SSC CGL 2021 Tier-I (Held On : 12 April 2022 Shift 2) (Previous Year Paper)

According to BODMAS rule

Given equation 88 * 120 * 42 * 240 * 48 * 2

Option 1 : Using the combination =, ×, +, ÷, –

88 = 120 × 42 + 240 ÷ 48 – 2

By BODMAS rule

88 = 120 × 42 + 5 – 2

88 = 5040 + 5 – 2

88 = 5045 - 2

88 ≠ 5043 (LHS ≠ RHS)

Option 2 : Using combination ×, ÷, =, –, +

88 × 120 ÷ 42 = 240 - 48 + 2

88 × 2.85 = 240 - 48 + 2

251.42 = 240 – 48 + 2

251.42 = 242 – 48

251.42 ≠ 194 (LHS ≠ RHS)

Option 3 : Using the combination +, ÷, –, =, ×

88 + 120 ÷ 42 - 240 = 48 × 2

88 + 2.85 - 240 = 48 × 2

88 + 2.85 - 240 = 96

90.85 – 240 = 96

• 149.15 ≠ 96 (LHS ≠ RHS)

Option 4 : Using the combination =, –, +, ÷, ×

88 = 120 - 42 + 240 ÷ 48 × 2

88 = 120 - 42 + 5 × 2

88 = 120 - 42 + 10

88 = 130 - 42

88 = 88 (LHS = RHS)

Hence, the answer is Option 4: “=, –, +, ÷, ×”.

The Venn diagrams best represent the relationship between - Peso, Currency, and Taka figures are shown below:

• Peso is an official national currency and is used in the Philippines.
• The Taka is an official national currency and is used in Bangladesh

Hence, ‘Option 4’ is the correct answer.

The logical and meaningful order of the given words is as follows:

LOGIC: The words have been arranged according to the book format.

4. Cover Page:- It is one of the first pages you encounter after you open the book where title is written.
5. Preface:- After cover page a preface page is written from the point of view of the book author.
6. Chapter list:- After preface page the contents list of a book show list of different chapters and sections.
7. Chapters:- After the content list of chapters comes details of chapter.
8. Bibliography:- Last page of any book where written sources of information on a book called bibliography.

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

The pattern followed here is:

Alternate Prime number added in series- 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67

 

Hence, '350' is the correct answer.

Given:

 

Here the pattern followed in each column is:

1st number + 2nd number – 3rd number = 4th number

Column 1: 18, 7, 8, 17

1st number + 2nd number – 3rd number

= 18 + 7 - 8

= 25 - 8

= 17 = 4th number

Column 3: 19, 9, 14, 14

1st number + 2nd number – 3rd number

= 19 + 9 - 14

= 28 - 14

= 14 = 4th number

Similarly,

Column 2: 24, 8, 11, ?

1st number + 2nd number – 3rd number

= 24 + 8 – 11

= 32 - 11

= 21 = 4th number

Hence, the correct answer is “21”.

According to the BODMAS rule:

Option 1 : ÷ and −

Given:

23 + 84 ÷ 14 × 8 − 3 = 5

After interchange the signs;

23 + 84 - 14 × 8 ÷ 3 = 5

By BODMAS rule

23 + 84 - 14 × 2.67 = 5

23 + 84 – 37.34 = 5

107 – 37.34 = 5

69.66 ≠ 5 (LHS ≠ RHS)

Option 2 : + and ×

Given: 

23 + 84 ÷ 14 × 8 − 3 = 5

After interchange the signs;

23 × 84 ÷ 14 + 8 − 3 = 5

By BODMAS rule

23 × 6 + 8 − 3 = 5

138 + 8 – 3 = 5

146 – 3 = 5

143 ≠ 5 (LHS ≠ RHS)

Option 3: − and ×

Given:

23 + 84 ÷ 14 × 8 − 3 = 5

After interchange the signs;

23 + 84 ÷ 14 - 8 × 3 = 5

By BODMAS rule

23 + 6 - 8 × 3 = 5

23 + 6 - 24 = 5

29 – 24 = 5

5 = 5 (LHS = RHS)

Option 4: − and +

Given:

23 + 84 ÷ 14 × 8 − 3 = 5

After interchange the signs;

23 - 84 ÷ 14 × 8 + 3 = 5

By BODMAS rule

23 - 6 × 8 + 3 = 5

23 – 48 + 3 = 5

26 – 48 = 5

• 22 ≠ 5 (LHS ≠ RHS)

Hence, the answer is Option 3: “− and ×”.

Table show alphabet serial number –

The pattern followed is,

Hence, “URH” is the complete series.

The correct mirror image of the given figure when the mirror is held at the right side is:

Hence, "option (2)" is the correct answer.

Additional Information

Given:

Seven friends sitting around a circular table with their backs towards the centre this means they are facing outside the centre: Subhi, Prince, Ketan, Vishal, Mahima, Krish and Naitik,

1. Subhi is sitting to the immediate right of Prince.

2. Vishal is sitting third to the left of Prince.

3. Mahima is sitting to the immediate right of Vishal.

4. Naitik and Krish are not sitting to the immediate left or right of Vishal.

Only Ketan is left so the final sitting arrangement is:

Thus, “Ketan” is sitting third to the right of Prince.

Preparing the family tree using the following symbols,

Given:

1. E is the sister of C.

2. C is the only son of F, who is the wife of D.

3. H is the only daughter-in- law of D.

4. B and G are the sons of H. 

Hence, G is the "Grandson" of F.

Statements:

1. All flowers are blue.
2. All blue are good.
3. No good is red.

The least possible diagram for the given statements is as follows

Conclusions:

I. No red is a flower → True (because all flowers are good and no good is red so no red is a flower)

II. No red is a blue → True (because all blue are good and no good is red so no red is a blue)

III. Some good are flowers → True (because all flowers are good so definitely some good are flowers)

IV. Some good are blue → True (because all blue are good so definitely some good are blue)

Hence, “All conclusions I, II, III and IV follow".

Given:

Five boxes A B C D and E

1. B is thrice as heavy as A.

=> B = 3A ---------- eq. (i)

2. C is 40 kg heavier than E.

=> C = 40 + E ---------- eq. (ii)

3. D is three and a half times as heavy as E.

=> D = 3.5E ---------- eq. (iii)

4. C is five times as heavy as A.

=> C = 5A ---------- eq. (iv)

5. The weight of E is 40 kg.

=> E = 40 kg ---------- eq. (v)

Putting the value if E in eq. (ii) and (iii)

=> C = 40 + E = 40 + 40 = 80 kg ---------- eq. (vi)

=> D = 3.5E = 3.5 × 40 = 140 kg ---------- eq. (vii)

Putting the value of C in eq. (iv)

=> C = 5A

=> 80 = 5A

=> A = 80 ÷ 5

=> A = 16 ---------- eq. (viii)

Putting the value of A is eq. (i)

=> B = 3A = 3 × 16 = 48 ---------- eq. (ix)

From eq. (vi), (vii), (viii) and (ix)

=> 16 < 40 < 48 < 80 < 140

So, A < E < B < C < D

Hence, “A” is the lightest of all and its weight is "16 kg".

The embedded part of this image is:

Hence, option (2) is the correct answer.

Given: j _ m b _ a _ _ u _ b _ a d j _ m _ b _ d

By checking options and substituting accordingly.

1)  u b m j m b u b a → j u m b b a m - j u m b b a d - j u m b b a d

2)  u b d j m b j b a → j u m b b a d - j u m b b a d - j j m b b a d

3)  u b d j m b u b a → j u m b b a d - j u m b b a d - j u m b b a d

• Here " j u m b b a d" is repeated itself.

4)  u b d j m b u m a → j u m b b a d - j u m b b a d - j u m m b a d

• Option (3) gives a pattern of j u m b b a d - j u m b b a d - j u m b b a d.

