SSC CGL Previous Paper (Held On: 11 August 2017 Shift 1) (Previous Year Paper)

Solution:

11 ÷ 6 - 2 + 5 × 3 can be written as

11 + 6 ÷ 2 x 5 - 3

= 23.

Hence, 23 is the correct ans.

Consider the position of the letters of the English Alphabet:

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

The pattern is as follows:

FS : LY  can be written as

F + 6 = L

S + 6 = Y

Similarly,

IV : ? will be written as

I + 6 = O  

V + 6 = B.

Hence, OB is the correct ans.

Consider the position of the letters of the English Alphabet:

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

1. AJ → A + 9 = J

2. EN → E + 9 = N

3. NW → N + 9 = W

4. PW → P + 7 = W

In all the pairs, the second letter is obtained by adding 9 to the first letter except in PW, where 7 is added.

Hence, PW is the odd letter group from the given alternatives.

The pattern is as follows:

19 + 26 = 45

26 + 45 = 71

45 + 71 = 116

116 + 71 = 187.

Hence, 187 is the correct ans.

In each row, second column element is the difference of the product of the digits of first column element and product of digits of third column element.

1^st row:

336 = 3 x 3 x 6 = 54

748 = 7 x 4 x 8 = 224

Now, subtract

224 - 54 = 170.

2^nd row:

523 = 5 x 2 x 3 = 30

349 = 3 x 4 x 9 = 108

Now, subtract

108 - 30 = 78.

Similarly,

3^rd row:

431 = 4 x 3 x 1 = 12

328 = 3 x 2 x 8 = 48

Now, subtract:

48 - 12 = 36.

Hence, 36 is the correct ans.

We draw the least possible Venn diagram:

Conclusions:

I. Some bags are red → It’s false. II. All bags are red → It’s false

Hence, neither conclusion I nor II follows.

Sea, ocean and lake are large water bodies whereas marsh is a very small area where water is collected.

Hence, Marsh is the odd word from the given alternatives.

Hence, there are a total of 26 triangles in the question figure.

The correct folded figure of the unfolded dice will be option 1. 

As in option 2: Tha blank face and single circle face are opposite to each other.

In option 3: Fully colored face and small square face are opposite to each other.

In option 4: The crossed face and single lined face are opposite to each other.

Only option 1  satisfies the above conditions.

Consider the position of the letters of the English Alphabet:

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

The pattern of the series is as follows:

C – 7 → V; V – 7 → O; O – 7 → H

11 + 6 → 17; 17 + 6 → 23; 23 + 6 → 29

Hence, H29 is the correct answer.

Consider the position of the letters of the English Alphabet:

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

13^th letter from the right end should be (26 – 13) + 1 from the left end → N.

Hence, N is the correct ans.

Consider the English alphabet series to gauge the numerical value of letters.

The followed pattern for ACCOUNT is:

Similarly,

MATHS can be written as:

Hence, PDWKV is the correct answer.

Here, # statnds for (×10 +) and * stands for (addition of digits).

3 # 6 * 9 = 45 can be written as

3 ×10 + 6 + 9 = 45 

30 + (6 + 9) = 45

9 # 8 * 7 = 105 can be written as

9 ×10 + 8 + 7 = 105

90 + (8 + 7) = 105

Similarly,

5 * 6 # 3 can be written as

5 + 6 ×10 + 3 

5 + (60+ 3) = 68.

Hence, 68 is the correct answer.

The missing figure will be the mirror image of its upper half/ left half.   

(iMAGE)

Hence, 

is the correct answer.

Hockey is played using sticks. Similarly, boxing is done using gloves.

Hence, Gloves is the correct ans.

1. 01, 03, 75, 00, 68 → T, R, A, I, A

2. 14, 30, 68, 13, 58 → T, R, A, I, H

3. 20, 44, 99, 21, 96 → T, R, A, I, S

4) 43, 11, 56, 34, 88 → T, R, A, I, L

Therefore, the set of numbers representing the word “TRAIL” is “43, 11, 56, 34, 88”.

3. Effaceable

4. Effacement

5. Effacements

6. Effacers

7. Effacing

Hence, the correct dictionary order will be 35412.

Distance from the starting point to the end point = 10 + 7 = 17 km.

Hence, 17 is the correct answer.

All tigers are carnivores and some animals are carnivores.

There are carnivorous plants too, e.g. Drosera. Therefore, all carnivores are not animals. 

Hence, option 4 is the correct answer.

19 : 367  can be written as

19 : (19² + 6)

Similarly

21 : (21² + 6)

→ 21 : 447

Hence, 21 : 447 is the correct ans.

​

Clearly, the question figure is embedded in this figure.

Hence, 

 is the correct ans.

There is no letter ‘T’ in the word HANDSOME.

Hence, the word ‘HATS’ cannot be formed.

The mirror image of the given figure is as follows:

Hence, 

 is the correct answer.

Since the paper is folded once from both the sides, we will obtain three parts of the folded paper.

Now, one upward triangle, one downward triangle and a circle is cut as shown in the figure. Since we have three parts of the paper, we will obtain three upward triangles, three downward triangles and three circles.

But, the first upward triangle will be towards the left and the last downward triangle will be towards the right.

Hence,

is the correct answer.

all are "square of a number + 1" like 170 = 169 + 1 , 290 = 289 + 1,530 = 529 + 1 except 360

Hence, 360 is the odd number from the given alternatives.

