SSC CGL 2020 Tier-I Official Paper (Held On : 13 Aug 2021 Shift 3) (Previous Year Paper)

The least possible Venn diagram is:          

Conclusions:

I. All pillows are rugs. → False (As, All rugs are blankets and All blankets are pillows → Some pillows are rugs)

II. Some pillows are rugs. → True (As, All rugs are blankets and All blankets are pillows → Some pillows are rugs)

III. All rugs are frames → False (As, there is no definite relation between rugs and frames. Hence, false)

Hence, only conclusion II follows.

The number of triangles in the given figure is shown below:

Hence, ‘12’ is the correct answer.

The paper when unfolded will appear as shown below: 

Hence, ‘option 3’ is the correct answer.

The pattern followed here is:

According to the alphabetical positions of the letters,

Hence, ‘EJWT’ is the correct answer.

The description is as follows:

 

Hence, ‘Ahmedabad’ is the odd one out.

In a certain code language, 'COUNTRY' is written as 'BOWKXLF'.

The logic followed here is:

In first letter we add three and shift to the last letter, in second letter we subtract 3 and shift to the second last letter, in third letter we add 3 and shift to the third last latter and so on.

The figure are given below- 

'DESPAIR' be written in that language as -

Hence, "UFDMVBG" is the correct answer.

Given that,

13 ∶  4 ∶∶ 19 ∶ ? ∶∶ 16 ∶ 5

For 13 : 4 → 4 × 3 + 1 = 12 + 1 = 13

For 16 : 5 → 5 × 3 + 1 = 15 + 1 = 16

Similarly, 

For 19 : ? 

? × 3 + 1 = 19

? × 3 = 19 - 1 = 18

? = 18 / 3 = 6

Hence, "6" is the correct answer.

Alternate Method

13 ∶  4 ∶∶ 19 ∶ ? ∶∶ 16 ∶ 5First number added with 6 and get first number of second term and first number of second term subtracted half of 6 (i.e. 3) and get first number of third term.

13 + 6 = 19, 19 - $\frac{6}{2}$ = 19 - 3 = 16

Similarly, second number added with 2 and get second number of second term and second number of second term subtracted half of 2 (i.e. 1) and get second number of third term.

4 + 2 = 6, 6 - $\frac{2}{2}$ = 6 - 1 = 5

We get -

13 ∶  4 ∶∶ 19 ∶ 6 ∶∶ 16 ∶ 5

Hence, "6" is the correct answer.

As E is the common face on both the dice, keeping it constant and then rotating in clockwise direction, we get the faces opposite to each other:

'I' is the letter that will be on the face opposite to the face having the letter 'J'.

Hence, ‘I’ is the correct answer.

The logic followed here is:

In this question, we subtract square root of first number of column 1 from second number of column 1 then we get third number of column 1. 

23 - $\sqrt{25}$ = 23 - 5 = 18

Now, we subtract square root of first number of column 2 from second number of column 2 then we get third number of column 2. 

41 - $\sqrt{64}$ = 41 - 8 = 33

Similarly, we subtract square root of first number of column 3 from second number of column 3 then we get third number of column 3. 

38 - $\sqrt{81}$ = 38 - 9 = 29

Hence, "29" is the correct answer.

The logic is:

1. (215, 338) → 338 - 215 = 123

2. (178, 308) → 308 - 178 = 130 ≠ 123

3. (169, 292) → 292 - 169 = 123 4. (11, 134) → 134 - 11 = 123

Hence, ‘(178, 308)’ is the odd one out.

The logic is:

Prime numbers at even position are added in the sequence to get the next term in the series - 2, 3, 5, 7, 11, 13, 17, 19, 23, 29

  

Hence, ‘69’ is the correct answer.

The logic is:

Nascent ∶ Young → Nascent and Young are synonyms of each other.

Similarly,

Adjunct ∶ ? → Adjunct and Supportive are synonyms of each other.

Hence, ‘Supportive’ is the correct answer.

Mistake Points

• Synonym of nascent → Just beginning, budding, developing, growing, embryonic, incipient, young, in its infancy, fledgling, evolving, emergent, emerging, rising, dawning, advancing, burgeoning.

The correct option that indicates the arrangement of the given words in the order in which they appear in an English dictionary is shown below:

4. Tamarind
5. Tame
6. Temperature
7. Terminal
8. Terminology
9. Tertiary

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

By using the symbols in the table given below, we can draw the following family tree:

Y + Z $H \% C$ D + S → Y is husband of Z, Z is mother of H, H is father of C, C is mother of D, D is husband of S.

1. C is the mother-in-law of S. → True 2. Z is the maternal grandmother of C. → False (Z is the paternal grandmother of C) 3. H is the son of Y. → True 4. H is the maternal grandfather of D. → True

Thus,  Z is the maternal grandmother of C statement is incorrect.

Hence, ‘Z is the maternal grandmother of C’ is the correct answer.

The logic is:

Handwriting ∶ Graphology → The study of handwriting is called Graphology.

Similarly,

Matter ∶ Chemistry → The study of matter is called Chemistry.

Hence, ‘Matter ∶ Chemistry’ is the correct answer.

Additional Information

1. Earthquakes ∶ Pomology

• Pomology is the study of fruits, not earthquakes.

2. Soil ∶ Ornithology

• Ornithology is the study of birds, not soil.

3. Fossils ∶ Pedology

• Pedology is the study of soils, not fossils.

The correct mirror image of the given combination when the mirror is placed at MN is shown below:

Hence, ‘option 1’ is the correct answer.

The pattern followed here is:

According to the alphabetical positions of the letters,

1. TYDI → T + 5 = Y; Y + 5 = D; D + 5 = I

2. ZEJP → Z + 5 = E; E + 5 = J; J + 5 = O ≠ P

3. HMRW → H + 5 = M; M + 5 = R; R + 5 = W
4. NSXC → N + 5 = S; S + 5 = X; X + 5 = C

Hence, ‘ZEJP’ is the odd one out.

The logic is:

Code = (Number of letters in each word)³

CROW, Number of letter = 4 and 4³ = 64

EAGLE, Number of letter = 5 and 53 = 125

Similarly,

PARROT, Number of letter = 6 and 63 = 216 

Hence, ‘216’ is the correct answer.

The option in which the given figure is embedded when rotation is NOT allowed is shown below:

Hence, ‘option 4’ is the correct answer.

1. +, ÷, −, =

Given equation: 68 * 138* 23 * 54 * 20

After replacing the * by the symbols in the option, we get:

68 + 138 ÷ 23 - 54 = 20

⇒ 68 + 6 – 54 = 20

⇒ 74 – 54 = 20

⇒ 20 = 20

2. ×, +, −, =

Given equation: 68 * 138* 23 * 54 * 20

After replacing the * by the symbols in the option, we get:

68 × 138 + 23 - 54 = 20

⇒ 9384 + 23 – 54 = 20

⇒ 9407 – 54 = 20

⇒ 9353 ≠ 20

3. =, ×, +, ÷

Given equation: 68 * 138* 23 * 54 * 20

After replacing the * by the symbols in the option, we get:

68 = 138 × 23 + 54 ÷ 20

⇒ 68 = 3174 + 2.7

⇒ 68 ≠ 3176.7

4. ×, +, =, ÷

Given equation: 68 * 138* 23 * 54 * 20

After replacing the * by the symbols in the option, we get:

68 × 138 + 23 = 54 ÷ 20

⇒ 9384 + 23 = 2.7

⇒ 9407 ≠ 2.7

Hence, ‘+, ÷, −, =’ is the correct answer.

The Venn diagram that best illustrates the relationship between Women, Mothers-in-law, and Housewives is shown below:

Some Housewives are Mothers-in-law and vice-versa.

