SSC CHSL Previous Paper 20 (Held On: 10 July 2019 Shift 1) (Previous Year Paper)

The correct answer is option 4 i.e. similar.

Explanation:

Identical- similar in every detail; exactly alike.

• legible- (of handwriting or print) clear enough to read.
• perfect- having all the required or desirable elements, qualities, or characteristics; as good as it is possible to be.
• detailed- having many details or facts; showing attention to detail.
• similar- having a resemblance in appearance, character, or quantity, without being identical.

Option 4 expresses the same meaning as the given word.

The correct answer is option 2.

The tense here is Present Perfect Tense.

Active voice-  Subject + Have/has + v3 + object + other word.

Passive voice-  Object + Have/has + been + v3 +By + subject + other word.

The structure will be followed by the given sentence.

Passive structure of this sentence is followed only by option 2.

So, this will be the right choice as the correct answer.

The correct answer is option  4 i.e. facilitate.

Meanings of the given words:

• complicate- make (something) more complicated.
• confuse- make (someone) bewildered or perplexed.
• felicitate- congratulate.
• facilitate- make (an action or process) easy or easier.

Option 4 fits the sentence contextually.

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

Explanation:

OSTENTATIOUS-characterized by pretentious or showy display; designed to impress.

• flashy- ostentatiously attractive or impressive.
• distinct- recognizably different in nature from something else of a similar type.
• disturb- interfere with the normal arrangement or functioning of.
• complete- having all the necessary or appropriate parts.

Option 1) express the same meaning as the given word.

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

Lets' look at the meaning of the given options-

• confederation- an organization that consists of a number of parties or groups united in an alliance or league. (छोटे वर्गों, राज्‍यों आदि का संगठन; परिसंघ)
• constellation- a group of stars forming a recognizable pattern that is traditionally named after its apparent form or identified with a mythological figure. (एक पहचानने योग्य पैटर्न बनाने वाले सितारों का एक समूह जिसे पारंपरिक रूप से उसके स्पष्ट रूप के नाम पर रखा जाता है या एक पौराणिक आकृति के साथ पहचाना जाता है।)
• conflagration- an extensive fire that destroys a great deal of land or property. (एक व्यापक आग जो बहुत अधिक भूमि या संपत्ति को नष्ट कर देती है।)
• concoction- a mixture of various ingredients or elements. (विभिन्न अवयवों या तत्वों का मिश्रण।)

Hence from the above-given meanings, we find that the correct answer is Option  2 i.e. constellation.

The correct answer is option 3 i.e. questionnaire.

The correct word will be-

qualification- a condition that must be fulfilled before a right can be acquired; an official requirement.

quieten- make or become quiet and calm.

questionnaire- a set of printed or written questions with a choice of answers, devised for the purposes of a survey or statistical study.

quantify- express or measure the quantity of.

The correct answer is option 2 i.e. something sudden that happens unexpectedly.

The meaning of the given idiom- A sudden, unexpected event.

The meaning of the idiom is the same as the chosen option.

The correct answer is option 3 i.e. spectaculer.

adjacent- next to or adjoining something else.

contiguous- sharing a common border; touching.

whimsical- playfully quaint or fanciful, especially in an appealing and amusing way.

The correct word will be-

spectacular- beautiful in a dramatic and eye-catching way.

The correct option is 1 i.e. herbarium.

Let's look at the meaning of given options-

• Herbarium- a systematically arranged collection of dried plants.
• warehouse- a large building where raw materials or manufactured goods may be stored prior to their distribution for sale.
• Greenhouse- a glass building in which plants that need protection from cold weather are grown.
• Nursery-  a place where young plants are grown and sold or a room in a house for the special use of young children.

Hence from the above-given meanings, we find that the correct answer is Option 1 i.e. herbarium.

The correct answer is incomplete.

Key Points

• The given sentence is talking about the reign of Harsha and its incompleteness without the mention of Hiuen Tsang.
• Let's look at the meaning of the correct answer:-
• Incomplete: not full or finished**.**
• Here, it means that Hiuen Tsang was an integral part of King Harsha's reign and without a reference to Tsang, an account of the reign of Harsha would be incomplete or unfinished.
• Thus, the only word from the option that fits in the blank is 'Incomplete'.
• Thus, the correct answer is Option 3.

Additional Information

The correct answer is option 1.

We need to change Please Into Requested that is done only in option 1 & 2.

We need to change will into Would and this is done in the only option 1.

Both conditions are fulfilled by option 1 so, this is the correct answer.

The correct answer is option 3 i.e. No improvement.

Had + v3 is construction makes it grammatically correct.

No option contains this structure.

The correct answer is option 4.

We need to replace in spite with in spite of because 'in spite' is always followed by 'of'

Otherwise, we may use despite at this place.

• The correct answer is Option 2.
• The given sentence is in Past tense, use of 'have' becomes an error. The underlined phrase should also be in the past tense.
• Option 1 is wrong because it is in present continuous tense.
• Option 3 is in present indefinite tense.
• Option 2 is in past tense and substitutes the underlined sentence.

• The correct answer is Option 2.
• The following prepositions mean:
• Preposition 'From' is used to indicate source or origin.
• Preposition 'with' is used to imply some particular relation especially when implying interaction, company, association.
• Preposition 'to' is used for expressing motion or direction toward a point, person, place, or thing approached and reached.
• Preposition 'in' is used to indicate inclusion within space, a place, or limits.
• Therefore, the most suitable blank is preposition 'with', also the word 'along' takes the preposition 'with'.

• The correct answer is Option 2.
• The passage is talking about the residents facing the extreme water crisis because of the dip in the ground water level.
• Therefore, 'acute' is the suitable word which means 'High, intense sharp'.
• The other words mean:
• Unlikely: Not likely, likely to fail.
• Average: neither very good nor very bad.
• Unknown: no known, unidentified.
• All other options except 'acute' do not give a proper meaning in the blank.