Hence, ‘u b d j m b u b a’ is the correct answer.

Mistake Points

Please note that the question is about rotating the option figure and NOT the question figure.

The question asked to find the options figure which is the same as the question figure after rotation.

So, We have to rotate the given options to get the question figure.

The rotation is 270° anticlockwise and then 45° clockwise.

= 270° - 45° = 225° (Anticlockwise)

This means we can directly rotate the figure at 225° anticlockwise.

Given:

Check option (1)

1. Figures when rotated 270° anticlockwise

2. Then 45° clockwise.

Hence, "Option (1)" is the correct answer.

The pattern followed here is:

Hence, '82' is the correct answer.

The pattern followed here is:

(1^st number × 5) + 2 = 2^nd number

Now follow the steps:

3 : 17

= (3 × 5) + 2

= 15 + 2 

= 17 = 2^nd number

And,

9 ∶ 47

= (9 × 5) + 2

= 45 + 2 

= 47 = 2^nd number

Similarly,

6 ∶ ?

= (6 × 5) + 2

= 30 + 2 

= 32 = 2^nd number

Hence, "32" is correct answer.

According to the given information

 

‘so’ is coded as 'lor'.

Hence, 'lor’ is the correct answer.

The table is alphabets place value:

The pattern followed here is:

‘TANKER’ is written as ‘VCPMGT’

Similarly,

SOCRATES is written as

Hence, 'SOCRATES' is coded as "UQETCVGU".

The table is alphabets place value:

The pattern followed here is:

UPRIGHT : PUVEKTH

Similarly,

DESTROY ∶ ?

Hence, 'DESTROY' is coded as "EDWPVYO".

• A cube of side 80 cm is painted yellow on all the faces and then cut into smaller cubes of sides 8 cm each.

• The number of smaller cube having all the three faces painted.

 

 

All corner cubes are painted on three sides there are 8 corners in cubes.

So, cubes with paint on 3 sides = 8

Hence, "8" is the correct answer.

Additional Information

If a cube has been painted red, blue, and black on pairs of opposite faces and divide it into X parts.

1. Total number of cubes = X³

2. Cubes that have three faces painted = 8 (Because there are only 8 corners in the cube)

3. Cubes which has only two faces painted = (X - 2) × No of Edges (12)

4. Cubes that have only one face painted = (X - 2)² × 6

5. Cubes that have no face painted = (X - 2)³

Table show alphabet serial number –

The pattern followed is,

All follow the same pattern, except 'CJQY’.

Hence, “CJQY” is the odd one.

The figure that will replace the question mark (?) in the following figure series is shown below:

1. Middle arrow rotates anticlockwise direction.

2. Heart and rhombus shape rotate anticlockwise square corner to corner and this figure also rotates anticlockwise at its own position

 

Final series is

Hence, ‘option 3’ is the correct answer.

The image obtained when the paper is unfolded is,

Hence, option 2 is the correct answer.

The pattern followed here is:

 ‘PARK’ is coded as ‘3749’

And,

‘RACE’ is coded as ‘4762’

So the code for C=6, A=7, R=4,E=2

Similarly,

‘CARE’’ = ?

Hence, ‘CARE’’ is coded as "6742".

The correct answer is Singapore.

Key Points

• Singapore has given U.S. start-up Eat Just the green light to sell its lab-grown chicken meat.
• It is the world's first regulatory approval for clean meat that does not come from slaughtered animals.
• Demand for alternatives to regular meat is surging due to consumer concerns about health, animal welfare and the environment.

Additional Information

• Singapore: 
• Capital - Singapore City.
• Currency - Singapore dollar.
• President - Halimah Yacob.
• National Sport - Football.

The correct answer is 56th Amendment.

Key Points

• 56th Amendment Act, 1987 of the Indian Constitution conferred Statehood on Goa and forms a new Union Territory of Daman and Diu.
• Goa thus became the 25th State of the Indian Republic.

Additional Information

• 52nd Amendment:
• 52nd Amendment Act, 1985 of the Indian Constitution provided provisions related to anti-defection in India.
• In this amendment, articles 101, 102, 190 and 191 were changed.
• It laid down the process by which legislators may be disqualified on grounds of defection and inserted the tenth schedule.
• 59th Amendment:
• 59th Amendment Act, 1988 of the Indian Constitution empowered the Central Government to impose an Emergency in Punjab when deemed necessary.
• Under the amendment, the President's rule can be extended up to three years.
• 48th amendment Act, 1984:
• Facilitated the extension of the President's rule in Punjab beyond one year without meeting the two special conditions for such extension.

The correct answer is Vinesh Phogat.

Key Points

• Vinesh Phogat won the Ukraine Wrestling Tournament in February 2021.
• Vinesh Phogat is an Indian wrestler who comes from a successful family of wrestlers, with her cousins Geeta Phogat and Babita Kumari, being international wrestlers and Commonwealth Games medalists as well.
• She became the first Indian woman wrestler to win Gold in both Commonwealth and Asian games.
• She has been honoured with the Rajiv Gandhi Khel Ratna Award in 2020.
• She is also conferred with the Arjuna Award.

Additional Information

• Some important sport's person associated with the game:

​The correct answer is Brain drain.

Key Points

• Brain drain is the emigration of a significant proportion of a country’s highly-skilled, highly educated professional population to other countries offering better economic and social opportunities.
• It is defined as the migration of health personnel in search of a better standard of living and quality of life, higher salaries, access to advanced technology and more stable political conditions in different places worldwide.

Additional Information

• The demographic transition theory is a generalized description of the changing pattern of mortality, fertility, and growth rates as societies move from one demographic regime to another. 
• The demographic transition shows shifts in the demographics of a population during economic and social development.
• The term closed population refers to a population with no migratory flow in or out so that changes in the population occur through births and deaths only.

​The correct answer is Coulomb’s Law.

Key Points

• Coulomb’s Law talks about the magnitude of the attraction between the two charges.
• It says that the force is directly proportional to the product of the quantity of the two charges.
• F ∝ q1q2, where (F is Force, q1 and q2 are charges).
• It is also inversely proportional to the square of the distance between them.
• i.e., F ∝ 1/r2 where (F is Force, r is the distance between the charges).
• Thus, the equation is
• $F; = ;k\frac{{{q_1}{q_2}}}{{{r_2}}};$where k is the proportionality constant and is equal to 9 × 109 Nm2/C2.
• The Law was given by Charles-Augustin de Coulomb in the year 1784.

Additional Information

• Lenz's law states that the direction of the induced current in the coil will be always in such a way that it opposes the change which produces the current.
• According to Gauss law, the total electric flux linked with a closed surface called Gaussian surface is $\frac{1}{ϵ_o}$ the charge enclosed by the closed surface.
• Ohm’s law states that at a constant temperature, the current through a conductor between two points is directly proportional to the voltage across the two points.

The correct answer is ​4%.

Key Points

• Current Repo Rate: 6.5 %, Reverse Repo Rate- 3.5 %
• The Repo rate is given by the Reserve Bank of India’s (RBI) Monetary Policy Committee (MPC) as of 7 April 2021 is 4%.
• The Reserve Bank of India (RBI) increased the policy repo rate by 40 basis points to 4.40 per cent w.e.f 21 May 2022.
• The Monetary Policy Committee (MPC) has unanimously voted to increase the policy repo rate by 40 basis points or 0.40 per cent.
• Cash Reserve Ratio (CRR) raised by 50 bps to 4.50% effective May 21.
• Standing Deposit Facility (SDF) adjusted to 4.15% while Marginal Standing Facility (MSF) to 4.65%.

