SSC CGL Previous Paper (Held On: 7 June 2019 Shift 3) (Previous Year Paper)

Afghanistan, Indonesia and Nepal are situated in Asia whereas Ireland is situated in Europe.

Hence, Ireland is the odd one among the given options.

The least possible Venn diagram is:

Hence, the figure in option 1 is the correct answer.

27 : 8 → 8 × 3 = 24; 24 + 3 = 27

Similarly,

12 : 3 → 3 × 3 = 9; 9 + 3 = 12

Hence, ‘12 : 3’ is the correct answer.

343 = 7³

1331 = 11³

2197 = 13³

But 731 is not a perfect cube.

Hence, 731 is the odd one among the given options.

‘Judgement’ is ‘delivered’ by the concerned authority.

Similarly, ‘rules’ are ‘implemented’ by the concerned authority.

Hence, ‘implement’ is the correct answer.

Mnemonic is used to aid one’s memory.

Similarly, sedative is used to induce sleep.

Hence, ‘sedative: sleep’ is the correct answer.

F + 4 → J; L - 3 → I; P + 2 → R; 17 - 1 → 16 (+4; -3; +2; -1)

Similarly,

D + 4 → H; J - 3 → G; N + 2 → P; R - 1 → Q (+4; -3; +2; -1)

Hence, ‘HGPQ’ is the correct answer.

3, 4, 5, and 6 are adjacent to 1. Therefore, 2 is opposite to 1.

Hence, if 3 is at the bottom of the dice, then 5 is at the top.

Hence, the figure in option 3 is the correct answer.

The least possible Venn diagram is as follows:

Conclusions:

I. No quadrilateral is a rhombus. → False (some quadrilaterals are squares and all squares are rhombuses)

II. All rhombuses are squares. → False (it is possible but not definite)

III. Some quadrilaterals are rhombuses. → True (some quadrilaterals are squares and all squares are rhombuses)

Hence, only conclusion III follows.

ANGEL: A + 1 → B; N + 1 → O; G + 1 → H; E + 1 → F; L + 1 → M

Similarly

SAVAGE: S + 1 → T; A + 1 → B; V + 1 → W; A + 1 → B; G + 1 → H; E + 1 → F

Thus, the code for SAVAGE is ABWBHF.

Third alphabet of ABWBHF = W.

Hence, ‘W’ is the correct answer.

Hence, there are 29 triangles in the given figure.

The correct logical order is

Sickness → Hospital → Doctor → Medicine Store → Recovery → Home

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

Given: 60 * 10 / 40 + 6 – 5

After replacing the symbols: 60 / 10 + 40 - 6 * 5

60 / 10 + 40 - 6 * 5

= 6 + 40 - 6 * 5

= 6 + 40 - 30

= 46 – 30

= 16

Hence, 16 is the correct answer.

Here, the figure rotates in a clockwise direction. Also, the first and the third symbols in the ends of the figure interchange their positions each time.

Hence, the figure in option 1 is the correct answer.

(11, 16, 20): 16 - 11 = 5; 20 - 16 = 4.

Similarly,

(15, 20, 24): 20 - 15 = 5; 24 - 20 = 4.

Hence, ‘(15, 20, 24)’ is the correct answer.

1. cddabbcdcabbbddacb → does not follow any pattern

2. cddabbcddabbcddabb → follows a pattern

3. cdbabbcdcabbdddabb → does not follow a pattern

4 cdcabbcddabbaddabb → does not follow a pattern

The actual series is: cddabb cddabb cddabb

Hence, the missing letters are d, b, d, c, b.

67 - 42 = 25 (Alternate Numbers)

74 - 33 = 41 (Alternate Numbers)

Similarly,

68 - 52 = 16 (Alternate Numbers)

Hence, 16 is the correct answer.

Cost price of cycle = 4140 × $\frac{{100}}{{115}}$ = Rs. 3,600

Selling price of cycle to earn 25

 profit = 3600 + 25% of 3600 = 3600 + 900 = Rs. 4,500.

Hence, Rs. 4,500 is the correct answer.

Hence, the figure in option 1 is the correct answer.

Tamil Nadu is located in the South of India

Assam is located in the North-east of India.

Punjab is located in the North of India.

But Kerala is located in the South of India.

Hence, Kerala is the odd one among the given options.

H + 4 → L; L + 4 → P

D + 4 → H; H + 4 → L

P + 4 → T; T + 4 → X

L + 4 → P; P + 1 → Q

Hence, ‘LPQ’ is the odd one among the given options.

7 + 11 = 18

11 + 18 = 29

18 + 29 = 47

29 + 47 = 76

Hence, 47 is the correct answer.

Hence, the figure in option 2 is the correct answer.

1. FNMG: F + 1 → G; N - 1 → M

2. SKLV: S + 3 → V; K + 1 → L

3. BKJC: B + 1 → C; K - 1 → J

4. PXWQ: P + 1 → Q; X - 1 → W

Hence, ‘SKLV’ is the correct answer.

