MP Police Constable : (14 Nov 2025, Shift 2) Memory-Based Paper (Previous Year Paper)

The correct answer is Article 143.

Key Points

• Article 143: Power of President to consult Supreme Court.

1. If at any time it appears to the President that a question of law or fact has arisen, or is likely to arise, which is of such a nature and such public importance that it is expedient to obtain the opinion of the Supreme Court upon it, he may refer the question to that Court for consideration and the Court may, after such hearing as it thinks fit, report to the President its opinion thereon.
2. The President may, notwithstanding anything in the proviso to article 131, refer a dispute of the kind mentioned in the said proviso to the Supreme Court for opinion and the Supreme Court shall, after such hearing as it thinks fit, report to the President its opinion thereon.

Additional Information

• Article 142 of the Constitution:
• Title: Enforcement of decrees, orders of Supreme Court and orders as to discovery, etc.
• Provisions: This article has 2 provisions –
• 142(1): The Supreme Court may pass an order for doing complete justice. Hence, option 2 is correct.
• 142(2): It confers three different powers on the Supreme Court.
• Article 144
• The Indian Constitution's Article 144 instructs civil and judicial agencies to support the Supreme Court in its work. It states that the Supreme Court shall get assistance from all civil and judicial bodies within the boundaries of India. Additional Reading: Indian Supreme Court.
• Article 145
• Rules of Court
• Subject to the provisions of any law made by Parliament the Supreme Court may from time to time, with the approval of the President, make rules for regulating generally the practise and procedure of the Court.

The correct answer is calcium and phosphorus.

Key Points:

• The structure that holds the body up is made of bone.
• Additionally, it supports the body's major organs and anchors the muscles.
• It is a solid, unyielding tissue.
• A dense matrix made of calcium and phosphate molecules contains the bone cells.
• A different kind of connective tissue called a ligament can join two bones together.
• This tissue is extremely flexible.
• Another form of connective tissue is the tendon, which links bones and muscles.

Additional Information:

• Tendons are fibrous tissues with little flexibility and tremendous strength.
• The cells of cartilage are widely spaced.
• Sugars and proteins make up the solid matrix.
• In addition to the nose, ear, trachea, and larynx, cartilage smoothes the surfaces of bones at joints.
• Areolar connective tissue can be found in the bone marrow, around blood vessels and nerves, and between the skin and muscles.
• It supports internal organs, fills empty space inside the organs, and aids in tissue restoration.

Six friends - Lata Mala, Neelu, Olly, Parmeet and Qadira.

All of them are sitting in a circle facing the centre and each person is seated exactly opposite one friend.

1. Qadira is sitting neither next to nor exactly opposite Mala or Parmeet.
2. Parmeet is sitting exactly opposite Lata.
3. Neelu is sitting to Parmeet's immediate right.
4. Mala is sitting opposite Neelu.
5. Olly is sitting to Parmeet's immediate left.

Now, the only place left for Qadira is to the opposite of Olly.

So, the final arrangement is:

Hence, ‘Qadira’ is the correct answer.

Given:

Speed of first train = 80 km/hr

Speed of another train = 120 km/hr

Time taken by first train to complete a journey = 18 hours.

Formula:

Distance = Speed × Time

Calculation:

Total distance covered by first train in 18 hours = 18 × 80 = 1440 km

Let distance 1440 km distance covered by another train in x hrs.

According to the question

120 × x = 1440

⇒ x = 1440/120

⇒ x = 12 hrs

∴ Time taken by another train to complete the same train is 12 hrs.

The correct answer is Multai.

• Tapti originates from Multai in Betul district of Madhya Pradesh in the Satpura range.
• The ancient name of the Tapti River is the Tapati River. It is one of the major rivers of peninsular India.

Facts about Tapti River - 

Additional Information

Key Points

• Rivers flow into the Bay of Bengal: The Mahanadi, Godavari, Krishna, and Kaveri (Cauvery) on the west and the Ganges (Ganga) and the Brahmaputra on the north.
• Rivers flow into the Arabian Sea: Narmada, Tapi, Sindhu, Sabarmati, Purna.

The correct answer is Banihal.

• Banihal pass joins the Jammu Division with the Kashmir Valley.