Emulsion is a type of colloidal solution in which both dispersion phase and dispersion medium are in a liquid state. Milk, butter, chocolate milk, cookie dough and whipped cream water in benzene and cream are some common examples of emulsion. Curds on the other hand are a dairy product obtained by coagulating milk in a process called curdling.

Nor westers or the Kalbaishakhi is a local thunderstorm and rainfall which occurs in India and Bangladesh.

Kalbaishakhi occurs from March till monsoon establishes over North-East India. Odisha, West Bengal, Assam, Bihar, Chhattisgarh, Jharkhand, Bangladesh, and North-Eastern states of India are affected by violent thunderstorms during this period.

Kal Baisakhi originates in the Chhotanagpur Plateau, in and around the cities of Ranchi and Jamshedpur. In times of incursion of moist air in these elevated regions, amidst high temperatures, these extremely destructive thunderstorms occur.

Kal Baisakhi definitely brings destruction in terms of lightning, thunderstorm, hailstorm, and rainfall. However, it is extremely helpful for pre-Kharif crops like jute, paddy, and a large number of vegetables and fruits. It gives the much-desired relief after mid-day heat and pours well on the thirsty soil for the development of crops.

The blue whale (Balaenoptera musculus) is a marine mammal which is the largest mammal in the world. It belongs to the suborder of baleen whales. At 30 meters (98 ft.) in length and 180 metric tons in weight, it is the largest known mammal to have ever existed.

• The Ghadar Party was an Indian revolutionary organisation primarily founded by Punjabis.
• The party was multi-ethnic and had Hindu, Sikh and Muslim leaders.
• The party had its headquarters in San Francisco.
• Key members included Bhai Parmanand, Sohan Singh Bhakna, Har Dayal, Mohammad Iqbal Shedai, Kartar Singh Sarabha, Abdul Hafiz Mohamed Barakatullah, Sulaman Choudhary, Aamir Choudhary, Rashbehari Bose and Gulab Kaur.

Netscape Navigator is a web browser which has been discontinued. It was the flagship product of the Netscape Communications Corp and was the dominant web browser in terms of usage share in the 1990s. But by 2002 its use came down and this was primarily due to the increased use of Microsoft's Internet Explorer web browser software.

Milk is slightly acidic as it has a pH of around 6.5 to 6.7. According to some sources milk is cited as neutral since it is so close to the neutral pH of 7.0.

Robert G. Edwards devised the technique IVF. He was awarded the Nobel Prize in Physiology in 2010. He co-developed the treatment together with Patrick Steptoe. In vitro fertilization (IVF) is a process of fertilization where an egg is combined with sperm outside the body, in vitro.

The Championships, Wimbledon, also known simply as Wimbledon, is the oldest and the most prestigious tennis tournament in the world. It has been held at the All England Club in Wimbledon, London, since 1877 and is played on outdoor grass courts.

• The United Kingdom is headed towards a confrontation with Spain over Gibraltar as the country who controls it can also exercise pretty thorough control of shipping going into and out of the Mediterranean from the Atlantic.
• That is why, for many years, it was valued as a major naval port by the British.
• In June 2016, British voters decided at a referendum to leave the European Union.
• Gibraltarians were also allowed to vote.
• Realizing that departure from the EU would leave them exposed to Spanish demands for sovereignty, they voted 96% in favor of staying.
• But when the UK leaves, Gibraltar must leave, too.
• This caused confrontation of the UK and Spain.
• Note: Morocco option is for confusing a candidate as Strait of Gibraltar divides Spain and Morocco.

2018 Arjun Awardees

Lalita Babar is the recipient of Arjuna Award 2016 in the field of athletics. Born 2 June 1989 she is an Indian long-distance runner. She predominantly competes in the 3000 meters steeplechase and is the current Indian national record holder and the reigning Asian Champion in the same event.

Medium term loans are loans where repayments are made over a period of between one and three years. The short term loan is basically for less than a year and the long-term loan can be repaid within a time limit of 20 - 30 years.

Under Article 360 if the President realizes that there is an economic situation in which the financial stability or credit of India is threatened, he/she can declare a financial emergency in the country. This type of an emergency must be approved by the Parliament generally within two months.

Explanation:

Celsius scale:

• In this scale, a lower fixed point (ice point) is taken 0° and the upper fixed point (steam point) is taken 100°.
• The temperature measured on this scale all in degree celsius (°C).

Fahrenheit scale:

• This scale of temperature has a lower fixed point at 32° F and an upper fixed point at 212° F.
• The change in temperature of 1° F corresponds to a change of less than 1° on the Celsius scale.

Kelvin scale:

• The Kelvin temperature scale is also known as the thermodynamic scale. The triple point of water is also selected to be the zero of the scale of temperature.
• The temperatures measured on this scale are in Kelvin (K).
• The S.I unit of temperature is Kelvin.

Note:

• The Kelvin is the primary unit of temperature but is often used in conjunction with the Celsius degree, which has the same magnitude. Therefore option 1 is correct.
• The definition implies that absolute zero (0 K) is equivalent to −273.15 °C.

All these temperatures are related to each other by the following relationship:

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

UV radiation from the sun is the main factor that causes skin cells to become cancer cells. Too much UV radiation from the sun or other sources such as Solaria (solariums, sunbeds, and sun lamps) are the major reason behind all skin cancers.

