SSC CGL Previous Paper (Held On: 12 June 2019 Shift 1) (Previous Year Paper)

Hence, the number of total triangles is 19.

Words Examine, explore, inquire are synonyms to each other.

While deliberate means done consciously and intentionally.

Hence deliberate is the odd among the given words.

Let Arman’s current age is = X

Vishal’s current age = 70 - X

Arman’s age 5 years ago = X - 5

Vishal’s age 5 years ago = 70 - X - 5 = 65 - X

According to condition given is question

2(X - 5) = 65 - X

2X - 10 = 65 - X

3X = 75

X = 25

Hence, Arman’s current age is 25 years.

Pattern followed is:

X - 6 = R

R - 5 = M

M - 4 = I

I - 3 = F

F - 2 = D

D - 1 = C

Hence, M is the answer.

Interchanging + and -

4 × 5 + 24 ÷ 12 - 8 = 20 + 2 - 8

22 - 8 = 14

Interchanging ÷ and ×

$4 \div 5 - 24 \times 12 + 8 = \frac{4}{5} - 288 + 8$

$\frac{4}{5} - 296 \ne 14$

Interchanging × and +

4 + 5 - 24 ÷ 12 × 8 = 9 - 2 × 8

9 - 16 ≠ 14

Interchanging + and ÷

$4 \times 5 - 24 + 12 \div 8 = 20 - 24 + \frac{3}{2}$

$- 4 + \frac{3}{2} \ne 14$

Hence by interchanging + and - we get correct equation.

Pattern followed is:

9² - 6² = 81 - 36 = 45

11² - 8² = 121 - 64 = 57

Similarly

8² - 3² = 64 - 9 = 55

Hence, the answer is 55.

Pattern followed is:

5² - 1 = 24

13² + 1 = 170

7² - 1 = 48

11² - 1 = 120

Hence, 13 : 170 is the different from the rest.

V + S means V is the sister of S

S × Q means S is the mother of Q

Q - P means Q is the brother of P

P ÷ T means P is the father of T

T + R means T is the sister of R

R × U means R is the mother of U

Tree diagram:

By looking at family tree diagram we know that R is the granddaughter of S.

Sequence followed is:

Idea - writing - book - seller - reader - feedback

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

Hence, option 1) is the correct answer.

In given diagrams we can see that 1, 4, 2, 5 are adjacent to 3 hence 6 will be on opposite face of 3.

Pattern followed is:

Cloak Room is place where we can keep Suitcase.

Similarly,

Bank is a place where we can keep Money.

Pattern followed is:

Hence, ETHCOCILA is the answer.

Political Science is a part of Social Science

Similarly, Chemistry is a part of Science.

Hence, Science is the correct answer.

Pattern followed is:

J + 1 = K, K + 3 = N, N + 4 = R, R + 4 = V

G+ 1 = H, H + 3 = K, K + 4 = O, O + 5 = T

P + 1 = Q, Q + 3 = T, T + 4 = X, X + 5 = C

U + 1 = V, V + 3 = Y, Y + 4 = C, C + 5 = H

Hence JKNRV is the odd among the given letters.

Pattern followed is:

Image 1st to 3rd:- Rectangle and triangle are moved by 1 corner place in anticlockwise direction

Image 2^nd  to 4th:- Rectangle and triangle are moved by 1 corner place in clockwise direction

Similarly; 

Image 3rd to 5th:- Rectangle and triangle are moved by 1 corner place in anticlockwise direction

Hence, option 4) is the correct answer.

Pattern followed is:

115 + 9 = 124

124 +10 = 134

134 + 11 = 145

145 + 12 = 157

157 + 13 = 170

Hence 124 is answer.

If we fold the transparent sheet of paper from dotted line:

Hence, option 2) is the correct answer.

Hence, the correct answer is option 3).

The pattern followed in each column :

15 - 11 = 4² = 16

23 - 17 = 6² = 36

Similarly,

10 - 8 = 2² = 4

Hence, the correct answer is 10.

Venn diagram:

Conclusions:

I. Some boxes are sticks → True.

II. Some sticks are drums → True.

III. All sticks are drums → False (It is possible but not definite).

Hence, only conclusions I and II follow.

Pattern followed is:

Y = 25, O = 15, G = 7, H = 8, U = 21, R = 18, T = 20

YOGHURT = 251578211820

Similarly,

D = 4, E = 5, V = 22, E = 5, L = 12, O = 15, P = 16.

DEVELOP = 45225121516

Hence, the correct answer is 45225121516.

Pattern followed is:

Hence NWF is the answer.

Pattern followed is:

Second number = First number × (First number + 1)

9 × 10 = 90

Similarly

12 × 13 = 156

Hence 156 is the correct answer.

The circle represents ‘businessmen’,

The triangle represents ‘Landlords’ and

The rectangle represents ‘income taxpayers’

We choose intersection of circle and rectangle outside of triangle.

Hence, the correct answer is 22.

• Gujrat has the longest mainland coastline in India having a length of 1214.7 Km.
• India has a land boundary of about 15,200 km whereas the total length of the coastline of the mainland, including Andaman and Nicobar and Lakshadweep, is 7,516.6 km, of this the mainland coastline length is 5422.6 kilometers whereas Island territories coastline length is 2094 kilometers.
• The States/UTs having coastlines are Gujarat, Maharashtra, Goa, Daman and Diu, Karnataka, Kerala, Tamil Nadu, Puducherry, Andhra Pradesh, Odisha, and West Bengal. Island territories having coastlines are – Andaman & Nicobar Islands and Lakshadweep Islands.
• Andhra Pradesh has the second-longest mainland coastline with a total length of 974 kilometers and with 906.9 kilometer-long coastline, Tamil Nadu is the third biggest mainland coastline state.
• It has the second-largest coastline in the country with a length of 974 Km. Telangana doesn't cover any coastal boundary.

