SSC CGL 2021 Tier-I (Held On : 12 April 2022 Shift 3) (Previous Year Paper)

Given:

Hence, the correct answer is "option 1".

The pattern followed here is:

According to the alphabetical positions of the letters,

Hence, ‘STN’ is the correct answer.

The pattern followed here is:

Hence, PVL is the correct answer.

Given:

Length of the side of the big cube = 125 cm.

Length of the side of the smaller cube = 25 cm.

Formula:

A cube is a three-dimensional figure with 8 corners, 6 surfaces, and 12 edges (sides).

If a cube is painted on all of its surfaces with the same colour, and then divided into smaller cubes of equal size, then the number of smaller cubes so obtained will be calculated as follows:

• Number of cubes with no face painted = (n - 2)³
• Number of cubes with one face painted = 6(n - 2)²
• Number of cubes with two faces painted = 12(n - 2)
• Number of cubes with three faces painted = 8(Always)

 where n = No. of parts of each side = Length of the side of larger cube ÷ length of the side of the smaller cube

Calculation:

n = 125 ÷ 25 = 5

⇒ n - 2 = 3

Number of smaller cubes having at least two faces painted

= total no. of cubes - (no. of cubes with no face painted + no. of cubes with only one face painted)

= 125 - (3³ + 6 × 3²)

= 125 - (27 + 54)

= 125 - 81

= 44

Hence, 44 is the correct answer.

The pattern followed here is:

Similarly,

 

Hence, ‘HKY’ is the correct answer.

1. ×, ÷, =, –, +

Given equation: 55 * 126 * 14 * 520 * 30 * 5

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

55 × 126 ÷ 14 = 520 - 30 + 5

⇒ 55 × 9 = 495

⇒ 495 = 495

2. +, ÷, –, =, ×

Given equation: 55 * 126 * 14 * 520 * 30 * 5

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

55 + 126 ÷ 14 - 520 = 30 + 5

⇒ 55 + 9 - 520 = 35

⇒ - 456 ≠ 35

3. =, ×, +, ÷, –

Given equation: 55 * 126 * 14 * 520 * 30 * 5

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

55 = 126 × 14 + 520 ÷ 30 - 5

⇒ 55 = 1764 + 17.33 - 5

⇒ 55 = 1781.33 - 5

⇒ 55 ≠ 1776.33

4. =, –, +, ÷, ×

Given equation: 55 * 126 * 14 * 520 * 30 * 5

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

55 = 126 - 14 + 520 ÷ 30 × 5

⇒ 55 = 126 - 14 + 86.67

⇒ 55 ≠ 198.67

Hence, ‘option 1’ is the correct answer.

The paper when unfolded will appear as shown below:

Hence, ‘option 1’ is the correct answer.

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

Six members - P, Q, R, S, T and U in a family.

1. T is the brother of P’s husband.
2. U is the mother of T.
3. Q is the daughter of S and P and the granddaughter of R.

Clearly, R is father of T.

Hence, ‘Father’ is the correct answer.

The logic is:

Hence, ‘144’ is the correct answer.

The least possible Venn diagram is:          

Conclusions:

I. Some sofas are couches. → True (As, All couches are sofas → Some sofas are couches)

II. Some couches are bean bags. → True (As, All bean bags are chairs and All chairs are couches → Some couches are bean bags)

III. All couches are bean bags. → False (it is possible but not definite)

Hence, only conclusions I and II follow.

The pattern followed here is:

Column 1: 24 × 6 = 144 = 12 × 12.

Column 2: 36 × 3 = 108 = 2 × 54

Column 3: 32 × 18 = 576 = 24 × 24

Hence, 18 is the correct answer.

The correct order of the given words as they would appear in an English dictionary is:

4. Malicious
5. Manuscript
6. Melody
7. Memory
8. Minor

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

The Venn diagram that best represents the relationship between Furniture, Bed, Chair, Dining table is shown below:

Bed, Chair, and Dining table are name of different kinds of Furniture.

Hence, ‘option 3’ is the correct answer.

The logic is:

Hence, ‘232’ is the correct answer.

The pattern followed here is:

According to the alphabetical positions of the letters,

Similarly,

Hence, ‘TBFGFMCJ’ is the correct answer.

• Avanish got 78% marks in an examination and Kapil got 64% marks in the same examination.

Let the exam be of 'x' marks.

• The sum of the marks obtained by Kapil and Avanish is 923.

According to question:

78% of x + 64% of x = 923

⇒ 78/100 × x + 64/100 × x = 923

⇒ (78x + 64x) / 100 = 923

⇒ 142x = 923 × 100

⇒ x = 92300 ÷ 142

⇒ x = 650

The marks obtained by Kapil in the examination = 64% of x 

= 64% of 650

= 64/100 × 650

= 416

Hence, ‘416’ is the correct answer.

1. − and +

Given equation: 9 × 98 ÷ 14 + 3 − 19 = 11

After interchanging the signs, we get:

9 × 98 ÷ 14 - 3 + 19 = 11

⇒ 9 × 7 - 3 + 19 = 11

⇒ 63 - 3 + 19 = 11

⇒ 79 ≠ 11 

2. • and ×

Given equation: 9 × 98 ÷ 14 + 3 − 19 = 11

After interchanging the signs, we get:

9 + 98 ÷ 14 × 3 − 19 = 11

⇒ 9 + 7 × 3 - 19 = 11

⇒ 9 + 21 - 19 = 11

⇒ 30 - 19 = 11

⇒ 11 = 11

3. − and ×

Given equation: 9 × 98 ÷ 14 + 3 − 19 = 11

After interchanging the signs, we get:

9 - 98 ÷ 14 + 3 × 19 = 11

⇒ 9 - 7 + 57 = 11

⇒ 59 ≠ 11

4. ÷ and –

Given equation: 9 × 98 ÷ 14 + 3 − 19 = 11

After interchanging the signs, we get:

9 × 98 - 14 + 3 ÷ 19 = 11

⇒ 882 - 14 + 0.157 = 11

⇒ 868.157 ≠ 11

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

Six friends, David, Bhanu, Minto, Krita, John and Nisan, are sitting in a circle with their backs towards the centre.

1. David and Minto are sitting to the immediate left and right of Bhanu, respectively.

2. John is not sitting to the immediate left of David.

3. Nisan is sitting third to the right of Bhanu.

Clearly, John is sitting immediate right of Minto as it is the only vacant position John can occupy and Krita is sitting exactly opposite to Minto.

So the arrangement will be as shown below:

Clearly, Krita is sitting second to the left of Bhanu.

Hence, ‘Krita’ is the correct answer.

The pattern followed here is:

• The figure in the series is rotating 90° clockwise direction.

 

Hence, ‘option 4’ is the correct answer.

• The code for each word is shown below:

safe → 5

vaccine → 2 

'safe vaccine' will be written as '52' in that language.

Hence, ‘52’ is the correct answer.

The logic followed here is:

• SALT → Number of letters in the word SALT is 4 and 4² = 16
• PICKLE → Number of letters in the word PICKLE is 6 and 62 = 36

Similarly,

• PRESERVATIVE → Number of letters in the word PRESERVATIVE is 12 and 122 = 144

Hence, ‘144’ is the correct answer.

The logic followed here is:

1^st number + 253 = 2^nd number

• 68 + 253 = 321.
• Similarly, 525 + 253 = 778.

Hence, 778 is the correct answer.

The mirror image of the given combination when the mirror is place at the right side is as shown below :

• The line AB is the mirror.
• The given image has letter "R", So, the mirror image should be "

" ⇒ Option 1 and Option 4 are eliminated.

• The right-angle triangle at the top of the image in option 2 is placed exactly in the same way as placed in the given image, which is not possible in case of mirror image ⇒ Option 2 is eliminated.

Hence, the correct answer is "Option 3".

One morning, Chitrashi and Aryan sit facing each other.

• If the shadow of Aryan falls to the left of Chitrashi.

• Aryan is facing the South direction.

Hence, ‘South​’ is the correct answer.

