SSC CGL Previous Paper (Held On: 7 June 2019 Shift 2) (Previous Year Paper)

The pattern followed here is,

Here, dbacbd is repeating,

Dbacbd dbacbd dbacbd

Hence, adcdb is the correct answer.

The pattern followed here is,

5 + (7 × 1) = 12;

12 + (7 × 2) = 26;

26 + (7 × 4) = 54;

54 + (7 × 8) = 110

Hence, 110 is the correct answer.

Hence, figure 1 is the correct answer.

Some graduates can be teacher,

But both graduates and teachers are literates.

Hence, figure 4 is the correct answer.

All numbers except 43, are divisible by 3.

But number 43 is not divisible by 3.

Hence, 43 is the correct answer.

All given options, except 'RSTY', contain at least one vowel.

Hence, RSTY is the odd one out.

The pattern followed here is,

Second Number = First number × 3 + 6

12 × 3 + 6 = 36 + 6 = 42

16 × 3 + 6 = 54 ≠ 53

15 × 3 + 6 = 51 ≠ 52

24 × 3 + 6 = 78 ≠ 82

8 × 3 + 6 = 30

Hence, 8 : 30 is the correct answer.

The pattern followed here is,

2 × (First number + Last number)

3 + 5 = 8; 8 × 2 = 16

Similarly,

7 + 9 = 16; 16 × 2 = 32.

Hence, (7, 32, 9) is the correct answer.

Concept:

If one face is common in both the dice,

then write the number in a clockwise direction from it.

Equivalent position number become Opposite number pair to it.

Here,

Here, 3-2-4 and 3-6-1 are the sequence.

(2 and 6 ), (1 and 4) and the remaining (3 and 5) become the opposite pair.

Thus, if 6 is at the bottom then 2 will be on the top.

Hence, 2 is the correct answer.

Here all excepts ‘Awkward’ are synonyms of each other.

Hence, ‘Awkward’ is the odd one out.

The logical and meaningful order is as follows,

4. Admission
5. College
6. Class
7. Learn
8. Assessment
9. Degree

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

The least possible Venn diagram according to the information is,

No road is a lane → False, it is possible but not definite.

All streets are lanes → False, it is possible but not definite.

Some lanes are roads → False, it is possible but not definite.

Conclusion I and III are complementary pairs

Hence, either conclusions I or III follows.

Let the present age of Mitali and Shabnam be 4x and 7x.

Mitali’s age after 5 years will be 4x + 5,

The difference between present age of Shabnam and Mitali’s age after 5 years = 7x - (4x + 5) = 13

7x - 4x - 5 = 13

3x = 13 + 5

3x = 18

x = 6

Hence present ages of Mitali and Shabnam will be 24 and 42.

Sum of the present age of Mitali and Shabnam = 24 + 42 = 66

Hence, 66 is the correct answer.

Given equation: 9 - 3 + 12 × 8 ÷ 4  = 11

1. Interchanging - and ÷

9 ÷ 3 + 12 × 8 - 4

= 3 + 96 - 4

= 99 - 4 = 95 ≠ 11

2) Interchanging + and ÷

9 - 3 ÷ 12 × 8 + 4

= 9 - 0.25 × 8 + 4

= 11

3. Interchanging + and -

9 + 3 - 12 × 8 ÷ 4

= 12 - 24

= - 12 ≠ 11

4. Interchanging × and +

9 - 3 × 12 + 8 ÷  4

= 9 - 36 + 8 ÷ 4

= 11 - 36

= -25 ≠ 11

Hence, by interchanging ÷ and + we get the correct equation.

The pattern followed here is,

Similarly,

Hence, ‘ORBSREH’ is the correct answer.

Hence, figure 2 is the correct answer.

Hence, 18 is the correct answer.

As Caress is synonym of Affection

Similarly,

Synonym of Kick is Hostility

Hence, ‘Kick : Hostility’ is the correct answer.

Hence, figure 1 is the correct answer.

Similarly,

Hence, “TPMK” is the correct answer.

The pattern followed here is,

(8, 15, 9) = 8 + 15 + 9 = 32

Similarly,

(4, 16, 12) = 4 + 16 + 12 = 32

Hence, (4, 16, 12) is the correct answer.

Note: the option has been modified as it was ambigious.

Mirror image is:

Hence, figure 3 is the correct answer.

The pattern followed here is,

Similarly,

Hence, 5111510 is the correct answer.

Hence, Q is the father of V.

The antonym of ‘disconnect’ is ‘unify’

Similarly,

The antonym of ‘mend’ is ‘damage’

Hence, Damage’ is the correct answer.

• The Hawa Mahal was built by Maharaja Sawai Pratap Singh in 1799.
• The Hawa Mahal is a grand palace situated in Jaipur.
• The structure was built in 1799 by the grandson of the original founder of Jaipur, Sawal Jai Singh.
• The palace is made out of red and pink sandstone and is five floors in height and has a pyramidal shape to it

• The new chairperson of the National Green Tribunal is Justice Adarsh Kumar Goel.
• He retired from the Supreme Court on 6 July 2018 and appointed the Chairperson on 7 July 2018.
• The post of chairperson had been lying vacant from 6 months since the retirement of Justice Swatanter Kumar.
• The National Green Tribunal (NGT) was set up to speed up the process for cases relating to environmental protection and conservation of forests and other natural resources on 18 October 2010.

