SSC CHSL Previous Paper 6 (Held On: 3 July 2019 Shift 2) (Previous Year Paper)

The correct answer is option 1 

Many of China's exports is a plural subject so the verb should also be in its plural form.

Thus, we need to replace 'has been' with 'have been'.

Improved Sentence: Many of China's exports have been redirected to the domestic market in view of the more consumption-driven economy.

ADDITIONAL INFORMATION-

in view of =  because     or     as a result of.

Eg- "the poor condition of libraries is of concern in view of the increased emphasis on reference work"

The correct answer is 'of organizing'

Key Points

In the given sentence, the usage of 'by organize' is incorrect Instead use 'of organizing' 

'Organize' is a verb that means 'arrange systematically or in order.' 

• In the given sentence,'of' is used which is a preposition and we know that we have to use a prepositional object after the preposition and it can be a noun/pronoun.
• The prepositional object can be a noun/pronoun/gerund, a Gerund is a verb form and if we make a gerund we have to use 'ing' form after it.
• We have to use the preposition 'of' instead of 'by' because the former one means 'expressing the relationship between and general category and something which belongs to such category' while 'by' means ‘as a means of’ something or someone.
• 'By' preposition often comes in a passive sentence.
• From the meaning of preposition, we can say that the noun 'responsibility' will take the preposition 'of'.

Additional Information

• When 'of' is used after the noun 'responsibility', the definite article must be used before the noun.
• Let's see an example
• The governor-general has the responsibility of appointing the members of the Queen’s Privy Council for Canada.

So the correct sentence is: Two senior officers have been entrusted with the responsibility of organizing the reception of the guest.

The correct answer is option 2 i.e. disintegrate.

Explanation:

ERODE (of wind, water, or other natural agents) means gradually wearing away (soil, rock, or land).

• fix- fasten (something) securely in a particular place or position.
• disintegrate- break up into small parts as the result of impact or decay.
• preserve- maintain (something) in its original or existing state.
• build- construct (something) by putting parts or material together.

The chosen option best expresses the meaning of the given word.

The correct answer is option 2 i.e. has not solved it.

Explanation 

Yet always follows the present perfect tense of the sentence.

As this sentence has Yet at the end of the sentence we need to write it in the present perfect tense.

He has been solving this sum for a couple of hours but he has not solved it yet.

The correct answer is Option 3)

Explanation:

• The correct spelling is 'gobble'. If you gobble food, you eat it quickly and greedily.
  

Example: Pete gobbled all the stew.

• Meaning of other rightly spelled words are:
• ​Glory is the fame and admiration that you gain by doing something impressive.
  

Example: Walsham had his moment of glory when he won a 20km race.

• Goggles are large glasses, often of coloured glass or covered with gauze, that fit closely to your face around your eyes to protect them from such things as water, wind, or dust
  

Example: a swimmer's goggles

• Global is used to describe something that happens in all parts of the world or affects all parts of the world.
  

Example: one of the most successful organizations fighting child poverty on a global scale.

The correct answer is option 1 i.e. proliferation.

Explanation:

• Let's look at the meaning of the given option:
• proliferation- the rapid increase in the number or amount of something.
• promotion- an activity that supports or encourages a cause, venture, or aim.
• propensity- an inclination or natural tendency to behave in a particular way.
• paucity- the presence of something in only small or insufficient quantities or amounts.
• Hence from the given meanings, we find that the correct answer is Option 1 i.e proliferation.

The correct answer is Option 3 i.e. aerial.

Explanation:

• Let's look at the meanings of the given options. 
• heavenly- of heaven; divine.
• feathery- having, covered with, or resembling feathers.
• aerial- existing, happening, or operating in the air.
• visual- relating to seeing or sight.
• Hence from the given meanings, we find that the correct answer is Option 3 i.e aerial.

The correct answer is option 2 i.e. encounter.

appointment- an arrangement to meet someone at a particular time and place.

encounter- unexpectedly be faced with or experience (something hostile or difficult).

enterprise- a project or undertaking, especially a bold or complex one.

commitment- the state or quality of being dedicated to a cause, activity, etc.

Chosen option fits the meaning of the sentence correctly.

The correct answer is option 1 i.e. aggrassive.

aggressive- ready or likely to attack or confront; characterized by or resulting from aggression.

agriculture- the science or practice of farming, including cultivation of the soil for the growing of crops and the rearing of animals to provide food, wool, and other products.

agitation- a state of anxiety or nervous excitement.

agreement- harmony or accordance in opinion or feeling.

The correct answer is 4 i.e. be in a dangerous situation.

The meaning of the given idiom is-  to be in a highly precarious state.

The correct answer is 4 i.e. vilify.

Key Points

• In the above-given sentence, vilify will be used because the sentence is trying to express the fact during elections political parties try to criticize their rivals unfairly in order to gain an advantage.
• Let's look at the meaning of the given options:-
• Laud- praise (a person or their achievements) highly. ((किसी व्यक्ति या उनकी उपलब्धियों की) अत्यधिक प्रशंसा करना)
• Covet- yearn to possess (something, especially something belonging to another). ((कुछ, विशेष रूप से दूसरे से संबंधित कुछ) पाने की लालसा)
• Commend- praise formally or officially. (औपचारिक या आधिकारिक तौर पर प्रशंसा करें)
• Vilify- speak or write about in an abusively disparaging manner. (अपमानजनक तरीके से बोलना या लिखना।)
• The chosen option i.e. vilify fits the context the best.

The correct answer is option  1.

Active => subject + v2 + object + other word.

Passive=> Object + was/were + v3 + by + subject + other words.

This structure is being followed by;  only option 1.