Housewives and Mothers-in-law both are women.

Hence, ‘option 1’ is the correct answer.

The figure from among the given options that can replace the question mark (?) in the following series is shown below:

Note: The oval shaped image in the figures though change their position by rotating 180° in clockwise direction, but the image itself does not rotates, while the square shaped image changes its position as well rotates in 180° in clockwise direction.

Hence, ‘option 1’ is the correct answer.

1. K, P, Q, R, D, A, P

Given sequence: Q _ A D _ R _ K A D P _ Q K A _ P R Q K _ D _ R

After filling the blanks with the letters/numbers in the option given above, we get:

Q K A D P R / Q K A D P R / Q K A D P R / Q K A D P R

A particular pattern is repeating itself when the sequence is divided into four equal parts

2. K, P, R, Q, D, A, P

Given sequence: Q _ A D _ R _ K A D P _ Q K A _ P R Q K _ D _ R

After filling the blanks with the letters/numbers in the option given above, we get:

Q K A D P R / R K A D P Q / Q K A D P R / Q K A D P R

No particular pattern is repeating itself when the sequence is divided into four equal parts.

3. K, P, Q, R, D, A, Q

Given sequence: Q _ A D _ R _ K A D P _ Q K A _ P R Q K _ D _ R

After filling the blanks with the letters/numbers in the option given above, we get:

Q K A D P R / Q K A D P R / Q K A D P R / Q K A D Q R

No particular pattern is repeating itself when the sequence is divided into four equal parts.

4. K, P, Q, R, A, D, P

Given sequence: Q _ A D _ R _ K A D P _ Q K A _ P R Q K _ D _ R

After filling the blanks with the letters/numbers in the option given above, we get:

Q K A D P R / Q K A D P R / Q K A A P R  / Q K D D P R

No particular pattern is repeating itself when the sequence is divided into four equal parts.

Hence, ‘K, P, Q, R, D, A, P’ is the correct answer.

The logic is:

Square of the 1st number  + 3 = Second number

Cube of the 1st number + 3 = third number

(7, 52, 346) → 7, 7² + 3 = 49 + 3 = 52 and 7³ + 3 = 343 + 3 = 346

Similarly,

(8, 67, 515) → 8, 82 + 3 = 64 + 3 = 67 and 83 + 3 = 512 + 3 = 515

Hence, ‘(8, 67, 515)’ is the correct answer.

Given:

In a training camp, three types of games hockey, cricket, and badminton were taught.

14% of the total students received cricket training.

Calculation:

Remaining students = (100 - 14)% = 86% 

22% of the remaining students received training for hockey.

Percentage of students who received training for hockey = 22/100 × 86 = 18.92%

Remaining students = (86 - 18.92)% = 67.08%

Half of the remaining students received training for badminton.

Percentage of students who received training for badminton = 50/100 × 67.08 = 33.54%

Percentage of students who did NOT receive training in any of the three games = 100 - (14 + 18.92 + 33.54) = 100 - 66.46 = 33.54%

Hence, ‘33.54%’ is the correct answer.

The correct answer is Bhilai.

• A steel plant under SAIL is located at Bhilai.

Key Points

• Steel Authority of India Limited (SAIL):
• It was established in 1954.
• It is a government-owned steel producer.
• It comes under the aegis of the Ministry of Steel.
• Its headquarters is in New Delhi, India.
• Soma Mondal is the current Chairman.
• SAIL currently owns and operates 5 steel plants namely at Bhilai, Bokaro, Burnpur, Durgapur and Rourkela.
• It also operates 3 special steel plants at Durgapur, Salem and Bhadravati.
• A ferroalloy manufacturing unit is also at Chandrapur, Maharashtra.

The correct answer is Hemis.

• Hemis National Park is in Ladakh.

Key Points

• Hemis National Park:
• It is the largest national park in India.
• The park has the highest density of snow leopards in any protected area in the world.
• The species found in the park are Snow leopards, Argali (Great Tibetan Sheep), Bharal (Blue Sheep), Shapu (Ladakhi Urial), Asiatic ibex, The Tibetan wolf, Eurasian brown bear, Red fox, Marmot, Mountain weasel.
• Other national parks and wildlife sanctuaries in Ladakh are Karakoram (Nubra Shyok) Wildlife Sanctuary and Changthang Cold Desert Wildlife Sanctuary.

Additional Information

• Namdapha National Park is in Arunachal Pradesh.
• Gir National Park is in Gujarat.
• Manas National Park is in Assam.

The correct answer is 1932.

• The All-India Harijan Sevak Sangh was founded in 1932.

Key Points

• All-India Harijan Sevak Sangh:
• It was founded by Mahatma Gandhi in the year 1932.
• It was founded in Delhi.
• It is an independent not for profit voluntary Organisation.
• It is also known as the All India Anti-Untouchability League.
• The main aim of the Sangh was to combat untouchability.
• Harijan Bandhua and Harijan Sevak were the two newspapers started by Mahatma Gandhi.

the correct answer is 330.

• The concept of ‘Reservation of seats for Scheduled Castes and Scheduled Tribes in the House of the People’ is highlighted in Article 330 of the Constitution of India.

Key Points

• Article 330 of the Indian Constitution deals with the Reservation of seats for Scheduled Castes and Scheduled Tribes in the House of the People from the:
• The Scheduled Castes.
• The Scheduled Tribes except for the Scheduled Tribes in the autonomous districts of Assam.
• The Scheduled Tribes in the autonomous districts of Assam.

Additional Information

• Article 345 deals with the official language or languages of a State.
• Article 326 deals with the elections to the House of the People and of the Legislative Assembly of every State shall be on the basis of adult suffrage.
• Article 361 deals states that the President or the Governor is not answerable to any court for the exercise of the powers and duties of his office.

The correct answer is Class VI.

• According to National Education Policy 2020, vocational education will start from Class VI with internships.

Key Points

• National Education Policy 2020:
• The new policy replaced the education policy of 1986.
• The policy will do universalization of education from preschool to secondary level with 100% Gross Enrolment Ratio (GER) in education by 2030.
• It will replace the current 10+2 system with a new 5+3+3+4 curricular structure corresponding to ages 3-8, 8-11, 11-14, and 14-18 years respectively.
• The policy lays emphasis on foundational literacy and numeracy.
• There will be no rigid separation between academic streams, extracurricular, vocational streams in schools.
• The policy also has the provision of vocational education for Class 6 with Internships.
• Teaching of students till Grade 5 will be in their mother tongue or the regional language.

The correct answer is Sarnath.

• Sarnath is a Buddhist site located in Uttar Pradesh.

Key Points

• Sarnath is located near Varanasi in Uttar Pradesh.
• Sarnath is an important Buddhist site because Buddha delivered his first sermon here to his five disciples.
• This is known as Dharmachaka Pravartana (turning of the wheel of law).
• The National Emblem of India is an adaptation of the Buddhist Lion Capital of Ashoka at Sarnath.

Additional Information

• Buddhism and Gautam Buddha:
• His real name was Siddharth.
• At the age of 29, he renounced home, this was his Mahabhiniskramana.
• At the age of 35, under a peepal tree at Uruvella (Bodh Gaya) on the bank of river Niranjana, he attained Nirvana after 49 days of continuous meditation he got fully enlightened (Buddha or Tathagat).
• He delivered his first sermon at Sarnath to his five disciples.
• This is known as Dharmachaka Pravartana
• He died in 483 BC at Kushinagar. 
• This is known as Mahaparinirvana.

The correct answer is Indo Tibetan Border Police (ITBP).

• Indo Tibetan Border Police (ITBP) won the 10th National Ice Hockey Championship trophy in Gulmarg in January 2021.