Additional Information

• Repo Rate:
• ​It is a rate at which the central bank (RBI) lends money to its clients against government securities.
• Reverse Repo:
• ​It is the rate at which the central bank (RBI) borrows money from its clients.
• Cash Reserve Ratio (CRR):
• The RBI (Amendment) Bill, 2006, empowers RBI to prescribe CRR–Cash that banks deposit with the RBI without any floor rate or ceiling rate.
• Statutory Liquidity Ratio (SLR):
• It is the ratio of a liquid asset, which all commercial banks have to keep in the form of cash, gold, and unencumbered approved securities equal to not more than 40% of their total demand and time deposit liabilities (ranges is 25‑40%).
• Bank Rate:
• It is also called the rediscount rate. It is the rate, at which the RBI gives finance to commercial banks.

The correct answer is Hemp

Key Points

• The word Bhangra is derived in the context of Bhangra Dance, from the word hemp.
• The dance was associated primarily with the spring harvest festival Baisakhi, and it is from one of the major products of the harvest—bhang (hemp).
• The term bhangra originally designated a particular dance performed by Sikh and Muslim men in the farming districts of the Punjab region of South Asia.​

Additional Information

The correct answer is ​Ceres.

Key Points

• The asteroid belt is a circumstellar disc in the Solar System.
• The asteroid belt is occupied by numerous irregularly shaped bodies called asteroids or minor planets.
• Ceres is the asteroid belt's only dwarf planet.
• Asteroids orbit the Sun and are small bodies in the solar system.
• They are made up of metals and rocks and also consist of organic compounds.
• They are found between the orbits of Mars and Jupiter.
• Four largest asteroids
• Ceres
• Vesta
• Pallas
• Hygiea

The correct answer is Dendroclimatology

Key Points

• Dendroclimatology is concerned with constructing records of past climates and climatic events by analysis of tree growth characteristics, especially growth rings.
• It is the analysis of tree ring growth patterns to determine past climate variations.

Additional Information

• Bioclimatology (biometeorology) is the study of the relationships between climate (weather) and living organisms.
• Historical climatology is the study of historical changes in climate and their effect on civilization from the emergence of homininis to the present day.
• Climatology is the study of climate and how it changes over time.

The correct answer is ​Kanailal Dutta.

Key Points

• Kanailal Dutta was arrested by the British as an accused in the Alipore Bomb Conspiracy Case.
• He was a revolutionary in India's freedom struggle belonging to the Jugantar group.
• He was born in Chandannagar, West Bengal.

Additional Information

• Alipore Conspiracy case, 1908: Also referred to as the Muraripukur conspiracy, or the Manicktolla bomb conspiracy, was a criminal case held in India in 1908.
• The case saw the trial of a number of Indian nationalists of the Anushilan Samiti in Calcutta, under charges of "Waging war against the Government" of the British Raj.
• The trial was held at Alipore Sessions Court, Calcutta, between May 1908 and May 1909.
• Among the famous accused were Aurobindo Ghosh, his brother Barin Ghosh as well as 38 other Bengali nationalists of the Anushilan Samiti.

​The correct answer is Zahiruddin.

Key Points

• Babur (Zahiruddin Muhammad) is the founder of the Mughal Empire in India.
• He was a descendant of Timur (on his father’s side) and Genghis Khan (on his Mother’s side).
• His original name was Zahiruddin Muhammad.
• In 1494 at the age of 11, Babur became the ruler of Farghana (at present in Chinese Turkistan) succeeding Umar Shaikh Mirza, his father.

Additional Information

• Babur
• He is the founder of the Mughal Empire.
• He fought the first Battle of Panipat in 1526 with Ibrahim Lodhi and laid the foundation of the Mughal Empire.
• His autobiography Tuzuk-i-Babri was written in the Turkish Language.
• In 1527 his general Mir Baki built Babri Maszid.
• He died in 1530.
• Humayun
• He was the son of Babur.
• He was a mathematician and astronomer.
• His biography Humayunama was written by his sister Gulbadan Begum.
• Akbar
• He was born in 1542 at Amarkot.
• He fought the second battle of Panipat in 1556 with Hemu and he defeated Hemu.
• He abolished the religious tax Jizya.
• He founded a new religion "Din-i- Allahi".
• His biography was written by Abul Fazal " Ain-i-Akbari".

The correct answer is Sreeshankar Murali.

Key Points

• Murali Sreeshankar broke his own national record and won the gold medal in the Federation Cup Senior National Athletics Championships in Patiala, Punjab in March 2021.
• He jumped for 8.26 meters.
• After this, he secured his berth for the Tokyo Olympics 2021.
• Murali Sreeshankar was born in Palakkad, Kerala on March 27, 1999.

Additional Information

• Tokyo Olympics 2020 was an international multi-sport event held from 23 July to 8 August 2021 in Tokyo, Japan, with some preliminary events that began on 21 July.​
• India finished 48th on the medal tally in Tokyo, its highest ranking in over four decades.
• India marched at the 21st number with the boxer Mary Kom and men’s hockey captain Manpreet Singh as flag-bearers.
• The teams entered the stadium in alphabetical order according to the language selected by the organizing committee, generally the dominant language in the host city.
• The 2024 Summer Olympics will be held in Paris.
• And all the way out in 2028, Los Angeles will play host.

The correct answer is 2003.

Key Points

• In 2003 India's ratio of public debt to GDP gone up to a record 84.2%.
• The N. K Singh committee on fiscal consolidation recommended that the government should target a fiscal deficit of 3 per cent by March 31, 2020, cut it to 2.8 per cent in 2020-21 and to 2.5 per cent by 2023.
• The Committee suggested using the public debt to GDP ratio as a medium-term anchor for fiscal policy in India.
• The committee advocated for a combined Debt to GDP ratio of 60% to be targeted by 2023, with a 40% limit for the centre and a 20% limit for the states.

The correct answer is Vikas Swarup.

Key Points

• Vikas Swarup is the author of the novel ‘Q and A’.
• Vikas Swarup served as the Secretary of the Ministry of Foreign Affairs, India, and previously worked in Canada as the High Commissioner of India and was the official spokesperson for the Ministry of Foreign Affairs of India.
• He is a 1986-batch officer of the Indian Foreign Service and is at present India’s High Commissioner in Ottawa.

Additional Information

• Prof. Muchkand Dubey is the President of CSD (Council for Social Development).
• ​Jyotindra Nath Dixit is the author of Bharatiya Videsh Neeti, India-Pakistan in War and Peace, Bharat-Pak Sambandh.

The correct answer is Vidisha Baliyan.

Key Points

• Vidisha Baliyan became the first Indian to win the Miss Deaf World title.
• Vidisha Baliyan is an Indian female deaf model and a retired tennis player.
• She wins the Miss Deaf World title in 2019.
• She is from Uttar Pradesh's Muzzafarnagar city.
• She has represented India at the 2017 Summer Deaflympics and at the 2019 Miss & Mister Deaf World contest.
• She also won the title of Miss Deaf India in February 2019 in Assam, Guwahati.

Additional Information

• Arunima Sinha is the World's first female amputee to scale Mount Everest, Mount Kilimanjaro (Tanzania), Mount Elbrus (Russia), Mount Kosciusko (Australia), and Mount Aconcagua (South America), Carstensz Pyramid (Indonesia), and Mount Vinson.
• Preethi Srinivasan was a cricket player for the Tamil Nadu women's cricket team.
• Raghavi Shankar is founder of started The Headway Foundation and the aim is to help, mentor, and encourage the disabled.
• Ravi Shankar KBE was an Indian sitarist and composer.

​The correct answer is 2005.