So, the chose option is correct.

The correct answer is option 1 i.e. sparse.

Explanation:

DENSE means closely compacted in substance.

• sparse- thinly dispersed or scattered.
• jammed- squeeze or pack tightly into a specified space.
• crammed- completely fill (a place or container) to the point of overflowing.
• piled- place (things) one on top of the other.

The chosen option expresses the opposite meaning of the given word.

• The correct answer is Option 2.
• The meaning of the given idiom 'To shake off' means 'to rid or free oneself from someone or something that one finds aggravating, upsetting, or annoying'
• Therefore, the only option that gives the meaning of the given context is Option 2 'to get rid of'.

• The correct answer is Option 1.
• The given sentence is in interrogative form when changed into indirect form it becomes an assertive sentence.
• 'said to' changes to 'asked', first person changes to the third person, can changes to could, this changes to that.
• Therefore, the correct sequence is followed by option 1 i.e. 'Bhola asked his friend how he could make that charcoal white'.

• The correct answer is Option 4.
• The error lies in the wrong usage of the preposition 'to' which is used to show direction.
• The correct preposition to be used here is 'of' which is used for belonging to, relating to, or connected with.
• In the above sentence, the launch is related to a small electric car.

The correct answer is Option 3) i.e. Compress

Explanation:

The meaning of the given words:

• Exaggerate: To overstate, to describe more than is fact.
• Heighten: To make high; yo raise higher; to elevate.
• Amplify: To render larger, more extended, or more intense.
• Compress: To make smaller, squash, squeeze, shorten, truncate.
• Overdo: to do too much of something.

Therefore, it is obvious that the word 'Compress' is the antonym of the given word and all other options are synonyms.

• The correct answer is Option 1.
• Sentence C is talking about a person called 'Mark Eklund', sentence B is introducing that person.
• Sentence D is describing his personality and his mischievousness which is continued in sentence A that talks about one of his mischievous things.
• Therefore, the correct sequence is followed in Option 1 i.e. CBDA.

The correct answer is Option 3) i.e. Implicate

Explanation: The meaning of the given words:

• Entangle: To involve in difficulties or embarrassments.
• Exclude: To keep out, to omit from consideration.
• Clarity: The state or measure of being clear.
• Implicate: To connect or involve in an unfavourable way with something.
• Release: The act of setting free.

Therefore, out of given options, the word 'implicate' is the appropriate synonym of 'entangle'.

• The correct answer is Option 1.
• The subject 'additives' is plural so the verb should also be in plural form. Option 2 gets eliminated.
• The sentence is in present indefinite tense, so the blank should satisfy the tense. Option 3 & 4 get eliminated.
• Therefore, 'make' is the correct word which fits in the blank

• The correct answer is Option 4.
• The passage is beginning with **'**People make plastic products'. The same context should be continued in the passage.
• Therefore, the correct word to be used is 'people'.

• The correct answer is Option 2.
• The meaning of the given words:
• Component: A smaller part of a larger entity.
• Material: Matter which may be shaped or manipulated.
• Thing: That which is considered to exist as a separate entity, object.
• Object: A thing that has a physical existence.
• Plastic is a material that can be shaped or manipulated. Therefore, option 2 is the correct answer.

• The correct answer is Option 4.
• The preposition 'to' is used to indicate the place, person, or thing that someone or something moves toward, or the direction of something.
• 'with' is used Used to indicate being together or being involved.
• 'in' is used Used for unspecific times during a day, month, season, year.
• 'of' is used Used for belonging to, relating to, or connected with.
• The correct preposition to be used here is 'of' as in the passage we are mentioning to which the new type of material belongs.

• The correct answer is Option 3.
• The correct conjunction to be used here is 'when' which is used when introducing a single completed event that takes place in the middle of a longer activity or event.
• The other conjunctions do not give a proper sense to the sentence.

The correct answer is ADBC.

Key Points

• The only independent sentence among the given sentences is A which is our first sentence.
• Sentence A is talking about Oliver making a big snowman which is continued in sentence D as it is describing how big the snowman is.
• Therefore, option beginning with AD sequence is in Option 1 i.e. ADBC.

Let the number of boys in a class in June = 2x

Then the number of girls in June = x

In July, the number of girls = x + 5

And the number of boys = 2x – 5

Now, according to the question, in July,

Number of girls = Number of boys

x + 5 = 2x – 5

→ x = 10

So, the number of boys in class in June = 2x = 2 × 10 = 20, and the number of girls in class in June = x = 10.

Hence, the total number of students is 20 + 10 = 30.

Let's check each option:

1)Q C Q D P C P C / Q C Q P P C P D / Q C Q D P C P D → doesn't follow a pattern

2)P C Q D P C P D / Q C Q D P C P D / Q C D D P C P D → doesn't follow a pattern

3)Q C Q D P C D D / Q C Q D P C P D / Q C Q D P D P D → doesn't follow a pattern

4)Q C Q D P C P D / Q C Q D P C P D / Q C Q D P C P D → follows a pattern

Q C Q D P C P D is repeated.

Hence, the correct answer is “QCPDDPQC”.

Using the below table of symbols, we can draw the family tree.

The possible family tree is as follows:

Hence, Mayank is the nephew of Naman.

When folded, the transparent sheet will look like the below figure.

Hence, option 2 is the correct answer.

The following logic is applied for 442 : 21

21² + 1 = 441 + 1 = 442

Similarly,

16² + 1 = 256 + 1 = 257

Hence, the correct answer is 257 : 16.

The codes are :

T ÷ V + Q - J × M + U means T is the husband of V. V is the mother of Q. Q is Wife of J who is brother of M. M is the mother of U.

