SSC CGL Previous Paper (Held On: 6 June 2019 Shift 1) (Previous Year Paper)

Pattern followed is:

1^st term is divisible by 2 i.e. 8 is divisible by 2.

2^nd term is divisible by 3 i.e. 12 is divisible by 3.

3^rd term is divisible by 6 i.e. 24 is divisible by 6.

Similarly

6 is divisible by 2

9 is divisible by 3

18 is divisible by 6

Hence (6, 9, 18) is answer.

Pattern followed is:

C = 3, A = 1, B = 2.

3 × 1 × 2 = 6

B = 2, E = 5, D = 4.

2 × 5 × 4 = 40

Similarly

HAD = 8 × 1 × 4 = 32

Hence 32 is answer.

Interchanging × and +

$10 \times 5 \div 10 + 8 - 10 = \frac{{10; \times 5}}{{10}} - 2$

5 - 2 ≠ 16

Interchanging – and +

$10 - 5; \div 10 \times 8 + 10 = 10 - \frac{{5 \times 8}}{{10}} + 10$

10 - 4 + 10 = 16

Interchanging ÷ and ×

$10 + 5 \times 10 \div 8 - 10 = 10 + \frac{{50}}{8} - 10$

$\frac{{25}}{4} \ne 16$

Interchanging + and ÷

10 ÷ 5 + 10 × 8 - 10 = 2 + 80 - 10

82 - 10 ≠ 16

Hence we get correct equation by interchanging - and +.

Here if we rotate face 2 and take 2 on front side, the common faces with number 2, are in same positions. Hence 6 is opposite to 5 and 2 is opposite to 1.

Hence 3 will be at top when 4 is at bottom.

Tapti river flows into westward direction and falls into Arabian sea.

Rest three flow in eastward direction.

Hence Tapti is the odd among them.

Pattern followed is:

1^st image is related to 3^rd image and 2^nd image is related to 4^th.

Following this pattern 5^th image will be related to 3^rd image.

If horizontal arrows of 1^st image are reversed, and vertical arrows kept same we get 3^rd image.

Similarly

If horizontal arrows of 3^rd image are reversed, and vertical arrows kept same we get 5^th image.

Pattern followed is:

Hence E H G J is the answer.

The question figure is embedded in,

Hence, option 3 is the correct answer.

Logical sequence is:

Student – Education – Degree – Interview – Job – Retirement .

Hence, the correct answer is 1, 4, 6, 3, 2, 5.

Hence the total number of squares are 14.

Pattern followed is:

98 – 3 = 95

95 - 3² = 86

86 – 4 = 82

82 - 4² = 66

66 – 5 = 61

61 - 5² = 36

Hence 61 is the correct answer.

Pattern is as follows:

5² + 12² = 13²

Adding square of 1^st and 3^rd term gives square of 2^nd term.

15² + 13² ≠ 19²

6² + 8² = 10²

11² + 9² ≠ 15²

13² + 11² ≠ 17²

Hence (6, 10, 8) is the answer.

Apathy and Enthusiasm are Antonyms.

Condemnation means “very strong disapproval”

Reverence means “a feeling of great respect”

Treaty and Friendship are synonyms

Enrolment and Employment are synonyms

War and Attack are also synonyms.

Hence, "Condemnation: Reverence" is the answer.

The pattern followed here is:

Number × [ (Number + 1) ÷ 2 ] + { (Number + 1) ÷ 2 } = RHS

$7 \times \left[ {\left( {7 + 1} \right) \div 2} \right] + \left[ {\left( {7 + 1} \right) \div 2} \right] = 7 \times 4 + 4 = 32$

Option 1 :

$12 \times \left[ {\left( {12 + 1} \right) \div 2} \right] + \left[ {\left( {12 + 1} \right) \div 2} \right] = 12 \times 7.5 + 7.5; \ne 85$

Option 2 :

$16 \times \left[ {\left( {16 + 1} \right) \div 2} \right] + \left[ {\left( {16 + 1} \right) \div 2} \right] = 16 \times 8.5 + 8.5; \ne 145$

Option 3 :

$3 \times \left[ {\left( {3 + 1} \right) \div 2} \right] + \left[ {\left( {3 + 1} \right) \div 2} \right] = 3 \times 2 + 2; \ne 11$

Option 4 :

$13 \times \left[ {\left( {13 + 1} \right) \div 2} \right] + \left[ {\left( {13 + 1} \right) \div 2} \right] = 13 \times 7 + 7 = 98$

Hence, 13 : 98 is answer.

Pattern followed is:

Here repeating term is b a c d c a

“b a c d c a b a c d c a b a c d c a” is full series.

Hence dacbd is the answer.

