SSC CHSL Tier-1 2022: Official Paper (Held On: 09 March, 2023 Shift 1) (Previous Year Paper)

According to the given Venn diagram:

The shaded area shows the "Red Cars".

So, there are: 14 + 5 + 6 + 8 = 33 red cars are there in the given figure.

Hence, the correct answer is "33".

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

Hence, "option (4)" is the correct answer.

Additional InformationIn Mirror image left side and right side changed vice-versa where top and bottom remain same.

Reflection of an object into the water is its water image. It appears by inverting an object vertically i.e. upside down.

The water image of the figure looks like the mirror image of the figure in case the mirror is horizontally at the bottom of the figure.

Water image is just a reflection where top and bottom part of the images changed where left and right side of the image remain same.

Mistake Points Even though 2^nd and 4^th figure looks similar, there is a difference.

2^nd Figure

4^th Figure

The pattern followed in the given options is:

Logic: First term × 4 = Second term

Now we consider the given options:

Option 1) 3375 – 13500

⇒ 3375 × 4 = 13500

Option 2) 2125 – 8600

⇒ 2125 × 4 = 8500 ≠ 8600

Option 3) 2685 – 10740

⇒ 2685 × 4 = 10740

Option 4) 1595 – 6380

⇒ 1595 × 4 = 6380

We can see that '2125 – 8600' does not follow the pattern so it is the odd one.

Hence, the correct answer is "Option 2".

The logic followed here is:

So, 'HZL' will complete the series.

Hence the correct answer is "HZL".

The logic followed here is:

So, '114' will complete the series.

Hence, the correct answer is "114".

The pattern followed here is:

Design : Architect → Design is created by an Architect.

Similarly,

Furniture : Carpenter → Furniture is created by a Carpenter.

Hence, the correct answer is "Option 4".

The logic followed here is:

Logic: 'C' represents '÷'.

Now,

96 C 3 → 96 ÷ 3 = 32.

288 C 8 → 288 ÷ 8 = 36.

Similarly,

408 C 6 → 408 ÷ 6 = 68.

Hence, the correct answer is "68".

The correct order according to the English dictionary is:

1. Wage
2. Waist
3. Waste
4. Wave
5. West

From the arrangement, the correct order is '12354'.

Hence, the correct answer is "Option 1".

The image embedded in given figure is as shown below:

Hence, "Option 2" is the correct answer.

The pattern followed in the given options is:

Logic: First term × 2 = Second term

Now we consider the given options:

Option 1) 3333 – 6666

⇒ 3333 × 2 = 6666

Option 2) 4444 – 8888

⇒ 4444 × 2 = 8888

Option 3) 2222 – 4444

⇒ 2222 × 2 = 4444

Option 4) 5555 – 7777

⇒ 5555 × 2 = 11110 ≠ 7777

We can see that '5555 – 7777' does not follow the pattern so it is the odd one.

Hence, the correct answer is "Option 4".

The logic followed here is: Letter is coded by its positional value.

‘TEFLOANS’ is coded as ‘2056121226138’.

‘SERGEANT’ is coded as ‘1951872226137’.

Similarly, for 'UNIQUELY'

So, 'UNIQUELY' will be coded as '2114917622152'.

Hence, the correct answer is "Option 1".

Statements:

I. All Z are D.

II. No Y is Z.

The least possible diagram for the given statements is as follows:

Conclusion:

I. Some D are not Y - True (Because All Z are D, so those part of D that is Z will be definitely not Y).

II. Some Z are not Y - True (No Y is Z, so some Z are not Y is also true).

III. Some D are Z - True (All Z are D so Some D are also Z).

Here, All conclusion follows.

Hence, the correct answer is "Option 1".

Given equation: 47 + 13 ÷ 65 × 5 – 16.

BODMAS Table: 

Let's check each option one by one.

Given: 47 + 13 ÷ 65 × 5 – 16.

After interchanging the signs '× and ÷' we get;

⇒ 47 + 13 × 65 ÷ 5 – 16

⇒ 47 + 13 × 13 – 16

⇒ 47 + 169 – 16

⇒ 216 – 16 = 200.

Hence, the correct answer is "200".

The logic followed here is:

Option 1) LMNO

Option 2) IJKL

Option 3) ABCD

Option 4) BDEF

Here, All the options except 'BDEF' followed a pattern.

Hence, the correct answer is "Option 4".

The logic followed here is:

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

Noe, for '14 : 210'

⇒ 14 × (14 + 1)

⇒ 14 × 15 = 210.

For, '16 : 272'

⇒ 16 × (16 + 1)

⇒ 16 × 17 = 272.

Similarly, for '13 : ?'

⇒ 13 × (13 + 1)

⇒ 13 × 14 = 182.

Hence, the correct answer is "182".

The quadrilaterals are:

Here, total 23 quadrilaterals are in the given figure.

Hence, the correct answer is "Option 4".

Family Chart:

Given: S is the sister of T. R is the brother of S. U is the wife of W. T is the father of U.

So, T is Father in law of W.

Hence, the correct answer is "Option 1".

The logic followed here is:

Step I: A Straight line given in a part of circle has shifted to its next place in next image.

Step II: Circle are shifted to its next place and shaded in alternate image.

Step III: The Polygons are shaded in each alternate image.

So, 'Option 1' will replace the question mark.

Hence, the correct answer is "Option 1".

The pattern followed here is:

Tea : Cup → Tea is served in a cup.

Similarly,

Food : Plate → Food is often served on a plate.

Hence, the correct answer is "Option 2".

The logic followed here is:

Banana, Apple and Grape is types of fruits,

Whereas,

"Cauliflower" is a vegetable.

Hence, the correct answer is "Option 4".

The paper when unfolded will appear as shown below:

Hence, the correct answer is "Option 1".

The logic followed here is:

‘GIRL’ is coded as ‘QWNL’.

Similarly, for 'KEPT'

So, 'KEPT' will be written as 'YUJP'.

Hence, the correct answer is "Option 3".

The logic followed here is:

Pen : Author →  An author typically uses a pen to write.

Similarly,

A Woodcutter typically uses an axe to chop down trees.

Hence, the correct answer is "Option 2".

The logic followed here is:

The pairs are given as: "Alternate Prime numbers".

Now,

(79, 89, 101)

⇒ 79 → 22^nd Prime number.

⇒ 89 → 24^th Prime number.

⇒ 101 → 26^th Prime number.

For (31, 41, 47)

⇒ 31 → 11^th Prime number.

⇒ 41 → 13^th Prime number.

⇒ 47 → 15^th Prime number.

Now, checking the options:

Option 1: (43, 47, 59)

⇒ 43 → 14^th Prime number.

⇒ 47 → 15^th Prime number.

⇒ 59 → 17^th Prime number.

Option 2: (53, 61, 67)

⇒ 53 → 16^th Prime number.

⇒ 61 → 18^th Prime number.

⇒ 67 → 19^th Prime number.

Option 3: (29, 37, 43)

⇒ 29 → 10^th Prime number.

⇒ 37 → 12^th Prime number.

⇒ 43 → 14^th Prime number.

Option 4: (17, 19, 23)

⇒ 17 → 7^th Prime number.

⇒ 19 → 8^th Prime number.