• The 86th Constitutional Amendment provided constitutional status for free and compulsory elementary education to all children.
• In other words, the Right To Education was inserted into the Constitution.
• The insertion was done by the means of Article 21A to provide free education for children between ages between 6 to 14 years.
• The education shall be free and no kind of fees are to be taken from children.

• Shah Jahan built Taj Mahal as a memorial for his wife Mumtaz Mahal.
• It acts as the tomb of Shah Jahan's deceased wife Mumtaz Mahal.
• The original name of  Mumtaz Mahal is Arjumand Banu Begum.
• The mausoleum was commissioned in 1632 and opened for visitors in 1648.
• It is now listed in the 7 Wonders Of The World and attracts millions of tourists every year.

• The Victoria Memorial as conceived by Lord Curzon is located in Kolkata.
• It is a marble architectural wonder present in the city of Kolkata.
• It was built in memory of Queen Victoria of England after her death in 1901.
• The building was built between 1906 and 1921 and has now been turned into a museum that attracts thousands of visitors annually.

• Thallium was discovered by William Crookes.
• He discovered the element by the means of a spectroscope in 1861.
• The element was later isolated by William Crooke and Claude Auguste Lamy independently in 1862.
• Thallium has symbol Tl with atomic number 81 and mass 204.38.

• Dinesh Dagar is not one of the three Indian bronze medallists at the 38th GeeBee Boxing Tournament.
• In fact, Dinesh Dagar was a silver medallist in the 69 kg category at the prestigious event.
• In total, India bagged 8 medals at the 2018 edition of the event listed below.

Key Points

• Akbar, the third Mughal Emperor was the heir to the Mughal Empire after the death of his father, Humayun.
• He was born on 15 October 1542 in Umerkot located in Sindh which is in present-day Pakistan.
• During Humayun's exile, Akbar was brought up in Kabul during his early childhood.
• After the death of his father, he succeeded the throne with the help of regent Bairam Khan who helped in his affairs.

• A major trade characteristic of trade in the colonial period of India was its export surplus.
• An export surplus is when a country exports more products than it imports from other countries.
• This was because in the colonial period the British allowed large exports of handicraft products and free export of India's raw material.
• Thus exported goods from India were sought after which led to a high volume of export.
• Half of India's export were restricted to Britain and the other major importers were China, Persia and Sri Lanka.

• Fitch ratings cut India's economic growth forecast to 6.8% for the financial year 2019-20
• This cut in forecasted growth was done before the Budget was presented for the year
• On the other hand the RBI had projected a growth of 7%
• Fitch Ratings is a credit rating agency and one of America's largest statistical rating organizations other than Moody's and Standard & Poor's

• The Yangtze is the longest river in Asia.
• It has a length of 6,380 kilometres.
• It is the third-largest river in the world.
• It starts from central China and flows out into the East China Sea from Shanghai.

• Indira Gandhi served as Prime Minister during the Emergency between 1975 to 1977.
• The emergency was a 21 month period where the then President Fakhruddin Ali Ahmed on the advice of Indira Gandhi imposed the Emergency under Article 352 of the Constitution.
• There was massive civil unrest in the country due to many factors such as:
• 1971 Bangladesh Liberation War
• Refugees of the war
• Slow industrial growth

• Wilhelm Röntgen was the first-ever awardee of the Nobel Prize in Physics in 1901.
• He was a German mechanical engineer and also a physicist.
• He received the award for discovering X Rays, which he discovered on 8 November of 1895.
• The Nobel Prize was started in 1901 founded by the Swedish inventor and businessman Alfred Nobel which was written in his will in 1896.
• The Nobel Prize is awarded in six fields which are physics, chemistry, medicine, literature, economics and peace.

• The Red Fort and Jama Masjid are two of the many architectural gems built in Shah Jahan's reign.
• Even though Shah Jahan is famously known for the Taj Mahal,  the Red Fort and Jama Masjid are the other wonders he built in Delhi itself.
• The Red Fort was built in 1639 as his palace for his then capital back then known as Shahjahanad.
• The Jama Masjid was finished in 1656 with a name of Masjid-e-Jahan Numa.

• The Danube river in Europe is the river that passes through the maximum number of countries in its journey.
• It passes through 10 countries: Germany, Hungary, Romania, Austria, Serbia, Bulgaria, Croatia, Moldova, Ukraine, Slovakia.
• It starts in Southern Germany and runs into the Black Sea through Romania.
• It is the second-longest river in Europe after the Volga with a length of 2,850 kilometres.

• The discovery of electron was done by J J Thomson in 1897.
• He discovered the subatomic particle in 1897 with experiments with the cathode ray tube.
• A cathode-ray tube is a vacuum tube that produces a stream of electrons that is emitted from a heated metal filament.
• This discovery led to J J Thomson proposing the first-ever atomic model theory known as the plum pudding model.
• The plum pudding model which has negatively-charged electrons embedded within a positively-charged "soup".