Pattern followed is:

R – 1 = Q, Q + 2 = S, S + 1 = T

M – 1 = L, L + 2 = N, N + 1 = O

F + 1 = G, G + 1 = H, H + 1 = I

C – 1 = B, B + 2 = D, D + 1 = E

Hence, FGHI is different from the rest.

Ratio of milk and juice in Mixture 1 = 2 : 1

Ratio of milk and juice in Mixture 2 = 4 : 5

Given, equal volumes of the two mixtures are mixed together

According to the question,

Ratio of milk to juice in resulting mixture = (m1 + m2) / (j1 + j2)

⇒ (2/3 + 4/9) / (1/3 + 5/9)

⇒ (10/9) / (8/9)

⇒ 5 : 4

Tree diagram:

Hence F is Sister-in-law of C.

The least possible Venn diagram is as follows:

Conclusion:

Some animals are crows → False (Possibility but not definitely true).

Some animals are birds → True.

No animal is a crow → False (Possibility but not definitely true).

Thus, I and III forms a complimentary pair.

Hence, Conclusion II and either conclusion I or III follows.

The pattern is as follows:

All the given numbers are cube + 1 of any number except option 3.

65 = 4³ + 1 = 64 + 1 = 65

217 = 6³ + 1 = 216 + 1 = 217

338 = 7³ - 5 = 343 - 5 = 338

28 = 3³ + 1 = 27 + 1 = 28

Hence, "338" is different from the rest.

Hence, the correct answer is option 4.

All snakes are reptiles,

And some snakes are Poisonous.

Hence, the correct answer is option 4).

Pattern followed is:

Hence ADREGUTH is answer.

Group of people who go to Cinema is called Audience

Group of people who go to Church is called Congregation

Hence, Congregation is the correct answer.

• Galvanisation is the process of coating Zinc on Iron to prevent rusting.

• Mid-Day Meal is a school meal (Hot meal with milk 2 times a week) program of the Ministry of Human Resource Development (MHRD), Government of India to improve the nutritional status of children.
• It is a Centrally Sponsored Scheme and the cost is shared 60:40 between the Center and States (It is 90:10 for North Eastern states).
• The Government has also made Aadhaar mandatory for students to avail of the Mid-Day Meal Scheme.
• The scheme was launched by former Prime Minister of India, P. V. Narasimha Rao in 1995.
• Human Resource Development Union Minister is Ramesh Pokhriyal Nishank.

• The First capital of the Chalukya Dynasty was Aihole which is clear from the inscriptions found in the caves of Aihole. Later the capital was changed to Badami by Pulkeshin 1 in 543.
• Aihole Inscription - Pulakesin II of Chalukya dynasty.  (Most Important for the Exam)

Some of the contemporaries important for the Exam:-

The correct answer is Nathu La.

Key Points Nathu La Pass

• Nathu means 'listening ears', and La means 'pass'.
• Located on the Old Silk Route, Nathu La Pass connects Sikkim to China’s Tibet Autonomous Region.
• The Nathu La Pass which connects Sikkim with Tibet was closed after the Chinese aggression on India in 1962 but was reopened in 2006 as the governments of the two countries decided to enhance their trade through land routes.

Additional Information

• Ala-ud-din Khilji was the first Muslim ruler whose empire covered almost the whole of India up to its extreme south. He fought many battles, conquered Gujarat, Ranthambhor, Chittor, Malwa, and Deccan.
• He was the second and most powerful ruler of the Khilji Dynasty. He implemented price control measures for a wide variety of market goods.The taxation system of Alauddin Khilji lasted for a long period up to the twentieth century.
• He was the first Delhi Sultan to resort price control and rationing among the local poor.

The correct answer is Karnataka.

• Bandipur National Park located in Karnataka houses deers,  tigers, elephants and other species.

Additional Information

The following National parks are most famous in India

• Chlorofluorocarbons(CFCs) contain Chlorine. It reacts with ozone as follows: - Cl + O₃ → ClO + O₂. The important part is O₃(ozone) gets converted to O_2.(oxygen). CFCs have been phased out. Ozone blocks harmful UV rays from reaching earth. It is present in the stratosphere.
• Montreal Protocol → Agreement among member states to protect the Ozone layer.
• Ozone day is celebrated on September 16th and 2018 was themed "Keep Cool and Carry On".

The correct answer is Option 1 i.e. Information Technology

• The Quarternary sector is also known as the knowledge sector.
• Activities falling under it are known as specialized tertiary activities, which include information technology, mutual funds, hospitals, theatres, brokerage firms, etc.
• Fishery and mining belong to the primary sector, while manufacturing belongs to the secondary sector.

