SSC CGL 2023 Tier-I Official Paper (Held On: 27 Jul 2023 Shift 2) (Previous Year Paper)

The logic followed here is:

Step 1: Letters in images are moving in clockwise direction skipping One letter.

Step 2: Number of  '

' are decreasing from image 1 to image 5.

Step 3: Number of '

' is increasing from image 1 to image 5.   

So, Image 5 will replace the question mark in the given series.

Hence, the correct answer is 'Option 4'.

The logic followed here is:

Logic: (First number × Second Number) × 3 = Third Number.

For, (3, 6, 54)

→ (3 × 6) × 3

→ 18 × 3

= 54.

For, (4, 2, 24)

→ (4 ×2) × 3

→ 8 × 3

= 24.

Similarly, (3, 4, 36)

→ (3 ×4) × 3

→ 12 × 3

= 36.

Hence, the correct answer is 'Option 3'.

Family Chart:

Given: Pointing to a man, Rocky (a man) said, “He is the father of the daughter of my daughter-in-law.”

 

So, Rocky is the Father of that Man.

Hence, the correct answer is 'Option 3'.

The logic followed here is:

Given Series:  _ T M _ P T _ R _ _ M R P _ _ R

Now, putting letter in blank spaces given in Options One by One.

Option 1) M P T R M T T

M T M P / P T T R / R M M R / P T T R → Does not follow pattern. 

Option 2) P R M P T T M

<br>

P T M R / P T M R / P T M R / P T M R → Follows pattern of 'PTMR'.

Option 3) P M T R R M T

P T M M / P T T R / R R M R / P M T R → Does not follow pattern.

Option 4) M T P R T M R

M T M T/ P T P R/ R T M R/ P M R R → Does not follow pattern.

Hence, the correct answer is 'Option 2'.

The paper when unfolded will appear as shown below:

Hence, the correct answer is 'Option 3'.

Given Statements: 

Some teachers are scientists.

All scientists are doctors.

All doctors are engineers.

The least possible Venn diagram for the statement is:

  

 

Conclusions:

I. Some doctors are teachers. → True. (Some teachers are Scientist and All Scientist are doctors, then the part of scientist who are doctors are also teachers.)

II. Some engineers are teachers. → True. (Some engineers are scientist and some scientist are teachers, then the part of engineers which are scientist are also teachers.)

III. Some doctors are scientists. → True. (All Scientist are Doctors, it gives some doctors are scientist.)

So, All Conclusions Follow.

Hence, the correct answer is 'Option 2'.

The logic followed here is: All the three Elements of images are moving in anticlockwise direction.

Here, image 5 will continue the series.

Hence, the correct answer is 'Option 2'.

The logic followed here is:

So, 166 will replace the question mark in the given series.

Hence, the correct answer is 'Option 4'.

The BODMAS Rule: 

Decoding the symbols:

<br>

Given Equation: 205 > 210 $ 15 ! 2 < 19

After replacing the symbols equation becomes:

→ 205 + 210 ÷ 15 × 2 - 19

→ 205 + 14 × 2 - 19

→ 205 + 28 - 19

→ 233 - 19

= 214.

Hence, the correct answer is 'Option 3'.

The Position and Positional value of English Alphabets are:

For, 'PLIERS' is coded as MMAFJO'

For, 'SHOVEL' is coded as FZRLFR'

Similarly, 'WRENCH' will be:

So, 'WRENCH' will be written as 'BXJBPV'.

Hence, the correct answer is 'Option 2'.

The position and positional values of English Alphabets are:

The logic followed here is:

For, 'SPIT' is coded as ‘USKW’

For, 'COPY' is coded as ‘ERRB’

Similarly 'MOCK' will be:

So, 'MOCK' will be written as 'OREN'.

Hence, the correct answer is 'Option 4'.

The position and positional values of English Alphabets are as:

The logic followed here is:

Option 1) ADZV

Option 2) MPNK

Option 3) FIUR

Option 4) TWGD

Here, 'ADZY' is odd among the given options.

Hence, the correct answer is 'Option 1'.

The logic followed here is:

Logic: (First number 3 - Second number2 =  Third Number).**

Now,

(12, 8, 20) ⇒ 12 * 3 - 8 * 2 = 36 - 16 = 20

(7, 3, 15) ⇒  7 * 3 - 3 * 2 = 21 - 6 = 15

Similarly,

(9, 4, 19) ⇒  9 * 3 - 4 * 2 = 27 - 8 = 19

Hence, the correct answer is 'Option 1'.

The logic followed here is: First Number² × (First number - 3) = Second number.

1) (8, 320) ⇒ 8² × (8 - 3) = 64 × 5 = 320

2) (11, 968) ⇒112 × (11 - 3) = 121 × 8 = 968

3) (5, 100) ⇒ 52 × (5 - 3) = 25 × 2 = 50 ≠ 100

4)  (6, 108) ⇒ 62 × (6 - 3) = 36 × 3 = 108

Hence, the correct answer is "(5, 100)".

Given Equation: 312 – 13 × 14 + 207 ÷ 4 = 539

BODMAS Rule:

Let's check each Option One by One:

Option 1) ÷ and –

Given: 312 – 13 × 14 + 207 ÷ 4 = 539

After interchanging the numbers we get;

312 ÷13 × 14 + 207 - 4 = 539

24 × 14 + 207 - 4 = 539

336 + 207 - 4 = 539

543 - 4 = 539

539 = 539.

Option 2) – and +

Given: 312 – 13 × 14 + 207 ÷ 4 = 539

After interchanging the numbers we get;

312 + 13 × 14 - 207 ÷ 4 = 539

312 + 13 × 14 - 51.75 = 539

312 + 182 - 51.75 = 539

494 - 51.75 = 539

442.25 ≠ 539.

Option 3) ÷ and +

Given: 312 – 13 × 14 + 207 ÷ 4 = 539

After interchanging the numbers we get;

312 – 13 × 14 ÷ 207 + 4 = 539

312 – 13 × 0.06 + 4 = 539

312 - 0.87 + 4 = 539

316 - 0.87 = 539

315.13 ≠ 539.

Option 4) + and ×

Given: 312 – 13 × 14 + 207 ÷ 4 = 539

After interchanging the numbers we get;

312 – 13 + 14 × 207 ÷ 4 = 539

312 – 13 + 14 × 51.75 = 539

312 – 13 + 724.5 = 539

1036.5 – 13 = 539

1023.5 ≠ 539.

Hence, the correct answer is 'Option 1'.

The correct dictionary order for the given words are:

5. Apparel
6. Apparition
7. Appear
8. Approach
9. Approximate

So, 5, 4, 1, 2, 3 is the correct dictionary order for the given words.

Hence, the correct answer is 'Option 3'.

The image embedded in given figure is as shown below:

<br> <br>

Hence the correct answer is 'Option 4'.

The logic followed here is:

Given Sequence: M_ _ KS _ ON _ SMO _ K _ _ _ NKS

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

Option 1) ONMNKOMS → M O N K S / M ON N S / M O K K O / M S N K S → (Does not follow pattern).

