SSC CHSL Previous Paper 22 (Held On: 10 July 2019 Shift 3) (Previous Year Paper)

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

• deprive: prevent (a person or place) from having or using something.
• The given sentence talks about the employees not being prevented from their freedom, hence, deprive fits in the context of the given sentence, so, it will be used in the given blank.
• deny: state that one refuses to admit the truth or existence of.
• dissipate: disperse or scatter.
• deploy: move (troops or equipment) into position for military action.

• The correct answer is Option 1 'avoid the topic'.
• The meaning of the given underlined idiom 'beat around the bush' means 'To delay or avoid talking about something difficult or unpleasant.'
• Therefore, only option 1 gives the meaning of the given idiom.

The correct answer is Option 2.

Explanation:​

Wary: Cautious, guarded, careful.

• Inattentive: of or pertaining to lack of attention; careless.
• Alert: Attentive, awake; on guard.
• Rash: Acting too quickly without considering the consequences, careless.
• Lax: lenient and allowing for deviation, not strict.

Therefore, out of given alternatives, the word 'alert' gives the similar meaning as the given word.

The correct answer is Option 1.

Explanation:

Porous: Something that is porous has many small holes, so liquid or air can pass through, especially slowly

1. Impermeable: Impossible to pass through, not allowing passage.
2. Absorbent: Having the ability or tendency to absorb.
3. Spongy: Having the characteristics of a sponge.
4. Permeable: that which allows the passage of fluids.

Therefore, out of given alternatives the word 'impermeable' is the opposite word to the given word.

• The correct answer is Option 4.
• The word 'excruciating' means 'causing great pain' is absolutely correct in the given sentence because the sentence is talking about the extreme pain caused when the hammer fell on his foot.
• Option 1 is wrong because the word 'affable' means 'friendly, courteous, sociable'. This word cannot be used to describe the pain.
• Option 2 is wrong because the word 'exciting' means stirring the emotions or causing excitement cannot be used to describe pain.
• Option 3 is wrong is because 'strong pains' is grammatically wrong as the word 'strong' means 'capable of producing great physical force'.
• Therefore, the correct answer is Option 4 'No Improvement'.

• The correct answer is Option 1 'controversy' which means 'A debate or discussion of opposing opinions'.
• The correct spelling and meaning of other words:
• Contradiction: To be contrary to something, to deny the truth of.
• Construction: The process of building.
• Contraption: A machine that is complicated and precarious.

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

Explanation:

• Let's look at the meanings of the given options. 
• Aborigines: a person, animal, or plant that has been in a country or region from the earliest times.
• Immigrants: a person who comes to live permanently in a foreign country
• Residents: a person who lives somewhere permanently or on a long-term basis.
• Slaves:  a person who is the legal property of another and is forced to obey them.
• Hence from the above-given meanings, we find that the correct answer is Option 3 i.e aborigines.

The correct answer is option 3) i.e. a new student asked me where the Principal's office was.

• when direct speech is in interrogation form 'said to' is changed into 'asked'.
• And the present tense of the sentence is also changed into the past tense.
• And the interrogative sentence is changed into the assertive sentence.
• All these rules are followed in option 3), hence, it is the correct answer.

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

Explanation:

amass: gather together or accumulate something over a period of time.

• distribute: give a share or a unit of something to each of a number of recipients. Hence, this is the most appropriate antonym of the given word.
• heap: a large amount or number of.
• collect: bring or gather together a number of things.
• horde: a large group of people.

The correct answer is option 4) i.e. waved feverishly.

• The given sentence is in the past tense, hence, 'waved' will be used in place of 'wave'.
• Hence, the correct answer is 'waved feverishly'.

ADDITIONAL INFORMATION

• feverishly = in a frenetically excited or energetic manner.

"a feverishly anticipated major sports tournament"

The correct answer is option 2) i.e. had been lives.

• The given sentence is in the present perfect continuous tense.
• And, in the present perfect continuous tense, has/have+ been + V1+ing is used.
• Hence, has been living will be used in the given sentence.
• So, the correct sentence will be: My grandmother has been living in Shimla since her childhood days.

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

Explanation:

• A pain in the neck means someone or something that is very annoying or irritating.

Example: He was a pain in the neck. I was glad when he left my department.

• ​Synonyms: Annoyance, nuisance, irritant, etc.

• The correct answer is Option 2.
• When changing active sentence to its passive form, subject and object interchange their places.
• Option 1 is wrong because the sentence is in the present tense but the given active sentence is in past tense. Tense remains the same in both sentences.
• Option 4 is wrong because the subject 'children' is in plural form so it is followed by the plural verb i.e. 'were'.
• Option 3 is wrong because 'being' is used while making the passive voice of continuous tenses but the given sentence is in past indefinite.
• Therefore Option 2 'The children were given prizes by the chief guest' is the correct answer.

• The correct answer is Option 2.
• The answer begins with sentence C as it is the introductory sentence. In all other remaining questions, there is a pronoun 'she/her' in which we do not know about the subject.
• The second sentence will be D because after introducing the grandmother, the sequence should be continued with her daily activities right from the morning.
• Sentence B will be the last sentence as we have the adverb 'finally'.
• Therefore, the correct sequence is followed by Option 2 i.e. 'CDAB'.