• Abhilash Tomy, an Indian naval officer Commander was the only Asian to participate in the esteemed Golden Globe Race.
• He is one of India's most prominent sailors and has already completed a solo circumnavigation of the globe in 2013.
• He participated in the Golden Globe Race is a global world sailing race which starts from Les Sables d’Olonne harbour in France.
• The 2018 edition of the race celebrated the 50th anniversary of the original race held in 1968.
• It does not allow the entrants to use modern technologies and yachts, they can only use yachts which are in the style of those built during the times of the original race which was 50 years ago.

• Mohammed Hussamuddin won a silver for India at the 38th GeeBee Boxing Tournament.
• He was defeated in the finals by fellow Indian boxer Kavinder Singh Bisht who got the gold medal.
• He competes in the 56 kg category.
• Three more silver medals were won by Indian boxers Govind Kumar Sahani (49kg), Shiva Thapa (60kg) and Dinesh Dagar (69kg).

• Salim took the title of Jahangir after his father, Akbar's death.
• The full name of Salim is Nur-ud-din Muhammad Salim.
• He was the fourth Mughal Emperor and ruled from 1605 to 1627 till he died.
• His tomb is located in Shahdara which is present in Lahore, Pakistan.

• The Ganga is the longest river in India.
• It has a length of about 2,525 kilometers.

• World Meteorological Day 2019 was observed on 23rd March.
• The day is celebrated because the World Meteorological Organization was established on 23rd March 1950.
• The theme for 2019 was 'The Sun, The Earth and The Weather' to emphasize the function of how the sun affects the weather and ocean currents on our planet.

• A fiscal deficit occurs when a government's total expenditures exceed the revenue that it generates, excluding money from borrowings.
• In other words, a fiscal deficit occurs when the government spends more money than it earns.
• This gap between income and spending is zeroed by the government borrowing money.
• Usually, a fiscal deficit is expressed as a percentage of a country's GDP (Gross Domestic Product).
• India's 2018-19 fiscal deficit was 3.39% of GDP at 6.45 Lakh Crores.

• The 1903 Nobel Prize in Physics was awarded to the three scientists for their discoveries in radioactivity
• Half of the share of the prize was awared to Henri Becquerel for his work in discovery of spontaneous radioactivity of uranium salts
• The other half of the Nobel Prize was shared by Pierre Curie and his wife Marie Curie equally for researching further into the discoveries of Becquerel
• They managed to extract two previously unknown radioactive elements polonium and radium from the mineral pitchblende

In News

• Shaheed Divas is observed on 23rd March as a tribute to Bhagat Singh, Sukhdev and Rajguru on their death anniversary.

Key Points 

• There are a total of 5 Shaheed Divas (Martyr's Day) celebrated in India.
• The one of 23rd March is a tribute to Bhagat Singh, Sukhdev and Rajguru on their death anniversary.
• This is because the three heroes of the nation were hanged to their deaths as they had sacrificed for the independence of our country.

• It was Santiago Ramón y Cajal who won a Nobel Prize along with Camillo Golgi.
• The prize was won for his neuron doctrine which is a theory that states that the nervous system is made up of discrete nervous cells.
• He discovered this using a silver staining technique developed by the Italian scientist Camillo Golgi.
• He first discovered this while investigating cells of bird brains in 1888.

Shortcut Trick

Use the direct relation: (Total Price₁ / (Quantity₁ × (100 − Loss%))) = (Total Price₂ / (Quantity₂ × (100 + Profit%)))

⇒ 2500 / (25 × 90) = 2400 / (n × 120)

⇒ 100 / 90 = 20 / n

⇒ 10 / 9 = 20 / n

⇒ n = (20 × 9) / 10 = 18

∴ The correct answer is 18.

Alternate Method

Given:

Quantity₁ = 25 articles, Total SP₁ = ₹2500, Loss = 10%

Desired Profit = 20%, Total SP₂ = ₹2400

Formula: Cost Price (CP) = (100 × SP) / (100 ± P/L%)

⇒ Selling Price (SP) of 1 article = 2500 ÷ 25 = ₹100

⇒ Since loss is 10%, 90% of CP = ₹100

⇒ CP of 1 article = 100 ÷ 0.9 = ₹1000/9

⇒ New SP required for 20% profit = 120% of CP

⇒ New SP = (120/100) × (1000/9) = ₹400/3

⇒ Number of articles for ₹2400 = Total SP ÷ New SP per article

⇒ Number of articles = 2400 ÷ (400/3) = (2400 × 3) ÷ 400 = 6 × 3 = 18

∴ The correct answer is 18.

Additional Information

Cost Price and Selling Price Relationship

Cost Price (CP) is always considered 100%. If there is a profit of P%, SP = (100 + P)% of CP. If there is a loss of L%, SP = (100 − L)% of CP.

Unitary Method in Profit and Loss

When the number of articles changes, it is easiest to find the CP or SP of one single unit before calculating the total for the new quantity.

