SSC CGL Previous Paper (Held On: 5 March 2020 Shift 2) (Previous Year Paper)

Preparing the family tree using the following symbols:

Possible tree diagram will be

According to the tree diagram,

Nitin is brother of Sanchi’s mother.

Hence, brother is the correct answer.

Suppose Vineet has Rs. x.

Rajesh has Rs. 2x.

Kriti has Rs. x + 6.

(2x) + (x + 6) = 147

3x + 6 = 147

3x = 141

x = 47

Vineet has Rs. 47.

Kriti has 47 + 6 = Rs. 53

Hence, 53 is the correct answer.

The logic followed here is,

For C, U and H → Positional value of same letter → C = 3, U = 21 & H = 8

For A, G and T → Positional values of opposite letter → A = 26, G = 20 & T = 7

Therefore, CAUGHT → 326212087

Similarly,

For S, L and E → Positional value of same letter → S = 19, L = 12 & E = 5

For O, D and R → Positional values of opposite letter → O = 12, D = 23 & R = 9

Therefore, SOLDER → 1912122359

Hence, 1912122359 is the correct answer.

Shape in option 1 is embedded in given figure.

Hence, option 1 is correct answer.

Some Income tax payers are employees, some employees are males and some income tax payers are males.

Hence, option 3 is the correct answer.

The diamond shape is moving clockwise, and the number of blocks it skips increases by 1 at each step.

Therefore, options 2 and 4 are eliminated.

The plus sign also repeats the same pattern but anticlockwise.

Hence, option 3 is correct answer.

The logic followed here is:

The difference between two consecutive numbers is equal.

Hence, "119" is the correct answer.

Alternate Method

The logic follows here is:

61 + (1)² + 1 = 61 + 2 = 63

63 + (2)² - 2  = 63 + 2 = 65

65 + (3)² + 3 = 65 + 12 = 77

77 + (4)² - 4 = 77 + 12 = 89

89 + (5)² + 5 = 89 + 30 = 119

119 + (6)² - 6 = 119 + 30 = 149

149 + (7)² + 7 = 149 + 56 = 205

Hence, the correct answer is "119".

Invigilator’s duty is to monitor the examination whereas Observer is responsible for monitoring the election.

Hence, Election : Observer is the correct answer.

Given Expression: 11 × 7 ÷ 35 – 64 + 56 = 47

1. Option 1: × and ÷; 35 and 11

 (35 ÷ 7) × 11 – 64 + 56

= (5 × 11) – 64 + 56

= 55 – 64 + 56

= 111 – 64

= 47

2. Option 2: × and ÷; 35 and 56

 (11 ÷ 7) × 56 – 64 + 35

= (1.57 × 56) – 64 + 35

= 88 – 64 + 35

= 123 – 64

= 59

3. Option 3: + and - ; 7 and 11

 7 × (11 ÷ 35) + 64 – 56

= 7 × 0.314 + 64 – 56

= 2.2 + 64 – 56

= 66.2 – 56

= 10.2

4. Option 4: + and -; 35 and 11

 35 × (7 ÷ 11) + 64 – 56

= 35 × 0.63 + 64 – 56

= 22.27 + 64 – 56

= 86.27 – 56

= 30.27

Hence, ‘× and ÷ ; 35 and 11’ is correct answer.

When unfolded, the paper will look like the following figure:

Hence, option 4 is correct answer.

The logic followed here is,

21 × 19 = 399; 399 – 100 = 299

18 × 22 = 396; 396 – 100 = 296

Similarly,

32 × 14 = 448; 448 – 100 = 348

Hence, 14 is the correct answer.

Mirror image of given figure is,

Hence, option 1 is correct answer.

Let’s check each option:

1. 11 × 13 = 143, where 13 is the next prime number after 11.

2. 19 × 23 = 437 ≠ 475

3. 23 × 29 = 667

4. 17 × 19 = 323

Hence, 19 : 475 is the odd one among the given options.

The logic followed here is,

Similarly,

Hence, UWTKJPIY is the correct answer.

Alphabetical arrangement of given words is:

5. Capacity,
6. Capsule,
7. Captain,
8. Caption,
9. Category

Hence, option 3 is correct answer.

Shortcut Trick

• Letter 2: A, E, I, and U are vowels. ⇒ the missing letter should be the vowel O. This eliminates options 2 and 3.
• Letter 1: S + 3 = V: V + 3 = Y; Y + 3 = B; B + 3 = E ⇒ Option 4 can be eliminated because there is no B in it.
• Hence, option 1 - BOC, is the correct answer.

The pattern followed here is,

• Letter 1:

• Letter 2: vowels are used - A, E, I, O, U

• Letter 3:

​

Hence, BOC is the correct answer.

Schizophrenia affects persons ability to think, feel and behave clearly. This is chronic disease and cannot be cured. Whereas Rabies, Measles and Polio are viral diseases and can be cured with vaccination.

Hence, Schizophrenia is the correct answer.

The logic followed here is,

7 × 14 = 98; 7 × 28 = 196 → (7, 98, 196)

Similarly,

11 × 14 = 154; 11 × 28 = 308 → (11, 154, 308)

Hence, (11, 154, 308) is the correct answer.

