SSC CHSL Tier-1 2023: Official Paper (Held On: 02 Aug, 2023 Shift 2) (Previous Year Paper)

The logic followed here is:

For, 'GAMU is related to JDPX'

For, 'LHTC is related to OKWF'

Similarly, for 'BRLQ'

So, 'BRLQ' will be related to 'EUOT'

Hence, the correct answer is "Option 1".

The logic followed here is:

So, '53' will complete the series.

Hence, the correct answer is "Option 2".

Given equation: 23 C 13 B 841 A 29 D 91 = ?

Decoding the given information :

Now, replacing the sign from left to right and using BODMAS rule, we get :

New equation : 23 + 13 × 841 ÷ 29 - 91 = ?

Calculation :

⇒ 23 + 13 × 841 ÷ 29 - 91 = ?

⇒ 23 + 13 × 29 - 91 = ?

⇒ 23 + 377 - 91 = ?

⇒ 400 - 91 = 309.

Hence, the correct answer is "Option 4".

The logic followed here is:

Given word: ANOTHER 

Now, arranged in reversed alphabetical order:

 

Here, 'Three'  letters will remain unchanged if each of the letters in the word ANOTHER is arranged in reversed alphabetical order.

Hence, the correct answer is "Option 2".

Given word: JOURNAL 

Now, arranging the word in alphabetical order:

 

Now, after arranged in alphabetical order the letter which is fourth from the left is: 'N',

and, the one which is second from the right is: R.

In the English alphabetical series there are three letter between 'N' and 'R' i.e: 'O', 'P', 'Q'.

Hence, the correct answer is "Option 2".

The logic followed here is:

For, 'XU289 is related to SP324'

For, 'QN361 is related to LI400'

Similarly, for 'JG441'

So, 'JG441' will be related to 'EB484'

Hence, the correct answer is "Option 1".

The logic followed here is:

Logic: The symbols are getting shifting upwards and downwards with increasing and decreasing order.

Hence, the correct answer is "Option 1".

The logic followed here is:

So, '7' will complete the series.

Hence, the correct answer is "Option 4".

The logic followed here is:

Logic: Number of letters in the word - 2 = Code of the word.

'RHETORIC' is coded as '6'

No. of letters in the word 'RHETORIC' is 8.

⇒ 8 - 2 = 6.

'GURGLE' is coded as '4'

No. of letters in the word 'GURGLE' is 6.

⇒ 6 - 2 = 4.

Similarly, for 'SIGNATURE'

No. of letters in the word 'SIGNATURE' is 9.

⇒ 9 - 2 = 7.

So, 'SIGNATURE' will be coded as '7'.

Hence, the correct answer is "Option 2".

The logic followed here is:

Logic: (Sum of the place value of all numbers) + Number of letter in that word = Code of the word.

'PACKET' is coded as '62'

⇒ (16 + 1 + 3 + 11 + 5 + 20) + 6

⇒ 56 + 6 = 62.

'POST' is coded as '74'

⇒ (16 + 15 + 19 + 20) + 4

⇒ 70 + 4 = 74.

'FAIR' is coded as '38'

⇒ (6 + 1 + 9 + 18) + 4

⇒ 34 + 4 = 38.

Similarly, for 'PEOPLE'

⇒ (16 + 5 + 15 + 16 + 12 + 5) + 6

⇒ 69 + 6 = 75.

So, 'PEOPLE' will be coded as '75'.

Hence, the correct answer is "Option 2".

The logic followed here is:

Logic: (1^st number × 6) + 2 = 2^nd number.

Now,

For, 9, 56

⇒ (9 × 6) + 2

⇒ 54 + 2 = 56.

For, 17, 104

⇒ (17 × 6) + 2

⇒ 102 + 2 = 104.

Similarly, for Option 4) 15 ∶ 92

⇒ (15 × 6) + 2

⇒ 90 + 2 = 92.

Hence, the correct answer is "Option 4".

The logic followed here is:

Logic: (1^st number × 2) + 5 = 2^nd number.

Now,

For, 12 ∶ 29

⇒ (12 × 2) + 5

⇒ 24 + 5 = 29.

For, 15 ∶ 35

⇒ (15 × 2) + 5

⇒ 30 + 5 = 35.

Similarly, for Option 2) 16 ∶ 37

⇒ (16 × 2) + 5

⇒ 32 + 5 = 37.

Hence, the correct answer is "Option 2".

The logic followed here is:

Logic: (1^st number)3 × 2 = 2^nd number.

Now,

For, 4 ∶ 128

⇒ (4)3 × 2

⇒ 64 × 2 = 128.

For, 7∶ 686

⇒ (7)3 × 2

⇒ 343 × 2 = 686.

Similarly, for 5 ∶ ?

⇒ (5)3 × 2

⇒ 125 × 2 = 250.

Hence, the correct answer is "Option 4".

The logic followed here is:

So, '45' will complete the series.

Hence, the correct answer is "Option 2".

Family Chart:

Decoding the Symbols:

 

Given: J + K ÷ L - T × R

It means: J is the Mother of K, K is the Daughter of L, L is the Brother of T, T is the Sister of R.

So, J is the 'Wife' of L.

Hence, the correct answer is "Option 3".

Given Statements:

Some mangoes are apples.

All apples are grapes.

No pears are mangoes.

The least possible Venn diagram for the given statement is:

Conclusions:

I. Some grapes are mangoes - True (Because, Those part of mangoes which is apples, that will also grapes).

II. No grapes are pears - False (Because, No definite relation given between grapes and pears, so it can be possible only).

So, Only conclusion I follows.

Hence, the correct answer is "Option 3".

Family Chart:

Given: 

M is the brother of N.

N is the father of O.

O is the mother of P who is married to Q.

Q is the son of R.

S is the father of N and married to T.

So, T is 'Father's mother' of O.

Hence, the correct answer is "Option 3".

The correct mirror image of the given figure is:

Hence, the correct answer is "Option 4".

The logic followed here is:

Given Sequence: G_IJG_HIJGGH_IJGGHH_IJ

Now, putting the letters in the blank spaces given in the option one by one:

Option 1) HIJG → GHIJ / GIHIJ / GGHJIJ / GGHHGIJ

Option 2) HGHI → GHIJ / GGHIJ / GGHHIJ / GGHHIIJ - Followed a pattern.

Option 3) JGGJ → GJIJ / GGHIJ / GGHGIJ / GGHHJIJ

Option 4) GHHI → GGIJ / GHHIJ / GGHHIJ / GGHHIIJ

Here, 'Option 2' followed a pattern.

Hence, the correct answer is "Option 2".

BODMAS Table: 

Given Equation: 69 - 44 × 726 ÷ 132 + 58 = ?

After interchanging '+' and '-' and '×' and '÷' we get;

⇒ 69 + 44 ÷ 726 × 132 - 58 = ?

⇒ $69 + ({44 \over 726} \times 132) - 58$ = ?

⇒  69 + 8 - 58 = ?

⇒ 77 - 58 = 19.

Hence, the correct answer is "Option 3".