Key Points

• Banihal Pass is located in the Pir Panjal Range.
• It connects the Jammu Division with the Kashmir Valley.
• Banihal in Kashmiri means “blizzard”.
• Passes in Kashmir Zoji La, Burzila, Pensi La, and Pir-Panjal Pass.

Additional Information

• Bomdi-La connects Arunachal Pradesh with Lhasa.
• Jelep La connects Sikkim with Lhasa.
• Diphu Pass is located on the disputed tripoint borders of India, China, and Myanmar.

Given: 

Ajay starts from his office and drives 3 km towards the east.

He then takes a right tum, drives 4 km,

tums left, and drives 5 km.

He then takes a left turn and drives 3 km and stops at a shop.

So, He should drive in 'North-West' direction to reach his office from that shop.

Hence, the correct answer is "Option 3".

Given:

Principal = Rs. 800

Rate = 10%

Amount = 926.10

Formula:

A = P(1 + r/100)^t

If interest compounded semi annually, then 

Rate = t/2

Time = 2t

Calculation:

As given interest compounded semi - annually then

Rate = 10/2 = 5%

Time = 2 × t

According to the question

\(926.1 = 800[1 + \frac{5}{100}]^{2t}\)

⇒ \([1 + \frac{1}{20}]^{2t} = \frac{926.1}{800}\)

⇒ \((\frac{21}{20})^{2t} = \frac{9261}{8000}\)

⇒ \((\frac{21}{20})^{2t} = (\frac{21}{20})^3\)

On Comparing the power

⇒ 2t = 3

⇒ t = 3/2

∴ Required time = 3/2 years

The correct answer is Dhar.

Key Points

• The 'Phadake studio' was made in Dhar district of Madhya Pradesh.
• The Maharaja of Dhar was a patron of art and would often invite several artists to his kingdom.
• Phadke was one of those.
• On his request, Phadke started an art studio in Dhar.
• It is today known as Phadke Art Studio.
• Raghunath Krishna Phadkewas a famous Indian sculptor from the state of Maharashtra.
• He received the Padma Shri Award in 1961.

The correct answer is option 1, i.e Ductility.

• The ability of metals to be drawn into thin wires is called ductility.
• Gold is the most ductile metal.
• A wire of about 2 km length can be drawn from one gram of gold.
• It is because of their malleability and ductility that metals can be given different shapes according to our needs.

Ductility:

• Ductility is the property of the material that enables it to be drawn out or elongated to an appreciable extent before rupture occurs.
• The percentage elongation or percentage reduction in the area before the rupture of a test specimen is the measure of ductility. Normally if the percentage elongation exceeds 15% the material is ductile and if it is less than 5% the material is brittle.
• Lead, copper, aluminium, mild steel are typical ductile materials.

Source: NCERT (Chapter - Metal and Non-Metal) please go through page no. 38

• Ductility- Ability of metals to be drawn into thin wires.
• Sonorous-  Ability of metals to produce sound when beaten hard on its surface.
• Malleability- Ability of metals to be beaten into thin sheets.

• Code: letters written in reverse alphabetical order
• RELATIONS

Alphabetical order: A < E < I < L < N < O < R < S < T 

Reverse order: T > S > R > O > N > L > I > E > A

Thus, code is TSRONLIEA

• NUMBER

​Alphabetical order: B < E < M < N < R < U

Reverse order: U > R > N > M > E > B

• Similarly, SPECULATION

Alphabetical order: A < C < E < I < L < N < O < P < S < T < U 

Reverse order: U > T > S > P > O > N > L > I > E > C > A

Hence, "option 1" is the correct answer.

Given:

Cost Price (CP) = ₹2,500

Repair Cost = ₹300

Selling Price (SP) = ₹3,000

Formula Used:

Profit Percentage = \(\frac{Profit}{CP} \times 100\)

Calculation:

Profit = SP - (CP + Repair Cost)

Profit = ₹3,000 - (₹2,500 + ₹300) = ₹200

Profit Percentage = \(\frac{200}{2800} \times 100\)

Profit Percentage = \(7\frac{1}{7}\)%

The correct answer is option 1.

The correct answer is Amarkantak.