Important Points

• An amendment to the Hindu Succession Act, 1956 was passed in the year 2005.
• The Hindu Succession (Amendment) Act, 2005 (39 of 2005) was enacted to remove gender discriminatory provisions in the Hindu Succession Act, 1956.
• Under the amendment, the daughter of a coparcener shall by birth become a coparcener in her own right in the same manner as the son.
• The daughter shall now have the same rights in the coparcenary property (ancestral property of the Hindu undivided family) as a son.
• This amendment also repeals Section 23 of the Hindu Succession Act which disentitled a female heir to ask for partition in respect of a dwelling house, wholly occupied by a joint family, until the male heirs choose to divide their respective shares.
• Section 24 of the Act which denied the rights of a widow to inherit her husband‟s property upon her re-marriage has been repealed.
• This Act has brought about a central amendment that is applicable to all state governments.

The correct answer is ​Germanium.

Key Points

• Silicon and germanium are not suitable because those junctions produce heat and no appreciable IR or visible light.
• Hence Germanium is NOT suitable for the fabrication of a light-emitting diode structure.

Additional Information

• The LED (light-emitting diode) is a PN junction device that emits light when a current passes through it in the forward direction, i.e. when LED is forward biased, it emits light.
• In an LED, this energy lies in the visible region of electromagnetic radiation, and the photon released is perceived as light.
• The compound semiconductor Gallium Arsenide – Phosphide is used for making LEDs of different colours.
• Gallium Arsenide is used for making infrared LED.
• Gallium phosphide, Indium gallium nitride, and Gallium arsenide are used for the fabrication of a light-emitting diode.
• LEDs are generally fabricated with Direct Band Gap (DBG) semiconductors like GaAs, GaAsP, and GaP.

The correct answer is One.

Key Points

• As per the Economic Survey, 2020, Only one bank in India are there on the list of the top global 100.
• India being the fifth largest economy, India should have at least six banks in the top 100 global list, and at least eight would be required for a country having a $5-trillion economy.
• Chief Economic Adviser-K V Subramanian said (in 2020) that India needs more global-sized banks to help the country achieve a $5 trillion economy by 2024-25.
• State Bank of India (SBI) at the 55th position is the only bank on the global top 100 list.
• China has 18 banks while the US has 12 on the list.

The correct answer is 23.

• Bhagat Singh was a 23-year-old revolutionary when he was hanged till death.
• Bhagat Singh was an Indian communist revolutionary whose two acts of spectacular brutality against the British in India and execution at the age of 23 made him a famous hero of the Indian independence movement.

Additional Information

• The freedom fighters Bhagat Singh, Sukhdev, and Rajguru were hanged to death in 1931.
• In December 1928, Bhagat Singh and an associate, Shivaram Rajguru, fatally shot a 21-year-old British police officer, John Saunders in Lahore.
• Surfacing again in April 1929, Bhagat Singh and Batukeshwar Dutt, set off two homemade bombs inside the Central Legislative Assembly in Delhi.
• 23 March is observed as Shaheed Diwas (Martyr's Day).
• In India, shaheed Diwas is observed twice a year - one is on 23 March and the other on 30 January, the day when Mahatma Gandhi was assassinated.

The correct answer is SDG 15.

Key Points

• Sustainable Development Goals (SDG)15 seeks to ‘Protect, restore and promote sustainable use of terrestrial ecosystems, sustainably manage forests, combat desertification, and halt and reverse land degradation and halt biodiversity loss.
• The United Nations General Assembly adopted the "2030 Agenda for Sustainable Development" in 2015, with global goals.
• The 193 members of GA  adopted the framework "Transforming our world: the 2030 Agenda for Sustainable Development" with 17 goals & 169 targets.

Additional Information

• Those 17 goals are:
• GOAL 1: No Poverty
• GOAL 2: Zero Hunger
• GOAL 3: Good Health and Well-being
• GOAL 4: Quality Education
• GOAL 5: Gender Equality
• GOAL 6: Clean Water and Sanitation
• GOAL 7: Affordable and Clean Energy
• GOAL 8: Decent Work and Economic Growth
• GOAL 9: Industry, Innovation and Infrastructure
• GOAL 10: Reduced Inequality
• GOAL 11: Sustainable Cities and Communities
• GOAL 12: Responsible Consumption and Production
• GOAL 13: Climate Action
• GOAL 14: Life Below Water
• GOAL 15: Life on Land
• GOAL 16: Peace and Justice Strong Institutions
• GOAL 17: Partnerships to Achieve the Goal

The correct answer is Intercellular spaces are present.

Key Points

• The characteristic features of permanent tissue are:
• Cells have intercellular spaces to keep them separated.
• The cells may be living or dead, i.e.the protoplasm is either present or absent.
• Tissue may have only one type of cell or may have different kinds of cells.
• The cell wall is either cellulosic or along with cellulose other complex carbohydrates may be present.
• Cells may vary in shape, i.e., either round or oval or polygonal, etc.
• In the living cells, the cytoplasm is present surrounding a large central vacuole.
• Cells do not divide at all.

Additional Information

• Types of permanent tissue:
• Permanent tissues are of three types, namely –
• (a) Simple tissue, (b) Complex tissue and (c) Secretory tissue.
• ​Simple permanent tissue
• Simple permanent tissue is composed of a single type of cells that have comparable origin, structure, and function.
• Types of simple permanent tissue
• Parenchyma – It  provides temporary support and maintains the shape of the plant body. They have thin-walled cells with large vacuoles.
• Collenchyma – It provides mechanical support and elasticity and flexibility to young dicotyledonous plants. They have thickened cell walls at corners, giving mechanical strength.
• Sclerenchyma – It provides strength and toughness to plant parts. They have dead cells with extremely thick walls (lignin deposition). Sclerenchyma may be either fibres or sclereids
• Complex permanent tissue
• Complex permanent tissue is composed of two or more two types of cells and contributes to a general function.
• They organize together to carry out similar particular functions in the plant body.
• It is also known as vascular tissue.
• Types of complex tissue:
• Xylem – The xylem tissue is accountable for the transmission of water and minerals from the roots to the leaves and stems.
• Phloem – This complex permanent tissue helps in the translocation of food that is prepared by photosynthesis in the leaves to diverse parts of the plant.

The correct answer is ​1956.

Key Points

• The States Reorganisation Act, 1956 was a major reform of the boundaries of India's states and territories, organizing them along linguistic lines.
• Although additional changes to India's state boundaries have been made since 1956, the States Reorganisation Act of 1956 remains the single most extensive change in state boundaries since the independence of India in 1947.
• The Act came into effect at the same time as the Constitution (Seventh Amendment) Act, 1956, which (among other things) restructured the constitutional framework for India's existing states and the requirements to pass the States Reorganisation Act, 1956 under the provisions of Part I of the Constitution of India, Article 3.

The correct answer is Only I and II.

Key Points

• Karnataka is the largest producer of coffee in the country.
• Karnataka accounts for nearly 71 per cent.
• Chikmagalur, Kodagu, and Hassan districts of Karnataka are the major coffee producer regions.
• Kerala is the second-largest producer of coffee in India.
• Hence Statement 1 is correct.
• Arabica, Robusta and Liberica are three common coffee beans used globally and they vary in flavour, price, body and caffeine content.
• Hence Statement 2 is correct.
• The Arabica is a variety of coffee is initially brought from Yemen.
• The Geographical Indications Registry has granted the Geographical Indication (GI) tag to Coorg Arabica Coffee(Karnataka), Wayanad Robusta Coffee(Kerela), Chikmagalur Arabica Coffee(Karnataka), Araku Valley Arabica Coffee(Andhra Pradesh), and Bababudangiris Arabica Coffee(Karnataka)
• Hence Statement 3 is incorrect.

The correct answer is Junagadh. 

Key Points

• Uparkot Buddhist Caves are located in Junagadh.
• Uparkot caves are ancient man-made caverns.
• The caves are a part of the Junagadh Buddhist Cave Groups.
• It is situated in the eastern part of Junagadh of Gujarat.