• The correct answer is Option 3.
• Here the modal 'might' fits the blank because in passage the writer has just expressed an assumption of residents facing water crisis.
• 'Might' is used to express the possibility.
• 'Shall' is used to to express the command and strong possibility of an action which is to take place in the near future
• 'Should' is used to express the duty/obligation.
• 'Can' is used to express the ability.
• Therefore, the correct answer is Option 3 'might'.

• The correct answer is Option 3.
• In passage, the word immediately after the blank is singular i.e. 'state' which means the determiner before it should also be in singular form.
• Therefore, option 1 gets eliminated.
• Option 2 is wrong because the use of 'across' and 'nearby' together doesn't make any sense.
• Option 4 is wrong because the article 'an' is used only before the vowel sounding words.
• Therefore option 3 is the suitable word that fits in the blank.

• The correct answer is Option 4.
• The following prepositions mean:
• Preposition 'with' is used to imply some particular relation especially when implying interaction, company, association.
• Preposition 'From' is used to indicate source or origin.
• Preposition 'on' is used to express the contact between two things.
• Preposition 'in' is used to indicate inclusion within space, a place, or limits.
• The word 'dip' means 'to lower or inclination downward' which is in the groundwater levels. 'In' is the suitable preposition to be used.

• The correct answer is Option 3.
• The meaning of the given idiom 'left-handed compliment' is 'An insulting or negative comment disguised/appeared as praise'.
• Therefore, only option 3 conveys the meaning of the given idiom and all other options are not relevant.

The correct answer is Option 2.

​

Explanation:

Salient: prominent, relevant.

• Prominent: important, eminent. (महत्वपूर्ण, प्रख्यात)
• Negligible: ignored, of little significance. (अवहेलना करना, कम महत्व का )
• Clear: Bright, transparent. (उज्ज्वल, पारदर्शी.)
• striking: making a strong impression. (प्रभावशाली)

Therefore, it is obvious that the word 'negligible' is the antonym of the given word.

The correct answer is Option 4.

Explanation:

​Complacent: Uncritically satisfied with oneself or one's achievements.

• Humble: Not pretentious, magnificent.
• Confident: very sure of something.
• Trusted: belief, faith, hope.
• Satisfied: pleased, happy, content.
• Therefore, the best alternative to the given word is 'satisfied'.

• The correct answer is Option 3.
• As we know there are two clauses and there should be an appropriate conjunction to join them.
• Therefore, 'whether' should be used before 'she'.
• The correct sentence is 'The lady listened carefully to my complaint but I doubt whether she will do anything about it.'

• The correct answer is Option 3.
• There is only one independent sentence in the given sentences i.e. C, so sentence C is our first sentence.
• Sentence C says that the person sold the jasmine flowers for some rupees later he feels he should have sold it for more amount which is in sentence A.
• Sentence D is the continuation of sentence A that if he had sold it for more mount he would have made a good profit.
• His overall profit is said in sentence B which is the last sentence.
• Therefore, option 3 CADB is the correct answer.

• The correct answer is Option 2 DBCA.
• Option 1 gets eliminated because the sentence B is beginning with a determiner.
• Sentence D is the first sentence as it is an independent sentence which is talking about a phenomenon of the job longevity.
• This is continued in sentence B which says that this phenomenon was noted in a recent research report.
• Sentence C talks about what the research report stated so C is the third sentence. The only remaining sentence i.e. A is our last sentence.
• Therefore, this sequence is followed in Option 2

Pi and Theta are the type of symbols.

Hence, the correct answer is figure 2.

The pattern followed here is,

Examine

Example

Excited

Exclaim

Execute

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

Given series

(24, 48, 36)

The pattern followed here is,

= 48 - 24 = 24 and 48 - 36 = 12

Option 1:

(25, 49, 37)

= 49 - 25 = 24 and 49 - 37 = 12

Option 2:

(45, 49, 77)

= 49 - 45 = 4 and 77 - 49 = 28

Option 3:

(26, 58, 46)

= 58 - 26 = 32 and 58 - 46 = 12

Option 4:

(15, 49, 37)

= 49 - 15 = 34 and 49 - 37 = 12

Therefore, only option 1 is followed the given series.

Hence, the correct answer is (25, 49, 37).

1 January 2018 to 1 January 2019 = 365 days i.e. 52 weeks and 1 odd day i.e. Tuesday.

So the day before one day of 1 January 2019 is 31 December 2018 is Monday.

Hence, the correct answer is Monday.

The pattern followed here is,

325 = 3 + 2 + 5 = 10;

425 = 4 + 2 + 5 = 11(odd number)

145 = 1 + 4 + 5 = 10;

235 = 2 + 3 + 5 = 10;

Hence, 425 is the odd one out..

Given series

6 : 40

The pattern followed here is,

(First term)² + 4 = Second term

= 6² = 36; 36 + 4 = 40

Option 1:

15 : 45

= 15² = 225; 225 + 4 = 229 ≠ 45

Option 2:

5 : 25

= 5² = 25; 25 + 4 = 29 ≠ 25

Option 3:

7 : 53

= 7² = 49; 49 + 4 = 53

Option 4:

9 : 72

= 9² = 81; 81 + 4 = 85 ≠ 72

Hence, the correct answer is 7 : 53.

According to the alphabetical positions of the letters,

DH = D + 4 = H 

HL = H + 4 = L

Similarly,

GK = G + 4 = K

K + 4 = O

Hence, the correct answer is KO.

According to the alphabetical positions of the letters,

The code for BUS = 2 + 21 + 19 = 42; 42 × 3 = 126 (as 3 letters are present)

FUEL = 6 + 21 + 5 + 12 = 44; 44 × 4 = 176 (as 4 letters are present)

Similarly, the code for

SHRUB = 19 + 8 + 18 + 21 + 2 = 68; 68 × 5 = 340 (as 5 letters are present)

Hence, the correct answer is 340.

The pattern followed here is,

Hence, the correct answer is MJ.

