SSC CGL Previous Paper (Held On: 4 June 2019 Shift 1) (Previous Year Paper)

The pattern followed is:

Except the number 254, all other numbers are completely divisible by 7. 

Option 1: 254 is not completely divisible by 7.

254 ÷ 7 = 36.28. 

Option 2: 217 is completely divisible by 7.

217 ÷ 7 = 31.

Option 3: 126 is completely divisible by 7.

126 ÷ 7 = 18.

Option 4: 189 is completely divisible by 7.

189 ÷ 7 = 27.

Hence, the correct answer is "254".

(1^st term + 1) × 3^rd term = first two terms

217 → (2 + 1) × 7 = 21

126 → (1 + 1) × 6 = 12

189 → (1 + 1) × 9 = 18

254 → (2 + 1) × 4 = 12 ≠25

Hence, 254 is odd among given numbers.

Hence 3 is correct answer.

Pattern followed is:

“b c b a b b” is a repeating term in the series.

Complete series is b c b a b b | b c b a b b | b c b a b b

Hence c b b c b will complete the series.

Pattern followed is:

Similarly

Hence, ARTHROT is the correct answer.

Pattern followed is:

C + 3 = F, F + 3 = I, I + 3 = L

P + 3 = S, S + 2 = U, U + 3 = X

M + 2 = O, O + 2 = Q, Q + 2 = S

G + 1 = H, H + 1 = I, I + 1 = J

Difference between letters is not constant in PSUX.

Hence, PSUX is the correct answer.

Pattern followed is:

Similarly,

Hence, correct answer is BHFL.

Hence, option 3 is the correct answer.

Concepts of BODMAS rule:

• BODMAS has to be used when there is more than one operation in a mathematical expression. There is a sequence of certain rules that need to be followed when using the BODMAS method.

Conditions to follow:

• If there is any bracket, open the bracket, then add or subtract the terms. a + (b + c) = a + b + c,  a + (b - c) = a + b - c
• If there is a negative sign just open the bracket, multiply the negative sign with each term inside the bracket. a – (b + c) ⇒ a – b – c
• If there is any term just outside the bracket, multiply that outside term with each term inside the bracket. a(b + c) ⇒ ab + ac

Remember BODMAS Rule:

One easy way to remember the BODMAS rule is to perform these steps:

Checking each option one by one:

Interchanging + and ÷

$12-8\div 12\times 9+3=12-\frac{2}{3}\times 9+3$

$12-6+3=9$

Interchanging + and ×

$12-8\times 12+9\div 3=12-96+3$

$15-96\ne 9$

Interchanging + and –

$12+8-12\times 9~\div 3=12+8-12\times 3$

$20-36\ne 9$

Interchanging – and ÷

$12\div 8+12\times 9-3=\frac{3}{2}+108-3$

$\frac{3}{2}+105~\ne 9$

Hence, by interchanging + and ÷ we get the correct equation.

Some rulers are costly items → False (It is a possibility but not definite)

Some costly items are machines → True

All costly items are machines → False (It is a possibility but not definite)

Hence,only conclusion II follows.

DIG → D = 4, I = 9, G =7 → 4 + 9 + 7 = 20, 20 + 5 = 25

CUT → C = 3, U = 21, T = 20 → 3 + 21 + 20 = 44, 44 + 5= 49

Similarly,

KICK → K = 11, I =9, C = 3, K = 11 → 11 + 9 + 3 + 11 = 34, 34 + 5= 39

Hence, 39 is the correct answer.

Pattern followed is:

(√1^st + √3^rd) × 5 = 2^nd term

(√9 + √16) × 5 = (3 + 4) × 5 = 35

Similarly,

(√36 + √25) × 5 = (6 + 5) × 5 = 55

Hence, (36, 55, 25) is the correct answer.

The pattern followed is:

Hence,  the correct answer is "74".

7 – 3 = 4

7 + (4 × 2 + 1) = 16

16 – 7 = 9

16 + (9 × 2 + 1) = 35

35 – 16 = 19

35 + (19 × 2 + 1) = 74

74 – 35 = 39

74 + (39 × 2 + 1) = 153

Hence, 74 is the correct answer.

Logical sequence is:

Market – Vegetables – Buy – Cook – Dinner

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

Hence, total number of squares is 14.

Hence, option 4 is the correct answer.

A + B + C = 1875     → (1)

B + C = 2A

A + C = 4B

Putting value of B + C in equation 1,

2A + A = 1875

A = 625

Putting value of A + C in equation 1,

4B + B = 1875

B = 375

Putting values of A and B in equation 1,

625 + 375 + C = 1875

C = 875

C – A = 875 – 625 = 250

Hence, 250 is the correct answer.

Pattern followed is:

1^st image has 2 vertical lines and 1 horizontal line, 2^nd image is mirror image of 1^st image.

3^rd image has 3 vertical lines and 2 horizontal lines, 4^th image is mirror image of 3^rd image.

Hence 5^th image will have 4 vertical lines and 3 horizontal lines.

Only option with 4 vertical lines and 3 horizontal lines is option 2.

Hence, option 2 is the correct answer.

Fennel, Mustard, Cumin are Spices.

Groundnut is not a spice.

Hence, Groundnut is the odd among them.

Pattern followed is:

1^st term ×  2 × 3^rd term = 2^nd term 

3 × 2 × 4 = 24

Similarly,

4 × 2 × 9 = 72

Hence, the answer is (4, 72, 9).

Tree diagram:

Hence, His the nephew of F.