• National Institution for Transforming India or NITI Aayog announces the launch of the schemes Lucky Grahak Yojana and the Digi-Dhan Vyapar Yojana to give cash awards to consumers and merchants who utilize digital payment instruments for personal consumption expenditures.
• The scheme focuses mostly on bringing the poor, lower middle class and small businesses into bringing them under the digital payment fold.
• Note:National Payments Corporation of India was the implementing agency for these schemes.

The correct answer is Fold Mountain.

Key Points

• The Himalayan mountain range is basically the Fold Mountains.
• It formed as a result of the collision between the Indian Plate and Eurasian Plate, which began 50 million years ago and continues today.
• Fold Mountains occur near convergent or compressional plate boundaries.
• Some of the Examples of Fold Mountains are the Alps, Rockies, Andes, and Himalayas.

• The Himalayas, a great mountain system of Asia, forming a barrier between the Plateau of Tibet to the north and the alluvial plains of the Indian subcontinent to the south.
• The Himalayas include the highest mountains in the world, with more than 110 peaks rising to elevations of 24,000 feet (7,300 meters) or more above sea level.

The full form of RNA is Ribonucleic Acid. There are 3 types of RNA, each encoded by its own type of gene:

• mRNA - Messenger RNA-Encodes amino acid sequence of a polypeptide.
• tRNA - Transfer RNA- Brings amino acids to ribosomes during translation.
• rRNA - Ribosomal RNA-With ribosomal proteins, makes up the ribosomes, the organelles that translate the mRNA.

The correct answer is 1600.

Key Points

• The Governor and company of merchants of London trading into the East Indies, popularly known as the English East India Company, were formed in 1600 AD.
• Captain William Hawkins arrived at Jahangir’s court (1609 AD) to seek permission to open a factory in Surat. A Farman was issued by Jahangir, permitting the English to build a factory in Surat (1613 AD).
• Sir Thomas Roe visited Jahangir’s court (1615 AD) as an ambassador of King James I to seek permission to trade in India.

Additional Information

• The Dutch East India Company established factories in India at Masulipatnam in 1605 AD, Pulicat (1610 AD), Surat (1616 AD), Bimlipatam (1641 AD), and Karaikal (1645 AD).
• The French East India Company was formed in 1664 AD by Colbert under state patronage during the reign of Louis XIV.

The Kyoto Protocol was adopted in Kyoto, Japan on 11 December 1997. There are currently 192 parties to the Protocol. The Kyoto Protocol is an international treaty which extends the 1992 United Nations Framework Convention on Climate Change (UNFCCC) that commits state parties to reduce greenhouse gas emissions

• Gayle's autobiography “Six Machine: I Don't Like Cricket... I Love it,” was published by Penguin Random House, and was released around the world on June 2.
• The book tells the inspiring story of his life from being a shy kid in the back streets of Kingston, who stole empty bottles to buy food, to becoming one of the most destructive batsmen in the world.

CONCEPT:

Weight:

• The weight of an object is defined as the force of gravity on the object and may be calculated as the mass times the acceleration of gravity, i.e.,

W = mg

Where m = mass of the object and g = acceleration due to gravity

• Since the weight is a force, so its SI unit is the Newton.

EXPLANATION:

• Acceleration due to gravity at the surface of the earth is given by:

$\Rightarrow g = \frac{{GM}}{{{R^2}}}$

• As Earth is elliptical in shape i.e., it is flattened at the poles and bulged out at the equator, due to which the equatorial radius is about 21 km longer than the polar radius.
• As the polar radius is smaller than the equatorial radius, therefore the acceleration due to gravity is maximum at poles and minimum at the equator.
• As we know the weight of an object is equal to the mass times the acceleration of gravity i.e., w = mg.
• As acceleration due to gravity is maximum at poles and minimum at the equator, therefore weight of the object will be maximum at poles. Hence option 1 is correct.

Facebook was blocked in China following the July 2009 Urumqi riots because Facebook was used as a part of the communications network by the Xinjiang independence activist. As informed by the "Blocked in China" website, Facebook is still blocked even there have been reports of Facebook being partially unblocked in China as in Hong Kong and Macau Facebook is not blocked.

In a federal government, there should be a clear division of power between federal and state Government so that the units and the center are required to enact and legislate within their sphere of activity and none violates its limits and tries to encroach upon the functions of others. Some of the other features of Federal Government are:

• Written Constitution
• Supremacy of the Constitution
• Rigid Constitution
• Independent Judiciary
• Bicameral Legislature

The prime lending rate is the rate at which banks lend to their most creditworthy customers, including large corporations. It is often used as a benchmark for other loans like credit card and small-business loans.