The mirror image will be:

Hence, the correct answer is figure 3.

The least possible Venn diagram is as follows:

Conclusions:

I. Some lions are eggs → True (as per diagram, some lions is eggs)

II. Some eggs are hens → True (as per diagram, some eggs are hens)

III. Some eggs are birds → True (as per diagram, some eggs are birds)

Hence, all the conclusions follow.

Important Points

Some is a subset of all.

If it is given that, 'All A are B' then the conclusion 'Some A are B' will always follow.

In this series, the image is rotating in a 90-degree clockwise direction.

Hence, the correct answer is figure 1.

The given series is

10 + 8 - 200 × 15 ÷ 5

Option 1:

• and ÷, 200 and 10

200 ÷ 8 - 10 × 15 + 5

= 25 – 10 × 15 + 5

= 25 – 150 + 5

= 30 -150

= -120 ≠ 407

Option 2:

10 + 8 - 200 × 15 ÷ 5

× and ÷, 8 and 5

= 10 + 5 - 200 ÷ 15 × 8

= 10 + 5 – 13.33 × 8

= 10 + 5 – 106.64

= 15 - 106.64

= 91.64 ≠ 407

Option 3:

10 + 8 - 200 × 15 ÷ 5

× and -, 5 and 15

10 + 8 × 200 - 5 ÷ 15

= 10 + 8 × 200 - 0.33

= 10 + 1600 - 0.33

= 1610 - 0.33

= 1609.67 ≠ 407

Option 4:

10 + 8 - 200 × 15 ÷ 5

+ and -, 15 and 10

= 15 - 8 + 200 × 10 ÷ 5

= 15 - 8 + 200 × 2

= 15 - 8 + 400

= 415 - 8

= 407 (follows the series)

Hence, the correct answer is '+ and -, 15 and 10'.

Given series

(16, 25, 82)

(Product of first and second term) × 2 Third term

= 16 + 25 = 41; 41 × 2 = 82

Option 1: (36, 49, 170)

= 36 + 49 = 85; 85 × 2 = 170 (it follows)

Option 2: (25, 49, 81)

= 25 + 49 = 74; 74 × 2 = 148 ≠ 81

Option 3: (25, 36, 51)

= 25 + 36 = 61; 61 × 2 = 122 ≠ 81

Option 4: (11, 121, 110)

= 121 + 11 = 132 × 2 = 264 ≠ 110

Hence, the correct answer is (36, 49, 170).

The option in which the given figure is embedded is,

Hence, the correct answer is option 1.

6 is a consant number in two both dice so if we rotate from 6 to anticlockwise or clockwise direction then we get “3 is the opposite site of 1”

Hence, the correct answer is 1.

The paper is unfolded in the manner given below,

Hence, the correct answer is figure 1.

Except Punjab, all other are capital of different cities.

Hence, Punjub is the odd one out.

The pattern followed here is,

Hence, the correct answer is ILEGFRA.

The pattern followed here is,

Option 1 does not follow the order.

Hence, 'IKM' is the odd one out.

The triangles are

ADC, ADB, ACB, CDE, CGF, GFE, CEF, DBE, CBE.

Hence, the correct answer is 9

Man is present in crowd, 

Similarly,

Student is present in class.

Hence, the correct answer is class.

Pen is used to write on paper,

Similarly,

Chalk is used to write on Blackboard.

Hence, the correct answer is Blackboard : Chalk.

According to given information,

As per diagram, Susma’s brother is the father of Manju’s husband so Manju’s husband is the nephew of Susma.

Hence, the correct answer is nephew.

The pattern followed here is,

Hence, 720 is the correct answer.

Let the length of up train = D

Then the length of down train = 2D

Speed of up train = D/8

Speed of down train = 2D/20 = D/10

Time the two trains take to cross each other = (D + 2D)/(D/8) + (D/10)

⇒ 3D/(9D/40) = (3D × 40)/9D = 40/3

∴ Time the two trains take to cross each other $= 13\frac{1}{3};sec$

Given

(x + y)^1/3 + (y + z)^1/3 = -(z + x)^1/3

⇒ (x + y)^1/3 + (y + z)^1/3 + (z + x)^1/3 = 0

Suppose (x + y) = a, (y + z) = b, (z + x) = c

⇒ a1/3 + b1/3 + c1/3 = 0

Cubing both sides

Formula: (a + b + c)3 = a3 + b3 + c3 + 3 (a +b) (b + c) (a+ c)

(a1/3 + b1/3 + c1/3)³ = a + b + c + 3(a1/3 + b1/3)(b1/3 + c1/3)(c1/3 + a1/3) = 0

⇒ a + b + c + 3(-c1/3)(-a1/3)(-b1/3) = 0

⇒ a + b + c = 3c1/3a1/3b1/3

Cubing both sides

⇒ (a + b + c)³ = 27abc

⇒ {(x + y) + (y + z) + (z + x)}3 = 27(x + y)(y + z)(z + x)

⇒ {2(x + y + z)}3 = 27(x + y)(y + z)(z + x)

⇒ (x + y + z)3 = (27/8)(x + y)(y + z)(z + x)

⇒ x3 + y3 + z3 + 3(x + y)(y + z)(z + x) = (27/8)(x + y)(y + z)(z + x)

⇒ x3 + y3 + z3 = {(27/8) - 3}(x + y)(y + z)(z + x)

= (3/8)(x + y)(y + z)(z + x)

There are twelve sticks each of length one unit

∴ Perimeter of equilateral triangle = 12 unit

⇒ 3 × side = 12

⇒ side = 4 unit

∴ Area of equilateral triangle = (√3/4) (side)² = (√3/4) × 4 × 4 = 4√3 sq. units

Calculation:

⇒ a + 1/a = 2

⇒ a + 1/a

⇒ 1 + 1

⇒ a = 1

⇒ a⁴ – 1/a⁴ 

⇒ 1 – 1

⇒ 0

∴ The answer is 0.

