SSC CGL Previous Paper (Held On: 4 June 2019 Shift 3) (Previous Year Paper)

Logic for coding SUNDAY is,

Similarly,

Hence, ‘HTOERM’ is the correct answer.

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

Given that,

÷ means Addition (+)

• means Subtraction (-)

• means Multiplication (×)

× means Division (÷)

After replacing the symbols we get,

54 ÷ 6 × 7 + 8 – 2 = 69.

Hence, 69 is the correct answer.

1. TUWZ: T + 1 → U; U + 2 → W; W + 3 → Z

2. PQTX: P + 1 → Q; Q + 3 → T; T + 4 → X

3. DEGJ: D + 1 → E; E + 2 → G; G + 3 → J

4. MNPS: M + 1 → N; N + 2 → P; P + 3 → S

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

Hence, the figure in option 4 is the correct answer.

Indulgences, Benevolence, Courtesy are qualities associated with a person’s attitude. Hindrance is a person or thing that interferes with or slows the progress of someone or something.

Hence, hindrance is the correct answer.

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

Number of triangle = 16

Total number of triangle in square = number of partition in square x 2

⇒ Total number of triangle in square = 8 x 2 = 16.

Hence, there are 16 triangles in the given figure.

Relation between the pairs of words in options 2, 3 and 4 →

Country : Currency

But, the currency of South Korea is South Korean Won.

Hence, ‘South Korea : Rupiya’ is the correct answer.

In the given figure, each square is divided into eight triangles.

Two symbols ‘X’ and ’O’ are changing their positions in the following manner:

1. Symbol ‘O’ is moving to the next alternate triangle in an anticlockwise direction.

2. Symbol ‘X’ is moving in a clockwise direction.

X moves to the adjacent triangle in the second figure.

It leaves one triangle in between while moving to its new position in the third figure.

It leaves two triangles in between while moving to its new position in the fourth figure.

Therefore, it must leave three triangles in between while moving to its new position in the fifth figure.

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

Frown is an expression caused by the feeling of displeasure.

Thus, the relation is expression: feeling

Similarly, smile is an expression caused by the feeling of ecstasy.

Hence, ‘smile: ecstasy’ is the correct answer.

Family tree diagram is as follows,

Hence, S is the sister-in-law of T.

From given fig. it can be concluded that 1,4,5,6 are on the four adjacent sides of 2. i.e. ‘3’ is on the opposite side of ‘2’.

Therefore, when ‘3’ is at the bottom, ‘2’ will be at the top.

Hence, ‘2’ is the correct answer.

Let’s check the options:

1. 15 - 9 × 6 ÷ 10 + 5 ≠ 25

2. 15 - 9 + 6 × 10 ÷ 5 ≠ 25

3. 15 × 9 ÷ 6 - 10 + 5 ≠ 25

4) 15 + 9 ÷ 6 × 10 - 5 = 25

Hence, ‘+ and -’ is the correct answer.

Similarly,

Hence, the code for KETTLE is ‘LGWXQK’.

The least possible Venn diagram for the given statements is as follows,

Conclusions:

I. Some mobiles are heavy items. → True (Some mobile are instruments and all instruments are heavy items)

II. No mobile is a heavy item. → False (conclusion I is true)

III. Some heavy items are instruments. → True (all instruments are heavy items)

Hence, only conclusion I and III follows.

The pattern followed here is:

D + 2 = F in the first pair.

Similarly, B + 2 = D in the second pair.

Hence, ‘DJIN’ is the correct answer.

1) G + E + S + O = 7 + 5 + 19 + 15 = 46 which is not a multiple of 4.

2. M + Z + L + Y = 13 + 26 + 12 + 25 = 76 = 4 × 19

3. I + V + H + U = 9 + 22 + 8 + 21 = 60 = 4 × 15

4. K + X + J + W = 11 + 24 + 10 + 23 = 68 = 4 × 17

All the other letter clusters are multiple of 4 except for GESO (46) hence the correct answer.

Hence, 'GESO’ is the correct answer.

Let’s consider each option:

1. cbadbccbabbccbaddc → no pattern followed

2. cbcdbacbabbcdbadcc → no pattern followed

3) cbadbc cbadbc cbadbc → follows a pattern

4. cbddbccbabbccbadbc → no pattern followed

Hence, ‘acdcb’ is the correct answer.

FLOWER (there are 6 letters in the word): 6 × 2 = 12; 12 + 2 = 14

DISTANCE (there are 8 letters in the word): 8 × 2 = 16; 16 + 2 = 18

Similarly,

BUREAUCRAT (there are 10 letters in the word): 10 × 2 = 20; 20 + 2 = 22

Hence, 22 is the correct answer.

Logic for relation between Second term to first term

(13 × 2) + 3 = 29.

Similarly,

(17 × 2) + 3 = 37.

Hence, 17 is the correct answer.