The logic followed here is:

For, 'BEH is related to GJM'

For, 'FOT is related to KTY'

Similarly, for 'LIN'

So, 'LIN' will be related to 'QNS'

Hence, the correct answer is "Option 4".

The logic followed here is:

So, 'GRTFD' will be the correct alternative that filled in the blanks in the same sequence will make the series logically complete.

Hence, the correct answer is "Option 2".

The logic followed here is:

So, 'PJU' will replace the question mark in the given series.

Hence, the correct answer is "Option 1".

The correct mirror image of the given figure is:

Hence, the correct answer is "Option 4".

The rectangles are:

So, there are '9' rectangles in the given figure.

Hence, the correct answer is "Option 1".

The correct solution is Ujjawala Scheme.

Key Points

• Ujjawala Scheme is not related to microfinance type of initiatives.
• The Ujjawala Scheme is a scheme launched by the Indian government to provide free LPG connections to women from poor households.
• Prime Minister of India Narendra Modi announced the Pradhan Mantri Ujjwala Yojana on May 1, 2016.
• The goal of scheme is to provide 50 million LPG connections to women from Below Poverty Line (BPL) households.
• Microfinance is the provision of financial services, such as loans, savings, and insurance, to low-income individuals or groups who lack access to traditional banking services.

Additional Information

• Jan Dhan Yojana:
• ​Jan Dhan Yojana is a financial inclusion scheme that aims to provide banking facilities to every household in India.
• It is related to microfinance initiatives.
• Jan Dhan Yojana was launched in August 2014.
• It also provides an overdraft facility of up to Rs. 10,000 and a RuPay debit card.
• Jeevika Project:
• It is a poverty alleviation programme that focuses on promoting sustainable livelihoods for the rural poor in Bihar, India.
• It includes microfinance initiatives.
• Jeevika Project is a joint initiative of the Government of Bihar and the World Bank.
• Indira Kranthi Patham Programme:
• Indira Kranthi Patham Programme was launched in 2005 by the Government of Andhra Pradesh with the aim of reducing poverty and promoting rural development.
• ​It is a poverty alleviation and rural development programme in Andhra Pradesh, India.
• It includes several components, such as microfinance, watershed development, and skill development.

The correct answer is Chhattisgarh.

Key Points

• Bastar Dussehra is a festival celebrated in the Bastar district of Chhattisgarh, which is located in central India.
• The festival is celebrated for 75 days and is known for its unique customs and traditions.
• The main attraction of the festival is the procession of the local deities, which is led by the king of Bastar.
• The festival is celebrated in the month of October or November and is considered to be one of the most important festivals in the state of Chhattisgarh.

Additional Information

• Uttar Pradesh:
• This state is located in northern India and is known for its rich cultural heritage.
• Some of the popular festivals celebrated in Uttar Pradesh include Diwali, Holi, and Eid.
• Haryana:
• This state is located in northern India and is known for its agricultural heritage.
• Some of the popular festivals celebrated in Haryana include Baisakhi, Teej, and Lohri.
• Jharkhand:
• This state is located in eastern India and is known for its tribal culture.
• Some of the popular festivals celebrated in Jharkhand include Sarhul, Karma, and Sohrai.

The correct answer is Koustav Chatterjee.

Key Points

• Koustav Chatterjee became India's 78^th Grandmaster by winning the MPL 59^th Senior National Chess Championship held in Delhi.
• He achieved the Grandmaster title at the age of 18, which is a remarkable feat.
• Chatterjee has been playing chess since the age of 5 and has won several national and international tournaments.
• The Grandmaster title is the highest title a chess player can achieve and is awarded by the World Chess Federation (FIDE).

Additional Information

• G Akash: 
• Akash Ganesan, an Indian chess grandmaster and former national champion, was born on October 1, 1996.
• Hs a 17-year-old chess prodigy from Tamil Nadu who has won several national and international tournaments.
• G Akash became India's 66^th chess Grandmaster.
• Pranav V:
• Grandmaster Pranav Venkatesh is an Indian chess player who was born on October 13, 2006.
• He is a 16-year-old chess player from Kerala who has won the National Under-15 Chess Championship in 2017.
• He won a competition in Romania, making him the 75^th Grandmaster of India.
• Prithu Gupta:
• He is a 16-year-old chess player from Delhi .
• He has won the National Under-13 Chess Championship in 2016 and the National Under-15 Chess Championship in 2018.
• Prithu Gupta became India's 64^th Grandmaster

The correct answer is Article 20 (2).

Key Points

• Double jeopardy means that a person cannot be prosecuted or punished for the same offense more than once.
• Double jeopardy is a fundamental principle of law in many countries, including the United States and India.
• The General Clauses Act of 1897 offers defense against double jeopardy as well.
• Article 20(2) of the Indian Constitution guarantees protection against double jeopardy.
• Article 20(2) also guarantees protection against self-incrimination and retroactive punishment.

Additional Information

• Article 21(2):
• ​It deals with the right to life and personal liberty.
• Article 21(2) guarantees the right to a fair trial and due process of law.
• Article 19(1):
• It guarantees freedom of speech.
• It guarantees several other freedoms, including the right to assemble peacefully and the right to practice any profession or occupation.
• Article 22(2):
• It deals with the rights of arrested persons.
• Article 22(2) guarantees the right to be informed of the grounds of arrest and to consult a legal practitioner.

The correct answer is point where the magnetic field is zero.

Key Points

• The neutral point in the magnetic field of a horizontally positioned bar magnet is the point where the magnetic field is zero.
• This point is also known as the magnetic equator or the magnetic neutral axis.
• At this point, the magnetic field lines of the magnet are parallel to the surface of the earth.
• The location of the neutral point depends on the strength and orientation of the magnet.

Additional Information

• Magnetic field does not change direction at the neutral point, but rather it changes direction at the poles of the magnet.
• Magnetic field is not necessarily the weakest at the neutral point, as it can be weaker or stronger depending on the distance from the magnet and the strength of the magnet.
• Magnetic field is strongest at the poles of the magnet.

The correct answer is Pellagra.

Key Points

• Pellagra is a nutritional disorder caused by vitamin B3 (niacin) deficiency.
• Clinical manifestations of pellagra include skin rashes, diarrhea, dementia, and eventually death if left untreated.
• Vitamin B3 is important for energy production, metabolism, and DNA repair.
• Pellagra was once a common disease in the United States, particularly in the southern states, but it became rare after the fortification of grain products with niacin.

Additional Information

• Anaemia:
• Anemia is a blood condition where the blood's capacity to carry oxygen is diminished because there are fewer red blood cells in the blood than usual.
• It can be caused by various factors such as iron deficiency, vitamin B12 deficiency, or chronic disease.
• Beri Beri:
• It is a disease caused by thiamine (vitamin B1) deficiency.
• It can lead to symptoms such as fatigue, muscle weakness, and nerve damage.
• Scurvy:
• It is a disease caused by vitamin C deficiency.
• It can lead to symptoms such as bleeding gums, skin rash, and joint pain.

The correct answer is Lord Rayleigh.

