible urban households by the year 2022 when India completes 75 years of its Independence.

The correct answer is Chittaranjan Das.

• Chittaranjan Das along with Motilal Nehru was instrumental in the creation of the Swaraj Party.

Additional Information

• Swaraj Party
• It was established on 1 January 1923 by Chittaranjan Das and Motilal Nehru.
• The two important leaders of the Party were CR Das and Motilal Nehru in which CR Das was the President and Motilal Nehru was its secretary.
• The Party was established as the Congress Khilafat Swaraj Party.
• The Swaraj Party sought greater self-government and political freedom from the British Raj for the Indian people.
• The party’s program was to obstruct the government. They wanted to create deadlocks on every measure.
• In 1923, the Swaraj Party won the most seats during elections to the Bengal Legislative Council.
• In 1925, Swarajist Vithalbhai Patel became the speaker of the Central Legislative Assembly. This is the main achievement of the Party.

The correct answer is Arunachal Pradesh.

Key Points

• The language ‘Idu Mishmi’ is spoken in the state of Arunachal Pradesh.
• The Idu Mishmi language is a small language spoken by the Mishmi people in some areas of Arunachal Pradesh.
• The language is also spoken in Zayü County of the Tibet Autonomous Region, China.
• There were 8569 speakers in India in 1981 and 7000 speakers in China in 1994.
• It is considered an endangered language.

Additional Information

• The official language of Arunachal Pradesh is English.
• The capital of Arunachal Pradesh is Itanagar.
• State animal: Mithun (also known as Gayal).
• State bird: Great hornbill.
• State tree: Hollong.
• State flower: Lady slipper orchid.

The correct answer is Valmiki.

• According to 'The Ramayana', Ratnakar was the other name of Valmiki.

Important Points

• Sage Valmiki is revered as adi kavi.
• Valmiki was known as Ratnakar.
• As per Hindu Mythology, it is believed that Narada Muni transformed him into a great devotee of Lord Rama by giving him the Rama Nama mantra.
• Ramayana is the most important Sanskrit epics of ancient India.
• The epic, traditionally ascribed to the Maharishi Valmiki, narrates the life of Rama, a legendary prince of Ayodhya city in the kingdom of Kosala.
• It consists of nearly 24,000 verses, divided into Seven kaṇḍas: Bala Kanda, Ayodhya Kanda, Aranya Kanda, Kishkindha Kanda, Sundara Kanda, Yuddha Kanda, Uttara Kanda and about 500 Sargas (chapters).
• The Ramayana Grantha depicts the duties of relationships, portraying ideal characters like the ideal father, the ideal servant, the ideal brother, the ideal husband, and the ideal king.

The correct answer is Six.

Key Points

• Six was the total number of goals scored in the finals of the FIFA World Cup 2018.
• France won the title by defeating Croatia by 4–2 in the final of the FIFA world cup played on 15 July 2018 at Luzhniki Stadium in Moscow.
• France received the distinction of becoming the World Cup winner for the second time under the captainship of Didier Deschamps.
• 2018 FIFA Men's World Cup was hosted by Russia.

Important Points 

• FIFA stands for Federation of International Football Association.
• It is the highest governing body of Football.
• It was founded in 1904.
• Its headquarter is in Zurich, Switzerland.
• President: Gianni Infantino

The correct answer is two.

• The river Ganga divides the state of Bihar into two parts.

Important Points

• Ganga enters the boundary of Bihar at Chausa a village near Buxar after its confluence with Karmanasa.
• The Bihar plain is divided into two unequal halves by the river Ganga which flows through the middle from west to east.
• The most common soil in Bihar is Gangetic alluvium of the Indo-Gangetic plain region
• Ganga river originates as Bhagirathi from the Gangotri glacier.
• Alaknanda river joins Bhagirathi at Devprayag, onwards known as Ganga.
• It is joined by the river Yamuna at Allahabad.
• At Farraka, it bifurcates into Bhagirathi-Hugli in West Bengal and Padma - Meghna in Bangladesh.
• It drains into the Bay of Bengal.
• Tributaries- Yamuna, Gandak, Ramganga, Son, Ghaghra, Gomti, Kosi, Tamsa, Punpun, and Mahananda.

The correct answer is 1000000.

Key Points

• 1000000 microns are there in a meter.
• One micron length = 1 micrometre = 1 μm = 1 × 10^-6 m
• Metric prefix
• A metric prefix is a unit prefix placed before a basic unit of measurement. It represents the multiple of the unit in a convenient way. ​

Important Points

A few common metric prefixes used are as follows-

The correct answer is 348 (1).