The pattern followed here is:

According to the alphabetical positions of the letters,

1. FUBY → FU and BY are pairs of opposite letters.
2. WEKP → WE is not a pair of opposite letters. 
3. SHOL → SH and OL are pairs of opposite letters.
4. PKRI → PK and RI are pairs of opposite letters.

Hence, ‘WEKP’ is the odd one out.

Alternate MethodFUBY = 6 + 21 + 2 + 25 = 54

WEKP = 23 + 5 + 11 + 16 = 55

SHOL = 19 + 8 + 15 + 12 = 54

PKRI = 16 + 11 + 18 + 9 = 54

All the other option has a sum of 54 except for WEKP.

The correct answer is Progressive tax.

Key Points

• Progressive Tax
• In progressive taxation, the tax liability increases with individual or entity income.
• This is based on the principle of ability to pay.
• Under this system, the lowest income people are generally exempted while the highest income people pay the highest taxes.
• Income Tax is thus an example of a progressive tax.
• Progressive taxation results in the redistribution of income from rich to poor.
• A progressive tax charges a higher tax rate for people who earn a higher income.

Additional Information

• Proportional Tax
• In this system, a flat tax is levied regardless of income or wealth.
• One example of corporation tax in India whereby government charges a flat rate of 30% on the income earned by the companies in India.
• Regressive Tax
• A regressive tax is when the tax rate decreases as the amount subject to taxation increases; the tax rate progresses from high to low.
• The lowest amount is subject to higher taxation and this leads to individuals with low income bearing the highest-burden of regressive taxes.
• Such tax does not take into account the ability to pay.
• Pay-roll tax:
• The tax that is withheld, charged, or levied on an employer's payroll is known as payroll tax.
• Wages, gross salary, incentives, and any other type of remuneration paid to employees shall be included.
• Payroll taxes are taxes that an employer is compelled to pay or withhold on behalf of his or her employees.

The correct answer is Daskathia.

Key Points

• Daskathia is a form of ballad singing prevalent in Odisha.
• Daskathia is a name derived from a unique musical instrument called “Kathi” or “Ram Tali”, wooden clappers used during the presentation.
• The performance is a form of worship and offering on behalf of the “Das”, the devotee.
• This folk form is mainly associated with the worship of Lord Shiva and thus, during the performances, dedications to Lord Shiva, mentioning its various forms like Rudra, Hara, Mahadeva, Shankar, Bholanath etc., is prescribed.

Additional Information

• Kajri Folk Song is related to India's state Uttar Pradesh as well as Bihar.
• Powada is the traditional folk art from Maharashtra.
• Sohar is a folk song sung during Childbirth, mainly a folk song of Uttar Pradesh and Bihar.

The correct answer is 21.6%.

Key Points

• The Ministry of Finance in January 2021 the economic survey announced, that external debt as a ratio to GDP stood at 21.6% at the end of September 2020 from 20.6% at the end-March 2020.
• Key Highlights of Economic Survey 2020-21.
• As per the advance estimates by NSO, India’s GDP is estimated to grow by (-) 7.7% in FY21.
• India’s real GDP to record an 11.0% growth in FY2021-22 and nominal GDP to grow by 15.4% – the highest since independence.
• Exports are expected to decline by 5.8% and imports by 11.3% in the second half of FY21.
• India expected to have a Current Account Surplus of 2% of GDP in FY21, a historic high after 17 years.
• On the supply side, Gross Value Added (GVA) growth was pegged at -7.2% in FY21 as against 3.9% in FY20.
• Agriculture is set to cushion the shock of the COVID-19 pandemic on the Indian economy in FY21 with a growth of 3.4%.
• Industry and services are estimated to contract by 9.6% and 8.8% respectively during FY21.
• Net FPI inflows recorded an all-time monthly high of US$ 9.8 billion in November 2020.
• Strong services exports and weak demand led to a sharper contraction in imports (merchandise imports contracted by 39.7%) than exports (merchandise exports contracted by 21.2%).
• Forex reserves increased to a level so as to cover 18 months' worth of imports in December 2020.
• External debt as a ratio to GDP increased to 21.6% in end-September 2020 from 20.6% in end-March 2020
• India became the fastest country to roll out 10 lakh vaccines in 6 days and also emerged as a leading supplier of the vaccine to neighbouring countries and Brazil$.

The correct answer is Red Sindhi.

Key Points

• Red Sindhi is a reputed heat-tolerant indigenous dairy cattle breed originating from the Sindh province of Pakistan.
• The breed is also known as “Malir”, “Red Karachi” and “Sindhi”.
• It is considered that breed evolved from Las Bela cattle of Bela, Baluchistan.
• The breed is of distinct red colour and darker than Sahiwal.
• The milk yield of the cattle ranges from 2000 to 4000 kg per lactation with an average yield of 1840 kg per lactation.
• Fat percentage in the milk varies from 4 to 5.2% with an average of 4.5%.
• Among the **indigenous cattle breeds are Sahiwal, Red Sindhi, Gir, Tharparkar, etc.**​

Additional Information

• ​Chippiparai, Kanni, and Kombai are breeds of sighthound dogs native to Southern India.
• Traditionally kept for hunting.

The correct answer is Allahabad.

Key Points

• George Yule became the President of INC in 1888 in the fourth session held at Allahabad.
• He was the first non - Indian to be the President of INC.
• He belonged to the business community. He was the chief of the well-known Andrew Yule and Co. in Calcutta.
• He had also been Sheriff of Calcutta and President of the Indian Chamber of Commerce.
• Yule was widely known in Indian circles for his breadth of outlook, liberal views, and marked sympathy for Indian aspirations.
• Surendranath Banerjee described him as **"a hard-headed Scotsman who saw straight into the heart of things, and never hesitated to express himself with the bluntness in which a Scotsman never fails if he wants to show it."**​

Important Points

• Important sessions of congress.
• First Session: 
• Held at Bombay in 1885. President: W.C. Bannerjee.
• Formation of Indian National Congress.
• Second Session:
• ​Held at Calcutta in 1886. President: Dadabhai Naoroji.
• Third Session: 
• Held at Madras in 1887.
• President: Syed Badruddin Tyabji, the first Muslim President.
• Fourth Session: 
• Held at Allahabad in 1888.
• President: George Yule, first English President.
• 1896: Calcutta Session.
• ​President: Rahimtullah Sayani.
• National Song ‘Vande Mataram’ was sung for the first time by Rabindranath Tagore.
• 1905: Benaras.
• President: Gopal Krishan Gokhale.
• The formal proclamation of the Swadeshi movement against the government.
• 1906: Calcutta.
• President: Dadabhai Naoroji.
• Adopted four resolutions: Swaraj (Self Government), Boycott Movement, Swadeshi & National Education.
• 1907: Surat.
• ​President: Rash Bihari Ghosh.
• Split in Congress- Moderates & Extremist.
• 1916: Lucknow.
• President: A.C. Majumdar.
• Unity between two factions-Moderates and Extremists of Congress.
• Lucknow Pact was signed between Congress and Muslim League to build political consensus.
• 1917: Calcutta.
• President: Annie Besant, First Woman President of Congress.
• 1924: Belgaum. 
• President: M.K. Gandhi.
• Only Session was presided over by Mahatma Gandhi.
• 1925: Kanpur. 
• President: Sarojini Naidu, First Indian Woman President.
• 1938: Haripura. 
• President: Subhas Chandra Bose.
• National Planning Committee set up under Jawahar Lal Nehru.

The correct answer is the 73^rd constitutional amendment.