Key Points

• 10th National Ice Hockey Championship:
• The tournament was organized by the Ice Hockey Association of India (IHAI).
• It was won by Indo Tibetan Border Police (ITBP).
• ITBP defeated Ladakh.
• The match was held at Gulmarg Ice Rink.
• The championship was held at an altitude of 8,694-feet and temperatures below freezing point.

Additional Information

• Indo Tibetan Border Police (ITBP):
• Founded: 24 October 1962.
• Headquarters: New Delhi, India.
• Ice Hockey Association of India:
• It is a governing body of ice hockey in India.
• The association became a member of the International Ice Hockey Federation (IIHF) in the year 1989.

The correct answer is cellulose.

• Viscose fibre is obtained from cellulose.

Key Points

• Viscose is made from natural cellulose like tree wood pulp, beech, pine, and eucalyptus.
• It is also obtained from bamboo.
• After the processing of viscose, it becomes semi-synthetic by the use of chemicals like sodium hydroxide and carbon disulfide.
• The fibre is absorbent, lightweight, breathable, soft and proves to be an ideal fabric for making clothes.

The correct answer is Jharkhand.

• Jharkhand State Assembly passed the resolution on Sarna Code in November 2020.

Key Points

• Sarna Code:
• The code of provisions of separate law for the Sarna tribal community.
• It was passed by the Jharkhand State Assembly.
• It empowers tribals to identify themselves as belonging to a distinct religious community.
• Before the code, they were not classified as a separate religious category.

 

Additional Information

• Jharkhand State Assembly:
• It is a unicameral legislative assembly.
• Rabindra Nath Mahato is the current speaker.
• Hemant Soren is the Leader of the House and the Chief Minister.
• Babulal Marandi is the Leader of the Opposition.

The correct answer is 1957.

• The Ramon Magsaysay Award was established in the year 1957.

Key Points

• Ramon Magsaysay Award:
• It is an annual award established to preserve former Philippine President Ramon Magsaysay’s example of integrity in government, courageous service to the people, and pragmatic idealism within a democratic society.
• The Ramon Magsaysay Award is also considered Asia’s Nobel Prize.
• The award was established in the year 1957 by the trustees of the Rockefeller Brothers Fund based in New York City with the concurrence of the Philippines government.
• Vinoba Bhave was the first Ramon Magsaysay Award winner. 
• He won the award in the year 1958 for Community Leadership.
• Ravish Kumar was the one to recently win the award in 2019 in the field of Journalism.

The correct answer is Sea waves.

• Sea waves are not an outcome of endogenic forces.

Key Points

• Endogenic forces:
• These forces are also called Internal Forces.
• The forces originating in the interior of the earth are called the internal or the endogenic forces.
• Volcanic eruptions, Earthquakes, and Landslides are examples of internal forces.
• Exogenic Forces:
• These forces are also called External Forces.
• The forces affecting the surface of the earth from outside are called the external or exogenic forces.
• Weathering and Erosion are examples of external forces.
• Sea waves are the outcomes of wind and gravitational energy.

The correct answer is Nagaland.

• 'Aaluyattu' is a folk dance form from the state of  Nagaland.

Key Points

• Aaluyattu is a folk dance form from the state of  Nagaland.
• The dance is performed by the Konyak tribe.
• Other folk dances of Nagaland are Modse, Agurshikukula, Sadal Kekai, Changai Dance, Kuki Dance, Leshalaptu, Khamba Lim, Mayur Dance, Rengma, Monyoasho, Seecha and Kukui Kucho.

Additional Information

• The folk dances of Kerala are Kaikottikali,  Mudiyett, Sangha Kali, Brahmanippattu, Dappu Kali, Kolkali and Vattakkali.
• The folk dances of Haryana are Ras Leela, Phag Dance, Loor, Daph dance.
• The folk dances of Goa are Dekhni, fugdi, Dashavatara, Dhalo, Goff and Kunbi.

The correct answer is Two.

• There are two arteries in an umbilical cord.

Key Points

• The umbilical cord:
• During pregnancy, it is a flexible, tube-like structure that connects the fetus to the mother.
• The cord transports nutrients to the baby and also carries away the waste products of the baby.
• The cord is made up of two arteries and one vein.
• Arteries carry pure blood from the heart to other parts of the body.
• Veins carry impure blood to the heart.

Additional Information

• Blood:
• The quantity of blood in the human body is 7% of the total weight.
• Blood is connective tissue and is composed of blood corpuscles, plasma, and platelets.
• It is slightly alkaline in nature.
• Its pH is 7.4.
• Its volume in an adult human is 5.8 L.
• Plasma:
• This is the liquid part of blood.
• 60% of the blood is plasma.
• 90% part of the blood plasma is water, 7% protein, 0.9% salt, and 0.1% is glucose.
• Blood corpuscles:
• The remaining 40% part of the blood is made of corpuscles

The correct answer is wave velocity.

• For a wave, wavelength divided by the time period is equal to wave velocity.

Key Points

• Wavelength:
• Wavelength is the distance between any two nearest particles of the medium, vibrating in the same phase.
• It is denoted by the Greek letter lambda.
• In a transverse wave distance between two consecutive crests or troughs, and in a longitudinal wave, the distance between two consecutive compressions or refractions is equal to the wavelength.
• Wave velocity is the distance traversed by a periodic motion (time period) per unit time.

Additional Information

• A phase difference is a difference in phase angle between two sinusoids or phasors.
• Amplitude is the maximum displacement of the vibrating particle on either side from the equilibrium position.
• The frequency of a particle is defined as the number of vibrations completed by the particle in one second.

The correct answer is Article 123.

• Article 123 of the Constitution of India provides power to the President for promulgating ordinances.

Key Points

• President:
• President is the head of the Union Executive.
• He is indirectly elected by an electoral college, in accordance with the system of proportional representation by means of the single transferable vote.
• Qualifications:
• ​He should be a citizen of India.
• He should have completed 35 years of age.
• He should be qualified for election as a member of the Lok Sabha.
• He should not hold any office of profit under the Union Government or any State Government or any local authority or any other public authority.
• Article 60 deals with the Oath and Affirmation of the President.
• The oath of the President is administered by the Chief Justice of India and in his absence, the seniormost Judge of the Supreme Court.
• According to Article 56, the President shall hold office for a term of five years from the date on which he enters his office.
• Article 123 of the Constitution of India provides power to the President for promulgating ordinances.

Additional Information

• Article 143 empowers the President to seek the opinion of the Supreme Court.
• The SC is bound to give its opinion which is not binding on President.
• Article 77 states that all the executive action of the Government of India shall be done in the name of the President.
• Article 111 states that the President shall declare his assent to a bill passed by both the Houses of Parliament or withhold his assent, provided he returns the bill to Parliament for reconsideration.

The correct answer is photosynthesis.

• The carbon and energy requirements of an autotrophic organism are fulfilled by photosynthesis.

Key Points

• Photosynthesis:
• In the presence of water, light, chlorophyll, and carbon dioxide, the formation of carbohydrates in the plant is called photosynthesis.
• The carbon and energy requirements of an autotrophic organism are fulfilled by this process.
• Terrestrial plants take CO₂ from the atmosphere whereas aquatic plants use carbon dioxide mixed in water.
• Water enters into cells of the leaves through osmosis and CO₂ through diffusion from the atmosphere or released during respiration.
• The green colour of the plants is due to the presence of chlorophyll.
• There is an atom of magnesium in the center of chlorophyll.
• Chlorophyll absorbs the violet, blue, and red colour of light.
• The rate of photosynthesis is maximum in red light and is minimum in violet light.
• The process of photosynthesis is a reaction of oxidation and reduction.

The correct answer is French.

• Chandernagore (Chandannagar) was a French colony captured by the British Navy on 23 March 1757.