Let the cost price of one article be Rs. y and other be Rs. z

From the given problem statement, 32% gain can be given as

⇒ y × (1 + 32/100) = 12000

⇒ y = 12000/1.32

⇒ y = Rs. 9090.9

32% loss can be written as

⇒ z × (1 – 32/100) = 12000

⇒ z = 12000/.68

⇒ z = 17647.05

⇒ Total cost price = 9090.9 + 17646.05 = Rs. 26736.95

⇒ Total selling price = 12000 + 12000 = Rs. 24000

⇒ Loss = 26736.95 – 24000 = Rs. 2736.95

⇒ Loss percent = loss × 100/CP = 2736.95 × 100/26736.95

⇒ Loss percent = 10.24%

∴ Loss percent is 10.24%

It can be written as (α² + β²)/(αβ)

⇒ {(α + β)² - 2αβ}/{αβ}

And from the quadratic equation αβ = 14/3 and α + β = 13/3, Putting this in the required

equation

⇒ {(13/3)² – 2(14/3)}/{14/3}

⇒ {(169/3) - 28}/{14}

⇒ 85/42

∴ the value of (α/β) + (β/α) is 85/42

Given 5^x = 30^-y 

⇒ 5^x = (5 × 6)^-y 

⇒ 5^{(x + y)} = 6^-y 

⇒ 5^{(x + y) / (-y)} = 6      ----(1)

Again, 30^-y = 6^z 

⇒ (5 × 6)^-y = 6^z 

⇒ 5^-y = 6^{(z + y)} 

⇒ 5^{(-y) / (z + y)} = 6      ----(2)

From equation (1) and (2)

⇒ 5(x + y) / (-y) = 5(-y) / (z + y) 

On comparing

⇒ (x + y) / (-y) = (-y) / (z + y)

⇒ (x + y) (z + y) = (-y) (-y)

⇒ zx + yz + xy + y² =  y² 

⇒ xy + yz + zx = 0

∴ (xy + yz + xz)/xyz = 0

Shortcut Trick

In an isosceles trapezium, the projection of the non-parallel side on the base is given by: projection = (BC − AD) ÷ 2 = (14 − 8) ÷ 2 = 3 cm.

Using the Pythagorean triplet (3, 4, 5) for the right-angled triangle formed by the height, projection, and slant side (5 cm), the height (h) is directly found to be 4 cm.

Area of the trapezium = Average of parallel sides × height = ((8 + 14) ÷ 2) × 4 = 11 × 4 = 44 cm².

∴ The correct answer is 44 cm².

Alternate Method

Given:

Parallel sides: AD = 8 cm, BC = 14 cm

Non-parallel sides: AB = CD = 5 cm

Formula Used:

Area of trapezium = (1 ÷ 2) × (sum of parallel sides) × height

By Pythagoras theorem: Hypotenuse² = Base² + Height²

Calculations:

Draw perpendiculars AP and DQ from A and D to BC respectively.

⇒ PQ = AD = 8 cm

⇒ BP = QC = (BC − PQ) ÷ 2

⇒ BP = (14 − 8) ÷ 2 = 3 cm

In right-angled triangle APB:

⇒ AB² = AP² + BP²

⇒ 5² = AP² + 3²

⇒ 25 = AP² + 9

⇒ AP² = 16

⇒ AP = 4 cm (height, h)

Now, calculate the area of the trapezium ABCD:

⇒ Area = (1 ÷ 2) × (AD + BC) × AP

⇒ Area = (1 ÷ 2) × (8 + 14) × 4

⇒ Area = (1 ÷ 2) × 22 × 4

⇒ Area = 11 × 4 = 44 cm²

∴ The correct answer is 44 cm².

Additional Information

Isosceles Trapezium Properties

The non-parallel sides are equal in length (AB = CD), the base angles are equal (∠B = ∠C), and the diagonals are equal in length (AC = BD).

Pythagorean Triplets

Common right-angled triangle side ratios like 3 : 4 : 5, 5 : 12 : 13, and 8 : 15 : 17 help find heights or slant sides instantly without full calculation.

Cyclic Quadrilateral Connection

Every isosceles trapezium is a cyclic quadrilateral, meaning all its vertices lie on a single circle, and opposite angles sum to 180°.

Let the number of days required by Amit alone to do remaining work be y day’s

Work done by Amit in 1 day is 1/25^th of the total work

work done by Punit in 1 day is 1/20^th of the total work

According to the problem statement

⇒ 10 × (1/20) + y × (1/25) = 1

⇒ y = 25/2 = 12½

∴ 12½ days are required by Amit to do remaining work

From the given ratio we can see that angles be 7y, 11y, 7y and 11y

We can see that alternate angles are equal and two consecutive angles are supplementary.

∴ The quadrilateral is a parallelogram.

It can be simplified as x² + y² = xy

⇒ x² + y² – xy = 0 …(i)

And we know that x³ + y³ = (x + y)( x² + y² - xy), From (i)

⇒ x³ + y³ = 0

∴ x³ + y³ = 0

Since we know that sec(x) = cosec (90 - x), From the given equation

⇒ sec (3x – 20) = sec{90 – (3y + 20)} comparing the terms in brackets on LHS and RHS

⇒ 3x - 20 = 90 – (3y + 20)

⇒ x + y = 30

∴ tan(x + y) = tan(30) = 1/√3

Total sale of sedan is given as

⇒ 450 + 500 + 575 + 625 = 2150

Total sale of SUV is given as

⇒ 150 + 250 + 400 + 750 = 1550

⇒ the ratio is 2150/1550

∴ the required ratio is 43 : 31

Before adding four new girls, average can be given as

⇒ Sum of age of 6 girls/6 = x

⇒ Sum of age of 6 girls = 6x

After adding age of 4 new girls average can be given as

⇒ New average = Sum of age of 6 girls + x – 2 + x + 2 + x + 4 + x + 6 /(6 + 4)

⇒ New average = (10x + 10)/10

⇒ New average = x + 1

∴ new average is x + 1

Let the fraction be a/b, From the questions statement

⇒ (a­ + 5)/b = 6/5

⇒ (5a + 25)/6 = b… (i)

When 4 is added to its denominator

⇒ a/(b + 4) = 1/2

⇒ 2a = b + 4 Using (i)

⇒ 2a = (5a + 25)/6 + 4

⇒ 7a = 49

⇒ a = 7 Put this in (i)

⇒ b = (5 × 7 + 25)/6

⇒ b = 10

∴ the fraction is 7/10

Shortcut Trick

Since only water is added, the quantity of milk remains constant.