Pattern followed is:

Ratio  $\frac{36}{84}=~\frac{3}{7}$

Similarly,

$\frac{27}{63}=~\frac{3}{7}$ 

Hence, 27:63 is the correct answer.

Thesaurus is a book.  Book can be of multiple types Thesaurus is one of it.

Similarly

Python is a reptile. There are multiple reptiles, Python is one of them.

Hence,Reptile: Python is the correct answer.

In 1^st cube 5 and 6 are adjacent face to 1

If we turn the 2^nd cube so that 1 faces towards front then 3 will be opposite of 5.

4 is opposite of 1 as it is not adjacent to 1 in any diagrams.

So, 6 and 2 will be opposite to each other.

Hence, 2 will be at top when 6 is at bottom.

Hence, option 3 is the correct answer.

Lawyer is a person who is appointed to get Justice.

Similarly,

Arbitrator is a person who is appointed for settlement.

Hence, Settlement is the correct answer.

• The first female Director General of Police of Puducherry is Sundari Nanda.
• Sundari Nanda is an 1988 batch IPS officer and she was in Delhi Police before getting posted in Puducherry.
• Now, she has been transferred back to the Delhi Police.

• The 33rd edition of the India-Indonesia coordinated patrol (IND-INDO CORPAT) held from 19th March to 4th April 2019 was inaugurated at Port Blair, Andaman and Nicobar Islands.
• The aim of the coordinated patrol to underscore India’s peaceful presence and solidarity with friendly maritime neighbours to ensure good order in the maritime region.
• The ships and aircraft from both the countries were the part of this programme to patrol on the respective sides of the 236 nautical-miles-long International Maritime Boundary line.

• The Indian National Association was established in 1876 by Surendranath Banerjee and Anand Mohan Bose in Calcutta now Kolkata.
• The Indian National Association was initially established as Bharat Sabha and in 1885, it merged with Indian National Congress (INC).
• Surendranath Banerjee, an eminent leader of INC, is also known as RashtraGuru.

• The Economist Intelligence Unit has published a report titled - the world’s most expensive city based on the Worldwide Cost of Living Survey.
• Singapore marks its sixth straight year at the top of the rankings and is joined there by Hong Kong and Paris.
• Among the South Asian cities, Bengaluru, Chennai, New Delhi and Karachi feature among the 10 cheapest locations surveyed.

The correct answer is Mahmud of Ghazni.

Key Points

• Mahmud of Ghazni in 1025 AD attacked and looted the Somnath Mandir located Prabhas Patan near Veraval in Saurashtra on the western coast of Gujarat.
• Mahmud of Ghazni was the ruler of Afghanistan.
• The plundered Somnath Mandir was rebuilt by the Paramara king Bhoja of Malwa and the Solanki king Bhimdev I of Anhilwara between 1026 and 1042 AD.
• Mahmud of Ghazni was a Turkish conqueror who attacked India 17 times between 1000 to 1027 AD.
• The biggest invasion of Mahmud of Ghazni was in 1025 AD wherein he invaded the Somnath temple in Gujarat.
• In all his 17 invasions, a number of dynasties were conquered by him.

• The frozen state of Carbon dioxide (CO2) called dry ice.
• The dry ice does not melt into a liquid when heated but it changes directly into a gas.
• Dry ice used in hospitals and clinics, food processing units, industrial cleaning, theatrical and special effects etc.

• The lone gold medal for India was won by Kavinder Singh Bisht at the 38th GeeBee Boxing Tournament held at Helsinki, Finland.
• He defeated his opponent Mohammed Hussamuddin in summit clash in the 56kg category.
• Mohammed Hussamuddin is also an India boxer and he won bronze medal in the same event.

The correct answer is France.

• France was the first country in the world to implement the Good and Services Tax (GST) in 1954.
• Since its evolution, around 160 countries of the world have adopted this tax-system in some form or another.
• The countries like United Kingdom, Australia, Singapore, Canada, Italy, Spain Vietnam and now India have adopted this tax-system.
• GST is a value-added tax-system levied on most goods and services that are sold for domestic consumption.
• It is paid by the consumers while it remitted to the Government by the businesses offering goods and services.

• Malimath Committee Report was constituted by the Ministry of Home Affairs under the chairmanship of Justice V.S. Malimath, former Chief Justice of the Karnataka and Kerala High Courts.
• It has been constituted to recommend the admissibility of confessions made before a police officer as evidence in a court of law.
• The committee has submitted its recommendations but any of the recommendations have not been implemented so far.
• It has also suggested constituting a National Judicial Commission and amending Article 124 to make impeachment of judges less difficult.

• Queen Durgavati died fighting Mughal armies while defending Garha Katanga in 1564.
• She was the ruling Queen of Gondwana from 1550 until 1564.
• Khwaja Abdul Majid Asaf Khan after taking permission from Mughal Emperor Akbar invaded Rani Durgavati's state.
• The attack was a part of the Mughal empire's policy of expansionism and imperialism.
• Rani Durgavati preferred to die respectfully while fighting opponents rather than being an imperial slave of Mughals.

Additional Information

• Ahilyabai Holkar (31 May 1725 – 13 August 1795) was the hereditary noble Queen of the Maratha Empire, India. Ahilya was born in the village of Chondi in Jamkhed, Ahmednagar, Maharashtra. She moved the seat of her kingdom to Maheshwar, south of Indore on the Narmada River.
• Avantibai Lodhi (or Avanti Bai Lodhi; died 20 March 1858) was an Indian freedom fighter and the queen of Ramgarh (present-day Dindori) in Madhya Pradesh.