⇒ 23 → 9^th Prime number.

Hence, the correct answer is "Option 3".

Additional Information

Prime number table from 1 to 100.

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

Hence, "option (3)" is the correct answer.

Additional InformationIn Mirror image left side and right side changed vice-versa where top and bottom remain same.

Reflection of an object into the water is its water image. It appears by inverting an object vertically i.e. upside down.

The water image of the figure looks like the mirror image of the figure in case the mirror is horizontally at the bottom of the figure.

Water image is just a reflection where top and bottom part of the images changed where left and right side of the image remain same.

The correct answer is Maharashtra.

Key Points

• Warli painting 
• Warli painting is a form of tribal art mostly created by the tribal people from the North Sahyadri Range in Maharashtra, India.
• This range encompasses cities such as Dahanu, Talasari, Jawhar, Palghar, Mokhada, and Vikramgad of Palghar district.
• This tribal art was originated in Maharashtra, where it is still practiced today.
• The Warli Painting tradition in Maharashtra are among the finest examples of the folk style of paintings.
• The Warli tribe is one of the largest in India, located outside of Mumbai.
• The style of Warli painting was not recognised until the 1970s, even though the tribal style of art is thought to date back as early as 10^th century A.D.
• The Warli culture is centered on the concept of Mother Nature and elements of nature are often focal points depicted in Warli painting.

Additional Information

• These rudimentary wall paintings use a set of basic geometric shapes a circle, a triangle, and a square.
• These shapes are symbolic of different elements of nature. The circle and the triangle come from their observation of nature.
• The circle represents the sun and the moon, while the triangle depicts mountains and conical trees.
• In contrast, the square renders to be a human invention, indicating a sacred enclosure or a piece of land.
• The central motif in each ritual painting is the square, known as the chauk or chaukat, mostly of two types known as Devchauk and Lagnachauk.
• Inside a Devchauk is usually a depiction of Palaghata, the mother goddess, symbolizing fertility.
• The ritual paintings are usually created on the inside walls of village huts.
• The walls are made of a mixture of branches, earth and red brick that make a red ochre background for the paintings.

The correct answer is Shri Krishna Sinha.

Key Points

• Sri Krishna Sinha ​
• Sri Krishna Sinha was the first Chief Minister of Bihar.
• He is also known as Sri Babu and Bihar Kesari.
• He served as the first Chief Minister of Bihar from 1946 to 1961.
• He along with Dr. Rajendra Prasad (First President of India) and Dr. Anugrah Narayan Sinha, is respected as one of the best architects of modern Bihar.
• He also served as the Finance Minister of Bihar (1957-1961) while dispensing his duties as the Chief Minister.

Additional Information

• Krishna Singh is credited to be the first Chief Minister in India to have ended the 'Zamindari' system.
• He led the Dalit entry into Baidyanath Dham temple, Deoghar.
• He was a Gandhian freedom fighter.

The correct answer is value of production of the firm – value of intermediate goods used by the firm.

Key Points

• Value Added
• Value-added describes the value that a company adds to a raw material or intermediate good during the production process.
• The difference between the value of output and the value of intermediate products is used to calculate the national income using the value-added method.

                      Value Added = Value of Output – Intermediate

• Value Added Method
• In a circular flow, national income is calculated using the value-added method at various phases of the production process. In the production process, it indicates the value added for each unit produced.
• Every business adds value to the goods it purchases as an intermediary good from other firms.
• The value of national income is the sum total of value added by all organisations.
• The following steps are used to calculate national income using the value-added method:
• Step 1
• The first step is to identify and classify all value of producing enterprises in  primary, secondary, and tertiary sectors.
• Step 2
• Next, the Gross Domestic Product at Market Prices (GDPMP) is calculated.
• Determine the Gross Value Added at Market Price (GVAMP) of each sector for the purpose of calculating the GDPMP; i.e. ∑GVAMP = GDPMP
• Step 3
• Next, determine domestic income (NDPFC).
• Value of depreciation and net indirect tax are deducted from the gross domestic product at market price (GDPMP) to calculate domestic income; NDPFC  = GDPMP – Depreciation – Net Indirect Taxes
• Step 4
• To determine national income (NNPFC), the final step is to calculate Net Factor Income from Abroad (NFIA).
• The NFIA is added along with the country's domestic income; National Income or NNPFC = Domestic Income or NDPFC + NFIA

The correct answer is 1240.

Key Points

• Razia Sultan (1236 AD-1240 AD):
• She belonged to the Slave Dynasty.
• She was the first and last Muslim woman ruler of Medieval India.
• She appointed Jamaluddin Yakoot as the highest officer of cavalry.
• She abandoned Pardah and appeared before the public in male dress.
• She saved the empire from Mongol invasion.
• She died in the year 1240 AD.​

Additional Information

• Delhi Sultanate (1206 AD-1526 AD)
• The First Muslim invasion was done by Mohammad Bin Qasim (712 AD).
• The First Turkish Invasion was done by Mahmud Ghaznavi (998 AD-1030 AD):
• In 1025, he attacked and raided the most celebrated Hindu temple of Somnath.
• Dynasties of Delhi Sultanate:
• The Slave dynasty (1206–1290)
• The Khalji dynasty (1290–1320)
• The Tughlaq dynasty (1320–1414)
• The Sayyid dynasty (1414–1451)
• Lodi dynasty (1451–1526)

The correct answer is Odisha.

Key Points

• Odisha CM Naveen Patnaik on 10^th Oct 2022 launched ‘Football for All’ in the state to take the culture of football to the grassroots.
• It has been initiated by FIFA in Odisha in partnership with the Kalinga Institute of Industrial Technology & Kalinga Institute of Social Sciences.
• This is the first such programme of FIFA in India that aims at promoting football among school children.

Additional Information

• The organization Utkal Sammilani was formed in 1903 to demand the unification of Odia-speaking regions into one state.
• The Province of Bihar and Orissa was formed on 1 April 1912.
• Bihar and Orissa were subdivided into separate provinces on 1 April 1936.
• The new Province of Orissa was created on a linguistic basis during the British rule in India, with Sir John Austen Hubback as the first governor.
• On 15 August 1947, the agreement to join Orissa was signed by 27 princely States.

The correct answer is Carlos Alcaraz.

Key Points

• Carlos Alcaraz Garfia was born on May 5, 2003, in Murcia, Spain.
• He started playing tennis at the age of three and trained at the Juan Carlos Ferrero Tennis Academy in Villena, Spain.
• Alcaraz turned professional in 2018 at the age of 15.
• In 2019, he won his first professional title at the ITF M15 in Manacor, Spain.
• In 2020, Alcaraz won his first ATP Challenger title at the age of 16, becoming the youngest player to win an ATP Challenger event in a decade.
• Carlos Alcaraz won his first Grand Slam after defeating C. Ruud in a nail-biting four-set match in the men’s singles Title of the US Open 2022 tournament.

Additional Information

• In the women’s singles tournament, Iga Swiatek easily defeated Ons Jabeur of Tunisia, winning 6-2 7-6 (5)
• Alexandra Eala won the girls’ singles title by defeating reigning French Open girls’ champion Lucie Havlickova 6-2, 6-4 in the final.

The correct answer is Australia and New Zealand.