The logic followed here is,

A + 2 = C

C + 2 = E

E + 2 = G

G + 2 = I

I + 2 = K

For second letter

R – 2 = P

P – 2 = N

N – 2 = L

L – 2 = J

J – 2 = H

Hence, EN is the correct answer.

Elimination method

• Faces 5 and 6 will lie on the opposite sides of the given dice. Therefore, figure B cannot be formed. Thus options 1 and 3 are eliminated.
• Faces 2 and 3 will lie on opposite sides of the given dice. Therefore, figure C cannot be formed. Thus option 4 is eliminated which makes us conclude that figure D cannot be formed.
• ⇒ only figure A can be formed.
• Hence, option 2 is the correct answer.

Let’s check each option

L + 4 = P; P + 5 = U

P + 4 = T; T + 5 = Y

A + 3 = D; D + 8 = L

N + 4 = R; R + 5 = W

Hence, ADL is the correct answer.

The logic followed here is:

• Monkey is a vertebrate
• Similarly, Starfish is an invertebrate.

Hence, the correct answer is 'Starfish'.

Important Points

Vertebrates have fully developed vertebral columns. 

• They have a proper skeletal structure.
• Example-  humans, birds, snakes, frogs.

Invertebrate animals are those which do not develop a vertebral column.

• Example-  insects like cockroach, flatworm, earthworm, crabs, snails, etc.

Triangles are ABO, BCO, ADO, CEO, DFO, EGO, PFO, GPO, HQR, IQR, HJR, IKR, JLR, KNR, LMR, MNR, ACF, GCF, ACG, AFG, HIN, HLN, HLI, NLI, AOC, AOF, COG, GOF, HRI, HRL, LRN, NRI.

Hence, 32 is the correct answer.

The logic followed here is,

4 → 4³ = 64 → 64 + 5 = 69

Similarly,

11 → 11³ = 1331 → 1331 + 5 = 1336

Hence, 1136 is the correct answer.

The logical Venn diagram according to given statements is,

Conclusions:

I. Some copies are papers → True (Some papers are copies)

II. Some papers are erasers. → False (it is possible but not definite)

III. No paper is an eraser. → False (it is possible but not definite)

Thus, II and III form a complementary pair.

Therefore, only conclusion I and either conclusion II or III follows.

Hence, option 3 is correct answer.

• The ‘Hyderabad Fund’ had been held by the National Westminster Bank  **(**Commonly known as NatWest Bank) in the account of the High Commissioner of Pakistan to the UK, Habib Ibrahim Rahimtoola.
• In 2019 UK High Court ruled in favour of India which resolved a decades-old legal dispute with Pakistan over funds belonging to the Nizam of Hyderabad at the time of Partition in 1947.
• This fund over around GBP 35 million was deposited in a London bank account.
• This legal battle was initiated by Prince Mukarram Jah – the titular 8^th Nizam of Hyderabad – and his younger brother Muffakham Jah with support from the Indian government.

• For hydrogenation reaction, it is necessary to use catalysts like palladium, platinum or nickel.
• The molecules of vegetable oil contain long and unsaturated carbon chains. Hydrogenation transforms them into saturated chains and thereby vanaspati ghee is formed.
• Hydrogen has three isotopes: protium, deuterium, and tritium.
• Hydrogen is the lightest atom and it is the most abundant element in the universe.

• The excavated remains of Nalanda Mahavihara found near Patna in Bihar was inscribed as a World Heritage Site by UNESCO in July 2016.
• World Heritage Sites in Bihar: Bodhgaya's Mahabodhi temple and Nalanda University ruins
• This ruin dates back to the period from the 3rd century BC to the 13th century AD.
• Kumargupta I of the Gupta dynasty founded Nalanda Mahavihara in 5th century CE.
• India has a total of 40 UNESCO world heritage sites which include 32 cultural sites,7 natural sites, and 1 mixed site. (till April 2020)
• Maximum world heritage sites are located in China and Italy (55).

About the United Nations Educational, Scientific and Cultural Organization (UNESCO):

• Director-General, UNESCO: Audrey Azoulay
• Headquarters of UNESCO: Paris, France
• The motto of UNESCO: "Building peace in the minds of men and women"

• The aggregate value of goods and services produced in an economy can be calculated by three methods: income method, expenditure method and product / value-added method.
• National income or Gross Domestic Product (GDP) refers to the money value of all final goods and services produced in an economy in an accounting year.
• The Central Statistics Office (CSO) (Ministry of Statistics and Program Implementation) publishes GDP/GVA figures.

Additional information about the Ministry of Statistics and Programme Implementation (MoSPI):

• Depreciation is an annual allowance for wear and tear of a capital good. In other words, it is the cost of the good divided by a number of years of its useful life.
• While calculating depreciation unexpected or sudden destruction or disuse of capital as can happen with accidents, natural calamities or other such extraneous circumstances are not taken into account.
• As an accounting term, depreciation is an expired cost or expense, charged against the revenue of a given accounting period.
• It is the diminution in the intrinsic value of the asset due to use and/or lapse of time.

The Correct answer is Mumbai.