• The Musi and Bhima are tributaries of the river Krishna.
• Krishna river is one of the largest rivers in peninsular India.
• It flows through the states of Maharashtra, Andhra Pradesh and Karnataka.
• Other tributaries of Krishna river are Tungabhadra, Mallaprabha, Yerla, Ghataprabha, Dindi, Koyna and Dudhganga.

• The Tata Iron and Steel company (TISCO) was established by Dorabji Tata in 1907.
• He was committed to fulfill the the dream of his father, Jamsetji Nusserwanji Tata, an Indian Pioneer industrialist who founded the Tata Group.
• Dorabji Tata was knighted by Edward VII, becoming Sir Dorabji Tata in January 1910.

• The Wadiyar dynasty or Wodiyar dynasty ruled the Kingdom of Mysuru from 1399 to 1947.
• After getting independence from the British rule in 1947, the Kingdom of Mysuru joined in the subsequent unification of Indian dominion and princely states into the Republic of India.
• Wadiyar dynasty was established by Vijaya and ruled Mysuru from 1399 CE to 1423 CE.
• Vijaya's Wadiyar dynasty belong to the Arasu Wadiyar community of Karnataka that includes several noble clans of the region.

• Olympic Council of Asia (OCA) has decided to reintroduce cricket in the 2022 Asian Games to be held at Hangzhou, China after it was dropped in Asian Games 2018.
• Earlier, the game of Cricket was featured in Asian Games 2014 and 2010.
• In Asian Games 2014, Sri Lanka and Pakistan won the men's and women's gold respectively while in 2010, Bangladesh and Pakistan won the gold medals in the same category.
• The Indian Team did not participate in both the 2014 and 2010 Asian Games.

• Chham dance is a dance form of Himachal Pradesh but this festival is also popular in other Buddhist regions.
• This dance form is majorly associated with the Tibetan Buddhism that prospered in the Great Himalayan Mountain Range.
• It is celebrated in masked and costumed ritual with roots in Buddhism.
• In the places like Ladakh, Dharamshala, Lahaul Valley, Spiti Valley & Sikkim, and Bhutan and Tibet, the Chham folk dance is still in practice among the Buddhist people.

The correct answer is option 3, i.e. mangrove forests.

• Sundari, a well-known species of trees found in mangrove forests.
• The mangrove forests can survive in saline water.
• In India, Sundari trees are found in Sunderban delta in West Bengal and in Andaman and Nicobar Islands.
• The Sunderbans named after the Sundari trees.

• The property of catenation is predominant in Carbon.
• The capability of atoms forming a long chain by bonding with each other called catenation.
• It is the linkage of atoms of the same element to form long chains.
• The catenation process predominantly in carbon and it forms covalent bonds with other carbon atoms to form larger chains and structures.

• Methyl propane is an isomer of Butane.
• Butane has the chemical formula C₄H₁₀ and it has two structure isomers also called as unbranched butane, or normal butane, and isobutane, or i-butane.
• As per the IUPAC nomenclature practice, the isomers of methyl propane called as the butane and 2-methyl propane.
• Butane is a straight-chain alkane comprised of 4 atoms of carbon.
• It acts as a food propellant and a refrigerant.
• It is a gas molecular entity and an alkane.

• Metalloids are those elements whose properties are in between those of metals and solid non-metals or semiconductors.
• The six commonly known metalloids are boron, silicon, germanium, arsenic, antimony and tellurium.
• The metalloids have a metallic appearance, but they are brittle and only fair conductors of electricity.

The correct answer is Pramod Sawant.

Key Points

• The incumbent Chief Minister of Goa is  Pramod Sawant of the Bharatiya Janata Party, who was sworn in on 19 March 2019 after the demise of Manohar Parrikar on 17 March 2019.
• In Goa, the Chief Minister is the chief executive of the state.
• Pramod Sawant is the 13th Chief Minister of Goa and Dayanand Bandodkar was the first Chief Minister of Goa.

• Veeraswami Ramaswami was the first judge of the Supreme Court of India against whom the impeachment process was initiated in independent India.
• During the middle of the year 1990, several media houses reported about his pretentious spending on his official residence during his tenure as a Chief Justice of Punjab and Haryana High Court.
• For his impeachment, the Bar Association of Supreme Court had passed a resolution on February 1, 1991, and requested Chief Justice of India not to assign him any legal assignment further.
• The Bharatiya Janta Party along with Left parties submitted a notice of motion to Indian Parliament for his removal from the office.

• 'Thoda' sport is a form of martial art belonged to the state of Himachal Pradesh.
• A person need to have an expertise in archery to participate in this sport.
• Bows and arrows are the main weapons needed to play this sport.
• The objective of this sport is to create highly energetic atmosphere with continuous leg-kicking on one-hand and constant attempts to hit the target on the other.

• J J Thomson received the Nobel Prize in Physics for the discovery of the electron in 1906.
• His work is related to the idea electricity is transmitted by a tiny particle related to the atom was first forwarded in the 1830s.
• He managed to estimate its magnitude by performing experiments with charged particles in gases in 1890.
• He also concluded that electrons are part of atoms.

• The iron ore, Hematite mined in the Badampahar mines of Odisha.
• In Odisha-Jharkhand belt, the high-grade hematite ore is found in Badampahar mines in the Mayurbhanj and Kendujhar districts.
• In the adjoining Singbhum district of Jharkhand, hematite iron ore is mined in Gua and Noamundi.
• Very high-grade hematites are also found in the famous Bailadila range of hills in the Bastar district of Chhattisgarh.
• The range of hills comprises of 14 deposits of super high-grade hematite iron ore.
• It has the best physical properties needed for steel making.