Profit/Loss Percentage

Profit or Loss percentage is always calculated on the Cost Price unless stated otherwise in the question. Profit % = (Profit/CP) × 100.

Total production of cars in 2014 = 63 + 64 + 56 + 65 + 72 = 320 thousands

Average production of cars in 2014 = 320/5 = 64 thousands

Total production of type B cars in 2013 and type D cars in 2010 = 68 + 42 = 110

∴ Required percentage = [(110 – 64)/110] × 100 = 41.81%

Divisibility rule of 9: A number divisible by 9 if the sum of its digit is divisible by 9.

Divisibility rule of 8: A number divisible by 8 if the last three digit of the number is divisible by 8

If 10 digit number 897359y7x2 is divisible by 72. So, we can say number also divisible by 9 and 8

⇒ 7x2 is divisible by 8 if x = 9

⇒ 897359y792 is divisible by 9 if y = 4

⇒ 3x – y

⇒ 3 × 9 – 4

⇒ 27 – 4

⇒ 23

⇒ x² – 3x – 1 = 0

Divided by x

⇒ x – 3 – (1/x) = 0

⇒ x – 1/x = 3

⇒ x² + 1/x² = 3² + 2 = 11

⇒ (x² + 8x – 1) (x³ + x^-1)^-1

$\Rightarrow \frac{{{{\rm{x}}^2}{\rm{;}} + {\rm{;}}8{\rm{x;}} - 1}}{{{{\rm{x}}^3}{\rm{;}} + {\rm{;}}\frac{1}{{\rm{x}}}}}$

Divided by x

$\Rightarrow \frac{{{\rm{x;}} + {\rm{;}}8{\rm{;}} - {\rm{;}}\frac{1}{{\rm{x}}}}}{{{{\rm{x}}^2}{\rm{;}} + {\rm{;}}\frac{1}{{{{\rm{x}}^2}}}}}$

⇒ (3 + 8)/11 = 1

Let the number of students in section B be x number of students in section A = x + 10

According to the question

⇒ x + 10 + x = 110

⇒ x = 50

Number of students in section A = 60

Number of students in section B = 50

Sum of score of all students = 110 × 72 = 7920

Let the average score of students in section A be x.

Average score of students in section B = x × [120/100] = 1.2x

According to the question

60x + 50 × 1.2x = 7920

⇒ 60x + 60x = 7920

⇒ x = 7920/120 = 66

∴ Average score of students of section A = 66

We can write, 20% = 1/5, 25% = 1/4

Ratio of A to B = 4 : 5      ---- 1

Ratio of C to D = 6 : 5     ---- 2

Ratio of A to D = 4 : 3     ---- 3

Multiply equation (1) and equation (3) by 5 and multiply equation (2) by 3

Ratio of A : B : C : D = 20 : 25 : 18 : 15

⇒ C : B = 18 : 25

⇒ C = 18/25 B

⇒ C = 0.72B

Shortcut Trick

Area of triangle with sides 50, 70, 80: s = 100, Area = √(100 × 50 × 30 × 20) = 1000√3 m².

Equilateral triangle area = (√3/4) × x².

Equating both: (√3/4) × x² = 1000√3 ⇒ x² = 4000.

x = √4000 ≈ 63.24 m.

∴ The correct answer is 63.2 m.

Alternate Method

Given: Sides of the second triangular field are 50 m, 70 m, and 80 m. The first field is an equilateral triangle with side x.

Formula Used: Heron's formula Area = √(s(s−a)(s−b)(s−c)) and Equilateral Area = (√3/4)x².

⇒ Semi-perimeter (s) = (50 + 70 + 80) / 2 = 100 m

⇒ Area of second field = √(100 × (100−50) × (100−70) × (100−80))

⇒ Area = √(100 × 50 × 30 × 20) = √(3,000,000) = 1000√3 m²

⇒ Area of first field = (√3 / 4) × x² = 1000√3

⇒ x² = 4000

⇒ x = √4000 = 20√10 ≈ 20 × 3.162 = 63.24 m

∴ The correct answer is 63.2 m.

Additional Information

Heron's Formula

Used for scalene triangles where sides a, b, c are known: Area = √(s(s−a)(s−b)(s−c)) where s = (a+b+c)/2.

Equilateral Triangle Properties

For side x, Area = (√3/4)x² and Height = (√3/2)x.

Square Root Approximations

Since 60² = 3600 and 70² = 4900, √4000 must lie between 60 and 70, specifically closer to 63 (63² = 3969).