Key Points 

• New Zealand and Australia will host the 2023 FIFA Women’s World Cup.
• FIFA announced its decision after its governing council held a vote by videoconference.
• The joint bid submitted by Football Federation Australia and New Zealand Football received 22 of the 35 valid votes cast by the FIFA Council members, with the Colombian Football Association having obtained 13 votes.
• FIFA’s decision means South America is still waiting to host its first Women’s World Cup, a tournament that was first played in 1991.​

Additional Information

• FIFA is a non-profit organization that describes itself as an international governing body of association football, fútsal, and beach soccer.
• It is the highest governing body of association football.
• Headquarters: Zürich, Switzerland
• Founded: 21 May 1904, Rue Saint-Honoré, Paris, France
• Main organ: FIFA Congress
• Founded at: Paris, France
• Current champion: Argentina

The correct answer is eight.

Key Points

• The Fifth Khelo India Youth Games 2022 will be held in the Eight cities of Madhya Pradesh.
• This was announced by Union Minister of Youth Affairs and Sports Anurag Singh Thakur at an event in New Delhi in the presence of Madhya Pradesh Chief Minister Shivraj Singh Chouhan.
• The Khelo India Youth Games will be held at eight locations. More than 8 thousand 500 athletes and sportspersons are expected to participate in the sporting event.
• Khelo India Youth Games was started in 2016 and provided a very effective platform for the youth of the country to showcase their performance and talents in sports.
• Minister Anurag Thakur said that Madhya Pradesh is now showing its excellence in every sector and State Chief Minister has improved the infrastructure of sports and built up a big infrastructure of shooting and water sports.

Additional Information

• Khelo India Youth Games (KIYG), formerly Khelo India School Games (KISG), are the annual national level multidisciplinary grassroot games in India held in January or February for two categories, namely under-17 years school students and under-21 college students.
• Every year best 1,000 kids will be given an annual scholarship of ₹5 lakh (US$6,300) for 8 years to prepare them for the international sporting events$.

The correct answer is Colloids are heterogeneous mixtures in which the particle size is large 

Key Points

• A mixture is a combination of two or more substances that are not chemically bonded to each other.
• Mixtures can be classified into two types: homogeneous and heterogeneous.
• Homogeneous mixtures have a uniform composition throughout, whereas heterogeneous mixtures have a non-uniform composition.
• The components of a mixture can be separated by physical methods such as filtration, distillation, chromatography, etc.
• Filtration is used to separate a solid from a liquid or a gas.
• Distillation is used to separate a mixture of two or more liquids with different boiling points.
• Colloids, also known as colloidal solutions or colloidal systems, are mixtures in which microscopically dispersed insoluble particles of one substance are suspended in another substance.
• The size of the suspended particles in a colloid can range from 1 to 1000 nanometres (10-9 meters) which is very small.

Additional Information

Solution 

• A solution is a homogeneous mixture of two or more substances, where one substance is called the solute and the other is called the solvent.
• The solute is the substance that is dissolved in the solvent, whereas the solvent is the substance in which the solute is dissolved.
• Solutions can be classified as solid, liquid, or gaseous, depending on the physical state of the solvent.
• The concentration of a solution is the amount of solute present in a given amount of solvent or solution.

The correct answer is J. Chadwick.

Key Points

• J. Chadwick discovered the presence of neutrons in the nucleus of an atom.
• An atom is the smallest unit of any chemical element.
• Atom is made up of electrons, protons, and neutrons.
• The electron carries a negative charge, proton carries an equal to an electron but a positive charge and a neutron is neutral.
• Proton and neutrons reside in the nucleus while the electron revolves around the nucleus.

Hence, we can conclude that J. Chadwick discovered neutrons.

Additional Information

The correct answer is The air always moves from high pressure areas to low pressure areas.

Key Points

• ​The air always moves from high-pressure areas to low-pressure areas.
• This is because air always moves along pressure gradients, from areas of high pressure to areas of low pressure, in an attempt to equalize the pressure.
• This movement of air is what we experience as wind.

Hence statement 3 is correct.

• High pressure is generally associated with clear skies and calm weather, not cloudy and wet weather.
• This is because high pressure involves air sinking toward the surface of the earth, which inhibits cloud formation.

Hence statement 1 is incorrect.

• Conversely, low pressure is often associated with cloudy skies and wet weather, not clear and sunny skies.
• Low pressure involves air rising from the earth's surface, which can lead to cloud formation and precipitation.

Hence statement 2 is incorrect.

• The air pressure is highest at sea level and decreases with height.
• This is due to the weight of the air above compressing the air at lower levels (like sea level), making it denser and therefore exerting more pressure.
• As you go higher, there's less air above you, so the pressure decreases.
• For this reason, it is difficult to breathe in the hilly areas and mountains.

Hence statement 4 is incorrect.

The correct answer is Gujarat.

Key Points

• Dhinodhar Hills is a scenic mountain range located in the Bhavnagar district of Gujarat, India.
• These hills are situated in the Gir Forest National Park, which is known for its population of Asiatic lions.
• The hills are home to a wide variety of flora and fauna and offer breathtaking views of the surrounding landscape.
• The area is also renowned for its spiritual significance, as there are several ancient temples and holy sites located in and around the hills.
• Additionally, the Dhinodhar Hills is a popular destination for trekking and adventure sports enthusiasts, offering several challenging trails and rock-climbing opportunities.

Additional Information

The correct answer is Gujarat.

Key Points

• India's first 24x7 solar-powered village, Modhera, is located in the state of Gujarat.
• The village is famous for its Sun Temple, which is a UNESCO World Heritage site.
• The solar power plant installed in the village generates enough electricity to meet the energy needs of the entire village, making it self-sufficient in terms of power.
• The initiative was taken by the Gujarat government under the "Mukhyamantri Solar Sahay Yojana" to promote the use of renewable energy in rural areas.

Additional Information

• Important Facts about Gujarat:
• Economy: Gujarat has a strong and diverse economy, with significant contributions from industries such as textiles, chemicals, pharmaceuticals, and agriculture.
• It is also the largest producer of cotton in India.
• Industrial Development: Gujarat is one of the most industrialized states in India, with well-developed infrastructure, including ports, highways, and airports.
• It is also home to several special economic zones, promoting foreign investment.
• Renewable Energy: Gujarat is a leading state in India in terms of renewable energy generation, with a significant capacity for wind and solar power.
• Gir Forest National Park: The Gir Forest National Park, located in Gujarat, is the last remaining habitat of the Asiatic lion, which is a critically endangered species.
• Sabarmati Ashram: The Sabarmati Ashram, located in Ahmedabad, is a significant historical site associated with Mahatma Gandhi's non-violent struggle for India's independence.
• Festivals: Gujarat is known for its vibrant festivals, including Navratri, the Kite Festival, and the Rann Utsav, which attract tourists from all over the world.

The correct answer is Karnataka, Andhra Pradesh, Tamil Nadu and Kerala.

Key Points 

• Carnatic Music
• Carnatic music is one of the forms of Indian classical music.
• It is confined to southern India, the states of Andhra Pradesh, Karnataka, Tamilnadu, and Kerala while the classical music of the rest of the country is under the name of Hindustani.
• The main emphasis in Carnatic music is on the vocals.
• The music is created in the traditional octave form and the music is Kriti based and focuses more on the Sahithya or the lyric quality of the musical piece.