• Asian Games, also known as Asiad, is a multi-sport event held every four years among athletes from all over Asia.
• The most recent one was held in Palembang and Jakarta, Indonesia from 18 August-2 September 2018.
• The next games will be held from 10 to 25 September 2022 in China.

• The base financial year for the calculation of the all India Index of Industrial Production (IIP) is 2011-2012.
• IIP index shows the performance of different industrial sectors of the economy of India.
• It is published on a monthly basis by CSO (Central Statistical Organisation).

• The Qutub Minar was named after the Sufi saint Khwaja Qutbuddin Bakhtiyar Kaki.
• The foundation stone for it was laid by Qutub-ud-Din Aibak, while Iltutumish got it completed.
• The monument is a UNESCO World Heritage Site in Delhi.
• It has 5 storeys and is 73 m tall.
• Khwaja Qutbuddin Bakhtiyar Kaki was a Sufi saint of the Chishti order from Delhi.

• Bajrang Punia won gold in the Men’s freestyle wrestling 65 kg category at the Dan Kolov 2019 wrestling event.
• Pooja Dhanda won gold in the 59 kg category at the event held in Russia.
• Sakshi Malik claimed a silver medal in the 65 kg category.

• The Almatti dam project on the Krishna river was an issue between Karnataka, Andhra Pradesh and Maharashtra.
• It is a hydroelectric project situated in the Bagalkot district, North Karnataka.
• It was chosen for the World Bank’s Award of Excellence for best utilization of funds for renovation in order to increase the strength of the dam.

• Guru Arjan Sahib, the Fifth Nanak, conceived the idea of creating a central place of worship for the Sikhs and he himself designed the architecture of Sri Harmandir Sahib.
• The planning to excavate the Amrit Sarovar was chalked out by Guru Amardas Sahib, the Third Nanak, but it was executed by Guru Ramdas Sahib under the supervision of Baba Budha Ji.
• The land for the site was acquired by the earlier Guru Sahibs on payment or free of cost from the Zamindars (landlords) of native villages.
• It is an important pilgrimage site for Sikhs.
• The temple is plated with gold.
• It is built around a Sarovar which was completed by Guru Ram Das in 1577.

• Zoji La is an important road link between Srinagar on one side and Kargil and Leh on the other side.
• It separates Kashmir valley and Dras valley.
• After Fotu La, it is the second-highest pass on the Srinagar-Leh National Highway.

• The Chinese traveller Hiuen Tsang visited India during the reign of Harshavardhana.
• He is also known as the Prince of Pilgrims.
• Harshavardhana ruled North India from 606-647 CE. He was the ruler of the Vardhana dynasty.
• Chandragupta Vikramaditya, Chandragupta I, and Samudragupta were all the rulers of the Gupta dynasty.

• Flying Officer Avani Chaturvedi of the Indian Air Force (IAF) created history by becoming the first Indian woman to fly her first solo fighter flight in a Russian made MiG-21 fighter.
• Bhawana Kanth and Mohana Singh will also fly the same flight soon.
• The trio was inducted in the IAF in 2016.

• The Speaker decides on the issue related to the disqualification of a Member of Lok Sabha under Tenth Schedule.
• The 10th Schedule of the Indian Constitution is also known as Anti-Defection Law.
• It was inserted by the 52nd Amendment in 1985.
• Defection means to abandon an association or position.

• The theory that dinosaurs were driven to extinction by the aftermath of a large asteroid impact on Earth was given by Luis Alvarez.
• This theory is known as the Alvarez Hypothesis.
• Luis Walter Alvarez was an American physicist.
• He was awarded Nobel Prize in Physics in 1968.

• William Crookes discovered the element thallium.

The correct answer is Jhum

Key Points

• ‘Shifting cultivation is also known as Jhum in north-east India.
• Shifting cultivation is an agricultural practice, wherein, plots of land are temporarily cultivated and then the cultivator abandons it and moves to another plot, leaving it to revert to its natural vegetation.
• Yams, sugarcane, vegetables, etc. are some of the crops grown by this method.

The correct answer is 0.

Key Points

• The maximum number of nominated members to Lok Sabha is 0.
• In January 2020, the Anglo-Indian reserved seats in the Parliament and State Legislatures of India were discontinued by the 126th Constitutional Amendment Bill of 2019, when enacted as the 104th Constitutional Amendment Act, 2019.

Additional Information

• Parliament, also called the Sansad, is the legislature of the Union.
• It has the President, and two houses- the Upper House and the Lower House.
• The Upper House is also called the Rajya Sabha or the Council of States while the Lower House is called the Lok Sabha or the House of the people.
• The current strength of Lok Sabha is 543.

• William Thomson codified the first two laws of thermodynamics and deduced that the absolute zero of temperature is −273.15°C.
• He was honoured for this with the naming of the Kelvin temperature scale.
• He was an Irish-Scottish engineer and physicist.
• | Scientists | Nationality | Inventions/Discoveries | | --- | --- | --- | | William Crookes | British | Crookes tube | | Luis Alvarez | American | Alvarez hypothesis | | William Thomson | Irish-Scottish | codified the first two laws of thermodynamics | | Robert Hooke | London | Hooke's law |

• The Lorenz Curve indicates income distribution.
• It is a graphical representation of the distribution of wealth or of income.
• It was developed in 1905 by Max O. Lorenz to represent inequality of the wealth distribution.