Option 2) ONMKNSMO → M O N K S / M ON K S / MO N K S / M O N K S → (Follows pattern of 'MONKS').

Option 3) ONMMMMMO → M O N K S / M ON M S / M O M K M / M O N K S → (Does not follow pattern).

Option 4) NMOKNSMO → M N M K S /O O N K S / M O N K S / M O N K S → (Does not follow pattern).

Here, 'ONMKNSMO' followed a pattern.

Hence, the correct answer is 'Option 2'.

The logic followed here is:

Logic: The second word is a synonym of the first word.

Here,

Vacant : Empty → "Empty" is a synonym of "Vacant".

Similarly,

Enormous : Huge → "Huge" is a synonym of "Enormous".

So, Huge is the second word.

Hence, the correct answer is 'Option 3'.

BODMAS Table:

Given Equation: 32 * 14 * 18 * 9 * 12 * 22

Let's check each Option One by One:

Option 1) −, +, ÷, ×, =

Given: 32 * 14 * 18 * 9 * 12 * 22

After replacing the * signs we get;

32 - 14 + 18 ÷ 9 × 12 = 22

32 - 14 + 2 × 12 = 22

32 - 14 + 24 = 22

56 - 14 = 22

42 ≠ 22.

Option 2) +, −, ÷, ×, =

Given: 32 * 14 * 18 * 9 * 12 * 22

After replacing the * signs we get;

32 + 14 - 18 ÷ 9 × 12 = 22

32 + 14 - 2 × 12 = 22

32 + 14 - 24 = 22

46 - 24 = 22

22 = 22.

Option 3) ×, +, ÷, −, =

Given: 32 * 14 * 18 * 9 * 12 * 22

After replacing the * signs we get;

32 × 14 + 18 ÷ 9 - 12 = 22

32 × 14 + 2 - 12 = 22

448 + 2 - 12 = 22

450 - 12 = 22

438 ≠ 22.

Option 4) ÷, −, +, ×, =

Given: 32 * 14 * 18 * 9 * 12 * 22

After replacing the * signs we get;

32 ÷ 14 - 18 + 9 × 12 = 22

2.28 - 18 + 9 × 12 = 22

2.28 - 18 + 108 = 22

110.28 - 18 = 22

92.28 ≠ 22.

Hence, the correct answer is 'Option 2'.

Logic: (Second number ×  Third number)/6 = First number

(3, 9, 2) ⇒ (9 × 2) / 6 = 18/6 = 3= First Number

(8, 6, 8) ⇒ (6 × 8) / 6 = 48/6 = 8 = First Number

(5, 3, ?) 

⇒ (3 × ?) / 6 = 5

⇒  30 /3 = 10 

Hence, the correct answer 10.

Family Chart:

Given: Azad points towards a picture and says it’s the picture of his mother’s father’s only granddaughter’s only brother.

So, Azad himself is in the picture.

Hence, the correct answer is 'Option 4'.

To find the face opposite the face showing 'X', we need to compare the common surface in the given dices,

Now, from the given dice,

'U' is the common surface in both the dice, S, T and X are the faces adjacent to it.

If we rotate Dice I, in anticlockwise direction it becomes Dice III

Then, if we compare the two adjacent faces of S, X and T, they are opposite to each other.

So, 'T' is the face opposite to 'X'.

Hence, the correct answer is 'Option 4'.

The image embedded in given figure is as shown below:

Hence, the correct answer is 'Option 3'.

The position and positional value of English Alphabets are as:

The logic followed here is:

\

So, QY will replace the question mark in the given series.

Hence, the correct answer is 'Option 2'.

The correct answer is Malegam Committee.

Key Points

• The creation of a separate category for NBFCs operating in the microfinance sector (NBFC-MFI) was done based on the recommendations of the Malegam Committee.
• The Malegam Committee was appointed by the Reserve Bank of India (RBI) in 2010 to review the microfinance sector in India and provide recommendations for its growth and development.
• The committee recommended the creation of a separate category of NBFCs for microfinance to regulate and supervise them effectively, and to ensure that they comply with the prescribed norms and standards.
• The NBFC-MFIs are required to obtain a certificate of registration from the RBI and comply with the regulations on interest rates, lending practices, borrower protection, and reporting requirements.

Additional Information

• Shah Committee: This committee was appointed by the Reserve Bank of India in 1989 to review the working of the monetary system in India and to suggest measures for its improvement.
• Kamath Committee: This committee was appointed by the Reserve Bank of India in 2014 to review the working of the asset reconstruction companies in India and to suggest measures for their improvement.

The correct answer is First.

Key Points

• First Five-Year Plan
• 1st five-year plan was from 1951 to 1956.
• The prime target of the first five-year plan of India was the Development of agriculture.
• The target Growth was 2.1 % and the Actual Growth was 3.6 %.
• It was based on Harrod-Domar.
• The influx of refugees, severe food shortage & mounting inflation confronted the country at the onset of the first five-year plan.

Additional InformationSecond Five Year Plan (1956-1961)

• The second five-year plan is based on the so-called Mahalanobis model.
• This was the USSR model Indianized by PC Mahalanobis, the founder of the Indian Statistical Institute and a close aide of Nehru.
• This model is known to have set the statistical foundations for state-directed investments and created the intellectual underpinnings of the license-raj through an elaborate input-output model.
• This Model suggested that there should be an emphasis on the heavy industries, which can lead the Indian Economy to a long-term higher growth path
• Started Industrial Policy Resolution 1956.

Third Five-Year Plan (1961-1966)

• The Third 5 year Plan focused on agriculture & enhancement in the production of wheat, but the succinct Sino - Indian War in the year 1962 exposed flaws in the economy & shifted the spotlight towards the Defence industry.
• On May 31 & June 1, 1961, the National Development Council considered the Draft Report on the Third Plan and generally approved it.
• In the course of this period, India's economy must not only enlarge swiftly but must, in unison, become independent and self-generating.
• This long-standing approach is projected to offer a wide-ranging design of expansion for the country's natural resources, industrial advance, and agricultural changes in the social structure & an incorporated scheme of regional & national development.

Fourth Five Year Plan (1969-1974)

• The fourth Five Year Plan was the first plan launched by the Indira Gandhi government amid the pressure of drought, devaluation, and inflationary recession.
• The country was fighting with population explosion, increased unemployment, poverty, and a shackling economy. In addition, the situation in East Pakistan (now independent Bangladesh) was becoming dire as the Indo-Pakistani War of 1971 and the Bangladesh Liberation War took place.
• Funds earmarked for industrial development had to be used for the war effort.
• The result was that this plan period was also no better than the third five-year plan.

The correct answer is statutory.

Key Points

• Fundamental duties come under Part IVA and Article 51A.
• These duties are statutory and are not enforceable by law but are taken into account by the courts while adjudicating any matter.
• Fundamental Duties in the Constitution are inspired by USSR.
• Japan is the only democratic country, other than India, to have Fundamental duties in its Constitution.
• These duties were incorporated through the 42nd Constitutional Amendment Act, 1976 in the Constitution on the recommendations of the Swaran Singh Committee.
• Only 8 Fundamental duties were based on the Swaran Singh Committee recommendation while the 42nd Constitutional Amendment Act added 10 Fundamental duties in the Constitution.
• Later, the 86th Amendment Act, 2002 was passed that introduced one more fundamental duty in the Constitution. Now there are Eleven Fundamental duties in the Constitution.
• Rights and duties are correlative and inseparable.