Milk in initial mixture = 10% of 80 L = 8 L.

In the new mixture, 5% of Total Volume = 8 L.

⇒ Total Volume = (8 × 100) ÷ 5 = 160 L.

Water added = Final Volume − Initial Volume = 160 L − 80 L = 80 L.

∴ The correct answer is 80 litres.

Alternate Method

Given:

Initial quantity of mixture = 80 litres

Percentage of milk in initial mixture = 10%

Target percentage of milk = 5%

Concept Used:

We apply the alligation method on the concentration of milk. Pure water added contains 0% milk.

Initial Mixture Added Water

10% 0%

5%

5 - 0 = 5 10 - 5 = 5

Ratio = 5 : 5 = 1 : 1

Calculations:

⇒ Ratio of Initial Mixture Quantity to Added Water Quantity = (5 − 0) : (10 − 5)

⇒ Ratio = 5 : 5 = 1 : 1

⇒ 80 / Added Water = 1 / 1

⇒ Added Water = 80 litres

∴ The correct answer is 80 litres.

Additional Information

Rule of Alligation

When two ingredients are mixed, the ratio of their quantities is inversely proportional to the differences of their concentrations from the mean concentration.

Constant Quantity Concept

In mixture problems where only one component is added or removed, the quantity of the other unadulterated component remains strictly constant throughout the process.

Successive Replacement

If V is the initial volume of pure liquid, and x volume is replaced by another liquid n times, the final amount of pure liquid left = V × (1 − x/V)ⁿ.

Let its usual speed be a km/hr.

From the questions statement 2/5^th of total journey is 2 × 200/5 = 80 km

⇒ 80/a + 120/(6a/7) – 200/a = 50/60

⇒ 80 + 140 – 200 = 5a/6

⇒ a = 24

∴ its usual speed is 24 km/hr

From the given figure

For triangle PQR

⇒ ∠P + ∠Q + ∠R = 180

⇒ x + y = 180 – 70 = 110

⇒ (x + y)/2 = 55….(i)

For triangle QAP

⇒ ∠PQA + ∠QAP + ∠APQ = 180

⇒ x/2 + ∠QAP = 180 – 70 = 110

⇒ ∠QAP = 110 – x/2….(ii)

For triangle RBP

⇒ ∠PRB + ∠RBP + ∠BPR = 180

⇒ ∠RBP + y/2 = 180 – 70 = 110

⇒ ∠RBP = 110 – y/2….(iii)

For Quadrilateral PAOB

⇒ ∠AOB + ∠OBP + ∠BPA + ∠PAO = 360

⇒ ∠AOB = 360 – 110 + x/2 - 110 + y/2 - 70

⇒ ∠AOB = 70 + x/2 + y/2 Using (i)

⇒ ∠QOR = ∠AOB = 70 + 55

∴ the ∠QOR is 125

Since we know that a³ + b³ + c³ – 3abc = (a + b + c)(a² + b² + c² - ab - bc - ca)

And (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca Using the given data

⇒ 9² = a² + b² + c² + 2(18)

⇒ a² + b² + c² = 45 Put all these things in the required expression

⇒ a³ + b³ + c³ – 3abc = (a + b + c)(a² + b² + c² - ab - bc - ca)

⇒ a³ + b³ + c³ – 3abc = 9 × (45 - 18) = 9 × 27 = 243

∴ a³ + b³ + c³ – 3abc = 243

(The ratio of the corresponding sides)² = The ratio of areas of two similar triangle

⇒ (The ratio of the corresponding sides)² = 5 : 7

⇒ The ratio of the corresponding sides = √​5 : ​√7

Area of bigger circle = πr²

⇒ Area of bigger circle = πr² = 1386

⇒ Radius of the bigger circle = 21 cm

We know that the radius of the inscribed circle in the equilateral triangle is 1/3rd times the altitude of that triangle.

Altitude of the equilateral triangle = 3 × 21 = 63 cm

Let radius of the smaller circle be x.

3x + (2 × 21) = 63

x = 7 cm

⇒ Four times of area of smaller circle = 4 × π × (7)² = 4 × 154 = 616 cm²

It can be simplified as 1/sin² θ – 1/tan² θ

cosec² θ – cot² θ which is an identity and equal to 1

∴ [(tan² θ – sin² θ)/tan² θ sin² θ] = 1

Let the amount be Rs. p

From the problem’s statement:

S.I = (p × r × t)/100

⇒ 25920 = (p × 12 × 6)/100

⇒ p = (25920 × 100)/(72)

⇒ p = 36000

Compound interest can be given as

⇒ CI = p((1 + 8/100)² - 1)

⇒ CI = 36000 × (1.08² - 1)