Key Points

• The main objective of the 73^rd Constitutional Amendment Act, 1992:
• To provide constitutional status to the panchayats.
• It aimed at democratic decentralization of power and resources among the central government and local bodies.
• Article 40 of the Indian Constitution obligated the state governments **to constitute panchayats and provide them such powers and functions so that they can work as a unit of self-government.**​

Additional Information

• Important committees that were constituted for the establishment of the Panchayati raj system:
• Balwant Rai Mehta Committee, 1957: 
• Constituted to monitor the functioning of the Community Development Program, 1952.
• The committee suggested democratic decentralization that came to be known as the “Panchayati Raj System."
• The committee also suggested a three-tier system at the village, block, and district levels.
• Sadiq Ali Committee, 1964:
• Constituted to report on the working of gram sabha in Rajasthan.
• The Committee reported the following weaknesses: 
• The main problem was the illiteracy of villagers.
• Poor representation of women.
• Avoidance of meetings by the Sarpanch to escape questions.
• Meetings are not being properly publicized.
• G.L. Vyas Committee, 1973:
• Constituted in order to rectify the dysfunction in the system recommended compulsory attendance of Sarpanch in every meeting.
• Statutory recognition of gram sabha.
• Meetings should be in May-June and January-December, with compulsory attendance of patwari.
• Ashok Mehta Committee, 1977: 
• The Committee recommended a two-tier system in panchayats.
• Regular social audits.
• Regular elections.
• Reservation of SCs and STs.
• G.V.K. Rao Committee, 1985: 
• ​This Committee was the first committee to recommend providing constitutional status to Panchayati Raj Institutions.
• L. M. Singhvi Committee, 1986: 
• This Committee recommended the establishment of Nyaya panchayats, enhancing the financial resources of panchayats.
• The Committee also recommended the establishment of a separate judicial tribunal to deal with the cases regarding elections or any other matters of panchayats.

The correct answer is 1971.

Key Points

• The Contempt of courts act, 1971:
• An Act to define and limit the powers of certain courts in punishing contempts of courts and to regulate their procedure in relation thereto.
• This Act has been promulgated by the Parliament of India in the Year 1971 with an aim to define what amounts to Contempt of Court.
• This means contempt jurisdiction enjoyed by the courts is only for the purpose of upholding the majesty of the judicial system that exists.
• Contempt is defined under Section 2(a)[3] of the Contempt of Courts Act, 1971 which says:
• “Contempt of court” means civil contempt or criminal contempt.
• “Civil contempt” is defined under Section 2(b) which means wilful disobedience to any judgment decree, direction, order, writ, or another process of a court or wilful breach of an undertaking given to the court.
• “Criminal contempt” is defined under Section 2(c) which means the publication (whether by words, spoken or written, or by signs, or by visible representation, or otherwise) of any matter or the doing of any other act whatsoever which:
• Scandalises or tends to scandalize, or lowers or tends to lower the authority of, any court.
• Prejudices, or interferes or tend to interfere with, the due course of any judicial proceeding.
• Interferes or tends to interfere with, or obstructs or tends to obstruct, the administration of justice in any other manner.

The correct answer is carbon dioxide.

Key Points

• Urea is now prepared commercially from liquid ammonia and liquid carbon dioxide.
• The chemical name of urea is carbamide, the diamide of carbonic acid.
• Its formula is NH₂CONH₂.
• Urea has important uses as a fertilizer and feeds supplement.
• It is a colourless substance existing in the crystalline form, which melts at 132.7°C (271° F).
• Urea is a waste product in the body with no physiological function.
• It dissolves in the kidney and blood before it is excreted as urine.

Important Points

• Uses of Urea
• It is mainly used as a nitrogen release fertilizer.
• Urea is used as a stabilizer in most nitrocellulose explosive products.
• It is used in manufacturing high explosive materials like urea nitrate (CH₅N₃O₄).
• It is used as an important reagent in lanthanide chemistry.
• It is used in creams/ointments that are used for rehydration.
• It is used in hair removal creams and dish soaps.
• It is used as a browning agent for pretzels.
• It is used in manufacturing melamine.
• It is used to detect the bacteria in the stomach through the urea breath test.

The correct answer is I.

Key Points

• The greater one-horned rhino is listed under Schedule I of the Wildlife Protection Act, 1972.
• Wildlife Protection Act 1972 was passed on August 21, 1972, but was later implemented on September 9, 1972.
• This act prohibits the capturing, killing, poisoning, or trapping of wild animals.
• It extends to the whole of India except the State of Jammu and Kashmir.

Additional Information

• Environment (Protection) Act: 
• The Environment (Protection) Act was enacted in 1986 with the objective of providing for the protection and improvement of the environment.
• The Forest Conservation Policy
• India’s forests are currently governed by the National Forest Policy of 1988.
• Maintenance of environmental stability through preservation and restoration of ecological balance.

The correct answer is 11^th to 14^th April 2021.

Key Points

• PM Modi urges everyone to observe Tika Utsav from April 11-14, 2021 after chairing a Covid review meeting with Chief Ministers on 8 April 2021.
• Tika Utsav is observed from April 11, the birth date of Jyotiba Phule, to April 14 which happens to be Bhimrao Ambedkar's birth date.
• The aim of the Tika Utsav is to vaccinate a maximum number of people during this period.
• Jyotirao Govindrao Phule was an Indian social activist, thinker, anti-caste social reformer, and writer from Maharashtra.

The correct answer is Nagaland.

Key Points

• Mount Tiyi is situated in Wokha in Nagaland.
• Nagaland is a state in North-Eastern India.
• It is bordered by the state of Arunachal Pradesh to the North, Assam to the West, and Manipur to the south and Myanmar to the East.
• Its Capital is Kohima.
• Its Largest City is Dimapur.

Additional Information

• Important hills in Northeastern states.

The correct answer is Jhelum.

Key Points

• Jhelum is also called Vitasta**.**
• A spring, Verinag is the source of the Jhelum river which flows across the Kashmir valley.
• It is located in the vicinity of Banihal Pass, 20kms from Anantnag,
• It is the first tourist spot of Kashmir valley when travelling from Jammu by road.

Additional Information

• Some of the rivers with their ancient and modern names are:

The correct answer is Sharankumar Limbale.

Key Points

• Sharankumar Limbale was selected for Saraswati Samman’2020.
• It was instituted by KK Birla Foundation in 1991 and is recognized as the most prestigious and highest literary award in the country.
• The Saraswati Samman is an annual award for outstanding prose or poetry literary works in any of the 22 languages of India listed in Schedule VIII of the Constitution of India
• Noted Marathi writer Dr Sharankumar Limbale received Saraswati Samman, 2020 for his book Sanatan.
• Sanatan is an important social and historical document of the Dalit struggle.

Additional Information

• Noted Sindhi writer Vasdev Mohi was honoured with 29^th Saraswati Samman in 2019 for his short stories collection:- Chequebook
• Telugu poet K Siva Reddy was honoured with the prestigious Saraswati Samman, in 2018 for his work Pakkaki Ottigilite(Turning Aside While Lying Down)’.
• The 27^th Saraswati Samman 2017 was conferred upon eminent Gujarati poet Sitanshu Yashaschandra for "Vakhar" (Poetry collection)

The correct answer is 1961.

Key Points

• Dowry Prohibition Act was enacted on July 1, 1961:
• Its purpose was to prevent the giving and receiving of dowry.
• According to the Dowry Prohibition Act, "dowry" means any property or valuable security given or agreed to be given directly or indirectly.
• The Dowry Prohibition Act is applicable to persons of all religions in India.
• Punishment for violation of law is 5 years imprisonment and Rs 15000/- or the value of dowry whichever is higher.

The correct answer is Swaminathan.

Key Points

• The Cabinet Committee on Economic Affairs (CCEA) approved an increase in the Minimum Support Prices (MSPs) for all mandated Rabi crops for the marketing season 2021–22 in line with the recommendations of the Swaminathan Commission.
• Swaminathan Commission was appointed by former Prime Minister Manmohan Singh.
• It was headed by Professor M.S. Swaminathan to address the nationwide calamity of farmers' suicides in India.
• According to the report, the major causes of the agrarian crisis are unfinished agenda in land reform, quantity and quality of water, technology fatigue, access, adequacy and timeliness of institutional credit, and opportunities for assured and remunerative marketing.
• The Commission recommended that land reforms are necessary to address the basic issue of access to land for both crops and livestock.
• Professor M.S Swaminathan is known for his role in India's Green Revolution.