• Mark Zuckerberg, full name Mark Elliot Zuckerberg is the founder of Facebook.
• He started Facebook from his college dorm room in 2004 with room-mates Dustin Moskovitz and Chris Hughes and from New York.
• He studied Computer Science at Harvard University before moving the company to Palo Alto, California.
• He was the Time Magazine Person Of The Year in the 2010.

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.

⇒ 2 × 3 ÷ 2 of 3 × 2 ÷ (4 + 4 × 4 ÷ 4 of 4 – 4 ÷ 4 × 4)

⇒ 2 × 3 ÷ 6 × 2 ÷ (4 + 4 × 4 ÷ 16 – 4 ÷ 4 × 4)

⇒ 2 × 1/2 × 2 ÷ (4 + 4 × 1/4 – 1 × 4)

⇒ 1 × 2 ÷ (4 + 1 – 1 × 4)

⇒ 1 × 2 ÷ (5 – 4)

⇒ 1 × 2 ÷ 1 = 2

Average of 12 numbers = 42

⇒ Sum of all 12 numbers = 12 × 42 = 504

Average of the first 4 numbers = 44

⇒ Sum of the first 4 numbers = 4 × 44 = 176

Average of last five numbers = 40

⇒ Sum of the last five numbers = 5 × 40 = 200

Let the 6^th number be x.

∴ 5^th number will be = x + 6

∴ 7^th number will be = x + 5

Sum of 5^th, 6^th and 7^th number = 504 – 176 – 200 = 128 cm

According to the question

⇒ x + x + 5 + x + 6 = 128

⇒ x = 39

⇒ 7^th number = x + 5 = 39 + 5 = 44

⇒ 5^th number = x + 6 = 39 + 6 = 45

∴ Average of 7^th and 5^th number = (44 + 45)/2 = 44.5

4 – 2sin²θ – 5cosθ = 0

Put θ = 60°

⇒ 4 – 2 × [3/4] – 5/2 = 0

⇒ 0 = 0 (Satisfied)

⇒ sin θ + tan θ

⇒ sin60° + tan60°

⇒ [√3/2] + √3

⇒ 3√3/2

Alternate solution:

4 – 2sin²θ – 5cosθ = 0

⇒ 4 – 2(1 – cos²θ) – 5cosθ = 0

⇒ 2cos²θ – 5cosθ + 2 = 0

⇒ 2cos²θ – 4cosθ – cosθ + 2 = 0

⇒ 2cosθ (cosθ – 2) – 1(cosθ – 2) = 0

⇒ (2cosθ – 1)(cosθ – 2) = 0

⇒ cosθ = 1/2

∴ θ = 60°

⇒ sin θ + tan θ

⇒ sin60° + tan60°

⇒ [√3/2] + √3

⇒ 3√3/2

9 digit number 985x3678y is divided by 72,

∴ We can say the number is also divisible by 8 and 9 both.

A number will be divisible by 8 if the last 3 digit of a number is divisible by 8.

⇒ 78y will be divisible by 8 if y = 4

A number will be divisible by 9 if the sum of the digits is divisible by 9.

⇒ 985x36784 will be divisible by 9 if x = 4

⇒ 4x – 3y = 4 × 4 – 3 × 4 = 4

⇒ sinθ = (Perpendicular)/(Hypotenuse) = (P² – 1)/(P² + 1)

By using Pythagoras theorem

⇒ (Hypotenuse)² = (Perpendicular)² + (Base)²

⇒ (P² + 1)² = (P² – 1)² + (Base)²

⇒ P⁴ + 1 + 2P² = P⁴ + 1 – 2P² + (Base)²

⇒ (Base)² = 4P²

⇒ Base = 2P

⇒ cosθ = (Base)/(Hypotenuse) = 2P/(P² + 1)

Given:

Decreasing 120 by x% gives the same result as increasing 40 by x%

Calculation:

According to the question

120 × [(100 – x)/100] = 40 × [(100 + x)/100]

⇒ (100 – x)/(100 + x) = 40/120 = 1/3

⇒ x = 50

Now, x% of 210 = 210 × 50/100 = 105

⇒ (x + 20)% of 180 = 180 × 70/100 = 126

∴ Required percentage = [(126 – 105)/126] × 100 = $16\frac{2}{3}\%$

Let the side of the bigger cube be 2 cm (or as you wish answer will be same in given condition)

Volume of the bigger cube = 2 × 2 × 2 = 8 cm

Let the side of smaller cube be x.

According to the question

⇒ x × 8 = 8

⇒ x = 1 cm

∴ Side of smaller cube be 1 cm.

As we know

Total surface area of the cube = 6 a²

Total surface area of the bigger cube = 6 × 2² = 6 × 4 = 24 cm²

Total surface area of the smaller cube = 6 × 1² = 6

Sum of the surface area of three of the smaller cubes = 3 × 6 = 18

∴ Required ratio = 24 : 18 = 4 : 3

⇒ x⁴ + x^-4 = 194

As we know,

⇒ x² + x^-2 = √(194 + 2) = √196 = 14

⇒ x + x^-1 = √(14 + 2) = √16 = 4 ----(1)

⇒ x – x^-1 = √(14 – 2) = √12 = 2√3         ----(2)

Adding equation (1) and equation (2)

⇒ 2x = 2√3 + 4

⇒ x = √3 + 2

⇒ x – 2 = √3

⇒ (x – 2)² = 3

Shortcut Trick

Ratio of areas of similar triangles is equal to the square of the ratio of their corresponding altitudes.