• Amarkantak was known as Maikal in ancient history.

Key Points

• It is known as Teerthraj or The King of Pilgrims.
• It is surrounded by three mountain ranges Satpura, Vindhya, and Maikal.
• It is at a height of 3500 ft from mean sea level.
• Three rivers Narmada, Johila, and Son originates from here.
• It is one of the best examples of radial drainage pattern found in the country.

Additional Information

• Bhojpur is famous for Bhojeshwar Temple.
• It was built by Parmara King Bhoj in the 11^th century.
• Bhedaghat is famous for the Dhunadhar waterfall of the Narmada river.
• It is located near the Jabalpur district of Madhya Pradesh.
• Rocks of marble can be found here.
• Khajuraho is famous for its 85 Hindu and Jain temples.
• It was named as “City of Gods” given by Muslim historian Abu Rihan Alberuni.
• Khajuraho group of temples were included in the UNESCO world heritage site list in the year 1986.

The correct answer is 'Total internal reflection'.

Key Points

• The endoscope is a therapeutic instrument.
• Endoscope works on the principle of Total Internal Reflection.
• Total Internal Reflection works on two conditions-
• The light must be propagating from a denser to a rarer medium.
• The angle of incidence must exceed the **critical angle.**​
• The endoscope employs the total internal reflection concept using optical fibers.
• This procedure is used to study the interior of a hollow organ or cavities throughout the body.

Hence, the correct answer is Total internal reflection.

Additional Information

Let's have a look at other options:

On 1^st January, 2008 it was Tuesday.

Number of odd days from year 2008 to 2011 = (2 + 1 + 1 + 1) = 5 days.

Therefore on 1^st January 2012, it was Tuesday + 5 days = Sunday.

Hence, on 1^st January 2012 it was Sunday.

GIVEN:

Salary of A =  25% more than that of B 

CALCULATION:

Let us assume B's salary to be 100

⇒ Here, the Salary of A = 25% more than that of B 

⇒ Salary of A =  100 + 100 × 25/100 = 125 

⇒ Now, Salary of B lower than that of A = (Difference of A - Difference of B) = ( 125 - 100 ) = 25 

⇒ Required percent = (25/125) × 100 = 20% 

Hence, the required percentage is 20%.

The correct answer is 1^st November 1956.

Key Points

• Madhya Pradesh is the central state in India.
• It is also called the "tiger state".
• It was given the status of a full-fledged state with effect from 1^st November 1956.
• It was the largest in India by area until 2000.
• The southeastern Chhattisgarh region was designated a separate state in 2000.
• Bhopal is the capital of Madhya Pradesh.
• The total geographical area of Madhya Pradesh covers approximately 308,000 sq km.
• Madhya Pradesh is the homeland of Kalidasa.

Additional Information

• Madhya Pradesh borders the states of:
• Uttar Pradesh to the northeast.
• Chhattisgarh to the southeast.
• Maharashtra to the south.
• Gujarat to the west.
• Rajasthan to the northwest.
• Madhya Pradesh state has 29 seats in Lok Sabha and 11 seats in Rajya Sabha.
• India's biggest diamond mine Panna is in Madhya Pradesh.
• Madhya Pradesh is the first state in India to start a happiness department.

The correct answer is Pyrometer.

Key Points

• A pyrometer is an instrument that is used for measuring very high temperatures.
• Pyrometer is a kind of remote-sensing thermometer.
• It works by measuring radiation from the body whose temperature is to be measured.
• Modern pyrometers are also used to measure the temperature of cooler objects.
• The pyrometer was invented by Josiah Wedgwood.​

Additional Information

• ​A photometer is an instrument used for measuring the intensity of light.
• A solarimeter is a device used to measure solar radiation.
• A Pyrgeometer  is a device that used for measuring the infrared radiation spectrum in the atmosphere.

The correct answer is Option 2: Help the old lady to get up, collect her things, and hire an auto to drop her at her destination.

Qualities Projected in this situation:  (Effective intelligence, speed of decision, and sense of responsibility).

Key Points

• Checklist for attempting SRT questions:

1. Read the question and options carefully.
2. Look for options that are realistic, optimistic, and reflect officer-like qualities.
3. Do not skip any situation.
4. Relegate the negative sentences and choose the most logical option among the remaining. As time is an important factor, hence your thinking ability should be swift.
5. React quickly and be logical.