• The correct answer is Option 4.
• 'little' is used before uncountable nouns. Metals are countable therefore we use 'few/a few' in the given sentence.
• Therefore, the correct sentence is 'few/a few metals are as precious as gold.'

The meanings of the given words are as follows:

Recede: (of a quality, feeling, or possibility) gradually diminish/decrease, to move back, to retreat.

1. Waver: to sway back and forth;
2. Increase: to become larger or greater.
3. Wane**: a gradual decrease in power, value, intensity.**
4. Intensify: To act with increasing power or energy.

Clearly, 'wane' and 'recede' are words with similar meanings.

Thus, the correct answer is Option 3.

• The correct answer is Option 1.
• Given sentences are part of a conversation. The correct sequence will be first asking for an order, taking the order, then asking if they something more.
• Therefore, the correct sequence is followed by Option 1 'BADC'.

• The correct answer is Option 2.
• The correct word that fits here is other. 'each other' indicates a mutual relation between two entity..

• The correct answer is Option 4.
• The word 'situation' fits in the given blank because further in the passage it is explained about the difficult situation that he faces.
• Therefore, the correct answer is 'situation'. All other words are not relevant according to the passage.

• The correct answer is Option 3.
• The word 'fight' fits correctly in the given blank because the sentence is talking about a difficult situation that he faces. In passage the word 'duel' means 'struggle between two people or parties'.
• Therefore the word 'fight' is a suitable word and all other options are irrelevant to the passage.

• The correct answer is Option 4.
• The suitable word that fits the blank is 'matter' which means 'an approximate amount or extent' according to the passage.
• In passage we are mentioning time so the use of other options 'in place/gap/time of three hours' do not make a proper sense.

• The correct answer is Option 3.
• In the given passage the person is in a situation in which he says If they kill him any way he shall be killed by his fellow soldier.
• Therefore, the word 'at least' fits the blank correctly as it means 'any way/at a minimum'.
• All other options do not give the proper meaning in the blank

The correct answer is Option 2.

The sentence 'The Prime Minister was extended with a ceremonial welcome' means he was bestowed long and warmly with honour at the time of 'welcome'. 

All other options are irrelevant as they mean :

• Invite: To make a polite request to welcome.
• Initiated: To begin, to start.
• Expected: regarded as likely; anticipated.

• The correct answer is Option 2.
• The meaning of the word 'necessary' is 'Required, essential'.

• The correct answer is Option 1 'dermatologist' which means 'a person who is skilled in, professes or practices dermatology(Study of skin & its diseases)'.
• The meaning of other words:
• Radiologist: The person who practices radiology(the use of radiation in diagnosis)
• Geologist: A person who is skilled at geology(study if structure of earth)
• Cardiologist: A physician who specializes in medical problems related to the heart.

The least possible Veen diagram is given below,

Conclusions:

I. All swords are knife → False (some swords are knives is true)

II. Some axes are saws → False (It is possible but not definite).

III. No axe is saw → False (It is possible but not definite).

So, conclusion II and III are complementary to each other.

Hence, the correct answer is Either conclusion II or III follows.

81 → 9²

121 → 11²

16 → 4²

100 → 10²

Therefore, all numbers are a square form of the compound number except 121,

Whereas, 121 is the square of a prime number.

Hence, 121 is the odd one out.

Considering 1^st two dice. We get

 as a constant term, so if we rotate these dice from this then we get

 is the opposite side of

”

Hence, the correct answer is

Wools, wood, and leather are three different things,

Therefore, figure 2 is the correct answer.

The correct meaningful order will be

Spring → Summer → Monsoon → Autumn → Winter

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

The pattern followed here is,

Similarly,

Hence, the correct answer is WJXPIU.

2016 is a leap year so we get an extra odd day with respect to the ordinary year. So we get one extra day.

Therefore, the day will be Friday + 1 = Saturday.

Hence, the correct answer is Saturday.

When the paper is unfolded it will appear as in the following figure:

Hence, the correct answer is figure 3.

The sum of the positional value of CAT = 3 + 1 + 20 = 24 and 24 × 3 (Number of letters) = 72 

Also,

TROT = 20 + 18 + 15 + 20 = 73 and 73 × 4 (Number of letters) = 292

So, the code for

The sum of the positional value of STAG = 19 + 20 + 1 + 7 = 47 and 47 × 4 (Number of letter) = 188

Hence, the correct answer is 188.

Given equation is

15 + 15 - 2 × 10 ÷ 35

Option 1:

• and –

15 - 15 + 2 × 10 ÷ 35

= 15 - 15 + 2 × 5/7

=15 - 15 + 10/7

= 10/7 ≠16

Option 2:

× and –

15 + 15 × 2 - 10 ÷ 35

=15 + 15 × 2 – 5/7

=15 + 30 -5/7

=45 – 5/7

=310/7 ≠16

Option 3:

× and ÷

15 + 15 × 2 - 10 ÷ 35

= 15 + 15 ÷ 2 – 10 × 35

= 15 + 15/2 - 10 × 35

= 15 + 15/2 – 350

= 45/2 – 350

= -655/2 ≠16

Option 4:

+ and ÷

15 + 15 - 2 × 10 ÷ 35

= 15 ÷ 15 - 2 × 10 + 35

= 1 – 20 + 35

= 1 - 20 + 35

= 36 – 20

= 16

Hence, the correct answer is + and ÷.