Additional Information

List of Fundamental Duties of India

• It shall be the duty of every citizen of India —

1. To abide by the Constitution and respect its ideals and institutions, the National Flag and the National Anthem;
2. To cherish and follow the noble ideals which inspired our national struggle for freedom;
3. To uphold and protect the sovereignty, unity, and integrity of India.
4. To defend the country and render national service when called upon to do so;
5. To promote harmony and the spirit of common brotherhood amongst all the people of India transcending religious, linguistic and regional or sectional diversities; to renounce practices derogatory to the dignity of women;
6. To value and preserve the rich heritage of our composite culture;
7. To protect and improve the natural environment including forests, lakes, rivers, wildlife and to have compassion for living creatures;
8. To develop the scientific temper, humanism, and the spirit of inquiry and reform;
9. To safeguard public property and to abjure violence;
10. To strive towards excellence in all spheres of individual and collective activity so that the nation constantly rises to higher levels of endeavor and achievement;
11. Who is a parent or guardian, to provide opportunities for education to his child, or as the case may be, ward between the age of six to fourteen years.

The correct answer is 1869.

Key Points

• Dmitri Mendeleev invented the periodic table in 1869, organizing elements based on their atomic weights and properties.
• Mendeleev left gaps in the table for elements yet to be discovered, predicting their properties accurately.
• On March 6, 1869, Mendeleev presented his first periodic table to the Russian Chemical Society.
• Mendeleev’s table demonstrated that when elements are arranged by increasing atomic weight, certain chemical properties repeat periodically.
• This periodic arrangement became the foundation for the modern periodic table used in chemistry today.

Additional Information

• Periodic Law: Mendeleev’s periodic table was based on the periodic law which states that the properties of elements are a periodic function of their atomic weights.
• Modern Periodic Table: Today, the periodic table is organized by atomic number (proton count) rather than atomic weight, as introduced by Henry Moseley in 1913.
• Predicted Elements: Mendeleev accurately predicted the existence and properties of elements like germanium (eka-silicon), gallium (eka-aluminum), and scandium.
• Contributors to Periodicity: Other scientists like John Newlands (law of octaves) and Lothar Meyer worked on periodic classification, but Mendeleev’s table was more comprehensive and widely accepted.
• Significance: Mendeleev’s periodic table provided a systematic framework for studying chemical elements, aiding in the discovery of new elements and advancing the field of chemistry.

The correct answer is Canada, USA, and Mexico.

• FIFA World Cup 2026 will be held in Canada, the USA, and Mexico

Key Points

• The 2026 FIFA World Cup will be the 23rd FIFA World Cup tournament and it will be hosted in Canada, Mexico, and the United States.
• The first football club in the world ‘Sheffield Football Club’ was founded in the year 1857 in England.
• The first football club in India, named 'Calcutta FC', was founded in 1872.
• The apex institution of football is ‘The Federation of International formed by seven countries on May 21, 1904.
• The headquarters of FIFA is in Zürich, Switzerland.

Additional Information

• Football was included as a competitive game in the Olympic Games officially in 1908.
• India took part in the World Olympic Football Competition in 1948 in London.
• The first World Cup was organized at Monte (Uruguay) in 1930.
• In India, the Indian Football Association (IFA) organizes the National Football Championship.
• The trophy awarded in their competition is called the Santosh Trophy.

The correct answer is Vinegar.

Key PointsEthanoic acid:

• Ethanoic acid commonly known as acetic acid belongs to a group of carboxylic acids.
• Vinegar is dilute acetic acid. Vinegar used in our day to day life is a 5-8% solution of acetic acid (Ethanoic acid ) in water.
• It is extensively used in kitchens around the world as a basic seasoning and preservative in the preparation and cooking of certain foods.
• Its chemical formula is CH3COOH.
• Vinegar is made by the fermentation of ethanol, which is typically derived from wine, beer, or other alcoholic beverages. During fermentation, acetic acid bacteria convert the ethanol into acetic acid, which gives vinegar its sour taste and pungent odor.
• Vinegar is a versatile ingredient that can be used in a wide range of culinary applications, such as salad dressings, marinades, sauces, pickles, and baked goods.

Additional Information

• Properties of Acetic Acid are as follows-
• Acetic acid has antibacterial qualities and hence used as an antiseptic.
• The manufacture of rayon fibre involves the use of ethanoic acid.
• It is useful in the treatment of cancer due to its direct injection into the tumour.
• Being the major constituent of vinegar, it finds use in the pickling of many vegetables.
• The manufacture of rubber involves the use of ethanoic acid.
• It is also used in the manufacture of various perfumes.
• It is widely used in the production of vinyl acetate monomer.

The correct answer is Lord Dalhousie.

Key Points

• The doctrine of Lapse:
• Lord Dalhousie introduced the Doctrine of Lapse for annexing the dependent states whose ruler died without a natural heir to succeed him.
• One kingdom after another was annexed simply by applying this doctrine: Satara (1848), Sambalpur (1850), Udaipur (1852), Nagpur (1853) and Jhansi (1854).
• Lord Dalhousie:
• In 1848, Lord Dalhousie arrived in India as the Governor-General and was determined to extend British rule over India.
• Dalhousie occupied the Punjab and Sindh through war and brought several subordinate states directly under the Company’s rule by annexing them on the basis of the Doctrine of Lapse.
• Lord Dalhousie also introduced the Doctrine of Good of Governed under which Awadh (1856) and Punjab (1849) were annexed.
• Dalhousie established Public Works Department, the objective behind the formation of this department was the construction and maintenance of canals, roads, bridges, etc.

Additional Information

• Lord Canning:
• Lord Canning served as Governor-General of India from 1856 to 1862.
• During his tenure, the Government of India Act, 1858 was passed which created the office of Viceroy to be held by the same person who was Governor-General of India.
• Thus, Lord Canning also served as the first Viceroy of India.
• The Mutiny of 1857, which he was able to suppress successfully,
• The Passing of the Indian Councils Act, 1861 which introduced a portfolio system in India,
• Bengal Rent Act (1859).
• Lord William Bentinck (1828-1835):
• Abolition of sati and other cruel rites (1829).
• Suppression of thugi (1830).
• Charter Act of 1833.
• Resolution of 1835, and educational reforms and introduction of English as the official language.
• Annexation of Mysore (1831), Coorg (1834) and Central Cachar (1834).
• Treaty of 'perpetual friendship with Ranjeet Singh.
• Abolished the provincial court of appeal and circuit.

The correct answer is Odissi.

Key Points

• Sonal Mansingh is a prominent Indian classical dancer who specializes in Bharatanatyam and Odissi.
• For her contributions to promoting ‘Classical dances’, she has received accolades from many national and international organizations.
• She was the youngest recipient of Padma Bhushan in 1992.
• In 2003, Sonal became the first Indian woman dancer to be awarded Padma Vibhushan.