• In February 2019, Deepak Singh won a gold medal at the Makran Cup in Chabahar, Iran in boxing.
• Manish Kaushik, Lalit Prasad, Satish Kumar, Sanjeet and Duryodhan Singh Negi finished second to win silver medal.
• India won a total of 6 medals, one gold medal and five silver medals at the Makran Cup Boxing in Chabahar, Iran.

The correct answer is Calcium.

Important Points

• Calcium (Ca) is the most reactive metal amongst these.
• An element's reactivity decreases while going down the reactivity series.
• Reactivity of metals:
• K > Na > Ca > Mg > Al > Zn > Fe > Pb > Cu
• Gold, silver and copper are the least reactive metals and they are also known as noble metals.

• Rana Dasgupta was awarded the Rabindranath Tagore Literary Prize 2019 for the Novel 'Solo'.
• The award carries a Tagore statue, a cash prize of $10,000, and a certificate for contribution to literature.
• Yohei Sasakawa, Goodwill Ambassador of WHO for Leprosy Elimination was awarded the Rabindranath Tagore Literary Prize for social achievement.

• In February 2019, India won one gold medal and five silver medals at the Makran Cup Boxing in Chabahar, Iran.
• Deepak Singh won a gold medal at the Makran Cup in Chabahar, Iran in boxing.
• Manish Kaushik, Lalit Prasad, Satish Kumar, Sanjeet and Duryodhan Singh Negi finished second to win the silver medal.

• Au (gold) is the most ductile metal.
• A ductile substance is easily pulled or stretched into a thin wire without breaking.
• Gold has an enormous ability to get stretched.

The correct answer is Madhya Pradesh.

Key Points

• Nandana block print is practiced in the Tarapur village of Neemuch district in Madhya Pradesh.
• It is practiced by the Bhil tribe.

 Additional Information

The correct answer is Qutub-ud-din Aibak.

• Qutubuddin Aibak became the ruler of India after the death of Mohammad Ghori in the year 1206 AD.
• He founded the Slave Dynasty in India and was also known as Lakh Baksh because of his generosity.
• He died in the year 1210 AD while playing Chaugan or Polo.

The Indian constitution under Article 19 provides for free movement throughout the territory of India. 

• During a National emergency(Article ​352) all fundamental rights except Article 20 and 21. Article 20: Ex post facto law, double Jeopardy, self-incrimination.

The correct answer is Andre Marie Ampère.

Ampere had come with the theory of Electromagnetism and also its relation with light.

Electromagnetism:- Phenomenon where the flow of electric current in a conductor produced a magnetic field.

Additional Information

Ampere's law → The law states that the mutual action of two lengths of current-carrying wire is proportional to their lengths and to the intensities of their currents.

Quantum theory → Light consists of tiny particles which have wavelike properties. Light is composed of particles called photons.

International Day of Forests 2019 observed on 21st March themed "Forests and Education".

• NALSA(National Legal Services Authority) conducts Lok Adalats with statutory backing from the Legal Services Authority Act 1987. The Legal Services Act stipulates free legal aid should be provided to the weaker sections of the society.
• Arbitration and Conciliation Act: Consolidate and amend the law relating to domestic arbitration, international commercial arbitration.

Bagh in Madhya Pradesh has murals depicting the life of Buddha and other religious stories.

Mural are those painted directly on rock or wall and Fresco is painted on a plaster applied on rocks or walls

The following are a few ancient Indian caves and locations.

• Kailash Satyarthi won the Nobel peace price in 2014.
• He shared it with Malala Yousafzai.
• He won the award for his efforts towards improving education and the life of children.
• He started Bachpan Bachao Andolan.

Nobel Foundation gives away prizes for the following fields:-

World Water Day 2019 was observed on 22nd March with the theme "Leaving no one behind"

The correct answer is K Radhakrishnan.

Key Points

• Koppillil Radhakrishnan is an Indian space scientist.
• He led the Indian Space Research Organization (ISRO) between November 2009 and December 2014.
• He served as a Member of the Space Committee, Secretary of the Space Department, and Chairman of ISRO.

Additional Information

• The present chairman of ISRO is S. Somanath.
• Nandan Nilekani: Co-founder of Infosys, Chairman of UIDAI.
• Sundar Pichai: CEO of Google LLC.

• Slave dynasty was founded by Qutubuddin Aibak He is the first Muslim ruler among the given options. He became the ruler of India after the death of Mohammad Ghori in the year 1206 AD.
• The very first Muslim ruler of India is Mohammad Ghori who invaded India with the objective of ruling the country. He laid the foundation for Muslim Rule in India and is also known as the 'founder of Muslim Rule' in the country.
• Though he was defeated in the First Battle of Tarain in 1191, he defeated Prithviraj Chauhan in the Second Battle of Tarain in the year 1192.
• Later on, he defeated other rulers of various provinces in India to expand his kingdom.
• Mohammad Ghori passed away in the year 1206 after being attacked in the Dhamyak District of Jhelum (Now in Pakistan).