Hence, T is the father-in-law of J.

The pattern followed here is:

Hence, the correct answer is 210.

A Chassis is the base frame of a car.

Similarly, a skeleton is the base frame of a body.

Hence, the correct answer is ‘Body’.

The figure (X) is embedded in the below figure.

Hence, option 2 is the correct answer.

The pattern followed here is:

GIven : (84, 60, 51) → (84 ÷ 4 = 21, 60 ÷  2 = 30) and (21 + 30 = 51)

Similarly, we will check with the other options.

option 1,

(64, 80, 72)

→ (64 ÷ 4 = 16, 80 ÷  2 = 40) and (16 + 40 = 56)

option 2,

(80, 98, 69)

→ (80 ÷ 4 = 20, 98 ÷  2 = 49) and (20 + 49 = 69)

option 3, 

(72, 56, 62)

→ (72 ÷ 4 = 18, 56 ÷  2 = 28) and (18 + 28 = 46)

option 4, 

(52, 64, 47)

→ (52 ÷ 4 = 13, 64 ÷  2 = 32) and (13 + 32 = 45)

Hence, (80, 98, 69) is the correct answer.

Cells, Tissues, and Organs are the different levels of organization of the bodies of living organisms.

An atom is a fundamental unit of a chemical element.

Hence, 'atoms' is the odd one among the given options.

All ‘Fathers’ are men. ‘Players’ can be men or fathers.

Hence, the correct answer is option 4.

From the first two positions of the dice, we can see that 1, 4, 5, and 6 are adjacent to 2.

Now, the only number left is 2.

Hence, 2 is the number on the face opposite to the face showing 3.

Conclusions:

I. No college is a school → True (No school is college.)

II. Some schools are parks → True (All parks are schools)

III. No park is a college → True (All parks are schools and no school is college so no park will be college)

Hence, the correct answer is ‘All the conclusions follow’.

The figure is rotating in the clockwise direction.

Hence, the correct answer is option 4.

The pattern followed here is:

Similarly,

Hence, SBUVLQXO is the correct answer.

The pattern followed here is:

(4, 6, 52) → 4² + 6² = 16 + 36 = 52

Similarly,

(3, 5, 34) → 3² + 5² = 9 + 25 = 34

Hence, the correct answer is (3, 5, 34).

Expression : 868 + 14 × 55 – 1064 ÷ 56

After interchanging the signs :

Option 1 ( + and ÷ )

868 ÷ 14 × 55 – 1064 + 56

= 62 × 55 – 1064 + 56

= 3410 – 1064 + 56

= 3466 - 1064

= 2402 ≠ 117

Option 2 ( × and -)

868 + 14 – 55 × 1064 ÷ 56

= 868 + 14 – 55 × 19

= 868 + 14 – 1045

= 882 - 1045

= - 163 ≠ 117

Option 3 ( + and -)

868 – 14 × 55 + 1064 ÷ 56

= 868 – 14 × 55 + 19

= 868 – 770 + 19

= 887 – 770

= 117

Option 4 ( ÷ and × )

868 + 14 ÷ 55 – 1064 × 56

= 868 + 14 ÷ 55 – 59584

= 868 + 0.25 – 59584

= 868.25 – 59584

= -58715.75 ≠ 117

Hence, the correct answer is ( + and -).

The pattern followed here is:

W  → 23 × 2 = 46 and

CAT → (3 + 1 + 20) × 2 = 24 × 2 = 48

Similarly, SALE → (19 + 1 + 12 + 5) × 2 = 37 × 2 = 74

Hence, the correct answer is 74.

Triangles in the given diagram is AHL, ALI, AHI, ABM, AGM, ABG, CJV, CVK, CJK, CBS, CSD, CBD, SNT, STQ, SNQ, SOU, SUR, SOR, SGF, SFE, SGE, CGE, CGF, CFE, CSG, CSE.

Thus, there are a total of 26 triangles.

Hence, 26 is the correct answer.

The mirror image of the question figure is as follows:

Hence, option 1 is the correct answer.

The pattern followed here is:

Similarly,

Hence, the correct answer is QUFW.

The pattern followed here is:

16 × 2 = 32; 32 - 2 = 30

30 × 2 = 60; 60 + 2 = 62

62 × 2 = 124; 124 - 2 = 122

122 × 2 = 244; 244 + 2 = 246

246 × 2 = 492; 492 - 2 = 490

Hence, 490 is the correct answer.

The pattern followed here is:

Hence, the correct answer is SPJ.

Nephrology is the study of Kidneys.

Similarly, Opthalmology is the study of Eyes.

Hence, Opthalmology : Eyes is the correct answer.

Given:

The ratio of speeds of A and B = 3 : 5

Time taken by A to cover a distance = 24 minutes more than B 

Formula used:

Speed = Distance traveled/Time taken

If Distance → Constant, then Speed ∝ 1/time

Calculation:

Ratio of speeds of A and B = 3 : 5

⇒ Ratio of time of A and B = 5 : 3

Let time taken by A and B be 5x and 3x respectively.

Difference in time taken by A and B = 5x – 3x = 2x = 24 mins.