Key Points

• The headquarters of the Board of Control for Cricket in India (BCCI) is located at Wankhede Stadium in Mumbai.
• Board of Control for Cricket in India (BCCI) was formed in December 1928 as 'Provisional' Board of Control'.
• Important domestic cricket tournaments: Ranji Trophy, Duleep Trophy, Deodhar Trophy, Vijay Hazare Trophy, Syed Mushtaq Ali Trophy, Irani Cup, etc.
• Current official Indian cricket team sponsor: BYJU
• Secretary, BCCI: Jay Shah
• Presidents, BCCI: Roger Binny
• Captain of Indian Men’s team: Rohit Sharma
• Coach of Indian Men’s team: Rahul Dravid
• Captain of Indian Women’s team: Harmanpreet Kaur
• Coach of Indian Women’s team: Woorkeri Raman

Additional Information

About International Cricket Council:

• The Grand Canal in China is the world’s longest man-made waterway.
• The Grand Canal starts in Beijing and ends at the city of Hangzhou in Zhejiang province. It connects the Yellow River with the Yangtze River.
• It is one of the world’s largest and most comprehensive civil engineering projects prior to the Industrial Revolution.
• The length of the Grand Canal is around 1800 km which makes it the world's longest manmade waterway.
• It is declared as World Heritage Site by UNESCO.

Deficiency of Vitamin B12 causes Pernicious anaemia.

Additional details about other vitamins are given in the following table:

• Rabindranath Tagore renounced his knighthood in protest for Jalianwalla Bagh mass killing.
• Rabindranath Tagore was awarded a knighthood in 1915 but in 1919 he repudiated it.
• Jalianwalla Bagh massacre took place on 13th April 1919 in Punjab province of British India.
• Brigadier-General Dyer directed British Indian Army troops to open fire on unarmed Indian civilians gathered for the Baisakhi festival in Jallianwala Bagh, Amritsar.

• The Indians living in America and Canada established the Gadar (Ghadar) organization. It was established in the year 1913.
• The word 'Gadar' means 'revolt'. 'Gadar' was the journal of this organization that acted as its mouthpiece. Through this journal, the effects of British rule in India were pointed out.
• Headquarters of Gadhar party was in San Francisco, United States.
• The primary objective of the Ghadar movement was to organize assassinations of British officials and publish revolutionary literature abroad.

• On 19 September 1960, the Indus Waters Treaty was signed between India and Pakistan.
• This treaty between Indian and Pakistan was brokered by the World Bank.
• At the time of agreement Indian side was represented by Jawaharlal Nehru who was Prime Minister of India and Pakistan's representative was Mohammad Ayub Khan- President of Pakistan.
• As per the treaty Pakistan was given control of three western rivers—the Indus, Jhelum, and Chenab
• India was given control of  three eastern rivers—the Ravi, Beas, and Sutlej

• In 2013 Arunima Sinha became the world's first female amputee to climb Mount Everest.
• Arunima Sinha is a mountaineer and former national level volleyball player.
• In 2015 Arunima was conferred the Padma Shri and Tenzing Norgay National Adventure award.
• Arunima has scaled following mountain peaks:

1. Mount Kilimanjaro in Africa
2. Elbrus in Europe
3. Kosciuszko in Australia
4. Aconcagua in Argentina
5. Carstensz Pyramid (Puncak Jaya) in Indonesia.

• Do you know?
• First Indian woman to climb Mount Everest: Bachendri Pal.
• Malavath Poorna is the first and youngest tribal woman in the world to set foot on the six tallest mountain peaks across six continents.

• Girish Chandra Murmu is the first Lieutenant Governor of the Union Territory of Jammu and Kashmir.
• He is an Indian Administrative Service officer of 1985-batch from the Gujarat cadre.
• Key positions held by G.C. Murmu:1.Principal Secretary to Narendra Modi during his tenure as Chief Minister of Gujarat. 2. Expenditure Secretary in the Ministry of Finance.
• According to Jammu and Kashmir Reorganisation Act, 2019 the state of Jammu and Kashmir was bifurcated into two union territories i.e. - Jammu and Kashmir with a legislature and Ladakh without legislature.

Additional Information

Important Points

• The current governor is Mr. Manoj Sinha.

CONCEPT:

Plane Mirror:

• A plane mirror is a mirror with a flat (planar) reflective surface.

The number of images formed when the object is placed between two plane mirrors:

⇒ θ = Angle between the two plane mirrors, and n = number of images formed

• If $\frac{360}{θ}$ = even number

$⇒ n=\frac{360}{θ}-1$

• If $\frac{360}{θ}$ = odd number and the object lies symmetrically

$⇒ n=\frac{360}{θ}-1$

• If $\frac{360}{θ}$ = odd number and the object lies asymmetrically

$⇒ n=\frac{360}{θ}$

• If $\frac{360}{θ}$ = fraction

⇒ n = only integer part of $\frac{360}{θ}$

CALCULATION:

Given that: θ = 120° 

Number of images (n) = (360/120) = 3  

So option 2 is correct.

​

Additional Information

• The first mirror was made by German Scientist Justus von Liebig. He coated the plane surface of a piece of ordinary glass with silver metal for making this mirror. Such a mirror is called a silvered glass mirror.
• Concave mirror: If the inner surface of the spherical mirror is the reflecting surface.
• Convex mirror: If the outer surface of the spherical mirror is the reflecting surface.