• In March 2019, the Government of UAE launched the 'Lose to Win' programme to assist overweight employees shed extra kilos and adopt a healthy lifestyle.
• It was launched by its Ministry of Health and Prevention.
• The programme team comprises of health educators and nutritionists from the Ministry.

• Brazilian physicist and astronomer Marcelo Gleiser was awarded the 2019 Templeton Prize, worth $1.4 million, for his work blending science and spirituality.
• He is the first person from Latin America to win this prize.
• The Templeton Prize was started in the year 1972 by a famous investor John Templeton.
• Mother Teresa and Dalai Lama have also received it in the past.

• Alessandro Volta was the first person to isolate methane gas.
• He discovered that methane mixed with air could be exploded using an electric spark.
• He is also known for inventing electric battery and discovering contact electricity.
• | Scientists | Nationality | Discoveries/Inventions | | --- | --- | --- | | William Thomson | Irish-Scottish | Codified the first two laws of thermodynamics | | William Crookes | British | Crookes tube | | Louis Pasteur | French | Pasteurization | | Alessandro Volta | Italian | Isolated methane gas |

• Sanchi is famous for outstanding specimen of Buddhist art and architecture, belonging to the period between the 3rd century B.C. and the 12th century A.D.
• It is famous for its Stupa, situated in the Raisen district of Madhya Pradesh.
• The Great Stupa was commissioned by Ashoka in 3rd century BCE.
• It is one of the oldest stones structures of India.

• In March 2018, Indian actress Katrina Kaif was named as the new ambassador of the international award-winning non-profit organisation, Educate Girls.
• She will attempt to bring renewed focus to gender equality and girl child education.

• The Suri king Sher Shah Suri defeated Humayun to regain his kingdom in 1538.
• He was the founder of Suri Empire.
• He ruled from 1538-1545.
• Humayun was the second Mughal Emperor and son of Babur.
• Sikandar Shah Suri was the 6th ruler of the Suri Empire.

• Henry Moseley invented the atomic battery in 1913.
• His battery contained a spherical glass globe with a silver lining.
• The glass sphere had an emitter of a radioactive isotope of radium.
• The emitted charged particles caused a build-up of charge, which effectively created a radioactively powered capacitor from which an electric current could be extracted.
• | Scientists | Nationality | Inventions/Discoveries | | --- | --- | --- | | Henry Moseley | English | Atomic battery | | Benjamin Franklin | American | Franklin stove | | Alessandro Volta | Italian | Electric battery | | Louis Pasteur | French | Pasteurisation |

• Guru Arjan Dev was the fifth of the ten Sikh Gurus.
• Guru Arjan Dev was executed by Jahangir.
• Guru Arjan Dev is known and remembered as the founder of Golden Temple.
• Guru Nanak Dev Ji was the first Guru of Sikhs.
• The 10th and the last Guru was Guru Gobind Singh Ji.
• Guru Angad was second, Guru Hargobind was sixth, and Guru Ramdas was the fourth Guru.

• In March 2019, a science teacher from rural Kenya named Peter Tabichi won the prestigious Global Teacher Prize 2019, worth $1 million, which honours the world’s best teacher.
• He is a physics and maths teacher and was awarded for his achievements in a deprived school with a few textbooks and crowded classes.
• He teaches at Keriko Secondary school and gives away 80% of his income for helping poor students.

Time = $1\frac{1}{4}$ years = [5/4] × 12 = 15 months

Rate = 8% annum

If the interest is compounded 5 monthly, then

Time = 15/5 = 3

Rate = [8/12] × 5 = [10/3]%

As we know,

Amount = P [1 + (r/100)]

A = 8100 × (31/30) × (31/30) × (31/30) = 8937.3

∴ Interest = A – P = 8937.3 – 8100 = 837.3

We can write, 20% = 1/5 and 6.25 = 1/16

Let the marked price of the article be 100x.

SP of the article after two successive discounts = 100x × [4/5] × [15/16] = 75x

∵ Net gain of 20% is made on the CP

⇒ CP of the article = 75x × (100/120) = 62.5x

MP is more than CP by = 100x – 62.5x = 37.5x

∴ Required percentage = [37.5/62.5] × 100 = 60%

⇒ AB = 5 cm, and CD = 11 cm

⇒ AM = MB = 5/2 cm

⇒ CN = ND = 11/2 cm

Let ON be x cm and radius OB = OD = r cm

In ΔOND

⇒ (OD)² = (ND)² + (ON)²                     [By Pythagoras theorem]

⇒ r² = (11/2)² + (x)²

⇒ r² = (121/4) + x²      ----(1)

In ΔOBM

⇒ (OB)² = (OM)² + (MB)²                    [By Pythagoras theorem]

⇒ r² = (3 + x)² + (5/2)²

⇒ r² = 3² + x² + 6x + [25/4]      ----(2)

From equation (1) and equation (2)

⇒ [121/4] + x² = 9 + x² + 6x + [ 25/4]

⇒ 6x = [121/4] – [25/4] – 9

⇒ x = 5/2 cm

From equation (1)

⇒ r² = [121/4] + [5/2]²

⇒ r = √(146)/2

⇒ Diameter of the circle 2r = √146 cm

In ΔABC

⇒ BC = 10 and AD = 12 cm

As we know, AD is perpendicular to BC.