Important PointsOdissi Dance:

• Odissi is a folk dance form of Odisha.
• This is a delicate dance backed by soothing lyrics and Is similar to Bharatnatyam in terms of Mudras and Expressions.
• The cave of Udayagiri-Khandagiri provides the earliest example of Odissi.
• It was primarily practiced by Maharis under patrons of Jain King Kheravela.
• "Mobile Sculpture" includes two major postures:
• Tribhanga - The body is deflected at the neck, torso, and knees.
• Chowk - A position imitating a square.
• Indrani Rehman, Charles Fabri, Guru Pankaj Charan Das, and Kelu Charan Mohapatra are some of the famous artists of Odissi dance

Additional Information

The correct answer is Delhi.

Key Points 

• Quwwat-ul-Islam Mosque is situated in the Qutb complex in Delhi.
• It was built by Qutub-ud-din-Aibak in 1193 AD.
• The Quwwat-ul-Islam is best known for its tower of victory, celebrating the Muslim conquest of India.
• It is built of red sandstone, grey quartz, and white marble.
• It is an intricately designed structure built on the principles of construction and ornamentation which was another feature of Islamic architecture.
• Quwwat-ul Islam Mosque stands northeast of the Qutb Minar.

Additional Information

• Qutub-ud-din Aibak:
• ​He was the founder of the Slave dynasty.
• He assumed the title of 'Sultan' for the first time in the history of India.
• He made Lahore the capital and later Delhi.
• He was also known as 'Lakh Baksh' or giver of lakhs for his magnanimity, as he gave a lot of liberal donations.
• He started the construction of the Qutub Minar in the memory of Khawaja Qutubuddin Bhaktiyar Kaki but could complete only the first storey.
• Aibak is known for having commissioned the Qutb Minar in Delhi, and the Adhai Din Ka Jhopra in Ajmer.

The correct answer is Sattriya.

Key Points 

• In Assamese, generally, Mati-Akhora means exercise done on the ground.
• The Sattriya dance training begins with these Mati-Akhoras.
• Mati-Akhoras are a foundation for the learners to make a healthy physical, mental, and spiritual set-up which is very necessary for a classical dancer.
• The great Assamese reformer and Vaishnava saint Mahapurusha Sankaradeva established the Sattriya dancing style in the 15th century A.D. as a potent means of spreading the Vaishnava religion.
• It is one of India's eight classical dance genres.
• Sankaradeva created this dance style by fusing ideas from numerous treatises with popular dance styles, regional folk dances, and his own unique perspective.
• The Sattriya dance is a blatant example of how the former influenced the latter.
• Bihu, Bodos, and other Assamese folk dances are other clearly discernible influences on Sattriya dance.
• These dancing styles have very similar hand movements and rhythmic syllables.

Additional Information 

The correct answer is Pradhan Mantri Jeevan Jyoti Bima Yojana (PMJJBY)

 

Key Points

• Pradhan Mantri Jeevan Jyoti Bima Yojana (PMJJBY)
• The government of India launched Pradhan Mantri Jeevan Jyoti Bima Yojana (PMJJBY) on 09 May 2015.
• It was proposed by the Finance(Arun Jaitley) Minister in the 2015 budget speech.
• It comes under the Ministry of Finance.
• It was a government-backed life insurance scheme in India
• In case of the death of the insured person, the next eligible beneficiary is provided with a death benefit including a death coverage of Rs. 2,00,000.
• Aim - PMJJBY was launched to increase the reach of life insurance among citizens.

Additional Information

• Other details of PMJJBY;

The correct answer is Motilal Nehru.

Key Points

• The Swaraj Party was established on 1 January 1923 by Chittaranjan Das and Motilal Nehru.
• The two important leaders of the Party were CR Das and Motilal Nehru in which CR Das was the President and Motilal Nehru was its secretary.
• The Party was established as the Congress Khilafat Swaraj Party.
• The Swaraj Party sought greater self-government and political freedom from the British Raj for the Indian people.

Additional Information

• In 1923, The Swaraj Party won the most seats during elections to the Bengal Legislative Council.
• Important leaders of the Swaraj Party included Huseyn Shaheed Suhrawardy, N C Kelkar, and Subhas Chandra Bose.

The correct answer is Bismillah Khan.

Key Points

• Bismillah Khan became the first Indian to be invited to perform at the prestigious Lincoln Centre Hall in the United States of America.
• He also took part in the World Exposition in Montreal, the Cannes Art Festival, and in the Osaka Trade Fair.
• So well known did he become internationally that an auditorium in Teheran was named after him — Tahar Mosiquee Ustaad Bismillah Khan.
• National awards like the Padma Shri, the Padma Bhushan, and the Padma Vibhushan were conferred on him.
• In 2001, Ustad Bismillah Khan was awarded India’s highest civilian award, the Bharat Ratna.

Additional Information

• M.S. Subbulakshmi was a renowned Carnatic vocalist and the first musician to be awarded the Bharat Ratna.
• She performed at several prestigious venues around the world including the United Nations General Assembly in 1966.
• Zakir Hussain and Ravi Shankar are also renowned Indian musicians who have performed at several prestigious venues around the world.

The correct answer is Cathode ray tube.

 Key Points

• Cathode ray tube were commonly used in older televisions and computer monitors.
• The electron beam is generated by a heated cathode and accelerated by an anode towards the screen.
• The phosphor coating on the screen emits light when struck by the electron beam, producing the image.

Additional Information

• Flat array tube: This is a type of CRT that uses a flat screen instead of a curved one. It is also known as a flat CRT or FED.
• Light Emitting Diode (LED) tube: It is a type of display technology that uses LEDs to emit light and create an image.
• Liquid Crystal Display (LCD) tube: It is a type of display technology that uses liquid crystals to create an image.

The correct answer is The Muri Alumina Plant.

Key Points

The Muri Alumina Plant

• Muri Works of Hindalco Industries Limited is India’s first alumina refinery commissioned in 1948 by the erstwhile Indian Aluminium Company (INDAL).
• In 2005, Hindalco merged the plant with itself after acquiring INDAL.
• The plant is located on the banks of Swarnarekha River at Chota Muri, 65km from Ranchi, the capital city of Jharkhand state.
• Muri Works is India’s first alumina refinery commissioned in 1948 by the Indian Aluminium Company.
• Later in 2005, Hindalco acquired Indian Aluminium Company (INDAL) and merged the plant with itself.
• Primary products include standard and special grades of Alumina and Alumina-hydrate.
• The present capacity of plant stands at 450 Kilo tonne per annum (KTPA).
• The plant and residential colony together cover an area of 334.2 acres.

The correct answer is Bihar.

Key Points

• The Rajgir Zoo Safari, also known as the Rajgir Wildlife Safari, is located in Rajgir, Nalanda district in the state of Bihar.
• It was officially opened in February 2022.

Additional Information

The correct answer is Football

Key Points 

• A free kick is a method of restarting play in association football.
• It is awarded after an infringement of the laws by the opposing team.
• These are given regularly in a game as the offenses committed are very common throughout a full match. This is different from the indirect free kick.