Total production of type D cars in five years = 46 + 50 + 54 + 68 + 67 = 285

⇒ Average production of type D cars in five years = 285/5 = 57

Production of type E cars in 2018 = 70

∴ Required percentage = [(70 – 57)/70] × 100 = 18.6 (Approx)

Total production of cars in 2018 = 38 + 40 + 54 + 68 + 70 = 270 thousand

Production of cars C in 2018 = 54 thousand

⇒ 270 thousand represents = 360°

∴ 54 thousand will represent = [360°/270] × 54 = 72°

Production of type B cars of 5 years = 54 + 45 + 47 + 50 + 40 = 236

Production of cars type A, B and D in 2017 = 43 + 50 + 67 = 160

∴ Required percentage = [(236 – 160)/160] × 100 = 47.5%

Production of type C cars in 2015 and type D in 2017 = 53 + 67 = 120 thousands

Production of type B cars in 2016 and type A in 2017 = 47 + 43 = 90 thousands

∴ Required ratio = 120 : 90 = 4 : 3

If A and B after crossing each other takes x and y hours, respectively, to reach their destinations then the ratio of their speed will be

(Speed of A) / (speed of B) = √(y/x)

According to the question

Speed of A/16.8 = √[8 ÷ (49/8)]

⇒ Speed of A/16.8 = √([8 × 8)/49] = 8/7

⇒ Speed of A = 8/7 × 16.8 = 19.2 km/hr

As we know, AR = AP, BP = BQ and QC = CR

⇒ AR = AP = 5cm and CR = QC = 6cm

⇒ AB = AP + BP

⇒ BP = 12 – 5 = 7

⇒ BP = BQ = 7cm

∴ Perimeter of triangle = AR + RC + QC + QB + BP + AP = 5 + 6 + 6 + 7 + 7 + 5 = 36 cm

Solution:

$\frac{{{\rm{sin\theta ;}}-{\rm{;cos\theta ;}} + {\rm{;}}1}}{{{\rm{sin\theta ;}} + {\rm{;cos\theta }} - 1}}$

Short trick∶

Put θ = 45°

⇒ (sin45° – cos45° + 1) / (sin45° + cos45° – 1)

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

⇒ 1/(√2 – 1)

⇒ √2 + 1

Go through option 3

⇒ sec45° + tan45°

⇒ √2 + 1 (Satisfied)

$∴ ;\frac{{\sin {\rm{\theta }} - \cos {\rm{\theta ;}} + {\rm{;}}1}}{{\sin {\rm{\theta ;}} + {\rm{;}}\cos {\rm{\theta }} - 1}}{\rm{}} = {\rm{;sec\theta }} + {\rm{;tan\theta }}$

∴ sec θ + tan θ

(5 + 3 ÷ 5 × 5) ÷ (3 ÷ 3 of 6) of (4 × 4 ÷ 4 of 4 + 4 ÷ 4 × 4)

⇒ (5 + 3/5 × 5) ÷ (3 ÷ 18) of (4 × 4 ÷ 16 + 1 × 4)

⇒ (5 + 3) ÷ 1/6 of (1 + 4)

⇒ 8 ÷ (1/6 × 5)

⇒ 8 ÷ 5/6

⇒ 8 × (6/5)

$\Rightarrow 9\frac{3}{5}$

Short trick∶

√(sec²θ + cosec²θ) × √(tan²θ – sin²θ)

Put θ = 45°

⇒ √(sec² 45° + cosec² 45°) × √(tan² 45° – sin² 45°)

⇒ √(2 + 2) × √[1 – (1/2)]

⇒ 2 × [1/√2]

⇒ √2

Going through option 2

sin θ sec²θ

⇒ sin 45°.sec² 45°

⇒  1/√2 × (√2)² = √2

Detailed solution∶

√(sec²θ + cosec²θ) × √(tan²θ – sin²θ)

⇒ √(1/cos²θ + 1/sin²θ) × √(sin²θ/cos²θ – sin²θ)

⇒ √[(sin²θ + cos²θ) / (sin²θ.cos²θ)] × √[sin²θ.(1/cos²θ – 1)

⇒ √[1/ (sin²θ.cos²θ)] × √[sin²θ.(1 – cos²θ) /cos²θ)

⇒ 1/ (sinθ.cosθ) × sin²θ/cosθ

⇒ sinθ.sec²θ

As we know, the difference between the loss percentage and the gain percentage = 10.5 – (-8)

According to the question

⇒ x × (18.5/100) = 92.50

⇒ x = Rs.500

∴ Required selling price = 500 × [112/100] = Rs. 560.