⇒ x = 12

Time taken by B to cover the same distance = 3x = 3 × 12 = 36 mins

By internal angle bisector theorem, the bisector of vertical angle of a triangle divides the base in the ratio of the other two sides”

AB/AC = BD/DC

⇒ c/b = x/(a – x)

⇒ bx = ac – cx

⇒ bx + cx = ac

⇒ x(b + c) = ac

⇒ x = ac/(b + c)

Now,

BD – DC = x – (a – x)

⇒ x – a + x

⇒ 2x – a

⇒ 2ac/(b + c) – a

⇒ (2ac – ab – ac)/(b + c)

⇒ ac – ab/(b + c)

⇒ a(c – b)/(c + b)

Calculation:

The average number of students enrolled in B during 2015, 2016, and 2018

⇒  (360 + 375 + 225)/3 = 320

The number of students enrolled in A during 2017 = 250

Required percentage = (320 – 250)/250 × 100 = 28%

Calculation:

The total number of students enrolled in A during 2014, 2016, and 2018

⇒ 160 + 300 + 260 = 720

The total number of students enrolled in B during the period of five years

⇒ 225 + 360 + 375 + 325 + 225 = 1510

Required percentage = 720/1510 × 100 = 47.7%

Calculation:

The total number of students enrolled in A during 2015 and 2018

⇒ 280 + 260 = 540

The total number of students enrolled in B during 2014 and 2016

⇒ 225 + 375 = 600

∴ Required ratio = 540 : 600 = 9 : 10

Calculation:

For year 2015:

The number of students enrolled in B is more than the number of students enrolled in A by 360 – 280 = 80

Percent by which the number of students in B exceeds by A = 80/280 × 100 = 28.57%

For year 2017:

The number of students enrolled in B is more than the number of students enrolled in A by 325 – 250 = 75

Percent by which the number of students in B exceeds by A = 75/250 × 100 = 30%

For year 2016:

The number of students enrolled in B is more than the number of students enrolled in A by 375 – 300 = 75

Percent by which the number of students in B exceeds by A = 75/300 × 100 = 25%

For year 2014:

The number of students enrolled in B is more than the number of students enrolled in A by 225 – 160 = 65

Percent by which the number of students in B exceeds by A = 65/160 × 100 = 40.625%

∴ In year 2015, the number of students enrolled in B is x% more, where 25 < x < 30, than the number of students enrolled in A in the same year

Shortcut TrickIf x + 1/x = a

⇒ x3 + 1/x3 = a³ - 3a

⇒ x3 + 1/x3 = 73 - (3 × 7) = 322

Detailed Solution:

x + 1/x = 7

⇒ (x + 1/x)³ = 343

⇒ x³ + 1/x³ + 3(x + 1/x) = 343

⇒ x³ + 1/x³ + 3(7) = 343

⇒ x³ + 1/x³ = 343 – 21

⇒ x³ + 1/x³ = 322

Given:

250√2 x3 – 5√5 y3 = (5√2 x - √5 y) × (Ax2 + Bxy + Cy2)      ----(1)

Formula used:

a³ - b³ = (a - b)(a² + b² + ab)

Calculation:

Taking L.H.S. of Eq(1)

250√2 x³ – 5√5 y³

⇒ (5√2 x - √5 y) × [(5√2 x)² + 5√10 xy + (√5 y)²]

⇒ (5√2 x - √5 y) × (50x² + 5√10 xy + 5y²)

Equating with R.H.S.

(5√2 x - √5 y) × (50x² + 5√10 xy + 5y²) = (5√2 x - √5 y) × (Ax² + Bxy + Cy²)

A = 50, B = 5√10, C = 5

A + C - √10 B = 50 + 5 – 50

∴ A + C - √10 B = 5

Given:

The ratio of two numbers A and B = 5 : 2

Ratio of two numbers if 4 is added to it = 9 : 4

Calculation:

Let the two numbers be 5x and 2x

When 4 is added to each number,

(5x + 4)/(2x + 4) = 9/4

⇒ 4(5x + 4) = 9(2x + 4)

⇒ 20x + 16 = 18x + 36

⇒ 20x – 18x = 36 – 16

⇒ 2x = 20

⇒ x = 10

The original number = 5x = 50 and 2x = 20

When 5 is subtracted from each number, the ratio

⇒ (50 - 5) : (20 - 5) = 45 : 15 = 3 : 1

Shortcut Trick

To make difference same, multiply 1st ratio by 5 and 2nd by 3, we get,

⇒ 2units = 4

⇒ 1 unit = 2

Then A = 25 × 2 = 50 and B = 10 × 2 = 20

When 5 is subtracted from each number, the ratio

⇒ (50 - 5) : (20 - 5) = 45 : 15 = 3 : 1

Given:

Amount = Rs. 29282

Rate = 10% per annum

Time = 4 years

Formula used:

For compound interest,

A = P(1 + r/100)ⁿ

For Simple Interest

S.I. = (P × R × T)/100

Where, A = Amount

P = Principal

r = rate of interest

n = time period in years

Calculation:

⇒ 29282 = P(1 + 10/100)⁴

⇒ 29282 = P(11/10)⁴

⇒ P = 29282 × 10/11 × 10/11 × 10/11 × 10/11

⇒ P = Rs. 20000

Now,

S.I. = PRT/100

⇒ S.I. = (20000 × 10 × 4)/100

⇒ S.I. = Rs. 8000

As the diagonals of the rectangle are equal and bisect each other,

AO = OC = DO = OB = ½ AC = ½ BD

Given:

AC = 2BC

⇒ AO = OC = BO = BC

In ΔOCB, OC = OB = BC

⇒ ΔOCB is an equilateral triangle

⇒ ∠COB = 60°

⇒ ∠DOA = 60° (∵ Vertically opposite angle)

In ΔODE, ∠ODE = 90° (∵ Angle made by a tangent and the radius is 90°)

In ΔODE, sum of the angles = 180°

(∵ ∠DOE = ∠DOA)

⇒ ∠DEC = 180 - ∠ODE - ∠DOE 

⇒ ∠DEC = 180 – 90° - 60°

⇒ ∠DEC = 30°

Given:

S.P. of an article = Rs. 2300

Gain% = 25%

Formula used:

C.P. = (S.P. × 100)/(100 + gain%)

Loss % = (Loss/C.P.) × 100%

Calculation:

C.P. of article = 2300 × 100/(100 + 25) = Rs. 1840

If the article is sold for Rs.1955, profit = 1955 – 1840 = 115

∴ Gain percent = 115/1840 × 100 = 6.25%

Shortcut TrickGain% = 25% = 1/4 

Ratio of C.P. to S.P. = 4 : 5

⇒ 5 units = 2300

⇒ 4 units = (2300/5) × 4 = Rs. 1840

If S.P. = Rs.1955, then Profit = 1955 - 1840 = 115

∴ Gain percent = 115/1840 × 100 = 6.25%

Given:

ΔABC ~ ΔQPR 

Area ΔABC : Area ΔPQR = 9 : 16

Concept used:

If two triangles are similar, then the ratio of their areas will be equal to the ratio of the squares of their corresponding sides.

⇒ Area ΔABC : Area ΔPQR = AB²/PQ²

Calculation:

⇒ Side ΔABC : Side ΔPQR = √9 : √16 = 3 : 4

ΔABC ~ ΔQPR

⇒ AC/QR = 3/4

⇒ 9/QR = 3/4

⇒ QR = 12 cm

Given:

Ratio of sides of rectangle = 7 : 4

Circumference of wire = 31.5 cm

Formula used:

Circumference of circle = 2πr

Perimeter of rectangle = 2(l + b)

Calculation:

Circumference of circle = 2 × 22/7 × 31.5

⇒ 198 cm

Let the length and breadth of rectangle be 7x and 4x respectively

Perimeter of rectangle = 2(l + b) = 2(7x + 4x) = 22x

Now,

Circumference of circle = perimeter of rectangle (as the wire is same)

⇒ 198 = 22x

⇒ x = 9

∴ The length of smaller side = 4x = 4 × 9 = 36 cm

Shortcut Trick

Total Work (LCM of 10, 15, 20) = 60 units.

Combined efficiency 2(A+B+C) = 6 + 4 + 3 = 13 ⇒ A+B+C = 6.5 units/day.

Work done in 8 days = 6.5 × 8 = 52 units.

Remaining work = 60 − 52 = 8 units.

Efficiency of C = (A+B+C) − (A+B) = 6.5 − 6 = 0.5 units/day.

Time taken by C = 8 ÷ 0.5 = 16 days.

∴ The correct answer is 16 days.

Alternate Method

Given: (A + B) takes 10 days, (B + C) takes 15 days, (C + A) takes 20 days.

Formula Used: Efficiency = Total Work ÷ Time Taken

⇒ Adding efficiencies: 2(A + B + C) = 6 + 4 + 3 = 13

⇒ Efficiency of (A + B + C) = 13 ÷ 2 = 6.5 units/day

⇒ Work completed by all three in 8 days = 6.5 × 8 = 52 units

⇒ Remaining work = 60 − 52 = 8 units

⇒ Efficiency of C = Efficiency of (A+B+C) − Efficiency of (A+B) = 6.5 − 6 = 0.5 units/day

⇒ Time taken by C alone = Remaining Work ÷ Efficiency of C = 8 ÷ 0.5 = 16 days

∴ The correct answer is 16 days.

Additional Information

Combined Efficiency Property

When pairs are given (A+B, B+C, C+A), the sum of their efficiencies is always twice the total efficiency of A, B, and C combined.

Pipes and Cisterns

This logic applies to pipes filling a tank, where negative efficiency is used for outlet pipes (leaks).

Work and Wages

Wages are always distributed in the ratio of the actual work done by each individual or their efficiencies if they work for the same duration.

Given:

The successive discount are 30% and 20%.

Formula used:

Equivalent single discount = X + Y - (XY)/100

Where,

X = First discount

Y = Second discount

Calculation:

Equivalent single discount = X + Y - (XY)/100

⇒ 30 + 20 – (30 × 20)/100

⇒ 50 – 6

⇒ 44%

∴ Equivalent single discount is 44%.

L.H.S.

$\sqrt {\frac{{1 - cos\theta }}{{1; + ;cos\theta }}} \times \sqrt {\frac{{cosec\theta - cot\theta }}{{cosec\theta ; + ;cot\theta }}}$

⇒ $\sqrt {\frac{{\left( {1 - cos\theta } \right)\left( {1; + ;cos\theta } \right)}}{{\left( {1; + ;cos\theta } \right)\left( {1; + ;cos\theta } \right)}}} \times \sqrt {\frac{{\left( {cosec\theta - cot\theta } \right)\left( {cosec\theta - cot\theta } \right)}}{{\left( {cosec\theta + cot\theta } \right)\left( {cosec\theta ; - ;cot\theta } \right)}}}$

⇒ $\sqrt {\frac{{(1 - co{s^2}\theta }}{{{{\left( {1; + ;cos\theta } \right)}^2}}}} \times \sqrt {\frac{{{{\left( {cosec\theta - cot\theta } \right)}^2}}}{{\left( {cose{c^2}\theta - ;co{t^2}\theta } \right)}}}$

⇒ $\sqrt {\frac{{si{n^2θ}}}{{{{\left( {1; + ;cos\theta } \right)}^2}}}} \times \sqrt {\frac{{{{\left( {cosec\theta - cot\theta } \right)}^2}}}{1}}$

⇒ $\frac{{sin\theta }}{{1; + ;cos\theta ;}} \times \frac{{cosec\theta - cot\theta }}{1}$

⇒ $\frac{{sin\theta }}{{1; + ;cos\theta ;}} \times \left( {\frac{1}{{sin\theta }} - ;\frac{{cos\theta }}{{sin\theta }}} \right)$

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

⇒ $\frac{{1 - cos\theta }}{{1; + ;cos\theta }}$

Comparing with R.H.S.