The correct answer is Colostrum.

Key Points

• Colostrum a fluid secreted by new mothers during the initial days of lactation contains nutrients that boost a baby's immune system and helps fight infection.
• Colostrum is a supplement made from a yellowish milky fluid that's released from the mothers during the initial days of lactation.
• It provides passive immunity.
• It is an antibody-rich fluid.
• It also provides several important growth hormones and other compounds such as lactoferrin for newborns.

Additional Information

• The sebum layer is an oily substance produced in the sebaceous glands.
• Synovial membranes are composed of connective tissue and surround the cavity of joints.
• A naturally occurring substance that protects, cleans and lubricated the outer auditory canal is known as 'Cerumen'.

The correct answer is Kuruwa.

Key Points

• In the state of Jharkhand, the ‘slash and burn' agriculture is known as ‘Kuruwa’.
• It is prevalent in the tropical region in different names:
• Jhuming in Northeastern states of India,
• Milpa in Central America and Mexico,
• Roca in Brazil,
• Ladang in Indonesia and Malaysia.

Additional Information

• Name of Slash and burn method in different states:

The correct answer is Austria. 

Key Points

• Dominic Thiem won his first Grand Slam title at the US Open 2020.
• He is an Austrian tennis player.
• He defeated Alexander Zverev.

Additional Information

• Spain's Rafael Nadal won the Australian Open Men's Singles final on 30 January 2022.
• Australian tennis player Ashleigh Barty defeated American Danielle Collins to win the Australian Open women's title on 29 January 2022.
• French tennis player Gael Monfils has won the men’s singles event of the 2022 Adelaide International 1 to claim the 11^th ATP title of his career.

The correct answer is Maharashtra.

Key Points

• Bhaja Caves is a group of 22 rock-cut caves that date back to the 2^nd century BC.
• It is located in the Pune.
• The caves belong to the Hinayana Buddhism sect in Maharashtra.
• These caves are famous for their indications of the awareness of wooden architecture.
• The caves share an architectural design with the Karla Caves.

Additional Information

• Karla Caves is a complex of Buddhist rock-cut caves.
• It is located at Karli near Lonavala Maharashtra.
• Barabar caves in Bihar are one of the oldest dating rock-cut caves from the times of the Mauryans and contain rare Hindu and Buddhist scriptures.
• Elephanta Caves are situated at Elephanta Islands in Mumbai, Maharashtra.
• Ajanta Caves are located in the Sahyadri ranges (Western Ghats) near Aurangabad (Maharashtra).

The correct answer is 1934.

Key Points

• On March 12, 1930, Gandhiji inaugurated the civil disobedience movement with the Dandi Salt March.
• He broke the Salt Laws imposed by the British Government.
• The civil disobedience movement broadened into people refusing to buy foreign goods, a refusal to pay taxes and not attending office and school.
• Disturbed by this movement the British imprisoned Mahatma Gandhi and Jawaharlal Nehru.
• By the end of 1930, thousands of Indians, were in jail and the movement had generated worldwide publicity.
• Lord Irwin (British viceroy from1926–31) was looking for a way to end it.
• Gandhiji was released from custody in January 1931, and the two men began negotiating the terms of the pact.
• The Gandhi-Irwin pact was signed on March 5, 1931, and the two main clauses of the pact were to ensure Congress's participation in the Round Table Conference and the end of the civil disobedience movement.
• The Second Round Table Conference in London which Gandhiji attended with Sarojini Naidu, proved to be futile as the British did not honour their demands.
• The Viceroy, Lord Willingdon, in the absence of Gandhiji, adopted the policy of repression, the Gandhi-Irwin Pact was violated and the Viceroy took to the suppression of the INC.
• Gandhiji resumed the movement in January 1932 and appealed to the country to join in.
• Gandhiji realised that the second phase of the civil disobedience movement lacked the organisation that marked its first phase, even though the entire nation put up a tough fight.
• The movement continued for six months. Gandhiji began a fast for 21 days on May 8, 1933, to make amends for the sins committed against the untouchables.
• He withdrew the mass Satyagraha on July 14, 1933, but the movement ceased completely on April 7, 1934.
• Hence Civil disobedience campaign completely ceased in 1934.

The correct answer is blue.

Key Points

• Gold and copper happen to absorb blue and violet light, leaving yellow light in the spectrum.
• So gold and copper are yellowish in colour.
• The only two non-silvery metals in the world are gold and copper.
• A metal is defined as an element that readily forms positive ions (cations) and has metallic bonds.
• These elements have electrons that are loosely held to the atoms, and will readily transfer them.
• Most metals' electrons reflect all colours equally which are in the visible spectrum of light.
• So those metals appear as white silver.

The correct answer is to ensure the availability and sustainable management of water and sanitation for all.

Key Points

• The UN’s Sustainable Development Goal 6 aims to ensure the availability and sustainable management of water and sanitation for all.
• The Sustainable Development Goals (SDGs) or Global Goals are a collection of 17 interlinked goals.
• The SDGs were set in 2015 by the United Nations General Assembly and are intended to be achieved by the year 2030.
• They are included in a UN Resolution called the Agenda 2030.

Additional Information

• The 17 SDGs are:

1. No Poverty.
2. Zero Hunger.
3. Good Health and Well-being.
4. Quality Education.
5. Gender Equality.
6. Clean Water and Sanitation.
7. Affordable and Clean Energy.
8. Decent Work and Economic Growth.
9. Industry, Innovation, and Infrastructure.
10. Reducing Inequality.
11. Sustainable Cities and Communities.
12. Responsible Consumption and Production.
13. Climate Action.
14. Life Below Water.
15. Life On Land.
16. Peace, Justice, and Strong Institutions.
17. Partnerships for the Goals.

The correct answer is Kashmir.

Key Points

• King Lalitaditya Muktapida ruled over Kashmir.
• Lalitaditya Muktapida was the grandson of Durlabahaka.
• Lalitaditya Muktapida extends the power of Kashmir beyond the normal mountain limits.
• Lalitaditya was able to defeat the Turks, Tibetans, Bhutias, and Kambojas.

Additional Information

• The Martand complex of temples perpetuates the memory of King Lalitaditya.
• The Karkota dynasty was associated with the history of Jammu and Kashmir.
• Karkota Dynasty was founded by Durlabhvardhana.
• Durlabahaka was the son of  Durlabhvardhana.

The correct answer is Jawaharlal Nehru.

Key Points

• Jawaharlal Nehru was India’s longest-serving prime minister.
• He was independent India’s first Prime Minister, he assumed office in 1947.
• His birth anniversary is celebrated as 'Children's Day' in India because of his advocacy for the cause of children's education.
• He was popularly called Chacha Nehru by children.

Additional Information

• Facts About Indian Prime Minister:

The correct answer is Yogasana. 

Key Points

• Yogasana sport for both male and female categories has also been included in Khelo India Youth Games 2021.
• The first Physical National Yogasana Championships will be held in Bhubaneshwar from November 11 to 13, 2021.
• The event will be organized by the National Yogasana Sports Federation (NYSF) in association with the Odisha government.

Additional Information

• About Khelo India Programme:
• Khelo India was formed by merging three schemes: Rajiv Gandhi Khel Abhiyan, Urban Sports Infrastructure Scheme, and National Sports Talent Search Scheme.
• It works to promote "Sports for All" and "Sports for Excellence".
• Its aim is the mass participation of youth in annual sports competitions through a structured competition.