Area(ΔAFE) : Area(ΔABC) = 1 : 2

⇒ (AG / AD)² = 1 / 2

⇒ AG / AD = 1 / √2

⇒ AD = √2 × AG

⇒ (AG + GD) = √2 × AG ⇒ GD = (√2 − 1)AG

∴ The correct answer is (√2 - 1) : 1.

Alternate Method

Given: FE || BC, Area(ΔAFE) = Area(BCFE), AD ⊥ BC.

Formula: For two similar triangles, Area₁ / Area₂ = (h₁ / h₂)².

⇒ Area(ΔAFE) = Area(BCFE)

⇒ Area(ΔABC) = Area(ΔAFE) + Area(BCFE) = 2 × Area(ΔAFE)

⇒ Since FE || BC, ΔAFE ∼ ΔABC by AA similarity.

⇒ Area(ΔAFE) / Area(ΔABC) = (AG / AD)²

⇒ 1 / 2 = (AG / AD)²

⇒ AG / AD = 1 / √2

⇒ AD = AG × √2

⇒ GD = AD − AG = AG√2 − AG = AG(√2 − 1)

⇒ GD / AG = (√2 − 1) / 1

∴ The correct answer is (√2 - 1) : 1.

Additional Information

Area of Similar Triangles

If two triangles are similar, the ratio of their areas is equal to the square of the ratio of any two corresponding linear dimensions (sides, altitudes, medians, or perimeters).

Basic Proportionality Theorem

If a line is drawn parallel to one side of a triangle intersecting the other two sides, it divides the two sides in the same ratio and creates a smaller triangle similar to the original.

Height Ratio in Similarity

For ΔAFE ∼ ΔABC, the ratio of altitudes AG/AD is equal to the ratio of corresponding sides FE/BC.

Given:

 x + y + z = 19

 x² + y² + z² = 133

 xz = y²

Formula Used:

(a + b)² = a² + b² + 2ab

(a - b)2 = a2 + b2 - 2ab

Calculation:

 x + z = 19 – y

 x² + z² = 133 – y²

Square on both side

x² + z² + 2xz = 361 + y² – 38y  

⇒ 133 – y² + 2y² = 361 + y² – 38y [x² + z² = 133 – y² and xz = y²]

⇒ 38y = 361 – 133 = 228

⇒ y = 6

(x – z)² = x² + z² – 2xz

⇒ (x – z)² = 133 – y² – 2y²

⇒ (x – z)² = 133 – 3y²

⇒ (x – z)² = 133 – 3 × 6²

⇒ (x – z)² = 25

⇒ (x – z) = √25 = 5

∴ The  difference between z and x is 5

As we know,

⇒ AR = AQ, BR = BP and QC = CP

⇒ AQ = 4.5 cm and PC = 5.5 cm and BR = 6 cm

⇒ AQ = AR = 4.5 cm and PC = QC = 5.5 cm

⇒ BR = BP = 6 cm

Perimeter of triangle = AR + BR + BP + PC + CQ + AQ = 4.5 + 6 + 6 + 5.5 + 5.5 + 4.5 = 32 cm

⇒ Production of cars of type A in 2014 and type C in 2013 = 48 + 36 = 84

⇒ Production of cars of type B in 2016 and type E in 2015 = 56 + 35 = 91

∴ Required ratio = 84 : 91 = 12 : 13

Production of cars type D over the years = 51 + 24 + 30 + 46 + 54 = 205

Average production of type D cars over the years = 205/5 = 41

Production of type B cars in 2014 and 2015 are 40 and 38 thousands respectively.

Now, we can say there are 2 years in which the production of cars of type B is less than the average production of type D cars over the years.

Production of type B cars in 2012, 2014 and 2015 = 42 + 40 + 38 = 120 thousands

Production of type A cars in 2013 and 2016 = 35 + 56 = 91 thousands

⇒ Required percentage = [(120 – 91)/91] × 100 = 31.9% (Approx)

Shortcut Trick

The angle bisectors of ∠B and ∠C meet at the incenter O inside ΔABC.

Using the standard incenter angle formula:

∠BOC = 90° + ∠A ÷ 2

⇒ 122° = 90° + ∠A ÷ 2 ⇒ ∠A ÷ 2 = 32° ⇒ ∠A = 64°

∴ The correct answer is 64°.

Alternate Method

Given:

In ΔABC, the bisectors of ∠B and ∠C meet at point O.

∠BOC = 122°

Formula Used:

Sum of angles in a triangle is 180°.

Angle bisector divides an angle into two equal halves.

Calculations:

Let the angles of ΔABC be ∠A, ∠B, and ∠C.

Since OB and OC are the angle bisectors of ∠B and ∠C respectively:

⇒ ∠OBC = ∠B ÷ 2

⇒ ∠OCB = ∠C ÷ 2

In ΔOBC, the sum of angles is 180°:

⇒ ∠OBC + ∠OCB + ∠BOC = 180°

⇒ ∠B ÷ 2 + ∠C ÷ 2 + 122° = 180°

⇒ (∠B + ∠C) ÷ 2 = 180° − 122°

⇒ (∠B + ∠C) ÷ 2 = 58°

⇒ ∠B + ∠C = 58° × 2 = 116°

In ΔABC, the sum of angles is 180°:

⇒ ∠A + ∠B + ∠C = 180°

⇒ ∠A + 116° = 180°

⇒ ∠A = 180° − 116°

⇒ ∠A = 64°

Option Evaluation:

⇒ Option (1) 72°: If ∠A = 72°, then ∠BOC = 90° + 72° ÷ 2 = 126°, which does not match the given 122°.