Ala-ud-din Khilji constructed Alai-Darwaza, the southern gateway of the Quwwat-ul-Islam mosque in Delhi.

• Jaisalmer is also known as the 'Golden City'.
• Jaisalmer is the largest district of Rajasthan which is spread over 38,401 sq. km. It shares the 471 km long international border with Pakistan.

Detailed information about other cities is in the following table:

• The Padma Awards are announced annually on the eve of Republic Day. This is one of the highest civilian honours of India.
• Padma Awards were started in the year 1954.
• The highest civilian award of India is Bharat Ratna which is awarded to a maximum of 3 awardees in a particular year.

 Important Points

• For 2024, the President had approved the conferment of 132 Padma awards, including two duo cases (in a duo case, the Award is counted as one). The list comprises 5 Padma Vibhushan, 17 Padma Bhushan and 110 Padma Shri Awards.
• In 2023, the President of India authorized the presentation of 106 Padma Awards, including: 91 Padma Shri Awards, 9 Padma Bhushan Awards, and 6 Padma Vibhushan Awards

Information about Padma Awards:

Additional information about days given in option:

• The Indian Army is set to commission the first batch of women soldiers by the year 2021.
• Women were given a permanent commission in only two streams prior to this announcement- Judge Advocate General and Army Education Corps.
• Other streams of Indian Army: 1.Signals 2.Army Aviation 3.Army Air Defence 4.Electronics and Mechanical Engineers 5.Army Service Corps 6.Army Ordnance Corps 7.Intelligence 8.Engineers
• The first batch of 100 women soldiers will be inducted in the army’s Corps of Military Police (CMP) by the end of 2021.
• Commander-in-Chief of Indian Army: President Ram Nath Kovind
• Chief of the Army Staff (COAS): General Manoj Mukund Naravane
• First Chief of Defence Staff: General Bipin Rawat
• Current Chief of Defence Staff: Lt General Anil Chauhan

Correct Answer Sonitpur Elephant Reserve

Key Points:

• Sonitpur Elephant Reserve is located in the state of Assam.
• Other Elephant reserve located in Assam: Dihing-Patkai ,Kaziranga-Karbi Anglong ,Dhansiri-Lungding,Chirang-Ripu
• In the year 1992, the Government of India launched the Project Elephant as a Centrally Sponsored Scheme.
• India has 27,312 elephants according to the 2017 All India Elephant Population Estimation. Karnataka has the highest (6049 elephants) population.
• The Government of Odisha has notified three elephant reserves. Information about it is given in the following table:

• In March 2019 India won its Fifth successive title at the South Asian Football Federation Women's Championship.
• India defeated host Nepal in the final by 3-1.
• By scoring 4 goals each India's Indumathi Kathiresan and Sabitra Tamang of Nepal topped tally of maximum goals in the tournament.
• The venue of tourlament was Sahid Rangashala stadium in Biratnagar, Nepal.
• Participant teams: India, Nepal, Bhutan, Bangladesh, Sri Lanka, Maldives.
• Indian women's football team captain: Loitongbam Ashalata Devi.
• Coach‎ of Indian women's football team: ‎Maymol Rocky

Key Points

• Cuprite (Cu₂O) is an ore of Copper.
• Hematite, magnetite, and siderite are main ores of Iron.
• Ores is an accumulation of any mineral mixed with other elements.
• If the mineral content in the ore is in adequate form then ores can be commercially viable for extraction.

Important Ores of Some Metals:

• Union Territories are covered under Part VIII of the Constitution of India.
• In Part VIII of the Constitution of India Articles 239 to 242 deal with the Union Territories.
• List of Union Territories: 1. Andaman and Nicobar 2. Chandigarh 3. Daman and Diu and Dadra and Nagar Haveli  4. Delhi 5. Jammu and Kashmir  6. Ladakh 7. Lakshadweep 8. Puducherry
• Recently parliament has amended Article 240(1) of the Constitution to merge 2 UTs into one which will be called UT of Dadra and Nagar Haveli and Daman and Diu.
• In August 2019 parliament passed the bill - Jammu and Kashmir (Reorganisation) Bill, 2019 which has removed Jammu and Kashmir's status of a state and converted it into 2 UTs - Jammu and Kashmir with a legislature and Ladakh without legislature.

• Solutions: A homogeneous mixture of two or more components.
• Solvent: Component of a solution, which is present in the largest proportion.
• Solutes: The other components which are in less proportion than the solvent
• Dissolution: The process of forming a solution by mixing solutes in a solvent.

Meaning of terms in options:

• National Commission for Backward Classes (NCBC) was established in 1993 as a statutory body.
• The 102^nd Amendment Act of 2018 inserted Article 338-B and gave constitutional status to the National Commission for Backward Classes (NCBC).
• The primary objective of the commission is to provide the constitutional and other legal safeguards of the socially and educationally backward classes. Recommending various welfare measures for the overall development of backward classes to state and central government.
• Policy matters affecting the socially and educationally backward classes are required to be consulted by central and state governments with NCBC.
• NCBC has all the powers of a civil court while investigating any matter or inquiring about any complaint.