Additional Information

• ​Trinity of Carnatic Music
• The Three Jewels of Carnatic music referred to trio composers – being Tyagaraja, Muthuswami Dikshitar, and Syama Sastri also known as the Trinity of Carnatic music.
• All three of the Trinities lived and composed music in Thanjavur, Tamilnadu.
• Thanjavur has been the capital of Carnatic Music, not only because the Trinities lived there but also because the place has nurtured Carnatic music for a long time.
• The Kings from Thanjavur – the Cholas, Nayaks, and the Marathas – have consistently supported Carnatic music and the artists, and contributed to its current-day greatness and preservation.
• Muthuswami Dikshitar was the youngest of the trinities.

The correct answer is Option 1. 

Key Points

• No, the Industrial Securities Market is not commonly known as the gilt-edged market.
• The gilt-edged market, also known as the gilt market, refers to the market for government bonds in the United Kingdom. These bonds are considered to be low-risk investments because they are backed by the UK government and are therefore seen as "gilt-edged" investments.
• On the other hand, the Industrial Securities Market refers to the market where industrial securities are traded. These securities include stocks, shares, and other investment products issued by companies in the industrial sector. This market is also commonly known as the stock market or the equity market.
• While both the gilt-edged market and the industrial securities market are important parts of the financial system, they are distinct markets with different investment products and characteristics.

Additional Information

• The secondary market is a financial market where investors buy and sell securities that have already been issued by companies or other entities. In contrast to the primary market, where securities are issued for the first time, the secondary market involves the trading of existing securities between investors.
• The secondary market includes exchanges such as the New York Stock Exchange (NYSE) and the NASDAQ, as well as over-the-counter (OTC) markets where securities are traded directly between buyers and sellers without a centralized exchange. In the secondary market, the price of a security is determined by supply and demand, and fluctuations in market conditions can affect the price of securities traded on the market.
• The Reserve Bank of India (RBI) plays a dominant role in the gilt-edged market through its open market operations (OMOs).
• In the gilt-edged market, government securities (G-secs) are traded, and these securities are issued by the government to raise funds.
• The RBI is responsible for managing the demand and supply of G-secs in the market. One of the primary tools that the RBI uses to manage the demand and supply of G-secs is through OMOs.OMOs are the buying and selling of government securities in the open market by the RBI.
• When the RBI wants to inject liquidity into the market, it buys G-secs from the market, and when it wants to absorb liquidity from the market, it sells G-secs in the market. This helps in regulating the money supply in the economy and controlling inflation.
• The primary market, also known as the new issue market, is where new securities are issued and sold for the first time to investors.
• Companies, governments, and other organizations raise capital in the primary market by selling securities, such as stocks or bonds, to investors. The primary market is distinct from the secondary market, where securities that have already been issued are bought and sold between investors.

The correct answer is Option 3. 

Key Points

• The Tropic of Cancer (23°30′ N) passes through 8 states of India, namely Gujarat, Rajasthan, Madhya Pradesh, Chhattisgarh, Jharkhand, West Bengal, Tripura, and Mizoram.
• The Tropic of Cancer is an imaginary line of latitude that circles the Earth at approximately 23.5 degrees north of the equator. It is one of the five major circles of latitude that mark maps of the Earth.
• The Tropic of Cancer passes through or near several countries including Mexico, the Bahamas, Egypt, Saudi Arabia, India, and China. It is also an important point for understanding the Earth's climate, as it marks the northern boundary of the tropics and the point where the Sun appears directly overhead on the summer solstice in the northern hemisphere.

Additional Information

• Punjab is a state located in the northern region of India.
• It is bordered by the Indian states of Jammu and Kashmir to the north, Himachal Pradesh to the east, Haryana to the south and southeast, Rajasthan to the southwest, and the Pakistani province of Punjab to the west.
• The capital city of Punjab is Chandigarh, which is a union territory and also serves as the capital of the neighboring state of Haryana.
• Maharashtra is a state located in the western region of India.
• It is the second-most populous state in India and has Mumbai as its capital city, which is also known as the financial capital of India. The state covers an area of 307,713 square kilometers and has a population of over 123 million people.
• Maharashtra is bordered by the Arabian Sea to the west, Gujarat to the northwest, Madhya Pradesh to the northeast, Chhattisgarh to the east, Telangana to the southeast, Karnataka to the south, and Goa to the southwest.
• The state is known for its rich history, diverse culture, and varied landscapes, including the Western Ghats mountain range, the Deccan Plateau, and the coastal region. Maharashtra is also home to several major industries, including the entertainment industry centered in Mumbai, the financial industry, and the manufacturing industry.
• Kerala is a state located in the southwestern region of India.
• It is bordered by the Arabian Sea to the west, Karnataka to the north, and Tamil Nadu to the east. Thiruvananthapuram is the capital city of Kerala.
• Kerala is known for its natural beauty, including its palm-lined beaches, serene backwaters, lush green hills, and wildlife reserves. The state is also famous for its cuisine, which features a variety of vegetarian and non-vegetarian dishes that are rich in spices and flavors.
• Kerala is a highly literate state with a strong focus on education, healthcare, and social welfare. The state has a diverse population and a rich cultural heritage that is reflected in its art, music, and dance forms.

The correct answer is Option 3. 

Key Points

• The Filmfare Awards are one of the most prestigious film awards in India.
• They are presented annually by the Filmfare magazine to honor excellence in the Hindi film industry, also known as Bollywood.
• The awards were first introduced in 1954 and have since become one of the most highly anticipated events in the Indian film calendar.
• The Filmfare Awards recognize outstanding performances and achievements in various categories, including Best Film, Best Director, Best Actor, Best Actress, Best Supporting Actor, Best Supporting Actress, Best Music, and more.
• The winners are chosen through a voting process that involves members of the film industry, including actors, directors, producers, and critics.

Additional Information

• List of FILMFARE AWARDS 2022 WINNERS
• Best Film: Shershaah (Dharma Productions)
• Best Director: Vishnuvardhan (Shershaah)
• Best Actor: Ranveer Singh (83) as Kapil Dev
• Best Actress: Kriti Sanon, Mimi as Mimi Rathore
• Best Supporting Actor: Pankaj Tripathi (Mimi)
• Best Supporting Actress: Sai Tamhankar (Mimi)
• Best Male Debut: Ehan Bhat – 99 Songs as Jay
• Best Female Debut: Sharvari Wagh – Bunty Aur Babli 2 as Sonia Rawat / Jasmine “Jazz”
• Best Debut Director: Seema Pahwa – Ramprasad Ki Tehrvi
• Best Story: Abhishek Kapoor, Supratik Sen and Tushar Paranjape (Chandigarh Kare Aashiqui)
• Best Screenplay: Shubendu Bhattacharya and Ritesh Shah (Sardar Udham)
• Best Dialogue: Dibakar Banerjee and Varun Grover (Sandeep Aur Pinky Faraar)
• Best Music Director: Tanishk Bagchi, B Praak, Jaani, Jasleen Royal, Javed-Mohsin And Vikram Montrose (Shershaah)
• Best Lyricist: Kausar Munir – “Lehra Do” (83)
• Best Playback Singer  (Male): B Praak – “Mann Bharrya” (Shershaah)
• Best Playback Singer (Female): Asees Kaur – “Raataan Lambiya” (Shershaah).
• Best Film (Best Director): Shoojit Sircar (Sardar Udham)
• Best Actor: Vicky Kaushal – Sardar Udham as Udham Singh
• Best Actress: Vidya Balan – Sherni as Vidya Vincent.
• Filmfare Lifetime Achievement Award: Subhash Ghai.