Key Points

• William Ramsay showed in 1894 that air contained an element unknown until then, which was named argon, with the help of Lord Rayleigh.
• Lord Rayleigh was a British physicist who won the Nobel Prize in Physics in 1904 for his discovery of argon.
• The discovery of argon, a noble gas that does not react with other elements, was made possible by the scientific collaboration of William Ramsay and John William Strutt, better known as Lord Rayleigh.

Additional Information

• Hermann Staudinger:
• He was a German chemist who is known for his work on macromolecules.
• He won the Nobel Prize in Chemistry in 1953.
• Glenn Seaborg:
• He was an American chemist who discovered several new elements.
• He won the Nobel Prize in Chemistry in 1951.
• Harold Urey:
• He was an American chemist who discovered deuterium, a heavy isotope of hydrogen.
• He won the Nobel Prize in Chemistry in 1934.

The correct solution is Nilgiri Hills.

Key Points

• The Western Ghats and Eastern Ghats are two parallel mountain ranges running along the western and eastern coasts of India respectively.
• The Nilgiri Hills are located at the junction of the Western and Eastern Ghats in southern India, making it a significant geographical landmark.
• In India's Northwestern Tamil Nadu, Southern Karnataka, and Eastern Kerala, the Nilgiri Mountains are a portion of the Western Ghats.
• The Moyar River divides the Karnataka Plateau to the north from the Nilgiri Hills.

Additional Information

• Satpura Hills:
• It is located in central India.
• The range begins in eastern Gujarat, travels east along the Madhya Pradesh and Maharashtra borders, and ends in Chhattisgarh.
• Nallamala Hills:
• It is located in the eastern part of the Deccan Plateau.
• It establishes the eastern boundary of the Indian states of Telangana and Andhra Pradesh, as well as the Rayalaseema region.
• Mahendragiri Hills:
• It is located in the Eastern Ghats.
• This mountain peak, located in the Koraput district, is the second highest in Odisha, after Deomali.

The correct answer is There is a possibility of free ridership in its consumption.

Key Points

• Public goods are goods or services that are non-excludable and non-rivalrous in nature.
• They are available to everyone and their consumption by one person does not diminish their availability to others.
• The possibility of free ridership in the consumption of public goods is a key characteristic, as individuals can benefit from the good without contributing to its provision.
• If users don't pay for such goods, they can't be prevented from using or accessing them.
• Multiple people can use the good at the same time.

Additional Information

• The principle of excludability:
• The ability of a good, service, or resource to be restricted to only those who can afford it is known as excludability.
• Excludability refers to the ability of a producer, supplier, or other managing body (such as the government) to stop "free" consumption of a good.
• Clear link between the producer and consumer which occurs through the payment process:
• It is more applicable to private goods.
• It is applicable where payment is necessary to access the good or service***.***
• Its consumption is rivalrous in nature:
• It suggests rivalrous consumption.
• It is also not applicable to public goods as their consumption does not reduce availability to others.

The correct answer is 12 yards.

Key Points

• The distance between the goal line and the penalty spot in football is 12 yards.
• The penalty spot is located 12 yards away from the goal line and is used for penalty kicks.
• The penalty kick is awarded when a team commits a foul inside their own penalty area, and the opposing team is given a free shot at goal from the penalty spot.
• The distance of 12 yards was established in the late 19^th century and has been used ever since.

Additional Information

• 11 yards is used for the width of the penalty area, which extends 11 yards from the goal line.
• An area of an association football pitch is called the penalty area, or 18-yard box (sometimes referred to less formally as the penalty box or just the box).
• The ball is deemed to be inside the penalty area if any portion of it crosses any portion of the line defining the area.

The correct answer is Shreya Ghoshal.

Key Points

• Shreya Ghoshal is a playback singer in Bollywood and not a professional Indian Classical Dancer.
• Singer Shreya Ghoshal was born in India on March 12, 1984 in a bengali brahmin family.
• Her achievements were recognized with multiple awards, such as five Filmfare Awards, seven Filmfare Awards South, four Kerala State Film Awards, two Tamil Nadu State Film Awards, two BFJA Awards, and five National Film Awards.

Additional Information

• Mallika Sarabhai:
• She is the daughter of famous Indian scientist Vikram Sarabhai.
• She has also been involved in activism and theatre.
• Vasundhara Doraswamy:
• She has performed extensively in India and abroad.
• She has also choreographed dance productions.
• Shovana Narayanan:
• She has been recognized for her contributions to Kathak.
• She has also been a member of the Rajya Sabha, the upper house of the Indian Parliament.

The correct answer is Article 47.,

Key Points

• Article 47 states that it is the duty of the state to improve public health and provide medical aid to all citizens.
• Ayushman Bharat Yojana is a scheme launched by the Government of India in 2018 which aims to provide health insurance coverage to vulnerable families and individuals.
• It is a nationwide public health insurance program designed to give low-income citizens of the nation free access to health insurance coverage. Approximately 50% of the population is eligible for this program.
• For individuals in need of specialized care or hospitalization, it offers free secondary and tertiary healthcare.

Additional Information

• Article 45:
• State shall endeavor to provide free and compulsory education for all children until they complete the age of 14 years.
• This clause demonstrates a dedication to guaranteeing that all children in India have access to a basic education and to the universalization of elementary education.
• Article 46:
• State shall promote educational and economic interests of the weaker sections of society.
• In particular, the Scheduled Castes and Scheduled Tribes are among the weaker segments of the population whose educational and economic interests the State will give particular attention to.
• Article 48:
• State shall endeavor to organize agriculture and animal husbandry on modern and scientific lines.
• State shall take steps for preserving and improving the breeds, and prohibiting the slaughter of cows, calves and other milch and draught cattle.

The correct answer is 1923.

Key Points

• The first radio broadcast in India was on June 23, 1923, by the Radio Club of Bombay.
• It was a test transmission, and the first regular broadcasting began on July 23, 1927, from the same club.
• The broadcasting was initially done in the evenings for 30 minutes, and the programs were mainly music concerts and talks.

Additional Information

 

• Radio broadcasting is the process of sending audio across radio waves to radio receivers owned by members of the general public, occasionally along with pertinent metadata.
• There are now four forms of radio broadcasting in use:
• AM: Electromagnetic radio waves are all around us but are invisible to the naked eye.
• FM: The term FM refers to frequency modulation.
• DAB: Digital Audio Broadcasting, or DAB, is an acronym.
• Internet radio: When a radio station streams its content online, it's known as internet radio.

The correct answer is Sarod.

Key Points

• Ustad Akbar Ali Khan is remembered for his contribution to the musical instrument 'Sarod'.
• He was a renowned Sarod player and contributed to the development of the instrument.
• The Sarod is a stringed musical instrument that originated in India and is played with a plectrum.
• It has a unique sound and is often used in Indian classical music.

Additional Information

• Tabla :
• Since the 18^th century, the tabla, a pair of small drums, has been an essential part of Hindustani music in northern India, Pakistan, and Bangladesh.
• Santoor:
• The Indian santoor is a hammered dulcimer in the shape of a trapezoid, which is a variant of the Iranian santur.
• The instrument typically has 25 bridges and is constructed of walnut.
• Sitar:
• ​It is a stringed instrument played in Hindustani classical music that is plucked and originated in the Indian subcontinent.
• The instrument originated in medieval India, reached its peak of popularity in the 18^_th century, and evolved into its current form in India during the 19^th century.