⇒ CI = 5990.4

∴ The CI is Rs. 5990.4

Increase in SUV is given as

⇒ 750 – 150 = 600

Increase in Sedan is given as

⇒ 625 – 450 = 175

Increase in Hatchback is given as

⇒ 800 – 500 = 300

∴ we can see that SUV is having highest increase in sale

Let A, B and C’s share be a, b and c respectively

From the problems statement

⇒ a = 2 × (b + c)/9 …(i) and

⇒ b = 3 × (a + c)/7….(ii)

given that total amount to be distributed is Rs. 60500

⇒ a + b + c = 60500 …(iii)

Put (i) in (ii)

⇒ b = 3 × ((2 × (b + c)/9) + c)/7

⇒ b = (2b + 11c)/21

⇒ 19b/11 = c …(iv) 

put (i) and (iv) in (iii)

⇒ 2 × (b + 19b/11)/9 + b + 19b/11 = 60500

⇒ b = 60500 × 99/330

⇒ b = 18150 Put this in (iv)

⇒ c = 19 × 18150/11

⇒ c = 31350

∴ C’s share is Rs. 31350

Alternate Method

a = 2 × (b + c)/9

⇒ (b + c) = 9a/2      ----(i)

b = 3 × (a + c)/7

⇒ (a + c) = 7b/3      ….(ii)

a + b + c = 60500      ----(A)

Putting equation i in the A

⇒ 9a/2 + a = 60500

⇒ a = 11000

Putting equation ii in the A

⇒ 7b/3 + b = 60500

⇒ b = 18150

Subtract 60500 with a and b value

⇒ c = 60500 - 11000 - 18150 

⇒ 31350

∴ C’s share is Rs. 31350

Percentage increase in the sale of Hatchback over year 2011 is given as

⇒ (sale in next year – sale in previous year) × 100/(sale in previous year)

⇒ (800 - 650) × 100/650

⇒ 23.07% increase

⇒ Sale of hatchback in year 2013 can be given as

⇒ 800 × (1 + 23.07/100)

⇒ 984.6

Percentage increase in the sale of Sedan over year 2011 is given as

⇒ (sale in next year – sale in previous year) × 100/(sale in previous year)

⇒ (625 - 575) × 100/575

⇒ 8.69% increase

⇒ Sale of sedan in year 2013 can be given as

⇒ 625 × (1 + 8.69/100)

⇒ 679.34

Percentage increase in the sale of SUV over year 2011 is given as

⇒ (sale in next year – sale in previous year) × 100/(sale in previous year)

⇒ (750 - 400) × 100/400

⇒ 87.5% increase

⇒ Sale of hatchback in year 2013 can be given as

⇒ 750 × (1 + 87.5/100)

⇒ 1406.25

⇒ Total sale = 984.6 + 679.34 + 1406.25 = 3069 (approximately)

∴ the total sale is approximately 3069

Given cot A = n/(n + 1) and cot B = 1/(2n + 1) and we know that

cot (A + B) = (cotA cotB - 1) / (cotA + cotB), Putting all values in this

⇒ cot(A + B) = [{1/(2n + 1)} × {n/(n + 1)} - 1] / [{1/(2n + 1) + n/(n + 1)]

⇒ cot(A + B) = [{n – (2n + 1)(n + 1)} / {(2n + 1)(n + 1)}] / [{(n + 1) + n(2n + 1)} / {(2n + 1)(n + 1)}]

⇒ cot (A + B) = -1

∴ the value of cot(A + B) = -1

From the question increase in sale is given as

⇒ 750 – 150 = 600

Let the rate be r%

⇒ 600 = (150 × r × 3)/100

⇒ r = 133.33%

∴ the simple annual growth rate is 133.33%

Discount can be calculated as (marked price – selling price) × 100/(marked price)

⇒ Discount = (2150 – 1892) × 100/ 2150

⇒ Discount = 12%

∴ The discount is 12%

Correct Answer: persuasions  Since the sentence talks about the army resorting to force, it is understandable that before that, a milder form of attack must have been used, such as persuading someone. Therefore, ‘persuasions’, meaning ‘the act of making someone believe something’, is the correct answer.

The correct answer is Rigorous

Key Points

• Stringent means strict and rigid.
  

Example: Stringent safety regulations were introduced after the accident.

• Rigorous: careful to look at or consider every part of something to make certain it is correct or safe.
  

Example: rigorous testing/checking/methods

• Therefore, the word ‘rigorous’ is the closest in meaning and the correct answer.

Additional Information

• The meaning of the words given in the options are:
• Annoying means causing irritation
• Revengeful means spiteful
• Incidental means occurring by chance

Here the correct answer is Hardly anything.

Key Points:-

• In the above given sentence, 'hardly anything' will be used.
• Hardly anything means ‘almost nothing or very little’.
• This fits the sentence better than the other options and is the correct answer.
• 'Hardly nothing' is incorrect.
• It is so because negative words like not/never are not used with deny, forbid, unless, until, lest, hardly, seldom, rarely, too and sacredly.
• 'Hardly little' and 'hardly something' are grammatically wrong.

Therefore, the correct sentence is Hardly anything was offered to the victims of the earthquake.

The correct answer is SRQP  

Key Points

• The given sentence is an example of a Sentence Jumble.
• The first statement of a sentence jumbled question is usually an independent general statement, a noun, a universal fact, or  the starting of an incident
• Part S will be the first sentence because the sentence is an independent general statement and introduces the 'villages' on which 4 statements are based.
• Part R will be the next sentence because it supports the first statement of why India is a country of villages.
• Part Q will be the next sentence because it tells us that cons of living in urban life are more than the pros.
• Lastly, Part P will be used because it contains the preposition 'despite'. You use despite to introduce a fact which makes the other part of the sentence surprising. P mentions that though the cons of living in urban overweigh its pros, still people are migrating to urban centers.