In right angled triangle ABD

⇒ AB² = BD² + AD² (Pythagoras theorem)

⇒ AB² = 5² + 12²

⇒ AB = 25 + 144 = 169 = 13 cm

Ratio of A and B = 7 : 12     ----(1)

Ratio of B and C = 8 : 5      ----(2)

Multiply by 2 in equation (1) and multiply by 3 in equation (2)

Ratio of A and B = 14 : 24

Ratio of A and B = 24 : 15

Ratio of A, B and C = 14 : 24 : 15

Difference of A and C = 15 – 14 = 1 unit

⇒ 1 unit represents = 214

⇒ A + B + C = 14 + 24 + 15 = 53 unit

53 unit will represent = 214 × 53 = 11,342

∴ Value of (A + B + C) = 11,342

Total production of type D cars in 2015 and type B cars in 2017 = 56 + 64 = 120 thousands

total production of cars in 2018 = 65 + 72 + 56 + 68 + 64 = 325 thousands

Average production of cars in 2018 = 325/5 = 65 thousands

∴ Required percentage = [(120 – 65)/120] × 100 = 45.83%

Total production of type A cars in 2016 and type E cars in 2014 = 44 + 46 = 90 thousands

total production of type C cars during 2014 to 2018 = 54 + 45 + 45 + 50 + 56 = 250 thousands

Required percentage = [90/250] × 100 = 36%

Inner radius of cylindrical road roller r = 27 cm

Outer radius of cylindrical road roller R = 27 + 9 = 36 cm

Height of road roller = 1 m = 100 cm

Volume of cylindrical road roller = π(R² – r²) h = π(36² – 27²) × 100 = 56700π cm³

Given that 1 cm³ = 8 g

Suppose, 56700π cm³ = X

X = 8 × 56700π = 453600π g

453600π g = 453.6π kg

Concept used:

Value of trigonometric functions at different angles 

Calculations:

sin²30° cos²45° + 4tan²30° + (sin²90°)/2 + 2cos90°

$\Rightarrow \frac{1}{{{2^2}}}{\rm{}} \times {\rm{}}\frac{1}{{{{\left( {\sqrt 2 } \right)}^2}}}{\rm{}} + {\rm{;}}4{\rm{;}} \times {\rm{}}\frac{1}{{{{\left( {\sqrt 3 } \right)}^2}}}{\rm{}} + {\rm{}}\frac{1}{2}{\rm{}} \times {\rm{}}1{\rm{}} + {\rm{}}2{\rm{}} \times {\rm{}}0$

$\Rightarrow \frac{1}{4}{\rm{}} \times {\rm{}}\frac{1}{2}{\rm{}} + {\rm{}}\frac{4}{3}{\rm{}} + {\rm{}}\frac{1}{2}{\rm{}} + {\rm{}}0$

⇒ 1/8 + 4/3 + 1/2

⇒ 47/24

∴ The correct answer is 47/24

If 10 digit number 67127y76x2 is divisible by 88, then number also divisible by 11 and 8 both.

⇒ 6x2 is divisible by 8 if x = 7 or 3

If x = 7, then,

⇒ 67127y7672 is divisible by 11 if y = 0

If x = 3, then

⇒ 67127y7632 is divisible by 11 if y = 7

When x = 7 and y = 0, then

⇒ 7x – 2y = 7 × 7 – 2 × 0 = 49

When x = 3, and y = 7, then

⇒ 7x – 2y = 7 × 3 – 2 × 7 = 21 – 14 = 7

Average of the first three numbers = 12

Sum of the first three numbers = 12 × 3 = 36

Let the greatest number among them be x.