• As per Article 348 (1) of the Constitution of India, English is the official language for all the high courts in the country.
• Article 348(1) stipulates the use of English in the Supreme Court and High Courts as well as for drafting Bills, Acts and Orders.
• Article 348(2) read with Section (7) of the Official Languages Act 1963 provides for Hindi or other official languages to be used in High Courts “in addition to English”.

Important Points

• Article 329A of the Constitution of India
• Special provision as to elections to Parliament in the case of Prime Minister and Speaker.
• 315 (1) of the Constitution of India
• Subject to the provisions of this article, there shall be a Public Service Commission for the Union and a Public Service Commission for each State.
• 336 (1) of the Constitution of India
• During the first two years after the commencement of this Constitution, appointments of members of the Anglo-Indian community to posts in the railway, customs, postal and telegraph services of the Union shall be made on the same basis as immediately before the fifteenth day of August, 1947.

The correct answer is Manpreet Singh Pawar.

Key Points

• Manpreet Singh Pawar- the captain of the Indian men's hockey team, as on January 2021.
• He led the Indian field hockey team to the bronze medal at the Tokyo 2020 Olympics.
• He plays as a halfback.
• The Indian men's national field hockey team represents India in international Field hockey competitions and is governed by Hockey India.
• The Indian hockey team won the gold medal while making its debut in the 1928 Olympics.
• The Indian hockey team won the gold medal in the Olympic Games six times consecutively between 1928 and 1956.
• The other two gold medals were won in Tokyo in 1964 and Moscow Olympics in 1980.

Additional Information

• Field Hockey:
• No of Players - 11 each side
• Terms used:- Advancing, Bully, Center pass, Dribble, Flick, Penalty corner, Scoop, Striker, Undercutting, etc.
• Some of the famous Indian Hockey players:
• Dhyan Chand
• Balbir Singh Sr.
• Dhanraj Pillay
• Mohammed Sahid
• Sardar Singh
• Harmanpreet Singh
• Sandeep Singh

The correct answer is Nath literature.

Key Points

• The story of Maynamati and Gopichandra is a part of Nath literature.
• Maynamati-Gopichandrer Gan is the story of Queen Maynamati and her husband, Manik Chandra, that propagates yoga guidelines.

Important Points

• Nath Literature
• It is a branch of medieval Bangla literature.
• It is based on the Nath cult or yoga-sadhana.
• The main god of the Naths is shiva, who is also called Adinath.
• The five Nath siddhas (or enlightened)- Minanath, Goraksanath, Hadipa, Kanupa and Chauranginath, are described as having been born from different parts of the body of Adinath.
• Nath literature was of two types, didactic and narrative.
• Didactic literature was in the form of doha, prahelika or chara, where secrecy was observed with the abundant use of code words and sentences.
• Narrative Nath literature was based on legends and stories about the siddhas. The aim of the stories was to attract people to the cult.

The correct answer is Krishna.

Key Points

• Yerla, Warna, and Dindi are tributaries of the Krishna river system.
• Krishna river
• It originates in the Western Ghats near Mahabaleshwar in the state of Maharashtra.
• It flows through Maharashtra, Karnataka, Telangana, and Andhra Pradesh. Krishna Basin extends nearly 8% of the total geographical area of the country.
• The river has a number of tributaries which include Tungabhadra as the principal tributary and others are Mallaprabha, Koyna, Bhima, Ghataprabha, Yerla, Warna, Dindi, Musi, and Dudhganga.
• Nagarjuna Sagar Dam on the Krishna river is the world’s tallest masonry dam (124 meters).

Additional Information

• Kaveri river
• It rises at Talakaveri on the Brahmagiri range (Karnataka) in the Western Ghats.
• It is the largest river in the state of Tamil Nadu and the third largest river after Godavari and Krishna in South India.
• Godavari river
• It originates from the Trimbak Plateau in the Nashik District of Maharashtra.
• It flows eastward across the Deccan Plateau and drains into the Bay of Bengal.
• The river is also known as Dakshin Ganga and Gautami.
• It is the longest river in Peninsular India.
• Brahmaputra river
• It originates under the name of Siang or Dihang, from the Angsi glacier of the Kailash range near the Mansarovar lake.
• It enters India west of Sadiya town in Arunachal Pradesh.
• Tributaries: Dibang, Lohit, Siang, Burhi Dihing, Tista, and Dhansari.