The correct answer is Saikhom Mirabai Chanu.

Key Points

• Saikhom Mirabai Chanu, won the silver medal in the women's 49 kg division at the World Weightlifting Championships 2022.
• She is a well-known Indian weightlifter who has won several medals in various international tournaments, including the 2018 Commonwealth Games and the 2020 Asian Championships.
• Her achievement is significant for Indian weightlifting as she has become the first Indian woman to win a medal at the World Weightlifting Championships since Karnam Malleswari's bronze in 1995.
• Her success at the World Weightlifting Championships 2022 has also boosted her chances of winning a medal at the upcoming Tokyo Olympics, where she will represent India in the women's 49 kg category.​

Additional Information

• Swati Singh
• She is a Weightlifter, an Indian.
• She won the bronze medal in the women's 53 kg weight class at the Glasgow 2014 Commonwealth Games.
• Santoshi Matsa
• Weightlifter Santoshi Matsa, an Indian, took home the silver medal in the women's 53 kg weight class at the Glasgow 2014 Commonwealth Games.
• Khumukcham Sanjita Chanu
• Weightlifter Khumukcham Sanjita Chanu hails from India.
• She has won two Commonwealth Games titles.
• In the women's 48 kg and 53 kg weight categories, Chanu won gold medals in both the 2014 Glasgow and 2018 Gold Coast events.

The correct answer is Rajasthan.

Key Points

• Rajasthan became the first Indian state to enact the 'Right to Health Act 2022'.
• The act aims to provide every citizen with access to quality healthcare services and facilities.
• It also includes provisions for free medical treatment and medicines for certain categories of people.
• The act also establishes a state health commission to oversee the implementation of the act.

Additional Information

• Punjab:
• Punjab has launched a universal health insurance scheme called Sarbat Sehat Bima Yojana.
• In order to provide better health outcomes, the Punjab government's Sarbat Sehat Bima Yojana offers cashless services and incentive money in the form of health insurance.
• Haryana:
• Haryana has launched a scheme called Mukhyamantri Muft Ilaaj Yojana.
• It provides free medical treatment to certain categories of people.
• Madhya Pradesh:
• Madhya Pradesh has launched a scheme called Ayushman Bharat Madhya Pradesh Niramayam Yojana.
• It provides free medical treatment and medicines to certain categories of people.

The correct answer is Karve Committee.

Key Points

• The Village and Small Scale Industries Committee was set up in 1948 to study the problems of small-scale industries in India and suggest measures for their development.
• The committee was headed by D.R. Karve, a renowned social worker and educationist.
• The committee submitted its report in 1949, which is also known as the Karve Report.
• The report highlighted the need for the development of small-scale industries in India and suggested various measures such as the establishment of industrial estates, provision of financial assistance, and technical training to entrepreneurs.

Additional Information

• Mahalanobis Committee was set up in 1953 to suggest a plan for the rapid industrialization of India.
• It is also known as the Planning Commission.
• Munshi Committee was set up in 1951.
• Its aim was to study the problems of small-scale industries in India and suggest measures for their development.
• Chakravarty Committee was set up in 1985 to suggest measures for the development of small-scale industries in India.
• It is also known as the High-Powered Committee on Urban and Rural Small-Scale Industries.

The correct answer is Moral Suasion.

Key Points

• Moral suasion is a qualitative measure of credit control used by the Reserve Bank of India.
• It is a persuasive technique used by the central bank to influence the behavior of the commercial banks.
• The RBI uses moral suasion to encourage banks to comply with the policy guidelines and regulations issued by the central bank.
• It is a non-binding measure and relies on the reputation and credibility of the RBI to convince the banks to follow the desired course of action.
• Other measures of credit control used by the RBI include quantitative measures such as CRR (Cash Reserve Ratio) and SLR (Statutory Liquidity Ratio).

Additional Information

• CRR (Cash reserve ratio) is the percentage of deposits that banks are required to keep with the RBI as a reserve.
• It is a quantitative measure of credit control as it directly affects the liquidity and lending capacity of the banks.
• SLR (Statutory Liquid Ratio) is the percentage of deposits that banks are required to invest in specified securities such as government bonds.
• It is also a quantitative measure of credit control as it restricts the funds available for lending by the banks.

The correct answer is 21.8%.

Key Points

• The crude birth rate is the number of live births per 1,000 population in a given year.
• As per Census 2011, the crude birth rate of India is 0.218.
• This means that for every 1,000 people in India, 0.218 births occurred in the year 2011.
• It is important to note that the crude birth rate is influenced by various factors such as age structure of the population, fertility rate, and socio-economic factors.
• In India, the crude birth rate has been declining over the years. For instance, it was 23.8 in 1991, 22.8 in 2001, and 21.8 in 2011.

Additional Information

• The ratio of all live births in a population during a given year to all mid-year population for that same year is called the crude birth rate.
• It is one of the key factors regulating a nation's population growth and is multiplied by 1000.
• The formula for CBR = *(number of births) 1000 / estimated population at mid-year.
• Population growth is calculated using the birth rate, mortality, and migration rates.

The correct answer is JLGs

Key Points

• JLGs stands for Joint Liability Groups.
• NABARD launched the JLGs scheme in 2004-05 to cater to the credit needs of small and marginal farmers, tenant farmers, and other vulnerable groups.
• The primary objective of JLGs is to improve the flow of credit to tenant farmers cultivating land as oral lessees, sharecroppers, and small farmers who do not have proper title to their landholding.
• By forming JLGs, these farmers can avail of credit without providing any collateral security, thereby ensuring financial inclusion and improving their livelihood.
• JLGs operate based on mutual guarantee, where each member of the group is responsible for the repayment of loans taken by any member of the group.

Additional Information

• NABARD (National Bank for Agriculture and Rural Development) is an apex development financial institution in India, established on 12^th July 1982.
• NABARD's primary focus is on the development of agriculture and rural areas through various credit and non-credit initiatives.
• The JLG model encourages group lending and ensures that credit is available to those who might otherwise be excluded from the formal banking system.
• Other initiatives by NABARD include SHG-Bank Linkage Program (SBLP), Micro-Enterprise Development Program (MEDP), and various other schemes aimed at rural development and financial inclusion.
• NABARD also plays a crucial role in policy planning, capacity building, and providing refinance support to rural financial institutions.

The correct answer is Chola.

Key Points

• Rajarajeshwara Temple is also known as Brihadeeswarar Temple and is located in the city of Thanjavur (formerly known as Tanjore) in Tamil Nadu, India.
• The temple was built by the Chola dynasty ruler Rajaraja Chola I in the 11^th century AD.
• The temple is a UNESCO World Heritage Site and is considered one of the best examples of Dravidian architecture in India.
• The temple is dedicated to Lord Shiva and has a towering vimana (temple tower) that is one of the tallest in India.