According to the question

$\Rightarrow \left[ {{\rm{x}} - \frac{{\left( {36{\rm{;}} + {\rm{;x}}} \right)}}{4}{\rm{}} \times {\rm{}}\frac{1}{3}} \right]{\rm{}} = {\rm{}}19$

⇒ 12x – 36 – x = 19 × 12

⇒ x = 24

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

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

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

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

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

$\Rightarrow 6{\rm{}}-{\rm{}}6{\rm{;}} \div {\rm{;}}6{\rm{;}} \times {\rm{;}}6{\rm{}} + {\rm{}}\left( {6{\rm{;}} \div {\rm{;}}6{\rm{;of;}}6} \right){\rm{}} \times {\rm{}}6{\rm{;}}-\left( {3\frac{2}{3} \div \frac{{11}}{3}{\rm{;of;}}\frac{2}{3} \div 5} \right)$

$\Rightarrow 6 - 6 \div 6{\rm{}} \times {\rm{}}6{\rm{}} + {\rm{}}\left( {6 \div 36} \right){\rm{}} \times {\rm{}}6{\rm{}}-{\rm{}}\left( {\frac{{11}}{3} \div \frac{{22}}{9} \div 5} \right)$

$\Rightarrow 6 - 6 \div 6{\rm{;}} \times {\rm{;}}6{\rm{}} + {\rm{}}\frac{1}{6}{\rm{}} \times {\rm{}}6 - \left( {\frac{{11}}{3}{\rm{}} \times {\rm{}}\frac{9}{{22}}{\rm{}} \times {\rm{}}\frac{1}{5}} \right)$

⇒ 6 – 1 × 6 + 1 – 3/10

⇒ 1 – 3/10

⇒ 7/10

Let the income of Surbhi be 100x.

Expenditure of Surbhi = 100x × (75/100) = 75x

Savings of Surbhi = 100x – 75x = 25x

Surbhi’s new income = 100x × (120/100) = 120x

New savings of Surbhi = 25x × (99/100) = 24.75x

New Expenditure of Surbhi = 120x – 24.75x = 95.25x

∴ Required percentage = [(95.25x – 75x)/75x] × 100 = (20.25x/75x) × 100 = 27%

Shortcut Trick

Let Speed of A be x km/h. Speed of B = (x − 16) km/h.

Use formula: Difference in Time = (Distance × Difference in Speed) ÷ (Product of Speeds).

1 = (96 × 16) ÷ (x × (x − 16))

x(x − 16) = 1536. Testing options: 48 × (48 − 16) = 48 × 32 = 1536.

∴ The correct answer is 48 km/h.

Alternate Method

Given: Total Distance = 96 km, Time Difference = 1 hour, Speed of B = Speed of A − 16 km/h.

Formula: Time = Distance ÷ Speed

⇒ Time taken by B − Time taken by A = 1

⇒ [96 ÷ (x − 16)] − [96 ÷ x] = 1

⇒ 96 [ (x − (x − 16)) ÷ (x(x − 16)) ] = 1

⇒ 96 [ 16 ÷ (x² − 16x) ] = 1

⇒ x² − 16x − 1536 = 0

⇒ x² − 48x + 32x − 1536 = 0

⇒ x(x − 48) + 32(x − 48) = 0

⇒ (x − 48)(x + 32) = 0

⇒ x = 48 (Since speed cannot be negative)

∴ The correct answer is 48 km/h.

Additional Information

Relative Speed

When two objects move in the same direction, relative speed is the difference (S₁ − S₂); in opposite directions, it is the sum (S₁ + S₂).

Average Speed Formula

If a journey covers equal distances at speeds u and v, the average speed is (2 × u × v) ÷ (u + v).

Speed-Time Relation

For a constant distance, speed is inversely proportional to time. Ratio of speeds S₁:S₂ = Ratio of times T₂:T₁.

Important Trigonometric values

Calculation:

$\Rightarrow \left( {\frac{{2\tan 30^\circ }}{{1 - {{\tan }^2};30^\circ }}} \right){\rm{}} = {\rm{}}\frac{{2{\rm{}} \times {\rm{}}\frac{1}{{\surd 3}}}}{{1{\rm{}} - \frac{1}{3}}}{\rm{}} = {\rm{}}\frac{2}{{\surd 3}}{\rm{}} \times {\rm{}}\frac{3}{2}$

⇒ √3

∴ √3

Let the CP of the article be x.

If the person sells the article of 12% Profit, then SP of the article = x × (112/100)

If the person had purchased the article for 12% less, the new CP of the article = x × (88/100)

According to the question

⇒ [(112x/100) – 9] – (88x/100) = (27/100) × (88x/100)

⇒ 1.12x – 9 – 0.88x = 0.2376x

⇒ 1.12x – 1.1176x = 9

⇒ x = 9/0.0024 = 3750

Alternate solution∶

Let the cost price of the article be Rs. 100.

⇒ Selling price would be Rs. 112.

New cost price (12% less) = Rs  88

New selling price (27% profit) = 127% of 88 = Rs. 111.76

Now, the difference between both selling prices = 112 – 111.76 = Rs. 0.24

When the difference is 0.24, CP = Rs. 100

When the difference is 9, CP = 100 × 9/0.24 = Rs. 3750

Hence the cost price of the article is Rs. 3750.