Additional Information

Officer qualities:

Shortcut Trick

Using the identity sec² θ − tan² θ = 1, we know (sec θ + tan θ) and (sec θ − tan θ) are reciprocals.

If sec θ + tan θ = 4, then sec θ − tan θ = 1 / 4.

1 / 4 = 0.25.

∴ The correct answer is 0.25.

Alternate Method

Given: sec θ + tan θ = 4

Formula Used: sec² θ − tan² θ = 1

⇒ sec² θ − tan² θ = 1

⇒ (sec θ + tan θ)(sec θ − tan θ) = 1

⇒ 4 × (sec θ − tan θ) = 1

⇒ sec θ − tan θ = 1 / 4

⇒ sec θ − tan θ = 0.25

∴ The correct answer is 0.25.

Additional Information

Fundamental Identity

The relation sec²θ − tan²θ = 1 is derived from the Pythagorean theorem applied to 1 + tan²θ = sec²θ.

Reciprocal Property

If sec θ + tan θ = x, then sec θ − tan θ = 1/x. Similarly, if cosec θ + cot θ = y, then cosec θ − cot θ = 1/y.

Finding individual values

Adding both equations gives 2 secθ = x + 1/x, and subtracting them gives 2 tanθ = x − 1/x.

The correct answer is Arabic, Chinese, English, French, Russian and Spanish.

Key Points

• The official languages of the United Nations are Arabic, Chinese, English, French, Russian, and Spanish.
• These six languages are used in meetings and for all official documents of the United Nations.
• The decision to have multiple official languages reflects the UN's commitment to multilingualism and cultural diversity.
• Having these languages ensures that a broad range of member states can effectively participate in the organization's work.
• The rules of procedure for the principal organs of the United Nations, such as the General Assembly, the Security Council, and the Economic and Social Council, specify the use of these official languages.
• Interpretation and translation services are provided in these six languages for all official meetings and documents.
• This allows representatives from different linguistic backgrounds to understand and contribute to the discussions.
• The Department for General Assembly and Conference Management (DGACM) within the UN Secretariat is responsible for providing these language services.
• DGACM employs a large number of interpreters, translators, editors, and other language professionals.
• These professionals work to ensure the accuracy and quality of multilingual communication within the UN system.
• The use of six official languages also helps to disseminate information about the UN's work to a global audience.
• Official documents, reports, and press releases are typically issued in all six languages.
• This ensures that people around the world can access information about the UN's activities in a language they understand.
• The selection of these six languages reflects historical, political, and geographical factors.
• English and French were among the working languages of the League of Nations, the UN's predecessor.
• Chinese, Russian, and Spanish represent significant global populations and cultural influence.
• Arabic was later added as an official language in 1973, reflecting the growing importance of the Arab world in international affairs.
• While these are the official languages, many other languages are used in specific contexts within the UN system.
• For example, field operations may use local languages for communication with communities.
• The UN also promotes multilingualism through various initiatives and campaigns, recognizing the importance of linguistic diversity for achieving its goals.
• The commitment to six official languages underscores the UN's role as a global organization that strives to be inclusive and accessible to all its member states and the people they represent.

The correct answer is Bone.

Key Points

• Bones will be affected in case of osteoporosis and osteomalacia.
• Osteoporosis causes bones to become weak and brittle, so brittle that a fall or even mild stresses such as bending over or coughing can cause a fracture.
• It is related to fractures most commonly occur in the hip, wrist, or spine.
• Osteomalacia is sometimes referred to as the softening of the bones.
• Osteoporosis can be caused due to a deficiency of vitamin D, while osteomalacia is caused by a deficiency in calcium and phosphorus.