The correct answer is Andhra Pradesh.

Key Points

• Andhra Pradesh banned online gaming in October 2020.
• The Legislative Assembly adopted the Andhra Pradesh Gaming Amendment Bill-2020.
• The Andhra Pradesh Gaming Act, 1974 was amended.
• With the amendment, the government inserted in the Act “playing an online game for winning money or any other stakes” after the words matka or satta.
• Instruments of gaming include cards, dice, gaming, tables or cloth boards, or any other article intended to be used physically or in any virtual or intangible mode, including electronically, as subject means of gaming.
• Every offense under this Act is cognizable and non-bailable.
• Online gambling could induce criminal behaviour in society and increase the number of organized crimes such as money laundering and fraud.
• Many websites that claim to provide gambling services were not authentic and there were no regulatory measures to check the legitimacy of such sites.

The correct answer is An increase in money supply implies a price rise in an economy.

Key Points

• Positive economics is a stream of economics that focuses on the description, quantification, and explanation of economic developments, expectations, and associated phenomena.
• It relies on objective data analysis, relevant facts, and associated figures.
• It attempts to establish any cause-and-effect relationships or behavioral associations which can help ascertain and test the development of economics theories.
• Under this, an increase in money supply implies a price rise in an economy.
• Positive economics is sometimes described as "what is" economics.
• An example of a positive economic argument is as follows: An increase in government spending will reduce the unemployment rate.

The correct answer is Sri Lanka.

• Indian Peace Keeping Force (IPKF) was sent to Sri Lanka in the year 1987.

Important Points

• Operation PAWAN
• It was the code name assigned to the operation by the Indian Peace Keeping Force (IPKF) to take control of Jaffna from the Liberation Tigers of Tamil Eelam (LTTE) in late 1987.
• It was formed under the India-Sri Lanka Agreement of 1987.
• This was to implement the disarmament of the LTTE as a part of the India-Sri Lanka accord.
• It was formed under the India-Sri Lanka Agreement of 1987.
• Sri Lanka's newly elected President Ranasinghe Premadasa and V.P. Singh started withdrawing from Sri Lanka after the 1989 governmental election.
• The last units of the IPKF left Sri Lanka in March 1990.

The correct answer is MM Naravane.

Key Points

• MM Naravane was conferred the honorary rank of General of the Nepali Army in November 2020.
• He was honored at a special ceremony at 'Sheetal Niwas', the official residence of the President in Kathmandu.
• He was also presented with a sword and scroll during the ceremony.
• After the ceremony, General Naravane called on President Bhandari and expressed his gratitude for the honor accorded to him.
• They also discussed measures to further enhance bilateral cooperation.
• The practice follows a seven-decade-old tradition of conferring honorary titles on the army chiefs of each other's country.
• Commander-in-Chief General KM Cariappa was the first Indian Army Chief to be conferred with this title in 1950.
• Nepalese Army Chief General Purna Chandra Thapa was also made an Honorary General of the Indian Army by President Ram Nath Kovind at a ceremony in New Delhi.

The correct answer is One-horned Rhino.

• The one-horned Rhino is the state animal of Assam.

Additional Information

• Great one horned rhino
• They are commonly found in Nepal, Bhutan, Pakistan and in Assam, India.
• They are confined to the tall grasslands and forests in the foothills of the Himalayas.
• Indian Rhinos are brownish-gray in color and are hairless.
• They have knobby skin that appears to be armor-plated.
• A single horn sits on top of their snout, and their upper lip is semi-prehensile.
• The Indian state of Assam is home to the largest population of greater-one horned rhinos, with more than 90% in Kaziranga National Park.
• Since 2008, the Indian government, along with WWF and other partners, has translocated 18 rhinos from Kaziranga National Park and Pobitora Wildlife Sanctuary to Assam’s Manas National Park on the India-Bhutan border.

The correct answer is Jainism.

Key Points

• Mahavira, who was known in Pali literature as Nigantha Nataputta, founded a religion called Jainism.
• Mahavir Swami was the 24th Tirthankar.
• He is considered the real founder of Jainism.
• The lion is a symbol of Mahavir and his discipline is known as Chandrababu.
• He was also known as Vardhamana, Jaina, Jitendriya, Kevalin and Arihant.
• He was born to Siddhartha and Trisha (Lichchhavi princess) in the early 599 BC at Kundagrama near Vaishali in Bihar.
• He died at the age of 72 in Pawapuri which is presently in Bihar.