Additional Information

• The Important ports of Gujarat are – Alang, Kandla, Mandavi, Okha, Porbandar, Veraval, Jafarabad, Pipavav, Bhavnagar, Dahej, Magadalla, Hazira, Mandvi (Surat), Mundra and Maroli.
• Among them, Kandla is the Major port in Gujarat which is also the largest port of India, when measured by the volume of cargo handled.
• The Jawaharlal Nehru Port in Mumbai is the largest container port in India handling around half of the containers of all major ports and is also known by the name  Nhava Sheva.

• The Dolphin kick is associated with the Swimming.
• The Dolphin kick technique is used by professional swimmers, they use that motion that propels them forward underwater after diving in, and at the underwater turns.
• This technique is not just about the legs but It requires a swimmer's entire body to crack like a whip, creating a fluid wave that starts at the chest and increases in amplitude as it travels all the way through the toes, and it seems like a dolphin that's why it is called Dolphin kick.
• The Dolphin Kick is assumed as the fastest way to get from one point to another underwater but it needs a lot of practice as it is a very difficult move.

Extra Information :

• The international rules for swimming disciplines are laid down by Federation Internationale de Natation (International Swimming Federation) FINA.
• There are four standard strokes in swimming a front crawl, backstroke, breaststroke, and butterfly.

• Litmus paper test is done to find whether a solution is Acidic or Basic in nature.
• Litmus paper is a type of pH paper made by treating paper with natural dyes from lichens.
• The blue litmus paper turns red or pink when it comes into contact with an acidic solution of pH value below pH 4.5
• It becomes purple if the pH of the solution is between 4.5 and 8.3 and if the pH is above 8.3 it stays blue.
• The solution which is Basic in nature having a pH range between 8.5 and 14 changes the colour of red litmus paper to blue.

• The 2019 Swiss Open badminton tournament officially known as the YONEX Swiss Open 2019 was held in March 2019 in St. Jakobshalle, Munchenstein, Switzerland.
• The Swiss Open badminton tournament is an annual badminton tournament held in Switzerland since 1955.
• Indian badminton player Sai Praneeth was runner-up at the 2019 Swiss Open tournament.
• Shi yuqi won the men's singles and Chen Yufei was the winner of the women's singles in this tournament.

• Kalsubai Shikhar is the highest mountain peak in Maharashtra.
• It is also called Everest of Maharashtra having an elevation of 5400 feet (1636 m).
• The mountain range and peak lies inside the Kalsubai Harishchandragad sanctuary, situated at an elevation of 5400 feet.
• Salher is the second highest peak in Maharashtra at an elevation of 5,141 feet after the Kalsubai peak. It is also the site of the highest fort in Maharashtra, situated in the Sahyadri mountains in Nasik.
• Anjaneri is one of the beautiful attractions in the Nasik city and an important fort in the Trimbakeshwar region. It is the birthplace of Lord Hanuman and also home to 108 Jain caves.
• Taramati peak is also one of the highest peaks in Maharashtra, it is one of two peaks on Harishchandragad and offers a great trekking experience in the state.

• Dashain is the biggest festival of Nepal which is also celebrated in several parts of India.
• It is mainly celebrated for two weeks with prayers and offerings to Durga, the Universal Mother Goddess.
• The famous festival Fulpatti is also celebrated during these days. It is observed on the 7th day of the Dashain festival.

Extra Information :

• Nepal is a landlocked country whose capital is Kathmandu and currency is Nepalese rupee (NPR).
• Bidhya Devi Bhandari is the current president and Sher Bahadur Deuba is the current prime minister of Nepal (2022)
• The world's tallest mountain Mount Everest is located in Nepal. Its height is ‎8,848 metres (29,029 ft).
• Recently Kajin Sara lake is discovered in Singarkharka area of Chame in Manang district of Nepal.
• Surya Kiran is a joint military exercise between India and Nepal.

• The Lok Sabha or House of the People is the lower house of India's bicameral Parliament with a maximum strength of 550 members who represent the people of India.
• The lower house of a parliament or Lok sabha is called a Popular Chamber because it is composed of representatives of the people chosen by direct election on the basis of universal adult suffrage.
• Universal Adult Suffrage means all the adult citizens of a country have the right to vote without any discrimination of class, caste, colour, religion, and gender.
• The Lok Sabha is elected for a period of five years.

Extra Information :

• Lok Sabha is not permanent chamber and it is also known as ‘temporary house'.
• Om Birla is the current speaker of the Lok Sabha (2019).
• The age of voting is different in different countries, In Denmark and Japan one can vote after attaining the age of 25 years while in Norway, the age limit is 23 and in Britain, the United States, Russia, and Turkey it is 18.
• The 61st Amendment Act lowered the voting age from 21 to 18 years in India.

• The famous Indian filmmaker Yash Chopra was given the honorary title of 'Ambassador of Interlaken' in 2011 in Switzerland.
• Interlaken is a small town in mountainous Bernese Oberland region of central Switzerland.
• A 250 kg bronze statue was made in the year 2016 in Kursaal garden in Interlaken, Switzerland by the government of Switzerland for his work in the cinema industry and boosting the popularity of alpine nation among Indian tourist. This statue is a replica of the one in Chopra's film studio in Mumbai.
• Yash raj Chopra was a famous film director and producer of the Indian film industry who is also known as the 'king of the romance' of Indian cinema.
• He was honored with Dada Sahib Phalke (2001) and Padam Bhushan (2005) by the government of India.
• Bern is the capital and Swiss franc is the currency of Switzerland.