​

Additional Information

• Common Eye Disorders and Diseases:
• Myopia
• Hypermetropia
• Cataract
• Amblyopia
• Common Skin Disorders and Diseases:
• Acne
• Atopic dermatitis
• Hives
• Diaper Rash
• Sunburn
• Common Blood Vessel Disorders and Diseases:
• Atherosclerosis
• Raynaud's Disease
• Erythromelalgia
• Stroke

Eight friends: K, L, M, N, O, P, Q and R

• Number of friends = 8, namely, K, L, M, N, O, P, Q, R
• K, L, M and N are sitting in a straight line and are facing North.
• O, P, Q and R are sitting on a parallel line and are facing South.
• ​Each of the persons sitting in a line, faces another person sitting in the parallel line.
• **M faces a person who has two people sitting to his right. M is facing North.**​

​

• N is sitting between M and K.

• Q faces K.

​

• O is neither an immediate neighbour of P nor Q.

Hence, R is the correct answer.

Given:

[76 – {90 ÷ 5 × (24 – 36 ÷ 3) ÷ 3}]

Formula used:

BODMAS Rule

Calculation:

\([76 - \{90 \div 5 \times (24 - 12) \div 3\}]\)

⇒ \([76 - \{18 \times 12 \div 3\}]\)

⇒ \([76 - 72]\)

⇒ 4

∴ The correct answer is option (3).

The correct answer is ​By being carried on in the name of the Mughal emperor.

Key Points

• The revolt acquired legitimacy because it was carried on in the name of the Mughal emperor, Bahadur Shah.
• The sepoys demanded his blessings and he had no other option but to comply.
• This provided a kind of legitimacy to the rebels and it soon spread throughout the country as people began to join the revolt.
• The sepoys were also able to garner the support of the locals, who were disgruntled by the oppressive actions of the British.
• They joined in the revolt, providing the sepoys with more strength and legitimacy.
• The revolt also acquired legitimacy because the sepoys were able to draw on the anti-British sentiment among the people of India.
• This sentiment was further fuelled by the beliefs of the sepoys that they were fighting for the freedom of the country from foreign rule.
• This gave the revolt even more strength and legitimacy.

The correct answer is Chemically unreactive.

Key Points

• Inert gases are Chemically unreactive.
• An inert gas is a gas that does not undergo chemical reactions under a set of given conditions.
• The noble gases often do not react with many substances and were historically referred to as inert gases.
• The group 18 elements include - 
• helium, neon, argon, krypton, xenon, and radon.
• But recent studies have shown reactive compounds of xenon, krypton, and radon.
• Hence, option 4 is correct.

Additional Information

• The IUPAC is responsible for maintaining the periodic table.
• Nobel gas :
• Noble gas, any of the seven chemical elements that make up Group 18 (VIII a) of the periodic table.
• The noble gases are colourless, odourless, tasteless, nonflammable gases.
• They traditionally have been labelled Group 0 in the periodic table because for decades after their discovery.
• it was believed that they could not bond to other atoms, that is, that their atoms could not combine with those of other elements to form chemical compounds.

Given: Seven people, A, B, C, D, E, F and G are sitting in a straight row, facing north.

1. A sits second from the left.

2. Only two people sit between A and C.

3. Only three people sit between D and F and D is an immediate neighbour of A.

4. B is an immediate neighbour of D and E is not an immediate neighbour of C.

Here, 'G' sits to the immediate left of F.

Hence, the correct answer is "Option 4".

Shortcut Trick

The ratio of Amount to Principal is 13,310 ÷ 10,000 = 1331 ÷ 1000.

Since the rate is 10%, the multiplying factor is 1.1 or 11/10 per annum.

We see that (11/10)³ = 1331/1000.

The power of the factor directly gives the number of years.

∴ The correct answer is 3 years.

Alternate Method

Given values:

⇒ Principal (P) = ₹10,000

⇒ Amount (A) = ₹13,310

⇒ Rate of Interest (R) = 10% per annum

Formula used:

⇒ A = P × (1 + R/100)ⁿ

Calculations:

⇒ 13,310 = 10,000 × (1 + 10/100)ⁿ

⇒ 13,310 / 10,000 = (11/10)ⁿ

⇒ 1331 / 1000 = (11/10)ⁿ

⇒ (11/10)³ = (11/10)ⁿ

⇒ n = 3 years

∴ The correct answer is 3 years.

Additional Information

Compound Interest Formula

The formula for compounding annually is A = P × (1 + R/100)^t, where A is the amount, P is the principal, R is the rate, and t is the time.