Chairperson of National Commission for Backward Classes

• Panch Rathas at Mahabalipuram (also known as Mamallapuram) from north to south are in following order—1. Draupadi Ratha 2.Arjuna Ratha 3.Nakula-Sahadeva Ratha 4.Bhima Ratha 5.Dharmarja Ratha.
• These Panch Rathas located in Mahabalipuram dates back to the 7th century during the Pallava Dynasty. In ancient times Mahabalipuram was an important coastal town.
• There are three large sculptures of Lion, Elephant and Nandi Bull at Mahabalipuram.
• The shore temple at Mahabalipuram, Tamil Nadu was built during the reign of Narasimhavarman II.
• In October 2019 there was a 2^nd informal meeting between Indian Prime Minister-Narendra Modi and President of China- Xi Jinping at Mamallapuram. The first meeting was held in Wuhan, China, in April 2018.

Let CP of the article be Rs. 100

MP of the article = 100 × (125/100) = Rs. 125

SP of the article = 100 × (92/100) = Rs. 92

Discount = 125 – 92 = 33

Discount percentage = 33/125 × 100 = 26.4%

Short Trick:

-8 = 25 – x – (25x/100)

-8 = 25 – x – x/4

5x/4 = 33

x = 132/5 = 26.4%

If, x is added to each of 10, 16, 22 and 32, the numbers so obtained in this order are in proportion, then

According to the question

(10 + x) : (16 + x) :: (22 + x) : (32 + x)

(10 + x)/(16 + x) = (22 + x)/(32 + x)

We can solve this using cross multiplication or Using Componendo or Dividendo but hare we can solve this using equal difference between 16 – 10 = 6 and 32 – 22 = 10. For makes calculation easy and saves time.

6 × 5 = 30 and 10 × 3 = 30

Now,

5 (10 + x) = 3 (22 + x)

50 + 5x = 66 + 3x

2x = 16

x = 8

Now,

Let the mean proportional between the numbers (x + 1) and (3x + 1) be A, then

(x + 1) : A :: A : (3x + 1)

(8 + 1)/A = A/(3 × 8 + 1)

A² = 9 × (24 + 1)

A = √(9 × 25)

A = 3 × 5 = 15

Given:

Average of 4 numbers = 54.6

Concept Used:

Average = Sum of all Observation/ Number of Observation

Calculation:

Let us assume there are 4 numbers,

⇒ Sum of 4 numbers = 54.6 × 4 = 218.4

According to the question,

75% of the numbers of total numbers increased by 5.6 each

⇒ 4 × (3/4) × (54.6 + 5.6) = 3(54.6 + 5.6)

25% of the numbers of total numbers decreased by 8.4 each

⇒ 4 × (1/4) × (54.6 - 8.4) = (54.6 – 8.4) 

New sum of 4 numbers = 3(54.6 + 5.6) + (54.6 – 8.4)

⇒ New sum of 4 numbers = 3 × 60.2 + 46.2 = 180.6 + 46.2 = 226.8

New average of 4 numbers = 226.8/4 = 56.7

∴ The average of the numbers obtained is 56.7.

11 sin² θ – cos² θ + 4 sin θ – 4 = 0

Put θ = 30, and (satisfied)

Now,

$\Rightarrow \frac{{\cos 60; + ;\cot 60}}{{\sec 60 - \tan 60}}$

$\Rightarrow \frac{{\frac{1}{2}; + ;\frac{1}{{\sqrt 3 }}}}{{2 - \sqrt 3 }}$

$\Rightarrow \frac{{2{\rm{;}} + {\rm{;}}\sqrt 3 }}{{2\sqrt 3 {\rm{;}}\left( {2 - \sqrt 3 } \right)}}{\rm{;}} \times {\rm{;}}\frac{{\left( {2{\rm{;}} + {\rm{;}}\sqrt 3 } \right)}}{{\left( {2{\rm{;}} + {\rm{;}}\sqrt 3 } \right)}}$

$\Rightarrow \frac{{7{\rm{;}} + {\rm{;}}4\sqrt 3 }}{{2\sqrt 3 }}$

$\Rightarrow \frac{{12; + ;7\sqrt 3 }}{6}$

Detailed Method:

11 sin² θ – cos² θ + 4 sin θ – 4 = 0

⇒11 sin²θ – (1 – sin²θ) + 4 sin θ – 4 = 0

⇒11 sin²θ – 1 + sin²θ + 4 sinθ – 4 = 0

⇒12 sin²θ + 4 sin θ – 5 = 0

⇒12 sin²θ + 10 sinθ – 6 sinθ – 5 = 0

⇒2 sinθ (6sinθ + 5) – 1 (6sinθ + 5) = 0

⇒(2 sinθ – 1) (6 sinθ + 5) = 0

Taking,

⇒2 sin θ – 1 = 0

⇒sinθ = ½

⇒sinθ = sin 30

⇒θ = 30

Now,

$\Rightarrow \frac{{\cos 2;\theta ; + ;\cot 2\theta }}{{\sec 2\theta - \tan 2;\theta }}$