The mirror image will be,

Hence, option 3 is the correct answer.

Hence, option 4 is the correct answer.

“Machine” is operated by “operator” similarly, “car” is operated by “driver”.

Hence, the correct answer is Driver.

The pattern followed here is,

Similarly,

Hence, the correct answer is WB

Hairs are trim according to their growth,

Similarly,

Shrubs are pruned if they grow more.

Hence, the correct answer is 'Prune : Shrub'.

The 'waves' shown in the figures are moving in the anticlockwise direction in each figure.

Hence the next figure will be,

Hence, the correct answer is option 2.

The squares are:

ABCD, EFGH, IJXT, JKWX, KLMW, TXUS, XWVU, WMNV, SUQR, UVPQ, VNOP, IKVS, JLNU, TWPR, XMOQ, ILOR.

Hence, the correct answer is 16.

The pattern followed here is,

(45, 49, 47) → 45 + 49 = 94 ÷ 2 = 47

Similarly,

(35, 59, 47) → 35 + 59 = 94 ÷ 2 = 47

Hence, (35, 59, 47) is the correct answer.

The family tree is as shown below:

Therefore, the girl is the sister of Deepthi.

Hence, the correct answer is sister.

The pattern followed here is,

Hence, the correct answer is 720.

Given series:

Similarly,

Hence, the correct answer is 12 : 20.

Alternate Method

The logic followed here is:

For, 

42 : 56

→ 62 + 6 = 42.

→ 72 + 7 = 56.

Similarly, for 12 : 20

→ 32 + 3 = 12.

→ 42 + 4 = 20.

Hence, the correct answer is '12 : 20'.

The pattern followed here is,

Hence, the correct answer is PM.

The pattern followed here is,

Therefore, the correct term will be BFJ,

Hence, 'BFM' is an odd one out.

All options except disaster are the effect of all of them.

Hence, 'Disaster' is the odd one out.

Given series

(64, 100, 328) = 64 → 8² = 64, 100 → 10² and 10 + 8 = 18² = 324 + 4 = 328

Option 1:

(25, 49, 148)= 25 → 5² = 25, 49 → 7² and 5 + 7 = 12² = 144 + 4 = 148;

Option 2:

(49, 81, 137) = 49 → 7² = 49, 81 → 9² and 7 + 9 = 16² = 256 + 4 = 260 (not follow)

Option 3:

(16, 36, 54) = 16 → 4² = 16, 36 → 6² and 4 + 6 = 10² = 100 + 4 = 104 (not follow)

Option 4:

(36, 64, 97) = 36 → 6² = 36, 64 → 8² and 8 + 6 = 14² = 196 + 4 = 200 (not follow)

Hence, the correct answer is (25, 49, 148)

Calculation:

CP = Rs.100

MP = 100 + 100 × 25/100 = 125

Profit % = 15% = 15/100 = 3/20

CP/SP = 20/23

20 units = 100

1 unit = 5

SP (23 units) = 5 × 23 = Rs.115

Discount% calculation,

115 = 125 × (100 - x)/100

⇒ X = 8%

∴ The answer is 8%.

By options,

Sin(75° + 15°) = sin90° = 1

Cos(75° - 15°) = cos60° = ½

The only option satisfying is option 4.

Shortcut Trick

The total area of a circle in terms of circumference C is given directly by A_total = C² / 4π.

A sector with a central angle of 60° covers exactly 60° ÷ 360° = 1/6 of the total area of the circle.

Area of sector (A) = (1/6) × (C² / 4π) = C² / 24π.

∴ The correct answer is C² / 24π.

Alternate Method

Given:

⇒ Central angle of the sector (θ) = 60°

⇒ Circumference of the circle = C

Formula Used:

⇒ Circumference of a circle, C = 2πr (where r is the radius)

⇒ Area of a sector, A = (θ ÷ 360°) × πr²

Calculations:

⇒ From the circumference formula, we find the radius in terms of C:

⇒ r = C / 2π

⇒ Substitute the values of r and θ into the area formula:

⇒ A = (60° ÷ 360°) × π × (C / 2π)²

⇒ A = (1 / 6) × π × (C² / 4π²)

⇒ The π in the numerator cancels out with one π in the denominator:

⇒ A = (1 / 6) × (C² / 4π)

⇒ A = C² / 24π

∴ The correct answer is C² / 24π.

Additional Information

Area of a Complete Circle

The total area enclosed by a circle corresponds to a central angle of 360° and is given by A = πr².

Length of an Arc

The length of an arc (l) forming a central angle θ is given by l = (θ ÷ 360°) × 2πr.

Area of a Circular Segment

The area of a minor segment is obtained by subtracting the area of the corresponding triangle from the total area of the sector.