Alternate Method Given:

Selling price with 8% loss

If 10.5% Gain, then he would get Rs.92.50 more

Desired profit = 12%

Concept used :

Cost Price = Initial Selling Price / (1 - Loss%) and New Selling Price = Cost Price × (1 + Desired Profit%)

Calculation:

Change from 8% loss to 10.5% gain = 18.5% change = Rs. 92.50

⇒ 18.5% of Cost Price = Rs. 92.50

⇒ Cost Price = 92.50 / (18.5/100) = Rs. 500

⇒ Selling Price for 12% profit = Cost Price × (1 + 12%)

⇒ Selling Price = 500 × (1 + 12%) = Rs. 560

If 8 digit number 2074x4y2 is divisible by 88, the number will also be divisible by 8 and 11 both.

A number will be divisible by 8 if the last three digits of a number is divisible by 8.

The divisibility rule of 11 is that you must subtract and then add the digits in an alternating pattern from left to right. If your answer is 0 or 11 then it is divisible by 11.

⇒ 4y2 is divisible by 8 if y = 3 or 7

If y = 3, then

⇒ 2074x432 will be divisible by 11 if x = 9

If y = 7, then

⇒ 2074x472 is divisible by 11 if x = 5

Now we can say, if y = 3 then x = 9 and if y = 7, then x = 5

⇒ (4x + 3y)

⇒ (4 × 9 + 3 × 3) = 36 + 9 = 45

⇒ (4 × 5 + 3 × 7) = 20 + 21 = 41

⇒ √(x⁴ + y⁴ – 2x²y²)

As we know,

⇒ x² + y² – 2xy = (x – y)²

⇒ √(x² – y²)² = x² – y² = (x – y)(x + y)

$\Rightarrow \left( {{\rm{a}} + {\rm{;}}\frac{1}{{\rm{a}}} - {\rm{a;}} + {\rm{;}}\frac{1}{{\rm{a}}}} \right)\left( {{\rm{a;}} + {\rm{;}}\frac{1}{{\rm{a}}}{\rm{;}} + {\rm{;a}} - \frac{1}{{\rm{a}}}} \right)$

⇒ [2/a] × 2a

⇒ 4

Calculation:

If x is subtracted from each of 21, 22, 60 and 64, then all number will be in proportion

According to the question

(21 – x) / (22 – x) = (60 – x) / (64 – x)

By Dividendo and Componendo

⇒ (21 – x + 22 – x) / (21 – x – 22 + x) = (60 – x + 64 – x) / (60 – x – 64 + x)

⇒ (43 – 2x) / (-1) = (124 – 2x) / (-4)

⇒ 172 – 8x = 124 – 2x

⇒ 6x = 48

⇒ x = 8

∴ Required mean proportional = √[(8 + 1) (7 × 8 + 8)] = √(9 × 64) = 24

Shortcut Trick

Convert times to minutes: A = 60, B = 120, C = −75. LCM (Total Capacity) = 600 units.

Efficiencies: A = +10, B = +5, C = −8.

From 9 a.m. to 11 a.m. (2 hrs): Net fill = (10 − 8) × 120 = 240 units.

After 11 a.m. (B and C on): Net rate = 5 − 8 = −3 units/min (emptying).

Time to empty 240 units = 240 ÷ 3 = 80 minutes = 1 hour 20 minutes.

11:00 a.m. + 1 hr 20 min = 12:20 p.m.

∴ The correct answer is 12 : 20 p.m.

Alternate Method

Given: Filling time A = 60 min, B = 120 min. Emptying time C = 75 min.

⇒ Work done by A and C from 9:00 a.m. to 11:00 a.m. (120 min):

⇒ Filled quantity = (10 − 8) × 120 = 2 × 120 = 240 units.

⇒ At 11:00 a.m., A is closed and B is opened. Combined efficiency of B and C:

⇒ Net efficiency = 5 − 8 = −3 units/min (Emptying).

⇒ Time taken to empty 240 units = 240 ÷ 3 = 80 minutes.

⇒ 80 minutes = 1 hour 20 minutes.

⇒ Final time = 11:00 a.m. + 1 hour 20 minutes = 12:20 p.m.

∴ The correct answer is 12 : 20 p.m.

Additional Information

Efficiency Convention

In pipes and cisterns, inlet pipes are assigned a positive efficiency (+), while outlet/leakage pipes are assigned a negative efficiency (−).

Emptying Rate

If the net efficiency of the operating pipes is negative, the tank will eventually be emptied. The time taken is (Current Volume) ÷ (Net Emptying Rate).

Pipes & Cisterns Formula

Net work done in 1 hour = (1/x + 1/y − 1/z), where x and y are filling times and z is the emptying time.