Additional Information 

• Pandya:
• ​The Pandya dynasty ruled over parts of South India, including Tamil Nadu, in the 6^th-17^th centuries AD.
• Maravarman Sundara I established the groundwork for the Pandya empire in southern India around the beginning of the thirteenth century.
• The pinnacles of Pandya architecture are, in fact, the Meenakshi Temple in Madurai and the Aranganathar Temple in Srirangam.
• Pallava:
• ​The Pallava dynasty was an early medieval South Indian dynasty that ruled from the 3^rd-9^th centuries AD.
• They were known for their patronage of the arts and architecture.
• The Shore Temple and the Vaikuntha Perumal Temple in Kanchipuram are two of the best specimens of Pallava art and architecture.
• Chola:
• ​The Chola dynasty was one of the most powerful South Indian dynasties that ruled from the 9^th-13^th centuries AD.
• They were known for their military conquests, administrative skills, and patronage of the arts.
• The Brihadisvara Temple in Thanjavur, the Airavatesvara Temple in Darasuram, and the Brihadisvara Temple in Gangaikonda Cholapuram are the three well-known temples that date back to the Chola era.
• Chera:
• The Chera dynasty was an ancient dynasty that ruled over parts of South India, including present-day Kerala and Tamil Nadu, from the 3^rd century BC to the 12^th century AD.
• Kerala's Thiruvanchikulam Temple, which is devoted to Lord Shiva and has a distinctive architectural style, is situated in the Ernakulam district.

The correct answer is 100.

Key Points

• 100 days of guaranteed wage employment in every financial year has to be provided to every household whose adult members volunteer to do unskilled manual work under the Mahatma Gandhi National Rural Employment Guarantee Act (MGNREGA).
• The MGNREGA was enacted in 2005 to provide a legal guarantee of 100 days of wage employment in a financial year to every rural household whose adult.
• By generating long-lasting assets, raising rural people standards of living, and lowering poverty, the program seeks to give those living in poverty in rural areas security of income.

Additional Information

• The Mahatma Gandhi National Rural Employment Guarantee Act (MGNREGA) is a social security measure that aims to provide employment and livelihood security to rural households in India.
• The MGNREGA is implemented by the Ministry of Rural Development, Government of India, and is the largest employment generation programme in the world.
• The Act aims to create durable assets and infrastructure in rural areas, enhance the livelihoods of rural households, and promote sustainable development in rural India.

The correct answer is Kuchipudi.

Key Points

• Manju Barggavee won the Sangeet Natak Akademi Award of 2019 for the dance form Kuchipudi.
• Actress and dancer Manju Bhargavi is most known for her roles in the Telugu blockbusters Sankarabharanam (1980) and Nayakudu Vinayakudu (1980).
• The Sangeet Natak Akademi, India's National Academy of Music, Dance, and Drama, gives the Sangeet Natak Akademi Award.
• It is the greatest honor bestowed upon those working in the performing arts in India.
• The prize included a tamrapatra (a brass plaque), an angavastram (a shawl), a citation, and Rs. 1,00,000.​

Additional Information 

• Kuchipudi is a classical Indian dance form that originated in the village of Kuchipudi in Andhra Pradesh, India.
• Mohiniattam is a classical Indian dance form that originated in Kerala, India.
• It is known for its graceful movements and expressions.
• Chhau is a semi-classical Indian dance form that originated in the eastern states of India, primarily in West Bengal, Odisha, and Jharkhand.
• It involves acrobatic movements and martial arts.
• Kathak is a classical Indian dance form that originated in Northern India.
• It is known for its fast footwork and intricate hand movements.

The correct answer is from 51 cm to 151 cm.

Key Points

• Dry Tropical Forests are characterized by a long dry season and a short rainy season.
• Sal, acacia, and bamboo are some of the common tree species found in Dry Tropical Forests.
• These forests receive an annual rainfall ranging from 51 cm to 151 cm, which is lower than the rainfall received by other forest types.
• This are found between 10^o and 25^o latitude.
• These forests are important habitats for a variety of wildlife species and provide various ecosystem services, such as carbon sequestration, soil conservation, and water regulation.

Additional Information

• Sal is a tree species found in tropical and subtropical regions of Asia and Africa.
• It is also known as Shorea robusta.
• Acacia is a genus of trees and shrubs found in arid and semi-arid regions of Africa, Australia, and the Americas.
• ​Based on the African species Acacia nilotica, it was first described by the Swedish scientist Carl Linnaeus in 1773.
• Bamboo is a type of grass that grows in tropical and subtropical regions of Asia, Africa, and the Americas.
• The Indian Forest Act, 1927 considered it a tree. Accordingly, cutting bamboo from outside forests and transporting it was made unlawful.
• In 2017 an amendment was made to the Indian Forest Act, 1927 and bamboo has been removed from the tree category.

The correct answer is Ministry of Science and Technology.

Key Points

• The Council of Industrial Research (CSIR) was established in 1942 and has its headquarters in New Delhi.
• The CSIR has a network of 38 national laboratories and 39 outreach centers spread across the country.
• The Council of Scientific undefined Industrial Research (CSIR) comes under the Ministry of Science and Technology.
• CSIR is a premier national organization in India and is among the world's largest publicly funded organization.
• The Ministry of Science and Technology is responsible for promoting the development and application of science and technology in various sectors of the economy.

 Additional Information

• The Ministry of Commerce and Industry is responsible for formulating and implementing policies for the promotion of internal, external trade and commerce in India as well as for the promotion of industrial development in India.
• The Ministry of Earth Sciences is responsible for promoting sustainable development of oceans, atmosphere, and other natural resources and provide weather and climate-related services to various sectors of the economy.
• The Ministry of Education is responsible for the formulation of policies, laying down of norms, and standards for education in India.

Calculation:

Total cost of the computer = Rs. 39000

Down payment = Rs. 19000

Balance = Rs. (39000 - 19000) = Rs. 20000.

Let the rate of interest be R% p.a.

Amount of Rs. 20000 for 5 months

=Rs.( 20000 + 20000 × 5/12 × R/100)=Rs.(20000+250R/3)

The customer pays the shopkeeper Rs. 4200 after 1 month,

Rs. 4200 after 2 months, ...... and Rs. 4200 after 5 months.

Thus, the shopkeeper keeps Rs. 4200 for 4 months, Rs. 4200 for 3 months, Rs. 4200 for 2 months, Rs. 4200 for 1 months and Rs. 4200 at the end.