(9, 15, 27): 9 + 6 = 15; 15 + 12 = 27 where 12 = 2 × 6

Similarly,

(12, 20, 36): 12 + 8 = 20; 20 + 16 = 36 where 36 = 2 × 8

Hence, ‘(12, 20, 36)’ is the correct answer.

Alternate solution:

(9, 15, 27):  3 × 3 = 9, 3 × 5 = 15, 3 × 9 = 27

Similarly,

(12, 20, 36): 4 × 3 = 12, 4 × 5 = 20, 4 × 9 = 36

Hence, ‘(12, 20, 36)’ is the correct answer.

789, 567 and 123 are multiples of 3 but 457 is not.

Alternate solution:

7 + 9 = 16 and 16 ÷ 2 = 8

5 + 7 = 12 and 12 ÷ 2 = 6

1 + 3 = 4 and 4 ÷ 2 = 2

4 + 7 = 11 and 11 is not divisible by 2

Hence, 457 is the correct answer.

The correct logical order is:

School → Education → Recruitment → Employment → Salary → Promotion

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

• | Name | Post held | | --- | --- | | Leila Seth | First Woman Chief Justice of High Court(1991) | | Syeda Tahira Safdar | First Woman High Court Chief Justice In Pakistan(2018) | | M. Fathima Beevi | First female judge to be a part of the Supreme court of India | | Indira Gandhi | First Female Prime Minister | | Prathibha patil | First Female President | | Sarojini Naidu | First Female Governor | | Sucheta krupalini | First Female Chief Minister |

The correct answer is Pratihara.

Key Points

Mihira Bhoja was the 5^th ruler in the Gurjar pratihara dynasty. Pratihara dynasty founded by Nagabhatta I (8^th century)

Communicable disease: Harmful Microbes are transmitted from one host to another through direct contact or carriers.

Non Communicable diseases: They are chronic in nature. They may be acquired through a combination of genetic, physiological, environmental factors.

Key Points

Additional Information

White blood cells provide immunity to our body. They help in fighting against diseases, infections, allergies and foreign particles. These cells keep our body safe and healthy. White blood cell is called as "soldiers of the human body”.

The correct answer is option 1 i.e 1206 A.D. and 1526 A.D.

• Delhi Sultanate (1206 -1526) consists of Islamic rulers.
• It started with the Mamluk (Slave)dynasty and ended with the Lodi dynasty.
• Qutub-Ud-Din-Aibak (Mamluk Dynasty) was the first ruler and Ibrahim Lodhi (Lodhi Dynasty) the last of Delhi Sultanate.
• Mughal Sultanate (1526 -1857) started with Babar (Founder, Battle of Panipat 1) and ended with Bahadur Shah II who was exiled to Myanmar after the 1857 revolt.

Chennai Spartans defeated Calicut Heroes in the Pro Volleyball League or RuPay Pro Volleyball League .

Pro Volleyball League is a professional men's indoor volleyball league started for the first time in February 2019.

• Vidarbha (Represents Maharashtra) won against Saurashtra(Represents Gujarat) in  85^th Ranji Trophy .
• Ranji Trophy is First class domestic cricket.Named after Ranjithsinji(Maharaja of Nawanag an erstwhile Princely state of India), who played for England.
• Highest runs: Milind(1331 runs)
• Highest wickets: Ashutosh aman(68 wickets)
• | Ranji Trophy Edition/Year | Winners | Runner Up | | --- | --- | --- | | 85^Th Ranji Trophy,2019 | Vidarbha (Captain :Faiz Fazal) | Saurashtra (Captain:Jaydev Unadkat) | | 84^Th Ranji Trophy 2018 | Vidarbha (Captain :Faiz Fazal) | Delhi (Captain: Ishanth Sharma) |

Because of the lack of money supply , there will be less demand in the market and the customers will try to spend less because the market is sucked out dry. So retailers will reduce prices to maintain affordability again, reducing prices, which is called deflation.

• "Dams are the temples of modern India" proclaimed by Jawaharlal Nehru.
• The oldest dam in India is the Kallanai dam in Tamil Nadu built on the Kaveri river.
• Tehri Dam on Bhagirathi river is the biggest, highest and tallest dam in India.

According to the Census of 2001, Agricultural sector employs 56 %. This is mainly due large availability of unskilled labor.

The Manufacturing sector is the second largest employer ,which employs 13.4%.

The Electricity,gas and water supply sector employs the least 0.5%

Kunwar Singh belonged to the Rajput house of Jagdispur. He leads the Revolt of 1857 from Bihar. He died at the age of 80 fighting the British soldiers.

• 21 March 2019 ,UN celebrated World Down syndrome day themed "Leave no one behind”.
• Down syndrome is a naturally occurring chromosomal arrangement ,exists in all regions across the globe and commonly results in variable effects on learning styles, physical characteristics or health.