Given:

tan2 A + 5 sec A = 13, 0 < A < 90°

Formula used:

tan² A = sec² A - 1

Calculation:

tan2 A + 5 sec A = 13

⇒ sec2 A - 1 + 5 sec A - 13 = 0

⇒ sec2 A + 5 sec A - 14 = 0

⇒ sec2 A + 7 sec A - 2 sec A - 14 = 0

⇒ sec A (sec A + 7) - 2 (sec A + 7) = 0

⇒ (sec A - 2) (sec A + 7) = 0

⇒ sec A + 7 = 0 ⇒ sec A = - 7  [Not possible because 0 < A < 90°]

⇒ sec A - 2 = 0 ⇒ sec A = 2

⇒ sec A = sec 60°

⇒ A = 60°

∴ The value of A (in degrees) is 60°

Given:

∠ABC = 58° and ∠ACB = 34°

Concept used:

The sum of all three angles of a triangle = 180°

A bisector of an angle divides the angles into equal parts

Calculation:

In, ΔABC, ∠BAC = 180° - 58° - 34° = 88°

∴ ∠BAE = 88°/2 = 44°

Here, AD ⊥ AC

In ΔBAD, ∠BAD = 180° - 58° - 90° = 32°

So, ∠DAE = ∠BAE - ∠BAD = 44° - 32° = 12°

∴ The measure of ∠DAE is 12°

Shortcut TrickAD is perpendicular to BC and AE is the bisector of ∠BAC, then

∠DAE = (∠B - ∠C)/2

⇒ (58° - 34°)/2

⇒ 24°/2 = 12°

Given:

∠AEB = 36°

Concept used:

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

Calculation:

Suppose, AC = BD

Then, ∠CAO = ∠ACO = ∠OBD = ∠ODB

So, ∠CAO = ∠ACO = ∠OBD = ∠ODB = (180° - 36°)/2 = 72°

∴ ∠AOC = ∠BOD = 180° - (2 × 72°) = 180° - 144° = 36°

So, ∠DOC = 180° - ∠AOC - ∠BOD

= 180° - 36° - 36° = 108°

∴ The measure of ∠DOC is 108°

Alternate Method:

In ΔABE, E = 36^∘ 

∴ ∠A + ∠B = 144^∘ 

Let ∠A = a and ∠B = 144^∘ - a

Now in ΔOAC and ΔOBD,

∠OAC = ∠OCA and ∠OBD = ∠ODB

∴ ∠AOC = 180^∘ - 2a

∠BOD = 2a - 108^∘ 

 ⇒ ∠AOC + ∠BOD + ∠DOC = 180^∘

⇒ 180^∘ - 2a + 2a - 108^∘ + ∠DOC = 180^∘ 

⇒ ∠DOC = 108^∘ 

Given:

8k6 + 15k3 – 2 = 0

Calculation:

Let, k3 = x

So, 8x² + 15x - 2 = 0

⇒ 8x2 + 16x - x - 2 = 0

⇒ 8x (x + 2) - 1 (x + 2) = 0

⇒ (8x - 1) (x + 2) = 0

⇒ 8x - 1 = 0 ⇒ x = 1/8

⇒ x + 2 = 0 ⇒ x = - 2 [Not possible because of negative value]

Now, k3 = 1/8

⇒ k = 1/2 ⇒ 1/k = 2

Then, (k + 1/k) = (1/2 + 2) = 5/2 = $2\frac{1}{2}$

∴ The value of (k + 1/k) is $2\frac{1}{2}$

Given:

2k sin 30° cos 30° cot 60° = $\frac{{{{\cot }^2}30^\circ \sec 60^\circ \tan 45^\circ }}{{{\rm{cose}}{{\rm{c}}^{\rm{2}}}{\rm{45^\circ cosec 30}}^\circ }}$

Calculation:

2k sin 30° cos 30° cot 60° = $\frac{{{{\cot }^2}30^\circ \sec 60^\circ \tan 45^\circ }}{{{\rm{cose}}{{\rm{c}}^{\rm{2}}}{\rm{45^\circ cosec 30}}^\circ }}$

⇒ 2k × (1/2) × (√3/2) × (1/√3) = $\frac{(\sqrt3)^2×2×1}{(\sqrt2)^2×2}$

⇒ 2k × (1/4) = $\frac{3×2}{2×2}$

⇒ k/2 = 6/4

⇒ k = (6 × 2)/4 = 12/4 = 3

∴ The value of k is 3

Given:

A, B, and C invested ₹40000, ₹48000, and ₹80000, respectively

The total profit = ₹ 672000

Calculation:

After six months, for the remaining time of the year, A added ₹4000, B added ₹4000 and C withdrew ₹4000 every month.

So, (4000 × 6) + (4000 × 5) + (4000 × 4) + (4000 × 3) + (4000 × 2) + (4000 × 1) = 4000 × 21 = 84000

A : B : C = [(40000 × 12) + 84000] : [(48000 × 12) + 84000] : [(80000 × 12) - 84000]

= (480000 + 84000) : (576000 + 84000) : (960000 - 84000)

= 564000 : 660000 : 876000

= 564 : 660 : 876

The share of C = [876/(564 + 660 + 876)] × 672000

= (876/2100) × 672000

= 280320

∴ C's share is ₹ 280320

Given:

The average of 15 numbers = 30

The average of 13 of these numbers = 32

Calculation:

Let, each of the two same numbers = x

2x = (15 × 30) - (13 × 32)

2x = 450 - 416

2x = 34

x = 34/2 = 17

∴ The each of the two numbers is 17

Shortcut Trick

On simple interest, a certain sum becomes Rs. ₹49,600 in 3 years and ₹56,000 in 5 years.

The total interest in 2 years = 56000 - 49600 = Rs. 6400

The total interest in 1 year = 6400/2 = Rs. 3200

The total interest in 5 years = 3200 × 5 = Rs. 16000

So, the total amount = 56000 - 16000 = Rs. 40000

The rate of percentage = (3200/40000) × 100 = 8%

The new rate of percentage = 8 + 2 = 10%

So, time required 100%/10% = 10 years

∴ The sum have become doubled in 10 years

Alternate Method

Given:

On simple interest, a certain sum becomes Rs. ₹49,600 in 3 years and ₹56,000 in 5 years.

Formula used:

The simple interest = (p × r × t)/100

Where, p = Total amount

r = Rate of interest

t = Time (years)

Calculation:

Let, the amount = P and Rate of interest = R

So, (P × R × 3)/100 = (49600 - P)

⇒ (P × R)/100 = (49600 - P)/3   .....(1)

Also, (P × R × 5)/100 = (56000 - P)

⇒ (P × R)/100 = (56000 - P)/5   .....(2)

Then, (49600 - P)/3 = (56000 - P)/5

⇒ 168000 - 3P = 248000 - 5P

⇒ 5P - 3P = 248000 - 168000

⇒ 2P = 80000

⇒ P = 80000/2 = 40000

∴ The amount is 40000

Putting P = 40000 in the equation (1),

⇒ (40000 × R)/100 = (49600 - 40000)/3

⇒ 400 × R = 9600/3

⇒ R = 9600/(3 × 400) = 8

∴ The rate of interest = 8%

The required interest = (2 × 40000) - 40000 = 40000

The rate of interest = 8 + 2 = 10%

Let, the time required = T

So, (40000 × 10 × T)/100 = 40000

⇒ 400 × 10 × T = 40000

⇒ T = 40000/(400 × 10) = 10

∴ The sum have become doubled in 10 years

Given:

AB = AC and ∠BAC = 48°

Concept used:

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

Calculation:

∠ABC = ∠ACB  [∵ AB = AC]

∠BAC + ∠ABC + ∠ACB = 180°

So, ∠ABC = ∠ACB = (180° - 48°)/2 = 132°/2 = 66°

Also, ∠ADC + ∠ABC = 180°

⇒ ∠ADC + 66° = 180°

⇒ ∠ADC = 180° - 66° = 114°

∴ The measure of ∠ADC is 114°

Shortcut Trick

Equate work: (5M + 2B) × 30 = (7M + 10B) × 15

⇒ 10M + 4B = 7M + 10B ⇒ 3M = 6B ⇒ 1M = 2B

Total work in Boys = (5 × 2 + 2) × 30 = 360 units

Required in 4 days: 360 ÷ 4 = 90 Boys efficiency

40 Men = 80 Boys. Extra boys needed = 90 − 80 = 10

∴ The correct answer is 10 boys.

