SSC CGL Previous Paper (Held On: 10 June 2019 Shift 3) (Previous Year Paper)

Hence, Krish is a grandson of Suresh.

1. K + 2 = M; M + 7 = T

2. Q + 2 = S; S + 7 = Z

3. F + 2 = H; H + 7 = O

4) O + 2 = Q; Q + 5 = V

1. 14² = 196; 196 + 5 = 201

2) 13² = 169; 169 + 10 = 179

3. 12² = 144; 144 + 5 = 149

4. 8² = 64; 64 + 5 = 69

Hence,‘13 : 179’ is the odd one among the given options.

Diagram:

First word is written in reverse order to get second word.

So,

Hence, ‘WARD’ is the correct answer.

When opened, the figure will appear as below:

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

Dogri is a language spoken mostly in Jammu and Kashmir.

Bori is a language spoken mostly in Arunachal Pradesh

Konkani is a language spoken mostly in Goa.

But, Tamil is spoken mostly in Tamil Nadu and not in Kerala.

Hence, ‘Tamil: Kerala’ is the correct answer.

According to given conditions the new equation will be,

25 * 2 + 10 / 5 - 2

= 25 * 2 + 2 - 2

= 50 + 2 - 2

= 50

Hence, the correct answer is ‘50’.

Current age of Father = F; Son = S

F = 2S

Twenty years ago:

(F - 20) = 12 (S - 20)

F = 12S + 20 - 240

F = 12S - 220

2S = 12S - 220

10S = 220

Therefore, S = 22 and F = 44

Hence, the present ages of the son and father are 22 and 44 years respectively.

Chisel is a tool used by sculptor, scalpel is used by a surgeon, anvil is a tool used by a blacksmith.

Such a relation is not given in the first option.

Hence, ‘Paper : Book’ is the odd one among the given options.

Socks are worn on feet.

Similarly, turban is worn on head.

Hence, ‘Head : Turban’ is the correct answer.

Considering the first and third positions of the dice, it can be concluded that 1 is on the opposite side of 3.

Now consider fig.2 along with fig. 1 and 3, it can be concluded that 6 is on opposite side of 2 and 4 is on opposite side of 5.

Hence, number 5 appears on face opposite the number 4.

Differences between the given numbers are multiples of 4, starting from 4.

5 + 4 = 9

9 + 8 = 17

17 + 12 = 29

29 + 16 = 45

Hence, 17 is the missing number in the series.

Flying is a form of movement of birds.

Similarly, galloping is a form of movement of horses.

Hence, ‘gallop’ is related to ‘horse’.

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

Hence, there are 31 triangles in the figure.

First letter of each term,

C + 3 = F; F + 3 = I; I + 3 = L; L + 3 = O

Second letter of each term,

B + 5 = G; G + 5 = L; L + 5 = Q; Q + 5 = V

Third letter of each term,

A + 4 = E; E + 4 = I; I + 4 = M; M + 4 = Q

Hence, the next term in the series will be OVQ.

17 × 6 = 102

Similarly,

23 × 6 = 138

Hence, ‘138’ is the correct answer.

Let’s check the options one by one,

1. ÷ and + → 16 ÷ 3 – 5 × 2 + 4 ≠ 9

2. × and – → 16 + 3 × 5 – 2 ÷ 4 ≠ 9

3. × and + → 16 × 3 – 5 + 2 ÷ 4 ≠ 9

4) ÷ and × →16 + 3 – 5 ÷ 2 × 4 = 9

Hence, ‘÷ and ×’ is the correct answer.

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

Logic for coding SUN and TOP are,

Similarly,

Hence, ‘F’ is the last letter in the code for the word FUR.

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

Figures 1 and 3 are the same. i.e. the figures are repeating in alternate pattern

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

From the given codes,

And,

Similarly,

Hence, the code for RANDOM is 615342.

1) PQR:P + 1 = Q; Q + 1 = R

2. SUW: S + 2 = U;U + 2 = W

3. FHJ:F + 2 = H;H + 2 = J

4. KMO: K + 2 = M; M + 2 = O

Hence, ‘PQR’ is the odd one among the given options.