Note:  The iris opens and closes to control the amount of light entering the eye through the pupil. The pupil is the opening in the center of the iris where light enters the eye.

Vikramashila University: Built by Dharmapala(800's A.D), the second ruler of Pala dynasty.

Pala Dynasty:Founded by Gopala. Ruled  in west Deccan region.

Marabats and Badgyas: Celebrated in Nagpur(Maharashtra),Marabats are considered to act against diseases and Badgyas  act against social evils.

The 11^th part of the Indian constitution deals with center state relations.

• Constitution of India, as of 2019 has 448 articles in 25 parts and 12 schedules.
• The 101^st amendment made in the Indian constitution was for GST (2016).
• 103rd Constitutional Amendment Act, 2018 "Economic Reservation In India"

Soy bean has highest protein content among the given options.

• Fruits have lowest protein content, for example apple has 0.003 g/ one gram.
• Protein is a macro nutrient. Minimum quantity required per day is around 50 grams .Protein is used to make enzymes, hormones. Protein is an important building block of bones, muscles, cartilage, skin, and blood.

Of all states , only the following have state butterflies.

• Kazakhstan renamed its capital to Nur-Sultan from Asthana in 2019.The name of the capital has been changed in honor of the country's President Nur-Sulthan who resigned in 2019.
• Kassym-Jomart Tokayev was nominated by Nur-sultan as the next President. Nur-sultan is the "father of the nation" for Kazakhstan.He lead the nation for 30 years after Soviet Era.
• Kazakhstan is the world's largest land locked country. 9^th largest by area in the world.
• Currency is Kazakhstani tenge ( 1 Rupee INR= 5.6 Kazakhstani tenge) as of 2019.

Kleinman Center for Energy Policy presented the 4^th Carnot Prize 2018 to Union Minister Piyush Goyal, Minister of Railways & Coal .

Award recognizes the pathbreaking transformations in India’s energy sector.A few schemes implemented with regard to energy sector are:

• Saubhagya Scheme(100 % electrification by 2019)
• UDAY scheme(Discom distress and Electricity cost reduction)
• UJALA Scheme (LED distribution)

We know,

In-radius of triangle = (Area of triangle)/Semi Perimeter(s)

⇒ 3 = 15/s

⇒ Semi perimeter(s) = 5

∴ Perimeter = 2S = 2 × 5 = 10 cm

If the areas of the three adjacent faces of a cuboid are a, b and c, then the volume of cuboid = √abc

∴ Required volume = √(32 × 24 × 48) = 192 cm³

Total production of type C cars in 2015 and type E cars in 2018 = 42 + 60 = 102 thousand

Total production of cars in 2014 = 64 + 48 + 33 + 25 + 40 = 210

Total production of cars in 2017 = 63 + 64 + 57 + 55 + 61 = 300

Total production of cars in 2014 and 2017 = 210 + 300 = 510

∴ Required percentage = [102/510] × 100 = 20%

Total production of type D cars during 2015 to 2017 = 45 + 40 + 55 = 140

Total production of type E cars during 2014, 2015, 2016 and 2018 = 40 + 48 + 52 + 60 = 200

∴ Required percentage = [(200 – 140)/200] × 100 = 30%

Production of type A cars in 2015 and type B cars in 2014 taken together = 56 + 48 = 104

Production of type C cars in 2017 and type E cars in 2018 taken together = 57 + 60 = 117

∴ Required ratio = 104 ∶ 117 = 8 ∶ 9

⇒ AB = 6 cm

⇒ CD = 2 × 6 = 12 cm

⇒ AM = MB = AB/2 = 6/2 = 3 cm

⇒ CN = ND = CD/2 = 12/2 = 6 cm

Let ON be x.

⇒ OB = OD = radius of circle

In ΔMOB,

⇒ r² = (OM)² + (MB)²

⇒ r² = (3 + x)² + 3²      ----(1)

In ΔOND,

⇒ r² = (ON)² + (ND)²

⇒ r² = x² + 6²      ----(2)

From equation (1) and equation (2)

⇒ x² + 6² = (3 + x)² + 3²

⇒ 6² – 3² = (3 + x)² – x²

⇒ x = 3

From equation (2)

⇒ r² = 3² + 6²

⇒ r = 3√5

$\Rightarrow 2\frac{7}{8} \div \left( {3\frac{5}{6} \div \frac{2}{7}{\rm{of;}}2\frac{1}{3}} \right) \times \left[ {\left( {2\frac{6}{7}{\rm{of;}}4\frac{1}{5} \div \frac{2}{3}} \right) \times \frac{5}{9}} \right]$

$\Rightarrow \frac{{23}}{8} \div \left( {\frac{{23}}{6} \div \frac{7}{3} \times \frac{2}{7}} \right) \times \left[ {\left( {\frac{{21}}{5} \times \frac{{20}}{7} \div \frac{2}{3}} \right) \times \frac{5}{9}} \right]$

$\Rightarrow \frac{{23}}{8} \div \left( {\frac{{23}}{6} \times \frac{3}{2}} \right) \times \left[ {12 \times \frac{3}{2} \times \frac{5}{9}} \right]$

⇒ [23/8] × [4/23] × 10 = 5

Production of type D cars in 2015 = 45

Total production of type D cars = 25 + 45 + 40 + 55 + 35 = 200 thousands

⇒ 200 thousand represent = 360°

⇒ 45 thousand will represent = [360°/200] × 45 = 81°

As we know,

The angle between the external bisectors of two angles of a triangle is difference between the right angle and the half of the third angle.