• Ravi Shastri was the first Indian batsman to hit six consecutive sixes in first-class cricket.
• He scored six sixes in an over against left-arm spinner Tilak Raj in the year 1985 in a Ranji Trophy match between Bombay and Baroda.
• Ravi Shastri also scored the fastest ever double century in first-class cricket history in the same match.
• Before Ravi Shastri Garfield Sobers an all-rounder player of West Indies was the first batsman to smash 6 sixes in a single over in first-class cricket.

• 20th March has been established as the annual 'International Day of Happiness'.
• The International Day of Happiness is celebrated worldwide on 20th of March every year to recognize happiness as a “fundamental human goal” and call for “a more inclusive, equitable and balanced approach to economic growth that promotes the happiness and well-being of all peoples.
• The Idea of this day was given by Philonthipist, activist and prominent United Nations special advisor Jayme Illien to inspire, mobilize, and advance the global happiness movement.
• The first International Day of Happiness was celebrated on 20 March 2013.
• The theme for the 2019 International Day of Happiness was "Happier Together".

The correct answer is ​​Sodium carbonate

Key Points

• _​​Sodium carbonate (Na₂CO₃), also known as soda ash is a sodium product primarily used to make detergents and soaps.
• Sodium carbonate (Na2CO3) is an inorganic compound found in large natural deposits and mines. Its common name is washing soda and it is manufactured by the Solvay-ammonia process.

Additional Information

• Detergents are generally ammonium or sulphonate salts of long-chain carboxylic acids. They have almost the same properties as soaps but they are more effective in hard water.
• Amine Oxide, Carboxymethyl Cellulose (CMC), Citric Acid, Cyclodextrin, Alcohol Ethoxylate (AE) Non-ionic surfactant, Alkyl (or Alcohol) Ethoxy Sulphate (AES) and Alkyl Sulphate (AS) Anionic surfactant are some other chemicals present in detergents.
• Detergents with the straight chain of hydrocarbons are preferred over the branched chain as the latter are non-biodegradable and consequently cause environmental pollution.

• The Battles of Kohima and Imphal were fought between 8 March and 18 July 1944.
• In 1944, during the rise of the Second World War, the Japanese forces attacked the northeast region of India through Burma. They attacked Imphal first and then they move towards Kohima the capital city of Nagaland.
• The British and Indian forces fought valiantly and prevented the ambitious plans of Japan, resulting in the fiercest battles of Kohima and Imphal.

Extra Information :

• World War II was a global war that lasted from 1939 to 1945.
• World War II was fought between two groups of countries one side was Germany with Italy and Japan and opposite side were Britain, France, Australia, Canada, New Zealand, India, the Soviet Union, China and the United States of America.
• World War II was started due to the invasion of Germany on Poland on September 1, 1939, then Britain and France responded to the Germany move and they declared war on Germany on September 3.
• The Battle of Stalingrad was the most important battle of World war II it was the bloodiest battle in history as it caused about two million casualties.

The correct answer is option 1, i.e. Equilibrium price will fall.

Key Points

• A decrease in demand and an increase in supply will cause a fall in Equilibrium price.
• Equilibrium is a state of no change and clearly, at the equilibrium price, both buyers and sellers are in a state of no change.
• Technically, at the equilibrium price, the quantity demanded by the buyers is equal to the quantity supplied by the sellers.
• The equilibrium price is determined by the market forces of demand and supply in a perfectively competitive market.
• Market Demand is the sum total of demand for a commodity by all the buyers in the market whereas Market Supply is the sum total of supplies of a commodity by all the firms in the market.

• Article 153 in the Constitution of India provides that there shall be a Governor for each State.
• The 7th Constitutional Amendment Act of 1956 facilitated the appointment of the same person as governor for two or more states.
• Governor is the chief executive head of the state but like the president, he is the nominal head (titular or constitutional head)

• The Third  Anglo-Maratha War ended in 1818 with the surrender of the Marathas to the British.
• The Third Anglo-Maratha War took place in Maharashtra and its neighboring areas in 1817 and 1818.
• The main reason for the Third Anglo-Maratha war was British conflict with the Pindaris whom the British suspected were being protected by the Marathas.
• The Treaty of Mandasor was signed between the British and the Holkar chief in 1818.
• Main reasons for the loss of Marathas were lack of unity among the Maratha chiefs themselves, lack of good relations with other Indian princes and ruling dynasties and failure to understand the British political and diplomatic strengths.

• 'India Shastra: Reflections on the Nation in our Time' book is written by well known Indian politician, writer, and a former career international diplomat.
• The government of India changed in 2014 and BJP came to power after winning the 16th Lok Sabha elections. This book was published in the year 2015 and it is basically about the transformation of India’s politics, economy, foreign policy, media, civil rights, governance, etc.
• Sashi Tharoor is currently serving as Member of Parliament of Lok Sabha from Thiruvananthapuram, Kerala.
• Inglorious Empire, An Era of Darkness, Why I am a Hindu, and India from midnight to millennium are some other famous books written by Shashi Tharoor.

• India was ranked 140th position in a list of 156 nations in the Global Happiness Index 2019.
• The global happiness report was released on March 20, 2019, on World Happiness Day by the United Nations Sustainable Development Solutions Network.
• India fell seven spots in the ranking in 2019 as compared to 2018, India's rank was 132nd in 2018, 122nd in 2017 and 118th in 2016.
• Finland topped the index for the second year in a row. Finland is followed by Denmark, Norway, Iceland, and the Netherlands.
• India’s neighbors seem to do good with Pakistan (67), China (93), Bhutan (95), Nepal (100), Bangladesh (125) and Sri Lanka (130) all towering above it.