Time = from 1^st January 2008 to 31^st august 2008

T = 8 months or 2/3 year

Simple interest = P × R × T/100

SI = [3000 × 15 × (2/3)]/100 = Rs.300

The amount that is to be returned by A = P + SI

⇒ 3000 + 300 = Rs.3300

Given:

Capacities of three containers = 40 L, 30 L and 20 L respectively.

Ratio of Milk and Water are, 3 : 2, 5 : 1 and 7 : 2 respectively.

Concept used:

We will be using the concept of ratio.

Calculation:

The quantity filled in container 1 = 40 × 87.5/100 = 35 L

The quantity filled in container 2 = 30 × 80/100 = 24 L

The quantity filled in container 3 = 20 × 90/100 = 18 L

The quantity of milk in container 1 = 35 × 3/5 = 21 L

The quantity of milk in container 2 = 24 × 5/6 = 20 L

The quantity of milk in container 3 = 18 × 7/9 = 14 L

The quantity of water in container 1 = 35 × 2/5 = 14 L

The quantity of water in container 2 = 24 × 1/6 = 4 L

The quantity of water in container 3 = 18 × 2/9 = 4 L

Required ratio = (21 + 20 + 14) : (14 + 4 + 4) = 55 : 22 = 5 : 2

Given:

OABC is a quadrilateral

O is the centre of a circle and A, B and C are points in the circle 

∠ABC = 120° 

Concept used:

1.) In a cyclic quadrilateral, the sum of the opposite angles is 180° 

2.) The angle subtended by an arc of a circle at the centre is double the angle subtended by it any other point on the remaining part o the circle.

Calculations:

Let us assume  a point E on a circle and join with A and C to form a Cyclic quadrilateral

∵ EABC is a cyclic quadrilateral 

∴ ∠AEC = 180° – ∠ABC 

⇒ ∠AEC = 180° – 120° = 60° 

Let angle subtended by arc AC of a circle at centre be x 

So, The angle subtended by arc AC at the remaining part of circle

⇒ ∠AEC = x/2

⇒ 60° = x/2 

⇒ x = 120°

∠AOC = 120° 

∵ OC = OA (Radius of circle)

∴ ∠OAC = ∠OCA 

In ΔOAC

∠OAC + ∠OCA + ∠AOC = 180° 

⇒ 2∠OAA = 180 – 120° 

⇒ ∠OAC = 30° 

Ratio of ∠AOC and ∠OAC = 120° ∶ 30° = 4 ∶ 1

∴ Ratio of ∠AOC and ∠OAC is 4 ∶ 1

Alternate Method

Consider, a circle with centre O.

Given that ∠ABC = 120° 

∠ABC = 180° - ∠ AOC/2

∴ ∠ AOC = 360° - 2∠ABC ⇒ 120° 

now,

∠A + ∠B + ∠C + ∠O = 360° 

∠A + 120° + ∠C + 120° = 360° 

∠ A + ∠ C = 360° - 240° = 120°

∠ A = ∠ C ⇒ 60° 

∴ ∠OAC = 30° 

Ratio of ∠AOC/∠OAC = 120° : 30° = 4 : 1

We know that the length = speed × time

For same length,

S₁ × t₁ = S₂ × t₂

90 × t₁ = 162 × t₂

$t_1 = \frac{162}{90}=9/5$ seconds

Considering the given numbers 7, 11 and 13

 LCM of (11,13 and 7) = 1001

Now, 

Any number of the form abcabc will always be divisible by 1001

∴ From the given options 259259 will always divisible by 1001

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,

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.

Now, given expression:

$\Rightarrow \frac{1}{2} \ of \ \frac{8}{5}\div \left\lbrace 2\frac{1}{5}-\left(\frac{5}{16}+ \frac{3}{5}\times 1 \frac{7}{8}\div \frac{2}{3}\right)\right\rbrace$

$\Rightarrow \frac{1}{2}\times \frac{8}{5}\div \left\lbrace \frac{11}{5}-\left( \frac{5}{16} + \frac{3}{5}\times \frac{15}{8} \div \frac{2}{3}\right)\right\rbrace$

$\Rightarrow \ \frac{4}{5}\div \left\lbrace \frac{11}{5}-\left(\frac{5}{16}+ \frac{3}{5} \times \frac{15}{8}\times \frac{3}{2}\right)\right\rbrace$

$\Rightarrow \frac{4}{5}\div \left\lbrace \frac{11}{5}-\left(\frac{5}{16}+\frac{27}{16}\right)\right\rbrace$

$\Rightarrow \ \frac{4}{5}\div \left\lbrace \frac{11}{5}-\frac{32}{16}\right\rbrace$

$\Rightarrow \frac{4}{5}\div \frac{1}{5}$

$\Rightarrow \frac{4}{5}\times \frac{5}{1}=4$

$X=\frac{1}{12}-\frac{1}{13}+\frac{1}{13}- \frac{1}{14}+...-\frac{1}{24}$

$X=\frac{1}{12}-\frac{1}{24}$

$X=\frac{1}{24}$

$Y=\frac{1}{36}-\frac{1}{37}+\frac{1}{37}-\frac{1}{38}+...-\frac{1}{72}$

$Y=\frac{1}{36}-\frac{1}{72}=\frac{1}{72}$

$Y=\frac{1}{36}-\frac{1}{72}=\frac{1}{72}$

X/Y = (1/24) / (1/72) = 3

⇒ 0.01404/(24² + 6² – 144)