The logic followed here is:

In a row:

2^nd number = (First Number × 3) + 1,

3^nd number = (First Number × 9) + 4

For Row 1 → 9, 28, 85

2^nd number = (9 × 3) + 1 = 27 + 1 = 28

3^rd number = (9 × 9) + 4 = 81 + 4 = 85

For Row 3 →16, 49, 148

2^nd number = (16 × 3) + 1 = 48 + 1 = 49

2^nd number = (16 × 9) + 4 = 144 + 4 = 148

Similarly, 

For Row 2 → 12, 37, ?

2^nd number = (12 × 3) + 1 = 36 + 1 = 37

2^nd number = (12 × 9) + 4 = 108 + 4 = 112

Hence, the correct answer is "112".

Alternate Method

First row: 9 + 19 = 28 and 28 + 57 = 85 where 57 = 19 × 3

Third row: 16 + 33 = 49 and 49 + 99 = 148 where 99 = 33 × 3

Similarly,

Second row: 12 + 25 = 37 and 37 + 75 = 112 where 75 = 25 × 3

Hence, the missing number is 112.

• 6^th April 1919 was organised as National Humiliation day as a reaction to Rowlatt Act.
• Rowlatt Act was officially known as the Anarchical and Revolutionary Act,1919.
• It was passed in March 1919 by the Imperial Legislative Council.
• The Act gave the authority to the Britishers to detain anybody suspected of terrorist activities without any trials.

Nepal is divided into 7 provinces for administrative purposes.

• Amnesty International stripped Aung San Suu Kyi of the Ambassador of Conscience Award given in 2009.
• Amnesty International is a British Non-Governmental Organisation and its work is focused on the protection of Human Rights.
• The move came from the NGO in November 2018 after the failure of Aung San Suu Kyi and her government to speak out about military atrocities against the Rohingya Population in Myanmar.

• The maximum strength of the Bangladeshi Parliament is 350.
• It is also known by the name of Jatiya Sangsad.
• It is unicameral in nature with a term limit of 5 years.
• The first prime minister of Bangladesh was Tajuddin Ahmad.
• The first president of Bangladesh was Sheikh Mujibur Rahman.

• The Indian Prime Minister Narendra Modi has been conferred with the award of St Andrew the Apostle in 2019.
• It is the highest order of the Russian Federation.
• He was conferred with award for his exceptional services in promoting special and privileged strategic partnership between India and Russia.

• Janku is a celebration performed by the Newari commnity when a man or woman turns 77 years old.
• Some cultural festivals celebrated in Pakistan are Shab-e-Barat, Eid-e-Milad-un-Nabi.
• Some festivals celebrated in Sri Lanka are Vesak Poya, Poson, Kataragama Esala.
• Some of the festivals that are celebrated in Bhutan are Paro Tshechu, Punakha Drubchen.

The correct answer is Option 3 i.e. Intermediate goods ​

• Intermediate goods are the goods sold between industries for the resale or production of other goods.
• These products are also called semi-finished products because they are used as inputs to become part of the finished products.
• Examples of intermediate goods are Salt, Sugar, etc.

• The term "Gross Happiness Index" was coined by Jigme Singye Wangchuk in 1972.
• This index is still used by the government of Bhutan to measure the collective happiness and the well-being of a population of Bhutan.
• The first Prime Minister of Bhutan was Jigme Palden Doorji.

• Khilafat Movement was organised as a protest against the injustice done to Turkey.
• It was organised by the Indian Muslims in 1919 to recover the Caliph of Turkey as a symbol of unity among Muslim community in India.
• The movement was also supported by Mahatma Gandhi's Non-Cooperation movement.
• It was launched by  brothers Shaukat and Muhammad Ali and by Abdul Kalam Azad.
• The movement collapsed in 1924.

Key Points

• Acharya Vinoba Bhave was the first Indian to be conferred with Ramon Magsaysay Award for his contribution to community leadership.
• Ramon Magsaysay award, also known as the Nobel Prize of Asia is an annual established in the memory of the former Philippine President Ramon Magsaysay.