Key Points

• Battle of Chandannagar:
• Chandernagore was the administrative center of the French East India Company.
• The battle was fought between France and Great Britain.
• British East India Company was led by Robert Clive and Royal Navy was led by Charles Watson.
• They bombarded and captured Chandernagore (Chandannagar) in March 1757.
• French in India:
• The French Company was formed in 1664 AD by Colbert under state patronage during the reign of Louis XIV.
• The first French factory was established at Surat by Francois Caron in 1668 AD and the second at Masulipatnam in 1669 AD.
• They occupied Mahe, Yanam and Karaikal.
• The foundation of Pondicherry was laid in 1673 AD, which afterward became its capital.
• They also developed a factory at Chandernagar.
• The Anglo-French conflict was started with the arrival of Governor Dupleix in 1742 AD.

Additional Information

The correct answer is Raj Krishna.

• Raj Krishna coined the terminology 'Hindu Rate of Growth.

Key Points

• Hindu Rate of Growth:
• The term was coined by Professor Rajkrishna in the year 1978.
• The average growth of GDP during the period was around 3.5% while per capita income grew by an insignificant 1.3%.
• The country's annual population growth rate was over 2% in the 1980s.
• The per-capita GDP growth rate, with 3.5% GDP growth, was a meager 1 % characterizing the Hindu rate of growth.
• The term “Hindu” was used by some early economists to indicate that the Hindu outlook of acceptance and contentedness was responsible for the slow growth.

The correct answer is First slip.

• The first slip is fielding position behind the batsman.

Key Points

• Cricket: 
• The first official cricket test match was played in the year 1877 between Australia and England in Melbourne.
• The First One Day International cricket match was played in the year 1971 between England and Australia in Melbourne.
• The first World Cup of one-day matches was played in 1975 in London.
• The apex institution of world cricket is the International Cricket Council (ICC) and its headquarters are now in Dubai.
• Earlier it was in Lords (England).
• The ICC was founded in 1909.
• The Board of Control for Cricket in India (BCCI) was formed in 1927.
• Terminologies used in cricket are Toss, Run, Wicket, Bails, Crease, Pavilion, Maiden Over, Follow-on, Bowled, Stump Out, Run Out, L.B.W. Hit Wicket, Noball, Wide ball, Dead ball, Overthrow, Bye, Leg bye, Cover drive, Late cut, Hook, Glance, Stroke, Spot, Pull, Sixer, Followthrough, Googly, Cover, Gully, Long on, Silly point, Midwicket, Mid on, Forward short leg
• The first slip is a position behind the batsman.

Additional Information

• Mid-wicket is a position in front of square on the leg side of the batsman.
• Mid-off is the position closest to the bowler on the off side.

The correct answer is Narasimha Deva I.

• The Sun Temple of Odisha was built in the 13th Century AD by the Narasimha Deva I.

Key Points

• Sun Temple:
• It was built by Narasimha Deva I in the 13th century.
• True to its name, the temple is dedicated to Surya or the Sun God.
• The temple reflects the Kalinga architecture.
• Kama Konark means the sun and the four corners.
• Europeans called it the Black Pagoda.
• The temple was included in the UNESCO World Heritage Site in the year 1984.
• Eastern Ganga Dynasty:
• The dynasty is also known as Rudi Ganga or Oriental Ganga.
• It is also known as Chedaganga of Orissa.
• King Ananthavarman Ganga got the Jagannath temple built at Puri.

The correct answer is Mathematics.

• The ICTP Ramanujan Prize is awarded annually for excellence in mathematics.

Key Points

• ICTP Ramanujan Prize:
• The Prize is given to young mathematicians from developing countries.
• It is named after the mathematician Srinivasa Ramanujan.
• It was founded in 2004 and was first given in the year 2005.
• It was instituted by organizations ICTP, the Niels Henrik Abel Memorial Fund, and the International Mathematical Union (IMU).
• The participation of the Niels Henrik Abel Memorial Fund ended in 2012.
• The Department of Science and Technology of the Government of India (DST) started funding the prize in 2014.
• It is an annual award given to a researcher from a developing country who is less than 45 years of age.
• The Prize consists of a $15,000 cash award.

Additional Information

• Abel prize is given in the field of Mathematics.
• It is given by the King of Norway.
• The award is considered the Nobel Prize for  Mathematics.

The correct answer is Amritsar.

• Sri Harmandir Sahib is located in Amritsar, Punjab.

Key Points

• Sri Harmandir Sahib/Golden Temple of Amritsar
• It is the holy shrine of the Sikhs.
• It is also known as The Golden Temple of Amritsar.
• The Golden Temple complex includes the Akal Takht, Sikh history museum, the Amrit Sarovar and Guru Ram Das Langar (a large dining hall).

Additional Information

• Sikhism:
• Guru Nanak is the founder of Sikhism.
• Guru Granth Sahib is the holy book of Sikhs.

The correct answer is Ukraine.

• In 2020, the United Nations passed a resolution to remove cannabis and cannabis resin from the category of 'most dangerous substances' and Ukraine was absent from the voting.

Key Points

• The United Nations has passed a resolution to remove hemp and cannabis resin from the category of 'most dangerous substances'.
• India and 25 other countries including China, Pakistan, and Russia voted in favor of the resolution.
• Ukraine remained absent during the voting process.
• Cannabis and its resin were omitted from Schedule IV of the Single Convention on Narcotic Drugs, 1961.
• Two drugs were classified as "least dangerous" substances under the Schedule 1 list.
• In India, cannabis is a prohibited drug under the Narcotic Drugs and Psychotropic Substances (NDPS) Act, 1985.​

The correct answer is Wang Chhu River.

• Wang Chhu River is a tributary of the river Brahmaputra that flows through Bhutan.

Key Points

• Brahmaputra River System:
• It is known as Tsangpo in Tibet, Dihang or Siang in Arunachal Pradesh, the Brahmaputra in Assam, and Jamuna in Bangladesh.
• The river originates at the Manasarover lake in Tibet.
• Tributaries from the left bank are: 
• Lhasa River, Nyang River, Parlung Zangbo, Lohit River, Dhansiri River and Kolong River
• Tributaries from the right bank​ are:
• ​Kameng, Manas, Beki, Raidak, Jaldhaka, Teesta and Subansiri River
• Majuli is the largest riverine island in the world is in the Brahmaputra River.
• The combined stream of Ganga and Brahmaputra forms the biggest delta in the world, the Sunderbans.
• The Brahmaputra is the volume-wise largest river of India, whereas lengthwise Ganga is the longest in India.
• The Raidak river is also known as the Wang Chhu River.
• It flows through Bhutan, India, and Bangladesh.
• Chukha hydel plant and Tala Hydroelectric Power Station are located on the river.

The correct answer is bacteria.

• Lymph is a light clear fluid made up of white blood cells that attack harmful bacteria in the blood.

Key Points

• Lymph Circulatory System
• The light yellow fluid found in the intercellular spaces between different tissues and cells is called lymph.
• The corpuscles found in the lymph are called lymphocytes.
• Lymph flows only in one direction from the tissue towards the heart.
• Functions of Lymph
• Lymph forms the lymphocytes.
• The lymphocytes present in lymph help prevent the body from disease by killing the harmful bacteria.

Additional Information

• Diseases caused by bacteria:
• Diphtheria, pneumonia, cholera, tetanus, tuberculosis, plague, and gonorrhea.
• Diseases caused by fungi:
• Ringworm and athlete's foot.
• Diseases caused by protozoa:
• Malaria, Dysentery, Diarrhea, Kala Azari.