Additional Information

• Ajanta is a series of rock-cut caves in the Sahyadri ranges on the Waghora river near Aurangabad in Maharashtra.
• There are a total of 29 caves(all Buddhist).
• 25 caves were used as Viharas or residential caves while 4 were used as Chaitya or prayer hills.
• Kanheri caves are rock-cut caves related to Buddhism located in Sanjay Gandhi National Park, Maharashtra.
• These caves served as Viharas and Chaityas to the Buddhist monks.
• Ellora caves is a famous cave located in the Sambhajinagar (former Aurangabad) district of Maharashtra, India.
• It is one of the UNESCO World Heritage Sites in India.
• Designated as the UNESCO World Heritage Site in 1983.

The correct answer is tea.

Key Points

• Tea is a beverage made from the Camellia Sinensis plant.
• Tea (Camellia sinensis) belongs to the family Theaceae.
• The Centre of origin is China.
• Also known as Queen of beverage crop.
• The stimulative effect of tea is due to Caffeine (1.25 - 4.5%)
• Tea requires well-drained soil with a high amount of organic matter and a pH of 4.5 - 5.5.
• The performance of tea is excellent at elevations ranging from 1000 - 2500 m.
• Optimum temperature: 20 - 27°C.

Given:

The total number of students = 350

Calculation:

Arranging all values in a frequesncy chart:

 

Total number of students 

The text in the image is: ∑fi​xi​ = 350 

Also, ∑fi​xi = 300 + 900 + 2240 + 4050 + 6600 + 9750 + 8250 + 6800 + 2850 = 41740

The average marks (∑fi​xi / ∑fi​) = 41740/350 = 119.257... ≈ 119.3 (correct up to one place of decimal)

∴ The class average is 119.3

Shortcut Trick

In any quadrilateral ABCD, the angle formed by the bisectors of two adjacent angles is equal to half the sum of the other two angles:

∠CED = (∠A + ∠B) ÷ 2

Substitute the given values ∠CED = 57° and ∠A = 47°:

57° = (47° + ∠B) ÷ 2

⇒ 114° = 47° + ∠B

⇒ ∠B = 114° − 47° = 67°

∴ The correct answer is 67°.

Alternate Method

Given:

⇒ Quadrilateral ABCD where bisectors of ∠C and ∠D meet at E.

⇒ ∠CED = 57°

⇒ ∠A = 47°

Formula Used:

⇒ Angle sum property of a triangle: Sum of angles in a triangle = 180°

⇒ Angle sum property of a quadrilateral: Sum of interior angles in a quadrilateral = 360°

Calculations:

In ▵CED:

⇒ ∠CED + ∠ECD + ∠EDC = 180°

⇒ 57° + ∠ECD + ∠EDC = 180°

⇒ ∠ECD + ∠EDC = 180° − 57° = 123°

Since CE and DE are the angle bisectors of ∠C and ∠D respectively:

⇒ ∠ECD = ∠C ÷ 2

⇒ ∠EDC = ∠D ÷ 2

Substituting these into the equation:

⇒ (∠C ÷ 2) + (∠D ÷ 2) = 123°

⇒ (∠C + ∠D) ÷ 2 = 123°

⇒ ∠C + ∠D = 246°

Now, using the angle sum property of quadrilateral ABCD:

⇒ ∠A + ∠B + ∠C + ∠D = 360°

⇒ 47° + ∠B + 246° = 360°

⇒ ∠B + 293° = 360°

⇒ ∠B = 360° − 293° = 67°

Evaluation of Options:

⇒ Option (1) 47°: If ∠B = 47°, then ∠CED = (47° + 47°) ÷ 2 = 47°, which contradicts the given ∠CED = 57°.

⇒ Option (3) 77°: If ∠B = 77°, then ∠CED = (47° + 77°) ÷ 2 = 62°, which contradicts the given ∠CED = 57°.

⇒ Option (4) 57°: If ∠B = 57°, then ∠CED = (47° + 57°) ÷ 2 = 52°, which contradicts the given ∠CED = 57°.

⇒ Option (2) 67°: If ∠B = 67°, then ∠CED = (47° + 67°) ÷ 2 = 57°, which perfectly matches the given value.

∴ The correct answer is 67°.

Additional Information

Angle Bisector Theorem of Quadrilateral

The angle formed by the bisectors of two adjacent angles of a quadrilateral is equal to half the sum of the remaining two angles: ∠CED = (∠A + ∠B) ÷ 2.

Angle Sum Property of a Polygon

The sum of the interior angles of any closed polygon with n sides is (n − 2) × 180°. For a quadrilateral, this sum is always 360°.

Opposite Angle Bisectors

If the bisectors of two opposite angles of a quadrilateral intersect, the acute angle between them is equal to half the absolute difference of the other two angles: |∠B − ∠D| ÷ 2.

Given:

The given expression = 40 ÷ 5 of 2 × [18 ÷ 6 × (12 − 9) of 5 − (3 − 8)] ÷ 25

Calculation:

40 ÷ 5 of 2 × [18 ÷ 6 × (12 − 9) of 5 − (3 − 8)] ÷ 25

= 40 ÷ 10 × [18 ÷ 6 × 3 of 5 − (- 5)] ÷ 25

= 4 × [18 ÷ 6 × 3 of 5 + 5] ÷ 25

= 4 × [18 ÷ 6 × 15 + 5] ÷ 25

= 4 × [3 × 15 + 5] ÷ 25

= 4 × [45 + 5] ÷ 25

= 4 × 50 ÷ 25

= 4 × 2

= 8

∴ The value of the expression is 8

Shortcut Trick

A's 100% time = 15 × 4 = 60 days.

B's 100% time = 30 × (100/75) = 40 days.

Combined time for 100% work = (60 × 40) ÷ (60 + 40) = 24 days.

Time for 50% work = 24 ÷ 2 = 12 days.

∴ The correct answer is 12 days.

Alternate Method

Given:

Work done by A = 25% in 15 days.

Remaining work = 100% − 25% = 75%.

Work done by B = 75% in 30 days.

Calculations:

⇒ Total time for A (100% work) = 15 × (100 ÷ 25) = 60 days

⇒ Total time for B (100% work) = 30 × (100 ÷ 75) = 40 days

⇒ Let Total Work = LCM of 60 and 40 = 120 units

⇒ Combined Efficiency of A + B = 2 + 3 = 5 units/day

⇒ Target Work (50% of total) = 120 × 0.50 = 60 units

⇒ Time taken by A and B together = 60 ÷ 5 = 12 days

∴ The correct answer is 12 days.

Additional Information

Work and Efficiency Relationship

Efficiency is inversely proportional to time: Efficiency = Total Work ÷ Time.

Combined Work Formula

If A takes 'x' days and B takes 'y' days, they together take (xy) ÷ (x + y) days for 100% work.

Percentage Work Concept

Time taken for a fraction of work is proportional to the fraction: Time for n% work = (n/100) × Total Time.