Important Points

• Arvind Kejriwal won Ramon Magsaysay award in 2006.
• Verghese Kurien is known as the Father of White Revolution in India and he won the Ramon Magsaysay award in 1964.
• Baba Amte was an Indian social worker who won Ramon Magsaysay award in 1985.

• Karachi Post is the busiest sea port of Pakistan.
• It handles around 60% of the total cargo of Pakistan.
• Qasim port is in Sindh province of Pakistan.
• Keti port is in Sindh province of Pakistan.
• Gwadar port is situated in Balochistan Province of Pakistan.

• Venus Flytrap is a carnivorous plant.
• Carnivorous plants are adapted to capture and digest insects and protozoa.
• These plants derive most of their required nutrients by these insects.
• Examples of insectivorous plants are Venus Fly Trap, Pitcher plant, Drosera capensis etc.

• The Hindustan Socialist Republican Association was formed in 1928 with an aim to overthrow the British.
• It was founded by Bhagat Singh, Sachindra Nath Sanyal, Chandra Shekhar Azad, and Sukhdev Thapar.
• The HSRA bought out a manifesto known as 'Philosophy of a Bomb' written by Bhagwati Chandra Vohra.

• Latitude is defined as the angular distance of a place north or south of Earth's equator.
• Pole is a point on the either side of the surface of the Earth where lines of longitude meet.
• The Earth is divided by the 0 degree latitude into equal halves known as Hemisphere.
• Longitude are defined as the imaginary lines that bisects the globe through the North and South poles.

• Heena Sidhu was the first female shooter from India to reach number 1 in world ranking by the International Shooting Sport Federation in 2014.
• She has also won Bronze in Asian Games Jakarta-Palembong 2018.
• Shreyasi Singh is an Indian Shooter who bagged a gold in double trap event at Gold Coast Common wealth event 2018.
• Angali Bhagwat is an Indian Shooter who became world number one in 10m Air rifle in 2002.
• Anisha Sayyed is an Indian pistol shooter who bagged two gold in 2010 Commonwealth games in Delhi.

• Sirimavo Bandaranaike was Sri Lanka's first woman prime minister.
• She served three terms: 1960–1965, 1970–1977 and 1994–2000.
• She was also the first woman prime minster of the world.
• First Woman Prime minster of India was Indira Gandhi.
• First Woman President of India was Pratibha Patil.

• There are four stages in the process of Metamorphosis of a butterfly.
• The first stage is the egg.
• The Butterfly eggs are laid on the plants by the female Butterfly.
• The second stage is the larva stage in which the butterfly exists in the form of a caterpillar.
• The Third stage is Pupa which is transitional phase in which the Caterpillar changes into Butterfly.
• The fourth stage is the Adult stage in which a full grown adult butterfly comes out of the pupa.

• The Traditional battery contains Sulfuric acid.
• The Battery acid is 30-50% sulfuric acid (H₂SO₄) in water.
• The Sulfuric acid is used as an electrolyte.
• The Traditional battery consists of two metals plates separated by a liquid or gel containing sulfuric acid in water.
• When the battery is in the use, the electrons move from the negatively-charged plate to the positively-charged plate.

• Human beings have four types of teeth which are Incisors, Canine, Molar and Premolar.
• A normal adult mouth has 32 teeth.
• Incisors (8) help in biting into the food.
• Canines (4) help in tearing the food.
• Molars (12) help in grinding the food.
• Premolars (8) help in crushing the food.

• Waziri Dance is a traditional dance form of Pakistani Tribe Pashtun.
• Dhol Chap is the traditional dance form of Brahuis Tribe of Pakistan.
• Chhej Dance is a traditional dance form of the Sindhi Tribe.
• Lewa is a traditional dance form of Baloch tribe.

• Mother Teresa was born in Macedonia on 26 August 1910.
• She was honoured in the Catholic Church as Saint Teresa of Calcutta.
• She received the Ramon Magsaysay Peace Prize in 1962 and Nobel Peace Prize in 1979.
• She became the Indian citizen in 1950 and was awarded Bharat Ratna in 1980.