Given:

$\frac{{6x}}{{\left( {2{x^2}{\rm{;}} + {\rm{;}}5x - 2{\rm{;}}} \right)}}{\rm{}} = {\rm{}}1$

Formula used:

(a + b)² - (a - b)² = 4ab

(a + b)³ = a³ + b³ + 3ab(a + b)

Calculation:

$\frac{{6x}}{{\left( {2{x^2}{\rm{;}} + {\rm{;}}5x - 2{\rm{;}}} \right)}}{\rm{}} = {\rm{}}1$

Divide by x

⇒ 6 = 2x + 5 – (2/x)

⇒ x – 1/x = 1/2

As we know, (x + 1/x)² – (x – 1/x)² = 4

⇒ (x + 1/x)² = 4 + 1/4 = 17/4

⇒ (x + 1/x) = √17/2

As we know, (x + 1/x)³ = x³ + 1/x³ + 3(x + 1/x)

⇒ (17 √17)/8 = x³ + 1/x³ + 3 × [√17/2]

⇒ x³ + 1/x³ = [17√17/8] – [3√17/2] = 5√17/8

∴ required value is 5√17/8

⇒ (8x³ + 27y³) ÷ (2x + 3y)

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

⇒ [(2x)³ + (3y)³] ÷ (2x + 3y)

⇒ [(2x + 3y) (4x² – 6xy + 9y²)] ÷ (2x + 3y)

⇒ (4x² – 6xy + 9y²)

Compare on (Ax² + Bxy + Cy²)

⇒ A = 4, B = (-6) and C = 9

⇒ 5A + 4B + 3C

⇒ 5 × 4 + 4 × (-6) + 3 × 9

⇒ 20 – 24 + 27

⇒ 23

Total production of type A cars in 2017 and type C cars in 2014 = 66 + 54 = 120 thousands

Total production of type B cars in 2014, type C cars in 2017 and type E cars in 2018 = 46 + 50 + 64 = 160 thousands

∴ Required ratio = 120 : 160 = 3 : 4

Total production of type D cars = 48 + 56 + 63 + 65 + 68 = 300 thousands

Total production of type D cars in 2017 = 65 thousands

⇒ 300 thousand represents = 360°

⇒ 65 thousand will represents = [360°/300] × 65 = 78°

⇒ ∠BQR = 70° (Given)

⇒ ∠BQR = ∠QBA = 70° (Alternate interior angle)

⇒ ∠BQR = ∠QAB = 70° (Alternate segment theorem)

In ΔAQB

⇒ ∠AQB + ∠QAB + ∠QBA = 180°

⇒ ∠AQB + 70° + 70° = 180°

⇒ ∠AQB = 180° – 140° = 40°

Detailed Method

$\Rightarrow \frac{{tan\theta }}{{1 - cot\theta }}{\rm{}} + {\rm{}}\frac{{\cot \theta }}{{1 - \tan \theta }}{\rm{}} = {\rm{}}1{\rm{;}} + {\rm{;}}k$

$\Rightarrow \frac{{tan\theta }}{{1 - \frac{1}{{tan\theta }}}}{\rm{;}} + {\rm{;}}\frac{{\frac{1}{{tan\theta }}}}{{1 - \tan \theta }}{\rm{}} = {\rm{}}1{\rm{}} + {\rm{}}k$

$\Rightarrow \frac{{ta{n^2}\theta }}{{tan\theta - 1}}{\rm{}} + {\rm{}}\frac{1}{{tan\theta (1 - \tan \theta )}}{\rm{}} = {\rm{}}1{\rm{;}} + {\rm{;}}k$

$\Rightarrow \frac{{(ta{n^3}\theta - 1)}}{{tan\theta \left( {tan\theta - 1} \right)}}{\rm{}} = {\rm{}}1{\rm{}} + {\rm{}}k$

$\Rightarrow \frac{{\left( {tan\theta - 1} \right)(ta{n^2}\theta {\rm{;}} + {\rm{;}}1{\rm{;}} + {\rm{;}}tan\theta )}}{{tan\theta \left( {tan\theta - 1} \right)}}{\rm{}} = {\rm{}}1{\rm{}} + {\rm{}}k$

$\Rightarrow \frac{{(ta{n^2}\theta {\rm{;}} + {\rm{;}}1{\rm{;}} + {\rm{;}}tan\theta )}}{{tan\theta }}{\rm{}} = {\rm{}}1{\rm{}} + {\rm{}}k$

⇒ tan θ + cot θ + 1 = 1 + k

⇒ [sin θ/cos θ] + [cos θ/sin θ] = k

⇒ (sin² θ + cos² θ)/(cos θ sin θ) = k

⇒ 1/(cos θ sin θ) = k

⇒ cosec θ sec θ = k

Short Trick

Put θ = 30°

$\Rightarrow \frac{{\frac{1}{{\sqrt 3 }}}}{{1 - {\rm{;}}\sqrt 3 }}{\rm{;}} + {\rm{;}}\frac{{\sqrt 3 }}{{1 - {\rm{;}}\frac{1}{{\sqrt 3 }}}}{\rm{}} = {\rm{}}1{\rm{}} + {\rm{}}k$

$\Rightarrow \frac{1}{{\surd 3\left( {1{\rm{;}} - \sqrt 3 } \right)}}{\rm{;}} + {\rm{;}}\frac{3}{{\left( {\sqrt 3 - {\rm{;}}1} \right)}}{\rm{}} = {\rm{}}1{\rm{}} + {\rm{}}k$