Additional Information

• Tirthankar
• A Tirthankar is referred to as a ‘teaching god’ or ‘Ford Maker’ in Jainism.
• In Jainism, it is believed that each cosmic age produces 24 Tirthankaras.
• The Tirthankaras in the art are shown in the Kayotsarga pose (dismissing the body).
• The 24 Tirthankaras are distinguished from each other by their symbolic colours or emblems.

Additional Information

Calculation:

Total no. of employees = 800

% of people woring in the field of marketing = 22%

Total no. employees working in the field of marketing = 800 × 22/100

⇒ 176

∴ 176 employees are working in the field of marketing.

Given:

CP = Rs. 720

MP = Rs. 900

Concept used:

SP = MP × (100 - discount)/100

SP = CP × (100 + profit)/100

Calculation:

According to the question,

900 × (100 - x)/100 = 720 × (100 + 5x/3)/100

⇒ 900 × (100 - x) = 720 × (100 + 5x/3)

⇒ 90000 - 900x = 72000 + 1200x

⇒ 90000 - 900x = 72000 + 1200x

⇒ 2100x = 18000

⇒ x = 18000/2100

⇒ x = 60/7

⇒ x = $8\frac{4}{7}$

∴ The vale of x is $8\frac{4}{7}$

Production of company A = 45 lakhs

Production of company B = 35 lakhs

Production of company C = 70 lakhs

Production of company D = 75 lakhs

Production of company E = 40 lakhs

Total production = 45 + 35 + 70 + 75 + 40 = 265 lakhs

Demand of company A = 40 lakhs

Demand of company B = 45 lakhs

Demand of company C = 55 lakhs

Demand of company D = 60 lakhs

Demand of company E = 50 lakhs

Total demand = 40 + 45 + 55 + 60 + 50 = 250 lakhs

Ratio of total production to total demand = 265 : 250 = 53 : 50

∴ Required ratio is 53 : 50

Given:

$\left(\frac{7}{16} \div \frac{1}{2}:of: \frac{1}{5}\right)\times \frac{4}{5}-\frac{1}{3}\times\frac{5}{8}\div \frac{1}{2}+\frac{3}{4}$

Concept used:

<br>

Calculation:

⇒ $\left(\frac{7}{16} \div \frac{1}{2}:\times: \frac{1}{5}\right)\times \frac{4}{5}-\frac{1}{3}\times\frac{5}{8}\div \frac{1}{2}+\frac{3}{4}$

⇒ $\left(\frac{7}{16} \div \frac{1}{10}\right)\times \frac{4}{5}-\frac{1}{3}\times\frac{5}{8}\div \frac{1}{2}+\frac{3}{4}$

⇒ $\left(\frac{7}{16}:\times:10\right)\times \frac{4}{5}-\frac{1}{3}\times\frac{5}{8}\div \frac{1}{2}+\frac{3}{4}$

⇒ $\frac{35}{8}:\times\frac{4}{5}-\frac{1}{3}\times\frac{5}{8}\div \frac{1}{2}+\frac{3}{4}$

⇒ $\frac{35}{8}:\times\frac{4}{5}-\frac{1}{3}\times\frac{5}{8}\times 2+\frac{3}{4}$

⇒ $\frac{7}{2}:-\frac{5}{12}+\frac{3}{4}$

⇒ $\frac{42:-:5;+;9 }{12}$

⇒ 46/12

⇒ 23/6

∴ The required answer is 23/6

Given:

$4x^4=5x^2-1, x>\frac{1}{\sqrt 2}$

Concept used:

ax² + bx + c = 0

Where a, b, and care the real terms

Calculation:

4x⁴ - 5x² + 1 = 0

⇒ 4x4 - 4x2 - x² + 1 = 0

⇒ 4x²(x² - 1) – 1(x2 - 1) = 0

⇒ (x2 - 1)(4x2 – 1) = 0

⇒ (x2 - 1) = 0 (4x2 – 1) = 0

x - 1 = 0

2x – 1 = 0

⇒ x = 1 or 1/2

(2x2 - x - 1)

Put x = 1

2 × 1 - 1 - 1

⇒ 2 - 2 = 0

∴ Required answer is 0

Given:

$\frac{108\times108\times108-92\times92\times92}{108\times108+92\times92+108\times92}$

Formula used:

(a)³ – (b)³ = (a – b)(a² + b² + ab)