Given:

Total profit = ₹1,62,000

Calculation:

Let, total investment = 3 units

So, A invest = 3/3 = 1  [∵ $33\frac{1}{3}\%$ = 1/3]

B invest = 3 - 1 = 2

A : B = 1 : 2

Here, 3 units → Rs. 162000

∴ 2 units → (162000/3) × 2 = Rs. 108000

∴ B's share (in Rupees) is Rs. 108000

Given:

Discount = 10%

Marked price = 20% higher than their cost price

Calculation:

Let, the cost price = 100

So, the marked price = 100 + (20% of 100) = 100 + 20 = 120

The selling price = 120 - (10% of 120) = 120 - 12 = 108

The gain percentage = 108 - 100 = 8%

∴ The shopkeeper's gain percentage is 8%

Given:

Total number of states = 5

Concept used:

Average = Sum of the terms/Number of terms

Calculation:

The average number of youth (in lakhs) = (12 + 8 + 11.5 + 10 + 9)/5 = 50.5/5 = 10.1

In the given graph, the number of youth (in lakhs) in state A = 12

The number of youth (in lakhs) in state C = 11.5

∴ The number of youth more than the average number of youth in the five states in states A and C

Given:

The six bells toll at intervals of 3, 4, 6, 7, 8, and 12 seconds

Calculation:

Prime factors of 3 = 3

Prime factors of 4 = 2 × 2

Prime factors of 6 = 2 × 3

Prime factors of 7 = 7

Prime factors of 8 = 2 × 2 × 2

Prime factors of 12 = 2 × 2 × 3

LCM of 3, 4, 6, 7, 8, and 12 = 2 × 2 × 2 × 3 × 7 = 168

∴ The six bells will toll together again after 168 seconds

Shortcut Trick

When angles of elevation from two points at distances a and b from the base are complementary, the height (h) of the building is the geometric mean of the distances.

Formula: h = √(a × b)

h = √(72 × 128) = √(9 × 8 × 8 × 16)

h = 3 × 8 × 4 = 96 m

∴ The correct answer is 96 m.

Alternate Method

Given: Distance a = 72 m, Distance b = 128 m. Angles are θ and (90−θ).

Formula Used: tan(θ) = Opposite / Adjacent

⇒ In first triangle: tan(θ) = h / 72

⇒ In second triangle: tan(90−θ) = h / 128

⇒ cot(θ) = h / 128 [Since tan(90−θ) = cot(θ)]

⇒ tan(θ) × cot(θ) = (h / 72) × (h / 128)

⇒ 1 = h² / (72 × 128)

⇒ h² = 9216

⇒ h = √9216 = 96 m

∴ The correct answer is 96 m.

Additional Information

Complementary Angles Rule

If angles of elevation from two points on the same side of a tower are complementary, the height is h = √(ab).

Trigonometric Identities

tan(90° − θ) = cot θ and tan θ × cot θ = 1 are key identities for solving such height and distance problems.

Geometric Mean

The result h = √ab shows that the height is the geometric mean of the two horizontal distances from the base.

Shortcut Trick

The simple interest = (p × r × t)/100

Let, the amount = 1

So, 1/8 = (1 × R × R/2)/100

1/8 = R2/200

⇒ R2 = 200/8 = 25

⇒ R = √25 = 5

The rate of interest = 5%

Total interest for 8 years = 5 × 8 = 40%

The final simple interest = 15000 × (40/100) = 6000

∴ The simple interest (in Rupees) is Rs. 6000

Alternate Method

Given:

The simple interest = 1/8 of the sum

Time (years) = Half of the rate of interest

Formula used:

The simple interest = (p × r × t)/100

Where, p = The total amount

r = Rate of interest

t = Time (years)

Calculation:

Let, the sum = P

So, the simple interest = P/8

Let, the rate of interest = R

So, the total time = R/2

Then, P/8 = (P × R × R/2)/100

⇒ P/8 = (P × R × R)/200

⇒ 1/8 = R²/200

⇒ R2 = 200/8 = 25

⇒ R = √25 = 5

∴ The rate of interest = 5%

Also, the final simple interest = (15000 × 5 × 8)/100 = 6000

∴ The simple interest (in Rupees) is Rs. 6000

Given:

There are the prime numbers between 70 and 90

Concept used:

Average = Sum of the terms/Number of terms

Calculation:

Prime numbers between 70 and 90 are 71, 73, 79, 83, and 89

Total prime numbers between 70 and 90 = 5

The average = (71 + 73 + 79 + 83 + 89)/5 = 395/5 = 79

∴ The average of all the prime numbers between 70 and 90 is 79

Shortcut Trick

We know incentre is a meet point of all the angle bisectors

So, ∠BIC = 90° + ∠A/2

⇒ ∠BIC = 90° + 88°/2

⇒ ∠BIC = 90° + 44°

⇒ ∠BIC = 134°

∴ The measure of ∠BIC is 134°

Alternate Method

Given:

In ∆ ABC*,* ∠A = 88°

Concept used:

Intersect is the meet point of all angle bisectors

Calculation:

In ΔBIC, ∠BIC + ∠IBC + ∠ICB = 180°

⇒ ∠BIC + ∠ABC/2 + ∠ACB/2 = 180°

⇒ ∠BIC = 180° - (∠ABC/2 + ∠ACB/2)

⇒ ∠BIC = 180° - [(∠ABC + ∠ACB)/2]

⇒ ∠BIC = 180° - [(180° - ∠A)/2]

⇒ ∠BIC = 180° - 90° + ∠A/2

⇒ ∠BIC = 90° + ∠A/2

⇒ ∠BIC = 90° + 88°/2

⇒ ∠BIC = 90° + 44°

⇒ ∠BIC = 134°

∴ The measure of ∠BIC is 134°

Given:

a2 + b2 + 49c2 + 18 = 2 (b - 28c - a)

Calculation:

a2 +  b2 + 49c2 + 18 = 2 (b - 28c - a)

⇒ a2 +  b2 + 49c2 + 18 = 2b - 56c - 2a

⇒ a2 +  b2 + 49c2 + 18 - 2b + 56c + 2a = 0

⇒ a2 + 2a + 1 + b2 - 2b + 1 + 49c2 + 56c + 16 = 0

⇒ (a + 1)² + (b - 1)² + (7c + 4)² = 0

Now the above equation is 0, only when

⇒ a + 1 = 0, b - 1 = 0, 7c + 4 = 0

⇒ a = - 1, b = 1, c = - 4/7

Then, (a + b - 7c) = (- 1) + 1 - [7 × (- 4/7)]

= - 1 + 1 + 4

= 4

∴ The value of (a + b - 7c) is 4

Given:

Total number of employees = 2400

Concept used:

A circle has a total angle = 360°

Calculation:

Required number of employees = 600

600 employees will make the angle = (600/2400) × 360 = 90°

In the pie chart, the angle of employees of office D = 90°

∴ The number of 600 employees are in office D

Given:

1 + $\sqrt{ {\cotθ + \cosθ} \over \cotθ - \cosθ}$

0° < θ < 90°

Formula used:

1 - sin² θ = cos² θ

Calculation:

1 + $\sqrt{ {\cotθ + \cosθ} \over \cotθ - \cosθ}$

⇒ $1+\sqrt{\frac{\frac{cos,θ}{sin,θ}+cos,θ}{\frac{cos,θ}{sin,θ}-cos,θ}}$

⇒ $1+\sqrt{\frac{\frac{cos,θ}{sin,θ\times cos,θ}+1}{\frac{cos,θ}{sin,θ\times \cos,θ}-1}}$ = $1+\sqrt{\frac{\frac{1}{sin,θ}+1}{\frac{1}{sin,θ}-1}}$

⇒ $1+\sqrt{\frac{\frac{1+sin,θ}{sin,θ}}{\frac{1-sin,θ}{sin,θ}}}$ = $1 + \sqrt{\frac{1+sin,θ}{1-sin,θ}}$

⇒ $1+\sqrt{\frac{1+sin,θ}{1-sin,θ}\times\frac{1+sin,θ}{1+sin,θ}}$

⇒ $1+\sqrt{\frac{(1+sin,θ)^2}{1-sin^2,θ}}$ = $1+\sqrt{\frac{(1+sin,θ)^2}{cos^2,θ}}$

⇒ 1 + ${1+ sin\theta}\over{cos\theta}$

⇒ 1 + $1\over cos\theta$ + $sin\theta\over cos\theta$

⇒ 1 + sec θ + tan θ

∴ The value of the given expression is 1 + sec θ + tan θ

Shortcut Trick 

By putting the $\theta$ = 30o we can solve the question quickly.