• Hibernation is defined as a state of reduced metabolic activity during winter season among some animals.
• Many organisms are hibernators such as Fishes, Amphibians and Reptiles.
• Snakes, Frogs and Lizards hibernate in cold weather because they are cold blooded animals.
• The Hibernators relies on a combination of reserve body fat, stored food supplies etc.
• Some animals become dormant in the summer season which is called Aestivation.

• Prithivi Narayan Shah was the last ruler of the Gorkha Kingdom.
• He started unification of Nepal and became the first monarch of the Kingdom of Nepal.
• Mahendra Bir Bikram Shah Dev was the king of Nepal ruled from 1955 to 1972.
• Tribhuvan Bir Bikram Shah was the King of Nepal from 1911 until his death.
• Rana Bahadur Shah was king of Nepal from 1777 to 1806.

• Atal Tinkering Labs is an initiative by NITI Aayog to create an environment of scientific temperament, innovation, creativity among Indian students.
• National AYUSH Mission is launched by the Ministry of Health and Family Welfare to promote AYUSH medical systems through cost effective services.
• Reserve Bank of India is the central bank of India.
• Central Board of Secondary Education is national level board of education in India.

⇒ x – 5√x – 1 = 0

Divide by √x

⇒ √x – 5 – 1/√x = 0

⇒ √x – 1/√x = 5

Squaring both the sides

⇒ (√x – 1/√x)² = 5²

⇒ x + 1/x – 2 = 25

⇒ x + 1/x = 27

Squaring both the sides again

⇒ (x + 1/x)² = 27²

⇒ x² + 1/x² + 2 = 729

⇒ x² + 1/x² = 727

⇒ sin²60° – cos²45° + sec60° + cos²40° + cos²50°

⇒ (√3/2)² – (1/√2)² + 2 + cos²(90° – 50°) + cos²50°

⇒ (3/4) – (1/2) + 2 + sin²50° + cos²50°

⇒ (3/4) – (1/2) + 2 + 1

⇒ (3 – 2 + 8 + 4)/4

⇒ 13/4

⇒ a ∶ b = 4 ∶ 5

Suppose a = 4x and b = 5x

⇒ (2a + 3b) ∶ (3a + 2b)

⇒ (2 × 4x + 3 × 5x) ∶ (3 × 4x + 2 × 5x)

⇒ (8x + 15x) ∶ (12x + 10x)

⇒ 23 ∶ 22

Using Apollonius theorem, we know that

⇒ 2(AM² + BM²) = AB² + AC²

⇒ 2[AM² + (65/2)²] = 16² + 63²

⇒ 2[AM² + (4225/4)] = 256 + 3969

⇒ AM² = 2112.5 – 1056.25

⇒ AM = 32.5 cm

Given, ∠BAC = 15°

⇒ ∠ACB = 90° [Angle in a semicircle is 90]

In ΔACB

⇒ ∠ACB + ∠CBA + ∠BAC = 180°

⇒ ∠CBA = 180° – 90° – 15° = 75°

⇒ ∠DCA = ∠CAB = 15° [Alternate interior angle]

⇒ ∠DCA = ∠ABD = 15° and ∠CAD = ∠DBC

∵ Two inscribed angles forming the same arc or forming two equal arcs are equal.

⇒ ∠CBA = ∠DBC + ∠ABD

⇒ 75° = ∠DBC + 15°

⇒ ∠DBC = 75° – 15° = 60°

⇒ ∠CAD = ∠DBC = 60°

Let radius of sphere be r cm

Volume of sphere = [4/3] × π r³

If radius increased by 140%

New radius of sphere = r × [240/100] = 2.4r

New volume of sphere = [4/3] × π × (2.4r)³ = [4/3] × π × 13.824 × r³

Volume increased by = $\frac{4}{3}{\rm{\pi }} \times {\rm{}}13.824{{\rm{r}}^3} - {\rm{;}}\frac{4}{3}{\rm{\pi }}{{\rm{r}}^3}{\rm{}} = {\rm{}}\frac{4}{3}{\rm{\pi }}{{\rm{r}}^3}\left( {13.824 - 1} \right){\rm{}} = {\rm{}}12.824{\rm{}} \times {\rm{}}\frac{4}{3}{\rm{\pi }}{{\rm{r}}^3}$