Total strike rate in all 5 match = 100 + 90 + 75 + 80 + 100 = 445

Average = 445/5 = 89

Total runs in all 5 matches = 50 + 45 + 30 + 20 + 100 = 245

Average = 245/5 = 49

Average strike rate of the seconds and the fifth match = 120

The total strike rate of the seconds and the fifth match = 2 × 120 = 240

Strike rate of the seconds match = 90

⇒ Required strike rate of the fifth match = 240 - 90 = 150

Let total number of balls faced be x

Now

x × 75/100 = 30

∴ x = 40

Centroid is the point where three medians meet. So, when point A of a triangle ABC moves parallel to the straight-line BC. Centroid will also move along a straight-line parallel to BC.

m₁ d₁ h₁ w₂ = m₂ d₂ h₂ w₁

Where m = man, d = day, h = hour, w = work

16 × 12 × 27 = 18 × 24 × h₂

∴ h₂ = 12

Follow the BODMAS rule as given in the below table:

\(\left[ {1\frac{1}{5};of;\left{ {\frac{3}{7} - \left( {1\frac{4}{{15}} - \frac{{13}}{{15}}} \right) \times \frac{5}{7};} \right}} \right]; \div \left( {\frac{6}{7}; \div 5} \right)\)

\(\Rightarrow \left[ {\frac{6}{5};of;\left{ {\frac{3}{7} - \left( {\frac{{19}}{{15}} - \frac{{13}}{{15}}} \right); \times ;\frac{5}{7}} \right}} \right]; \div \left( {\frac{6}{7} \times \frac{1}{5}} \right)\)

\(\Rightarrow \left[ {\frac{6}{5};of;\left{ {\frac{3}{7} - \frac{6}{{15}} \times \frac{5}{7}} \right}; \div \frac{6}{{35}}} \right]\)

\(\Rightarrow \left[ {\frac{6}{5};of;\left{ {\frac{3}{7} - \frac{2}{7}} \right} \times \frac{{35}}{6}} \right]\)

$\Rightarrow \left[ {\frac{6}{5} \times \frac{1}{7} \times \frac{{35}}{6}} \right]$

⇒ 1

Given

4(2sin² θ + 7cos² θ) = 13

⇒ 4[(2sin² θ + 7(1 – sin² θ)] = 13

⇒ 4[2sin² θ + 7 – 7sin² θ] = 13

⇒ 4[7 – 5sin²θ] = 13

⇒ 28 – 20sin²θ = 13

⇒ 20sin²θ = 15

⇒ sin²θ = 15/20 = 3/4

⇒ sin θ = √3/2 = sin 60°

∴ θ = 60°

Given

r₁ = 2.4 cm, r₂ = 4 cm and d = 6.5 cm

common tangent = $\sqrt {{d^2} - {{\left( {{r_1} - {r_2}} \right)}^2}} = \sqrt {{{\left( {6.5} \right)}^2} - {{\left( {2.4 - 4} \right)}^2}} = \sqrt {42.25 - 2.56} = \sqrt {39.69}$

∴ Common tangent = 6.3 cm

Here P = 1000

Rate = 12%

Number of days from 31 december 2015 to 1 may 2016 = 31 + 29 + 31 + 30 = 121

SI = (p × r × t)/100 = (1000 × 12 × 121)/(366 × 100) = 40 approx

∴ The amount A has to return to B = 1000 + 40 = 1040 rupees

LCM of 7, 11 and 13 = 1001

14993/1001 = 14.97

15004/1001 = 14.98

15015/1001 = 15

14982/1001 = 14.96

∴ 15015 is exactly divisible by 7, 11 and 13

Shortcut Trick

For any positive real number and its reciprocal, if x + 1/x = 2, then x = 1 is the only possible real solution.

Since cosec θ = 1/sin θ, we have sin θ + 1/sin θ = 2, which directly gives sin θ = 1 and cosec θ = 1.

Substituting these values: sin¹⁵³θ + cosec²⁵³θ = (1)¹⁵³ + (1)²⁵³ = 1 + 1 = 2.

∴ The correct answer is 2.

Alternate Method

Given:

sin θ + cosec θ = 2

Formula Used:

cosec θ = 1 ÷ sin θ

(a − b)² = a² − 2ab + b²

Calculations:

⇒ sin θ + 1 ÷ sin θ = 2

Let sin θ = x

⇒ x + 1 ÷ x = 2

⇒ x² + 1 = 2x

⇒ x² − 2x + 1 = 0

⇒ (x − 1)² = 0

⇒ x − 1 = 0

⇒ x = 1

Therefore:

⇒ sin θ = 1

Since cosec θ = 1 ÷ sin θ:

⇒ cosec θ = 1 ÷ 1 = 1

Substitute the values into the target expression:

⇒ sin¹⁵³θ + cosec²⁵³θ = (1)¹⁵³ + (1)²⁵³

⇒ sin¹⁵³θ + cosec²⁵³θ = 1 + 1 = 2

∴ The correct answer is 2.

Additional Information

Reciprocal Trigonometric Identities

Trigonometric functions cosec θ, sec θ, and cot θ are reciprocal to sin θ, cos θ, and tan θ respectively. Specifically, cosec θ = 1 ÷ sin θ.

Algebraic Property of x + 1/x

For any real number x, if x + 1 ÷ x = 2, then x must be equal to 1. If x + 1 ÷ x = −2, then x must be equal to −1.

Powers of 1

Any real power of 1 is always 1, i.e., 1ⁿ = 1 for any real exponent n.