Calculation:

$\frac{108\times108\times108-92\times92\times92}{108\times108+92\times92+108\times92}$

⇒ $\frac{(108)^3;-;(92)^3}{(108)^2;+;(92)^2;+;108;\times;92}$

⇒ $\frac{(108;-;92)[(108)^2;+;(92)^2;+;108;\times;92]}{(108)^2;+;(92)^2;+;108;\times;92}$

⇒ 108 – 92

⇒ 16

∴ Required answer is 16

Given:

BD : DC = 3 : 4

AE : ED = 2 : 3

Calculation:

We know if a line from vertex cuts the opposite side in a certain ratio then the area of two new triangles is also divided in that ratio

 $\text{Area ΔAEB}\over{\text{Area ΔEBD}}$ = $2\over3$ → (i)

$\text{Area ΔEBD}\over{\text{Area ΔECD}}$ = $3\over4$ → (ii) 

From Eqⁿ (I) and (ii), we have

ΔAEB : ΔEBD : ΔECD

    2    :     3     :     4

Now,

 $\text{Area ΔECD}\over{\text{Area ΔAEB}}$ = $4\over2$ = $2\over1$ = 2 : 1

∴ The required ratio is 2 : 1

Given:

∠QAM = 58°

∠QBN = 50°

Concept used:

The angles of an alternate segment subtended by a tangent to a circle are equal.

∠APM = ∠PNM and ∠BPN = ∠PMN

Alternate line segment theorem

cyclic quadrilateral theorem = The sum of a pair of opposite angles is 180° (supplementary)

Calculation:

 

The angles of an alternate segment subtended by a tangent to a circle are equal.

∠QAM = ∠ABQ = 58°

∠QBN = ∠BAQ = 50°

So, ∠AQB = 72° 

∠BOA = 2∠AQB = 2 × 72° = 144° 

In quadrilateral PBOA,

∠APB + ∠BOA = 180° (because OB ⊥ PN & OA ⊥ PM)

⇒ ∠APB = 180 - 144

⇒ ∠APB = 36°

∴ The measure of ∠APB is 36°

Given:

4sin2(2x - 10)° = 3

Formula used:

sin90° = 1, cos90° = 0

sin30° = $1\over2$, cos30° = $\sqrt3\over2$ 

Calculation:

4sin2(2x - 10)° = 3

⇒ sin2(2x - 10)° = $3\over4$

⇒ sin(2x - 10)° = $\sqrt3\over 2$

⇒ sin(2x - 10)° = sin60°

⇒ (2x - 10) = 60

⇒ 2x = 70

⇒ x = 35° 

$\frac{sin^4(x-5)^{\circ}+cos^4(x-5)^{\circ}}{1-2sin^2(3x-15)^{\circ}cos^2(3x-15)^{\circ}}$

⇒ $\frac{sin^4(35;-;5)^{\circ}+cos^4(35;-;5)^{\circ}}{1-2sin^2(105;-;15)^{\circ}cos^2(105;-;15)^{\circ}}$

⇒ $\frac{sin^430^{\circ}+cos^430^{\circ}}{1-2sin^290^{\circ}cos^290^{\circ}}$ = ${({1\over2})^4 + ({\sqrt3\over2})^4}\over{1-2\times1\times0}$

⇒ $\frac{1/16;+;9/16}{1}$

⇒ ${1+9}\over16$ = $10\over16$ = $5\over8$

∴ The required value is 5/8

Given:

Each man takes 20 days to complete the work

Calculation:

Let the efficiency of each man be 1

So, total work is 20 unit

So, on 1st day total work = 1 unit

Next day = 1 + 1 = 2 units

So according to this after 5th day total work has completed by 5 men = 1 + 2 + 3 + 4 + 5

⇒ 15 unit

So, remaining = 20 - 15

⇒ 5 unit

It will be completed in 5/5 = 1 day

So total time taken by them to complete the work is = 5 + 1 = 6 days

∴ In 6 days, the work will be completed.

Alternate Method

Hence, till the fifth days, the work done

⇒ (5 × 1) + (5 × 2) + .... + (5 × 5)

⇒ 75 units

Total time taken = {(100 - 75) ÷ 5} + 1 = 6 day

∴ In 6 days, will the work be completed.