Given, PQ = PR = 12 cm and OR = OQ = OP = 10 cm

Suppose SQ = RS = x cm and OS = y cm

PS = (10 – y)

In ΔPRS,

RP² = PS² + RS² [Using Pythagoras theorem]

12² = (10 – y)² + x²

⇒ 144 = 10² + y² – 2 × 10 × y + x²

⇒ 144 = 100 + y² – 20y + x²       ----(1)

In ΔRSO,

OR² = RS² + OS² [Using Pythagoras theorem]

⇒ 10² = x² + y²

⇒ 100 = x² + y²      ----(2)

Subtract equation (2) from equation (1)

144 – 100 = 100 + y² – 20y + x² – x² – y²

⇒ 20y = 56

⇒ y = 14/5

From equation (2)

100 = x² + (14/5)²

⇒ x² = 100 – [196/25]

⇒ x² = (2500 – 196)/25 = 2304/25

⇒ x = 48/5

⇒ 2x = 2 × [48/5] = 96/5 = 19.2 cm

∴ RQ = 2x = 19.2 cm

Given:

Time taken to cover a distance of 4 km upstream = 1 hour 20 minutes = 4/3 hours

Time taken to cover a distance of 4 km downstream = 24 minutes

Concept Used:

The direction along the stream is called downstream.

The direction against the stream is called upstream.

Formula Used:

Distance = Speed × Times

Downstream speed of the boat = Speed of boat + Speed of stream

⇒ D_s = x + y

Upstream speed of the boat = Speed of boat - Speed of stream

⇒ Us = x - y

Calculation:

Let Speed of boat in still water be x km/hr & speed of stream be y km/hr

According to the question,

⇒ 4/(x – y) = 4/3

⇒ x – y = 3      ----(1)

⇒ 4/(x + y) = 24/60

⇒ x + y = 10     ----(2)

Add equation (1) and equation (2) we get,

⇒ 2x = 13

⇒ x = 13/2 km/hr

Time taken to row 13 km in still water = Distance covered/Speed of boat

Time taken = 13 ÷ 13/2 = 2 hrs

∴ The time taken to row 13 km in still water is 2 hours.

Price of article are in the ratio = 4 : 5

According to the question

⇒ $\Rightarrow \frac{{4{\rm{;}} \times {\rm{;}}\frac{{\left( {100{\rm{;}} + {\rm{;x}}} \right)}}{{100}}}}{{5{\rm{;}} \times {\rm{;}}\frac{{\left( {100 - 30} \right)}}{{100}}}}{\rm{}} = {\rm{}}\frac{{10}}{7}$

⇒ $\frac{{4{\rm{;}} \times {\rm{;}}\left( {100{\rm{;}} + {\rm{;x}}} \right)}}{{5{\rm{;}} \times {\rm{;}}70{\rm{;}}}}{\rm{}} = {\rm{}}\frac{{10}}{7}$

⇒ (100 + x) = 125

⇒ x = 25%

In ΔABC,

⇒ (BC)² = (AC)² + (AB)² [Using Pythagoras theorem]

⇒ (10)² = 6² + AB²

⇒ AB = 8

In ΔACD,

⇒ (CD)² = (AD)² + (AC)² [Using Pythagoras theorem]

⇒ CD² = 4² + 6²

⇒ CD = √(16 + 36) = √52 = 2√13 cm

⇒ (135√5 x³ – 2√2 y³) ÷ (3√5 x – √2 y)

As we know,

⇒ (x³ – y³) = (x – y) (x² + y² + xy)

⇒ (3√5 x – √2 y) (45x² + 2y² + 3√10 xy) ÷ (3√5 x – √2 y)

⇒ (45x² + 2y² + 3√10 xy)

Comparing on (Ax² + By² + √10 Cxy)

⇒ A = 45, B = 2, C = 3

⇒ A + B – 9C = 45 + 2 – 9 × 3 = 20

Total production of type A cars in 2011 and type C cars and type E cars in 2012 = 69 + 45 + 61 = 175 thousands

Total production of type B cars during 2010 to 2014 = 40 + 56 + 52 + 68 + 64 = 280 thousands

∴ Required percentage = [175/280] × 100 = 62.5%

Total production of type B cars in 2011 and type E cars in 2013 = 56 + 64 = 120 thousands

Total production of type C cars in 2014 and type D cars in 2012 = 56 + 44 = 100 thousands

∴ Required ratio = 120 : 100 = 6 : 5

As we know,

Formula for installments in case of compound interest is P = x/(1 + r/100) + x/(1 + r/100)² ....x/(1 + r/100)ⁿ

Given, (each installment) x = 35,280, r = 5%, n = 2 and P = ?

P = x/(1 + r/100) + x/(1 + r/100)²

P = 35,280/(1 + 5/100) + 35,280/(1 + 5/100)²

P = [35,280 × (20/21)] + [35,280 × (20/21) × (20/21)]

P = 33,600 + 32,000 = 65,600

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

Suppose DC = x

⇒ BD = (a – x)

As we know,

⇒ AB/BD = AC/DC

$\Rightarrow \frac{{\rm{c}}}{{{\rm{a}} - {\rm{x}}}}{\rm{}} = {\rm{}}\frac{{\rm{b}}}{{\rm{x}}}$

⇒ cx = ab – bx

⇒ x(b + c) = ab

⇒ x = ab/(b + c)

SP of the article = Rs. 492

MP of the article = Rs. 492 × [100/82] = Rs. 600

CP of the article = Rs. 600 × [100/120] = Rs. 500

Given, ∠ADC = 130°

As we know,

⇒ ∠ADC + ∠ABC = 180°

⇒ 130° + ∠ABC = 180°

⇒ ∠ABC = 180° – 130° = 50°

As we know,

⇒ ∠ACB = 90°

In ΔABC

⇒ ∠ACB + ∠ABC + ∠BAC = 180°

⇒ ∠BAC = 180° – 90° – 50° = 40°

⇒ 9a² + 4b² + c² + 21 = 4(3a + b – 2c)