⇒ 0.01404/(576 + 36 - 144)

⇒ 0.01404/468

⇒ 3 × 10 ^{- 5}

Given that,

θ = 9°

10θ = 90°

Given expression,

Cotθ.Cot2θ.Cot3θ.Cot4θ.Cot5θ.Cot6θ.Cot7θ.Cot8θ.Cot9θ

⇒ Cotθ.Cot2θ.Cot3θ.Cot4θ. Cot(90° - 4θ).Cot(90° - 3θ).Cot(90° - 2θ).Cot(90° - θ).Cot90°

⇒ Cotθ.Cot2θ.Cot3θ.Cot4θ. tan 4θ. tan 3θ. tan 2θ. tan θ.1 = 1 (∵ tanθ = 1/cotθ)

Shortcut Trick

Fractional values of discounts: 10% = 1/10 and 5% = 1/20.

Multiplying factor for 10% discount = 1 − 1/10 = 9/10.

Multiplying factor for 5% discount = 1 − 1/20 = 19/20.

SP = MP × (9/10) × (19/20)

SP = 800 × (171 / 200) = 684

∴ The correct answer is Rs. 684.

Alternate Method

Given:

Marked Price (MP) = Rs. 800

First discount (D₁) = 10%

Second discount (D₂) = 5%

800 720 684

Marked Price After 1^st D Selling Price

− 10% (−80)

− 5% (−36)

Successive Discounts Method

Formula Used:

Selling Price (SP) = MP × (100 − D₁)/100 × (100 − D₂)/100

Calculation:

⇒ SP = 800 × (100 − 10)/100 × (100 − 5)/100

⇒ SP = 800 × (90/100) × (95/100)

⇒ SP = 800 × (9/10) × (19/20)

⇒ SP = 800 × (171/200)

⇒ SP = 4 × 171

⇒ SP = 684

∴ The correct answer is Rs. 684.

Additional Information

Successive Discounts Formula

When two successive discounts of x% and y% are given, the equivalent single discount is (x + y − xy/100)%.

Marked Price and Cost Price Relationship

MP / CP = (100 + Profit %) / (100 − Discount %)

Multiple Successive Discounts

For three successive discounts of a%, b%, and c%, SP = MP × (100 − a)/100 × (100 − b)/100 × (100 − c)/100.

(a + b)² = (a² + b² + 2ab)

(a + b)² = 169 + 2 × 60 = 289

(a + b) = 17

(a - b)² = (a² + b² - 2ab)

(a - b)² = 169 – 2 × 60 = 49

(a - b) = 7

∴ the value of (a² – b²) = (a + b)(a - b) = 17 × 7 = 119

Alternate Method

a2 + b2 = 169, ab = 60

So A.T.Q,

a = 12, b = 5 

∴ (a2 – b2) = (a + b) (a - b) = (12 + 5) (12 - 5) = 17 × 7 = 119

X = average of first 10 prime numbers = (2 + 3 + 5 + 7 + 11 + 13 + 17 + 19 + 23 + 29)/10 = 12.9

Y = average of first 10 prime numbers with two digits

Y = (11 + 13 + 17 + 19 + 23 + 29 + 31 + 37 + 41 + 43)/10 = 26.4

Difference between the averages = 26.4 – 12.9 = 13.5

1 man = 2 women

Work done by 3 men + 2 women = 2 days

Or (6 + 2) women do the work in 2 days.

Work done by 8 women in a day = ½

Work done by 1 woman in 1 day = 1/16

Hence, a woman working alone complete the work = 16 days

Let the length and breadth of the rectangular airport runway be l and b.

Area = l × b

New length = l × 110/100 = 1.1l

New breadth = b × 108/100 = 1.08b

New area (A) = 1.1l × 1.08b = 1.188lb

Change in cost,

R’ = R × 115/100 = 1.15R

Total cost of repairing = 1.15R × 1.188lb = 1.3662RA

Percentage change in cost = (1.3662RA - RA)/RA × 100 = 36.62%

The given expression,

$\sqrt {\frac{{\left( {1 - {\rm{sinx}}} \right)}}{{\left( {1{\rm{;}} + {\rm{;sinx}}} \right)}}} = a - \tan x$

$\Rightarrow ;\sqrt {\frac{{\left( {1 - {\rm{sinx}}} \right){\rm{;}} \times {\rm{;}}\left( {1 - {\rm{sinx}}} \right)}}{{\left( {1{\rm{;}} + {\rm{;sinx}}} \right)\left( {1 - {\rm{sinx}}} \right)}}} = a - \tan x$

⇒ (1 - sinx)/cosx = a – tanx

⇒ 1/cosx – tanx = a – tanx

⇒ 1/cosx = a

⇒ a = sec x

Theorem : the ratio of the area of two similar triangles = square of the ratio of their respective sides

Given that,

Area ABC : Area PRQ = 16 : 169 = (AC/PQ)2

⇒ AC/PQ = 4 : 13

⇒ y/PQ = 4 : 13

PQ = 13y/4

Given:

∠SAT = 45° 

SN = 10 cm

Concept used:

1. The length of the median drawn from the vertex of the right angle is half the length of the triangle's hypotenuse.

2. The angle between the tangent and the line joining the center of a circle and the point of contact of the tangent to the circle is equal to 90°.