$\Rightarrow \frac{1}{{\sqrt 3 \left( {1 - \sqrt 3 } \right)}}{\rm{;}} \times {\rm{;}}\frac{{\left( {1{\rm{;}} + {\rm{;}}\sqrt 3 } \right)}}{{\left( {1{\rm{;}} + {\rm{;}}\sqrt 3 } \right)}}{\rm{;}} + {\rm{;}}\frac{3}{{\left( {\sqrt 3 - {\rm{;}}1} \right)}}{\rm{;}} \times {\rm{;}}\frac{{\left( {\sqrt 3 {\rm{;}} + {\rm{;}}1} \right)}}{{\left( {\sqrt 3 {\rm{;}} + {\rm{;}}1} \right)}}{\rm{}} = {\rm{}}1{\rm{}} + {\rm{}}k$

$\Rightarrow \frac{{3\left( {\sqrt 3 {\rm{;}} + {\rm{;}}1} \right)}}{2} - \frac{{\left( {1{\rm{;}} + {\rm{;}}\sqrt 3 } \right)}}{{2\sqrt 3 }}{\rm{}} = {\rm{}}1{\rm{}} + {\rm{}}k$

$\Rightarrow \frac{{9{\rm{;}} + {\rm{;}}3\sqrt 3 - 1 - \sqrt 3 }}{{2\sqrt 3 }} = 1 + k$

$\Rightarrow \frac{{4{\rm{;}} + {\rm{;}}\sqrt 3 }}{{\sqrt 3 }} - 1{\rm{}} = {\rm{}}k$

⇒ k = 4/√3

With the help of option 1

⇒ cosec θ sec θ

⇒ cosec30 sec30

⇒ 2 × 2/√3 = 4/√3 (satisfied)

Given, ∠B = 55° & ∠C = 35°

As we know,

⇒ ∠A + ∠B + ∠C = 180°

⇒ ∠A = 180° – 55° – 35° = 90°

∴ ∠BAN = (∠A/2) = 90/2 = 45

In ΔAMB

⇒ ∠BAM + ∠ABM + ∠BMA = 180

⇒ ∠BAM = 180° – 55° – 90°

⇒ ∠BAM = 35°

Now,

⇒ ∠MAN = ∠BAN – ∠BAM = 45° – 35° = 10°

Short trick

⇒ ∠MAN = (∠B – ∠C)/2 = (55° – 35°)/2 = 10°

Calculation:

$\Rightarrow \frac{1}{{{\rm{cosec\theta }} - 1{\rm{;}}}}{\rm{;}} + {\rm{;}}\frac{1}{{{\rm{cosec\theta }} + {\rm{}}1}}{\rm{}} = {\rm{}}2{\rm{;sec\theta }}$

$\Rightarrow \frac{{{\rm{cosec\theta ;}} + {\rm{;}}1{\rm{;}} + {\rm{;cosec\theta }} - 1}}{{{\rm{cose}}{{\rm{c}}^2}{\rm{\theta }} - 1}}{\rm{}} = {\rm{}}2{\rm{sec\theta }}$

-$\Rightarrow \frac{{2{\rm{cosec\theta }}}}{{{\rm{co}}{{\rm{t}}^2}{\rm{\theta }}}}{\rm{}} = {\rm{}}2{\rm{sec\theta }}$

$\Rightarrow \frac{{\frac{2}{{{\rm{sin\theta }}}}}}{{\frac{{{\rm{co}}{{\rm{s}}^2}{\rm{\theta }}}}{{{\rm{si}}{{\rm{n}}^2}{\rm{\theta }}}}}}{\rm{}} = {\rm{}}\frac{2}{{{\rm{cos\theta }}}}$

⇒ tan θ = 1

⇒ tan θ = tan 45°

⇒ θ = 45°

⇒ cot θ + cos θ

⇒ cot45° + cos45°

⇒ 1 + (1/√2)

⇒ (√2 + 1)/√2

Shortcut Trick

⇒ θ = 45°

⇒ [1/(√2 – 1)] + [1/(√2 + 1 )] = 2√2

⇒ √2 + 1 + √2 – 1 = 2√2

⇒ 2√2 = 2√2 (Satisfied)

⇒ cot θ + cos θ

⇒ cot45° + cos45°

⇒ 1 + (1/√2)

⇒ (√2 + 1)/√2

Efficiency ratio of A, B and C = 3 : 5 : 1

Total work = (3 + 5 + 1) × 5 = 9 × 5 = 45

Work done by A and B in three days = (3 + 5) × 3 = 24

Remaining work = 45 – 24 = 21

C will complete the remaining work in = 21/1 = 21 days

From the context of the passage, we can understand that the blank is a word that needs to be coupled with the verb 'stay' and it needs to mean 'to stay awake'.

Out of the given prepositions, only the preposition 'up' fits the context since the phrasal verb 'stay up' means to stay awake, esp. for a long time.