⇒ Option (2) 64°: If ∠A = 64°, then ∠BOC = 90° + 64° ÷ 2 = 122°, which perfectly matches the given 122°.

⇒ Option (3) 62°: If ∠A = 62°, then ∠BOC = 90° + 62° ÷ 2 = 121°, which does not match the given 122°.

⇒ Option (4) 68°: If ∠A = 68°, then ∠BOC = 90° + 68° ÷ 2 = 124°, which does not match the given 122°.

∴ The correct answer is 64°.

Additional Information

Incenter of a Triangle

The point of intersection of the internal angle bisectors of a triangle is called the incenter. It is the center of the circle that touches all three sides of the triangle internally.

Excenter Angle Formula

If the external bisectors of ∠B and ∠C meet at an excenter E outside the triangle, then the angle formed is ∠BEC = 90° − ∠A ÷ 2.

Angle Bisector Theorem

An angle bisector of an angle of a triangle divides the opposite side into two segments that are proportional to the other two sides of the triangle.

Total production of type E cars over the year = 20 + 42 + 40 + 35 + 43 = 180

Production of type E cars in 2013 = 42 thousands

180 thousands represents = 360°

∴ 42 thousands will represent = [360°/180] × 42 = 84°

Let the cost of the article be x.

If he sold the article at a loss of 15% then SP of the article = x × [85/100] = 85x/100

If he sold the article at a gained of 9%, the SP of the article = x × [109/100] = 109x/100

According to the question

[109x/100] – [(85x)/100] = 30.60

⇒ x = 127.5

CP of the article = Rs. 127.5

SP of the article if he sold at 10% profit = 127.5 × [110/100] = Rs. 140.25

The ratio of the efficiency of A, B and C = 2 : 5 : 3

Total work = (2 + 5 + 3) × 27 = 270

⇒ 4/9^th part of the total work = 270 × [4/9] = 120

∴ Required time = 120/(5 + 3) = 120/8 = 15 days

Let the sum be Rs. x.

After 3 years, amount will be Rs. 8,028 and then after another 3 years amount will be Rs. 12,042.

⇒ [8,028/x] = [12,042/8,028]

⇒ x = (8,028 × 8,028)/12,042 = Rs. 5352

Alternate method,

p (1 + R/100)³ = 8028

⇒ (1 + R/100)3 = 8028/p ---- (i)

and,

p (1 + R/100)⁶ = 12042

(1 + R/100)6  = 12042/p ---- (ii)

from (i) and (ii), we get

(8028/p)² = 12042/p

therefore p = Rs. 5352

Total discount = [259.20/720] × 100 = 36%

Now, use this trick: Go through option (C)

Single equivalent discount of two successive discount of 20%.

⇒ 20 + 20 – (20 × 20)/100 = 36%

$\frac{{2 + {{\tan }^2}\theta + {{\cot }^2}\theta }}{{\sec \theta ;cosec;\theta }}$

$\Rightarrow ;\frac{{1 + {{\tan }^2}\theta ; + ;1; + ;{{\cot }^2}\theta }}{{\sec \theta ;cosec;\theta }}$

As we know, 1 + tan² θ = sec² θ and 1 + cot² θ = cosec² θ

$\frac{{{{\sec }^2}\theta + {\rm{cose}}{{\rm{c}}^2}\theta }}{{\sec \theta ;cosec;\theta }}$

$\Rightarrow \frac{{\frac{1}{{co{s^2}{\rm{\theta }}}} + ;\frac{1}{{si{n^2}{\rm{\theta }}}}}}{{\frac{1}{{cos{\rm{\theta }}}} \times \frac{1}{{sin{\rm{\theta }}}}}} = ;\frac{{\frac{{si{n^2}{\rm{\theta }} + co{s^2}{\rm{\theta }}}}{{si{n^2}{\rm{\theta }}co{s^2}{\rm{\theta }}}}}}{{\frac{1}{{sin{\rm{\theta cos\theta }}}}}} = \frac{1}{{sin{\rm{\theta cos\theta }}}} = sec{\rm{\theta ;cosec\theta }}$

Short Trick:

$\frac{{2 + {{\tan }^2}\theta + {{\cot }^2}\theta }}{{\sec \theta ;cosec;\theta }}$

put θ = 45°

$\frac{{2 + {{\tan }^2}45^\circ + {{\cot }^2}45^\circ }}{{\sec 45^\circ ;cosec;45^\circ }} = \frac{{2 + 1 + 1}}{{\sqrt 2 \times \sqrt 2 }} = \frac{4}{2} = 2$

Go through the option

sec θ cosec θ = sec 45° cosec45°

⇒ √2 × √2 = 2 satisfied

Let the ratio of ages four years ago of A and B = 4x : 5x

According to the question

⇒ (4x + 12) / (5x + 12) = 11/13

⇒ x = 8

Age of A four years ago = 4x = 4 × 8 = 32 years

⇒ Present age of A = 32 + 4 = 36

Age of B four years ago = 5x = 5 × 8 = 40 years

⇒ Present age of B = 40 + 4 = 44 years

∴ Sum of their present ages = 36 + 44 = 80 years

Suppose the speed of the truck = x km/h

Decreased speed of the truck = (x – 16) km/h

According to the question

$\Rightarrow \frac{{384}}{{x - 16}} - \frac{{384}}{x} = 2$

$\Rightarrow \frac{{384{\rm{;}} \times {\rm{;}}16}}{{x\left( {x - 16} \right)}} = 2$