⇒ ∠R = 90° – ∠A/2

Given, ∠R = 66°

⇒ 66° = 90° – ∠A/2

⇒ ∠A = 48°

Short trick∶

⇒ sec θ – tan θ = P

Putting θ = 45°

⇒ P = (√2 – 1)

∴ cosec45° = √2

Check option (1)

$\Rightarrow \frac{{{{\rm{P}}^2} + {\rm{;}}1}}{{1 - {{\rm{P}}^2}}} = \frac{{{{\left( {\sqrt 2 - 1} \right)}^2 + 1}}}{{1{\rm{;}}-{\rm{;}}{{\left( {\sqrt 2 {\rm{;}} - 1} \right)}^2}{\rm{;}}}} = \sqrt 2$ (Satisfied)

Detailed solution∶

⇒ sec θ – tan θ = P      ----(1)

As we know, sec²θ – tan²θ = 1

⇒ (sec θ – tan θ) (sec θ + tan θ) = 1

⇒ sec θ + tan θ = 1/P      ----(2)

Adding equation (1) and equation (2)

⇒ 2sec θ = P + 1/P

⇒ sec θ = (P² + 1)/2P

⇒ cos θ = 2P/(P² + 1)

We know, sin²θ = 1 – cos²θ

⇒ sin²θ = 1 – [(2P)²/(P² + 1)²]

⇒ sin²θ = [(P² + 1)² – (2P)²] / (P² + 1)²

⇒ sin²θ = (P⁴ + 1 + 2P² – 4P²) / (P² + 1)²

⇒ sin²θ = (P⁴ + 1 – 2P²) / (P² + 1)²

⇒ sin θ = (1 – P²) / (P² + 1)

⇒ cosec θ = (P² + 1) / (1 – P²)

Short trick∶

⇒ 25000 × (8/100) = 2000 × 3 = 6,000

⇒ 2000 × (8/100) = 160 × 3 = 480

⇒ 160 × (8/100) = 12.8

∴ Total interest = 6000 + 480 + 12.8 = Rs. 6492.8

Detailed solution∶

Total sum = Rs. 25000

Rate for 12 months = 12%

⇒ Rate for 8 months = 8% and Time (24 months)/8 = 3

⇒ Amount = 25000 × (27/25) × (27/25) × (27/25) = Rs. 31,492.8

∴ Required Interest = 31,492.8 – 25,000 = Rs. 6,492.8

⇒ a² + b² + 64c² + 16c + 3 = 2(a + b)

⇒ a² + b² + (8c)² + 16c + 3 – 2a – 2b = 0

⇒ [a² – 2 × a × 1 + 1²] + [b² – 2 × b × 1 + 1²] + [(8c)² + 2 × 8c × 1 + 1²] = 0

⇒ (a – 1)² + (b – 1)² + (8c + 1)² = 0

⇒ a = 1, b = 1 and c = [-1/8]

⇒ 4a⁷ + b⁷ + 8c² = 4 + 1 + 8 × [1/64] = $5\frac{1}{8}$

Short trick∶

Go through the options,

√3cosθ + sinθ = 1

Put θ = 90°

⇒ √3 × 0 + 1 = 1

⇒ 1 = 1 (Satisfied)

Detailed solution∶

√3cosθ + sinθ = 1

⇒ √3cosθ = 1 – sinθ

Squaring both the sides

⇒ 3cos²θ = 1 + sin²θ – 2sinθ

⇒ 3 – 3sin²θ = 1 + sin²θ – 2sinθ

⇒ 2sin²θ – sinθ – 1 = 0

⇒ 2sin²θ – 2sinθ + sinθ – 1 = 0

⇒ 2sinθ(sinθ – 1) + 1(sinθ – 1) = 0

⇒ (2sinθ + 1) (sinθ – 1) = 0

⇒ sinθ = 1 or -1/2

∴ θ = 90°

Short trick∶

⇒ Ratio of 100 copies and 50 copies = 2 ∶ 1

∴ Required discount = [(2 × 25%) + (1 × 10%)] / (2 + 1) = 20%

Detailed solution∶

Let MP of 1 copy of a book be Rs 1.