Given:

The radius of the circle = 5 cm

Concept used:

Diagonal of a square = √2a

Area of a square = a² 

a = side of the square

Calculation:

Radius, AO = 5 cm

Diagonal AC of Square= AO + OC = 10 cm

Diagonal of a square = √2a

⇒ 10 = √2 a

⇒ a = $10\over\sqrt2$ 

Area of a square = a2

⇒ ($10\over\sqrt2$)² = $100\over2$ = 50 cm

∴ The area of the square is 50 cm2

Given:

7cos2θ + 5sin2θ - 6 = 0

Formula used:

sin2θ + cos2θ = 1

Calculation:

7cos2θ + 5sin2θ - 6 = 0

⇒ 2cos2θ + 5cos2θ + 5sin2θ - 6 = 0

⇒ 2cos2θ + 5 - 6 = 0

⇒ 2cos2θ = 1

⇒ cos2θ = 1/2

⇒ cosθ = 1/√2

⇒ cosθ = cos45°

⇒ θ = 45°

$\sqrt{\frac{cosecθ+tanθ}{secθ-cotθ}}$

⇒ $\sqrt{\frac{cosec45^\circ+;tan45^\circ}{sec45^\circ-;cot45^\circ}}$ = $\sqrt{\frac{\sqrt2;+;1}{\sqrt2;-;1}}$ 

⇒ $\sqrt{{{\sqrt2+1}\over{\sqrt2-1}}\times {{\sqrt2+1}\over{\sqrt2+1}}}$ 

⇒ $\sqrt{{(\sqrt2+1)^2}\over{{\sqrt2}^2-1}}$ = ${\sqrt2+1}\over2-1$ 

⇒ √2 + 1

∴ The required value is √2 + 1

Alternate Method7cos2θ + 5sin2θ - 6 = 0

Put θ = 45°

⇒ 7/2 + 5/2 – 6 = 0

⇒ 3.5 + 2.5 – 6 = 0

⇒ 6 – 6 = 0

$\sqrt{\frac{cosecθ+tanθ}{secθ-cotθ}}$

⇒ $\sqrt{\frac{cosec45^\circ+;tan45^\circ}{sec45^\circ-;cot45^\circ}}$ = $\sqrt{\frac{\sqrt2;+;1}{\sqrt2;-;1}}$ 

⇒ $\sqrt{{{\sqrt2+1}\over{\sqrt2-1}}\times {{\sqrt2+1}\over{\sqrt2+1}}}$

⇒ $\sqrt{{(\sqrt2+1)^2}\over{{\sqrt2}^2-1}}$ = ${\sqrt2+1}\over2-1$ 

⇒ √2 + 1

∴ The required value is √2 + 1

Shortcut Trick

The perpendicular from the center of a circle to a chord bisects the chord.

Half of the chord length = 10 ÷ 2 = 5 cm.

Using the standard Pythagorean triplet (5, 12, 13):

The radius of the circle (r) = 13 cm.

Diameter of the circle = 2 × r = 2 × 13 = 26 cm.

∴ The correct answer is 26 cm.

Alternate Method

Given:

Length of the chord (AC) = 10 cm

Distance of the chord from the centre (OM) = 12 cm

Formula Used:

1. The perpendicular from the centre of a circle to a chord bisects the chord: AM = MC = AC ÷ 2
2. Pythagoras Theorem in right-angled triangle ΔAMO: OA² = AM² + OM²
3. Diameter of a circle = 2 × Radius (r)

Calculations:

Let O be the centre of the circle and AC be the chord of length 10 cm.

OM is the perpendicular distance from the centre O to the chord AC, so OM = 12 cm.

⇒ AM = AC ÷ 2

⇒ AM = 10 ÷ 2 = 5 cm

In the right-angled triangle ΔAMO, by Pythagoras theorem:

⇒ OA² = AM² + OM²

⇒ r² = 5² + 12²

⇒ r² = 25 + 144

⇒ r² = 169

⇒ r = √169 = 13 cm

Therefore, the radius of the circle is 13 cm.

⇒ Diameter = 2 × r

⇒ Diameter = 2 × 13 = 26 cm

Incorrect Options Explanation:

The value 20 cm is incorrect because it corresponds to a radius of 10 cm, which does not satisfy the Pythagorean relation with a distance of 12 cm.

The value 22 cm is incorrect because it corresponds to a radius of 11 cm, which does not form a valid right-angled triangle with the given dimensions.

The value 13 cm is incorrect because it represents the radius of the circle, whereas the question asks for the diameter.

∴ The correct answer is 26 cm.