$\Rightarrow \frac{{\cos 60; + ;\cot60}}{{\sec 60 - \tan 60}}$

$\Rightarrow \frac{{\frac{1}{2}; + ;\frac{1}{{\sqrt 3 }}}}{{2 - \sqrt 3 }}$

$\Rightarrow \frac{{\frac{{2{\rm{;}} + {\rm{;}}\sqrt 3 }}{{2\sqrt 3 }}}}{{2 - \sqrt 3 }}$

$\Rightarrow \frac{{2{\rm{;}} + {\rm{;}}\sqrt 3 }}{{2\sqrt 3 {\rm{;}}\left( {2 - \sqrt 3 } \right)}}{\rm{;}} \times {\rm{;}}\frac{{\left( {2{\rm{;}} + {\rm{;}}\sqrt 3 } \right)}}{{\left( {2{\rm{;}} + {\rm{;}}\sqrt 3 } \right)}}$

$\Rightarrow \frac{{{{\left( {2{\rm{;}} + {\rm{;}}\sqrt 3 } \right)}^2}}}{{2\sqrt 3 }}$

$\Rightarrow \frac{{4{\rm{;}} + {\rm{;}}3{\rm{;}} + {\rm{;}}4\sqrt 3 }}{{2\sqrt 3 }}$

$\Rightarrow \frac{{7{\rm{;}} + {\rm{;}}4\sqrt 3 }}{{2\sqrt 3 }}{\rm{;}} \times {\rm{;}}\frac{{\sqrt 3 }}{{\sqrt 3 }}$

$\Rightarrow \frac{{12; + ;7\sqrt 3 }}{6}$

Shortcut Trick

Use the formula: (Price₁ ÷ (Articles₁ × (100 − Loss%))) = (Price₂ ÷ (Articles₂ × (100 + Profit%)))

2,160 ÷ (48 × 90) = 2,016 ÷ (n × 112)

2,160 ÷ 4,320 = 2,016 ÷ (n × 112)

1 ÷ 2 = 2,016 ÷ (n × 112)

n × 112 = 4,032 ⇒ n = 4,032 ÷ 112 = 36

∴ The correct answer is 36 articles.

Alternate Method

Given: Selling Price (SP₁) = Rs. 2,160 for 48 articles, Loss = 10%. Target Profit = 12% for SP₂ = Rs. 2,016.

Formulas: CP = SP × 100 ÷ (100 − Loss%) | SP = CP × (100 + Profit%) ÷ 100

⇒ SP of 1 article = 2,160 ÷ 48 = Rs. 45

⇒ CP of 1 article = 45 × (100 ÷ 90) = Rs. 50

⇒ Required SP of 1 article for 12% profit = 50 × (112 ÷ 100) = Rs. 56

⇒ Number of articles for Rs. 2,016 = 2,016 ÷ 56 = 36

∴ The correct answer is 36 articles.

Additional Information

Unitary Method in P&L

When solving for multiple articles, it is often easiest to find the Cost Price (CP) of a single unit first.

Profit and Loss Percentage

Profit or Loss is always calculated on the Cost Price (CP) unless stated otherwise in the question.

Given, PO = 16.8, PQ = 12 and PR = 19.2

From the following figure

Let the radius of the circle AO = OB = x, then

PA = (16.8 + x) and PB = (16.8 – x)

As we know,

PB × PA = PQ × PR

(16.8 – x) (16.8 + x) = 12 × 19.2

16.8² – x² = 12 × 19.2

x² = 16.8² – 12 × 19.2 = 12² (1.4² – 1.6) = 144 × (1.96 – 1.60)

x = √(144 × 0.36)

x = 7.2

Hence, 2x = 14.4

∴AB = 14.4

For easy calculation

Given,

PO = 16.8, PQ = 12 and PR = 19.2

Divided by 12, then

PO = 1.4, PQ = 1 and PR = 1.6

Let the radius of the circle AO = OB = x, then

PA = (1.4 + x) and PB = (1.4 – x)

As we know,

PB × PA = PQ × PR

(1.4 – x) (1.4 + x) = 1 × 1.6

1.96 – x² = 1.6

x² = 0.36

x = √0.36

x = 0.6

2x = 1.2

AB = 1.2

Multiply by 12 in 1.2 and get correct answer = 1.2 × 12 = 14.4

Given:

PS = 14 and PT = 12 and PQ = 24

Calculation:

In ΔPQR and In ΔPST

∠P = ∠P = common

∠PQR = ∠PTS = 58°

ΔPQR ∼ ΔPTS

As we know,

PR/PS = PQ/PT

PR/14 = 24/12

PR = 28

RT = PR – PT = 28 – 12 = 16 cm

∴ THe value of RT is 16 cm.

Using option 4

Assuming Income of A be 25% less than B

So, Income of A = 75, Income of B = 100

Savings of A  after expenditure of 60% = 75 - 60% of 75 = Rs.30

Savings of B after expenditure of 75% = 100 - 75% of 100 = Rs. 25

Savings of A is more than B by = (30 – 25)/25 × 100 = 20% (As the Question says the savings of A are 20% more than that of B Hence our assumption is correct)

Detailed Method:

Let the income of A and B be Rs. x and y respectively.