$\frac{{1 - cos\theta }}{{1; + ;cos\theta }} = \frac{{1 - r}}{{1; + ;r}}$

r = cosθ 

in the second step we have not taken conjugate but simply multiplied by 1 whose value is ( 1 + cosθ )/( 1 + cosθ ).

Given:

AE = BE

⇒ ΔAEB is an isosceles triangle.

⇒ ∠EAB = ∠EBA

In ΔAEB, ∠AEB + ∠EAB + ∠EBA = 180°

⇒ 70° + 2∠EAB = 180°

⇒ 2∠EAB = 110°

⇒ ∠EAB = 55°

⇒ ∠EBA = 55°

Now, DO = AO = OC = OB = radius

In ΔADO,

AO = OD

⇒ ∠DAO = ∠ADO = 55°

⇒ ∠DOA = 180° - 55° - 55° = 70°

In ΔOCB

OC = OB

⇒ ∠CBO = ∠BCO = 55°

⇒ ∠COB = 180° - 55° - 55° = 70°

Now, ∠AOB = 180°

∠COD = 180° - ∠DOA - ∠COB

⇒ ∠COD = 180° - 70° - 70° = 40°

Given:

$\frac{1}{{1 - sinθ }}; + ;\frac{1}{{1; + ;sinθ }}$ = 4secθ 

Formula used:

cos²θ + sin²θ = 1

⇒ cos2θ = 1 - sin2θ

Calculation:

$\frac{1}{{1 - sinθ }} + \frac{1}{{1; + ;sinθ }}$ = 4secθ 

⇒ $\frac{1}{{1 - sinθ }} \times \frac{{1; + ;sinθ }}{{1; + ;sinθ }}; + ;\frac{1}{{1; + ;sinθ }} \times \frac{{1 - sinθ }}{{1 - sinθ }}$ = 4secθ

⇒ (1 + sinθ /1 – sin²θ) + (1 – sinθ /1 – sin²θ) = 4secθ

⇒ (1 + sinθ /cos²θ) + (1 – sinθ /cos²θ) = 4secθ

⇒ (1 + sinθ + 1 – sinθ)/cos² θ = 4secθ

⇒ 2/cos²θ = 4secθ

⇒ 2sec²θ = 4secθ

⇒ secθ = 2

⇒ θ = 60°

Now,

3 cotθ + cosecθ = 3cot60° + cosec60°

⇒ 3 cotθ + cosecθ = 3 × (1/√3) + (2/√3)

⇒ 3 cotθ + cosecθ = 5/√3

Multiply by √3 in numerator and denominator, Then we get 

⇒ 3 cotθ + cosecθ = 5√3/3

∴ The value of (3 cot θ + cosec θ) is 5√3/3.

Given:

Average of 1st three numbers = 4 × fourth no.

Average of all the four numbers = 52

Formula used:

Average  = Sum of observation/no. of observation

Calculation:

Let the four numbers be a, b, c and d

According to question:

(a + b + c)/3 = 4d

⇒ a + b + c = 12d

Also,

(a + b + c + d)/4 = 52

⇒ a + b + c + d = 52 × 4 = 208

⇒ 12d + d = 208

⇒ 13d = 208

⇒ d = 16

∴ The average of first 3 numbers = 4d = 4 × 16 = 64

Concept used:

Calculation:

$\left( {\frac{7}{5} \div \frac{7}{{10}};of\frac{3}{4}} \right) \div \frac{4}{9} - \left( {\frac{7}{{16}} \div 10\frac{1}{2}; \times ;7\frac{1}{5}} \right); \times ;\frac{5}{{12}}~~$

$\Rightarrow \left( {\frac{7}{5} \div \frac{{21}}{{40}}} \right) \div \frac{4}{9} - \left( {\frac{7}{{16}} \div \frac{{21}}{2}; \times ;\frac{{36}}{5}} \right); \times ;\frac{5}{{12}}~~$

$\Rightarrow \left( {\frac{7}{5}; \times ;\frac{{40}}{{21}}} \right); \times ;\frac{9}{4} - \left( {\frac{7}{{16}}; \times ;\frac{2}{{21}}; \times ;\frac{{36}}{5}} \right); \times ;\frac{5}{{12}}~~$

$\Rightarrow \left( {\frac{8}{3}} \right); \times ;\frac{9}{4} - \left( {\frac{3}{{10}}} \right); \times ;\frac{5}{{12}}~~$

⇒ 6 – $\frac{1}{8}$

$\Rightarrow \frac{{47}}{8}$

Shortcut Trick

For a triangle with interior angle bisectors, the angle between the bisectors of the other two angles is given by the formula:

Required Angle = 90° + (Third Angle / 2)

Given the third angle (A) = 64°.

⇒ Required Angle = 90° + (64° / 2)

⇒ 90° + 32° = 122°.

∴ The correct answer is 122°.

Alternate Method

Given:

In ΔABC, let ∠A = 64°. The bisectors of ∠B and ∠C meet at point I (the incenter).