The correct sequence is: India is a country of villages. The rural population still dominates the urban population as far as the number is considered. Generally, the gains of being a unit of the urban population are less than the disadvantages and risks that are inbuilt in the urban life. This is despite the fact that there is a rampant migration of rural families to urban centres

Correct Answer: Diwali was celebrated by the residents.  

When converting to passive voice, the action of celebrating Diwali comes first in the sentence followed by the doer. Sentence 3 does exactly that and is therefore, the correct answer. Note that the simple past tense is maintained while converting, which makes sentences 2 and 4 incorrect.

The correct answer is Option 3 i.e. 'Soothing'.

Key Points

• The word "vexatious" means causing annoyance, frustration, or distress. (अभिशापदायक)
• "Soothing" means calming, comforting, or alleviating distress or irritation. (शांतिपूर्ण)
• The opposite of "vexatious" is "soothing."

Therefore, the correct answer is:- "Soothing".

Additional Information

• Meanings of the other given words:
• Calamitous: This word means causing or involving a great disaster, destruction, or misfortune.( अपदायक)
• Treacherous: This word describes someone or something that is deceptive, unreliable, or likely to betray (अधर्मी )
• Pliable: This word refers to something that is easily bent, flexible, or adaptable. (मुलायम)

Correct Answer: 3

The preposition ‘of’ is used incorrectly since ‘of’ is used with ‘die’ in cases of diseases or illnesses.

The correct sentence is: “I was shocked to hear that her husband died in an accident.”

The correct answer is Option 4)

Explanation:

• An ergophile is someone who loves to work.
• Oenophile is a connoisseur of wines,
• A technophile is a person enthusiastic about new technology
• Romanophile is one who loves Ancient Rome.

Thus, the correct answer is Ergophile

The correct answer is Personnal  

Key Points

• ‘Personnal’ is the incorrectly spelt word. The correct spelling is ‘Personnel’. The personnel of an organization are the people who work for it.
  

Example: Since 1954 Japan has never dispatched military personnel abroad.

• Impression: Your impression of a person or thing is what you think they are like, usually after having seen or heard them. Your impression of a situation is what you think is going on.
  

Example: What were your first impressions of college?

• Terrorism: Terrorism is the use of violence, especially murder and bombing, in order to achieve political aims or to force a government to do something.
  

Example: Governments must cooperate if they are to fight/combat international terrorism.

• Illiterate: Someone who is illiterate does not know how to read or write.
  

Example: A large percentage of the population is illiterate.

The correct answer is The foreman told his workers that he could not pay them higher wages.

Key Points

• The given sentence is in Direct Speech. As per the given question we have to change it into Indirect Speech.
• The Process of Transformation as follows:
• 'Said' will be changed into 'told'. Because the reporting verb has an object after 'said'.
• Comma and inverted comma will be added.
• The conjunction 'that' will be added.
• 'I' will be changed into 'he'.
• 'you' will be changed into 'them'
• ''Can't'' will be changed into ''couldn't''.
• Therefore, the correct answer is Option 2.

Correct Answer: The foreman told his workers that he could not pay them higher wages.

Correct Answer: To bear the consequences  The idiom ‘face the music’ means ‘to listen to criticism or confront the consequences for actions’. An example sentence is: ‘Before doing the task, he was warned that he would have to face the music’.

The correct answer is threatened  

Key Points

• ‘Threatened’ means ‘to endanger or intimidate someone’. The passage talks about how votes are manipulated during an election by using force. It says that election officials have been intimidated by politicians to turn a blind eye to their incorrect practices.
• The meaning of the words given in the options are:
• Decided means clear and definite.
• Safeguarded: To safeguard something or someone means to protect them from being harmed, lost, or badly treated.
• Rejuvenated: If something rejuvenates you, it makes you feel or look young again.
• ​According to the given context, only 'threatened' fits in the given blank.

Correct Answer: To have enough money to live on and nothing extra.  

The idiom ‘live from hand to mouth’ means ‘to have just enough money to provide for food, shelter, clothing and nothing else’.

An example sentence is: ‘After the recession and the economic depression, he was forced to live from hand to mouth’.

The correct answer is Option 2)

Explanation:

• Filicide is the deliberate act of a parent killing one’s own child
• Foeticide is the abortion of a fetus
• Infanticide is the killing of an infant
• Lupicide is the killing of wolves.

Thus, the correct answer is Filicide

The correct answer is Surveillence

Key Points

• ‘Surveillence’ in the incorrectly spelt word. The correct spelling is ‘Surveillance', meaning close observation of a spy or criminal.
  

Example: More banks are now installing surveillance cameras.

• Stupefaction means the condition of being unable to think clearly, usually because someone is extremely tired or bored, or has taken drugs.
  

Example: He was intoxicated to the point of stupefaction.

• Preferential is used to say that something that someone is given is better than what other people receive.
  

Example: Single mothers have been given preferential access to council housing.

• Detrimental is used to cause harm or damage.
  

Example: These chemicals have a detrimental effect/impact on the environment.

Correct Answer: Shrivel  

‘Burgeon’ means to grow or increase rapidly. Since ‘shrivel’ means to wrinkle or contract, it is opposite in meaning and the correct answer. Bolster means support or strengthen, mount means to climb up and amplify means to make something more intense.