Savings of A = 40% of x

Savings of B = 25% of y

According to the question

(40% of x) = (25% of y) × (120/100)

x × 40% = y × 25% × 6/5

x : y = 3 : 4

Let income of A = 3 and income of B = 4

Income of A is less than that of B by = [(4 – 3)/4] × 100 = 25%

Short Trick:

U = upstream and D = downstream

3.6(U) + 5.4(D) = 54 and 5.4(U) + 3.6(D) = 58.5

Divide by 18

2U + 3D = 30 and 3U + 2D = 32.5

Now, Multiply by 3 in (1) and by 2 in (2), and then subtract (2) from (1), then

5D = 25 min

∴10D = 50 min

Detailed Method:

Let the speed of boat be x km/hr and speed of current be y km/hr

Upstream speed = (x – y) km/hr

Downstream speed = (x + y) km/hr

According to the question

3.6/(x – y) + 5.4/(x + y) = 54/60

5.4/(x – y) + 3.6/(x + y) = 58.5/60

Let 1/(x – y) = a and 1/(x + y) = b, then

3.6a + 5.4b = 54/60   ---(1)

5.4a + 3.6b = 58.5/60   ---(2)

Add equation (1) and equation (2)

9 (a + b) = 112.5/60

⇒a + b = 12.5/60

⇒a + b = 5/24   ---(3)

Subtract equation (2) from equation (1)

1.8 (b – a) = -4.5/60

⇒b – a = -2.5/60

⇒b – a = -1/24   ---(4)

Add equation (3) and equation (4)

2b = 4/24

⇒b = 1/12

⇒(x + y) = 12 km/hr

Downstream speed = 12 km/hr

∴Time taken to cover 10 km distance with downstream = 10/12 hr or (10/12) × 60 = 50 min

Let efficiency of y be 5 unit

Efficiency of X = 5 × (7/5) = 7

Efficiency of Z = 5 × (3/5) = 3

Total work = (5 + 7 + 3) × 21 = 315

Work done by y and Z in 35 days = (5 + 3) × 35 = 280

Remaining work = 315 – 280 = 35

∴Remaining work will be completed by X alone in = 35/7 = 5 days

20x² – 30x + 1 = 0

Divided by 4x

5x – 15/2 + 1/4x

5x + 1/4x = 15/2

As we know,

(5x + 1/4x)² = 25x² + 1/16x² + 2 × 5x × (1/4x)

(15/2)² = 25x² + 1/16x² + 10/4

25x² + 1/16x² = 225/4 – 10/4 = 215/4 = $53\frac{3}{4}$

Let the sum borrowed by A be Rs. x and by B be Rs. y, then

As we know,

A = P (1 + r/100)^t

According to the question

x (1 + 7/100)³ = y (1 + 7/100)⁴

x/y = [(1 + 7/100)⁴]/[(1 + 7/100)³]

x/y = (107/100)

Ratio of x : y = 107a : 100a

107a + 100a = 207a

207a = 51750

a = 51750/207

a = 250

∴The sum borrowed by A = 107a = 107 × 250 = 26750

Short Trick:

As we know, the difference between years 4 and 3 = 1 year, then

A : B = 107 : 100

107 + 100 = 207 unit

207 unit = 51750

1 unit = 250

107 unit = 26750

5 cosθ – 12 sin θ = 0

⇒5 cos θ = 12 sinθ

⇒sinθ/cosθ = 5/12

⇒tanθ = 5/12

As we know,

Hypotenuse = H, Perpendicular = P and Base = B

tan θ = P/B = 5/12

As we know,

H² = P² + B²

⇒H² = 12² + 5² = 144 + 25 = 169

⇒H = √169 = 13 cm

sinθ = P/H = 5/13 and cos θ = B/H = 12/13

Now,

(1 + sinθ + cos θ)/(1 – sinθ + cosθ)

⇒(1 + 5/13 + 12/13)/(1 – 5/13 + 12/13)

⇒(13 + 12 + 5)/(13 – 5 + 12)

⇒30/20

⇒3/2

[cosec (78 – θ) – sec (12 + θ) - tan (67 + θ) + cot (23 – θ)]/[tan13 cot 37 tan 45 tan53 tan77]

As we know,

cosec (90 – θ) = sec θ and tanθ cotθ = 1 and tan 45 = 1 and tan θ tan (90 – θ) = 1

⇒ [cosec (78 – θ) – cosec {90 - (12 + θ)} - tan (67 + θ) + tan {90 - (23 – θ)}]/1

⇒ [cosec (78 – θ) – cosec (78 - θ) - tan (67 + θ) + tan (67 + θ)]

⇒ 0

Ratio of volume before and after = 500 : 486

Again multiply by 2 in = 1000 : 972

Volume decreased by = 1000 – 972 = 28

As we know, 28 = 2.8%

Detailed Solution:

Let the radius of the cylinder be r cm and height of the cylinder be h cm,

As we know,

Volume of the cylinder = πr²h

New radius of the cylinder = r × (90/100) = 0.9r cm

New height of the cylinder = h × (120/100) = 1.2h cm

New volume of the cylinder = π × (0.9r)² × 1.2h = 0.81r² × 1.2h × π = 0.972rhπ

Required percentage = [(πr²h - 0.972πrh)/πrh] × 100 = 2.8%

Given:

When a positive number is divided by d, the remainder is 15

When ten times of the same number is divided by d, the remainder is 6

Calculation:

As given, Remainder is 15 so we can say the value of d is greater than 15. Only 16 and 18 is greater than 15.