⇒ x² – 16x = 3072

⇒ x² – 16x – 3072 = 0

⇒ x² – 64x + 48x – 3072 = 0

⇒ x(x – 64) + 48(x – 64) = 0

⇒ (x – 64) (x + 48) = 0

⇒ x = 64 and x = -48 (not possible)

Speed of truck = 64 km/h

∴ 75% speed of the truck = 64 × [75/100] = 48 km/h

As we know,

⇒ (a³ – b³) = (a – b) (a² + b² + ab)

⇒ 5√5 x³ – 81√3 y³ =

(√5 x – 3√3 y)(Ax² +By² + Cxy)

⇒ (√5 x)³ – (3√3 y)³ = (√5x – 3√3y) (Ax² + By² + Cxy)

⇒ (√5 x – 3√3 y) (5x² + 27y² + 3√15 xy) = (√3x – √2y) (Ax² + By² + Cxy)

⇒ 5x² + 27y² + 3√15xy = Ax² + By² + Cxy

On comparing

⇒ A = 5, B = 27 and C = 3√15

⇒ (6A + B – √15 C)

⇒ 6 × 5 + 27 – √15 × 3 √15

⇒ 57 – 45 = 12

Given:

PQ = PR = 12 cm  

OR = OQ = OP = 10 cm

Concept used:

When a line is drawn from the centre of a circle to the mid-point of a chord, then the line is perpendicular to the chord.

Calculation:

Suppose SQ = RS = x cm and OS = y cm

⇒ PS = (10 – y)

Since QR is a chord and S is the midpoint.

⇒ ∠PSQ = ∠PSR = 90°

In ΔPRS

⇒ RP² = PS² + RS²      [Using Pythagoras theorem]

⇒12² = (10 – y)² + x²

⇒ 144 = 10² + y² – 2 × 10 × y + x²

⇒ 144 = 100 + y² – 20y + x²      ---- (1)

In ΔRSO,

⇒ OR² = RS² + OS² [Using Pythagoras theorem]

⇒ 10² = x² + y²

⇒ 100 = x² + y²      ---- (2)

Subtract equation (2) from equation (1)

⇒ 144 – 100 = 100 + y² – 20y + x² – x² – y²

⇒ 44 = 100 – 20y

⇒ y = 2.8

∴ Length of OS = 2.8

The correct answer is Plentiful

Key Points

• The word 'scarce' can be defined as 'insufficient or not available in enough quantity'.
• This meaning is directly in contrast to the meaning of the word 'plentiful' which means 'existing in large quantities'.
• As for the other options, here are their meanings:
• Seldom - not common or infrequent
• Few - a small number of something
• Scanty - insufficient in amount
• We can see that these meanings are in fact synonymous with the given word and cannot be its antonyms.
• Therefore, option 3 is correct.

The correct option here is 'alike'. This is because 'calling on subject1 + subject2 alike' is a phrase construction that is used to mean that an appeal, offer or announcement is being made to one group of people as well as another.

For example: For this job opportunity, we are calling on freshers and seasoned professionals alike!

Therefore, option 4 is correct.

The correct answer is- 'calander'

Key Points

• All options except option 1 have been spelt wrongly.
• The given word in option 1 should be correctly spelled as: calendar.
• Calendar: a chart or series of pages showing the days, weeks, and months of a particular year, or giving particular seasonal information. (किसी विशेष वर्ष के दिनों, सप्ताहों और महीनों को दर्शाने वाला या विशेष मौसमी जानकारी देने वाला पृष्ठों का एक चार्ट या श्रृंखला।)
• Callous: showing or having an insensitive and cruel disregard for others. (दूसरों के प्रति असंवेदनशील और क्रूर अवहेलना दिखाना या होना)
• Carriage: a four-wheeled passenger vehicle pulled by two or more horses. (दो या दो से अधिक घोड़ों द्वारा खींचा गया चार पहिया यात्री वाहन vehicle)
• Career: an occupation undertaken for a significant period of a person's life and with opportunities for progress. (एक व्यक्ति के जीवन की एक महत्वपूर्ण अवधि के लिए और प्रगति के अवसरों के साथ किया गया व्यवसाय)

Therefore, the correct answer is option 1.

The correct answer is pressurize

Key Points

• The word 'coerce' means 'to persuade someone to do something by force'.
• Let's look at the meanings of the given options:
• Cajole - persuade someone to do something by flattery
• Leave - to go away
• Enchant - to influence someone with charm
• Pressurize - to strongly persuade someone into doing something
• We can see that the word closest in meaning to the given word is 'pressurize'.

Therefore, option 4 is correct.

The correct answer is bitterly hostile

Key Points

• The idiom 'at daggers drawn' means to be 'unfriendly or bitterly hostile towards each other'.
• Example: They used to be friends once, but have been at daggers drawn since their fight last year.
• As we can see, this meaning is clearly conveyed by option 1.

The correct answer is will fine you

Key Points

• ​Conditional sentences are statements discussing known factors or hypothetical situations and their consequences.

• ​If two actions take place one after the other in the future, the structure will be as given below:

• ​If/unless/suppose + Subject + V1 + Object, Subject + shall/will + V1 + Object.

• For example:

• If George will be there, I will not go at any cost. 

• If George is there, I will not go at any cost. 

• According to the rule and the example given above, 'will fine you' will be used instead of 'has fined you' in the 2nd part of the sentence.

Thus, the correct sentence is: If you park your car here, the traffic police will fine you.

The correct answer is to behave recklessly

Key Points

• The idiom 'to play ducks and drakes' means 'to behave recklessly or misuse one's resources'.
• Example: He lost his job for playing ducks and drakes with the fund of corporation.
• We can see that option 3 is the correct explanation for this idiom.