Important Points

• China is the largest producer of wheat in the world according to FAOSTAT (Food and Agriculture Organization Corporate Statistical Database)  with a production of near about 134,340,630 tonnes of wheat.
• India is the second-largest producer of wheat in the world after China with a production of 98,510,000 Tonnes having about 12% share in total world Wheat production.
• Kalyansona, Sonalika, Lerma Rojo, Chhoti Lerma, Arjun, Sujata, etc. are some of the important wheat varieties produced in India.

Additional Information

• Wheat is Rabi crop and the Rabi cropping season is from October-March (winter) therefore wheat is sown in the months of October - November and harvested in the month of March - April.
• Uttar Pradesh is the largest Wheat producing state of India, followed by Punjab, Haryana and Madhya Pradesh.
• Recently in April 2019, the government has raised import duty on wheat from existing 30% to 40% to support local farmers interest.

The correct answer is Ranjit Singh. 

Key Points

• Sri Harmandir Sahib, also known as Sri Darbar Sahib or Golden Temple is a gurudwara located in the city of Amritsar, Punjab, and is a central religious place of the Sikhs, named after Hari(God) the temple of God.
• Sri Harmandir Sahib was built by the fifth Sikh Guru, Guru Arjan Dev Ji, and Adi Granth, the holy scripture of Sikhism was installed in Harmandar Sahib in 1604.
• A Muslim saint Hazrat Mian Mir Ji laid the foundation of the Sri Harmandir Sahib (Golden Temple), at the request of Guru Arjan Dev Ji.
• The golden beautification of the Harmandir Sahib Gurdwara with 750 kg of gold was done under the aid of Maharaja Ranjit Singh  (1801–39).

• Nyishi is one of the major ethnic groups and major tribes in the northeastern state of  Arunachal Pradesh.
• It is also known by the name Bangni and Dafla in some areas of Arunachal Pradesh.
• The people belonging to the Nyishi tribe are also found in eastern Bhutan and they speak Tibeto-Burman language of the Sino-Tibetan family. They support themselves with slash-and-burn agriculture and with hunting and fishing.
• Adis, Buguns, Hrusso, Singphos, Mishmis, Sherdukpens, Tagins, Wanchos, Noctes, and Khambas and Membas are other major tribes of the Arunachal Pradesh.

• Marsupials are the mammal of an order whose members are born incompletely developed and are typically carried and suckled in a pouch on the mother's belly.
• The distinctive characteristic of 'Marsupials' is that they carry their young ones in pouches.
• They take their name Marsupials from the word 'Marsupium' means pouch which protects eggs, offspring, or reproductive structures.
• The main examples of Marsupials animals are kangaroos, wallabies, koalas, possums, opossums, wombats, and Tasmanian devils.

Concept:

Explanation:

From the above explanation, we can see that,

• A person with hypermetropia can see distant objects clearly but cannot see nearby objects distinctly.

• Hypermetropia is also known as farsightedness. Such a person has to keep a reading material much beyond 25 cm from the eye for comfortable reading.

• Hypermetropia defect can arise mainly due to two reasons (i) the focal length of the eye lens become too long or (ii) the eyeball becomes too small.

• This defect can be corrected by using a convex lens of appropriate power.

• A concave lens is used for the correction of Myopia which is also known as near-sightedness.

• The bifocal lens can be used for the correction of Presbyopia (a person suffering from both myopia and hypermetropia).

• Progressive lenses also called multifocal lenses are the lenses that have a seamless progression of added magnifying power for intermediate and near vision.

The correct answer is Option 3 i.e. Fiscal Deficit.

• Fiscal Deficit is the sum of revenue and capital expenditure minus(-) all revenue and capital received other than the loan is taken. A substantial increase in capital expenditure or revenue deficit leads to Fiscal Deficit
• Fiscal Deficit = Revenue Received + Capital Received - Total Expenditure
• Revenue Deficit = Revenue Expenditure - Revenue Received
• The Primary deficit is the fiscal deficit of the current year minus interest payments on previous borrowings.
• Primary Deficit = fiscal Deficit - Interset Payment.
• Budgetary deficit is the sum of deficits of the revenue and capital accounts.

• Phloem is a vascular tissue through which the food prepared by the leaves is transported to various organs of the plants.
• Phloem is a composition of four types of cells Sieve tubes, Companion cells, Pholeom parenchyma, and phloem fibers.
• Xylem is a water-conducting tissue of vascular plants which consists of dead hollow cells in the form of fibers and sclereids.
• Parenchyma are the simple permanent tissues whose cells are usually isodiametric but in various organs, due to pressure and surface tension of the neighborhood cells, their shapes sometimes change. These tissues store the foodstuffs and the parts of the leaf mesophyll, endosperms, fruit pulp etc are made from the parenchyma.
• Sclerenchyma are also the simple permanent tissues which are scattered in the organs of the plants to provide mechanical support and rigidity to the plant organs.

Important Points

Difference between Phloem and Xylem:-

• The Vaghela dynasty was an Indian dynasty that ruled Gujarat for a short time period in the13th century CE.
• The Vaghela's were the last Hindu kings to rule large parts of Gujarat, with capital Dholka before the Alauddin Khilji's army conquest of the region.
• In 1304, a second attack by Alauddin's forces defeated Karandev, the last ruler of the Vaghela Dynasty of Gujarat and permanently ended the Vaghela dynasty. This resulted in the annexation of Gujarat to the Delhi Sultanate.

Shortcut Trick

For a number to be divisible by 72, it must be divisible by both 8 and 9.