⇒ (3a)² + (2b)² + c² + 21 = 12a + 4b – 8c

⇒ [(3a)² – 2 × 3a × 2 + 2²] + [(2b)² – 2 × 2b × 1 + 1²] + [c² + 2 × c × 4 + 4²] = 0

⇒ (3a – 2)² + (2b – 1)² + (c + 4)² = 0

⇒ (3a – 2)² = 0

⇒ a = 2/3

⇒ (2b – 1)² = 0

⇒ b = 1/2

⇒ (c + 4)² = 0

⇒ c = -4

⇒ (9a + 4b – c)

⇒ 9 × (2/3) + 4 × (1/2) – (-4)

⇒ 6 + 2 + 4

⇒ 12

Shortcut Trick

Total time = 11(1/3) days (B starts first). B works on days 1, 3, 5, 7, 9, 11 (6 days); A works on days 2, 4, 6, 8, 10 and 1/3 of day 12 (5 + 1/3 = 16/3 days).

Work done by A = (16/3) ÷ 48 = 1/9. Remaining work done by B = 1 − 1/9 = 8/9.

B finishes 8/9 work in 6 days ⇒ B finishes full work in (6 × 9)/8 = 27/4 days.

B finishes 4 times the work in (27/4) × 4 = 27 days.

∴ The correct answer is 27 days.

Alternate Method

Given: A alone = 48 days. Total alternate time = 11(1/3) days. B starts on day 1.

Distribution of work days:

⇒ B works on days: 1, 3, 5, 7, 9, 11 → Total 6 days.

⇒ A works on days: 2, 4, 6, 8, 10, and 1/3 of the 12th day → Total 5 + 1/3 = 16/3 days.

⇒ Work done by A in 16/3 days = (16/3) × (1/48) = 1/9 of total work.

⇒ Work done by B in 6 days = 1 − 1/9 = 8/9 of total work.

⇒ Time taken by B to finish 1 complete work = 6 ÷ (8/9) = (6 × 9) / 8 = 27/4 days.

⇒ Time taken by B to finish 4 times the same work = 4 × (27/4) = 27 days.

∴ The correct answer is 27 days.

Additional Information

Alternate Day Work

In alternate work, identify who starts first. If total time is T, and B starts, B works for ceil(T/2) days if T is not an even integer and cycle is 2 days.

Efficiency and Time

Time is inversely proportional to Efficiency. Work = Efficiency × Time. For multiple works, New Time = Original Time × Multiplier.

$\Rightarrow \left( {\frac{{{\rm{tan\theta ;}}-{\rm{;sec\theta ;}} + {\rm{;}}1}}{{{\rm{tan\theta ;}} + {\rm{;sec\theta ;}}-{\rm{;}}1{\rm{;}}}}} \right){\rm{sec\theta }} = {\rm{}}\frac{1}{{\rm{k}}}$

$\Rightarrow \left[ {\frac{{ - \left( {{\rm{sec\theta }} - {\rm{tan\theta }}} \right){\rm{;}} + {\rm{;;}}({\rm{se}}{{\rm{c}}^2} - {\rm{;ta}}{{\rm{n}}^2}{\rm{\theta }})}}{{{\rm{tan\theta ;}} + {\rm{;sec\theta ;}}-{\rm{;}}1}}} \right]{\rm{sec\theta }} = {\rm{}}\frac{1}{{\rm{k}}}$

$\Rightarrow \left[ {\frac{{ - \left( {{\rm{sec\theta }} - {\rm{tan\theta }}} \right){\rm{;}} + {\rm{;}}\left( {{\rm{sec\theta }} - {\rm{tan\theta }}} \right)\left( {{\rm{sec\theta ;}} + {\rm{;tan\theta }}} \right)}}{{{\rm{tan\theta ;}} + {\rm{;sec\theta ;}}-{\rm{;}}1}}} \right]{\rm{sec\theta }} = {\rm{}}\frac{1}{{\rm{k}}}$

\(\Rightarrow \left[ {\frac{{\left( {{\rm{sec\theta }} - {\rm{tan\theta }}} \right){ {\rm{;}}\left( { - 1} \right){\rm{;}} + {\rm{;sec\theta ;}} + {\rm{;tan\theta }}}}{{{\rm{tan\theta ;}} + {\rm{;sec\theta ;}}-{\rm{;}}1}}} \right]{\rm{sec\theta }} = {\rm{}}\frac{1}{{\rm{k}}}\)