Additional Information

• This expression comes from the game of ducks and drakes, played by throwing a flat stone across the surface of water in such a way as to make it skim and skip before it finally sinks.

The correct answer is Medicines should not be bought without the doctor's prescription

Key Points

• Imperative sentences are sentences that express advice, request, or command.
• There are some sentences which contain suggestion.
• Let’s see how to convert these sentences into passive by some examples.

Ex:

• Respect parents. (Active Voice)
  

Parents should be respected. (Passive Voice)

• Love the kids. (Active Voice)
  

The kids should be loved. (Passive Voice)

• Follow your dreams. (Active Voice)
  

Your dreams should be followed. (Passive Voice)

• Thus, we use 'should' in imperative sentences in passive sentences containing 'suggestion'.
• While changing from active to passive voice, we change the subject to the object and vice versa. Thus, the object 'Medicines' will become the subject in passive voice.
• At Last lining up the remaining sentence: without the doctor's prescription.
• Thus, the sentence becomes: Medicines should not be bought without the doctor's prescription

The correct answer is compression

Key Points

• The word 'expansion' means 'the action of becoming larger'.
• Let's look at the meanings of the given options:
• Inflation - the action of filling something with air or gas so that it increases in size
• Extension - the action of causing something to become larger
• Compression - the action of flattening or pressing something into a smaller space
• Augmentation - the action of adding to something so that it becomes larger
• We can see that the word directly opposite in meaning to the given word is 'compression'. In fact, the other options are synonymous with the given word.
• Therefore, option 3 is correct.

The first sentence of the passage must stand independently in meaning. Out of the given options, this is only true for sentence D. The other sentences are clearly referring to subjects that have been mentioned before. Hence, D must be the first sentence.

The second sentence must expand on the topic introduced in the first sentence which we can see in sentence C. It starts with the word 'here', referring to 'the cafe' introduced in the first sentence. Hence, C is the second sentence.

Again, for the next sentence, we must look for a sentence that refers to the topic of the previous sentence: snakes. This can be found in sentence B which uses the phrase 'none of them' to refer to the snakes from the previous sentence. Hence, B is the third sentence.

Finally, sentence A is the last sentence which ends with a bit of trivia about the topic explore in the the first three sentences. 

Therefore, the correct order is DCBA and the correct option is option 3.

The correct option here is 'mistake'. We can understand from the context of the sentence that the Korean city Seoul's government is rewarding people for pointing out faults with street signs that have been poorly translated into English and other languages.

The words 'blunder', 'guffaws' and 'oversight' have meanings similar to the word 'mistake' but they are generally used for far more serious mistakes.

Therefore, the correct option is option 3.

The phrase 'in case' is used in situations where we talk about being prepared for something that may happen. 

It acts as a conjunction between two clauses where one clause mentions a precaution and the second mentions a possibility.

Clause 1 + in case + Clause 2

Constructions with 'in case' do not need the conjunction 'that' to join the two clauses. Therefore, the 'that' in the given sentence is unnecessary.

Hence, option 2 has the error. 

The correct sentence is: We had to decline several orders in case the production was held up due to labour strike.

In this question, we must choose one of these demonstratives which are words used to refer to a subject mentioned earlier in the sentence or passage.

In this case, the blank will be referring to 'people who spot the most errors' and is hence, plural. Since these people are yet unknown, the correct demonstrative for this context would be 'those'.

Hence, option 3 is correct.

The correct answer is 'BADC'.

Key Points

• The logical order of the sentences is to start with the event of the whale's death after it was stranded a day earlier. This event is mentioned in sentence B.
• Sentence A provides explicit detail about why the whale died (as a result of 40 kilograms of plastic in its stomach) and this directly links to the ending of sentence B.
• Sentence D introduces Darrell Blatchley, who explains the cause of the animal's death, providing a summary of and commentary on the information in sentence A.
• Sentence C presents further commentary by Blatchley, adding context to the extent of the issue by comparing this case to other instances of plastic found during necropsies.

Therefore, the correct order is 'Option 2'.

Additional Information

• The other options do not provide a logically coherent and chronologically sensible sequence of events based on the content of the sentences.

The correct answer is persistent

Key Points

• Chronic:  continuing for a long time; constantly recurring
• Example: The individuals with certain chronic diseases who lived the longest were the fattest.
• Persistent: continuing to exist or occur over a prolonged period.
• ​Example: persistent rain will affect many areas
• Thus, chronic and persistent are synonyms

Additional Information​

• Meaning of other options are:
• Ordinary: with no special or distinctive features; normal
• Common: occurring, found, or done often; prevalent
• Temporary: lasting for only a limited period of time; not permanent

The correct answer is: Option 4.

Key Points

• The word "exploite" is incorrectly spelt. The correct spelling is "exploit" which means to make full use of and derive benefit from a resource. (शोषण करना)
• Example: They were accused of exploiting child labor in their factories.
• "Exploit" means to make full use of and derive benefit from a resource. (शोषण करना)
• Example: The company aims to exploit the new technology to gain a competitive advantage.

Therefore, the correct answer is: Option 4.

Additional Information

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

• Explicit (स्पष्ट): Stated clearly and in detail, leaving no room for confusion or doubt.
• Example: The instructions were explicit, so everyone understood what to do.
• Expire (समाप्त होना): To come to an end or to no longer be valid after a period of time.
• Example: My driver's license will expire next month.
• Explode (विस्फोट होना): Burst or shatter violently and noisily as a result of rapid combustion, excessive internal pressure, or other process.
• Example: The bomb could explode at any moment.