Divisibility by 8: Last three digits 6x2 must be divisible by 8. If x = 3, 632 ÷ 8 = 79 (True).

Divisibility by 9: Sum of digits (9+1+8+7+6+x+2) = 33 + x must be divisible by 9.

If x = 3, 33 + 3 = 36, which is divisible by 9.

∴ The correct answer is 3.

Alternate Method

Given: Seven digit number 91876x2 is divisible by 72.

Formula Used: Divisibility rule of 72 = Divisibility by 8 × Divisibility by 9.

⇒ Divisibility by 8: Check 6x2. Possible values for x are 3 (632) or 7 (672).

⇒ Divisibility by 9: Sum = 9 + 1 + 8 + 7 + 6 + x + 2 = 33 + x.

⇒ For 33 + x to be a multiple of 9, the nearest multiple is 36.

⇒ 33 + x = 36 ⇒ x = 3.

⇒ Checking x = 7: 33 + 7 = 40 (Not divisible by 9).

∴ The correct answer is 3.

Additional Information

Divisibility by 8

A number is divisible by 8 if the last three digits are divisible by 8 or are all zeros.

Divisibility by 9

A number is divisible by 9 if the sum of its digits is divisible by 9.

Composite Divisibility

To check divisibility by a composite number n, the number must be divisible by its co-prime factors (e.g., 72 = 8 × 9).

Concept Used:

If the height of two triangles are same then 

The Ratio of area = Ratio of their base

Calculation:

Given, BP : PC = 2 : 3

Suppose BP = 2 unit and PC = 3 unit

BC = BP + PC = 2 + 3 = 5 unit

If Q is the midpoint of BP, then BQ = QP

BQ = BP/2 = 2/2 = 1 unit

ar ΔABQ : ar ΔABC = BQ : BC

∴ ar ΔABQ : ar ΔABC = 1 : 5

Confusion Points

This is not a case of similarity 

So, Here ratio of area = ratio of base of triangle  [As height of triangle is constant]

Given, AB = 10 cm, AP = 4 cm, PC = 5 cm

⇒ AB = AP + PB

⇒ 10 = 4 + PB

⇒ PB = 10 – 4 = 6 cm

⇒ CD = PC + PD

As we know,

⇒ AP × PB = PC × PD

⇒ 4 × 6 = 5 × PD

⇒ PD = 24/5 = 4.8 cm

⇒ CD = PC + PD = 5 + 4.8 = 9.8 cm

Let the initial price of sugar be 100x.

Price of sugar after increased = 100x × [117/100] = 117x

Person wants his expenditure increase by 7% only, so his expenditure should be = 100x × [107/100] = 107x

Required percentage = [(117 – 107x)/117] × 100 = 8.54% ≈ 8.5%

⇒ cos θ = base/hypotenuse = 4/5

Using Pythagoras theorem

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

⇒ 5² = (Perpendicular)² + 4²

⇒ Perpendicular = √(25 – 16) = 3

⇒ sin²θ cosθ + cos²θ sinθ

⇒ (3/5)² (4/5) + (4/5)² × (3/5) [sin θ = P/H, cos θ = B/H and tan θ = P/B]

⇒ 9/25 × 4/5 + 16/25 × 3/5

⇒ [36/125] + [48/125]

⇒ 84/125

Total students of all five college = 8,000 + 10,000 + 15,000 + 9,000 + 11,000 = 53,000

Number of students of college E = 11,000

53,000 students represents = 360°

11,000 students will represent = [360°/53,000] × 11,000 = 74.7 ≈ 75°

Total students from the Economics discipline of college B = 10,000 × 40/100 = 4,000

Total students from the science discipline of college C = 15,000 × 45/100 = 6,750

Required percentage = [4,000/6,750] × 100 = 59.25% = 59% (approx)

As we know,

Difference between the compound interest and simple interest for 2 years formula,

Given, r = 12%, time = 2 years and P = x

⇒ Pr²/(100)² = difference

⇒ (P × 12 × 12)/100 × 100 = 43.20

⇒ P = 3,000

As we know,

⇒ (a + b)³ = a³ + b³ + 3ab (a + b)

Given, a + b = 6 and ab = 8

⇒ 6³ = (a³ + b³) + 3 × 8 × 6

⇒ (a³ + b³) = 216 – 144 = 72

Given:

A train without stoppage travels with an average speed of 80 km/h and with

the stoppage, it travels with an average speed of 64 km/h

Calculation:

Without stoppage average speed = 80 km/h

With stoppages average speed = 64 km/h

As we know,

The time of rest per hour is equal to the difference in average speed divided by the

speed without stoppage.

Required time = [(80 – 64)/80] × 60 = 12

Hence, the train stops at an average of 12 minutes/hr.

As we know,

⇒ (x + 1/x)² = x² + 1/x² + 2

Given, √x + 1/√x = 2√2

⇒ (√x + 1/√x)² = (√x)² + (1/√x)² + 2

⇒ [2√2]² = x + 1/x + 2

⇒ x + 1/x = 8 – 2 = 6

⇒ (x + 1/x)² = x² + (1/x)² + 2

⇒ 6² = x² + 1/x² + 2

⇒ x² + 1/x² = 36 – 2 = 34

Given ΔABC ~ ΔRPQ,

⇒ PQ = 10 cm, QR = 12 cm, RP = 16 cm and ar(ΔPQR)/ar(ΔABC) = 9/4

As we know,

⇒ (PQ/BC)² = ar(ΔPQR)/ar(ΔABC)

⇒ 10²/BC² = 9/4

⇒ BC² = 10² × 4/9

⇒ BC = 10 × 2/3 = 20/3 cm

Total students from the science discipline of college A = 8,000 × 25/100 = 2,000

Total students from the science discipline of college B = 10,000 × 35/100 = 3,500