Alternate Method

Calculations:

⇒ 30(5M + 2B) = 15(7M + 10B)

⇒ 2(5M + 2B) = 7M + 10B

⇒ 10M + 4B = 7M + 10B

⇒ 3M = 6B ⇒ M = 2B

⇒ Total Work (W) = 30(5(2B) + 2B) = 30(12B) = 360B

⇒ Let x boys join 40 men to finish work in 4 days:

⇒ (40M + xB) × 4 = 360B

⇒ (40(2B) + xB) = 90B

⇒ 80B + xB = 90B

⇒ x = 10

∴ The correct answer is 10 boys.

Additional Information

Work Equivalence Formula

The fundamental relation used is M₁D₁H₁ = M₂D₂H₂, where M is efficiency-adjusted manpower.

Efficiency Ratio

In problems involving different categories (men, women, boys), always find the ratio of their individual efficiencies to convert the entire group into a single unit.

Total Work Concept

Total Work = (Number of persons × Efficiency) × Number of days. This remains constant for the same task.

Given:

The given number = 8A5146B

Concept used:

Divisibility rule of 8: If the last three digits of a number is divisible by 8, the number will be divisible by 8

Divisibility rule of 11: The provided integer is divisible if the difference between the sum of the digits at odd places and the sum of the digits at even places is 0 or divisible by 11.

Calculation:

8A5146B is divisible by 88

So, 8A5146B is divisible by 8 and 11

⇒ 46B should be divisible by 8

Put B = 4, 464 is divisible by 8

Hence, B = 4

Now, 8A51464 should be divisible by 11

⇒ (8 + 5 + 4 + 4) - (A + 1 + 6) should be divisible by 11

⇒ 21 - (A + 7) should be divisible by 11

⇒ 14 - A should be divisible by 11

Put A = 3 then, 14 - 3 = 11 which is divisible by 11

So, A = 3

Now, BA = 4³ = 64

∴ The value of BA is 64

Given:

The angles of a triangle are (8x - 15)°,(6x - 11)°, and ( 4x – 10)°

Concept used:

The sum of three angles of a triangle = 180°

Calculation:

(8x - 15) + (6x - 11) + ( 4x – 10) = 180

⇒ 8x - 15 + 6x - 11 + 4x – 10 = 180

⇒ 18x - 36 = 180

⇒ 18x = 180 + 36 = 216

⇒ x = 216/18 = 12

∴ The value of x is 12°

Given:

x - y + z = 0

Calculation:

Let, x =1; y = 2; and z = 1

So, x - y + z = 1 - 2 + 1 = 0 [Satisfied]

Then, (y²/2xz) - (x²/2yz) - (z²/2xy)

= (22/2 × 1 × 1) - (12/2 × 2 × 1) - (12/2 × 1 × 2)

= (4/2) - (1/4) - (1/4)

= 2 - 1/4 - 1/4

= 3/2

∴ The value of the given expression is 3/2

Alternate Methodx - y + z = 0,

⇒ x + z = y

⇒ x³ + z³ + 3xyz = y³

⇒ 3xyz = y3 - x3 - z3 

$\frac{{{y^2}}}{{2xz}}, - ,\frac{{{x^2}}}{{2yz}}, - ,\frac{{{z^2}}}{{2xy}}$

⇒ $\frac{{{y^3}}}{{2xzy}}, - ,\frac{{{x^3}}}{{2xyz}}, - ,\frac{{{z^3}}}{{2xyz}}$

⇒ (y³ - x³ - z³)/2xyz

⇒ 3xyz/2xyz = 3/2

∴ The value of the given expression is 3/2

Given:

The given expression = \frac{2}{7} - \frac{3}{8} - \left[ {2\frac{1}{4} ÷ 3\frac{1}{2},,{\rm{of}},{\rm{1}}\frac{1}{3} + \left{ {1\frac{{17}}{{40}}, - ,\left( {3, - ,1\frac{1}{5}, - ,\frac{3}{8}} \right)} \right}} \right]

Calculation:

\frac{2}{7} - \frac{3}{8} - \left[ {2\frac{1}{4} ÷ 3\frac{1}{2},,{\rm{of}},{\rm{1}}\frac{1}{3} + \left{ {1\frac{{17}}{{40}}, - ,\left( {3, - ,1\frac{1}{5}, - ,\frac{3}{8}} \right)} \right}} \right]

= 2/7 - 3/8 - [9/4 ÷ 7/2 of 4/3 + {57/40 - (3 - 6/5 - 3/8)}]

= 2/7 - 3/8 - [9/4 ÷ 14/3 + {57/40 - 57/40}]

= 2/7 - 3/8 - [9/4 ÷ 14/3]

= 2/7 - 3/8 - [(9 × 3) ÷ (4 × 14)]

= 2/7 - 3/8 - 27/56

= - 32/56

= - 4/7

∴ The value of the expression is - 4/7

Shortcut Trick

Distance 1 = (2/5) × 900 = 360 km

Time 1 = 360 ÷ 60 = 6 hours

Remaining Distance = 900 − 360 = 540 km

Remaining Time = 11 − 6 = 5 hours

Required Speed = 540 ÷ 5 = 108 km/h

∴ The correct answer is 108 km/h.

Alternate Method

Given: Total Distance = 900 km, Total Time = 11 h, Speed₁ = 60 km/h, Distance₁ = 2/5 of Total.

Formula Used: Speed = Distance ÷ Time | Time = Distance ÷ Speed

⇒ Distance of first part = 900 × (2/5) = 360 km

⇒ Time taken for first part = 360 ÷ 60 = 6 hours

⇒ Remaining distance = 900 − 360 = 540 km

⇒ Remaining time = 11 − 6 = 5 hours

⇒ Required speed for remaining journey = 540 ÷ 5

⇒ Required speed = 108 km/h

∴ The correct answer is 108 km/h.

Additional Information

Average Speed

The Average Speed of a journey is calculated as Total Distance ÷ Total Time. If a journey is split into two equal distances with speeds x and y, the average speed is 2xy ÷ (x + y).

Speed-Time Relation

When the distance is constant, the speed is inversely proportional to the time (S₁ ÷ S₂ = T₂ ÷ T₁). When time is constant, speed is directly proportional to distance (S₁ ÷ S₂ = D₁ ÷ D₂).

Unit Conversion

To convert speed from km/h to m/s, multiply by 5/18. To convert from m/s to km/h, multiply by 18/5.

Shortcut Trick

In a 30°-60°-90° triangle, the side opposite to 30° is x and the side opposite to 60° is x√3.

Given: Height (opposite to 30°) = 110√3 m.

Distance (opposite to 60°) = Height × √3 = 110√3 × √3 = 110 × 3 = 330 m.

∴ The correct answer is 330 m.

Alternate Method

Given:

Height of Tower (QR) = 110√3 m

Angle of Elevation at P = 30°

Formula Used:

tan θ = Perpendicular ÷ Base

Calculations:

⇒ tan 30° = QR ÷ PQ

⇒ 1/√3 = 110√3 ÷ PQ

⇒ PQ = 110√3 × √3

⇒ PQ = 110 × 3

⇒ PQ = 330 m

∴ The correct answer is 330 m.

Additional Information

Standard Ratios in Height & Distance

For a 30° elevation, the ratio of Height : Base : Hypotenuse is 1 : √3 : 2.

Angle of Elevation vs Depression

The angle of elevation from a point to the top is always equal to the angle of depression from the top to that point.

Trigonometric Values

tan 30° = 1/√3, tan 45° = 1, tan 60° = √3.

Given:

Total number of students = 40

Calculation:

The total number of students who scored 20 or more marks = 10 + 5 = 15

The percentage = (15/40) × 100 = 37.5%

∴ The total 37.5% of students scored 20 or more marks.