∴ Required percentage = $\left[ {\frac{{12.824{\rm{;}} \times {\rm{;}}\frac{4}{3}{\rm{\pi }}{{\rm{r}}^3}}}{{\frac{4}{3}{\rm{\pi }}{{\rm{r}}^3}}}} \right]{\rm{}} \times {\rm{}}100 = 1282.4\%$

Short trick∶

⇒ 140 + 140 + [(140 × 140)/100] = 280 + 196 = 476%

⇒ 476 + 140 + [(476 × 140)/100 = 616 + 666.4 = 1282.4%

Given, Total number of students are = 1800

Number of girls in college D = 1800 × [22/100] × [5/11] = 180

Number of girls in college E = 1800 × [10/100] × [3/5] = 108

Number of girls in college F = 1800 × [16/100] × [7/16] = 126

Total number of students in colleges D, E and F = 1800 × (22 + 10 + 16)% = 864

Required percentage = [(180 + 108 + 126)/864] × 100 = 47.91%

Given, AB = 5, AC = 10 and BC = 8

If ΔABC ∼ ΔEDF, then

⇒ Ar(ΔABC) / Ar(ΔDEF) = BC² / DF²

⇒ DF² = (4 × 8²)/9

⇒ DF = (2 × 8)/3 = 16/3

Divisibility law of 8∶ A number divisible by 8 if its last 3 digit is divisible by 4

Divisibility law of 11∶ If the difference of the alternating sum of digits of the number is a multiple of 11 (e.g. 2343 is divisible by 11 because 2 - 3 + 4 - 3 = 0, which is a multiple of 11).

⇒ 6x2904 is divisible by11 if x = 6

Or

⇒ (x + 9 + 4) – (6 + 2 + 0) = 11

⇒ x = 11 – 5 = 6

⇒ x³ + 1/x³ = (x + 1/x)³ – 3 (x + 1/x)

⇒ x + 1/x = √5

⇒ x³ + 1/x³ = (√5)³ – 3√5

⇒ x³ + 1/x³ = 5√5 – 3√5 = 2√5

Without stoppage average speed = 70 km/h

With stoppages average speed = 56 km/h

As we know,

Time of rest per hour equal to the difference in average speed divided by the speed without stoppage.

∴ Required time = [(70 – 56)/70] × 60 = 12

So, A train stops on an average 12 minute/h.

If a³ + b³ + c³ – 3abc = 0, then

a + b + c = 0 or a = b = c

⇒ (3x – 1)³ + (4x – 3)³ + (2x + 1)³ = 3(3x – 1) (4x – 3) (2x + 1)

⇒ (3x – 1)³ + (4x – 3)³ + (2x + 1)³ – 3(3x – 1) (4x – 3) (2x + 1) = 0

Using the above formula, 

⇒ (3x – 1) = (4x – 3) 

⇒ 3x – 1 = 4x – 3

⇒ – 1  + 3 = 4x – 3x

⇒ x = 2

Percentage difference between the number of boys and girls in college A = [(5 – 4)/9] × 100 = 11.11%

Percentage difference between the number of boys and girls in college B = [(2 - 1)/3] × 100 = 33.33%

Percentage difference between the number of boys and girls in college C = [(4 – 3)/7] × 100 = 14.28%

Percentage difference between the number of boys and girls in college D = [(6 – 5)/11] × 100 = 9.09%

Percentage difference between the number of boys and girls in college E = [(3 – 2)/5] × 100 = 20%

Percentage difference between the number of boys and girls in college F = [(9 - 7)/16] × 100 = 12.5%

In college D the percentage difference between the number of boys and girls is minimum

Note: As there are only four colleges A, E, D and C our answer must be any one of these. So, no need to calculate for college B and F.

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.

⇒ 3.8 – (4.2 ÷ 0.7 × 3) + 5 × 2 ÷ 0.5

⇒ 3.8 – (6 × 3) + 5 × 4

⇒ 3.8 – 18 + 20

⇒ 23.8 – 18

⇒ 5.8

Let the initial price of sugar be 100x.