Additional Information

• Some important terms related to sports are listed here-
• Football: Corner kick, direct free kick, indirect free kick, dribble, goal kick, penalty, hat trick, off side, tripping, etc.
• Volleyboll: Blocking, Doubling, heave, holding, love service, volley
• Basketball: Ball, basket, blocking, dribbling, free throw, held ball, holding, jump ball, multiple throws, pivot, etc.
• Hockey: Bully, carry, corner, dribble, hat trick, off-side, scoop, short corner, long corner, penalty stroke, etc.
• Cricket: Power-play, boundary, bowling, wicket, l.b.w, leg-bye, maiden over, no ball, off break, out, over, pitch, run out, sixer, straight drive, stumped, yorker, etc.
• Tennis: Ace, Backhand, Stroke, deuce, deep volley, double fault, fault, ground stroke, half volley, let, lov, slice, smash, volley, etc.
• Table tennis: Anti loop, Backspin, chop, loop, penhold grip, twiddle, etc.

The correct answer is 100.

Key Points

• Union Education and Skill Development Minister Dharmendra Pradhan launched a 100-day Reading Campaign ‘Padhe Bharat’ on Jan 01, 2022.
• Children studying in Balvatika to grade VIII will be part of this campaign.
• The reading campaign aims to have the participation of all stakeholders at the national and state levels including children, teachers, parents, community, educational administrators, etc.

Additional Information

Objectives of the Padhe Bharat Campaign

• The campaign strives to support and motivate students, along with all stakeholders at the state and national levels, including schools, teachers, parents, and communities, to foster a joyful learning experience through reading.
• It has designed one activity per week per group, emphasizing making reading an enjoyable activity and building a lifelong association with the joy of reading.
• Children studying from Balvatika to Grade 8 are the primary focus of the campaign.
• It also emphasizes Indian languages, including mother tongue/local/regional languages.
• The campaign celebrates International Mother Tongue Day on 21st February with the activity of "Kahani Padho Apni Bhasa Main" (Reading story in own language), promoting local languages and culture.
• The reading campaign will run from 1st January 2022 till 10th April 2022, spanning 100 days (14 weeks).
• The campaign aligns with the vision and goals of the foundational Literacy and Numeracy mission (NIPUN Bharat).

The correct answer is Mahatma Gandhi.

Key Points

• To accelerate the efforts to achieve universal sanitation coverage and to put the focus on sanitation, the Prime Minister of India launched the Swachh Bharat Mission on 2nd October 2014.
• Under the mission, all villages, Gram Panchayats, Districts, States and Union Territories in India declared themselves "open-defecation free" (ODF) by 2 October 2019 in First Phase.
• On the 150th birth anniversary of Mahatma Gandhi, by constructing over 100 million toilets in rural India.
• To ensure that the open defecation-free behaviours are sustained, no one is left behind, and that solid and liquid waste management facilities are accessible.

Additional Information

Jawaharlal Nehru

• Jawaharlal Nehru was the first Prime Minister of India.
• He was born on November 14, 1889, in Allahabad.
• November 14 is celebrated as Children's Day in India.
• He is the Prime Minister who has had the longest term in office.
• He served as the prime minister of India from 15th August 1947 to 1964.
• He is the architect of the Preamble of the Indian constitution.
• He was the Prime Minister of India during the Indo-China war in 1962.
• He served as the first chairman of the planning commission of India.
• He was honoured with the Bharat Ratna in 1955.
• The name Panchayati raj was given by Jawaharlal Nehru.
• National herald is the newspaper started by Jawaharlal Nehru.
• He is the first prime minister to die in harness.
• Glimpses of the world, Discovery of India are the famous works of Nehru.
• Shantivan is the cremation ground of Jawaharlal Nehru.
• He died on May 27, 1964, in New Delhi​​

Lal Bahadur Shastri

• He was born on 2nd October 1904 in Mughalsarai, a small railway town seven miles from Varanasi in Uttar Pradesh.
• Participated in the freedom movement since 1930.
• He joined the Kashi Vidyapeeth in Varanasi, one of the many national institutions set up in defiance of British rule.
• ‘Shastri’ was the bachelor’s degree awarded to him by the Vidya Peeth but has stuck in the minds of the people as part of his name.
• He was a minister in the Union Cabinet from 1951 to 1956 when he resigned taking responsibility for the railway accident and later from 1957-1964.
• He was India’s second Prime Minister (1964-66).
• He signed an agreement with then Ceylon (now Sri Lanka) on persons of Indian origin there, in 1964 — an endorsement of the importance of neighbourhood.
• He was the first person to be posthumously awarded the Bharat Ratna (1966).

Sardar Vallabhbhai Patel

• He was the first Deputy Prime Minister of India.
• He was often called Sardar.
• He was also called an Indian Bismarck.
• Served as the first Home Minister of India.
• He was appointed as the President of the Indian National Congress during the Karachi session in 1931.

The correct answer is Asian Development Bank.

Key Points

• The Asian Development Bank (ADB) approved a $500 million loan to the Government of India in December 2021 to help improve the quality of the country's school education and mitigate the impact of the COVID-19 pandemic on the students' learning.
• The loan will be used to support India's flagship education program, Samagra Shiksha Abhiyan, which aims to improve the quality of school education across the country.
• The loan will also help in providing additional support to students and teachers affected by the COVID-19 pandemic, including the provision of digital devices and internet connectivity.
• ADB has been working closely with the Government of India to support its efforts in responding to the COVID-19 pandemic and mitigating its impact on the country's economy and people.

Additional Information Asian Development Bank

• The Asian Development Bank is a regional development bank established on 19 December 1966.
• Which is headquartered in the Ortigas Center located in the city of Mandaluyong, Metro Manila, Philippines.
• The company also maintains 31 field offices around the world to promote social and economic development in Asia.
• Headquarters: Mandaluyong, Philippines
• Founded: 19 December 1966
• Motto: ADB is committed to achieving a prosperous, inclusive, resilient, and sustainable Asia & the Pacific while sustaining its efforts to eradicate extreme poverty.

The correct answer is 1971.

Key Points

• In 1971, the state of Himachal Pradesh was granted its own High Court, which replaced the jurisdiction of the High Court of Delhi in the state.
• The High Court of Delhi initially had jurisdiction over the Union Territory of Delhi and the states of Himachal Pradesh and Punjab.
• In 1966, Punjab was divided into two states - Punjab and Haryana - and the jurisdiction of the High Court of Delhi was limited to the Union Territory of Delhi and Himachal Pradesh.
• The state of Himachal Pradesh was granted its own High Court on January 25, 1971, by the Himachal Pradesh High Court Act, 1971.

Additional Information

• The highest judicial court in a state is the High Court.
• It is termed as the second-highest in the country after the Supreme Court of India.
• The Parliament passed the Indian High Courts Act 1861 which suggested the establishment of High Courts in three Presidencies: Calcutta, Madras, and Bombay.

The correct answer is Henry Chandler Cowles.