Additional Information Bolster: Support or strengthen.

Shrivel: Wither or become smaller and wrinkled.

Mount: Climb, set up, or prepare.

Amplify: Increase in volume, intensity, or impact.

The correct answer is realistic

Key Points

• ‘Realistic’ means practical or pragmatic. The passage says it is not wise to ignore all accusations of booth capturing as in most of the cases, they are real and correct.
• Meaning of other words given in the options are:
• Reliable: People or things that are reliable can be trusted to work well or to behave in the way that you want them to.
• Required: essential, needed, or necessary
• Essential: Something that is essential is extremely important or absolutely necessary to a particular subject, situation, or activity.
• According to the given context, only 'realistic' fits in.

The correct answer is disgruntled

Key Points

• ‘Disgruntled’ means ‘angry or dissatisfied’. It is the correct word since losers are generally angry and find reasons to blame their loss, such as booth capturing and rigging. The other words do not correctly fit in as an adjective.
• Meaning of other options:
• Rational decisions and thoughts are based on reason rather than on emotion.
• Something or someone that is huge is extremely large in size.
• Idealist: a person who cherishes or pursues high or noble principles, purposes, goals, etc
• According to the given context, only 'disgruntled' fits in.

Here the correct answer is Had done.

Key Points:- 

• ‘Had done’ uses the past perfect tense of the ‘do’ verb.
• Past perfect tense is used to express an action which has  been completed a long time ago.
• Structure of past perfect tense - Subject + had +  V₃ + Object.
• When two actions occur in the past, one after the other, the, the first action is expressed in past perfect tense and the second action is expressed in simple past tense.
• For Example - He came after she had gone.
• This indicates that the action was completed before another action happened, i.e., the ‘thanking’ happened after the ‘do’ verb.
• The other options use the incorrect tense.

Therefore, the correct sentence is He thanked me for what I had done for his wife.

The correct answer is instances  

Key Points

• ‘Instances’ means cases or occurrences. It fits in the blank correctly as the sentence then says that there have been cases of intimidation of whole villages for voting.
• The meaning of the other words given in the options are: 
• Sources: The source of something is the person, place, or thing from which you get it from.
• Reasons: The reason for something is a fact or situation which explains why it happens or what causes it to happen.
• Ideas: An idea is a plan, suggestion, or possible course of action.
• According to the context, only 'instances' fits in the given blank.

The correct answer is 2

Key Points

• 'his failure is that' should be there in place of 'his failure is because'

• There are two reasons why 'the reason is' not followed by 'because':

• Because is redundant because it means ‘for the reason that’ (The reason is for the reason that…)

• Is is a linking verb and should not be followed by an adverbial clause introduced by the conjunction because.

• ​Example: 

• ​The reason why he was rejected was because he was too young. 

• The reason why he was rejected was that he was too young. 

• ​Thus, the correct sentence is: The reason for his failure is that he didn't study at all.

The correct answer is ‘in’ since the phrase ‘feather in one’s cap’ means an achievement to be proud of. The other words are not used as they do not complete the phrase properly.

The correct answer is SRQP  

Key Points

• The given sentence is an example of a Sentence Jumble.
• The first statement of a sentence jumbled question is usually an independent general statement, a noun, a universal fact, or the starting of an incident
• Part S will be the first sentence because it is clear that that the flow of topics is from knowledge to power to education. Therefore, Sentence S comes first introducing knowledge and power.
• Part R will be the next sentence because it mentions the agent that imparts 'knowledge'
• Part Q will be the next sentence because it starts with 'therefore'. You use therefore to introduce a logical result or conclusion. Here it is concluding why people in power during the ancient era try to supervise or control education.
• Lastly, Part P will be used because it concludes all the sentences.

The correct sequence is: It is an old saying that knowledge is power. Education is an instrument that imparts knowledge and therefore, indirectly controls power. Therefore, ever since the dawn of civilization, persons in power have always tried to supervise or control education. It has been the handmaid of the ruling class.

The correct answer is unjust

Key Points

• ‘Unjust’ means ‘not morally right or fair’. It fits the blank since the politicians threaten election officials to ignore their immoral practices during election time.
• Meaning of other words given in the options are:
• Significant: A significant amount or effect is large enough to be important or affect a situation to a noticeable degree.
• Rare: Something that is rare is not common and is therefore interesting or valuable.
• Usual: Usual is used to describe what happens or what is done most often in a particular situation.
• According to the given context, only 'unjust' fits in.

The correct answer is: Option 2.

Key Points

• The word "Pernicious" means having a harmful effect, especially in a gradual or subtle way. (हानिकारक)
• Example: The pernicious influence of social media on teenagers can lead to anxiety and depression.
• "Dangerous" refers to something that is likely to cause harm or injury. (खतरनाक)
• Example: Driving at high speeds on icy roads is extremely dangerous.

Therefore, the correct answer is: Option 2.

Additional Information

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

• Beneficial (लाभकारी): Producing good or helpful results or effects.
• Example: Regular exercise is beneficial for overall health.
• Innocuous (अहानिकर): Not harmful or offensive.
• Example: The comment was meant to be innocuous, but it offended many people.
• Advantageous (फायदेमंद): Providing an advantage; favorable.
• Example: Speaking multiple languages is advantageous in today’s global job market.