∴ sum of the amounts of these installments

⇒  (Rs. 4200 + S.I. on Rs 4200 for 4 months) + (Rs. 4200 + S.I. on Rs. 4200 for 3 months) + ...... + (Rs. 4200 + S.I. on Rs. 4200 for 1 month) + Rs. 4200

⇒ Rs. (4200 × 5) + S.I. on Rs. 4200 for (4 + 3 + 2 + 1) months

⇒ Rs. 21000 + S.I. on Rs. 4200 for 10 months

⇒ Rs.(21000 + 4200 × R × 10/12×1/ 100)

⇒ (21000 + 35R)

(20000+250R/3) =  (21000 + 35R)

R = $20\frac{20}{29}$%

Alternate Method Total amount = 39000

Down payment = 19000

Remaining amount = 20000

Installment = 4200

So,

Principal 

At Starting         =   20000

after 1 month →  20000 - 4200 = 15800

After 2 months → 15800 - 4200 = 11600

After 3 months →  11600 - 4200 = 7400

After 4 months →  7400 - 4200 = 3200

So, 

total principal = 20000 + 15800 + 11600 + 7400 + 3200 = 58000

and

Interest = 4200 × 5 - 20000 = 1000

So,

rate of interest for 1 month = (1000/58000) × 100 = 100/58 = (50/29)%

rate of interest for 12 months or annual rate of interest = 12 ×  (50/29)% = (600/29)%

Shortcut Trick

The length of the transverse common tangent (TCT) is calculated using the direct formula:

TCT = √[d² − (r₁ + r₂)²]

Where d is the distance between centres, and r₁, r₂ are the radii.

⇒ TCT = √[12² − (5 + 4)²]

⇒ TCT = √[144 − 81] = √63

∴ The correct answer is √63 cm.

Alternate Method

Given:

Distance between the centres of two circles = 12 cm

Radii of the two circles = 5 cm and 4 cm

Formula Used:

Length of transverse common tangent = √[(Distance between the centres)2 − (r1 + r2)2]

Calculation:

Let the length of the transverse common tangent = D

According to the formula,

D = √[122 − (5 + 4)2]

⇒ D = √(144 − 92)

⇒ D = √(144 − 81)

⇒ D = √63 cm

∴ The correct option is 3.

Additional Information

Direct Common Tangent (DCT)

The length of the direct common tangent is given by the formula: DCT = √[d² − (R − r)²].

Existence of Tangents

A transverse common tangent exists only if the distance between the centres is greater than or equal to the sum of the radii (d ≥ R + r).

Common Tangent Cases

If two circles touch each other externally, d = R + r, and there are 3 common tangents (2 direct and 1 transverse).

Shortcut Trick

For successive discounts, use the multiplying factor method.

Net Multiplier = (100 − 18)% × (100 − 12)% × (100 − 5)%

Net Multiplier = 0.82 × 0.88 × 0.95 = 0.68552

Net Selling Price = 36000 × 0.68552 = Rs. 24,678.72

∴ The correct answer is Rs. 24,678.72.

Alternate Method

Given: Marked Price (MP) = Rs. 36,000, Successive Discounts = 18%, 12%, and 5%.

Step-by-step Calculation:

⇒ Price after 18% discount = 36000 − (18 ÷ 100 × 36000) = 36000 − 6480 = Rs. 29,520

⇒ Price after 12% discount = 29520 − (12 ÷ 100 × 29520) = 29520 − 3542.4 = Rs. 25,977.60

⇒ Price after 5% discount = 25977.60 − (5 ÷ 100 × 25977.60) = 25977.60 − 1298.88 = Rs. 24,678.72

∴ The correct answer is Rs. 24,678.72.

Additional Information

Successive Discount Formula

For two successive discounts d₁ and d₂, the single equivalent discount is [d₁ + d₂ − (d₁ × d₂ ÷ 100)]%.

Selling Price and Marked Price

Selling Price (SP) = Marked Price (MP) × (100 − Discount%) ÷ 100. Discounts are always calculated on the Marked Price.

Effective Discount for Three Rates

Net SP = MP × (1 − d₁/100) × (1 − d₂/100) × (1 − d₃/100). The overall discount percentage is 1 − [(1 − d₁/100)(1 − d₂/100)(1 − d₃/100)].

Calculation:

Total as we know, 2100 + 800 + 700 = 3600

So the value of 3600= 360° 

So the value of 1° = 10

The angles made by the cities C  on pie chart is 1200 / 10 = 120°

The angles made by the cities  D on pie chart is 900 / 10 = 90° 

 ∴ The correct option is 4

Given:

Two circles of radius 25 cm and 20 cm. The centres of the two circles are 35 cm apart.

Formula used:

Direct common tangent = √ (distance between the two centers2 - ( r1  - r2)2

Calculation: 

Direct common tangent = D

As per the formula,

D = √ (352 - ( 25  - 20)2.

⇒ √ (352 - 52)

⇒ √(30 × 40)

⇒ √1200 = 20√ 3

∴ The correct option is 3

Shortcut Trick

Use the direct algebraic identity: a³ − b³ = (a − b)((a − b)² + 3ab)

Substitute the given values: 4401 = 9 × (9² + 3ab)

⇒ 4401 ÷ 9 = 81 + 3ab

⇒ 489 − 81 = 3ab

⇒ 408 = 3ab ⇒ ab = 136

∴ The correct answer is 136.

Alternate Method

Given:

Difference (a − b) = 9

Difference of cubes (a³ − b³) = 4401

Formula Used:

a³ − b³ = (a − b)(a² + ab + b²)

Since a² + b² = (a − b)² + 2ab, we have:

a³ − b³ = (a − b)((a − b)² + 3ab)

Calculation:

⇒ 4401 = 9 × (9² + 3ab)

⇒ 4401 = 9 × (81 + 3ab)

⇒ 4401 ÷ 9 = 81 + 3ab

⇒ 489 = 81 + 3ab

⇒ 3ab = 489 − 81

⇒ 3ab = 408

⇒ ab = 408 ÷ 3

⇒ ab = 136

∴ The correct answer is 136.

Additional Information

Cube of a Binomial

(a − b)³ = a³ − b³ − 3ab(a − b). This is a rearranged version of the identity used to find ab or a³ − b³.

Sum of Cubes Identity

a³ + b³ = (a + b)(a² − ab + b²) = (a + b)((a + b)² − 3ab).

Square of a Binomial

(a − b)² = a² + b² − 2ab and (a + b)² = a² + b² + 2ab.

Given:

Average weight of group A = 12 kg and  group B = 24 kg

The ratio of the members in group A to group B is 1 ∶ 2

Concept used:

Total value = average × numbers of observation

Calculation:  

Let the number of A is x and B is 2x

Total numbers of observations is 2x + x = 3x

As per the question,

The combined average of both the groups is,

 (12 × x + 24 × 2x) / 3x

⇒ 60x /3x = 20

∴ The correct option is 3

Given:

A = 60°, B = 30°

Formula used:

Sin (A+B) =  sin A cos B + cos A sin B

Calculation:

sin A cos B + cos A sin B

⇒ Sin (A+B)

⇒ Sin (60+30)

⇒ Sin 90° = 1

∴ The correct option is 4

Given:

(a + $\frac{1}{a}$) = 6

Formula used:

(a + $\frac{1}{a}$) ² = a² + 1/a² + 2

⇒ a2 + 1/a2 = (a + $\frac{1}{a}$) 2  - 2

Calculation: 

$\rm \frac{3}{4}\left(a^2+\frac{1}{a^2}\right)$

⇒ 3/4 ( (a + $\frac{1}{a}$) 2  - 2)

⇒ (3/4) ( (6) 2  - 2)

⇒ (3/4) × (36 - 2)

⇒ (3/4) × (34)

⇒ 3 × (8.5) = 25.5

∴ The correct option is 3

Shortcut Trick

B is a sleeping partner, so he receives his share only from the profit remaining after A's managing fee.