In ∆ABC and ∆ DBA

∠ABC = ∠DBA

∠ACB = ∠DAB

∴ ∆ ABC ~ ∆ DBA

∴ AB/BD = BC/AB

⇒ AB² = BD × BC      …(1)

In ∆ ABC and ∆ CAD

∠ABC = ∠CAD

∠ACB = ∠DCA

∴ ∆ ABC ~ ∆ CAD

∴ AC/CD = BC/AC

⇒ AC² = CD × BC …(2)

Dividing eq..(1) by eq..(2)

AB²/AC² = (BD × BC)/(BC × CD)

⇒ AB²/AC² = BD/CD

∴ AB² : AC² = BD : CD

Given

a + b + c = 20

squaring both sides

a² + b² + c² + 2(ab + bc + ca) = 400

⇒ 152 + 2(ab + bc + ca) = 400

⇒ 2(ab + bc + ca) = 400 – 152 = 248

∴ ab + bc + ca = 124

We know that total first n natural odd number is n²

∴ The average of first n natural odd number = n²/n = n

∴ The average of the first 1234 odd numbers is equal to 1234

Let the cost price of profit article be 11x and loss article be 9x

The total cost price of two articles = 2000

⇒ 11x + 9x = 2000

⇒ 20x = 2000

⇒ x = 100

∴ The cost price of profit article = 11x = 11 × 100 = 1100 rupees

Given, (cosα/sinα + cosβ) + cosβ/(sinβ – cosα) = (x/sinα – cosβ) + (cosβ/sinβ + cosα)

⇒ cosβ/(sinβ – cosα) - (cosβ/sinβ + cosα) = (x/sinα – cosβ) -  (cosα/sinα + cosβ)

⇒ cosβ (sinβ + cosα -sinβ + cosα)/(sin ²β - cos ²α) = [x(sinα + cosβ) - cosα (sinα - cosβ)]/(sin ²α - cos ²β)

⇒ cosβ (sinβ + cosα -sinβ + cosα)/(1 - cos 2β - 1 +  sin ²α) = [x(sinα + cosβ) - cosα (sinα - cosβ)]/(sin 2α - cos 2β)

⇒ cosβ (sinβ + cosα -sinβ + cosα) = [x(sinα + cosβ) - cosα (sinα - cosβ)]

⇒ 2 cosα .cosβ = x(sinα + cosβ) - sinα.cosα + cosα. cosβ 

⇒ cosα. cosβ = x(sinα + cosβ) - sinα.cosα

⇒ cosα. cosβ + sinα.cosα = x(sinα + cosβ)

⇒ cosα(sinα + cosβ) = x(sinα + cosβ)

⇒ cosα = x

Ratio of amounts received by A, B and C = 15 : 2 : 3

Let amounts received by A, B and C be 15x, 2x and 3x respectively

According to question

15x + 2x + 3x = 8000

⇒ 20x = 8000

⇒ x = 400

Now,

Amounts received by A = 15x = 15 × 400 = 6000

Amounts received by B = 2x = 2 × 400 = 800

Amounts received by C = 3x = 3 × 400 = 1200

Ratio of number of notes of A, B and C = 6000/500 : 800/200 : 1200/100 = 12 : 4 : 12

∴ Ratio of number of notes of A, B and C = 3 : 1 : 3

Let cost price of an article be 100

After 19% discount cost price will be = 100 – 100 × 19% = 81

Let the third discount be x

∴ 100 × 90% × 96% × (100 – x)% = 81

⇒ 100 × 90/100 × 96/100 × (100 – x)/100 = 81

⇒ 100 × 9/10 × 96/100 × (100 – x)/100 = 81

⇒ 96/1000 × (100 - x) = 9

⇒ 96 × (100 - x) = 9000

⇒ 32(100 – x) = 3000

⇒ 3200 – 32x = 3000

⇒ 32x = 3200 – 3000 = 200

⇒ x = 200/32

∴ x = 6.25%

Let initial price of tea be Rs. 100

After increasing the price of tea = 100 + 100 × 20% = 100 + 20 = 120

But it is decided that expenditure towards tea in increase by 15%

∴ New expenditure = 100 + 100 × 15% = 115

Decrease in consumption = 120 – 115 = 5

Percentage decrease in consumption = (5/120) × 100 = 4.2%

Shortcut Trick

Radius of circumcircle = side of inscribed regular hexagon = r

Area of circle = πr²

Area of regular hexagon = (3√3/2)r²

Uncovered Area = πr² − (3√3/2)r² = r²(2π − 3√3) / 2

Ratio = Area of circle ÷ Uncovered Area = 2π / (2π − 3√3)

∴ The correct answer is 2π/(2π − 3√3).

Alternate Method

Given:

A regular hexagon is inscribed in a circle.

Formula Used:

Area of a circle = πr²

Area of a regular hexagon = 6 × (√3 / 4)a² (where a is the side length)

For a regular hexagon inscribed in a circle, the side length (a) equals the radius (r).

O r Shaded blue region = Area not covered by hexagon

Calculations:

⇒ Let the radius of the circle be r.

⇒ Side of the inscribed regular hexagon = r

⇒ Area of the circle = πr²

⇒ Area of the hexagon = 6 × (√3 / 4)r² = (3√3 / 2)r²

⇒ Area not covered by hexagon = Area of circle − Area of hexagon

⇒ Area not covered = πr² − (3√3 / 2)r²

⇒ Area not covered = r²(2π − 3√3) / 2

⇒ Required Ratio = (Area of circle) ÷ (Area not covered)

⇒ Ratio = πr² ÷ [r²(2π − 3√3) / 2]

⇒ Ratio = 2π / (2π − 3√3)

∴ The correct answer is 2π/(2π − 3√3).

Additional Information

Circumcircle of a Regular Hexagon

The circumcenter and incenter of a regular hexagon coincide. The radius of the circumscribed circle is exactly equal to the side length of the hexagon (R = a).

Incircle of a Regular Hexagon

The radius of a circle inscribed inside a regular hexagon is given by r = (a√3)/2. The ratio of the area of the circumcircle to the incircle is 4:3.

Area of an Equilateral Triangle

A regular hexagon is composed of exactly 6 identical equilateral triangles. The area of one such triangle with side a is (√3 / 4)a².

The correct answer is option 3, i.e. 1881.