Given:

Distance covered by the train = 370 km 

Formula used:

Time = Distance/Speed

Calculation:

Let the speed of the train = x km/h

As per the question;

[100/x + 270/(x - 5)] - 370/x = 36/60 

⇒270/(x - 5) - 270/x = 3/5

⇒ 1/(x - 5) - 1/x = 1/450

⇒ [x - (x - 5)]/(x - 5)x = 1/450

⇒ 5/(x - 5)x = 1/450

⇒  5 × 450 = x² - 5x 

⇒ x2 - 5x - 2250 = 0

⇒x2 - 50x + 45x - 2250 = 0 

⇒ x(x - 50) + 45(x - 50) = 0

⇒ (x + 45)(x - 50) = 0

⇒ x ≠ 45, x = 50

∴ The required speed of the train = 50 km/h

Alternate MethodBy Hit and Trial Method:

[100/x + 270/(x - 5)] - 370/x = 36/60

Option 1: [100/40 + 270/(35)] - 370/40 ≠  36/60

Option 2: [100/45 + 270/(40)] - 370/45 ≠  36/60

Option 3: [100/50 + 270/(45)] - 370/50 = 36/60

Option 4: [100/48 + 270/(43)] - 370/48 ≠  36/60

Given:

3 tan θ = 2√3 sin θ, 0° < θ < 90°

Calculation:

3 tan θ = 2√3 sin θ

⇒ 3 × sin θ/cos θ = 2√3 sin θ

⇒ 3/cos θ =  2√3

⇒ cos θ =  3/2√3 = √3/2

⇒ cos θ = cos 30° 

⇒ θ = 30° 

At  θ = 30°; 2 sin2 2θ - 3 cos2 3θ 

⇒ 2 sin2 2 × 30° -  3 cos2 3 × 30°

⇒ 2 sin2 60° -  3 cos2 90°

⇒ 2 × (√3/2)² - 3 × 0

⇒ 2 × 3/4 - 0 

⇒ 3/2 

∴ 2 sin2 2θ - 3 cos2 3θ = 3/2 

Alternate MethodBy value Putting Method

At θ = 30°, 3 tan θ = 2√3 sin θ

At θ = 45°, 3 tan θ ≠ 2√3 sin θ

At θ = 60°, 3 tan θ ≠ 2√3 sin θ

So, at  θ = 30°; 

⇒ 2 sin2 2θ - 3 cos2 3θ 

⇒ 2 sin2 2 × 30° -  3 cos2 3 × 30°

⇒ 2 sin2 60° -  3 cos2 90°

⇒ 2 × (√3/2)2 - 3 × 0

⇒ 2 × 3/4 - 0 

⇒ 3/2

Shortcut Trick

Initial Profit% = 30 − 10 − (30 × 10 ÷ 100) = 17%.

New required Profit% = 17 + 6.5 = 23.5%.

Let new discount be d%. Using effective change formula: 30 − d − (30d ÷ 100) = 23.5.

6.5 = 1.3d ⇒ d = 6.5 ÷ 1.3 = 5%.

∴ The correct answer is 5%.

Alternate Method

Given: Markup = 30%, Initial Discount = 10%, Additional Profit required = 6.5%.

Formulas: SP = CP × (100 + Profit%) ÷ 100 | MP = CP × (100 + Markup%) ÷ 100 | Discount% = (MP − SP) ÷ MP × 100

⇒ Let CP = 100. Then Marked Price (MP) = 100 + 30% of 100 = 130.

⇒ Initial Selling Price (SP) = 130 − 10% of 130 = 130 − 13 = 117.

⇒ Initial Profit = 117 − 100 = 17.

⇒ New Profit required = 17 + 6.5 = 23.5. New SP = 100 + 23.5 = 123.5.

⇒ New Discount Amount = MP − New SP = 130 − 123.5 = 6.5.

⇒ New Discount Percent = (6.5 ÷ 130) × 100 = 5%.

∴ The correct answer is 5%.

Additional Information

Markup and Discount Relation

The relationship between Cost Price and Marked Price can be expressed as: MP ÷ CP = (100 + Profit%) ÷ (100 − Discount%).

Effective Profit Percentage

When a markup of m% and a discount of d% are applied, the Net Profit% = m − d − (md ÷ 100).

Given:

A circle inscribed in a quadrilateral ABCD, AB = 8.4 cm, BC = 9.8 cm and CD = 5.6 cm

Concept:

Let the circle touches the sides AB, BC, CD and DA at P, Q, R and S, respectively.

∴ AP = AS

⇒ BP = BQ

⇒ DR = DS

⇒ CR = CQ (Lengths of two tangents drawn from an external point of circle, are equal)

Calculation:

Adding all these, we get

(AP + BP) + (CR + DR) = (BQ + QC) + (DS + AS)

AB + CD = BC + DA

8.4 + 5.6 = 9.8 + DA

⇒ DA = 14.0 - 9.8 = 4.2 cm

∴ AD = 4.2 cm

Given:

ΔABC ∼ ΔDEF, BC = 3.15 cm

Area of ΔABC = 13.5 cm2 

Area of ΔDEF = 24 cm2

Concept:

The ratio of the areas of two similar triangles is equal to the ratio of the square of their corresponding sides. 

⇒ $\text {Area of (ΔABC)}\over \text{Area of (ΔDEF)}$ = $({BC\over EF})^2$ 

Calculation:

$\text {Area of (ΔABC)}\over \text{Area of (ΔDEF)}$ = $({BC\over EF})^2$ 

⇒ $13.5 \over24$ = $({3.15\over EF})^2$

⇒ ${3.15\over EF}$ = $\sqrt{13.5\over24}$ = $\sqrt{9\over16}$

⇒ ${3.15\over EF}$ = $3\over4$

⇒ EF = $3.15\times4\over3$ = 4.2 cm

⇒ EF = 4.2 cm

Given:

Quantity of rice = 640 kg 

Overall profit percent = 15% 

Calculation:

Let the part sold at 5% loss be = a kg

a × - 5% + (640 - a) × 20% = 640 × 15/100 

⇒ - 5a + 640 × 20 - 20a = 640 × 15

⇒ 640 × 20 - 640 × 15 = 25a   

⇒ 640 × (20 -15)/25 = a  

⇒ a = 128 

∴ The part that was sold at 5% loss is 128 kg.

Alternate MethodBy Alligation Method

<br>

⇒ 1 + 4 = 5 = 640 kg 

∴ 1 = 640/5 = 128 kg

Given:

25 < x < 30

Calculation:

Year 2014: 

Percentage difference of the no of students in institute A than that of institute B = (225 - 160)/225 × 100 

⇒ 65/225 × 100 = 28.88% Less 

Year 2015:

Percentage difference of the no of students in institute A than that of institute B = (360 - 280)/360 × 100 

⇒ 80/360 × 100 = 22.22% Less 

Year 2016:

Percentage difference of the no of students in institute A than that of institute B = (375 - 300)/300 × 100 

⇒ 75/375 × 100 = 20% Less 

Year 2017:

Percentage difference of the no of students in institute A than that of institute B = (325 - 250)/325 × 100 

⇒ 75/325 × 100 = 23% Less 

∴ For 25 < x < 30, in the year 2014 the number of students enrolled in institute A is 28.88% less, than the number of students enrolled in institute B

Shortcut Trick

Find the Inner radius (r) using Area = 12474 ⇒ r = √(12474 × 7/22) = 63 m.

For a path of width (w) around a circle, Path Area = πw(2r + w).

Path Area = (22/7) × 3.5 × (2 × 63 + 3.5) = 11 × 129.5 = 1424.5 m².

∴ The correct answer is 1424.5 m².