Calculation:

As AT is the tangent,

∠OAT = 90°

Again ∠SAT = 45°

∴ ∠OAS = 90° - 45° = 45°

In ΔOAS,

OA = OS = Radius

∠OAS = ∠OSA = 45°

Then ∠NOS = 180° - 45° - 45° = 90°

⇒ ΔSON is a right-angles triangle

Thus, OM = SN/2

⇒ OM = 10/2 = 5 cm

∴ The length of the median OM of ΔSON is 5 cm.

In ΔABC,

Let AB = c, BC = a and AC = b

And BP = PQ = QR = RC = a/4

Now, AP² = AB² + BP² = c² + (a/4)²

AQ² = AB² + BQ² = c² + (2a/4)²

AR² = AB² + BR² = c² + (3a/4)²

Add the above three equations,

AP² + AQ² + AR² = 3c² + 14a²/16 = 3c² + 7a²/8

Again from ΔABC,

b² = a² + c²

c² = b² - a²

AP² + AQ² + AR² = 3(b² - a²) + 7a²/8 = 3b² -3a² + 7a²/8

 = 3b² (- 24a² + 7a²)/8  = 3b² + 17.n.a² 

(3b² - 17na²/8) = 3b² + 17na²

Hence, n = - (1/8)

Savings for 2012 = (6 - 5) = 1 lakh, required ratio = 1 : 5

Savings for 2013 = (7 – 5.5) = 1.5 lakh, required ratio = 1.5 : 5.5 = 3 : 11

Savings for 2014 = (8 - 6) = 2 lakh, required ratio = 2 : 6 = 1 : 3

Savings for 2015 = (9 – 7.5) = 1.5 lakh, required ratio = 1.5 : 7.5 = 1 : 5

Savings for 2016 = (10 – 8) = 2 lakh, required ratio = 2 : 8 = 1 : 4

∴ the ratio is similar for year 2012 and 2015.

His total income for the period 2012 - 15 = (6 + 7 + 8 + 9) = 30 lakh

His total expenditure = (5 + 5.5 + 6 + 7.5) = 24 lakh

Total savings = (30 - 24) = 6 lakh

Required percentage = (6/30) × 100 = 20%

Expenditure from year 2012 - 13 = (5 + 5.5) = 10.5

Income from year 2012 - 13 = (6 + 7) = 13

Savings = (13 – 10.5) = 2.5

ratio = 2.5 : 10.5 = 5 : 21

Income from year 2015 - 16 = (9 + 10) = 19

Expenditure from year 2015 - 2016 = (7.5 + 8) = 15.5

Savings in years 2015 - 16 = (19 – 15.5) = 3.5

Ratio = 3.5 : 15.5 = 7 : 31

Required ratio = (5 : 21) : (7 : 31) = 155 : 147.

Income from year 2015 - 16 = (9 + 10) = 19

Expenditure from year 2015 - 2016 = (7.5 + 8) = 15.5

Savings in years 2015 - 16 = (19 – 15.5) = 3.5

average monthly savings (in Rs.) in 2015 and 2016 = (3.5 × 100000)/24 = 14,583.33

The correct answer is  Aurangzeb.

Key Points

• The alternative title "Alamgir" was adopted by Mughal emperor Aurangzeb which means 'world conqueror'.
• His original name was "Muhi-al-Din Muhammad".
• He was the last of the great Mughal emperors of India, from 1658 to 1707.
• Aurangzeb was the third son of the emperor Shah Jahan and Mumtaz Maḥal.
• He conquered Bijapur and Golconda.
• He discontinued the practice of jarokhadarshan, started by Akbar.
• He began a policy of destroying Hindu temples.
• He destroyed Mathura temple and Benares temple.
• In 1679, he reimposed Jizya and pilgrim tax, which was discontinued by Akbar.
• He was also against the Sikhs and he executed the ninth Sikh Guru Teg Bahadur.
• Aurangazeb is held responsible for the decline of the Mughal emperor due to his policies.

The correct answer is option 2, i.e. Badruddin Tyabji.

• Hindustan Socialist Republican Army(HSRA) established in 1928 at Feroz Shah Kotla ground in Delhi by Chandrasekhar Azad, Bhagat Singh, Sukhdev Thapar, Jatin Das, and Ajay Ghosh.
• Earlier it was known as the Hindustan Republican Association (HRA) whose written constitution and published a manifesto titled 'The Revolutionary' were produced as evidence in the Kakori conspiracy case of 1925.

About Badruddin Tyabji

• He was the first Muslim president of Indian National Congress in 1887 Madras session.

The correct answer is option 2, i.e. Kerosene.