Price of sugar after increased = 100x × [118/100] = 118x

Person wants his expenditure increase by 12% only,

So, his expenditure should be = 100x × [112/100] = 112x

∴ Required percentage = [(118 – 112x)/118] × 100 = 5.08% ≈ 5.1%

SP of each article = Rs. 10,384

CP of first article = 10,384 × [100/118] = 8800

CP of second article = 10,384 × [100/88] = 11,800

Total SP of both article = 10,384 × 2 = 20,768

Total CP of both article = 8,800 + 11,800 = 20,600

Total gain = 20,768 – 20,600 = 168

Number of boys in college A = 1800 × [20/100] × [4/9] = 160

Number of girls in college A = 1800 × [20/100] × [5/9] = 200

Number of boys in college B = 1800 × [18/100] × [1/3] = 108

Number of girls in college B = 1800 × [18/100] × [2/3] = 216

Total number of boys in college A and B = 160 + 108 = 268

Total number of girls in college A and B = 200 + 216 = 416

Required ratio = 268 ∶ 416 = 67 ∶ 104

Average marks of 50 students = 64

Sum of marks of 48 students = 64 × 50 = 3200

According to the question

Correct sum of marks of 50 students = 3200 – 38 – 42 + 83 + 24 = 3227

Correct average marks of 50 students = 3227/50 = 64.54

Short trick∶

⇒ 64 + [(83 + 24 – 38 – 42)/50]

⇒ 64 + [27/50]

⇒ 64.54

Number of girls in college A = 1800 × 20/100 × 5/9 = 200

10% of girls of college A = 200 × [10/100] = 20

Number of girls in college E = 1800 × [10/100] × [3/5] = 108

According to question,

the increased number of girls in college E = 20

Increased in the percentage of girls in college E = (20/108) × 100

⇒ 18.51%

∴ Increase in percentage of girls = 18.51%

Given, a + b + c = 11 and ab + bc + ca = 38

As we know,

⇒ a³ + b³ + c³ – 3abc = (a + b + c) [(a + b + c)² – 3(ab + bc + ca)]

⇒ 11 [11² – 3 × 38]

⇒ 11 (121 – 114)

⇒ 11 × 7

⇒ 77

Given tan θ = 3/4

\Rightarrow ;\frac{{4{\rm{sin\theta ;}} - {\rm{;cos\theta }}}}{{4{\rm{sin\theta ;}} + {\rm{;cos\theta }}}}$

Divide by cos θ

$\Rightarrow ;\frac{{4{\rm{tan\theta ;}} - {\rm{;}}1}}{{4{\rm{tan\theta ;}} + {\rm{;}}1}}{\rm{;}} = {\rm{;}}\frac{{4{\rm{;}} \times {\rm{;}}\frac{3}{4}{\rm{;}} - 1}}{{4{\rm{;}} \times {\rm{;}}\frac{3}{4}{\rm{;}} + {\rm{;}}1}}{\rm{;}} = {\rm{;}}\frac{{3 - 1}}{{3{\rm{;}} + {\rm{;}}1}}$

⇒ 2/4

⇒ 1/2$

SP of the article = Rs. 642.60

Let MP of the article be Rs x

According to the question

⇒ x × [85/100] × [90/100] = 642.60

⇒ x = 840

As we know, the formula of difference between the compound interest and simple interest is

⇒ Pr²/(100)² = Difference

Given, r = 9%, t = 2 years and Difference = 20.25

⇒ [P × 9 × 9] / [100 × 100] = 20.25

⇒ P = 2,500

For 3 years,

If CI – SI = D, Principle is P,

Then r% = 1/x × 100

Where,

(3x + 1)/x³ = D/P

As we know,

AD is median, so AD divides triangle in two equal parts.

Ar ΔADB = Ar ΔADC

In ΔABD

⇒ Ar ΔBDG/Ar ΔBGA = DG/AG

⇒ Ar ΔBDG/ar ΔBGA = 1/2

Let the area of ΔBDG be 1 unit.