Formula Used:

1. Angle Sum Property: ∠A + ∠B + ∠C = 180°
2. In ΔBIC, ∠BIC + ∠IBC + ∠ICB = 180°

Calculations:

In ΔABC:

⇒ ∠A + ∠B + ∠C = 180°

⇒ 64° + ∠B + ∠C = 180°

⇒ ∠B + ∠C = 180° − 64° = 116°

Dividing the entire equation by 2:

⇒ (∠B / 2) + (∠C / 2) = 116° / 2 = 58°

In ΔBIC, where I is the intersection of bisectors:

⇒ ∠BIC + ∠IBC + ∠ICB = 180°

Since BI and CI are bisectors, ∠IBC = ∠B / 2 and ∠ICB = ∠C / 2:

⇒ ∠BIC + (∠B / 2) + (∠C / 2) = 180°

⇒ ∠BIC + 58° = 180°

⇒ ∠BIC = 180° − 58° = 122°

∴ The correct answer is 122°.

Additional Information

Incenter (I)

The point where all three internal angle bisectors of a triangle intersect. It is the center of the incircle.

External Bisector Angle

The angle between the external bisectors of two angles of a triangle is given by 90° − (A / 2).

Angle Sum Property

The sum of the interior angles of any triangle is always equal to 180°.

Excenter Angle

The angle formed by one internal bisector and one external bisector of the other two angles is A / 2.

Given:

Increase % in price of commodity = 36%

Decrease in quantity = 30%

Concept used:

Expenditure = Price of commodity × Quantity

Calculation:

Let the price of a commodity be Rs. 100/unit and the quantity purchased be 10 units

⇒ Amount spent = 100 × 10 = Rs. 1000

Now the price increased by 36%

⇒ The new price will be Rs.136/unit

The quantity purchased decreases by 30%

The new quantity purchased will be 10 × (100 – 30)/100 = 7 units

⇒ The new expenditure = 136 × 7 = 952

Decrease in amount spent = 1000 – 952 = Rs. 48

∴ Required percentage = 48/1000 × 100 = 4.8%

Given:

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

Formula used:

a³ - b³ = (a - b)(a² + b² + ab)

Calculation:

x³ - 8 can be written as (x - 2)(x² + 4 +2x)

(x² - x -2) can be written as in factor form (x - 2)(x + 1)

(x² - 4x - 5) will be (x +1)(x - 5)

(x² + 2x +1) = (x + 1)²

⇒ $\frac{{2\left( {x - 2} \right)\left( {{x^2}; + ;2x; + ;4} \right)}}{{\left( {x - 2} \right)\left( {x; + ;1} \right)}} \times \frac{{{{\left( {x; + ;1} \right)}^2}}}{{\left( {x; + ;1} \right)\left( {x - 5} \right)}} \times \frac{{3\left( {x - 5} \right)}}{{\left( {{x^2}; + ;2x; + ;4} \right)}}$

⇒ 6

Given:

M.P. of an article = Rs. 400

Discount % = 20%

Profit = Rs. 32

Formula used:

S.P. = M.P. × (100 - Discount%)/100

Profit = S.P. - C.P.

Profit % = Profit/C.P. × 100

Calculation:

S.P = M.P. × 80/100

⇒ 400 × 80/100

⇒ Rs. 320

C.P. = S.P. – Profit

⇒ 320 – 32

⇒ Rs. 288

∴ Gain percentage = 32/288 × 100 = 11.11%

The correct answer is option 2) i.e. Turtles.

Key Points

• Gahirmatha sanctuary located within the close vicinity of the Bhitarkanika National Park is Odisha’s only Turtle Sanctuary.
• It is very famous for its nesting beach for Olive Ridley Turtles. It is one of the most important nesting beaches for turtles.
• The Gahirmatha Marine Wildlife Sanctuary is the only marine sanctuary of Orissa. In 1997 the Government of Orissa declared the area as Gahirmatha Marine Sanctuary considering its ecological significance and diverse floral and faunal resources.
• These turtles are known for the epic journeys that they undertake annually to breed and recuperate. It has been observed that Olive  Ridley Sea Turtles migrate from the pacific ocean through the coastal water of Sri Lanka in the Indian Ocean to the coastal water of Gahirmatha in the north.
• They usually mate between November and January and the breeding period is of eight months from October to May.

The correct answer is option 3) i.e. Himachal Pradesh.

• Chamera Power Station was established to harness the hydropower potential of river Ravi.
• It is located in Chamba district of Himachal Pradesh.
• The project comprises of a 121 m high, 295 m long concrete arch-gravity dam with 9.5 m dia., 6.414 Km long headrace tunnel.
• The underground powerhouse with an installed capacity of 540 MW houses 3 units of 180 MW capacity each designed to generate 1664.56 million units in a 90% dependable year with 95% machine availability.
• All the three generating units of the power station were commissioned in the month of April-1994.
• Uttarakhand, UP, Delhi, HP, Haryana, J&K, Punjab, Rajasthan and Chandigarh (UT) are the beneficiary states of this power station.

The correct answer is option 1) i.e. Bengaluru.

• Vishwaroopa Mahavishnu statue, which is 64 feet tall, is to be installed in the premises of Kothandaramaswamy temple in Viveknagar area of Bengaluru, Karnataka.
• This massive monolithic statue of Vishwaroopa Mahavishnu, weighing 300-tonne, was brought to the temple from Korakkotai village in Tiruvannamalai district in Tamil Nadu.

The correct answer is option 4) i.e. Ministry of Culture.

• Project ‘Mausam’ is a Ministry of Culture project to be implemented by Indira Gandhi National Centre for the Arts (IGNCA), New Delhi as the nodal coordinating agency with the support of Archeological Survey of India and National Museum as associate bodies.
• This project aims to explore the multi-faceted Indian Ocean ‘world’–collating archaeological and historical research in order to document the diversity of cultural, commercial and religious interactions in the Indian Ocean
• The project was launched by India at the 38th World Heritage Session at Doha, Qatar on 20th June 2014.