• Census was conducted non-synchronously between 1865 and 1872 in different parts of the country.
• This effort culminating in 1872 has been popularly labelled as the first Census of India.
• However, the first synchronous Census in India was carried out in 1881.
• An unbroken chain of censuses since then gives the Indian Census a unique historical legacy unparalleled in the world.
• Census 2011 is the 15th Census in this continuous series from 1872 and the 7th since Independence.

The correct answer is option 3, i.e. Floppy Disk Drive.

• FDD stands for Floppy Disk Drive.
• A floppy disk drive (FDD), or floppy drive, is a hardware device that reads data storage information.
• It was invented in 1967 by a team at IBM and was one of the first types of hardware storage that could read/write a portable device.
• FDDs are used for reading and writing on removable floppy discs.
• Floppy disks are now outdated, and have been replaced by other storage devices such as USB and network file transfer.

The correct answer is option 4, i.e. Axis.

• Axis Bank has become the first bank in the country to introduce the Iris Scan Authentication feature for Aadhaar-based transactions through its micro ATM tablets.
• This service, which requires a customer to scan their iris on a tablet, will boost the Bank’s Financial Inclusion efforts by making Aadhaar authentication process hassle-free and offering easier access to digital banking for consumers especially in the rural parts of the country.
• Micro ATMs completely eliminate the requirement of debit cards, passwords, PINs, user IDs, etc. and empower consumers to avail banking services using only their Aadhaar numbers and biometrics (iris scan/fingerprint scan).

The correct answer is option 4, i.e. Uttar Pradesh.

• Khurja is a small city (and a municipal board) in the Bulandshah district in Uttar Pradesh.
• It is situated around 200 km from Delhi.
• Khurja supplies a large portion of the ceramics and pottery used in the country, hence it is sometimes called Khurja, The Ceramics City, which has thrived for over 500 years.
• One can find a workshop or a factory with an attached shop in almost every nook and corner of this town.
• Each workshop produces a wide range of ceramic products, which are popular buys among the tourists and businessmen visiting here.
• The products range from everyday items such as crockery and planter pots to decorative miniatures and wind chimes.

The correct answer is option 2, i.e. Eurasian plate is largely an oceanic plate.

• Plate tectonics is the theory that Earth’s outer shell is divided into several plates that glide over the mantle, the rocky inner layer above the core.
• The plates act like a hard and rigid shell compared to Earth’s mantle. This strong outer layer is called the lithosphere.
• Volcanic activity, earthquakes, mountain-building and oceanic trench formation occur along these plate boundaries. The relative movement of the plates typically ranges from zero to 100 mm annually.
• Plates move horizontally over the asthenosphere as rigid units.
• The Eurasian Plate has an estimated area of 67,800,000 square kilometers. It is the third-largest of the major tectonic plates. Most of the continents of Europe and Asia are in the Eurasian Plate.

The correct answer is option 1, i.e. Karolina Pliskova.

• ​Karolina Pliskova (Czech Republic) defeated Johanna Konta (United Kingdom) 6-3, 6-4 to win Women's Single Titles at Women's Tennis Association (WTA) Italian Open 2019.
• Rafael Nadal (Spain) defeated Novak Djokovic (Serbia) 6-0, 4-6, 6-1 to win Men's Single titles at Italian Open 2019.
• The 2019 Italian Open was a professional tennis tournament played on outdoor clay courts in Rome, Italy.
• It was the 76th edition of the Italian Open.

The correct answer is option 3, i.e. Raghuram Rajan.

• Former Reserve Bank of India (RBI) Governor Raghuram Rajan has been chosen for the 'Yashwantrao Chavan National Award 2018' for his contribution towards economic development.
• Raghuram Rajan has presented the award at a function on March 12 on the occasion of 106th birth anniversary of late Yashwantrao Chavan, who was the first chief minister of Maharashtra
• Rajan served as RBI governor between September 2013 and September 2016.
• The award is given every year by the Yashwantrao Chavan Prathisthan to individuals/institutions in recognition of their outstanding contribution towards national integration, democratic values, and social and economic development

The correct answer is option 1, i.e. Virat Kohli.

• The Five Cricketers of the Year are chosen by Lawrence Booth, the editor of the Wisden Cricketers' Almanack, with the 2019 version serving as the 156th edition.
• Indian captain Virat Kohli was named The Wisden Almanack’s Leading Cricketer of the Year for 2018 while Smriti Mandhana won the Women’s Leading Cricketer award.
• The Indian skipper was picked as one of the five Wisden Cricketers of the year, along with England's Tammy Beaumont, Jos Buttler, Sam Curran and Rory Burns.
• Kohli topped the run charts in India’s 4-1 Test series defeat to England last summer. On the naming of the batsman as one of Wisden’s Five Cricketers of the Year.
• Kohli is only the third cricketer ever to have won the award more than three times after Don Bradman (10 times) and Jack Hobbs (8 times) having amassed 2735 runs across the three formats in 2018.
• On October 24, 2018, Kohli became the fastest cricketer to score 10,000 runs in One-Day Internationals.
• In January 2018, Kohli became the first player in the history of the game to win the Sir Garfield Sobers Trophy for ICC Cricketer of the Year
• The Almanack was first introduced in 1889 to recognise the excellence of players who have performed in England during the previous summer and it is considered as one of the more prestigious awards in the sport.

The correct answer is option 1, i.e. peasants who were affected by crop failure and a plague epidemic.

• ​​The Kheda Satyagraha of 1918, in the Kheda district of Gujarat, India during the period of the British Raj, was a Satyagraha movement organized by Mohandas Gandhi.
• People of Kheda were unable to pay the high taxes levied by the British due to crop failure and a plague epidemic.
• It was a major revolt in the Indian independence movement. It was the third Satyagraha movement after Champaran Satyagraha and Ahmedabad mill strike.
• Gandhi organised this movement to support peasants of the Kheda district.

The correct answer is option 3, i.e. Bolo.