Key Points 

• Henry Chandler Cowles studied ecological succession in the Indiana Dunes of Northwest Indiana in the 1890s.
• Henry Chandler Cowles (1869-1939) was a University of Chicago botany professor and conservationist, his studies of plant life in the Indiana Dunes made Cowles one of America's most notable early ecologists.
• In 1896, Cowles traveled to the southern shore of Lake Michigan to see the Indiana Dunes for the first time and studied them.
• His study explained the development and distribution of local plant communities in terms of topography, moisture, wind, erosion, sedimentation, and other geological processes.

The correct answer is Mantle.

Key Points

The mantle: 

• The mantle extends up to a depth of 2900 km below the crust.
• It separates the crust from the core.
• The upper part of the mantle is known as the asthenosphere.
• Nearly 84% of the earth’s volume and 67% of the earth’s mass is occupied by the mantle.
• The major constituent elements of the mantle are Silicon and Magnesium and hence it is also termed as SIMA.

Additional InformationThe crust:

• The crust is the uppermost layer over the earth’s surface.
• It is the thinnest layer.
• it is only about 5 km on the ocean floors, which mainly consists of silica and alumina thus called sial (si-silica and al-alumina), and 35 km on the continental masses, which mainly consists of silica and alumina.

The core:

• The innermost layer is the core with a radius of about 3500 km and divided into Inner and Outer core.
• It is called nife (ni – nickel and fe – ferrous – iron) as it's mainly made up of nickel and iron.
• Central core is called the Inner core and has a very high temperature and pressure.

The correct answer is bronze.

Key Points

• The Iron Age is a period in human history characterized by the widespread use of iron tools and weapons.
• This period began around 1200 BCE in the Middle East and gradually spread to other parts of the world.
• Before the Iron Age, bronze was the preferred material for making tools and weapons.
• **Bronze is an alloy made from copper and tin.**​

Additional Information

• The most significant development was the use of iron for tools, weapons, and agricultural implements.
• Iron is stronger and more durable than bronze, the dominant material of the preceding era.
• Iron led to advancements in agriculture, construction, and warfare. For example, iron plowshares improved farming efficiency, while iron weapons gave rise to powerful warrior classes.
• The Iron Age saw the transition from small tribal settlements to larger, more complex societies. This was likely facilitated by increased agricultural productivity and trade enabled by iron tools.
• The Painted Grey Ware culture, associated with the early Iron Age, is characterized by distinctive pottery and iron tools found across North India.
• In the later period, we witnessed the rise of powerful Mahajanapadas, competing states that laid the foundation for larger empires like the Mauryas and Guptas.

The correct answer is Bhutan.

Key Points

• Paro Tschechu is a famous annual religious festival celebrated in Bhutan.
• It is a four-day festival held in the Paro Valley of Bhutan, usually in March or April, to commemorate the birth anniversary of Guru Rinpoche, the patron saint of Bhutan.
• The festival features colorful traditional dances, mask performances, and religious rituals performed by monks and laypeople in elaborate costumes and masks.
• The festival also attracts a large number of tourists from around the world who come to witness the vibrant cultural heritage of Bhutan.

Additional Information 

• Japan is known for its own unique festivals such as the Cherry Blossom Festival and the Gion Matsuri Festival.
• Thailand is known for festivals such as Songkran (Thai New Year) and Loi Krathong (Festival of Lights).
• Burma is known for festivals such as Thingyan (Burmese New Year) and Taunggyi Tazaungdaing (Hot Air Balloon Festival).

Shortcut Trick

Interest difference % = (11 years − 6 years) × 4% = 5 × 4% = 20%.

Given that 20% of the Amount (Principal) = ₹7,500.

Total Amount (100%) = 7,500 × (100 ÷ 20) = 7,500 × 5 = ₹37,500.

∴ The correct answer is ₹37,500.

Alternate Method

Given: Rate (R) = 4% p.a., Time₁ (T₁) = 6 years, Time₂ (T₂) = 11 years, SI difference = ₹7,500.

Formula Used: Simple Interest (SI) = (P × R × T) ÷ 100

⇒ SI₂ − SI₁ = 7500

⇒ [(P × 4 × 11) ÷ 100] − [(P × 4 × 6) ÷ 100] = 7500

⇒ (44P ÷ 100) − (24P ÷ 100) = 7500

⇒ 20P ÷ 100 = 7500

⇒ P ÷ 5 = 7500

⇒ P = 7500 × 5

⇒ P = 37500

∴ The correct answer is ₹37,500.

Additional Information

Simple Interest Concept

Simple interest is calculated only on the Principal amount for the entire duration. Formula: SI = P × R × T ÷ 100.

Direct Proportionality

When Principal (P) and Rate (R) are constant, the Simple Interest is directly proportional to the Time (T). Doubling the time doubles the interest.

Total Amount (Maturity)

The total amount (A) after T years is the sum of Principal and Interest: A = P + SI = P[1 + (RT ÷ 100)].

Given:-

<br>

A laptop is sold for Rs. 54,000 after a discount of 20%.

<br>

Formula used:-

<br>

Selling Price = Marked Price × (1 - Discount%)

<br>

Calculation:-

<br>

The marked price of the laptop

<br>

⇒ MP = SP/ (1 - Discount%)   

<br>

⇒ MP = 54000/(80/100)  

<br>

⇒ MP = 67500  

<br>

∴ The marked price of the laptop is Rs. 67500.

<br>

  

Shortcut Trick

<br>

20% discount means MP = 5 and SP = 4

<br>

Here,

<br>

4 unit → 54000 then,

<br>

5 unit → (54000/4)× 5 = 67500

Given: -

<br>

x² -1/x² = 4√2

<br>

Formula used:-

<br>

(A + B)² = A² + B² + 2AB

<br>

(A² - B²) = (A+ B) (A - B)

<br>

Calculation:-

<br>

Square both side

<br>

⇒ (x2  -1/x2)² = (4√2 )² 

<br>

⇒ x⁴ + 1/x⁴ - 2 = 32 

<br>

⇒ x4 + 1/x4  = 34

<br>

Add 2 on both sides 

<br>

⇒ x4 + 1/x4 + 2 = 34 +2  

<br>

⇒ (x2  + 1/x2)2 = 6² 

<br>

⇒ (x2  + 1/x2) = 6 ....(1)

<br>

According to the question,  

<br>

⇒ x4 - 1/x4  =  (x2  + 1/x2) (x2  -1/x2) 

<br>

⇒ (4√2) × 6 = 24√ 2   

<br>

∴ The required answer is 24√ 2.

Detailed solution:-

<br>

P, Q, and R can complete a work in 9, 12, and 18 days, respectively. 

<br>

Rate of P = 1/9 (work/day)

<br>

Rate of Q = 1/12 (work/day)

<br>

Rate of R = 1/18 (work/day)

<br>

Combined rate = Rate of P + Rate of Q + Rate of R

<br>

= 1/9 + 1/12 + 1/18 = (4 + 3 + 2)/36 = 9/36 = 1/4 (work/day)

<br>

∴ when P, Q, and R work together, they can complete 1/4 of the work in one day.