So, area of ΔBGA will be = 2 unit

So, area of ΔBAD = Ar ΔBDG + Ar ΔBGA = 1 + 2 = 3 unit

Area of ΔABC = 2 × Ar ΔBAD = 2 × 3 = 6 unit

∴ Ar ΔABG ∶ Ar ΔABC = 2 ∶ 6 = 1 ∶ 3

If 2sin²θ = 3cosθ

⇒ 2(1 – cos²θ) = 3cosθ

⇒ 2cos²θ + 3cosθ – 2 = 0

⇒ 2cos²θ + 4cosθ – cosθ – 2 = 0

⇒ 2cosθ(cosθ + 2) – 1(cosθ + 2) = 0

⇒ (2cosθ – 1) (cosθ + 2) = 0

⇒ 2cosθ – 1 = 0

⇒ cosθ = 1/2

⇒ cosθ = cos60°

⇒ θ = 60°

Short trick

Put θ = 60°

⇒ 2 × (√3/2)² = 3 × 1/2

⇒ 3/2 = 3/2 (Satisfied)

The correct answer is 'renounce'.

Key Points

• The word 'repudiate' refers to refuse to accept or be associated with. It involves denying the truth or validity of something. ('अस्वीकार करना'.)
• Example: The politician repudiated the allegations of corruption levied against him.
• The word 'renounce' means to formally declare one's abandonment of a claim, right, or possession. It is a voluntary act and does not necessarily imply that the renunciation is unwilling or forced. ('त्याग करना'.)
• Example: The king renounced his throne for his love of a common woman.
• Therefore, the correct answer is 'Option 2'.

Additional Information

• 'regret' means to feel sad or sorry about something that happened or was done, particularly a lost opportunity. ('पछतावा'.)
• 'enforce' means to make people obey a rule or law. ('लागू करना'.)
• 'sanction' implies official permission or approval for an action. ('मंजूरी'.)

The correct answer is he was bited.

Key Points

• Option 3 is the segment with the error.
• he was bited is grammatically wrong because past participle of a bite is bitten.

Option 1 is the correct solution.

Samaritan means a charitable or helpful person.

veteran means a person who has had long experience in a particular field.

collaborator means a person who works jointly on an activity or project; an associate.

mercenary means primarily concerned with making money at the expense of ethics.

The correct answer is  "indignant".

Key Points

• The context of the sentence tells us that the watchman let the stranger in the house which might have made the owner angry.
• Hence, the most suitable word to fill in the blank is "Indignant".
• "Indignant" means feeling or showing anger or annoyance.
• Example: I was indignant because I felt that I had been punished unfairly.
• Therefore the correct answer is option 1.

Correct sentence: The owner of the house was indignant at the watchman for letting in a stranger.

Additional Information

• Indulgent means having or indicating a readiness or over-readiness to be generous to or lenient with someone. 
• Example: My indulgent parents give me everything I want.
• Indifferent means having no particular interest or sympathy; unconcerned. 
• Example: People have become indifferent to the suffering of others.
• Impatient means restlessly eager; having or showing a tendency to be quickly irritated or provoked. 
• Example: We are growing impatient with the lack of results.

Option 1 is the correct solution.

The passive form is of order object+auxillary verb+past participle of verb+subject. Here, the world cup is singular so has is used. so, the passive form would be Has the world cup cricket team been announced?

Option 3 is the correct solution.

prudent means showing care and thought for the future. The most appropriate antonym for prudent would be indiscreet which means to reveal things that are private or imprudent.

Option 4 is the correct solution.

The order of the active form is subject+verb+object. Here, the verb used is taken which is the past participle of the verb take. So, the active form of the sentence would be The enemy will either take you a prisoner or shoot you.

Option 1 is the correct solution.

patent means a government authority or licences conferring a right or title for a set period to make and sell some invention  

copyright means the exclusive and assignable legal right.

inheritance means a thing that is inherited or legacy.

heirloom a valuable object that has belonged to a family for several generations.

The correct answer is Mild

Key Points

Let's look at the meaning of the following options-

• Severe- (of something bad or undesirable) very great; intense; acute, critical
• Mild- not severe, serious, or harsh; Lenient
• Hence, the meaning of both i.e. severe and mild express the opposite meaning

​Let's look at the meaning of other given options-

• Morose- unhappy, annoyed, and unwilling to speak or smile
• Meticulous- showing great attention to detail; very careful and precise
• Mediocre- of only average quality; not very good

Option 3 is the correct solution.