In ΔABC,

If AB = BC

then ∠BAC = ∠BCA = 30°

⇒ ∠BAC + ∠BCA + ∠ABC = 180°

⇒ ∠ABC = 180° – 30° – 30° = 120°

⇒ ∠ABC = ∠ABD + ∠DBC

⇒ 120° = ∠ABD + ∠DBC

⇒ ∠ABD = 50°

As we know,

⇒ ∠ABD = ∠ACD = 50° (angles drawn from the same base to the circumference of circle)

and we can write ∠ACD = ∠PCD

or ∠PCD = 50°

Average of 13 numbers = 80

⇒ Sum of 13 numbers = 80 × 13 = 1040

Average of the first 5 numbers = 74.5

⇒ Sum of the first 5 numbers = 74.5 × 5 = 372.5

Average of next five numbers (6^th to 10^th) = 82.5

⇒ Sum of the next five numbers (6^th to 10^th) = 82.5 × 5 = 412.5

⇒ Sum of the last 3 numbers = 1040 – 372.5 – 412.5 = 255

Let the 12^th number be x.

11^th numbers = x + 6 and 13^th number = x + 6

According to the question

⇒ x + 6 + x + x + 6 = 255

⇒ x = 81

⇒ 11^th number = x + 6 = 81 + 6 = 87

⇒ x + 6 = 81 + 6 = 87

∴ Average of 11^th and 13^th number = (87 + 87)/2 = 87

and AC = 25 cm

⇒ 25² = 7² + 24²

Now we can say ΔABC right angle triangle 90° at B.

Point G is on BD

As we know, BD is circum-radius

⇒ circum-radius = ΔABC = (Hypotenuse)/2

= 25/2 cm

⇒ BD = BG + GD

⇒ BG : GD = 2 : 1

⇒ BG = (25/2) × (2/3) = 25/3 cm

$\therefore ;{\rm{BG}}; = ;8\frac{1}{3}{\rm{;}}$cm

Shortcut Trick

Interest for 1^st year = 16% of 15,000 = 2,400.

Interest for 2^nd year = 2,400 + (16% of 2,400) = 2,400 + 384 = 2,784.

The difference between CI of two consecutive years is the interest on the previous year interest.

Difference = 16% of 2,784 = 0.16 × 2,784 = 445.44.

∴ The correct answer is Rs. 445.44.

Alternate Method

Given:

Principal (P) = Rs. 15,000

Rate (R) = 16% p.a.

Formula Used:

Compound Interest for the n^th year = P(1 + R/100)ⁿ⁻¹ × (R/100)

Calculations:

⇒ CI for 2^nd year (CI₂) = 15,000 × (1 + 16/100)²⁻¹ × (16/100)

⇒ CI₂ = 15,000 × 1.16 × 0.16 = 2,784

⇒ CI for 3^rd year (CI₃) = 15,000 × (1 + 16/100)³⁻¹ × (16/100)

⇒ CI₃ = 15,000 × (1.16)² × 0.16

⇒ CI₃ = 15,000 × 1.3456 × 0.16 = 3,229.44

⇒ Difference = CI₃ − CI₂ = 3,229.44 − 2,784 = 445.44

∴ The correct answer is Rs. 445.44.

Additional Information

Relationship between Consecutive Year Interests

In compound interest, the interest for the (n+1)^th year is equal to the interest for the n^th year plus the interest on that interest: CI_n+1 = CI_n × (1 + R/100).

Difference between CI and SI for 2 years

The difference between Compound Interest and Simple Interest for 2 years is given by the formula: Difference = P × (R/100)².

Effective Rate for Compound Interest

For two years, the effective rate of interest is x + y + (xy/100). For 16%, it would be 16 + 16 + (256/100) = 34.56%.

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

⇒ (8x³ – 27y³) ÷ (2x – 3y)

⇒ [(2x)³ – (3y)³] ÷ (2x – 3y)

⇒ [(2x – 3y) {(2x)² + (3y)² + 2x × 3x}] ÷ (2x – 3y)

⇒ [4x² + 9y² + 6xy]

Comparing with (Ax² + Bxy + Cy²)

⇒ A = 4, B = 6 and C = 9

⇒ (2A + B – C) = 2 × 4 + 6 – 9 = 5

GIven:

Length of the cylinder (h) = 1.4 m = 140 cm, External radius of cylinder, R = 9 cm and internal radius of cylinder = r cm

Concept:

Volume of solid cylinder, $V_s=\pi R^2h$

Volume of hollow cylinder, $V_h=\pi (R^2-r^2)h$

Calculation:

Volume of hollow cylinder = $V_h= \pi (R^2-r^2)h$

$\Rightarrow 7480=\frac{22}{7} \times (9^2-r^2) \times 140$

$\Rightarrow(81-r^2) = 17$

⇒ r = 8 cm

∴ Thickness of the cylindrical pipe = R – r = 9 – 8 = 1 cm

As we know,

⇒ AP/PC = PB/PD

⇒ (3x – 1) / (5x – 3) = (2x + 1) / (6x – 5)

⇒ (3x – 1)(6x – 5) = (2x + 1)(5x – 3)

⇒ 18x² – 21x + 5 = 10x² – x – 3

⇒ 2x² – 5x + 2 = 0

⇒ (x – 2) (2x – 1) = 0

⇒ x = 2 and x = 1/2

Taking x = 2

⇒ BD = PD + BP = (6x – 5) + (2x + 1) = 6 × 2 – 5 + 2 × 2 + 1 = 12 cm

Given:

ab + bc + ca = 8 and a² + b² + c² = 20

Formula used:

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

Calculation:

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

⇒ (a + b + c)² = 20 + 2 × 8 = 36

⇒ (a + b + c) = 6

Now,

1/2 × (a + b + c)[(a – b)² + (b – c)² + (c – a)²]

⇒ 1/2(a + b + c)(a² + b² – 2ab + b2 + c2 – 2bc + c2 + a2 – 2ac) 

⇒ 1/2(a + b + c)[2(a2 + b2 + c2) – 2(ab + bc + ac)]

Now substituting the values,

⇒ (a + b + c)[(a2 + b2 + c2) – (ab + bc + ac)]

⇒ 6(20 – 8)

⇒ 6 × 12 = 72

∴ The required answer is 72.

Let the cost price of an article be 100x.

MP of an article = 100x × [140/100] = 140x

SP of an article = 140x × [75/100] = 105x

∴ Required profit percentage = [(105x – 100x)]/100x × 100 = 5%

Let the income of B be 100x.

Income of A = 100x × [150/100] = 150x

Sum of their income = 100x + 150x = 250x

New income of A = 150x × [140/100] = 210x

New income of B = 100x × [190/100] = 190x

Sum of their New income = 210x + 190x = 400x

∴ Required percentage = [(400x – 250x)/250x] × 100 = 60%

Given:

12cot² θ – 31cosec θ + 32 = 0

Calculation:

12cot2 θ – 31cosec θ + 32 = 0

⇒ 12(cosec²θ – 1) – 31cosec θ + 32 = 0

⇒ 12cosec² θ – 31cosec θ + 20 = 0

⇒ 12cosec² θ – 16cosec θ – 15cosec θ + 20 = 0

⇒ 4cosecθ(3cosec θ – 4) – 5(3cosec θ – 4) = 0

⇒ (4cosecθ – 5) (3cosec θ – 4) = 0

⇒ cosec θ = 5/4 or 4/3

⇒ sin θ = 4/5 or 3/4

We know that cos²θ = 1 – sin²θ

⇒ cos² θ = 1 – (4/5)² = 9/25 or 1 – (3/4)² = 7/16

⇒ cos θ = 3/5 or √7/4

⇒ tan θ = sin θ/cos θ

⇒ tan θ = (4/5) / (3/5) or (3/4) / (√7/4)

⇒ tan θ = 4/3 or 3√7/7

So, the value of  tan θ is 4/3 or 3√7/7

The correct answer is option 2.

Key Points

The misspelled word is 'expereince'.

• The correct spelling would be 'experience'.
• The word 'experience' is a noun and verb that refers to the practical contact with and observation of facts or events. (अनुभव)
• For Example -
• Her experience in the field of marketing is impressive.

Therefore, the correct answer would be 'experience'.

Additional Information

Let's understand the meanings of the other marked words - 

• Explain - make (an idea, situation, or problem) clear to someone by describing it in more detail or revealing relevant facts (समझाना)
• Except - not including; other than (सिवाय)
• Expire - (of a document, authorization, or agreement) come to an end (समाप्त होना)

The correct answer is option 1.

The burning of the effigy of Ravana on Dussehra symbolizes the burning of all evils.

Symbolizes means be a symbol of.

It is clear that symbolizes is the correct word as the sentence means that the burning of the effigy of Ravana on Dussehra is a symbol of burning evils.

Intensifies means to become or make more intense.

Epitomizes means be a perfect example of.

Personifies means represent (a quality or concept) by a figure in human form.

So, options 2,3 and 4 are incorrect.

The correct answer is option 1.

The first statement should be A i.e. '' Mango, the so-called "king of fruits", is something of a national obsession in India.'' This is because it gives a suitable introduction about what is going to be talked about in the following statements.

After A it should be D, i.e '' 2017 proved to be a very good year for mango lovers.'' This is because B and C seem to be in continuation with another statement.