The correct answer is Option 1. 

Key Points

• The troposphere is the lowest layer of the Earth's atmosphere, extending from the surface up to an average altitude of about 7 to 12 kilometers (4.3 to 7.5 miles).
• The height of the troposphere varies depending on the location, season, and weather conditions. However, the average height of the troposphere is about 11 kilometers (6.8 miles) above sea level.

Additional Information

• Earth's atmosphere can be divided into five primary layers based on their temperature and altitude:
• Troposphere: This is the lowest layer of the Earth's atmosphere, extending from the surface up to an average altitude of 12 kilometers (7.5 miles) at the equator. The majority of Earth's weather occurs in this layer, and it is where most of the Earth's greenhouse gases are concentrated.
• Stratosphere: This layer lies above the troposphere, extending from about 12 to 50 kilometers (7.5 to 31 miles) in altitude. The ozone layer is located in this layer, which absorbs harmful ultraviolet radiation from the sun.
• Mesosphere: Above the stratosphere, the mesosphere extends from about 50 to 85 kilometers (31 to 53 miles) in altitude. This layer is known for its extremely low temperatures, as low as -100°C (-148°F) at the top.
• Thermosphere: This layer extends from about 85 kilometers (53 miles) to the edge of space, around 600 kilometers (372 miles) above the Earth's surface. The temperature increases with altitude in this layer, reaching up to 2,000°C (3,632°F) due to the absorption of solar radiation.
• Exosphere: The outermost layer of Earth's atmosphere, the exosphere, begins at an altitude of about 600 kilometers (372 miles) and extends into space. This layer is where the Earth's atmosphere gradually thins out and merges with the vacuum of space.

The correct answer is Option 4. 

Key Points

• Mahatma Gandhi organized a Satyagraha in the Kheda district of Gujarat in the year 1918.
• The Satyagraha was a non-violent resistance movement in support of the peasants who were facing immense difficulties due to the oppressive policies of the British government, particularly the high taxes they imposed on the farmers.
• The Satyagraha was successful in achieving its objectives, and it helped establish **Mahatma Gandhi's leadership in the Indian independence movement.**​

Additional Information

• Mahatma Gandhi (Mohandas Karamchand Gandhi) was born on October 2, 1869.
• He was an Indian lawyer, politician, social activist, and writer.
• He became the leader of the nationalist movement against the British rule of India.
• He was known as the Father of the Nation.
• Gandhi is internationally esteemed for his doctrine of nonviolent protest (Satyagraha) to achieve political and social progress.
• He died January 30, 1948, in Delhi, and the day is celebrated as Shaheed Diwas or Martyrs' Day.
• His autobiography is titled My Experiments with Truth.
• Important movements led by Mahatma Gandhi:
• ​Champaran Movement (1917)
• Kheda Movement (1918)
• Khilafat Movement (1919)
• Non-Cooperation Movement (1920)
• Civil Disobedience Movement: Dandi March (1930)
• Quit India Movement (1942)

Correct Answer repeater

Key Points

• A repeater is a device that receives a signal, amplifies it, and then re-transmits it to extend its range or reach.
• Repeaters are commonly used in telecommunications and broadcasting to increase the coverage area of signals, particularly in areas with obstacles or weak signal strength.
• Repeaters can also be used in networking to extend the range of a wireless network or to improve signal quality.
• Additionally, in firearms, a "repeater" can refer to a type of gun that can quickly fire multiple rounds without needing to reload after each shot.

Additional Information

The correct option is Thallophyta

**Key Points:**Concept:

• Based on whether plants have a well-differentiated body and the presence or absence of specialized tissues for transport, and the ability to bear seeds Kingdom Plantae (Plant Kingdom) is can be classified into different divisions.
• Thallophyta
• The plant body is not differentiated from roots, stems, and leaves.
• They are commonly called algae.
• Bryophyta
• These are small terrestrial plants.
• They show differentiation in the body design, with stem, leaf-like structures, and root-like structures.
• Pteridophyta
• The plant body is differentiated into roots, stems, and leaves, apart from having a specialized tissue for conduction.
• Gymnosperms
• Gymnosperms are plants with naked seeds.
• Angiosperms
• Angiosperms are seed-bearing plants. Seeds develop inside tissues that get modified to form the fruit of the plant.

Explanation:

• All the plants that lack a well-differentiated body structure belong to the subgroup Thallophyta.
• Thallophytes are commonly known as algae.
• The majority of them are aquatic.
• It includes the primitive form of plant life.
• They do not have vascular tissues which help in the transportation of water and minerals, hence, they are usually found in moist places.
• Thallophyta is further divided into - Algae and Fungi.
• Chara, Lichen, and Spirogyra are examples of Thallophyta.

The correct answer is Ctrl + W

Key Points:

• In Microsoft workbook, the Ctrl+W shortcut key closes the currently open slide deck.
• To use the keyboard shortcut Ctrl+W, press and hold the Ctrl key on the keyboard and while continuing to hold, press the "W" key with either hand.
• In Microsoft Word and other word processor programs, pressing Ctrl+W closes the open document.

Additional Information

• Ctrl+N: Create a new document
• Ctrl+O: Open an existing document
• Ctrl+S: Save a document
• Ctrl+W: Close a document
• Ctrl+Z: Undo an action
• Ctrl+Y: Redo an action
• Alt+Ctrl+S: Split a window or remove the split view
• Ctrl+Alt+V: Print Layout View
• Ctrl+Alt+O: Outline View
• Ctrl+Alt+N: Draft View
• Ctrl+F2: Print Preview View
• F1: Open the Help pane
• F12: Open the Save As dialogue box
• Ctrl + V shortcut is used for any copy data paste using that key.
• Ctrl+x shortcut is used to cut any data and paste that data anywhere else.
• Ctrl+C shortcut is used to copy data.

​The correct answer is 'Indore'.

Key Points:

• Indore was adjudged India's cleanest city for the sixth time in a row, while Surat and Navi Mumbai followed it in the next two spots in the Central government's annual cleanliness survey.
• In the category of best-performing states in 'Swachh Survekshan Awards 2022', Madhya Pradesh has secured the first position, followed by Chhattisgarh and Maharashtra.
• Indore and Surat retained their top positions in the big cities category this year, while Vijaywada lost its third spot to Navi Mumbai.
• Among the states having fewer than 100 urban local bodies, Tripura has bagged the top rank, according to the survey results.
• Haridwar was adjudged the cleanest Ganga town in the category of more than 1 lakh population, followed by Varanasi and Rishikesh.