Alternate Method

Given:

Area of the circular park (A_inner) = 12474 m²

Width of the path (w) = 3.5 m

Formula Used:

Area of circle = πr²

Area of path = πR² − πr² = π(R² − r²)

Calculations:

⇒ πr² = 12474

⇒ (22/7) × r² = 12474

⇒ r² = (12474 × 7) / 22 = 567 × 7 = 3969

⇒ r = √3969 = 63 m

⇒ Outer radius (R) = r + width = 63 + 3.5 = 66.5 m

⇒ Area of Path = π(R² − r²) = π(R + r)(R − r)

⇒ Area of Path = (22/7) × (66.5 + 63) × (66.5 − 63)

⇒ Area of Path = (22/7) × 129.5 × 3.5

⇒ Area of Path = 22 × 129.5 × 0.5 = 11 × 129.5 = 1424.5 m²

∴ The correct answer is 1424.5 m².

Additional Information

Area of Annulus (Ring)

The region between two concentric circles is called an annulus. Its area is given by π(R² − r²), where R is the outer radius and r is the inner radius.

Circumference of Circle

The total boundary length of a circle is calculated as 2πr, where r is the radius of the circle.

Relation between Radius and Area

If the radius of a circle is multiplied by a factor 'k', then its Area is multiplied by k² and its Circumference is multiplied by k.

Given:

$\rm x^4+\frac{1}{x^4} = 727,x>1$

Formulas used:

(a + b)² = a² + b² + 2ab

(a - b)² = a2 + b2 - 2ab

Calculation:

$\rm x^4+\frac{1}{x^4} = 727$ 

By adding 2 on both sides 

x⁴ + 1/x⁴ + 2 = 727 + 2 

⇒ (x² + 1/x²)² = 729

⇒ (x2 + 1/x2) = √729  

⇒  (x2 + 1/x2) = 27

By subtracting 2 from both sides

⇒ (x2 + 1/x2) - 2 = 27 - 2

⇒ (x - 1/x)² = 25

⇒  (x - 1/x) = √25

∴ (x - 1/x) = 5

Given:

In ΔABC

∠C = 90°

AB = 10 cm

AC = 2√10 cm

Q is midpoint of BC

Concept used:

Pythagoras Theorem

AB² = AC² + BC²

Calculation:

Q is midpoint of BC

∴ CQ = BQ = 1/2 × BC 

10² = ( 2√10)² + BC2

⇒ BC = 100 - 40 = √60 

∴ CQ = 2√15/2 = √15

In triangle ACQ, AQ2 = CQ2 + AC2

⇒ 15 + 4 × 10 =  AQ2 

⇒ AQ² = 55

⇒ AQ = √55

So, the length of AQ = √55 cm.

Given:

$\rm x-\frac{1}{x}=1$

Formula used:

(a + b)2 = a2 + b2 + 2ab

(a - b)2 = a2 + b2 - 2ab

Calculation:

(x - 1/x) = 1

By squaring both sides

⇒ x² + 1/x² - 2 × x × 1/x = 1

⇒  x2 + 1/x2 = 1 + 2 

⇒  x2 + 1/x2 = 3

By squaring both sides again;

⇒ x⁴ + 1/x⁴ + 2 = 9

⇒ x4 + 1/x4 = 9 - 2 = 7

By squaring both sides one more time;

⇒  x⁸ + 1/x⁸ + 2  = 49

⇒ x8 + 1/x8 = 49 - 2 = 47

∴ x8 + 1/x8 = 47

Calculation:

No of vacant seats in 2nd non-AC class & 1st class non-AC class on Monday = (900 - 850) + (500 - 460) = 90

No of vacant seats in 2nd non-AC class & 1st class non-AC class on Tuesday = (900 - 840) + (500 - 400) = 160

No of vacant seats in 2nd non-AC class & 1st class non-AC class on Wednesday = (900 - 830) + (500 - 390) = 180

No of vacant seats in 2nd non-AC class & 1st class non-AC class on Thursday = (900 - 790) + (500 - 480) = 130

No of vacant seats in 2nd non-AC class & 1st class non-AC class on Monday = (900 - 840) + (500 - 470) = 90

∴ No of seats remained vacant taking all the days together in non-AC classes = 90 + 160 + 180 + 130 + 90 

⇒ 650

Follow BODMAS rule to solve this question, as per the order given below, 

Calculation:

90 ÷ 20 of 6 × [11 ÷ 4 of {3 × 2 - (3 - 8)}] ÷ (9 ÷ 3 × 2)

⇒ 90/120 × [11 ÷ 4 of {6 + 5}] ÷ (9 × 1/3 × 2)

⇒ 90/120 × [11 ÷ 4 of {6 + 5}] ÷ 6

⇒ 3/4 × [11 ÷ 4 of {11}] ÷ 6

⇒ 3/4 × [11 ÷ 44] ÷ 6

⇒ 3/4 × 1/4 × 1/6 

⇒ 1/32

∴ 90 ÷ 20 of 6 × [11 ÷ 4 of {3 × 2 - (3 - 8)}] ÷ (9 ÷ 3 × 2) = 1/32

Given:

Radius of the bigger circle = 13 cm

Radius of the smaller circle = 12 cm 

AB is the diameter of the bigger circle.

BD is a tangent to a smaller circle. 

Calculation:

By Pythagoras Theorem; in triangle ODB

OB² = OD² + BD²

⇒ 169 = 144 + BD2

⇒ BD = 5 cm 

BD = DE = 1/2 × BE     ∵ [Perpendicular drawn from the center on a chord bisects it in two equal parts]

⇒ DE = BD = 5 cm 

⇒ BE = 10 cm 

In triangle ABE, 

∠AEB = 90°     ∵ [Angle made in semicircle] 

⇒  AB2 = EB2 + AE2

⇒ 676 = 100 +  AE2

⇒ AE = √576

⇒ AE = 24 cm 

In triangle ADE

⇒ AD2 = ED2 + AE2

⇒ AD2 = 25 + 576

⇒ AD2 = 601

⇒ AD = √601 

⇒ AD = 24.51 cm 

So, the length of AD = 24.5 (Approximately)

Calculation:

The number of boys in Science stream in the years 2012 and 2016 = 40 + 38 = 78

The number of girls for all the years in the Commerce stream = 45 + 42 + 38 + 34 + 41 = 200

∴ The required percentage = 78/200 × 100 = 39%

Shortcut Trick

Net deviation from the overall average (56) = 3 × (52 − 56) + 5 × (60 − 56) = −12 + 20 = +8.

To balance the average, the deviation of the last 3 numbers must be −8. Thus, their total sum = 3 × 56 − 8 = 160.

Let the 11th number be x. Then, 9th number = x + 3 and 10th number = x + 1.

Sum = x + 3 + x + 1 + x = 160 ⇒ 3x = 156 ⇒ x = 52.

The average of the 9th and 11th numbers = (x + 3 + x) ÷ 2 = x + 1.5 = 52 + 1.5 = 53.5.

∴ The correct answer is 53.5.

Alternate Method

Given:

Average of 11 numbers = 56

Average of first 3 numbers = 52

Average of next 5 numbers = 60

Let the 11th number = x. Then the 9th number = x + 3 and the 10th number = x + 1.

First 3 Next 5 Last 3

Avg = 52 Avg = 60 Sum = 160

Total 11 Numbers : Avg = 56, Sum = 616

Calculations:

⇒ Sum of all 11 numbers = 11 × 56 = 616

⇒ Sum of first 3 numbers = 3 × 52 = 156

⇒ Sum of next 5 numbers = 5 × 60 = 300

⇒ Sum of the 9th, 10th, and 11th numbers = Total sum − (Sum of first 3 + Sum of next 5)

⇒ Sum of the last 3 numbers = 616 − (156 + 300) = 616 − 456 = 160

⇒ (x + 3) + (x + 1) + x = 160

⇒ 3x + 4 = 160

⇒ 3x = 156

⇒ x = 52

⇒ 11th number = 52

⇒ 9th number = 52 + 3 = 55

⇒ Average of 9th and 11th numbers = (55 + 52) ÷ 2 = 107 ÷ 2 = 53.5

∴ The correct answer is 53.5.