⇒ (secθ – tanθ)secθ = 1/k

⇒ [(1/cosθ) – (sinθ/cosθ)] × [1/cosθ] = 1/k

⇒ (1 – sinθ)/cos²θ = 1/k

⇒ (1 – sinθ) / (1 – sin²θ) = 1/k

⇒ [(1 – sinθ] / [(1 – sinθ)(1 + sinθ)] = 1/k

⇒ 1/(1 + sinθ) = 1/k

⇒ k = 1 + sinθ

$sin;\theta = \frac{{Perpendicular{\rm{;}}}}{{Hypotenuse{\rm{;}}}}{\rm{}} = {\rm{}}\frac{a}{{\sqrt {{a^2}{\rm{;}} + {\rm{;}}{b^2}} }}$

Using Pythagoras theorem

⇒ (Hypotenuse)² = (Base)² + (Perpendicular)²

$\Rightarrow {\left( {\sqrt {{a^2}{\rm{;}} + {\rm{;}}{b^2}} } \right)^2}{\rm{}} = {\rm{}}{\left( {{\rm{Base}}} \right)^2}{\rm{}} + {\rm{}}{{\rm{a}}^2}$

⇒ Base = √(a² + b² – a²) = b

$\Rightarrow sec;\theta = \frac{{{\rm{Hyptenuse}}}}{{{\rm{Base}}}}{\rm{}} = {\rm{}}\frac{{\sqrt {{{\rm{a}}^2}{\rm{}} + {\rm{}}{{\rm{b}}^2}} }}{{\rm{b}}}$

⇒ tan θ = Perpendicular/Base = a/b

⇒ sec θ + tan θ

$\Rightarrow \frac{{\sqrt {{{\rm{a}}^2}{\rm{;}} + {\rm{;}}{{\rm{b}}^2}} }}{{\rm{b}}}{\rm{}} + {\rm{}}\frac{{\rm{a}}}{{\rm{b}}}$

$\Rightarrow \frac{{\sqrt {{{\rm{a}}^2}{\rm{;}} + {\rm{;}}{{\rm{b}}^2}} {\rm{;}} + {\rm{;a}}}}{{\rm{b}}}$

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, and in the bracket,

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.

$\Rightarrow 7\frac{1}{2}{\rm{}} \times {\rm{}}\left( {3\frac{1}{5}{\rm{}} \div {\rm{}}5\frac{1}{3}{\rm{of;}}4\frac{1}{2}} \right){\rm{}} + {\rm{}}\left[ {11 - \left( {\frac{5}{8}{\rm{}} + {\rm{}}3 - 1\frac{1}{4}} \right)} \right]{\rm{}} \div {\rm{}}5\frac{3}{4} - 5{\rm{;}} \div {\rm{;}}5{\rm{}} \times {\rm{}}5{\rm{;of;}}5{\rm{}} \div {\rm{}}25$

$\Rightarrow \frac{{15}}{2}{\rm{}} \times {\rm{}}\left( {\frac{{16}}{5}{\rm{}} \div {\rm{}}\frac{{16}}{3}{\rm{;}} \times {\rm{;}}\frac{9}{2}} \right){\rm{}} + {\rm{}}\left[ {11 - \left( {\frac{5}{8}{\rm{;}} + {\rm{;}}3 - \frac{5}{4}} \right)} \right]{\rm{}} \div {\rm{}}\frac{{23}}{4} - 5{\rm{}} \div {\rm{}}5{\rm{;}} \times {\rm{;}}1$

$\Rightarrow \frac{{15}}{2}{\rm{}} \times {\rm{}}\frac{2}{{15}}{\rm{}} + {\rm{}}\left[ {11 - \frac{{19}}{8}} \right]{\rm{;}} \div {\rm{;}}\frac{{23}}{4} - 1$

$\Rightarrow 1{\rm{}} + {\rm{}}\frac{{69}}{8}{\rm{}} \times {\rm{}}\frac{4}{{23}} - 1$

⇒ 1 + (3/2) – 1 = 3/2

$\Rightarrow 1\frac{1}{2}$

⇒ cos²θ – 3cosθ + 2 = sin²θ

⇒ cos²θ – 3cosθ + 2 = 1 – cos²θ

⇒ 2cos²θ – 3cosθ + 1 = 0

⇒ 2cos²θ – 2cosθ – cosθ + 1 = 0

⇒ 2cosθ(cosθ – 1) – 1 (cosθ – 1) = 0

⇒ (2cosθ – 1) (cosθ – 1) = 0

⇒ 2cosθ – 1 = 0

⇒ θ = 60°

⇒ cosθ = 1

⇒ cosθ = cos0°

⇒ θ = 0°      (∵ 0° < θ < 90°)

2cosecθ + 4cotθ

⇒ 2cosec60° + 4 cot60°

⇒ 2 × (2/√3) + 4 × (1/√3)

⇒ [4/√3] + [4/√3]

⇒ 8/√3

⇒ 8√3/3

Total production of type C cars = 54 + 55 + 45 + 60 + 56 = 270 thousands

Production of type C cars in 2012 = 45 thousands

270 thousands represents = 360°

45 thousands will represent = [360°/270] × 45 = 60°

Option 2 is the correct solution.

'look beautiful' contains grammatical error. It should be 'looks beautiful' its more appropriate.

The correct answer is: Option 3 i.e. bristel.