Additional Information:

• The 7^th edition of Swachh Survekshan was conducted to study the progress of the Swachh Bharat Mission (Urban) and rank the Urban Local Bodies (ULBs) based on various cleanliness and sanitation parameters.
• The Survekshan has evolved from being an assessment of 73 cities in 2016 to covering 4,354 cities this year.

The correct answer is 355.

Key Points:

• Article 355 states, "It shall be the duty of the Union to protect every State against external aggression and internal disturbance and to ensure that the Government of every State is carried on in accordance with the provisions of this Constitution.”
• Part 18 of the Indian Constitution defines the Article.
• Part 18 of the Indian constitution envisages the following three emergencies:
• General Emergency (also called national emergency)
• Break-down of constitutional machinery in the states (also called state emergency)
• Financial Emergency
• Article 359 allows the President of India to suspend the right to move any court for the enforcement of Fundamental Rights during a National Emergency.
• Article 354 explains provisions relating to the distribution of revenues while a Proclamation of Emergency is in operation.
• Article 356 empowers the President of India to withdraw from the Union the executive and legislative powers of any state.
• Article 357 deals with the exercise of legislative powers under the Proclamation issued under Article 356 by the central government.

Article 353 -

• Article 353 of the Indian constitution deals with the effect of the Proclamation of Emergency.
• ​Parliament was given the power to impose emergency legislation on any state which is different from the state in which the emergency proclamation is in force.

Article 358:

• Article 358 is confined to Fundamental Rights under Article 19.
• The Right to freedom of Speech and Expression comes under Article 19.
• Once an emergency is declared in India, Article 358 automatically suspends these rights.
• Article 358 operates only in the case of an external emergency and not in the case of an internal disturbance.
• Article 358 suspends Fundamental Rights under Article 19 for the complete duration of the Emergency.
• Article 358 is enforced all over India.
• Article 358 enables the State to form any law or take any executive action inconsistent with Fundamental Rights under Article 19.
• Article 358 suspends Article 19 completely.

The correct answer is Advisory jurisdiction of the Supreme court.

Key Points

• Canadian Constitution: 
• Advisory Jurisdiction of Supreme Court.
• A federal system with a strong center.
• Residual powers vest at the center.
• Appointment of State Governors.​

Additional Information 

Sources of Indian Constitution

Shortcut Trick

Use the Value Putting Method by assuming values that satisfy the condition a + b + c = 0.

Let a = 1, b = 1, and c = −2. Then, 1 + 1 + (−2) = 0.

Substitute these in the expression: 1³ + 1³ + (−2)³ − 3(1)(1)(−2)

⇒ 1 + 1 − 8 − (−6) ⇒ 2 − 8 + 6 = 0.

∴ The correct answer is 0.

Alternate Method

Given: a + b + c = 0

The standard algebraic identity is:

⇒ a³ + b³ + c³ − 3abc = (a + b + c)(a² + b² + c² − ab − bc − ca)

Substitute the given condition a + b + c = 0 into the formula:

⇒ a³ + b³ + c³ − 3abc = (0) × (a² + b² + c² − ab − bc − ca)

⇒ a³ + b³ + c³ − 3abc = 0

∴ The correct answer is 0.

Additional Information

Conditional Identity

If a + b + c = 0, then a³ + b³ + c³ = 3abc. This is used to simplify cubic expressions involving variables that sum to zero.

Alternative Form of the Identity

a³ + b³ + c³ − 3abc = 1/2(a + b + c)[(a − b)² + (b − c)² + (c − a)²].

Sum of Squares Property

If a² + b² + c² − ab − bc − ca = 0, then a = b = c.

Given:

Radius of wheel = 14 cm

Number of revolutions = 10

Formula Used:

The circumference of a circle = 2πr

The distance travelled by a wheel in one revolution = circumference of the wheel

Solution:

The circumference of the wheel = 2πr = 2 x π x 14 cm = 28π cm

The distance travelled by the wheel in one revolution = circumference of the wheel = 28π cm

Therefore, the distance travelled by the wheel in 10 revolutions = 10 x distance in one revolution

= 10 x 28π cm

= 280 × 22/7

= 880

∴ The wheel will travel a distance of 880 cm in 10 revolutions.

Shortcut Trick

For the identity sec²θ − tan²θ = 1, it follows that (secθ + tanθ)(secθ − tanθ) = 1.

This means secθ − tanθ is the reciprocal of secθ + tanθ.

Given secθ + tanθ = 5, then secθ − tanθ = 1/5.

∴ The correct answer is 1/5.

Alternate Method

Given:

⇒ secθ + tanθ = 5

Formula Used:

⇒ sec²θ − tan²θ = 1

Calculations:

⇒ (secθ + tanθ) × (secθ − tanθ) = 1

⇒ 5 × (secθ − tanθ) = 1

⇒ secθ − tanθ = 1/5

∴ The correct answer is 1/5.

Additional Information

Trigonometric Identities

Standard identities: sin²θ + cos²θ = 1 and 1 + cot²θ = cosec²θ.

Cosecant-Cotangent Relation

Similar to sec-tan, if cosecθ + cotθ = x, then cosecθ − cotθ = 1/x.

Finding Individual Ratios

By adding the two equations, 2secθ = x + 1/x and 2tanθ = x − 1/x.

Calculation:

Now, the total number of girls in school P and R

⇒ 3000 × (17 + 31)%

⇒ 1440

∴ The total number of girls in school P and R is 1440.

Given:

The angle subtended by a chord xy on the centre of a circle is 180 degrees.

The length of this chord is 36 cm.

Concept used:

1. Only the diameter of a circle can subtend an angle of 180° at the centre of the circle.
2. Radius × 2 = Diameter
3. Diameter is the largest chord of any circle.

Calculation: 

According to the concept,

XY has to be the diameter of the circle.

Now, the radius of the circle = 36/2 = 18 cm

∴ The radius of the circle is 18 cm.

Shortcut Trick

Assume an angle, say A = 45°, to quickly evaluate the expression.

⇒ sec²45° = 2, cos²45° = 1/2, sin²45° = 1/2, cosec²45° = 2

⇒ Expression = [(1 + 2) ÷ (1 + 1/2)] × [(1 + 1/2) ÷ (1 + 2)]

⇒ Expression = (3 ÷ 3/2) × (3/2 ÷ 3) = 2 × 1/2 = 1

From the given options, tan²45° = (1)² = 1.

∴ The correct answer is tan² A.

Alternate Method

Given:

Expression = [(1 + sec²A) ÷ (1 + cos²A)] × [(1 + sin²A) ÷ (1 + cosec²A)]

Formula Used:

sec A = 1 / cos A, cosec A = 1 / sin A, tan A = sin A / cos A

Calculations:

⇒ First part = (1 + 1/cos²A) ÷ (1 + cos²A)

⇒ First part = [(cos²A + 1) / cos²A] ÷ (1 + cos²A) = 1 / cos²A

⇒ Second part = (1 + sin²A) ÷ (1 + 1/sin²A)

⇒ Second part = (1 + sin²A) ÷ [(sin²A + 1) / sin²A] = sin²A

⇒ Complete Expression = (1 / cos²A) × sin²A

⇒ Expression = sin²A / cos²A = tan²A

∴ The correct answer is tan² A.

Additional Information

Reciprocal Trigonometric Identities

Functions that are inverted forms of each other: sec θ = 1 ÷ cos θ and cosec θ = 1 ÷ sin θ.