• The amount of heat energy produced on complete combustion of 1 kg of a fuel is called its calorific value.
• The calorific value of a fuel is expressed in a unit called kilojoule per kg (kJ/kg).
• The calorific values of some fuels are given in Table.

• As we can see in the table Calorific value of Petrol, Kerosene, and Diesel are the same.

The correct answer is option 1, i.e. France and England.

• The Channel Tunnel is an undersea tunnel linking southern England and northern France.
• It is operated by the company Eurotunnel, who also runs a railway shuttle between Folkestone and Calais, carrying passengers in cars, vans and other vehicles.
• The Channel is actually comprised of three tunnels: two rail tunnels, used for freight and passenger trains, and a service tunnel.
• The idea of a tunnel under the Channel was first proposed in 1802 but construction wasn't started until 1988. It was completed in 1993.

The correct answer is option 2, i.e Dhansari.

• The important tributaries of Ganga are the Ramganga, the Gomati, the Ghaghara, the Gandak, the Kosi and the Mahanada.
• At Devprayag, the Bhagirathi meets the Alaknanda, then it is known as the Ganga.
• The Yamuna, the westernmost and the longest tributary of the Ganga, has its source in the Yamunotri glacier, it joins the Ganga at Prayag (Allahabad).
• The Hindon River, being a tributary of the Yamuna traces its origin from the lower Himalayan ranges housing the Upper Shivalik.
• The Kali River, originating in the Doon Valley, is a tributary of the Hindon river.
• The Son is the major right-bank tributary of the Ganga River. It is a large south bank tributary of the Ganga, originating in the Amarkantak plateau.
• While the River Dhansiri is one of the major south bank tributaries of the river Brahmaputra

The correct answer is option 3, i.e. Manufacturing brass and copper utensils.

• The craft of the Thatheras of Jandiala Guru constitutes the traditional technique of manufacturing brass and copper utensils in Punjab.
• The metals used are copper, brass and certain alloys, are believed to be beneficial for health.
• Heating the plates while hammering and curving them into different shapes requires temperature control.
• Utensils are manually finished by polishing with traditional materials like sand and tamarind juice.

The correct answer is option 3, i.e. 3^rd Schedule.

• ​In the Indian Constitution, presently there are 12 Schedules.
• The third Schedule consists of Forms of Oaths or Affirmations for:

1. The Union ministers
2. The candidates for election to the Parliament
3. The members of Parliament
4. The judges of the Supreme Court
5. The Comptroller and Auditor-General of India
6. The state ministers
7. The candidates for election to the state legislature
8. The members of the state legislature
9. The judges of the High Courts

• Articles which covered the third Schedule are 75, 84, 99, 124, 146, 173, 188 and 219.

The correct answer is option 4, i.e. World Economic Forum.

• The annual Global Competitiveness Index is compiled by the Geneva-based World Economic Forum (WEF).
• About Global Competitiveness Index 2019:
• The Global Competitiveness Index ranks 140 nations on the basis of 98 indicators organized into 12 pillars including infrastructure, institution, ICT adoption, macroeconomic stability, health, skills, product market, labour market, financial system, market size, business dynamism, and innovation capability.
• This year’s Global Competitiveness Report is the latest edition of the series launched in 1979 that provides an annual assessment of the drivers of productivity and long-term economic growth.
• Singapore is the world’s most competitive economy in 2019, overtaking the United States, Hong Kong SAR, Netherlands and Switzerland are the top 5 countries.
• India ranked 68^th in the annual Global Competitiveness Index 2019.

​

About WEF:

• The World Economic Forum is the International Organization for Public-Private Cooperation.
• It was established in 1971 as a not-for-profit foundation and is headquartered in Geneva, Switzerland.
• The Forum is chaired by Founder and Executive Chairman Professor Klaus Schwab.

The correct answer is option 3, i.e. GR Reddy.

• The book “Indian Fiscal Federalism” is written by Dr Y. V. Reddy, former Governor of RBI and Chairman of the 14^th Finance Commission of India along with Dr G. R. Reddy, Advisor (Finance) to the Government of Telangana
• The book offers a historical perspective on fiscal federalism, in particular, the interplay and overlap of institutional mechanisms.
• It examines the pivotal role of Finance Commissions and assesses momentous events since 2014, such as the replacement of the Planning Commission by NITI Aayog, the emergence of the GST Council, and the controversies surrounding the Fifteenth Finance Commission.

The correct answer is option 4, i.e. Cabinet Ministers of Union.

• The Indian Order of Precedence is the hierarchy of important positions.
• The order of the Precedence in India is only to indicate the ceremonial protocol. It is not applicable in the day-to-day functioning of the Government of India.

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

• The heart has four valves - one for each chamber of the heart.
• The valves keep blood moving through the heart in the right direction.
• The mitral valve and tricuspid valve are located between the atria (upper heart chambers) and the ventricles (lower heart chambers).
• The aortic valve and pulmonic valve are located between the ventricles and the major blood vessels leaving the heart.
• The septum of the heart is the dividing wall between the right and left sides of the heart.

The correct answer is option 1, i.e. Pooja Dhanda.