Additional Information

Perpendicular Bisector Theorem

A line drawn from the center of a circle perpendicular to a chord always bisects the chord. Conversely, the line joining the center to the midpoint of a chord is perpendicular to the chord.

Pythagorean Triplets

Sets of three positive integers (a, b, c) that satisfy a² + b² = c². Common triplets include (3, 4, 5), (5, 12, 13), (8, 15, 17), and (7, 24, 25).

Equal Chords and Distance

Chords of a circle that are equal in length are equidistant from the center of the circle. Conversely, chords equidistant from the center are equal in length.

Given:

PR : RQ = 3 : 5

QR = 20 cm

Concept used:

In a ΔABC, if P and Q are the mid-points of AB and AC respectively, then 

PQ||BC

ΔAPQ ~ ΔABC

PQ = $1\over2$ BC

Calculation:

Let the length of PQ be x

PR : RQ = 3 : 5

x × $5\over8$ = 20 

⇒ x = 20 × $8\over5$ = 32 cm

PQ = 32 cm

PQ = $1\over2$ BC

⇒ BC = 2 × PQ

⇒ BC = 2 × 32 = 64 cm

∴ The length of BC is 64 cm

Given:

45082K is divisible by 3

Concept used:

Divisibility rule of 3 = Sum of the digits should be divisible by 3

Calculation:

4 + 5 + 0 + 8 + 2 + K = 19 + k

Possible values of K = 2, 5, 8

Greatest = 8

Lowest = 2

2² + 8²

⇒ 4 + 64

⇒ 68

∴ Required answer is 68

Given:

Marked price = Rs. 240

Discount = 18%

Profit = 23%

Concept used:

SP = MP × (100 – Discount%)/100

CP = SP × 100/(100 + Profit%)

Calculation:

CP = 240 × 82/100 × 100/123

⇒ 240 × 82/123

⇒ 240 × 2/3

⇒ 160

⇒ CP = Rs. 160

∴ The cost price of the article is Rs. 160

Shortcut TrickMP/CP = (100 + Profit %)/(100 – Discount %)

240/CP = (100 + 23)/(100 – 18)

⇒ 240/CP = 123/82

⇒ 240/CP = 3/2

⇒ CP = 160

∴ The cost price of the article is Rs. 160

Given:

Total distance = 24km

Time taken = 7/4 hours

Concept used:

Speed = D/t

D= Distance

t = time

Calculation:

Let the speed of man and current be v and s respectively. 

According to the question,

${8\over v ;+;s} = {6\over v ;-;s}$

⇒ 8v - 8s = 6v + 6s

⇒ 2v = 14s

⇒ v : s = 7 : 1

Let speed of man = 7x

Speed of current = x

So,

24/8x + 24/6x = 7/4

⇒ 3/x + 4/x = 7/4

⇒ 7/x = 7/4

⇒ x = 4

⇒ speed of the current = 4 km/h

∴ The speed of the current is 4 km/h

Shortcut Trick

Present ratio of A : B = 7 : 8 and after 6 years ratio = 8 : 9.

The difference in both ratio parts is constant: (8 − 7) = 1 and (9 − 8) = 1.

1 unit → 6 years.

Present age of A = 7 × 6 = 42 years.

Present age of C = 42 + 10 = 52 years.

∴ The correct answer is 52 years.

Alternate Method

Given:

Present ratio of A and B = 7 : 8

Ratio after 6 years = 8 : 9

C's present age = A's present age + 10 years

Calculations:

Let the present ages of A and B be 7x and 8x respectively.

⇒ (7x + 6) / (8x + 6) = 8 / 9

⇒ 9 × (7x + 6) = 8 × (8x + 6)

⇒ 63x + 54 = 64x + 48

⇒ 64x − 63x = 54 − 48

⇒ x = 6

⇒ Present age of A = 7 × 6 = 42 years.

⇒ Present age of C = 42 + 10 = 52 years.

Therefore, the present age of C is 52 years, which matches Option (4).

∴ The correct answer is 52 years.

Additional Information

Constant Age Difference

The mathematical difference between the ages of two individuals remains the same regardless of how many years pass (Difference = A − B = constant).

Ratio Balancing

If the difference between ratio parts is not initially equal, multiply the ratios by the difference of the opposite ratio parts to balance them.

Future Age Formula

If the present age is P, then the age after n years is P + n and the age n years ago was P − n.