Total students from the science discipline of college C = 15,000 × 45/100 = 6,750

Total students from the science discipline of college D = 9,000 × 28/100 = 2,520

Total students from the science discipline of college E = 11,000 × 35/100 = 3,850

Total students from the science discipline of all the colleges = 2,000 + 3,500 + 6,750 + 2,520 + 3,850 = 18,620

Required average = 18,620/5 = 3724

Let the efficiency of B be 100

Efficiency of A will be = 100 × [150/100] = 150

Efficiency of C will be = 100 × [60/100] = 60

Efficiency ratio of A, B and C = 150 : 100 : 60 = 15 : 10 : 6

Total work = (15 + 10 + 6) × 20 = 620

30% of total work = 620 × [30/100] = 186

30% of total work C will complete in = 186/6 = 31 days

⇒ tan 4θ = cot(40° – 2θ),

⇒ tan 4θ = tan[90° – (40° – 2θ)] [tan(90 – θ) = cot θ]

⇒ 4θ = 90° – 40° + 2θ

⇒ θ = 25°

SP of each article = Rs. 4,956

CP of the first article = 4,956 × [100/118] = 4,200

CP of the second article = 4,956 × [100/84] = 5,900

Total SP of both article = 4,956 × 2 = 9,912

Total CP of both article = 4,200 + 5,900 = 10,100

Total loss = 10,100 – 9,912 = 188

Loss percentage = [188/10,100] × 100 = 1.86%≈ 1.9%

Total students from the discipline of Mathematics for college A = 8,000 × 40/100 = 3,200

Total students from the discipline of Mathematics for college C = 15,000 × 35/100 = 5,250

Total students from Mathematics discipline of college A and C = 3,200 + 5,250 = 8,450

Total students of college A and C = 8,000 + 15,000 = 23,000

Required percentage = [8,450/23,000] × 100 = 36.7%

Given, ∠BAC = 28°

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

In ΔACB

⇒ ∠ACB + ∠CBA + ∠BAC = 180°

⇒ ∠CBA = 180° – 90° – 28° = 62°

⇒ ∠DCA = ∠CAB = 28° [Alternate interior angle]

⇒ ∠DCA = ∠ABD = 28° and ∠CAD = ∠DBC

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

⇒ ∠CBA = ∠DBC + ∠ABD

⇒ 62° = ∠DBC + 28°

⇒ ∠DBC = 62° – 28° = 34°

⇒ ∠CAD = ∠DBC = 34°

Shortcut Trick

When height h = 21 cm and π = 22/7, the expression (1/3) × π × h = 22.

Direct Volume = 22 × (R² + r² + R × r)

⇒ Volume = 22 × (5² + 3² + 5 × 3)

⇒ Volume = 22 × (25 + 9 + 15) = 22 × 49 = 1078 cm³.

∴ The correct answer is 1078 cm³.

Alternate Method

Given:

Height of frustum (h) = 21 cm

Radius of larger face (R) = 5 cm

Radius of smaller face (r) = 3 cm

Formula Used:

Volume of a frustum of a cone = (1/3) × π × h × (R² + r² + R × r)

  h = 21 cm  r = 3 cm  R = 5 cm Frustum of a Cone

Calculations:

⇒ Volume = (1/3) × (22/7) × 21 × (5² + 3² + 5 × 3)

⇒ Volume = (1/3) × (22/7) × 21 × (25 + 9 + 15)

⇒ Volume = 22 × 49

⇒ Volume = 1078 cm³

∴ The correct answer is 1078 cm³.

Additional Information

Slant Height of Frustum

The slant height (l) is the length of the side of the frustum, calculated as l = √(h² + (R − r)²).

Surface Area Formulas

Curved Surface Area (CSA) = π(R + r)l and Total Surface Area (TSA) = CSA + πR² + πr².

Relationship with Cone

A frustum is a part of a cone that remains after the top portion is cut by a plane parallel to the base.

⇒ a : b = 2 : 3

Suppose a = 2and b = 3

⇒ (5a – 2b) : (5a + 2b)

⇒ (5 × 2 – 2 × 3) : (5 × 2 + 2 × 3)

⇒ (10 – 6) : (10 + 6)

⇒ 4 : 16 = 1 : 4

Let the MP of the article be Rs. x

According to the question

⇒ x × [70/100] × [85/100] = 547.40

⇒ x = 920

MP of the article = Rs. 920

Given, a + b + c = 6 and ab + bc + ca = 5

As we know,

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

⇒ 6 [6² – 3 × 5]

⇒ 6 (36 – 15)

⇒ 6 × 21

⇒ 126

⇒ sin44°/cos46° + sin²60° – cos²45° + sec60°

⇒ [sin44°/cos(90° – 44°)] + (√3/2)² – (1/√2)² + 2

⇒ [sin44°/sin44°] + 3/4 – 1/2 + 2 [∵ cos(90° – θ) = sinθ]

⇒ 1 + 3/4 – 1/2 + 2

⇒ (4 + 3 – 2 + 8)/4

⇒ 13/4

Number of girls in class = 60 × 40/100 = 24

Number of boys in class = 60 – 24 = 36

Average weight of girls is = 55

Sum of weight of girls is = 55 × 24 = 1320

Average weight of boys is = 62

Sum of weight of boys is = 62 × 36 = 2232

Total sum of weight of all class = 1320 + 2232 = 3552

Average weight of whole class = 3552/60 = 59.2 kg

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 + (8.2 ÷ 4.1 × 2) – 4 × 3 ÷ 1.2

⇒ 3.8 + (2 × 2) – 4 × 3/1.2

⇒ 3.8 + 4 – 10

⇒ 7.8 – 10

⇒ -2.2

The correct answer is cursing

Key Points

• Meaning of the words given in the options are:
• Invoking means **call on (a deity or spirit) in prayer, as a witness, or for inspiration. (**आह्वान करना)
• Blessing means **a prayer asking for divine favour and protection. (**आशीर्वाद देना )
• Tormenting means inflicting severe physical or mental suffering.(पीड़ा देना)
• Cursing means utter offensive words in anger or annoyance. (शाप देना )
• For eg; He cursed him loudly as she burned his hand.
• It is clear that cursing will be used as the person was annoyed because nothing was working for him.
• So, options 2,3, and 4 are incorrect.
• Thus, the complete sentence is: I sat cursing my life as nothing seemed to be working for me.