Investment Ratio of A and B = 30,000 : 50,000 = 3 : 5.

Remaining profit after A's 20% fee = 80% of ₹10,000 = ₹8,000.

B's share in profit = (5 / 8) × 8,000 = ₹5,000.

∴ The correct answer is ₹5,000.

Alternate Method

Given:

A's investment = ₹30,000

B's investment = ₹50,000

Total Profit = ₹10,000

A's managing fee = 20% of total profit

Calculations:

⇒ Profit is divided by capital ratio since both invested for the same duration.

⇒ Capital Ratio of A and B = 30,000 : 50,000 = 3 : 5

⇒ Total Ratio parts = 3 + 5 = 8 parts

⇒ A's managing fee = 20% of ₹10,000 = ₹2,000

⇒ Remaining divisible profit = 10,000 − 2,000 = ₹8,000

⇒ B's share = (B's ratio ÷ Total ratio) × Divisible profit

⇒ B's share = (5 ÷ 8) × 8,000

⇒ B's share = 5 × 1,000 = ₹5,000

∴ The correct answer is ₹5,000.

Additional Information

Working Partner vs Sleeping Partner

A Working Partner actively manages the business and usually receives a salary or fixed percentage of profit before the division. A Sleeping Partner only invests capital and receives a share only from the remaining divisible profit.

Partnership Profit Distribution

Profit ratio is equal to the product of Capital and Time invested: Profit Ratio = (C₁ × T₁) : (C₂ × T₂). If the time period is the same, profit is distributed directly in proportion to their initial capitals.

Calculation:

The total number of students in class 5 is , 65 + 58 = 123

The total number of students in class 6 is , 59 + 57 =116

The total number of students in class 7 is , 60 + 62 = 122

The total number of students in class 8 is , 61 + 59 = 120

Class V has the maximum number of students.

Given:

The ratio of milk: water = 2:1 ,  

The solution must contain 90% milk in it.

Calculation: 

Let the total volume of milk is v = 30 liter

So the quantity of milk initially is 30 × 2/3 = 20 liter

amount of milk tobe added is x liter

As per the question,

 (20 + x) / 10 = 9/1

x = 90 -20

= 70 liter

Now the volume is v = 30

So the volume will be (70/30) v

⇒ $\frac{7}{3}$v

∴ The correct option is 4

Concept used:

If a number has to be divided by 6 it has tobe divided by both 2 and 3

Calculation:

Here all these options are divided by 2 

Again, (i) 1,97,232 , (ii) 9,72,132 and (iv) 17,90,184 is divided by 3 also because sum of digit is divided by 3

But in option (iii) 8,00,552 , the sum of digit is 8 + 5 + 5 + 2 = 20 which is not divided by 3

∴ The correct option is 2

Given:

A man buys a toy car for Rs. 225 and sells it for Rs. 210

Concept used:

Loss = cost price - selling price

Calculation: 

The cost price is Rs 225 and selling price is Rs 210

The loss amount is 225 - 210 = Rs 15

The loss percentage is,

⇒ 15 / 225 × 100

⇒ 100 /15

⇒ 20/3 = 6.67%

∴ The correct option is 4

Given:

In Δ ABC , PQ is parallel to the side BC . AP = QC , Ab = 16cm and AQ = 4cm

Concept used:

In Δ ABC , PQ parallel to the side BC

So AP / PB = AQ /QC

Calculation:

Let AP = QC = x , PB = 16 - x

As per the question,

$\frac{x}{16-x}=\frac{4}{x}$

⇒ x² + 4x - 64 = 0

⇒ x = $-b \pm \sqrt{b^2-4ac} \over 2a$

⇒ x = $-4 \pm \sqrt{4^2-4(1)(-64)} \over 2(1)$

⇒ x = $-4 \pm \sqrt{16+256} \over 2$

⇒ x = $-4 \pm \sqrt{272} \over 2$

⇒ x = $-4 \pm 4\sqrt{17} \over 2$

⇒ x = $2\sqrt{17}-2$

∴ The correct option is 3.

Shortcut Trick

The surface area of a sphere with diameter (d) is given by πd².

Surface Area = (22/7) × 7 × 7 = 154 m².

Total Painting Cost = Area × Rate = 154 × 13 = ₹2,002.

∴ The correct answer is ₹2,002.

Alternate Method

Given:

Diameter (d) of the spherical tank = 7 m

Radius (r) = d ÷ 2 = 7 ÷ 2 = 3.5 m

Cost of painting = ₹13/m²

Formula:

Surface Area of a sphere = 4πr²

Calculations:

⇒ Surface Area = 4 × (22/7) × (3.5)²

⇒ Surface Area = 4 × (22/7) × (7/2) × (7/2)

⇒ Surface Area = 22 × 7 = 154 m²

⇒ Total Cost of painting = Surface Area × Rate per m²

⇒ Total Cost = 154 × 13

⇒ Total Cost = ₹2,002

∴ The correct answer is ₹2,002.

Additional Information

Volume of a Sphere

The total space occupied by a sphere is given by V = (4/3)πr³.

Surface Area of a Hemisphere

For a hemisphere of radius r, the Curved Surface Area (CSA) is 2πr² and the Total Surface Area (TSA) is 3πr².

Relationship between Diameter and Radius

The diameter (d) is twice the radius (r), i.e., d = 2r. In terms of diameter, the area of a sphere is πd².

Given:

(sin θ - cos θ) = 0

Concept used:

If sin θ - cos θ = 0

then  sin θ = cos θ

then θ = 45°

sin (180 - θ) = sin θ 

sin (90 - θ) = cos θ

Calculation: 

Now by putting θ = 45° 

we get ,

 sin (π − θ) + sin ($\frac{π}{2}$ - θ)

⇒  sin (180 − 45 ) + sin (90 - 45)

⇒  sin (45) + cos (45)

⇒  1/√2 +  1/√2 = √2

∴ The correct option is 4

Given:

The price increased  by 12$\frac{1}{2}$% and the sale increased by 8$\frac{1}{2}$%

Concept used:

Total revenue = Price × number of tickets sold

Calculation:  

As we know 12$\frac{1}{2}$%= 1/8 and  8$\frac{1}{2}$% = 17/200

Let the previous price is Rs 8 now the increased price is 8 + 1 = Rs 9

Again, Let the previous number of people is 200 now the increased number is 200 +17 = 217 

Previous total revenue is 8 × 200 = Rs 1600

Now total revenue is 217 × 9 = Rs 1953

So revenue is increased by

⇒ (1953 - 1600) / 1600 × 100

⇒ 353 /16 = 22.0625%

∴ The correct option is 4

Calculation:

The respective number of girls studying English is, 70 × 50 /100 = 35

The respective number of girls studying computers is 90 × 40 /100 = 36

The respective ratio of the number of girls studying English to that of girls studying computers is 35 ∶ 36

∴ The correct option is 4

Shortcut Trick

If A + B = 90°, then cot A × cot B = 1.