We use the simple past tense(in the plural form) of the 'be' verb 'were' when we talk about something which might not happen at all/does not happen in reality.

The correct answer is "In". 

Key Points

• The question is related to filling in the blanks within the context of a passage about Portia's situation from Shakespeare's play.
• The preposition "in" effectively sets a precise condition or circumstance, which is essential for interpreting the sentence correctly.
• It indicates the specific manner or condition under which Portia's claiming is valid, adhering closely to the storyline and legal peculiarities of her father's will.
• The use of "in" properly contextualizes the manner specified by her father's will as a condition or state under which Portia can be claimed, making it the most fitting option for the sentence's intended meaning.
• Therefore, the correct answer is "Option 1".

The correct answer is pure.

Key Points

Let's refer to the options:

• Clear: easy to perceive, understand, or interpret
• Real: actually existing as a thing or occurring in fact; not imagined or supposed
• Pure: free from anything of a different, inferior, or contaminating kind
• Plain: not decorated or elaborate; simple or ordinary in character

The given sentence talks about Portia who is said to have a character like Diana. 

According to the passage, pure is the most appropriate word to fill in blank No.2

Option 1 is the correct solution.

It has been conveyed to all the residents is the correct substitution. In the sentence, now is used which says it must be in the present tense. So, has been must be used.

Option 3 is the segment with the error

that where had her mother gone...  is grammatically wrong. The correct formation would be -- Supriya asked Kiran where her mother had gone when the results of the contest were being declared.

Option 1 is the correct solution.

particular is the correctly spelt word.

Option 1 is the correct solution.

Casket test is a definite word so the is used.

Option 2 is the correct solution.

Explanation:

lament means a passionate expression of grief or sorrow.

Torment means severe physical or mental suffering

Mourn means feel or show sorrow for the death of (someone)

Distress means extreme anxiety, or pain

Afflict means cause pain or trouble to; affect adversely

So, the synonym of lament must be mourn.

Option 3 is the correct solution.

  keep the wolf from the door means have enough money to avert hunger or starvation.

Option 2 is the correct solution.

accommodation is the correctly spelt word.

Option 2 is the correct solution.

Under is the most appropriate word to be used and with to-infinitive form of the verb must be used. land is singular so is must be used. The world's agricultural land is under pressure to raise more and more crops.

Option 4 is the correct solution.

dispose means to get rid off. So, the sentence would be I was frustrated at not being able to dispose of my old car.

The correct answer is 'BADC'.

Key Points

• Sentence B introduces the scene where men and women are holding flaming torches, suggesting some kind of activity or event that involves fire.
• Sentence A logically follows B because it shows where the fire from the torches ended up, igniting the wooden beams of the grand palace built by Xerxes.
• Sentence D then follows as it describes another action that happens during the fire - looters dragging out gold and silver vessels amidst the heat of the inferno.
• Finally, sentence C brings a conclusion to the occurrence, describing the end result - the remainder of the palace after the fire has died out are the stone columns.

Therefore, the correct answer is 'Option 3'.

Option 4 is the correct solution.

'worries' is the most appropriate option because the blank needs a plural simple present tense.

The correct answer is 'DACB'.

Key Points

• The most logical order to arrange these sentences is to start with Mr. Oliver seeing a boy, as mentioned in sentence D.
• Sentence A follows naturally from D, explaining the unusualness of the situation, that the boy was out of school at a late hour.
• Sentence C then explains Mr. Oliver's anger resulting from rules being broken.
• Finally, sentence B concludes the paragraph by showing Mr. Oliver's decision, moving closer to recognise and punish the boy.

Therefore, the correct order is 'Option 2'.

Additional Information

• The other options do not present the sequence of events in a way that seems logical or following a proper narrative progression. They start in the middle of the story or leave the conclusion in between, making the story unintelligible and disjointed.

Option 1 is the correct solution.

ended in smoke means to come to nothing.