• Tech giant Google unveiled a new app 'Bolo' that aims to help children in primary school learn to read in Hindi and English.
• The free app, which is being launched in India first, uses Google's speech recognition and text-to-speech technology.
• The app features an animated character 'Diya', who encourages children to read stories aloud and helps if the child is unable to pronounce a word.
• It also lauds the reader when she completes the reading.
• The Bolo app will be available on Google Play Store in India for all smartphones running Android 4.4 (Kit Kat) and higher, and can also work offline.

The correct answer is option 2, i.e. Committee on Estimates.

• The Estimates Committee is a Committee of Lok Sabha.
• The motion for election of the first Estimates Committee was adopted by the Provisional Parliament on 3rd April 1950 and the Committee was elected on 10th April 1950.
• The Committee consists of not more than 30 members from Lok Sabha who shall be elected by the House every year from amongst its members according to the principle of promotional representation by means of a single transferable vote.
• The Speaker is empowered to appoint the Chairman of the Committee from amongst its members.
• Currently, Shri Girish Bhalchandra is the chairperson of the Estimate Committee.

The correct answer is option 2, i.e. Bank Rate.

• A bank rate is the interest rate at which a nation's central bank lends money to domestic banks.
• Managing the bank rate is a method by which central banks affect economic activity. Lower bank rates can help to expand the economy by lowering the cost of funds for borrowers, and higher bank rates help to reign in the economy when inflation is higher than desired.
• Besides CRR, Banks have to invest a certain percentage of their deposits in specified financial securities like Central Government or State Government securities. This percentage is known as SLR.
• This money is predominantly invested in government-approved securities (bonds), Gold, which mean the banks can earn some amount as 'interest' on these investments as against CRR where they do not earn anything.
• Prime Lending rate: The interest rate charged by banks to their largest, more secure and most creditworthy customers on short-term loans.
• Sub-prime lending usually refers to the practice of giving loans to those who do not qualify for regular loans at market interest rates because of their poor credit history.
• Due to the increased risk associated with the takers, sub-prime loans are offered at a rate higher than market rates.
• These loans are risky for both, those who are giving and those who are taking because these combine high-interest rates, bad credit history, and often, murky financial situations of the takers.

The correct answer is option 3, i.e. Kalibangan.

Key Points

• The Indus Valley Civilization sites spread over the whole of Sind, Baluchistan, almost the whole of Punjab, northern Rajasthan, Kathiawar, and Gujarat.
• Kalibangan, is one of the famous Indus cities discovered in 1953 by A Ghosh, is situated in Rajasthan on the banks of River Ghaggar. Kalibangan stands for black bangles.
• Ploughing field and the bronze figure of a bull have been found at Kalibangan, Indus valley civilization sites.
• Harappa the first Indus site, was discovered by Dayaram Sahni in 1921.
• It is situated in the province of West Punjab, Montgomery district in Pakistan.

Additional Information 

Harappa: It is an archaeological site in Punjab, Pakistan, about 24 km west of Sahiwal. The site takes its name from a modern village located near the former course of the Ravi River which now runs 8 km to the north.

Mohenjo Daro: It is an archaeological site in the province of Sindh, Pakistan. Built around 2500 BCE, it was one of the largest settlements of the ancient Indus Valley Civilisation.

Chanhudaro: It is an archaeological site belonging to the Indus Valley Civilization. The site is located 130 kilometers south of Mohenjo-daro, in Sindh, Pakistan.

The correct answer is option 2, i.e. 0 and 1.

• Binary code, code used in digital computers, based on a binary number system in which there are only two possible states, off and on, usually symbolized by 0 and 1.
• A binary code signal is a series of electrical pulses that represent numbers, characters, and operations to be performed.
• A device called a clock sends out regular pulses, and components such as transistors switch on (1) or off (0) to pass or block the pulses.
• Whereas in a decimal system, which employs 10 digits, each digit position represents a power of 10 (100, 1,000, etc.), in a binary system each digit position represents a power of 2 (4, 8, 16, etc.).

The correct answer is option 3, i.e. Rishabh Pant.

• India’s fast-rising wicketkeeper-batsman Rishabh Pant named the International Cricket Council’s Emerging Player of the Year in the world body’s annual awards.
• He became the first Indian wicket-keeper to score a Test century in England and equalled the record for the most catches taken in a Test, with 11 against Australia in Adelaide
• He was also the first Indian wicket-keeper to score a Test hundred in Australia.
• Kohli, who was the ODI Cricketer of the Year and Cricketer of the Year last year, was named the captain of both the Test Team and ODI Team of the Year for the second year in a row.

The correct answer is option 4, i.e. Karnataka.

• Kasuti is a traditional form of folk embroidery practiced in the state of Karnataka.
• Kasuti work which is very intricate sometimes involves putting up to 5,000 stitches by hand and is traditionally made on dress wear like Ilkal sarees, Ravike and Angi or Kurta.
• The Karnataka Handicrafts Development Corporation (KHDC) holds a Geographical Indications (GI) protection for Kasuti embroidery which provides Intellectual Property rights on Kasuti to KHDC.
• GI is an indication used on products that have a specific geographical origin and possess the qualities or reputation that are due to that origin.

The correct answer is option 4, i.e. Ural.

• Russia recently launched nuclear-powered Arctic icebreaker named ‘Ural’ at Baltic Shipyard in St. Petersburg.
• Russian President Vladimir Putin announced in April 2019 that Russia will step up construction of icebreakers with aim of significantly boosting freight traffic along its Arctic coast.
• The ship, named as ‘Ural’ was floated out from a dockyard at Baltic Shipyard in St Petersburg. It is one of the trio which when completed will be largest and most powerful icebreakers in world.
• Russia launched a nuclear-powered icebreaker, part of an ambitious programme to renew and expand its fleet of the vessels in order to improve its ability to tap the Arctic’s commercial potential.