MP of 150 copies of a book = Rs. 150

SP of 100 copies of a book = 100 × [3/4] = Rs. 75

SP of 50 copies of a book = 50 × [9/10] = Rs. 45

Total SP = 75 + 45 = Rs. 120

Total MP = Rs. 150

∴ Overall discount = [(150 – 120)/150] × 100 = 20%

Let CP of the article be 100x.

∴ SP of the article be = 125x

According to the question

⇒ 125x – 100x = 44.80

⇒ 25x = 44.80

⇒ 100x = 44.80 × 4 = 179.20

Short Trick∶

Suppose a = 1, b = 2 and c = 4,

ab + bc + ca = 1 × 2 + 2 × 4 + 4 × 1 = 2 + 8 + 4 = 14

Detailed solution∶

As we know, (x + y + z)² = x² + y² + z² + 2xy + 2yz + 2zx

Given a² + b² + c² = 21 and a + b + c = 7

⇒ (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)

⇒ 7² = 21 + 2(ab + bc + ca)

⇒ 2(ab + bc + ca) = 49 – 21 = 28

⇒ ab + bc + ca = 14

As we know, x³ – y³ = (x – y) (x² + y² + xy)

⇒ (27x³ – 343y³) ÷ (3x – 7y) = Ax² + By² + 7Cxy

⇒ [(3x)³ – (7y)³] ÷ [(3x – 7y)] = Ax² + By² + 7Cxy

⇒ [(3x – 7y) (9x² + 49y² + 21xy)] ÷ [(3x – 7y)] = Ax² + By² + 7Cxy

⇒ 9x² + 49y² + 21xy = Ax² + By² + 7Cxy

On comparing

⇒ A = 9, B = 49 and C = 3

⇒ 4A – B + 5 × 3

⇒ 4 × 9 – 49 + 5 × 3 = 2

Let the three number be a, b and c.

According to the question

⇒ [(a + b)/2] + c = 168

⇒ a + b + 2c = 336      ----(1)

⇒ [(b + c)/2] + a = 174

⇒ b + c + 2a = 348      ----(2)

⇒ [(a + c)/2] + b = 180

⇒ a + c + 2b = 360      ----(3)

Adding equation (1), equation (2) and equation (3)

⇒ 4(a + b + c) = 1044

⇒ a + b + c = 261

∴ Average of all the three numbers = 261/3 = 87

The ratio of efficiency of A, B and C = 7 ∶ 5 ∶ 4

Total work = (7 + 5 + 4) × 35 = 560

Work completed by A and B in 28 days = (7 + 5) × 28 = 336

Remain work = 560 – 336 = 224

∴ Remain work will be completed by C alone = 224/4 = 56

Shortcut Trick

Let Income of B = 100.

Then Income of A = 125 and Income of C = (125 + 100) × 0.35 = 78.75.

Difference between A and C = 125 − 78.75 = 46.25.

Required % = (46.25 ÷ 125) × 100 = 37%.

∴ The correct answer is 37%.

Alternate Method

Given:

Income of A is 25% more than B.

Income of C is 65% less than (A + B).

Calculations:

⇒ Let Income of B = 100 units

⇒ Income of A = 100 + 25% of 100 = 125 units

⇒ Sum of A and B = 125 + 100 = 225 units

⇒ Income of C = 225 − 65% of 225 = 35% of 225

⇒ Income of C = 0.35 × 225 = 78.75 units

⇒ Difference between A and C = 125 − 78.75 = 46.25 units

⇒ Percentage less = (Difference ÷ Income of A) × 100

⇒ Percentage less = (46.25 ÷ 125) × 100 = 37%

∴ The correct answer is 37%.

Additional Information

Percentage Comparison Formula

To find how much % X is less than Y, use: [(Y − X) ÷ Y] × 100.

Base Value Selection

Always identify the than part in the question to determine the denominator (base) for percentage calculation.

Successive Percentage

For two successive changes a% and b%, the effective change is [a + b + (ab ÷ 100)]%.

Given:

The selling price of the article = Rs 800

Loss percentage = 20% of SP

Gain percentage = 25% of CP

Concept used:

Profit % = (SP - CP)/CP × 100

In this particular case,

Loss % = (CP - SP)/SP × 100 

Calculation:

0.20 = (CP - 800)/800

CP = 160 + 800 = Rs 960

Profit % = 25% = (SP - 960)/960

SP = 960 + 0.25 × 960 = Rs 1,200

The cost price of the article = 800 × [120/100] = Rs. 960

∴ New selling price of the article = 960 × [5/4] = Rs. 1200

Common mistake∶

It has been mentioned in the question that the loss is counted on the selling price.