Additional Information

Sum of Observations

The total sum of any set of observations is simply the average multiplied by the number of observations (Sum = Average × N).

Net Deviation Method

The sum of all deviations of the individual values from their arithmetic mean is always zero. This property helps significantly in breaking down complex averages without multiplying large numbers.

Combined Average

When multiple groups are combined, their total average is given by (N₁A₁ + N₂A₂ + N₃A₃) ÷ (N₁ + N₂ + N₃).

Given:

2x2 - 8x - 1 = 0

Formula used:

(a - b)³ = a³ - b³ - 3ab(a - b)

Calculation:

2x2 - 8x - 1 = 0

By dividing the above equation by x;

⇒ 2x - 8 - 1/x = 0

⇒ 2x - 1/x = 8       

By cubing both sides;

⇒ (2x)³ - 1/x³- 3 × 2x × 1/x(2x - 1/x) = 512 

⇒ 8x3 - 1/x3 - 6 × 8 = 512 

∴ 8x3 - 1/x3 = 560

Given:

Cost of Bread = Rs.20

Rest of money left with Atul = 100 - 20 = Rs.80

Ratio of the coins of denominations of Rs.2, Rs.5 and Rs.10 = 5 : 4 : 1

Calculation:

Ratio of the coins of denominations of Rs.2, Rs.5 and Rs.10 = 5 : 4 : 1

As per the question;

Ratio of amount = 5 × Rs.2 : 4 × Rs.5 : 1 × Rs.10 

⇒ 1 : 2 : 1 = 80

⇒ 4 = Rs.80

⇒ 2 = Rs.40

∴ No of Rs.5 coins = Rs.40/5 = 8

Shortcut Trick

Identify complementary angles: tan(45° − α) = cot(45° + α), so the first term is 1.

Simplify numerator: (cos 19° + cos 19°)(sec 19° + sec 19°) = 2 cos 19° × 2 sec 19° = 4.

Simplify denominator: tan 12° × tan 78° = 1 and tan 24° × tan 66° = 1.

Final calculation: 1 − (4 ÷ 1) = −3.

∴ The correct answer is -3.

Alternate Method

Given: Expression involving trigonometric ratios of complementary angles.

Formula Used: tan(90° − θ) = cot θ | sin(90° − θ) = cos θ | sec(90° − θ) = cosec θ | tan θ × cot θ = 1

Step-by-step Calculations:

⇒ cot(45° + α) = tan(90° − (45° + α)) = tan(45° − α)

⇒ Part 1: tan(45° − α) ÷ tan(45° − α) = 1

⇒ sin 71° = cos(90° − 71°) = cos 19° and cosec 71° = sec(90° − 71°) = sec 19°

⇒ Numerator of Part 2: (cos 19° + cos 19°)(sec 19° + sec 19°) = (2 cos 19°)(2 sec 19°) = 4(cos 19° × sec 19°) = 4 × 1 = 4

⇒ tan 78° = cot 12° and tan 66° = cot 24°

⇒ Denominator of Part 2: (tan 12° × cot 12°) × (tan 24° × cot 24°) = 1 × 1 = 1

⇒ Final Value: 1 − (4 ÷ 1) = 1 − 4 = −3

∴ The correct answer is -3.

Additional Information

Complementary Angles in Trigonometry

If A + B = 90°, then sin A = cos B, tan A = cot B, and sec A = cosec B.

Product of Tangents

When A + B = 90°, tan A × tan B = 1 because tan B = cot A.

Reciprocal Relations

Trigonometric identities include sin θ × cosec θ = 1, cos θ × sec θ = 1, and tan θ × cot θ = 1.

Given:

Average amount with A, B and C = Rs.4520 

Share of A = $10\frac{2}{3}\%$% more than that of B 

Share of A = $33\frac{1}{3}\%$% less than that of C

Formula used:

Average amount = Sum of the amount/No of people dividing the amount 

Calcualtion:

Share of A = $10\frac{2}{3}\%$% more than that of B 

$10\frac{2}{3}\%$ % = 32/300 = 8/75 

⇒ B = 75 , A = 75 + 8 = 83 

∴ Ratio of amount with A and B = 83 : 75 

Share of A = $33\frac{1}{3}\%$% less than that of C

$33\frac{1}{3}\%$% = 1/3 

⇒ C = 3 , A = 2 

∴ Ratio of amount with A and C = 2 : 3

Now, by equalising the value of ratio of A with B and C;

⇒ A : B : C = 166 : 150 : 249

As per the question:

Sum of the amount with A, B and C = 4520 × 3 = 13560

⇒ 166 + 150 + 249 = 565

⇒ 565 = Rs.13560

⇒ Share of B (150) = 13560 × 150/565

∴ Share of B = Rs.3600

Formula used:

Average production = Total production/No of years

Calculation:

Average production of company X = (40 + 55 + 35 + 60 + 50)/5 = 48 (ten lakh tonnes)

Average production of company Y = (35 + 45 + 45 + 50 + 60)/5 = 47 (ten lakh tonnes)

Average production of company Z = (45 + 50 + 55 + 45 + 45)/5 = 48 (ten lakh tonnes)

∴ X and Z both have the maximum average production for the 5 years.

Given:

Time taken by 1 man and 1 woman = 66 days

Ratio of the efficiency of man and woman = 3 : 2

Formula used:

Total work = Time × Efficiency

Calculation:

Total work = 66 × (3 + 2) = 66 × 5

∴ Time taken by 6 men and 2 women to do the same job = (66 × 5)/(6 × 3 + 2 × 2)

⇒ (66 × 5)/22 

⇒ 15 days

Given:

3 sec θ + 4 cos θ - 4√3 = 0, where θ is an acute angle.

Calculation:

3 sec θ + 4 cos θ - 4√3 = 0 

⇒ 3 × 1/cos θ + 4cos θ = 4√3

⇒ 3 + 4 cos²θ = 4√3 × cos θ

⇒ 4 cos2θ - 2√3cos θ  - 2√3cos θ + 3 = 0

⇒ 2cos θ(2cos θ - √3) -√3(2cos θ - √3) = 0

⇒ (2cos θ - √3)² = 0

⇒ cos θ = √3/2

⇒ cos θ = cos 30°

∴ θ = 30°

Alternate MethodBy Value Putting Method

For θ = 30°; 3 sec θ + 4 cos θ - 4√3 = 0

For θ = 20°; 3 sec θ + 4 cos θ - 4√3 ≠ 0

For θ = 60°; 3 sec θ + 4 cos θ - 4√3 ≠ 0

For θ = 45°; 3 sec θ + 4 cos θ - 4√3 ≠ 0

Formulas used:

Simple Interest = P × r × t/100 

Amount = Simple Interest + Principal

Calculation:

Let year be t and principal be P

As per the question;

(t + 2) × 6% = t × 10%

⇒ 6% t + 12% = 10% t 

⇒ 12% = 4% t 

⇒ t = 3

Amount = Principal + Simple Interest 

⇒ P + P × 6/100 × 5 = 1105

⇒ P + 3/10 × P = 1105

⇒ 13P/10 = 1105

⇒ P = 1105 × 10/13

∴  P = Rs.850

Given:

30a68b (a > b) is divisible by 11

Concept:

If the difference between the sum of the digits at the odd and even places equal 0 or divisible by 11, the number is divisible by 11.

Calculation:

(3 + a + 8) - (0 + 6 + b) = 0 or 11

⇒ 11 + a - 6 - b = 0 or 11

⇒ 5 + a - b = 0 or 11

⇒ 5 + a - b ≠  0  [a > b]

Let 5 + a - b = 11 

⇒ a - b = 6 

⇒ For a = 9, b = 3      ∵  [a > b]

⇒ 9 - 3 = 6

∴ The greatest value of b is 3, when 30a68b (a > b) is divisible by 11.