The correct answer is option 4) i.e. Dinaras.

• During the Gupta Period, gold coins were called Dinaras.
• After the Kushanas, the Guptas were the most important dynasty.
• The Gupta period has been described as the Golden Age of Indian history.
• The first famous king of the Gupta dynasty was Ghatotkacha's son Chandragupta I. He married Kumaradevi, the daughter of the chief of the Licchavis.
• Chandragupta I was succeeded by Samudragupta in about 330 A.D., who reigned for about fifty years.
• Samudragupta's successor Chandragupta II, also known as Vikramaditya, conquered the extensive territories of Malwa, Gujarat and Kathiawar.
• Kalidasa, the greatest Sanskrit poet and dramatist prospered during his reign.

Important Points 

Gupta Dynasty:

• The founder of the Gupta dynasty was Sri Gupta.
• He was succeeded by Ghatotkacha. These two were called Maharajas.
• The next ruler was Chandragupta I and he was the first to be called Maharajadhiraja.
• He was a great military genius and is said to have commanded a military campaign across the Deccan, and also subdued the forest tribes of the Vindhya region.

Key Points

Some famous events during the rule of Gupta Kings:

• The famous Chinese pilgrim, Fahien visited India during the reign of Chandragupta II.
• Out of his nine years of stay in India, he spent six years in the Gupta empire.
• Chandragupta II waged war against the Saka satraps of western India.
• Rudrasimha III, the last ruler of the Saka satrap was defeated, dethroned, and killed. His territories in western Malwa and the Kathiawar Peninsula were annexed into the Gupta Empire.
• Kumaragupta laid the foundation of Nalanda University.

The correct answer is option 4) i.e. Tapti(  Tapi) 

• Tapti is also known as the river Tapi.
• Tapi River is known as the ‘Handmaid’ of the Narmada river.
• Place of origin of Tapti river in Eastern Satpura range in Madhya Pradesh.
• The Tapti River is agriculturally very important as it drains an area of over 65,145 sq. km. spread over Madhya Pradesh, Maharashtra and Gujarat.
• The Melghat Tiger Reserve in Amravati district in Maharashtra, a part of Project Tiger, is situated on the southeast bank of the Tapti River along the Madhya Pradesh and Maharashtra boundary.

The correct answer is option 4) i.e. 5.

• Protective helmets, when not in use by fielders, should be placed only on the ground behind the wicket-keeper and in line with both sets of stumps.
• If a protective helmet belonging to the fielding side is on the ground within the field of play, and the ball while in play strikes it, the ball shall become dead and 5 penalty runs shall then be awarded to the batting side, in addition to the penalty for a No ball or a Wide, if applicable.
• Additionally runs completed by the batsmen before the ball strikes the protective helmet shall be scored, together with the run in progress if the batsmen had already crossed at the instant of the ball striking the protective helmet.
• http://ndca.nsw.cricket.com.au/files/2977/files/laws/Law41.htm

The correct answer is option 2) i.e. Oil and Natural Gas Corporation.

• ONGC, India's top oil and gas producer toppled Indian Oil Corporation (IOC) and regained the crown of being the country's most profitable public sector unit (PSU).
• ONGC reported a 34 % jump in its 2018-19 fiscal net profit to Rs 26,716 crore.
• In the previous two financial years, IOC was the country's most profitable PSU.
• IOC had also lost the title of being India's largest company by turnover tag to billionaire Mukesh Ambani-led Reliance Industries in FY19.

The correct answer is option 2) i.e. Stratigraphy.

• The scientific discipline concerned with the description of rock successions and their interpretation in terms of a general time scale is called Stratigraphy.
• The lowest layers are the oldest and the highest are the most recent.
• Artefacts found in layers can be assigned to specific cultural periods and can thus provide the cultural sequence for a site.
• Palaeontology is the study of the history of life on Earth as based on fossils. Fossils are the remains of plants, animals, fungi, bacteria, and single-celled living things that have been replaced by rock material or impressions of organisms preserved in rock.
• Geodesy is the science of accurately measuring and understanding three fundamental properties of the Earth: its geometric shape, its orientation in space, and its gravity field— as well as the changes of these properties with time.

The correct answer is option 1) i.e. Basketball Federation of India.

• K. Govindaraj was unanimously re-elected as president of the Basketball Federation of India (BFI) at its annual general body meeting here on Sunday.
• Chander Mukhi Sharma was re-elected secretary-general as the BFI promised a bunch of new ideas and tournaments.
• Mrs.Praveen Mahajan is the President of the All India Tennis Association.
• Dushyant Chautala is the President of Table Tennis Federation of India.
• Kiren Rijiju is the Minister of Youth Affairs and Sports.

The correct answer is option 3) i.e. Kerala.

• Vembanad lake located at Kottayam district of Kerala is the longest lake in India.
• Vembanad Lake is having 83.72km length and 14.48km width.
• In the Vembanad Lake, there is a small beautiful island called Pathiramanal or the Midnight sands.

The correct answer is option 1) i.e. Registry.

Key Points

• The registry or Windows registry is a database of information, settings, options, and other values for software and hardware installed on all versions of Microsoft Windows operating systems.
• For example, when a program is installed, a new subkey containing settings like a program's location, its version, and how to start the program, are all added to the Windows registry.

Additional Information

• Cookies are small files that are stored on a user's computer.
• They are designed to hold a modest amount of data specific to a particular client and website and can be accessed either by the web server or the client's computer.
• Cache stores data for temporary use.
• Cache memory is very small in size as compared to memory.
• Cache memory has a separate bus for data transfer