Given x + y = 1 and xy(xy – 2) = 12

⇒ (x + y)² = 1²

⇒ x² + y² + 2xy = 1

⇒ (x² + y²)² = (1 – 2xy)²

⇒ x⁴ + y⁴ + 2x²y² = 1 + 4x²y² – 4xy

⇒ x⁴ + y⁴ = 1 + 2x²y² – 4xy

⇒ x⁴ + y⁴ = 1 + 2xy(xy – 2)

⇒ x⁴ + y⁴ = 1 + 2 × 12

⇒ x⁴ + y⁴ = 25

Shortcut Trick

For numbers a, b, c, d in proportion after adding x, use the formula:

x = (ad − bc) ÷ (a + d − b − c)

⇒ x = (12 × 45 − 28 × 21) ÷ (12 + 45 − 28 − 21)

⇒ x = (540 − 588) ÷ (57 − 49) = −48 ÷ 8 = −6 (Taking magnitude, x = 6)

Mean Proportional = √((6 + 3) × (4 × 6 + 1)) = √(9 × 25) = 3 × 5 = 15.

∴ The correct answer is 15.

Alternate Method

Given: Numbers are 12, 28, 21, 45. x is added to each.

Formula Used: If a, b, c, d are in proportion, then a/b = c/d. Mean proportional of p and q is √(p × q).

⇒ (12 + x) ÷ (28 + x) = (21 + x) ÷ (45 + x)

⇒ (12 + x)(45 + x) = (21 + x)(28 + x)

⇒ 540 + 12x + 45x + x² = 588 + 21x + 28x + x²

⇒ 540 + 57x = 588 + 49x

⇒ 57x − 49x = 588 − 540

⇒ 8x = 48 ⇒ x = 6

⇒ First term = x + 3 = 6 + 3 = 9

⇒ Second term = 4x + 1 = 4 × 6 + 1 = 25

⇒ Mean Proportional = √(9 × 25) = √225 = 15

∴ The correct answer is 15.

Additional Information

Mean Proportional

The mean proportional between two numbers a and b is defined as √(ab).

Third Proportional

If a, b, c are in continued proportion, then c = b²/a is the third proportional.

Fourth Proportional

If a, b, c, d are in proportion, then d = (b × c) / a is the fourth proportional.

8 digit number 179x091y is divisible by 88 means that the number is divisible by 11 and 8 both.

⇒ 91y is divisible by 8 if we put y = 2 as the last three digits are divisible by 8.

⇒ 179x0912 is divisible by 11 if we put x = 4 as the difference between the sum of odd digit place and the sum of the even digit place is 11.

⇒ 5x – 8y = 5 × 4 – 8 × 2 = 4

Short trick∶

Required difference = ∠B – ∠C = 92° – 67° = 25°

Detailed solution∶

As we know, the sum of the opposite angles of a cyclic quadrilateral is 180°.

⇒ ∠A + ∠C = 180°

⇒ ∠C = 180° – 67° = 113°

⇒ ∠B + ∠D = 180°

⇒ ∠D = 180° – 92° = 88°

⇒ ∠C – ∠D = 113° – 88° = 25°

The correct answer is option 3.

The sentence given in the question is an imperative sentence. Imperative sentences are sentences which express advice, request or command.

For eg:

• Close the door.
• Please give me the bottle.
• Pick up the phone.

These sentences express advice, request or command.

The passive voice of sentences containing a request starts with ‘You are requested to’.

Generally, sentences containing request have the word ‘please’ in it.

Normal structure of the sentence in passive voice is: You are requested to + verb + object

Eg: Please close the door. (Active Voice)

You are requested to close the door. (Passive Voice)

Hence the answer is “You are requested to show me my son’s Mathematics book.”

The correct answer is option 2.

The idiom “pull someone’s leg” means “deceive someone playfully; tease someone.”

In a sentence: I think he was just pulling your leg when he said you've failed in the exam. 

The phrase first appeared in the late 1800s in America. The origin is not clear, though there are two popular theories, but both implausible. The first theory says that thieves used to pull the legs of their victims to put them off guard so that they could rob them. The second one refers to hangings that were held in Tyburn, England. It is said that people were hired to hang on the victim's leg to give them a quick execution. 

The rest of the options are incorrect.

The underlined part of the sentence is incorrect and has to be improved.

It should be replaced with “has been reading that novel”. This is in the present perfect continuous tense.

The present perfect continuous tense (also known as the present perfect progressive tense) shows that something started in the past and is continuing at the present time. The present perfect continuous is formed using the construction has/have been + the present participle (root + -ing).

Eg: I have been reading War and Peace for a month now.

The rest of the options makes the sentence grammatically incorrect.

The correct answer is: Option 1.

Key Points

• The word "Exite" is incorrectly spelt. The correct spelling is "Excite". (उत्तेजित करना)
• Example: The news of their victory will excite the fans.
• "Exclaim" means to cry out suddenly in surprise, strong emotion, or pain. (आश्चर्यचकित होना)
• Example: She couldn't help but exclaim in delight when she saw the surprise party.
• "Exchange" refers to the act of giving one thing and receiving another in return. (अदला-बदली करना)
• Example: They decided to exchange gifts during the festival.
• "Exercise" means physical activity that you do to make your body strong and healthy. (व्यायाम)
• Example: Regular exercise is important for maintaining good health.