None of the other prepositions combines with 'stay' to convey this exact meaning. 

Hence, option 4 is correct.

The word 'transient' means 'temporary or lasting for only a short time'.

The meanings of the the other words are:

• Celestial - belonging or relating to heaven
• Temporal -  relating to time
• Stationary - not moving or not intended to be moved
• Permanent - lasting for a long time or for ever

We can see that the meaning of transient is completely opposite to the meaning of the word 'permanent'.

Hence, option 2 is correct.

The idiom 'bolt from the blue' means 'a sudden, unexpected event'. 

For example: The resignation of the chairman came like a bolt from the blue.

Out of the given options, we can see that option 2 exactly expresses this meaning.

Hence, option 2 is correct.

The sentence is in passive voice. In active voice. the object 'everyone' must be written before the subject 'hunchback.'

In passive voice:

Object + verb + by subject

In active voice :

Subject + verb + object

The tense here is past continuous thus 'was laughing' will be the correct verb to be used here.

Hence, option 3 is the correct answer.  All the other options make use of incorrect tenses thereby changing the meaning of the sentences.

The word 'fury' means 'wild or extreme anger'.

For example: The fury of the crowd was directed towards the police.

It is clear that 'fury' means the same thing as option 2 i.e. 'anger'.

Hence, option 2 is correct.

Here are the meanings of the given options:

• Bequeath -  to arrange for money or property to be given to somebody after your death
• Abdicate - to give up a throne, high office, dignity, or function
• Consign- to send something to someone
• Usurp -  to take control of a position of power, especially without having the right to

Out of the given words, we can see that the word 'abdicate' means exactly what the given words convey.

Here's an example: In 1918, Kaiser Wilhelm abdicated as German emperor.

Hence, option 2 is correct.

The word 'each' is always used to refer to a single individual. Even as it is followed by a plural noun such as in the construction 'each of the girls', the subject of the sentence will remain singular. 

Hence, the verb must also take its singular form. 

Therefore, the correct form of the verb should be 'has', not 'have' and the correct sentence will be: Each of the girls has given an impressive dance performance.

Hence, the correct answer is option 1, since that is the part of the sentence with error.

The correct answer is: Option 3.

Key Points

• The word "contemptible" means something or someone deserving contempt; despicable. (घृणित)
• Example: His contemptible behavior towards his colleagues made him very unpopular.
• "Correct word" refers to the accurate or proper spelling of a term. (सही शब्द)
• Example: The correct word for 'घृणित' in English is 'contemptible'.
• Hence, we can infer that the correct answer is 'Option 3'.

Therefore, the correct answer is: Option 3.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• Concious (सचेत): Incorrect spelling of 'conscious'.
• Example: She was conscious during the entire procedure.
• Complacant (आत्मसंतुष्ट): Incorrect spelling of 'complacent'.
• Example: His complacent attitude towards his work led to many mistakes.
• Corigible (सुधार योग्य): Incorrect spelling of 'corrigible'.
• Example: The errors in the document are corrigible.

The last part of the passage talks about 'Mo's calm breathing' and the sleepy effect it has on Meggie.

Out of the given options, the preposition 'beside' makes the most sense since it logically describes that Meggie and Mo are sitting next to each other. Meggie couldn't possibly hear Mo's breathing 'around' or 'under' her. Also, it is unlikely that Mo would be sitting 'behind' Meggie.

Therefore, option 1 is correct.

The first clause of the sentence in which the given blank is located, starts with the words 'when she'.

'She' i.e. Meggie must also be the person being discussed in the second clause since no other character is mentioned anywhere in the sentence.

Hence, the correct answer must be the pronoun 'her', referring to Meggie.

Therefore, option 4 is correct.

The first sentence of the passage should stand independent in meaning and introduce the topic of the passage.

While sentences A, C and D all seem independent, we can see that only sentence C introduces the broader topic that A and D further elaborate upon. 

Hence, sentence C is the first sentence.

Sentence B must be next since it directly refers to and expands upon 'these differences' that were being talked about in C ('people who think and act differently').

Now, out of the remaining two sentences, we can see that the next logical sentence should be sentence A, since sentence D is directly in response to the question that is asked by A. Hence, D must follow A.

Finally, the last sentence will be D and we can see that it elaborates upon and answers the questions asked in A before it.

Therefore, the order will be CBAD and the correct option is option 2.

Here are the meanings of the given words:

• Dissent -  a strong difference of opinion on a particular subject
• Difference - the way in which two or more things which you are comparing are not the same
• Deference- respect and politeness
• Descent - movement from a higher to a lower level or position

Out of the given words, we can see that 'dissent' is the most logical answer for the given blank. It conveys the meaning that the committee members could not agree about the budget for the function.

Hence, option 1 is correct.

The idiom 'kick up a row' means 'to show great anger about something, especially when this does not seem necessary'; in other words 'to create a fuss'.

For example: Rahul kicked up an enormous row about having to wait just 5 more minutes at the office.

We can see that option 4 mentions this meaning.

Hence, option 4 is correct.