Key Points

• The word "bristel" is spelled incorrectly.
• Meaning: This word does not exist in English. The intended word is likely "bristle".
• Hindi Meaning: नुकीले बाल
• Example: The artist used a brush with stiff bristles to create texture in the painting.

Therefore, the correct answer is: bristle.

Additional Information

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

• Brittle (भंगुर): Easily broken when subjected to pressure; fragile.
• Example: The brittle glass shattered on impact.
• Brisk (तेज़): Quick and energetic.
• Example: She went for a brisk walk in the fresh morning air.
• Bridle (लगाम): A headgear used to control a horse, consisting of buckled straps to which a bit and reins are attached.
• Example: He carefully fitted the bridle onto the horse.

The correct answer is 'BACD.'

Key Points

• The correct sequence for these sentences to form a meaningful paragraph would be B, A, C, D.
• Sentence B introduces the main topic of the paragraph, which is the dominant position of the United States in the world due to its high economic development.
• Sentence A provides more specific information on why the U.S. has such economic development - it leads in the production of both industrial and agricultural goods.
• Sentence C links back to the high output mentioned in sentence A and further elaborates on its result, a major share in world trade.
• Finally, sentence D expands on the reasons for the U.S.'s dominance, pointing out its leadership in the development and application of innovative technology.

Hence, the correct answer is option 3.

The correct answer is option 1 i.e. broke up.

Break up means to separate something into smaller pieces.

Break out means to start suddenly

Break off means abruptly stop talking.

Break in means to interrupt or disturb; to enter by force.

Seeing this, it is clear that only option1 fits the sentence meaningfully and according to the context.

Option 4 is the correct solution.

'Exempt' means free from an obligation or liability imposed on others. So, the nearest synonym for 'exempt' would be 'exclude'.

Option 3 is the correct solution.

Here, please says that it is an imperative sentence. So, in 'requested' is used. Option 1 is wrong because 'taking' is used which is inappropriate. Option 2 is wrong because it makes the sentence as a command. Option 4 is wrong because its formation of the sentence is wrong.  So, the passive form of 'Please take the guest to his room on the 6th floor'. would be 'You are requested to take the guest to his room on the 6th floor.'

Option 3 is the correct solution.

'On tenterhooks' means in a state of suspense or agitation because of uncertainty about a future event. So, the most appropriate meaning of the given idiom would be 'anxious'.

Option 4 is the correct solution.

 'impression' is the most appropriate word for the sentence: The company management is of the opinion that not wearing a suit and tie at the workplace could create a bad impression on clients.

'outlook' is a person's point of view.

'notion' is a conception about something.

'response' means a verbal or a written answer.

'impression' is an idea or feeling about something.

The correct answer is: Option 3 i.e. straighten.

Key Points

• The word "swerve" means to change direction abruptly.
• Hindi Meaning: मुड़ना
• Example: The driver had to swerve to avoid hitting the deer.
• "Straighten" is the antonym of swerve, meaning to make or become straight.
• Hindi Meaning: सीधे करना
• Example: She had to straighten the picture frame on the wall.

Therefore, the correct answer is: straighten.

Additional Information

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

• Droop (मुरझाना): To bend or hang downward.
• Example: The flowers began to droop in the heat.
• Lurch (झटका): To make an abrupt, unsteady, uncontrolled movement or series of movements.
• Example: The boat gave a sudden lurch and threw the passengers off balance.
• Deviate (भटकना): To depart from an established course.
• Example: You must not deviate from the path of righteousness.

Option 2 is the correct solution.

'lend an ear' means that you are listening to someone or paying attention to someone.

The correct antonym of the given word is 'agitated'.

Key Points

• Let us see the meanings of all the words given in the question-

• A sensible person can never be troubled, so Agitated will be the antonym of Sober.

The correct answer is "excessive"

Key Points

• Let's see the meanings of the given words-
• Rampant- flourishing or spreading unchecked.
• Limited- small or controlled in number, amount, etc.
• Excessive- too much; too great or extreme
• Rare- not done, seen, happening, etc. very often
• Gentle- not strong, violent or extreme
• Hence, according to the meanings of the given words, the correct answer is Option 2.

Option 1 is the correct solution.

The correct order is 'CBAD'. 'C' is an independent sentence so it should be first. 'B' is the continuation of 'C'. 'A' also speaks about the same thing as B & C. 'D' is the last sentence.

Here the correct answer is Casserole.

Key Points

• A casserole is a kind of large, deep pan or bowl used for cooking a variety of dishes in the oven and as a serving vessel; it is also a category of foods cooked in such a vessel.
• So, 'casserole' is the most appropriate word for the group of words given.
• Thus, the correct answer is Option 3.

Additional Information

• Let's look at the meaning of other words given in options:
• Cauldron - a large metal pot with a lid and handle, used for cooking over an open fire.
• Sauce-pan - a deep cooking pan, typically round, made of metal, and with one long handle and a lid.
• Skillet - a small metal cooking pot with a long handle, typically having legs.

Option 1 is the correct solution.

The correct formation of the sentence would be " We can't live without water, can we?". in the sentence, 'can't' is used so its question tag will be 'can'.