Therefore, the correct answer is: Option 1.

Additional Information

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

• Exclaim (आश्चर्यचकित होना): To cry out suddenly in surprise, strong emotion, or pain.
• Example: She couldn't help but exclaim in delight when she saw the surprise party.
• Exchange (अदला-बदली करना): The act of giving one thing and receiving another in return.
• Example: They decided to exchange gifts during the festival.
• Exercise (व्यायाम): Physical activity that you do to make your body strong and healthy.
• Example: Regular exercise is important for maintaining good health.

The correct answer is option 3.

Pardon means “release (an offender) from the legal consequences of an offense or conviction, and often implicitly from blame.” The word that is an antonym of this is “Punish: inflict a penalty or sanction on (someone) as retribution for an offense, especially a transgression of a legal or moral code.”

The meanings of the rest of the words are:

Kindness: the quality of being friendly, generous, and considerate.

Grace: courteous goodwill.

Mercy: compassion or forgiveness shown towards someone whom it is within one's power to punish or harm.

Options 1, 2 and 3 are nouns and are not antonyms of the verb “pardon”.

The word to be used in the blank is “where”.

“Where” is an adverb that means “at, in, or to which (used after reference to a place or situation). Here the place mentioned is the island on the South American coast.

The rest of the adverbs makes the sentence grammatically incorrect as:

There means “in, at, or to that place or position.

Eg- "we went to Paris and stayed there for ten days."

When means “at what time”.

Eg- "when did you last see him?"

Wherever means “in or to whatever place (emphasizing a lack of restriction).

Eg-"meet me wherever you like."

Hence the correct answer is option 2.

The correct answer is 'The inadequate rainfall adversely affected the crop.'

Key Points

• The given sentence is in a passive voice form, hence we need to convert it into an active voice form.
• Find the subject (The crop) and object (the inadequate rainfall. ) of the sentence and exchange their places.
• The given sentence is in the simple past tense. The active verb form for simple past is: 
• Subject + V2 + object.
• So, 'was adversely affected' changes to adversely affected'.
• At last line up the remaining part.

Following these steps, we finally get- The inadequate rainfall adversely affected the crop.​

The correct answer is option 2. 

A barrel is a cylindrical container bulging out in the middle, traditionally made of wooden staves with metal hoops around them.

Barrels hold liquid in them — anything from wine to beer to oil. A barrel can also be the tube in a gun that a bullet travels through. You might hear the expression "stare down the barrel of a gun," which means you're looking at a gun pointed right at your face. A barrel is also used as a unit of measure or to refer to a large unit of measure. When someone says they are having "barrels of fun," they're having a really great time.

The rest of the options are incorrect as:

Bale means a large wrapped or bound bundle of paper, hay, or cotton.

Bushel is a measure of capacity equal to 8 gallons (equivalent to 36.4 litres), used for corn, fruit, liquids, etc.

Bin is a receptacle in which to deposit rubbish.

The word to be used in the blank is “appeared”.

“Appeared” means “came into sight; became visible or noticeable, especially without apparent cause- "smoke appeared on the horizon".

The rest of the options are incorrect as they mean:

Stood up: to put your body into an upright position from a sitting or lying position

Came out: emerged; became known

Showed: be, allow, or cause to be visible.

Hence the correct answer is option 3.

The correct answer is option 1.

The word Consceince is wrongly spelt here.

The correct spelling is Conscience. It means "a person's moral sense of right and wrong, viewed as acting as a guide to one's behaviour."

All the other words are spelt correctly.

The underlined part of the sentence is incorrect and has to be improved.

It should be replaced with “I will purchase”. This is in the simple future tense. 

The simple future is a verb tense that’s used to talk about things that haven’t happened yet.

Eg: This year, Jen will read War and Peace. It will be hard, but she’s determined to do it.

Use the simple future to talk about an action or condition that will begin and end in the future.

In the above sentence, the first part of the sentence is “If I have money”. This shows that the person doesn’t have the money as of now, but he/she may have it in the future, and then only he/she can purchase the house.

The rest of the options makes the sentence grammatically incorrect.

Hence the correct answer is option 2.

The correct answer is option 1.

"Knocking down" which is in the present continuous tense should be changed to "knocked down" which is in the 

simple past tense.

The other phrasal verb given in the sentence "swept away" is in simple past and the sentence would become grammatically incorrect if the other word is in present continuous. 

The simple past tense is a verb tense that is used to talk about things that happened or existed before now.

The rest of the options are grammatically correct and shouldn't be changed.

The word to be used in the blank is “largest”.