CONCEPT:

• The temperature is usually measured with a thermometer which is marked in several temperature scales mainly Celsius, Fahrenheit, and Kelvin.
• The SI unit of temperature as per the International System of Units is Kelvin which is represented by the symbol K.

EXPLANATION:

• Ampere is the SI unit of current. Therefore option 1 is incorrect.
• In certain fields of engineering, there is another absolute temperature scale for temperature measurement and that is the Rankine scale. Therefore option 2 is incorrect.
• The candela is the SI unit of luminous intensity. Therefore option 3 is incorrect.
• From above it is clear that the SI unit of temperature is Kelvin. Therefore option 4 is correct.

Important Points

• All the temperatures are related to each other by the following relationship –

$\frac{{F - 32}}{9} = \frac{C}{5} = \frac{{K - 273}}{5}$

The correct answer is option 2, i.e. 14th.

• In June 2017 the BJP announced Kovind as the party’s candidate to succeed Pranab Mukherjee in the ceremonial office of president.
• Ram Nath Kovind became the 14th President of India.
• Chief Justice of India Justice JS Khehar administered the oath of office to Kovind in the historic central hall of parliament.
• He faced Meira Kumar, former speaker of the Lok Sabha (the lower house), and herself a Dalit.
• In spite of the fact that his low-key profile made him relatively unknown, he won nearly two-thirds of the vote. Kovind was sworn in as India’s 14th president in July 2017.

The correct answer is option 4, i.e. Maharashtra.

• Matheran, a hill station deep in the forests of the Western Ghats, but just 81 km from Mumbai.
• This 800m high hill station is located in Alibagh district of Maharashtra​.
• Automobiles are banned in Matheran, declared an eco-sensitive zone by the by the Ministry of Environment and Forests. in 2003.
• It is appealing to have a view of the valleys from this green and calm hill station.

The correct answer is option 4, i.e. Goa.

• Ghumot is Goa’s indigenous traditional percussion instrument made from an earthen vessel.
• This year in February 2019, ghumot was notified as a heritage instrument of Goa, Art, and Culture.
• The instrument was banned due to the use of the skin of the endangered monitor lizard for the drum membrane.
• In recent years, ghumot makers have started using goatskin instead.
• A few years ago, minister Rohan Khaunte had made a case to lift the ban by using permissible material.
• Since the ban is applicable to the use of any animal listed in the Wildlife (Protection) Act, 1972, but the goat is not one of them.

The correct answer is option 1, i.e. The range lying to the immediate south of the Himadri is called the Shiwaliks.

• The Himalayas, which literally means the abode of snow, is the youngest and the highest range of fold mountains in the world, covering a distance of about 2500 km.
• The Himalayas consist of three parallel ranges, the Greater Himalayas known as the Himadri, the Lesser Himalayas called the Himachal, and the Shivalik hills, which comprise the foothills.
• The following are the three major divisions of the Himalayas running from north to south:
• The Himadri: It is the northernmost range of the young Himalayan mountains. It contains most of the highest peaks like Mt Everest, Kanchenjunga, etc.
• The Himachal: It is also known as the lesser Himalayas. This range lies to the south of the Himadri. Almost all the hill stations such as Shimla, Nainital, and Manali are located along with this range. Hence, statement 1 is incorrect, and hence the correct option (the question asks NOT correct)
• The Shiwaliks: This is the outermost range of the Himalayas. These ranges are made up of the sediments which are brought down from the rivers flowing from the northern Himalayan ranges. The valleys which separate the lesser Himalayas and the Siwaliks are called Duns or Doons, like Dehra Dun, Patli Dun, and Kotli Dun.

The correct answer is option 1, i.e. 20 Hz - 20000 Hz.

 Concept:

Frequency: The number of waves that pass a fixed point in unit time.

The unit of frequency is Hertz (Hz).

• Infrasonic sounds have the frequency of less than 20 Hz and these are generally produced by sources of a bigger size such as earthquakes, volcanic eruptions, etc.
• Sound waves with frequencies below the audible range are called infrasonic.
• Audible sounds have the frequency of 20-20000 Hz since these are sensitive to the human ears
• And if the frequency is greater or less then audible frequency, human ear won't be able to sense it
• Ultrasonic sounds have a frequency greater than 20000 Hz and certain creatures such as dog, cat, a bat can hear this kind of sound.

Explanation:

From the above explanation, we can see that,

• Humans can detect sounds in a frequency range from about 20 Hz to 20 kHz(20000 Hz).
• The human hearing range depends on both the pitch of the sound – whether it is high or low – and the loudness of the sound. Pitch is measured in Hertz (Hz) and loudness is measured in decibels (dB).
• However, elephants can hear waves as low as 14 Hz, while cats can hear up to 64,000 Hz frequencies, and bats can sometimes pick up noises as high as 200,000 Hz.

The correct answer is option 3, i.e. Alharthi is the second Arabic author to win this prize.

• Omani author Jokha al-Harthi wins the Man Bookers International Prize 2019.
• She has become the first Arabic-language writer to win the Man Booker International Prize with Celestial Bodies.
• The author plans to split the £50,000 prize money with her translator, US academic professor Marilyn Booth.
• Jokha Alharthi’s winning novel tells the story of three sisters and a desert country confronting its slave-owning past and a complex modern world.

CONCEPT: 

• Electromagnetic spectrum: It is a collection of a range of different waves in sequential order from radio to gamma electromagnetic waves.

EXPLANATION:

• Radar is an acronym for Radio Detection and Ranging.  The term "radio" refers to the use of electromagnetic waves with wavelengths in the so-called radio wave portion of the spectrum, which covers a wide range from 10⁴ km to 1 cm.
• It is basically an electromagnetic system used to detect the location and distance of an object from the point where the RADAR is placed.
• It works by radiating energy into space and monitoring the echo or reflected signal from the objects.
• Due to their short wavelengths, microwaves are suitable for the radar systems used in aircraft navigation.
• Radar also provides the basis for the speed guns used to time fastballs, tennis serves, and automobiles