The correct answer is option 3.

Ishwar Chand Vidyasagar used the ancient texts to suggest that widows could remarry.

In the given question, it is clear that we are talking about something in the past so the past tense of the verb should be used i.e. used instead of use. Also, before suggestion, to is placed which means that an action is performed. So, instead of the noun suggestion , we must use the verb suggest. 

So, options 1,2 and 4 are incorrect.

The correct answer is option 3.

Devout means having or showing deep religious feeling or commitment.

For eg; She was a devout catholic.

Revered means feeling or showing deep and solemn respect.

Respectable means regarded by society to be good, proper, or correct.

Pious means devoutly religious.

For eg; My grandmother was a deeply pious person.

It is clear that devout and pious are synonyms.

Loyal means giving or showing firm and constant support or allegiance to a person or institution.

So, options 1,2 and 4 are incorrect.

The correct answer is option 4.

Renown means the condition of being known or talked about by many people; fame.

For eg; He was a renown author.

Obscurity means the state of being unknown, inconspicuous, or unimportant.

Wisdom means the quality of having experience, knowledge, and good judgement; the quality of being wise.

Conceit means excessive pride in oneself.

Fame means the state of being known or talked about by many people, especially on account of notable achievements.

For eg; Winning the medal bought him fame and fortune.

It is clear that fame and renown are synonyms.

So, options 1,2 and 3 are incorrect.

The correct answer is option 1.

It has managed to (5) pervade the entire world.

Pervade means spread through and be perceived in every part of.

It is clear that pervade is the appropriate word as the statement suggests that English has managed to spread in every part of the world.

Persuade means cause (someone) to believe something, especially after a sustained effort; convince.

Invade means enter (a country or region) so as to subjugate or occupy it.

Saturate means fill (something or someone) with something until no more can be held or absorbed.

So, options 2,3 and 4 are incorrect.

The correct answer is option 2.

Ascent means an upward slope or path that one may walk or climb.

For eg; The ascent grew steeper which scared me.

Depression means feelings of severe despondency and dejection.

Descent means an act of moving downwards, dropping, or falling.

For eg; The plane had gone into a steep descent because of which there was utter chaos.

It is clear that ascent and descent are antonyms.

Decent means conforming with generally accepted standards of respectable or moral behaviour.

Distant means far away in space or time.

So, options 1,3 and 4 are incorrect.

The correct answer is out of danger

Key Points

• Out of the woods means when one comes out of danger, difficulty or trouble.
• The given sentence means that the man was relaxed when he was sure that he was out of danger.
• So, options 1,2 and 4 are incorrect.

The correct answer is option 1.

English is more (4) prevalent than any single Indian language!

Prevalent means widespread in a particular area or at a particular time.

It is clear that prevalent is the appropriate word as the statement suggests that English is the most widespread language than any other Indian language.

Frequented means visited often or habitually.

Extended means cause to cover a wider area; make larger.

Comprehensive means including or dealing with all or nearly all elements or aspects of something.

So, options 2,3 and 4 are incorrect.

The correct answer is option 2.

The first statement should be  In popular Indian cinema, lyrics are to music what the heart is to the body. This gives a brief account or introduction of what is going to be talked about in the following statements.

After D, it should be A   Lyrics help in creating a distinctive narrative, some conventions of which have been carried over from the talkies era. This is because the first statement talks about lyrics so, A should be in continuation with D. Also, B and C talk about songs so, they cannot come after D.

The correct order is DACB.

So, options 1,3 and 4 are incorrect.

The correct answer is exhilarate

Key Points

• The correct spelling of the given word is exhilarate.
• Exhilarate means to make lively and cheerful; gladden; elate
• Example: S**he was exhilarated by the day's events.
• So, options 1,2, and 3 are incorrect.

The correct answer is option 1.

To feather their own nest means to utilize one's own position at work for own monetary gain.

It is clear that the sentence means that many people join politics to promote their own interests or to gain for themselves.

So, options 2,3 and 4 are incorrect.

The correct answer is Equilibrium.

Key Points

• Equinox means the time or date (twice each year) at which the sun crosses the celestial equator when day and night are of equal length (about 22 September and 20 March)
• Equivalent means equal in value, amount, function, meaning, etc.
• Equilateral means having all its sides of the same length.
• Equilibrium means a state in which opposing forces or influences are balanced or a state of perfect balance.
• After understanding the meanings, options 1,2, and 3 can be easily eliminated.
  

Hence, the correct choice is option 4.

The correct answer is option 2.

The correct spelling is a proportion.

So, options 1,3 and 4 are incorrect.

The correct answer is option 4.

Philanthropist means a person who seeks to promote the welfare of others, especially by the generous donation of money to good causes.

Omnipotent means having unlimited power; able to do anything.

Pedestrian means a person walking rather than travelling in a vehicle.

Somnambulist means a person who walks in sleep.