The superlative(the third or highest degree of comparison in adjectives or adverbs) of “large”, which is “largest” has to be used here since the word preceding the blank is “world’s”. This indicates that when considering all the water bodies on this earth, the Pacific Ocean covers a vast area. 

“Larger” is a comparative(the second or middle degree of comparison in adjectives or adverbs).

The comparative and superlative degrees are formed by adding the -er and -est suffix to adjectives and adverbs with a single consonant for an ending.

Comparative adjectives are used to compare differences between the two objects they modify (larger, smaller, faster, higher). They are used in sentences where two nouns are compared, in this pattern:

Noun (subject) + verb + comparative adjective + than + noun (object).

Superlative adjectives are used to describe an object which is at the upper or lower limit of a quality (the tallest, the smallest, the fastest, the highest). They are used in sentences where a subject is compared to a group of objects.

Noun (subject) + verb + the + superlative adjective + noun (object).

“Large” means “of considerable or relatively great size, extent, or capacity” and “more large” is grammatically incorrect, both these options are cancelled.

Hence the correct answer is option 1.

The word to be used in the blank is “with”.

The idiom “task (one) with (something) means “to assign one the responsibility of completing some task.” So we cannot use any other preposition in the blank. It is often used in passive constructions.

This part of the sentence means that the British Navy had given Admiral Byron the responsibility of settling an island off the South American coast.

Eg: The boss tasked me with scanning all the documents so that we have a digital copy of each one.

The rest of the options will make the sentence grammatically incorrect.

Hence the correct answer is option 1.

The correct answer is option 1.

The idiom “actions speak louder than words” means “means that what you do is more significant than what you say.”

Example of Use: "You always speak of the importance of charity, but never do anything. Actions speak louder than words!" 

The origin of the idiom 'actions speak louder than words' is found in literature and is hundreds of years old. This interesting and meaningful statement was first seen in Gersham Bulkeley’s book Will and Doom, published in 1692: “Actions are more significant than words.” It has been a very popular idiom ever since. 

The rest of the options are incorrect.

The word to be used in the blank is “route”.

“Route” means “a way or course taken in getting from a starting point to a destination.”

Although “road” and “path” are synonyms of “route” they are not the correct answers. The passage mentions travelling by sea, and the pathways used by ships are generally referred to as sea routes. 

“Road” means “a wide way leading from one place to another, especially one with a specially prepared surface which vehicles can use.”

“Path” is a way or track laid down for walking or made by continual treading.

“Means” is also an incorrect answer as it means “an action or system by which a result is achieved; a method.”

Hence the correct answer is option 3.

The correct answer is option 2. 

A cartographer is a person that makes maps.

Up until the 18th century, maps were often decorated with fanciful beasts and monsters, at the expense of accurate details about places. French mapmakers of the 1700s and 1800s encouraged the use of more scientific methods in the art they called "cartographie." The French word cartographie (the science of making maps), from which we get our English word "cartography," was created from "carte," meaning "map," and "-graphie," meaning "representation by." Around the same time, we adopted "cartography" in the mid-19th century, we also created our word for a mapmaker, "cartographer.”

The rest of the options are incorrect as:

A choreographer is a person who composes the sequence of steps and moves for a performance of dance.

A lexicographer is a person who compiles dictionaries.

A calligrapher is one who practices calligraphy. It is the art of producing decorative handwriting or lettering with a pen or brush.

The correct answer is option 3.

Fierce means “having or displaying an intense or ferocious aggressiveness.” It also means “cut-throat; relentless.”

Although Chinese products are generally of lower quality, Indian producers have to face stiff competition from the Chinese as Chinese products are cheaper. 

The meanings of the rest of the words are:

Bold: (of a person, action, or idea) showing a willingness to take risks; confident and courageous.

Powerless: weak.

Angry: feeling or showing strong annoyance, displeasure, or hostility; full of anger.

These words are not the appropriate adjectives to be used here.

The correct answer is option 4.

Inarticulate means “unable to express one's ideas or feelings clearly or easily; not clearly expressed or pronounced. The word that is a synonym of this is “Incoherent:  unable to speak intelligibly.”

The meanings of the rest of the words are:

Eloquent: fluent or persuasive in speaking or writing.

Fluent: able to express oneself easily and articulately.

Inevitable: certain to happen; unavoidable.

Options 1 and 2 are antonyms of “inarticulate” while option 3 is neither.

The correct word to be used in the blank is “confiscated”. It means “took or seized (someone's property) with authority.

Eg: The guards confiscated his camera.

The meanings of the rest of the words are:

Appropriated: took(something) for one's own use, typically without the owner's permission

Annexed: add (territory) to one's own territory by appropriation

Hijacked: unlawfully seize (an aircraft, ship, or vehicle) in transit and force it to go to a different destination or use it for one's own purposes

Hence, these options are incorrect.

Hence the correct answer is option 2.