These types of questions should be attempted by value-putting methods.

Shortcut Trick

Equate the volumes directly: (4/3)πr³ = πr²h

Cancel π and r² from both sides: (4/3)r = h

Rearrange for the ratio r/h: r/h = 3/4

∴ The correct answer is 3 ÷ 4.

Alternate Method

Given: Volume of sphere = Volume of cylinder and radius of sphere = radius of cylinder = r.

Formula Used: Volume of sphere = (4/3)πr³; Volume of cylinder = πr²h

⇒ Volume of sphere = Volume of cylinder

⇒ (4/3) × π × r³ = π × r² × h

⇒ (4/3) × r = h

⇒ r / h = 3 / 4

⇒ r ÷ h = 3 ÷ 4

∴ The correct answer is 3 ÷ 4.

Additional Information

Surface Area of Sphere

Total surface area of a sphere is given by 4πr².

Surface Area of Cylinder

Curved Surface Area (CSA) = 2πrh and Total Surface Area (TSA) = 2πr(h + r).

Volume of Cone

Volume of a cone with the same radius and height as a cylinder is (1/3)πr²h.

Given:

$\left({ {1 - \cotθ} \over 1 - \tanθ}\right)^2$ - 1

0° < θ < 90°

Concept used:

(sinθ - cosθ)2 = (cosθ - sinθ)² 

Calculation:

$\left({ {1 - \cotθ} \over 1 - \tanθ}\right)^2-1$

⇒ $\left(\frac{1-\frac{cos,θ}{sin,θ}}{1-\frac{sin,θ}{cos,θ}} \right)^2-1$

⇒ $\frac{\frac{(sin,θ-cos,θ)^2}{sin^2,θ}}{\frac{(cos,θ-sin,θ)^2}{cos^2,θ}}-1$ = ${{(sin\theta-cos\theta)^2}\over sin^2\theta}\times{{cos^2\theta}\over(cos\theta-sin\theta)^2}$ -1

(sinθ - cosθ)2 = (cosθ - sinθ)² 

⇒ ${cos^2\theta}\over{sin^2\theta}$ -1

= cot2​ θ - 1

∴ The value of given expression is cot2​ θ - 1

Shortcut Trick

Given, ∠A = 78°

If the bisectors of ∠CBD and ∠BCE meet at P

∠P = 90° - ∠A/2

⇒ ∠P = 90° - 78°/2

⇒ ∠P = 90° - 39° = 51°

∴ The measure of ∠P is 51°

Alternate Method

Given:

∠A = 78°

Concept used:

The sum of all angles on a straight line is 180°

The sum of all angles of a triangle is 180°

Calculation:

∠ABC + ∠CBD = 180°

⇒ ∠CBD = 180° - ∠ABC

⇒ ∠CBD/2 = (180° - ∠ABC)/2

⇒ ∠CBP = 90° - ∠ABC/2  [∵ BP is the bisector of ∠CBD]

Similarly, ∠BCP = 90° - ∠ACB/2

In ΔBCP, ∠CBP + ∠BCP + ∠P = 180°

⇒ (90° - ∠ABC/2) + (90° - ∠ACB/2) + ∠P = 180°

⇒ 180° - (∠ABC + ∠ACB)/2 + ∠P = 180°

⇒ 180° - (180° - ∠BAC)/2 + ∠P = 180°

⇒ ∠P = (180° - ∠BAC)/2

⇒ ∠P = (180° - 78°)/2

⇒ ∠P = (102°)/2 = 51°

∴ The measure of ∠P is 51°

Given:

Time is taken by A after crossing (T₁) = $6\frac{1}{8}$ hours = 49/8 hours

Time is taken by B after crossing (T₂) = 8 hours

The speed of A = 32 km/h

Concept used:

If two cars start at the same time from two points P and Q towards each other and after crossing they take a and b hours in reaching Q and P respectively. Then P's speed : Q's speed = √b : √a

Calculation:

We know, Speed of A/Speed of B = √(T₂/T₁)

32/Speed of B = √[8/(49/8)]

32/Speed of B = √(64/49) = 8/7

Speed of B = (32 × 7)/8 = 28 km/h

∴ The speed, in km/h of B is 28 km/h

Given:

The following bar chart shows the number of students enrolled in two summer Camps A and B from 2014 to 2019.

Calculation:

The number of students enrolled in Camp A in 2016 and 2019 = 140 + 180 = 320

The number of students enrolled in Camp B in 2015 and 2017 = 240 + 260 = 500

The percentage = (320/500) × 100 = 64%

∴ The number of students enrolled in Camp A in 2016 and 2019 together is 64% of the number of students enrolled in Camp B in 2015 and 2017 together.

Given:

∠ABC = 2p and ∠ADC = 3p

Concept used:

The reflex angle is more than 180° but less than 360°

The sum of the opposite angles of a cyclic quadrilateral is 180°

The angle at the center of a circle is twice the angle at the circumference of the circle.

Calculation:

∠ABC + ∠ADC = 180°

⇒ 2p + 3p = 180°

⇒ 5p = 180°

⇒ p = 180°/5 = 36°

So, ∠ABC = 2 × 36° = 72° and ∠ADC = 3 × 36° = 108°

Then ∠AOC = 2 × 72° = 144°  [∵ ∠ABC = 72°] (Concept used)

Another side of ∠AOC =360° - 144° = 216°

∴ The measure (in degrees) of the ∠AOC reflex is 216°

Shortcut Trick

Number 8A5146B is divisible by 88, so it must be divisible by 8 and 11.

For divisibility by 8: Last three digits 46B must be divisible by 8 → 464 is divisible by 8, so B = 4.

For divisibility by 11: (Sum of odd places) − (Sum of even places) → (B+4+5+8) − (6+1+A) = (4+4+5+8) − (7+A) = 21 − 7 − A = 14 − A.

For 14 − A to be divisible by 11, A must be 3.

Value of B − A = 4 − 3 = 1.

∴ The correct answer is 1.

Alternate Method

Given: Number = 8A5146B, Divisor = 88.

Formula Used: Divisibility rules for 8 and 11.

⇒ Divisibility by 8: 46B ÷ 8 → 8 × 5 = 40, Remainder 6. Next multiple is 64. ∴ B = 4.

⇒ Divisibility by 11: (8 + 5 + 4 + B) − (A + 1 + 6) = 0 or multiple of 11.

⇒ (17 + B) − (A + 7) = (17 + 4) − (A + 7) = 21 − 7 − A = 14 − A.

⇒ 14 − A = 11 ⇒ A = 3.

⇒ Value of B − A = 4 − 3 = 1.

∴ The correct answer is 1.

Additional Information

Divisibility by 8

A number is divisible by 8 if the last three digits of the number are divisible by 8.

Divisibility by 11

A number is divisible by 11 if the difference between the sum of digits at odd places and even places is either 0 or a multiple of 11.

Co-prime Factors

If a number is divisible by two co-prime numbers a and b, then it is also divisible by their product (a × b). Here, 8 and 11 are co-prime.

Given:

a + b + c = 6

a2 + b2 + c2 = 32

a3 + b3 + c3 = 189

Formula used:

x³ + y³ + z³ - 3xyz = (x + y + z) [x² + y² + z² - (xy + yz + zx)]

(x + y + z)² = x2 + y2 + z2 + 2 (xy + yz + zx)

Calculation:

(a + b + c)2 = a2 + b2 + c2 + 2 (ab + bc + ca)

⇒ 6² = 32 + 2 (ab + bc + ca)

⇒ 36 = 32 + 2 (ab + bc + ca)

⇒ 2 (ab + bc + ca) = 36 - 32 = 4

⇒ (ab + bc + ca) = 4/2 = 2

Also, a3 + b3 + c3 - 3abc = (a + b + c) [a2 + b2 + c2 - (ab + bc + ca)]

⇒ 189 - 3abc = 6 (32 - 2)

⇒ 189 - 3abc = 6 × 30

⇒ 3abc = 189 - 180 = 9

⇒ abc = 9/3 = 3

⇒ abc - 3 = 3 - 3 = 0

∴ The value of abc - 3 is 0

Given:

The ratio of the cost prices of two articles A and B = 4 ∶ 5

The difference in the selling price of the article = Rs. 480

Formula used:

S.P. = [(100 + Profit%)/100] × C.P.