Given:

The radius of the base of cone = 21 cm = 210 mm

The height of the cone = 30 cm = 300 mm

The radius of the sphere = 5 mm

Formula used:

The volume of a sphere = (4/3) × π × (radius)³

The volume of a cone = (1/3) × π × (radius)² × height

Calculation:

Let, the number of sphere required = x

So, x × (4/3) × (22/7) × (5)3 = (1/3) × (22/7) × (210)2 × 300

x × (4/3) × (22/7) × 125 = (1/3) × (22/7) × 44100 × 300

x × 4 × 125 = 44100 × 300

x = (44100 × 300)/(4 × 125)

x = 26460

∴ The total number of required solid spheres is 26460

Given:

There is the percentage of students in five schools in the given pie chart and the table shows the ratio of boys and girls in each school.

Concept used:

The total angle of a pie chart = 360°

Calculation:

Let, the total number of students = 100

So, the total students of each schools are:

A = 28; B = 15; C = 24; D = 18; E = 15

Then, the total number of girl student in school B = (2/5) × 15 = 6

The total number of girl student in all schools = [(3/7) × 28 + (2/5) × 15 + (5/8) × 24 + (1/3) × 18 + (4/5) × 15]

= 12 + 6 + 15 + 6 + 12

= 51

The angle = $\frac{Number of girls in school B}{Total number of girls} \times 360$

⇒ (6/51) × 360 = 42.35...° ≈ 42° (the nearest integer)

∴ The measure of the sector angle (to the nearest integer) will be 42°

Shortcut Trick The LCM of two prime numbers is simply their product. ⇒ A × B = 209 ⇒ 209 = 19 × 11 Given A > B, we get A = 19 and B = 11. ⇒ A2 − B = 192 − 11 = 361 − 11 = 350 ∴ The correct answer is 350.

Alternate Method Given: A and B are prime numbers with A > B. LCM(A, B) = 209 Concept Used: The LCM of distinct prime numbers is exactly their product, as they do not share any common factors other than 1. Calculations: ⇒ LCM = A × B ⇒ A × B = 209 Factorising 209 into prime numbers: ⇒ 209 = 11 × 19 Since A and B are prime and A > B: ⇒ A = 19 ⇒ B = 11 Substituting the values into the required expression A2 − B: ⇒ A2 − B = 192 − 11 ⇒ A2 − B = 361 − 11 ⇒ A2 − B = 350 ∴ The correct answer is 350.

Additional Information LCM of Prime Numbers The lowest common multiple (LCM) of distinct prime numbers is always their product. LCM(a, b) = a × b. HCF of Prime Numbers The highest common factor (HCF) of distinct prime numbers is always 1, as they have no other common divisors. Co-prime Numbers Two numbers are co-prime if their HCF is 1. All prime numbers are co-prime to each other, and certain pairs of composite numbers can also be co-prime (e.g., 4 and 9).

Shortcut Trick

Use the ratio formula: CP / MP = (100 − Discount%) / (100 + Profit%)

1560 / MP = (100 − 18) / (100 + 24) = 82 / 124

MP = 1560 × (124 ÷ 82) = 1560 × 1.51219...

MP ≈ ₹2359.02

∴ The correct answer is ₹2359.

Alternate Method

Given:

Cost Price (CP) = ₹1,560

Profit% = 24%

Discount% = 18%

Formula Used:

Selling Price (SP) = CP × (100 + Gain%) ÷ 100

Marked Price (MP) = SP × 100 ÷ (100 − Discount%)

CP ₹1,560

+24% Gain

SP

−18% Disc

MP ? (Req.)

Calculations:

⇒ SP = 1560 × (124 ÷ 100)

⇒ SP = 1560 × 1.24 = ₹1,934.40

⇒ MP = 1934.40 × 100 ÷ (100 − 18)

⇒ MP = 1934.40 ÷ 0.82

⇒ MP = 2359.024...

⇒ Nearest value ≈ ₹2359

∴ The correct answer is ₹2359.

Additional Information

Marked Price and Cost Price Relationship

The most efficient way to solve problems involving CP, MP, Profit, and Discount is the direct ratio: MP / CP = (100 + P%) / (100 − D%).

Successive Discounts

If two discounts d₁% and d₂% are given, the effective discount is (d₁ + d₂ − (d₁ × d₂) ÷ 100)%.

Dishonest Dealer

Profit % = [ (True Weight − False Weight) ÷ False Weight ] × 100.

Given:

The following bar graph shows the receipts and expenditures of a business firm over 5 years.

Calculation:

The increase in receipts from 2017 to 2018 (in lakhs) = 80 - 64 = 16

The increase percentage = (16/64) × 100 = 25%

∴ The increasing percentage in receipts is 25% from 2017 to 2018

Shortcut Trick

Let the initial salary of the person be 100.

Applying the successive percentage changes directly as multiplying factors:

New Salary = 100 × (1 − 0.5) × (1 + 0.5) × (1 + 1)

New Salary = 100 × 0.5 × 1.5 × 2 = 150

Since the final salary is 150, the net change is 150 − 100 = 50 increase over the base of 100.

∴ The correct answer is Gain of 50%.

Alternate Method

Given:

First change = 50% decrease

Second change = 50% increase

Third change = 100% increase

100 Initial

50

75

150 Final

−50%

+50%

+100%

Net Change: +50%

Formula Used:

Final Value = Initial Value × (1 ± R₁/100) × (1 ± R₂/100) × ...

Calculation:

Let the original salary of the person be x.

⇒ Salary after first 50% decrease = x × (100 − 50)/100 = x × (1/2)

⇒ Salary after subsequent 50% increase = [x × (1/2)] × (100 + 50)/100

⇒ Salary after 50% increase = x × (1/2) × (3/2) = x × (3/4)

⇒ Salary after final 100% increase = [x × (3/4)] × (100 + 100)/100

⇒ Final Salary = x × (3/4) × (2/1) = 1.5x

⇒ Net change = Final Salary − Initial Salary

⇒ Net change = 1.5x − x = 0.5x (A positive value implies a gain)

⇒ Percentage Gain = (0.5x / x) × 100% = 50%

∴ The correct answer is Gain of 50%.

Additional Information

Successive Percentage Change

When a value is sequentially changed by a% and then by b%, the net percentage change is evaluated using the formula (a + b + a × b / 100)%. Use a positive sign for any increase and a negative sign for any decrease.

Base Change Method

It is highly effective to assume an initial base value of 100. This strictly avoids intermediate fraction algebra and quickly yields the final result relative to 100, making it easier to directly see the net percentage gain or loss.

Multiplying Factor Approach

For any x% increase, the corresponding multiplying factor is (1 + x/100). For an x% decrease, the factor is (1 − x/100). The total overall change can be found simply by taking the product of all individual factors in a single continuous expression.

Given:

The number of youth (in lakhs) and the number of employed youth (in lakhs) in five states A, B, C, D, and E are shown in the bar graph.

Calculation:

The percentage of employed youth in state A = (10.5/12) × 100 = 87.5%

The percentage of employed youth in state B = (7/8) × 100 = 87.5%

The percentage of employed youth in state C = (10/11.5) × 100 = 86.95...%

The percentage of employed youth in state D = (7.5/10) × 100 = 75%

The percentage of employed youth in state E = (8/9) × 100 = 88.88...%

∴ The state D has employed youth less than 80% of its total youth population

Shortcut Trick

Ratio method: Watch 1 (26% gain) ⇒ CP₁ : SP₁ = 100 : 126 = 50 : 63.

Ratio method: Watch 2 (10% loss) ⇒ CP₂ : SP₂ = 100 : 90 = 10 : 9.

Since Selling Price (SP) is same (₹12,600), make SP parts equal: SP₂ = 9 × 7 = 63, so CP₂ = 10 × 7 = 70.

Total CP = 50 + 70 = 120 units | Total SP = 63 + 63 = 126 units.

Overall Gain% = (6 ÷ 120) × 100 = 5%.

∴ The correct answer is Gain of 5%.

Alternate Method

Given: SP₁ = SP₂ = ₹12,600. Profit₁ = 26%, Loss₂ = 10%.

Formulas: CP = SP × 100 ÷ (100 + P%) | CP = SP × 100 ÷ (100 − L%) | Gain% = (Total SP − Total CP) ÷ Total CP × 100.

⇒ CP₁ = 12,600 × 100 ÷ 126 = ₹10,000.