Quotient Identities

These identities relate tan and cot to sine and cosine: tan θ = sin θ ÷ cos θ and cot θ = cos θ ÷ sin θ.

Value Putting Technique

In the simplification of trigonometric expressions, substituting an angle like θ = 45° easily converts complex variables into numerals, aiding rapid elimination of wrong options.

Given:

$\frac{\frac{5}{2}\div\frac{2}{5}\times \frac{1}{5}-\frac{1}{5}\div\frac{3}5{\times \frac{5}{2}}}{\frac{2}{5}\div\frac{1}{5}-\frac{1}{2}\times \frac{5}{2}\div\frac{25}{4}+\frac{1}{2}\div\frac{2}{5}\times\frac{1}{5}}$

Concept used:

Calculation:

According to the concept,

$\frac{\frac{5}{2}\div\frac{2}{5}\times \frac{1}{5}-\frac{1}{5}\div\frac{3}5{\times \frac{5}{2}}}{\frac{2}{5}\div\frac{1}{5}-\frac{1}{2}\times \frac{5}{2}\div\frac{25}{4}+\frac{1}{2}\div\frac{2}{5}\times\frac{1}{5}}$

⇒ $\frac{\frac{5}{2}\times\frac{5}{2}\times \frac{1}{5}-\frac{1}{5}\times\frac{5}3{\times \frac{5}{2}}}{\frac{2}{5}\times\frac{5}{1}-\frac{1}{2}\times \frac{5}{2}\times\frac{4}{25}+\frac{1}{2}\times\frac{5}{2}\times\frac{1}{5}}$

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

⇒ ${{(5 \times 6) - (5 \times 4)}\over4 \times 6}\over{(2 \times 20)\over1 \times 20}- {(1 \times 4)\over5 \times 4}+ {(1 \times 5)\over 4 \times 5}$

⇒ $\frac {\frac {5}{12} }{\frac {41}{20}}$

⇒ $\frac {5 \times 20 }{12 \times 41}$

⇒ $\frac {25}{123}$

∴ The simplified value is $\frac {25}{123}$.

Given:

Length of side a = 13 inches

Length of side b = 15 inches

Length of side c = 14 inches

Formula Used:

Heron's formula: Area of a triangle = $√(s(s-a)(s-b)(s-c))$, where s is the semi-perimeter of the triangle.

Solution:

We can use Heron's formula to find the area of the triangle.

First, we need to calculate the semi-perimeter of the triangle:

s = (a + b + c)/2

⇒ (13 + 15 + 14)/2

⇒ 21

Next, we can use Heron's formula to find the area of the triangle:

Area = $√(s(s-a)(s-b)(s-c))$

⇒ $√(21(21-13)(21-15)(21-14))$

⇒  √(21(8)(6)(7))

⇒ √(2⁴ x 3² x 7²)

⇒ 84

Therefore, the area of the triangle is 84 square inches.

Given:

20% of P + 40% of Q = 80% of Q

Formula Used:

Percentages can be expressed as fractions or decimals. For example, 20% can be written as 0.2 or 1/5.

Solution:

20% of P + 40% of Q = 80% of Q

0.2P + 0.4Q = 0.8Q

0.2P = 0.8Q - 0.4Q

0.2P = 0.4Q

Now we can solve for P/Q:

P/Q = 0.4 / 0.2

P/Q = 2

This tells us that P is equal to 2Q.

 P is 200% of Q.

Given:

2/5 of marked price = 5/8 of selling price

Formula Used:

Discount percent = (Marked price - Selling price) / Marked price x 100%

Solution:

Let's start by simplifying the given equation:

2/5 of marked price = 5/8 of selling price

We can rewrite this as:

8/5 x 2/5 of marked price = selling price

16/25 of marked price = selling price

Now we can use the formula for discount percent:

Discount percent = (Marked price - Selling price)/Marked price x 100%

Substituting the values we have:

Discount percent = (Marked price - 16/25 of marked price) / Marked price x 100%

Simplifying this expression:

Discount percent = (9/25) x 100

⇒ 9 × 4 = 36

Discount percent = 36%

Therefore, the discount percent is 36%.

Calculation:

Number of students who scored more than 60% = 25 + 9 = 34

Total students = 2 + 2 + 12 + 25 + 9 = 50

Now, the required % = $\frac {34}{50} \times 100\%$ = 68%

∴ 68% of total students scored more than 60%.

Given:

The length of a chord is 30 cm in a circle whose radius is 17 cm.

Concept used:

1. The perpendicular from the center of a circle to a chord bisects the chord. 2. Pythagorean theorem states that the sum of the squares on the legs of a right triangle is equal to the square on the hypotenuse.

Calculation:

Let O and PQ be the center and aforementioned chord respectively. 

So, OP is the radius of the circle and OD, a perpendicular from O on PQ is drawn.

⇒ PQ = 30 cm and OP = 17 cm.

According to the concept,

⇒ PD = DQ = 30/2 = 15 cm

So, ΔODP is a right-angled triangle at D.

According to the Pythagorean theorem,

OP² = OD² + PD²

⇒ 17² = OD² + 15²

⇒ OD² = 289 - 225

⇒ OD² = 64

⇒ OD = 8

∴ The distance of this chord from the center is 8 cm.

Given:

Tina can do a piece of work in 12 days

Meena can do a piece of work in 15 days

Concept used:

If A can do work in n days then one day work of A will be 1/n

Calculation:

According to the problems 

A = 12 × 5 = 60

B = 15 × 4 = 60

LCM of 12 and 15 = 60

A can do 5 unit in one day

B can do 4 unit in one day 

Total days to complete work = 60/9 days  =20/3

Meena does 4 × (20/3) units of work 

⇒ $\frac{{4 \times \frac{{20}}{3}}}{{60}} \times 18000 = 8000$

∴ Meena will get  Rs. 8000.

Given:

Radii of two circles are 12 cm and 5 cm. Distance between their centres is 25 cm.

Formula used:

Length of the direct common tangent of two circles = $\sqrt {D^2 - (r_1 - r_2)^2}$ (D = Distance between their centres, r₁ = radius of the bigger circle, and r₂ = radius of the smaller 

Calculation:

Let the centres be at P and Q.

QN = Radius of the bigger circle = 12 cm

PM = Radius of the smaller circle = 5 cm

Let MN be the direct common tangent.

According to the formula,

Length of MN

⇒ $\sqrt {25^2 - (12 - 5)^2}$

⇒ $\sqrt {576}$

⇒ 24 cm

∴ The length of the direct common tangent is 24 cm.

Calculation:

The average expenditure of all companies = (200 + 800 + 600 + 400 + 2000) ÷ 5 = 800

The average savings of all companies = (600 + 1600 + 1200 + 600 + 800) ÷ 5 = 960

Now, the required % = $\frac {960}{800} \times 100\%$ = 120%

∴ The average savings of all companies is 120% of the average expenditure of all companies.

Given:

Number of students = 30

Average age (incorrectly calculated) = 15 years

Age of one student was incorrectly taken as 15 years instead of the actual age of 9 years.