Shortcut Trick

Net change in sum = (Correct values) − (Incorrect values)

Net change = [(25 × 2) + 38] − [(35 × 2) + 32] = 88 − 102 = −14

Change in average = Net change ÷ Total students = −14 ÷ 40 = −0.35

Actual average = Original average + Change = 45 − 0.35 = 44.65

∴ The correct answer is 44.65.

Alternate Method

Given:

Total students = 40

Initial average = 45

Incorrect readings: 35 (twice), 32 (once)

Correct readings: 25 (twice), 38 (once)

Calculations:

⇒ Total sum = Average × Number of students = 45 × 40 = 1800

⇒ Sum of incorrect values = (35 × 2) + 32 = 70 + 32 = 102

⇒ Sum of correct values = (25 × 2) + 38 = 50 + 38 = 88

⇒ Corrected total sum = 1800 − 102 + 88

⇒ Corrected total sum = 1800 − 14 = 1786

⇒ Actual average = 1786 ÷ 40

⇒ Actual average = 44.65

∴ The correct answer is 44.65.

Additional Information

Average Correction Formula

Correct Average = Observed Average + [(Total Correct Value − Total Incorrect Value) ÷ Number of Items].

Effect of Constant on Average

If every observation is increased or decreased by a constant value 'k', the average also increases or decreases by 'k'.

Weighted Average

When two groups with averages A₁ and A₂ and sizes n₁ and n₂ are combined, the new average = (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Given:

Rate of interest = 10%

Concpet used:

A = P(1 + r/100)ⁿ

A = amount

P = principal

r = rate

n = no. of years

Calculation:

For the payment of Rs. 4000 at the end of the first year :

P1(1 + 10/100) = 4000

⇒ P1(11/10) = 4000

⇒ P1 = 40000/11       ------(1)

Similarly, for the payment of Rs. 7700 at the end of the second year 

⇒ P₂(11/10)² = 7700

⇒ P2[(11 × 11)/(10 × 10)] = 7700

P2 = 70000/11        ------(2)

Hecne, sum borrowed

P = P1 + P2

⇒ P = (40000/11) + (70000/11) = 110000/11

∴ The sum borrowed is Rs. 10000.

Alternate Method

Amount = P(1 + 10/100)1

⇒ A = P(11/10)

⇒ P = (10/11)A

2nd he paid Rs. 7700

So, Principal = Rs. 7700 × 10/11

⇒ Rs. 7000

Amount = Principal + interest

A = 7000 + 4000

⇒ Rs. 11000

So, Principal = 11000 × 10/11

⇒ Rs. 10000

∴ The sum borrowed is Rs. 10000.

Given:

$\frac{√2tan(60^{\circ}-θ)tan(30^{\circ}+θ)}{sin^2(45^{\circ}+θ)+sin^2(45^{\circ}-θ)}$

Concept used:

sin²θ + cos²θ = 1

sin(90 - θ)° = cosθ

tanθ = $1\over cot\theta$

Calculation:

$\frac{√2tan(60^{\circ}-θ)tan(30^{\circ}+θ)}{sin^2(45^{\circ}+θ)+sin^2(45^{\circ}-θ)}$

⇒ $\frac{√2tan(60^{\circ}-θ)tan(90^{\circ};-;(60^{\circ}-;θ)}{sin^2(45^{\circ}+θ)+sin^2(90^{\circ} ;-;(45^{\circ}+;θ))}$

⇒ $\frac{√2tan(60^{\circ}-θ)cot(60^{\circ}-;θ)}{sin^2(45^{\circ}+θ)+cos^2(45^{\circ}+;θ)}$

⇒ $\frac{√2tan(60^{\circ}-θ)\frac{1}{tan(60^{\circ}-;θ)}}{sin^2(45^{\circ}+θ)+cos^2(45^{\circ}+;θ)}$

⇒ √2

∴ The required value is √2

Alternate Method$\frac{√2tan(60^{\circ}-θ)tan(30^{\circ}+θ)}{sin^2(45^{\circ}+θ)+sin^2(45^{\circ}-θ)}$

Put θ = 15^o

^{⇒ $\frac{√2tan(60^{\circ}-15)tan(30^{\circ}+15)}{sin^2(45^{\circ}+15)+sin^2(45^{\circ}-15)}$}

⇒​ ${√2tan45tan45}\over{sin^260 + sin^230}$ ⁼ ${√2\times1}\over{({√3\over2})^2+({1\over2})^2}$

⇒​ ${√2}\over{{3\over4}+{1\over4}}$ = ${√2}\over{4\over4}$ = √2

∴ The required value is √2