⇒ CP₂ = 12,600 × 100 ÷ 90 = ₹14,000.

⇒ Total CP = 10,000 + 14,000 = ₹24,000.

⇒ Total SP = 12,600 × 2 = ₹25,200.

⇒ Overall Gain = 25,200 − 24,000 = ₹1,200.

⇒ Gain% = (1,200 ÷ 24,000) × 100 = 5%.

∴ The correct answer is Gain of 5%.

Additional Information

Combined Gain/Loss Formula

When SP is same, Net % = [100(x + y) + 2xy] ÷ [200 + x + y], where x and y are profit/loss percentages with signs.

Special Case: Same % Gain and Loss

If an item is sold at x% gain and another at x% loss with same SP, there is always a loss of x² ÷ 100 %.

The erroneous part is 'since two hours,'.

Key Points

• The given sentence is grammatically incorrect.
• Here, 'for two hours' should be used instead of 'since two hours'.
• We use 'for' with a period of time in the past, present, or future.
• We use 'since' with a point in time in the past.
• Example: 
• He lived in Oxford for 3 years and then he moved. (completed past)
• They’ve lived in Oxford since 2004.
• In the given sentence 'two hours' is a period of time hence 'for' will be used.
• Thus, the correct answer is Option 2.

Correct Sentence: As it has been raining heavily for two hours, the children are at home.

The correct answer is 'Leave'.

Key Points

• The most appropriate antonym of the given word 'Linger' is 'Leave'.
• Linger: to stay somewhere or do something for longer than usual. (किसी जगह देर तक रुके रहना या कोई काम देर तक करते रहना)
• Example: His eyes lingered on the money in her bag.
• Leave: to go away from somebody/something. (किसी व्‍यक्ति या वस्‍तु से दूर जाना)
• Example: We should leave now if we’re going to get there by eight o’clock.

Correct Answer: Leave.

Additional Information

• Let's look at the meaning of other words:
• Choose: to decide which thing or person you want out of the ones that are available. (उपलब्‍ध वस्‍तुओं या व्‍यक्तियों में से चयन या चुनाव करना; चुनना)
• Entertain: to interest and amuse somebody in order to please him/her. [किसी का जी बहलाना (ताकि वह ख़ुश रहे)]
• Annoy: to make somebody angry or slightly angry. (किसी को क्रोधित या नाराज़ करना; परेशान या तंग करना; ग़ुस्‍सा दिलाना)

The correct answer is 'Amnesia'.

Key Points

• The most appropriate word for the given group of words is 'Amnesia'.
• It means 'the loss of memories, such as facts, information and experiences (यादों की हानि, जैसे तथ्य, सूचना और अनुभव)'.
• Example: She'd been terrified since being told she had amnesia, but she'd stayed strong

Correct Answer: Amnesia.

Additional Information

• Let's look at the meaning of other words:
• Asphyxia: the state of being unable to breathe, which causes somebody to die or to become unconscious. (साँस न ले पाने की स्थिति, जो बेहोशी या मृत्‍यु का कारण बन सकती है; श्‍वासरोध)
• Anaemia: a medical condition in which there are not enough red cells in the blood. (रक्त में लाल कणों की कमी; रक्ताल्‍पता, ख़ून की कमी, अरक्तता)
• Alopecia: the partial or complete absence of hair from areas of the body where it normally grows; baldness. (शरीर के उन क्षेत्रों से बालों की आंशिक या पूर्ण अनुपस्थिति जहां यह सामान्य रूप से बढ़ता है; गंजापन)

The correct answer is 'so friendly as'.

Key Points

• The underlined part in the given sentence is grammatically incorrect.
• Here, 'so friendly as' should be used instead of 'so friendly like'.
• We often use so when we mean ‘to such a great extent’.
• With this meaning, 'so' is a degree adverb that modifies adjectives and other adverbs.
• We use 'as' to connect a result with a cause.
• Example: His comments on the book were so childish as to be not worth considering.
• Thus, the correct answer is Option 1.

Correct Sentence: He's not so friendly as she is.

The correct answer is 'Option (2)' i.e. 'Stratagy'.

Key Points

• The word "Stratagy" is incorrectly spelt; the correct spelling is "Strategy", which means a plan of action designed to achieve a long-term goal. (रणनीति)
• Example: The team's strategy helped them win the final match.
• The correct word "Strategy" is widely used in management, planning, and competitive contexts. (सही वर्तनी: Strategy — रणनीति)
• Example: A good business strategy ensures long-term success.
• Hence, "Stratagy" is identified as the incorrectly spelt word among the options.

Therefore, the correct answer is- Stratagy.

Additional Information

• Statutory (वैधानिक): Something required or authorized by law.
• Example: Attendance at the meeting is a statutory requirement.
• Stationary (स्थिर / न चलने वाला): Something that is not moving.
• Example: The vehicle remained stationary at the signal.
• Stationery (लिखने-पढ़ने का सामान): Materials such as pens, paper, envelopes, etc.
• Example: She bought new stationery for the office.

The correct answer is 'No error'.

Key Points

• The given sentence is grammatically correct.
• Here, everything is well arranged.
• In the given sentence 'eggs' is plural. Hence, a plural auxiliary verb 'were' is used after it.
• Thus, the correct answer is Option 2.

The correct answer is 'convenient'.

Key Points

• The most appropriate word for the given blank is 'convenient'.
• It means 'suitable or practical for a particular purpose; not causing difficulty'. (विशेष उद्देश्‍य की दृष्टि से उपयुक्त या व्‍यावहारिक; आसान, सुविधाजनक)
• Example: I’m willing to meet you on any day that’s convenient for you.
• Thus, the correct answer is Option 3.

Correct Sentence: This app is a very convenient one for online shopping.

Additional Information

• Let's look at the meaning of other words:
• convenience: the quality of being easy, useful, or suitable for somebody. (आसानी, सुविधा, उपयुक्तता)
• competency: the fact of having the ability or skill that is needed for something. (कुछ करने की क्षमता, विशिष्‍ट योग्‍यता सामर्थ्य, सक्षमता)
• capable: having the ability or qualities necessary to do something. (कुछ करने में सक्षम या समर्थ)

The correct answer is 'No improvement required'.

Key Points

• The given sentence is grammatically correct.
• We know that after the modal verb the base form of the verb is used.
• Here, 'watch' is used which is in the base form.
• Thus, the correct answer is Option 1.

Correct Sentence: We might as well watch a film on TV as there's nothing much to do. 

Additional Information

• In the given question, "as well" is an adverbial phrase that is written in-between the auxiliary verb and the main verb. In the sentence, it means "also". Hence, the improvement is not required in the given sentence.

Important Points 

We use might as well or may as well to suggest doing something because there is nothing better to do or because it has some advantage. For example:

• We might as well watch a film on TV as there’s nothing much to do. (There is no better alternative than watching a film on TV.)
• You may as well tell me the truth. I’ll find out anyway. (It is better for you to tell me the truth.)

The other options are incorrect and do not make sense in the sentence.

The correct answer is 'The firemen rescued all the inmates from the building.'

Key Points 

• The given sentence is in Passive Voice. As per the given question, we have to change it into Active 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 'All the inmates'.​​
• The object of the given sentence is 'the firemen'.
• The subject will be put in place of the object and the object will be put in place of the subject.
• And 'were rescued' will be changed into 'rescued'.
• Lastly, the preposition 'by' will be removed. 

Correct Sentence: The firemen rescued all the inmates from the building.

The erroneous part is 'since six months'.

Key Points

• The given sentence is grammatically incorrect.
• Here, 'for six months' should be used instead of 'since six months'.
• We use 'for' with a period of time in the past, present, or future.
• We use 'since' with a point in time in the past.
• Example: 
• He lived in Oxford for 3 years and then he moved. (completed past)
• They’ve lived in Oxford since 2004.
• In the given sentence 'six months' is a period of time hence 'for' will be used.
• Thus, the correct answer is Option 1.

Correct Sentence: We have not met some of our friends for six months.