After D it should be B as it gives the reason as to why 2017 was a good year for mango lovers.

The correct order is ADBC.

So, options 2,3 and 4 are incorrect.

The correct answer is victory

Key Points

• Triumph means a great victory or achievement.
  

For eg; This garden was built to celebrate the king's triumphs.

• Victory means an act of defeating an enemy or opponent in a battle, game, or other competition.
  

For eg; The victory in elections was most important to him.

• It is clear that triumph and victory are synonyms.

Additional Information

• Peace means freedom from disturbance; tranquillity.
• Attack means take aggressive military action against (a place or enemy forces) with weapons or armed force.
• Fight means take part in a violent struggle involving the exchange of physical blows or the use of weapons.
• So, options 1,2, and 4 are incorrect.

The correct answer is option 1.

The first sentence should be B i.e ''India is suffering from the worst water crisis, with one billion people living in water scarcity.'' This is because out of all the other sentences B gives an account of what is being talked about in the following sentences.

After B it should be A i.e '' Around 600 million of them live in areas of high to extreme water stress.'' This is because in B it was mentioned how many people lived in water scarcity and among these how many live in areas of high to the extreme water crisis is mentioned in A.

After A, it should be D as it gives the reason for the problem mentioned in the preceding statements.

The correct order is BADC.

So, options 2,3 and 4 are incorrect.

The correct answer is it will improve.

Key Points

• The given sentence is a first conditional sentence. It is used to talk about things that might happen in the future.
• The first conditional describes a particular situation.
• The first conditional has the present simple after 'if', then the future simple in the other clause.
• The format is: if + present simple, ... will + infinitive.
• Examples:
• If it rains, I won't go to the park.
• If I study today, I'll go to the party tonight.

Thus, the correct sentence is: If you listen to English news, it will improve your English.

The correct answer is Let the outer gate be locked at night

Key Points

• The given sentence is an imperative sentence in active voice.
• Sentences that express request, order, advice, suggestion, prohibition, etc., are called imperative sentences.
• The imperative sentence in the passive voice has the following structure:
• Let + object + be + past participle
• When the active voice begins with do not, the passive voice has the following structure:
• Let not + object + be + past participle
• Example:
  

Active: Bring it home.

Passive: Let it be brought home.

• Thus, the passive voice for the given sentence is: Let the outer gate be locked at night.

The correct answer is option 2.

Give someone the cold shoulder means to ignore someone or treat someone in an unfriendly way.

So, options 1,3 and 4 are incorrect.

The correct answer is calm down

Key Points

• Pull yourself together means to become calm after being angry or upset.
• For eg; You need to stop crying and pull yourself together.
• So, options 1,2, and 4 are incorrect.

The correct answer is option 2.

Slab means a large, thick, flat piece of stone or concrete, typically square or rectangular in shape.

Epitaph means a phrase or form of words written in memory of a person who has died, especially as an inscription on a tombstone.

So, clearly epitaph is the correct word.

Pillar means a tall vertical structure of stone, wood, or metal, used as a support for a building, or as an ornament or monument.

Basilica means a large oblong hall or building with double colonnades and a semicircular apse, used in ancient Rome as a law court or for public assemblies.

So, options 1, 3 and 4 are incorrect.

The correct answer is option 1.

Eminent means famous and respected within a particular sphere.

For eg; She was one of the most eminent personalities.

Inconspicuous means not clearly visible or attracting attention.

For eg; He had an inconspicuous behaviour.

It is clear that eminent and inconspicuous are antonyms.

Exalted means at a high or powerful level.

Impressive means evoking admiration through size, quality, or skill; grand, imposing, or awesome.

Distinguished means very successful, authoritative, and commanding great respect.

So, options 2,3 and 4 are incorrect.

The correct answer is option 2.

Key Points

• The correct spelling of the word in option 2 is contemporary. Contemporary things are modern and relate to the present time.
• ​Example: Perhaps he should have a more updated look, a more contemporary style.
• Controversial: If you describe something or someone as controversial, you mean that they are the subject of intense public argument, disagreement, or disapproval.
• Example: Immigration is a controversial issue in many countries.
• ​Conquer: If one country or group of people conquers another, they take complete control of their land.
• Example: During 1936, Mussolini conquered Abyssinia.
• ​Cooperation: the action or process of working together to the same end.
• ​Example: They worked in close cooperation with the British Tourist Authority

The correct answer is option 1.

I try to solve this problem at least for two hours. 

In the given sentence, the subject is performing a task in the present (present continuous tense will be used) which was started at some point in the past i.e for two hours. So, we will use the present perfect continuous tense in this sentence. For the present perfect tense, we use have been and for continuous we use trying. So, the correct sentence will be-