Formula:

Correct Average Age = (Sum of all ages of students - incorrect age + correct age) / Number of students

Solution:

Sum of all ages of 30 students = 30 x 15 = 450

Incorrectly added age = 15

Correct age = 9

Therefore, the correct sum of all ages = 450 - 15 + 9 = 444

Correct Average Age = 444 / 30 = 14.8 years (approx)

Hence, the correct average age of the 30 students is 14.8 years.

Given:

Distance traveled by the car = 60 km

Let the original speed of the car be 's' km/hr

Increased speed of the car = (s + 8) km/hr

Formula:

Time = Distance/Speed

Solution:

Let T_a & T_b be the time required to complete distance at original speed & increased speed respectively

⇒ T_a = $\frac{60}{s}$ hours

⇒ T_b = $\frac{60}{s+8}$

According to the question

⇒ T_a - T_b = $\frac{60}{s}$ - $\frac{60}{s+8}$ = 2

⇒ 60s + 480 - 60s = 2s² + 16s

⇒ s² + 8s - 240 = 0

On solving s = -20 or s = 12     (∵ s is speed, neglecting negative value)

∴ The original speed of the car is 12 km/hr.

Calculation:

Let the cost price be Rs. y

When he had a profit,

Selling price = cost price + profit % of cost price

⇒ y + 25% × y = 1.25y

When he had a loss,

Selling price = cost price – loss% of cost price

⇒ y – 25% × y = 0.75y

According to the question,

⇒ 1.25y – 0.75y = 40

⇒ 0.50y = 40

⇒ y = 80

∴ Initial selling price = 1.25y = 1.25 × 80 = Rs.100

Alternate MethodCalculation:

Taking profit percentage as positive and the loss percentage as negative.

⇒ 25% - (-25%) = 40

⇒ 50% = 40

⇒ 1 = 80

S.P = 1.25 = 1.25 × 80 = 100

∴ The selling price is Rs.100.

Shortcut Trick

Given expression: 44 × 12 − (25 + 13 × 10)

Apply BODMAS directly, solving multiplication inside the bracket first.

⇒ 44 × 12 − (25 + 130)

⇒ 528 − 155

⇒ 373

∴ The correct answer is 373.

Alternate Method

Given:

Expression = 44 × 12 − (25 + 13 × 10)

Formula Used:

BODMAS rule (Bracket, Order/Of, Division, Multiplication, Addition, Subtraction)

Calculation:

Step 1: Solve the innermost parts of the bracket first (Multiplication before addition).

⇒ 13 × 10 = 130

Step 2: Complete the bracket by adding the values.

⇒ 25 + 130 = 155

Step 3: Perform multiplication outside the bracket.

⇒ 44 × 12 = 528

Step 4: Subtract the bracket's result from the multiplication's result.

⇒ 528 − 155 = 373

∴ The correct answer is 373.

Additional Information

BODMAS Rule

It dictates the order of mathematical operations: Bracket, Of/Order, Division, Multiplication, Addition, and Subtraction. This ensures that everyone calculates an expression exactly the same way.

Multiplication Shortcuts

To multiply by numbers like 12, split the multiplier into (10 + 2). E.g., 44 × 12 = 44 × (10 + 2) = 440 + 88 = 528. Distributive property simplifies mental calculations effectively.

Fraction and Decimal Rules

Always convert mixed fractions into improper fractions before performing multiplication or division. When working with decimals, make sure to align the decimal points correctly before adding or subtracting.

Given:

$\rm \cot y=\frac{12}{5}$

Concept used:

1. $cosec^2\alpha - cot^2\alpha = 1$ 2. sinα = $\frac {1}{cosec\alpha}$ 3. $sin^2\alpha + cos^2\alpha = 1$

Calculation:

According to the concept,

$\rm \cot y=\frac{12}{5}$

⇒ $cot^2 y={(\frac{12}{5})^2}$

⇒ $cot^2 y= \frac{144}{25}$

⇒ $cosec^2 y - 1= \frac{144}{25}$

⇒ $cosec^2 y = \frac{144}{25} + 1$

⇒ $cosec^2 y = \frac{144 + 25}{25}$

⇒ $cosec^2 y = \frac{169}{25}$

⇒ $sin^2 y = \frac{25}{169}$

⇒ $1 - sin^2 y = 1 - \frac{25}{169}$

⇒ $cos^2 y = \frac{169- 25}{169}$

⇒ $cos^2 y = \frac{144}{169}$

∴ The value of cos2 y is $\frac{144}{169}$.

Given:

p/q = r/s = t/u = 2/5

Calculation:

Let's assume the common ratio as k. Therefore,

p = 2k, q = 5k

r = 2k, s = 5k

t = 2k, u = 5k

Now, we need to find the value of (4p + 3r + 7t) : (4q + 3s + 7u)

Substituting the values of p, q, r, s, t, and u, we get:

(4p + 3r + 7t) : (4q + 3s + 7u) = (4(2k) + 3(2k) + 7(2k)) : (4(5k) + 3(5k) + 7(5k))

= (8k + 6k + 14k) : (20k + 15k + 35k)

= 28k : 70k

= 4: 10

= 2: 5

Therefore, the value of (4p + 3r + 7t) : (4q + 3s + 7u) is 2 : 5.

Given

The average of 32, 34, 38, 21, 26 and x is 30.

Formula:

Average = (Sum of observations) / (Number of observations)

Calculation:

We know the sum of the given 5 observations, which is:

32 + 34 + 38 + 21 + 26 = 151

We also know that the average of these 5 observations and x is 30. Therefore, we can write the equation:

(32 + 34 + 38 + 21 + 26 + x) / 6 = 30

Multiplying both sides by 6, we get:

32 + 34 + 38 + 21 + 26 + x = 180

Simplifying the left side, we get:

151 + x = 180

Subtracting 151 from both sides, we get:

x = 29

Therefore, the value of x is 29.

Calculation:

J1 = (100 + 80 + 40 + 30 + 10) ÷ 5 = 52

J2 = (10 + 20 + 120 + 60 + 50) ÷ 5 = 52

Now, (J1/J2) = 52/52 = 1

∴ The value of (J1/J2) is 1.

Given

$\rm \frac{1+x^2}{1-x}\div\frac{1-x^4}{x-1}\times \frac{x(1-x)}{(1+x)}$

Concept used:

Follow the BODMAS rule according to the table given below:

Calculation:

$\rm \frac{1+x^2}{1-x}\times \frac{x - 1}{1-x^4}\times \frac{x(1-x)}{(1+x)}$

$\rm \frac{1+x^2}{1-x}\times \frac{-(1-x)}{1-x^4}\times \frac{x(1-x)}{(1+x)}$

$\rm- \frac{1+x^2}{1-x^4}\times \frac{x(1-x)}{(1+x)}$

$\rm- \frac{1+x^2}{(1-x^2)(1+x^2)}\times \frac{x(1-x)}{(1+x)}$

$\rm \frac{-1}{(1-x^2)}\times \frac{x(1-x)}{(1+x)}$

$\rm \frac{-1}{(1-x)(1 + x)}\times \frac{x(1-x)}{(1+x)}$

$\rm \frac{-1}{(1 + x)}\times \frac{x}{(1+x)}$

$\rm \frac{-x}{(1 + x)^2}$

∴ Option 3 is the correct answer.