Mistake PointsDon't get confused about the value of 'b'.

We need to look at the 'boundary condition' given in the question i.e. a > b

Thus, b cannot be more than a.

The correct answer is 'Bit.' 

Key Points

• The given word 'IOTA' means a very small amount. (अत्यंत छोटी मात्रा; तनिक मात्रा, लेशमात्र)
• ​Let's see the meaning of other given options:-
• 'Bag' means a lot of something; plenty of something. (भरपूर, काफ़ी)
• 'Lot' means a large number or amount. (एक बड़ी संख्या या राशि)
• 'Box' means a container with a flat base and sides, typically square or rectangular, and having a lid. (डिब्बा, चौखटा)
• 'Bit' means a small piece, amount, or part of something. (किसी वस्‍तु आदि का छोटा टुकड़ा, मात्रा या अंश)
  

Hence, the correct answer is option 4.

Additional Information

• The synonyms of the word 'IOTA' are "bit, little, ounce".
• The antonyms of the word 'IOTA' are "aggregate, mass, whole".

The correct answer is 'were rotten.'​

Key Points

• In the underlined part of the sentence, the singular form of the verb 'was' is incorrect.
• The subject of the sentence is composed of the plural noun 'apples'.
• We know that a plural subject always takes a plural verb.
• Therefore, the plural form of the verb 'were' should be used in place of the singular form 'was'.
  

Hence, the correct answer is option 1.

Correct sentence: Many of the apples were rotten.

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Additional Information

• Subjects and verbs must agree with one another in number (singular or plural).
• Thus, if a subject is singular, its verb must also be singular; if a subject is a plural, its verb must also be plural.
  

Hinglish

• वाक्य के रेखांकित भाग में 'was' क्रिया का एकवचन रूप गलत है।
• वाक्य का subject, बहुवचन संज्ञा 'apples' से बना है।
• हम जानते हैं कि बहुवचन subject हमेशा बहुवचन क्रिया लेता है ।
• इसलिए, क्रिया का बहुवचन रूप 'were' एकवचन रूप 'was' के स्थान पर प्रयोग किया जाना चाहिए।
  

अत: सही उत्तर विकल्प 1 है ।

सही वाक्य: Many of the apples were rotten.

The correct answer is 'BDCA'.

Key Points

• The sentence 'B' is independent of any other sentence as it is giving general information about "a man". Hence, 'B' is the first part.
• Sentence D will come after B because it explains what the man decided to do after he went away from home and whether he succeeded in it or not.
• Sentence C will come after D because it explains how the man reacted after he failed to send the letter to his family.
• The sentence 'A' is the concluding part because it explains what the man finally decided to do.
  

Paragraph after rearranging the sentences: A man went away from his home. One day he wrote a letter to his family, but could not find anyone to take the letter to his town. Disappointed, he decided to take it himself. When he reached his town, he went to his house and knocked at the door.

Additional Information 

• Important Rules to Solve the Para Jumbles:
• Read the sentences attentively and try to comprehend the idea or theme of the sentence and eliminate the irrelevant options.
• Try to identify the opening (independent sentence) and closing sentences (concluding sentence).
• Try to identify the mandatory pairs. Two sentences can be connected through various connectors and other determinants.
  

Hinglish

• वाक्य 'B' किसी अन्य वाक्य से स्वतंत्र है क्योंकि यह "एक आदमी" के बारे में सामान्य जानकारी दे रहा है। अतः 'B' पहला भाग है।
• वाक्य D, B के बाद आएगा क्योंकि यह बताता है कि घर से चले जाने के बाद आदमी ने क्या करने का फैसला किया और वह उसमें सफल हुआ या नहीं।
• वाक्य C, D के बाद आएगा क्योंकि यह बताता है कि अपने परिवार को पत्र भेजने में विफल रहने के बाद आदमी ने कैसे प्रतिक्रिया दी।
• वाक्य 'A' समापन भाग है क्योंकि यह बताता है कि आदमी ने आखिरकार क्या करने का फैसला किया।

The correct answer is 'Humble.'

Key Points

• The given word 'Pompous' means showing that you think you are more important than other people. (स्‍वयं को दूसरों से अधिक महत्वपूर्ण समझते हुए और भाषा व्‍यवहार में इसका प्रदर्शन करते हुए; गर्वित, आडंबरपूर्ण)
• ​Let's see the meaning of other given options:-
• 'Showy' means having a striking appearance or style. (प्रभावशाली, शानदार)
• 'Boastful' means showing too much pride. (शेख़ीबाज़, आत्‍मश्‍लाघी, घमंडी)
• 'Flaunting' means to show something that you are proud of so that other people will admire it. (किसी बात पर इतराना)
• 'Humble' means not thinking that you are better or more important than other people. (विनम्र, विनीत; घमंडी नहीं)
  

Hence, the correct answer is option 4.

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Additional Information

• The antonyms of the word 'Humble' are "pompous, lordly, impudent".
• The synonyms of the word 'Humble' are "modest, submissive, meek".

The correct answer is 'Feel terribly ashamed and sorry.'

Key Points

• Given Idiom: Want to curl up and die means to feel very ashamed and sorry. (बहुत शर्म और खेद महसूस करना)
• Example: I just wanted to curl up and die when I spilled coffee on her new dress!
• From the given options, the third option is the most appropriate meaning of the given idiom.
  

Hence, the correct answer is option 3.

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Mistake Points

• We may think from the phrase "Want to curl up and die" that it is all about someone wanting to stop living.

The correct answer is 'Neice'.

Key Points

• Let us explore the options:-
• 'Friend' means a person with whom one has a bond of mutual affection. (मित्र, दोस्‍त)
• 'Fiery' means quick to become angry. (ग़ुस्‍सैल; तुरंत क्रोधित हो जाने वाला)
• 'Scenic' means having beautiful scenery. (सुंदर दृश्‍यों वाला)
• 'Neice': There is no such word in English or we can say that there is some spelling mistake in this word.
• ​The correct spelling is 'Niece' and it means the daughter of your brother or sister. (भतीजी या भाँजी)
  

Hence, the correct answer is option 4.

Additional Information

• Example of 'Niece' in a sentence:
• His niece is attractive and mature for her age.

The correct answer is 'rate.'

Key Points

• The given sentence is saying something about why there is no population problem in the advanced nations. (दिया गया वाक्य इस बारे में कुछ कह रहा है कि विकसित देशों में जनसंख्या की समस्या क्यों नहीं है)
• Rate means a measurement of the speed at which something happens or the number of times something happens or exists during a particular period. (दर)
• Example: The government predicted a growth rate of 7.8 percent in the year 2022.
  

Conclusion: The advanced nations do not have to worry about the population problem because they are already settling down to zero growth rate of the population. (उन्नत राष्ट्रों को जनसंख्या की समस्या के बारे में चिंता करने की ज़रूरत नहीं है क्योंकि वे पहले से ही जनसंख्या की शून्य वृद्धि दर पर बस रहे हैं)

Hence, the correct answer is option 2.

Complete Sentence: The advanced nations face no population problem since they were already settling down to zero growth rate in the population.

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Additional Information

• Let us explore the other options:
• Frequency means the number of times something happens in a particular period. (विशेष अवधि में होने वाली किसी क्रिया की आवृत्ति संख्‍या; बारंबारता)
• Scale means the size of something, especially when compared to other things. (किसी वस्‍तु का आकार, पैमाना विशेषतः तुलनात्‍मक दृष्टि से)
• Degree means a certain amount or level. (एक विशेष मात्रा या स्‍तर)