Here, (13° + 77°) = 90° and (27° + 63°) = 90°.

So, cot 13° × cot 77° = 1 and cot 27° × cot 63° = 1.

Expression = 1 × 1 × cot 60° = 1/√3

∴ The correct answer is 1/√3.

Alternate Method

Given:

cot 13° × cot 27° × cot 60° × cot 63° × cot 77°

Formula Used:

cot (90° − θ) = tan θ

tan θ × cot θ = 1

Calculations:

⇒ cot 13° × cot 27° × cot 60° × cot (90° − 27°) × cot (90° − 13°)

⇒ cot 13° × cot 27° × cot 60° × tan 27° × tan 13°

⇒ (cot 13° × tan 13°) × (cot 27° × tan 27°) × cot 60°

⇒ 1 × 1 × (1/√3)

⇒ 1/√3

∴ The correct answer is 1/√3.

Additional Information

Complementary Angles

Trigonometric ratios of complementary angles: sin(90° − θ) = cos θ, sec(90° − θ) = csc θ, and tan(90° − θ) = cot θ.

Reciprocal Identities

The product of reciprocal ratios is always 1: sin θ × csc θ = 1, cos θ × sec θ = 1, and tan θ × cot θ = 1.

Standard Trigonometric Values

Important values of cotangent are: cot 30° = √3, cot 45° = 1, and cot 60° = 1/√3.

Shortcut Trick

In this case, since the Selling Price is equal to the List Price, the Gross Profit is simply the Discount amount.

Net Profit = Discount − Expenses

Discount = 20% of 1,574.80 = 314.96

Net Profit = 314.96 − 45.40 = 269.56

∴ The correct answer is Rs. 269.56.

Alternate Method

Given:

List Price = Rs. 1,574.80

Discount Rate = 20%

Freight Expenses = Rs. 45.40

Selling Price = List Price

Formula Used:

Purchase Price = List Price − Discount

Total Cost Price = Purchase Price + Expenses

Profit = Selling Price − Total Cost Price

Calculations:

⇒ Discount = 20% of 1,574.80

⇒ Discount = (20 ÷ 100) × 1,574.80 = 314.96

⇒ Purchase Price = 1,574.80 − 314.96 = 1,259.84

⇒ Total Cost Price = 1,259.84 + 45.40 = 1,305.24

⇒ Selling Price = 1,574.80

⇒ Profit = 1,574.80 − 1,305.24 = 269.56

∴ The correct answer is Rs. 269.56.

Additional Information

Total Cost Price (Effective CP)

It includes the Purchase Price plus all additional overhead expenses such as freight, transportation, repairs, and labor charges.

Discount on List Price

Discount is always calculated on the List Price (or Marked Price) unless specified otherwise. Net Price = LP × (100 − D)%.

Profit Percentage

Profit % = (Profit ÷ Total Cost Price) × 100. It measures the gain relative to the total investment.

Formula Used:

1. For x > 1

   If  $x+\frac{1}{x}=k$, then $x-\frac{1}{x}=\sqrt{k^2-4}$

2. If $x+\frac{1}{x}=k$, then $x^3+\frac{1}{x^3}=k^3-3k$

3. If $x-\frac{1}{x}=k$, then $x^3-\frac{1}{x^3}=k^3+3k$

4. a² - b² = (a + b) (a - b)

Calculation:

$x+\frac{1}{x}=5\sqrt2$

⇒ $x-\frac{1}{x}$ = $\sqrt{(5\sqrt2)^2-4}$ = $\sqrt{46}$           ----(1)

$x+\frac{1}{x}=5\sqrt2$

⇒ $x^3+\frac{1}{x^3}$ = $(5\sqrt2)^3-3(5\sqrt2)$

⇒ $x^3+\frac{1}{x^3}$ = $250\sqrt2-15\sqrt2$ = $235\sqrt2$  ----(2)

$x-\frac{1}{x} = \sqrt{46}$

⇒ $x^3-\frac{1}{x^3}$ = $(\sqrt{46})^3+3\sqrt{46}$

⇒ $x^3-\frac{1}{x^3}$ = $46\sqrt{46}+3\sqrt{46}$ = $49\sqrt{46}$  ----(3)

Now,

$x^6-\frac{1}{x^6}$ = ($x^3+\frac{1}{x^3}$) ($x^3-\frac{1}{x^3}$)

⇒ $x^6-\frac{1}{x^6}$ = $235\sqrt2$ × $49\sqrt{46}$

⇒ $x^6-\frac{1}{x^6}$ = $11515\sqrt{92}$ = $11515\sqrt{4\times23}$

⇒ $x^6-\frac{1}{x^6}$ = $11515\times2\sqrt{23}$ = $23030\sqrt{23}$

Concept used:

The sum of angles of triangle is 180° 

Calculation:

From option 1 the sum of the angles is 60 + 70 + 80 = 210°

From option 2 the sum of the angles is 60 + 70 +3 0 = 160°

From option 3 the sum of the angles is 60 + 40 + 80 = 180°

 ∴ The correct option is 3

Given:

The market price is 20% above the cost price. 

Concept used:

The discount is calculated on market price while profit is calculated on cost price.

Calculation: 

Let the cost price is 100

Then the market price is 120

The selling price will be 100 × 105 /100 = Rs 105

So the discount will be 120 -105 = 15

So the discount percentage will be ,

⇒ 15 /120 × 100

⇒ 100 /8 =12.5%

∴ The correct option is 2

Shortcut Trick

Effective Rate of Interest for two half-yearly periods at 4% each (8% ÷ 2) = 4 + 4 + (4 × 4) ÷ 100 = 8.16%.

Compound Interest = 8.16% of Principal (₹50,000).

CI = 50,000 × 0.0816 = ₹4,080.

∴ The correct answer is ₹4,080.

Alternate Method

Given:

Principal (P) = ₹50,000

Annual Rate (R) = 8% per annum

Time (T) = 1 year

Formula Used:

Amount (A) = P(1 + r/100)ⁿ, where r = rate per period and n = number of periods.

Calculations:

⇒ For half-yearly compounding, rate (r) = 8% ÷ 2 = 4% per half-year.

⇒ Number of periods (n) = 1 year × 2 = 2 half-years.

⇒ A = 50,000 × (1 + 4/100)²

⇒ A = 50,000 × (104/100) × (104/100)

⇒ A = 50,000 × 1.04 × 1.04

⇒ A = 50,000 × 1.0816

⇒ A = ₹54,080

⇒ Compound Interest (CI) = Amount − Principal

⇒ CI = 54,080 − 50,000

⇒ CI = ₹4,080

∴ The correct answer is ₹4,080.

Additional Information

Compounding Frequency

When interest is compounded half-yearly, the annual rate is divided by 2 and the time in years is multiplied by 2. For quarterly, divide rate by 4 and multiply time by 4.

Effective Rate Formula

For two successive periods with interest rates x% and y%, the net effective rate is given by (x + y + xy/100)%.

CI − SI Difference

The difference between Compound Interest and Simple Interest for 2 years (or 2 periods) is given by P(r/100)².