• Pooja Dhanda claimed gold in the 59kg category at the Dan Kolov-Nikola Petrov wrestling tournament in Ruse, Bulgaria.
• Bajrang Punia also won the 65kg category gold at the Dan Kolov-Nikola Petrov wrestling tournament.
• Dhanda finished undefeated in the round-robin format of the competition which included a win over her compatriot Sarita Mor.

The correct answer is option 1, i.e. Badminton.

• The Sudirman Cup is the World Team Badminton Championships, held every two years.
• The event was first held in the Bung Karno Stadium, Jakarta, Indonesia with 28 nations taking part.
• Nanning, China was the host of the 2019 edition of the mixed team event from 22-29 May.
• The Cup is named after Dick Sudirman, a former Indonesian badminton player and the founder of the Badminton Association of Indonesia (PBSI).
• Until 2003 the Sudirman Cup took place alongside the World Badminton Championships (Individuals) before becoming a stand-alone Championships for the first time in Eindhoven, the Netherlands in 2003.
• Since 1989, only three countries – Indonesia, Korea, and China, have won the Sudirman Cup.

The correct answer is PPT.

Key Points

• The functioning of the Internet is not controlled by any particular organization.
• It is managed by a group of voluntary organizations.
• These voluntary organizations have formed the Internet Society.
• They decide on the rules, known as protocols, for communication over the Internet.

Additional Information

Concept:-

• Liver: The liver is the largest gland of the body.
• Location: in the abdominal cavity, just below the diaphragm.
• Weight: 1.4 to 1.5 kg

Important Points

• Glycogen is the storage form of carbohydrates in mammals. In humans, the majority of glycogen is stored in skeletal muscles (∼500 g) and the liver (100 g).
• Glycogen is the liver released into the bloodstream when your blood sugar is low, such as between meals or during exercise.
• At least 25 grams of carbohydrates circulate in your bloodstream at a time.
• The sugar in your bloodstream that was released from your liver can then travel to the organ that needs it, such as the brain or exercising muscles.

The correct answer is option 2, i.e. 1024 kilobytes

Additional Information

• 1 Kilobyte = 1024 Bytes.
• 1 Megabyte = 1024 Kilobytes.
• 1 Gigabyte = 1024 Megabytes.
• 1 Terabyte = 1024 Gigabytes.
• Bits are usually assembled into a group of eight to form a byte.
• A bit can hold only one of two values: 0 or 1.

The correct answer is option 1, i.e. Shooting.

• Anjum Moudgil is an Indian Shooter.
• At ISSF World Cup in Beijing in April 2019, Anjum Moudgil and Divyansh Singh Panwar opened the country's gold account in the 10 metres Air Rifle Mixed Team event.
• ISSF stands for  International Shooting Sports Federation.
• The Headquarter of the International Shooting Sports Federation (ISSF) is located in Munich, Germany.
• It was founded in 1907.
• Vladimir Lisin is the current president of ISSF.

The correct answer is option 1, i.e. Gibraltar.

• The strait of Gibraltar separates Morocco and Spain.
• It joins the Mediterranean Sea and the Atlantic Ocean.
• A strait is a narrow channel of water that lies between two land masses and connects two larger water bodies.

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

• In Mexico, Prof. Norman Borlaug and his associates developed new varieties of wheat which were early-maturing, highly productive and disease resistant and these varieties were imported and planted in selected regions of India having adequate irrigation facilities.
• It was conclusively demonstrated that the yields from the new varieties exceeded 25 to 100 per cent compared to the yields from traditional varieties.
• High Yielding Variety Seeds (HYV seeds) are seeds that are of better quality than normal quality seeds.
• The produce from these seeds is a bit more compared to the normal ones.
• These seeds are a better option of seeds in order to obtain a healthy and surplus crop.
• These seeds have a good immune system to fight with insects and other diseases.

The correct answer is option 3, i.e. John Maynard Keynes.

• Macroeconomics is a branch of economics that studies how an overall economy—the market systems that operate on a large scale—behaves.
• Macroeconomics studies economy-wide phenomena such as inflation, price levels, rate of economic growth, national income, gross domestic product (GDP), and changes in unemployment.
• Macroeconomics, as it is in its modern form, is often defined as starting with John Maynard Keynes and the publication of his book The General Theory of Employment, Interest, and Money in 1936.

The correct answer is option 2, i.e. ensuring a minimum income for farmer families who own up to two hectares of cultivable land.

• Pradhan Mantri Kisan Samman Nidhi (PM-KISAN):
• Scheme Type: Central Sector Scheme.
• Ministry: Ministry of Agriculture and Farmer's Welfare.
• Launched Year: 2019
• Place of Launch: Gorakhpur, Uttar Pradesh
• Beneficiaries: All farmers irrespective of landholding (earlier land up to 2 hectares) are eligible for financial support.
• Financial Support: 6000 Rs. in three equal instalments of Rs.2000/- each every four months.
• Funds will be directly transferred to the bank account of the beneficiaries under the direct benefit scheme.
• Budget allocation: 20,000 crore for 2018-19, 75,000 crores for 2019-20.