Given:

Ram and Ramesh can do work together =12 days

Ramesh and Somesh can do work together = 15 days

Somesh and Ram can do work together = 10 days

Formula used:

Work = Efficiency × Time

Calculation:

Let the Ram, Ramesh, and Somesh can complete the work together in X days

One day work of Ramesh and Ram =  ${1\over12}$

One day work of Ramesh and Somesh = ${1\over15}$

One day work of Somesh and Ram = ${1\over10}$

One day work of all three = ${1\over12}+{1\over15}+{1\over10}$ = ${5+4+6\over60}={15\over60}={1\over4}$

Working twice they can complete the work in = 4 days

They can complete the work = 8 days

∴ The required result will be 8 days.

Alternate MethodCalculation:

Ram and Ramesh = 12 days

Ramesh and Somesh = 15 days

Somesh and Ram = 10 days 

LCM of (12,15, & 10)  = 60 units

Efficiency of Ram and Ramesh = 60/12 = 5 units

Efficiency of Ramesh and Somesh = 60/15 = 4 units

Efficiency of Somesh and Ram = 60/10 = 6 units

Efficiency of 2(Ram, Ramesh & Somesh) = 15 units(5 + 4 + 6)

Total Efficiency of  Ram, Ramesh & Somesh = (5 + 4 + 6)/2 = 7.5 units

Time taken by Ram, Ramesh, and Somesh together to complete the work:

Time = Total work / Total Efficiency

⇒ 60/7.5 = 8 days 

∴ Ram, Ramesh, and Somesh together will complete the work in 8 days.

Given:

They give us a relation between speed and time.

Formula used:

$Speed={Distance\over Time}$

Calculation:

Let the distance of the first person be D and time will be T.

The second person cover the distance = 25% of D = ${25\over100}\times D={D\over4}$

Time taken by second person = 3T

The speed of the first person = ${D\over T}$

The speed of the second person = ${{D\over4}\over3T}={D\over12T}$

The ratio of their speed = ${{D\over T}\over{D\over 12T}}={12\over1}$

The speed of the first and second person = 12 : 1

∴ The required result will be 12 : 1.

Given:

A dishonest dealer sells articles at 15% loss on cost price.

Concept:

Loss = Cost price - Selling price

Formula used:

$P\%={SP-CP\over CP}× 100$     Where, P = Profit, SP = Selling price, and CP = Cost price

Calculation:

Let the cost price of the 25 g article be X.

The selling price of the article = ${(1\ -\ {15\over 100})}\ × X={({100-15\over100})}\ × X={85\over100}\ × X=0.85X$

The cost price of the 20g article = ${X\over 25}\ × 20={4X\over5}$

The profit percentage = ${0.85X-0.8X\over0.8X}× 100={0.05X\over 0.8X}× 100={0.0625\ × 100}=6.25\%$

∴ The required result will be 6.25% Profit.

Shortcut Trick CP     :      SP

20 4    :      17

20 4    :      25 5

---

16        :      17

SP > CP so it is profit

Profit% = (1/16) × 100 = 6.25% profit.

∴ The required result will be 6.25% Profit.

Given

AL, BM, and CN are the three altitudes of triangle ABC

Concept used

The side opposite to the greater angle is a greater

Calculation

In the above diagram,

∠ALB = 90

∠ABL < 90

Now side opposite to ∠ALB  is AB and the side opposite to ∠ABL is AL

Since the side opposite to the greater angle is a greater

AB > AL  ..(1)

Similarly in triangle BMC

BC > BM  ..(2)

Similarly in triangle ANC

CA > CN ..(3)

Adding all three:

AL + BM + CN < AB + BC + CA

The answer is AL + BM + CN < AB + BC + CA

Given:

The total fund received by school from different sources = 10 lakh

The school received fund from internal source = 15%

Concept:

$X\%={X\over100}$

Calculation:

Let the fund received by internal source is X

⇒ X = 15% of 10 lakh

⇒ X = ${15\over100}\times{1000000}=150000$

∴ The required result will be 150000.

Given

3x = sec A and $\frac{3}{x}$ = tan A

Formula used

sec² A  - tan² A = 1

Calculation

3x = sec A

Squaring both sides:

9x² = sec2 A  ..(1)

3/x = tan A

Squaring both sides:

9/x2 = tan2 A  ..(2)

Subtracting 2 from 1.

⇒ 9x2 - 9/x2 = sec2 A - tan2 A

⇒ 9(x2 - 1/x2) = 1

The answer is 1.

Given:

The angle subtended by a chord at the centre = 180°

Concept Used:

The angle subtended by a chord at the centre is twice the angle subtended on the circumference.

Calculation:

⇒ Angle subtended on the circumference = 180° / 2 = 90°

Therefore, the angle subtended by the same chord on the circumference is 90°.

Given:

The expression = $\frac{[120×120×120-100×100×100]}{[120×120+120×100+100×100]}$

Formula used:

a³ - b³ = (a - b) × (a² + ab + b²)

Calculation:

According to the question

⇒  $\frac{[120×120×120-100×100×100]}{[120×120+120×100+100×100]}$

⇒ $\frac{[120^3-100^3]}{[120^2+120×100+100^2]}$

⇒ $\frac{[120-100]\ \times [120^2+120×100+100^2] }{[120^2+120×100+100^2]}$

⇒ 120 -100 = 20

∴ The required result will be  20.

Given:

A can do a work alone = 20 days

B can do a work alone = 30 days

C can do a work alone = 60 days

Formula used:

$Work = Efficiency × Time$

Calculation:

The efficiency of the A = ${1\over 20}$

The efficiency of the B = ${1\over 30}$

The efficiency of the C = ${1\over 60}$

The two-day work of A = ${2\over20}={1\over10}$

The work done by A, B, and C together on third day = ${1\over20}+{1\over30}+{1\over 60}={3+2+1\over60}={6\over60}={1\over 10}$

The first three days' work = ${1\over 10}+{1\over10}={2\over10}={1\over5}$

The 20% work done by them in 3 days.

The whole work they can complete in = 3 × 5 = 15 days

∴ The required result will be 15 day.

Given:

Initially ratio of expenditure and saving of Soham's = 5 : 3

The initial saving = Rs. 4500

Formula used:

Income = Saving + Expenditure

Calculation:

Let the initial ratio of saving and expenditure be 3X and 5X

⇒ 3X = 4500

⇒ X = 1500

The initial income = 3X + 5X = 8X = 1500 × 8 = 12000

The income after increment = ${(1\ +{25\over100})}\ \times 12000 ={(1+{1\over4})}\times 12000={5\over4}\times 12000=5\times 3000 = 15000$

∴ The required result will be 15000.

Given:

a + b + c = 14

a³ + b³ + c³ - 3abc = 98

Concept used:

a³ + b³ + c³ - 3abc = (a + b + c)[(a + b + c)² - 3(ab + bc + ca)]

Calculation:

a3 + b3 + c3 - 3abc = (a + b + c)[(a + b + c)2 - 3(ab + bc + ca)]

⇒ 98 = 14 × [(14)² - 3(ab + bc + ca)]

⇒ 7 = 196 - 3(ab + bc + ca)

⇒ 189 = 3(ab + bc + ca)

⇒ ab + bc + ca = 63

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

(a2 + b 2 + c2) = 14² - 2 × 63

= 196 - 126

= 70

∴ The value of given identities is 70.