Let us try with the least of the two options

Since the minimum value for the positive number, for 15 to be remainder when divided by 16 = 31

Ten times of 31 = 310

310/16 → 6 (remainder) 

Since from there only we got the solution, we need not check for 18 as it is asked for the least value of d.

So the value of d is 16.

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

$\frac{3}{5}; \times ;\frac{{15}}{8} \div \frac{4}{3}{\rm{;}} \times {\rm{;}}\frac{3}{{16}} - \left( {\frac{{16}}{5} \div \frac{9}{2}{\rm{;}} \times {\rm{;}}\frac{{16}}{3}} \right); \times ;\frac{5}{2}; + ;\frac{1}{2}; + ;\frac{1}{2}$

$\frac{3}{5}; \times ;\frac{{15}}{8} \div \frac{1}{4} - \left( {\frac{{16}}{5} \div 24} \right); \times ;\frac{5}{2}; + ;1$

$\frac{3}{5}; \times ;\frac{{15}}{8}{\rm{;}} \times {\rm{;}}4 - \left( {\frac{{16}}{5}{\rm{;}} \times {\rm{;}}\frac{1}{{24}}} \right); \times ;\frac{5}{2}; + ;1$

$\frac{9}{2} - \frac{2}{{15}}; \times ;\frac{5}{2}; + ;1$

$\frac{9}{2} - \frac{1}{3}; + ;1$

$\frac{{27 - 2; + ;6}}{6}$

$\frac{{31}}{6}$

$5\frac{1}{6}$

Given:

x² – xy + y² = 13      ----(1)

x⁴ + x²y² + y⁴ = 273 

Formula used:

(x2 – xy + y2)(x2 + xy + y2) = x4 + x2y2 + y4

Calculation:

(x² – xy + y²)(x² + xy + y²) = x⁴ + x²y² + y⁴

⇒ 13 × (x² + xy + y²) = 273

⇒ (x² + xy + y²) = 273/13 = 21      ----(2)

eq(2) - eq(1),

2xy = 8

⇒ xy = 4

∴ xy = 4

Total number of cars sold by companies A, B and D in 2017 = 52 + 53 + 75 = 180

Total number of cars sold by all four companies in 2018 = 63 + 67 + 76 + 74 = 280

Required ratio = 180 : 280 = 9 : 14

Total number of cars sold by companies A in 2017 and C in 2013 = 52 + 65 = 117

Total number of cars sold by all four companies in 2013 and 2016 = 45 + 63 + 65 + 67 + 72 + 58 + 70 + 63 = 503

Required percentage = [117/503] × 100 = 23.3%

Total number of cars sold by company A during 2014 to 2018 = 52 + 61 + 72 + 52 + 63 = 300

Average cars sold by A during 2014 to 2018 = 300/5 = 60

Cars sold by company C in 2018 = 76

The total number of cars sold by company C in 2018 exceeds the average number of cars sold by company A during 2014 to 2018 by = 76 – 60 = 16

The given table represents the sale (in thousands), so 16 = 16000

Calculation:

$\frac{{{x^2}{{\left( {x - 4} \right)}^2}}}{{{{\left( {x; + ;4} \right)}^2} - 4x}} \div \frac{{{{\left( {{x^2} - 4x} \right)}^3}}}{{{{\left( {x; + ;4} \right)}^2}}}; \times ;\frac{{64 - {x^3}}}{{16 - {x^2}}}$

⇒ $\frac{{{{\left( {x^2 - 4x} \right)}^2}}}{{{{\left( {x; + ;4} \right)}^2} - 4x}} \div \frac{{{{\left( {{x^2} - 4x} \right)}^3}}}{{{{\left( {x; + ;4} \right)}^2}}}; \times ;\frac{{4^3 - {x^3}}}{{4^2 - {x^2}}}$

⇒ $\frac{{{{\left( {x^2 - 4x} \right)}^2}}}{{{{\left( {x; + ;4} \right)}^2} - 4x}} \times \frac{(x+4)^2}{(x-4x)^3} \times \frac{(4-x)(4^2 +x^2 + 4x)}{(4 - x)(4 + x)}$

⇒ $\frac{1}{(x + 4)^2 - 4x} \times \frac{(x + 4)^2}{(x^2 - 4x)} \times \frac{4^2 + x^2 + 4x}{(4 + x)}$

⇒ $\frac{x \ \ 1}{(x + 4)^2 - 4x} \times \frac{(x + 4)}{(x^2 - 4x)} \times (4^2 + x^2 + 4x)$

⇒ $\frac{ 1}{x^2 +16+8x - 4x} \times \frac{(x + 4)}{x(x - 4)} \times (4^2 + x^2 + 4x)$

⇒ $\frac{(x+4)}{x(x -4)} \times \frac{16+x^2 + 4x}{x^2 +16+4x}$