So, options 1,2 and 3 are incorrect.

The correct answer is option 2.

Not complying by any of the laws can land you into serious trouble.

By is used mostly to state proximity, purpose or method while with is used to state : together, involved, having, using, feeling, agreement, understanding. In the given statement, complying should be followed by with as the statement describes the action of agreement with laws.

So, options 1,3 and 4 are incorrect.

The correct answer is option 3.

Raja Ravi Varma was one of the first artist who tried to create a style that was both modern and traditional.

The singular noun artist is followed by the quantifier one of the which always requires a plural form of the verb. Instead of artist , it should be artists. 

So, options 1,2 and 4 are incorrect.

The correct answer is rarefied.

Key Points

• Meaning of the words given in the options are:
• Intensified means of extreme force, degree, or strength.
• Elevated means situated or placed higher than the surrounding area.
• Exalted means raise to a higher rank or position.
• Rarefied means (of air, especially that at high altitudes) of lower pressure than usual; thin.
• It is clear that rarefied is the appropriate word as rarefied is specifically used to describe air.
• So, options 1,2 and 4 are incorrect.
• Thus, the complete sentence is: The roads at 15000 feet are not easily navigable and the air is rarefied and freezing.

The correct answer is option 3.

Cash transactions are being replaced by credit cards.

While changing from active to passive form, we interchange the subject and the object of the sentence. The given sentence is in present continuous tense identified by  are replacing  so, we change the form of the main verb to the past participle form i.e replaced and add being.

So, options 1,2 and 4 are incorrect.

The correct answer is option 1.

But it is used extensively in (2) the country.

The is used before specific plural and singular nouns. Here, the country is a specific noun, so the will be used.

A is used when we are referring to any member of a group and not a specific thing.

For eg; I need a knife.

An is used before vowels.

For eg; I want an apple.

So, options 2,3 and 4 are incorrect.

The correct answer is native

Key Points

• Foreign means of, from, in, or characteristic of a country or language other than one's own.
• For eg; She visited a foreign island.
• Native means a person born in a specified place or associated with a place by birth, whether subsequently resident there or not.
• For eg; She is a native of North America.
• Foreign and native are antonyms.

​

Additional Information

• Indian means a person born in a specified place or associated with a place by birth, whether subsequently resident there or not.
• Rural means in, relating to, or characteristic of the countryside rather than the town.
• Rustic means relating to the countryside; rural.
• So, options 2,3, and 4 are incorrect.

The correct answer is They gave us very little time to prepare the presentation.

• In Active Voice, a sentence emphasizes the subject, performing an action.
• In Passive Voice, a sentence emphasizes the action or the object of the sentence.
• The given sentence is in the passive voice and 'We' is the subject and the object is hidden**.**
• When we convert this sentence into active voice, the subject 'We' of the passive voice becomes the object (objective case for 'we' is 'us'), the hidden object 'they' becomes the subject.
• The passive format "were + V3 (given)" should be changed into the active format "V2 (gave)".
• This is the active and passive voice rule for the past simple tense.
• Hence, the correct answer is option 4.

*Verbs of passive format have a different set of tenses (V3 - Past participle or Third form of the Verb) as given below in the table:

The correct answer is option 4.

The first statement should be  One of the things I really missed when I set up home in Maryland, was a restaurant that served authentic Indian food. This is because all other statements are in continuation with other statements as A starts with so ,

B is talking about a place which is not been mentioned till now and

D uses this idea but the reader does not know which idea is being talked about.

The next statement is A So, I had thoughts of setting up an Indian restaurant there with my wife's support. This is because in the first statement the speaker misses authentic Indian food so, after that the correct order should be the thought of setting up an Indian restaurant.

After A, it should be D i.e after having the thought, he decided to pursue the idea.

The correct order is CADB.

So, options 1,2 and 3 are incorrect.

The correct answer is seen him since I last left

Key Points

• When since introduces an action or event at a point of time in the past, we the past simpleafter since and the present perfect in the main clause.
• Example: They haven’t received any junk mail since they moved house.
• ​*'left'*** is the past indefinite form of 'leave'

The correct sentence is: I have not seen him since I last left town.

The correct answer is option 2.

India comes second in the list of countries (3*) with** most English speakers, albeit not as the first language.*

With is used when we include something with another.

For eg; The meal with wine was delicious.

It is clear that with is the most appropriate word as it is used to state that India includes most English speakers.

Among is used when we are talking about a group or to indicate that something belongs to a group.

For eg; She was always comfortable when she was among them.

By is used to indicate a method or an action with a purpose.

For eg; He has gone by train.

From is used to show the origin of something or who sent/gave something.

For eg; This is from my mother.

So, options 1,3 and 4 are incorrect.

The correct answer is "Originated."

Key Points

• The verb "originated" refers to the point or place where something begins, arises, or is derived. This fits perfectly in the context of describing where the English language originally comes from.
• English, as known historically, originated in what is now England; it did not originate in India. This makes "originated" the most appropriate choice to convey that English was not native to India.
• The sentence structure requires a verb that indicates the beginning or source of the English language, and "originated" correctly fulfills this requirement.
• Using "originated" correctly establishes the distinction between English and indigenous languages of India.
• Example: Think of a popular game like Cricket which originated in England but is played and loved in India. Similarly, English originated (or started) in Britain but is widely used in India today.

Therefore, the correct answer is Option 1.

Additional Information

• Option 2, "derived," is incorrect as it suggests that English was directly obtained from another source, which is not the intended meaning in this context.
• Option 3, "developed," might imply that English evolved independently in India, which is not accurate.
• Option 4, "created," is also incorrect as it would imply English was invented in India, which is historically inaccurate.