Where, C.P. = Cost price; S.P. = Selling price

Calculation:

Let, the cost price of two articles are 4x and 5x

So, [5x × (120/100)] - [4x × (110/100)] = 480

⇒ (600x/100) - (440x/100) = 480

⇒ 160x/100 = 480

⇒ x = 480 × (100/160) = 300

The difference in the cost price = 5x - 4x = x = Rs. 300

∴ The difference in the cost price (in Rs.) of articles B and A is Rs. 300

Shortcut Trick

(11/5) × A = (22/100) × B

⇒ A = B/10

⇒ A/B = 1/10

Also, B = (2.5/100) × C

⇒ B = C/40  [∵ 2.5% = 1/40]

⇒ B/C = 1/40

⇒ B/C = 10/400 [∵ A/B = 1/10]

Here, 400 units = 5500

⇒ 1 unit = 5500/400 = 55/4

The sum of 80% of A and 40% of B = [(4/5) × (55/4)] + [(2/5) × (550/4)]  [∵ 80% = 4/5 and 40% = 2/5]

= 11 + 55

= 66

∴ The sum of 80% of A and 40% of B is 66

Alternate Method

Given:

11/5 of a number A is 22% of a number B

The number B is equal to 2.5% of a third number C

The value of C = 5500

Calculation:

B = (2.5/100) × C

⇒ B = (2.5/100) × 5500

⇒ B = 137.5

Also, (11/5) × A = (22/100) × B

⇒ (11/5) × A = (22/100) × 137.5

⇒ A = (22/100) × (1375/10) × (5/11)

⇒ A = 13.75

Then, the sum of 80% of A and 40% of B = [13.75 × (80/100)] + [137.5 × (40/100)]

= 11 + 55

= 66

∴ The sum of 80% of A and 40% of B is 66

​The correct answer is 'to seeing'.

Key Points

• In this case “to” is a preposition, and you always need to use the ‘ing’ form (gerund) after a preposition.
• ‘looking forward’ is a phrasal verb. A phrasal verb contains a verb and a preposition and in this case, two prepositions (forward and to).
• To look forward to is a transitive verb which means that it needs an object ( a noun or a verb).
• As ‘seeing’ is a gerund (noun form of verb), the answer should be 'to seeing'.
• This option uses the gerund form "seeing" after the preposition "to." It is the most appropriate choice as it maintains parallel structure and conveys the idea of anticipation or expectation. "Looking forward to seeing" is a common phrase used to express excitement about a future event.

Therefore, the correct answer is: Are you looking forward to seeing Nikhil again?

Additional Information

• seeing
• This option uses the gerund form "seeing" as the object of the verb "looking forward." While gerunds can function as nouns, in this context, it feels incomplete. "Looking forward" is typically followed by a preposition such as "to" to indicate what is being anticipated.
• to see
• This option uses the infinitive form "to see" as the object of the verb "looking forward." The infinitive form is commonly used after "looking forward" to express anticipation or expectation. It is a valid choice and grammatically correct.
• to be seeing
• This option uses the present progressive form "to be seeing" as the object of the verb "looking forward." However, using the present progressive form in this context suggests ongoing or continuous action, which may not be appropriate. "Looking forward" implies anticipation of a specific event or action, rather than an ongoing process.

The correct answer is 'Alien'.

Key Points

• The most appropriate word for the given group of words is 'Alien'.
• It means 'a person who comes from another country'. (विदेशी व्‍यक्ति)
• Example: It is alien to the school discipline.
  

Correct Answer: Alien.

Additional Information

• Let's look at the meaning of other words:
• Stranger: a person that you do not know. (अपरिचित व्‍यक्ति, अजनबी )
• Native: connected with the place where you were born or where you have always lived. (जन्‍म स्‍थान या निवास-स्‍थान से संबंधित)
• Foreigner: a person who belongs to a country that is not your own. (आपने देश से भिन्‍न देश का निवासी; विदेशी व्‍यक्ति)

The correct answer is 'Punctilious'.

Key Points

• The most appropriate word for the given group of words is 'Punctilious'.
• It means 'showing great attention to detail or correct behaviour'. (विस्तार या सही व्यवहार पर बहुत ध्यान देना​)
• Example: He was punctilious in providing every amenity for his guests.
  

Correct Answer: Punctilious.

Additional Information

• Let's look at the meaning of other words:
• Punctual: doing something or happening at the right time; not late. (सही समय पर कुछ करने या होने वाला, वक़्त का पाबंद, समय पालक; विलंब न करने वाला, समयनिष्‍ठ)
• Zealous: using great energy and enthusiasm. (ऊर्जावान या ऊर्जापूर्ण उत्‍साही, उत्‍साहपूर्ण)
• Disciplined: to train somebody to obey and to behave in a controlled way. (किसी को) अनुशासित करना, नियंत्रित आचरण का प्रशिक्षण देना

The correct answer is '​The door was opened by him for his mother'.

Key Points

• The given sentence is in Active Voice. As per the given question, we have to change it into Passive Voice.
• The structure of the given sentence is as follows:
• Subject + V₂ + Object. (Active Voice)
• Subject (objective case) + was/were + V₃ + Object (subjective case). (Passive Voice)
• Example:
• Their cousin showed them some rare photographs. (Active Voice)
• They were shown some rare photographs by their cousin. (Passive Voice)
• The subject of the given sentence is 'He'.​​
• The object of the given sentence is 'the door'.
• The subject will be put in place of the object and the object will be put in place of the subject.
• And 'opened' will be changed into 'was opened'.
• Lastly, the preposition 'by' will be added. 
  

Correct Sentence: The door was opened by him for his mother.

​The correct answer is 'CDBA'.

Key Points

• The given question is an example of a Para Jumble.
• We know that the first statement of a para jumbled question is usually an independent general statement, a noun, a universal fact, starting of an incident, or it starts with 'most' or 'once'.
• Sentence C will be the first sentence because it is an independent introductory sentence that tells us about the fixed deposits.
• Sentence D will be the next sentence because it explains what is a fixed deposit.
• Sentence B will be used afterward because it is connected with the previous sentence.
• Lastly, Sentence A will be used.
• Thus, the correct sequence is:
• C: One of the best ways to secure your money is by investing in fixed deposits.
• D: Under the fixed deposit scheme, the depositor deposits the money only once at the time of opening the account.
• B: It not only helps you to save money but also helps you to earn a substantial interest on it.
• A: The interest rates offered depends on the bank, deposit amount and the tenure you choose.
  

Correct Sequence: One of the best ways to secure your money is by investing in fixed deposits. Under the fixed deposit scheme, the depositor deposits the money only once at the time of opening the account. It not only helps you to save money but also helps you to earn a substantial interest on it. The interest rates offered depends on the bank, deposit amount and the tenure you choose.

The correct answer is 'On the decline'.

Key Points

• The most appropriate meaning of other given idiom 'On the wane' is 'On the decline'.
• On the wane: becoming smaller, less important, or less common. (क्षीण होना, उतार पर होना, कमज़ोर होना)
• Example: If something is on the wane, it is becoming weaker or less.
  

Correct Answer: On the decline.