Shortcut Trick

In ΔABC, if a point D lies on BC such that ∠ADC = ∠BAC, then AC is the geometric mean of BC and CD.

Given: BC = 16 cm and BD = 11 cm ⇒ CD = 16 − 11 = 5 cm.

Using the property: AC² = BC × CD

AC² = 16 × 5 = 80

AC = √80 = 4√5 cm.

∴ The correct answer is 4√5 cm.

Alternate Method

Given: BC = 16 cm, BD = 11 cm, and ∠ADC = ∠BAC.

Formula Used: AA Similarity Criterion (If two angles of one triangle are equal to two angles of another triangle, the triangles are similar).

In ΔADC and ΔBAC:

⇒ ∠ADC = ∠BAC (Given)

⇒ ∠ACD = ∠BCA (Common angle)

⇒ ΔADC ∼ ΔBAC (By AA similarity criterion)

Since the triangles are similar, their corresponding sides are proportional:

⇒ AC / BC = CD / AC

⇒ AC² = BC × CD

⇒ CD = BC − BD = 16 − 11 = 5 cm

⇒ AC² = 16 × 5 = 80

⇒ AC = √80 = 4√5 cm

∴ The correct answer is 4√5 cm.

Additional Information

AA Similarity Criterion

Two triangles are similar if two corresponding angles are equal. This leads to the proportionality of all corresponding sides.

Geometric Mean in Triangles

In a triangle where an interior angle equals the opposite whole angle, the shared side acts as the geometric mean: Side² = Segment × Whole Side.

Ratio of Areas

If two triangles are similar, the ratio of their areas is equal to the square of the ratio of their corresponding sides: Area(Δ1) / Area(Δ2) = (s₁ / s₂)².

Concept used

Any 6-digit number formed by a consecutive natural number is always divisible by 3 because the sum of digits of any such number is divisible by 3.

Calculation

For ex. take 123456, 234567, 345678, and 456789, as a number, the sum of its digit is always divisible by 3.

The answer is 3.

Shortcut Trick

 

Let x be the total time to complete the work,

B(x - 4) + C(x - 10) + D x = 144

⇒ 6(x - 4) + 4(x - 10) + 3x = 144

⇒ 6x - 24 + 4x - 40 + 3x = 144

⇒ 13x = 144 + 40 + 24

⇒ x = 208/13 = 16

Thus, time taken to complete the work = x = 16 days

Alternate Method

Given:

The Benny can do a piece of work = 24 days

The Chethan can do a piece of work = 36 days

The David can do a piece of work = 48 days

Formula used:

Work = Efficiency × Time

Calculation:

Let the work was complete in X days.

One day work of Benny = ${1\over24}$

One day work of Chethan = ${1\over36}$

One day work of David = ${1\over48}$

According to the question

⇒ ${{X-4\over24}+{X-10\over36}+{X\over 48}}=1$

⇒ ${{6\ × (X-4)}+{4× (X-10)+3X}\over144}=1$

⇒ 6X - 24 + 4X - 40 + 3X = 144

⇒ 13X - 64 = 144

⇒ 13X = 208

⇒ X = 16

∴ The required result will be 16.

Given:

The distance between police and thief = 1150 m

The speed of the thief = 6 km/h

The speed of the police = 11 km/h

Formula used:

$Speed\ =\ {Distance \over Time}$

Calculation:

Let the distance travelled by thief is X

The relative speed of the police and thief = 11 - 6 = 5 km/h 

The distance between police and thief in kilometers = ${1150\over 1000}={1.150\ km}$

The time taken by police to catch the thief = ${1.150\over5}={0.23\ h}$

The thief will cover the distance in 0.23 hours = 0.23 × 6 = 1.38 × 1000 = 1380

∴ The required result will be 1380 m.

Given:

The expression = 1$\frac{3}{4}$ + 1$\frac{5}{7}$ ÷ 2$\frac{3}{7}$ × 2$\frac{3}{7}$ 

Concept:

Calculation:

⇒ 1$\frac{3}{4}$ + 1$\frac{5}{7}$ ÷ 2$\frac{3}{7}$ × 2$\frac{3}{7}$ 

⇒ ${7\over4}+{12\over7}\div {17\over7}\times{17\over7}$

⇒ ${7\over4}+{12\over7}\times {7\over17}\times{17\over7}$

⇒ ${7\over 4}+{12\over7}$

⇒ ${(49+48)\over28}={3{13\over28}}$

∴ The required result will be 3${13\over28}$.

Shortcut Trick

For two terms A and B, the third proportional is given by B² ÷ A.

Given: A = 3x², B = 4xy, and the third proportional is 48.

Formula: (4xy)² ÷ 3x² = 48

⇒ 16x²y² ÷ 3x² = 48 ⇒ 16y² ÷ 3 = 48 ⇒ y² = 9 ⇒ y = 3 (since y is positive).

∴ The correct answer is 3.

Alternate Method

Given:

First term (A) = 3x²

Second term (B) = 4xy

Third proportional (C) = 48

Formula Used:

If A, B, and C are in continued proportion, then:

A ÷ B = B ÷ C

⇒ B² = A × C

Calculations:

⇒ (4xy)² = 3x² × 48

⇒ 16x²y² = 144x²

Since x is non-zero, we can divide both sides by x²:

⇒ 16y² = 144

⇒ y² = 144 ÷ 16

⇒ y² = 9

⇒ y = √9

⇒ y = 3 (taking positive value as requested)

∴ The correct answer is 3.

Additional Information

Third Proportional

The third proportional of two numbers A and B is a value C such that A : B = B : C, which simplifies to C = B² ÷ A.

Mean Proportional

The mean proportional between two quantities A and B is given by √(A × B).

Fourth Proportional

If A, B, C, and D are in proportion (A : B = C : D), then D is the fourth proportional and is calculated as (B × C) ÷ A.

Given:

Radius of bigger circle r₁ = 22 cm

Radius of smaller circle r₂ = 18 cm

Distance between two circles = 32 cm

Formula used:

Length of direct tangent, l = $\sqrt {d^2\ -\ (r_1\ -\ r_2)^2}$     

Where, d = Distance between two circles,

r₁ = Radius of bigger circle, r₂ = Radius of smaller circle

Calculation:

According to the question

The length of the direct tangent (I)

⇒  $\sqrt{32^2-(22-18)^2}$

⇒ $\sqrt{32^2-4^2}$

⇒ $\sqrt{1024-16}$

⇒ $\sqrt{1008}$ = 2$\sqrt{252}$ cm

∴ The required result will be 2$\sqrt{252}$ cm.

Given:

The number of delivery partner joined Clipkart in 2019 & 2020 respectively = 5.6 and 6.4 thousand

The number of delivery partners joined Tomato in 2019 and 2020 respectively = 2.7 and 3.3 thousand

Calculation:

According to the question

The sum of the joined partners of the Clipkart = 5.6 +  6.4 = 12 thousand

The sum of the joined partners of the Tomato = 2.7 +  3.3 = 6 thousand

The required ratio = 12 : 6 = 2 : 1

∴ The required result will be 2 : 1.