Half-Yearly Compounding

When compounded half-yearly, the rate is halved (R/2) and the time period is doubled (2t) in the standard formula.

Rule of 72

A quick shortcut to estimate doubling time is t ≈ 72 ÷ R, where R is the annual interest rate percentage.

4

The correct answer is 21^st June.

• International Yoga Day

• International Yoga Day is also known as World Yoga Day and it is celebrated every year since 2015, following its inception in the United Nations General Assembly in 2014.

• The date 21^st June was suggested by Indian Prime Minister Narendra Modi in his UN address, as it is the longest day of the year in the Northern Hemisphere and the shortest in the Southern Hemisphere of the earth shares a special significance in many parts of the world.

• India's Permanent Representative Asoke Mukherji introduced the draft resolution in the United Nations General Assembly on 11 December 2014 and a total of 177 nations co-sponsored the resolution, which is the highest number of co-sponsors ever for any UNGA Resolution of such nature.

• The first International Yoga Day celebrated at Rajpath, New Delhi became the largest yoga class ever held, with the largest number of nations (84) and 35,985 people, including PM Modi participating in the event.

• A 10 rupees commemorative coin was issued by the Reserve Bank of India in 2015 to mark the first International Yoga Day.

• Later in 2017, 10 stamps on 'Asanas' were issued on a single sheet by the UN Postal Administration (UNPA) to mark International Day of Yoga.

• The theme for International Yoga Day 2020 was 'Yoga at Home and Yoga with Family'.

• 21^st March is celebrated as World Petry Day, World Forestry Day, and World Down Syndrome Day.

• 5^th June is celebrated as World Environment Day.

The correct answer is Bipin Chandra Pal.

Key Points

• Bipin Chandra Pal was one in Lal Pal Bal Triumvirate.
• He started the Swadeshi movement against the partition of Bengal.
• He stood against the Partition of Bengal by the British government.
• He was a social reformer.
• Bal Gangadhar Tilak, Bipin Chandra Pal, Lala Lajpat Rai are the key people in the swadeshi movement.
• Bipin Chandra Pal is known as the father of revolutionary thoughts.
• He founded English weekly "New India" in 1901.

Swadeshi movement:

• ​It was officially proclaimed on 7 August 1905 at the Calcutta Town Hall, in Bengal.
• Lord Curzon was the viceroy of India during Swadeshi Movement.
• The two main goals of this movement were the boycott of foreign-made goods and the use of Swadeshi goods.
• In Andhra Pradesh, the Swadeshi movement was also known as the Vandemataram movement.
• In 1909, the movement had spread across the country and people had started anti-partition and anti-colonial movements.
• Key people in the Swadeshi movement:
• ​Bal Gangadhar Tilak.
• Bipin Chandra Pal.
• Lala Lajpat Rai
• Aurobindo Ghosh

Lala Lajpat Rai:

• Lala Lajpat Rai participated in Swadeshi Andolan from the Hissar district of Haryana.
• He was popularly known as Punjab Kesari.

Bal Gangadhar Tilak:

• ​He was popularly known as Lokmanya Tilak.
• He published a series of articles in his Marathi newspaper Kesari, against the British.
• He also launched the Maratha newspaper in English.

The pattern followed here is:

The sum of squares of both the digits is written on the right side.

54 : 41 = (5)² + (4)² = 25 + 16 = 41

Similarly,

32 : ? = (3)² + (2)² = 9 + 4 = 13

Hence, “13” is the correct answer.

Shortcut Trick

Interest Paid by A = 5% × 6 = 30% of Principal

Interest Received by A = 9% × 3 = 27% of Principal

Net Loss % = 30% − 27% = 3%

Loss Amount = 3% of ₹3,500 = 3 × 35 = ₹105

∴ The correct answer is ₹105 loss.

Alternate Method

Given: Principal (P) = ₹3,500, Rate 1 (R₁) = 5%, Time 1 (T₁) = 6 years, Rate 2 (R₂) = 9%, Time 2 (T₂) = 3 years.

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

⇒ Interest to be paid by A = (3500 × 5 × 6) ÷ 100

⇒ Interest to be paid = 35 × 30 = ₹1,050

⇒ Interest received from B = (3500 × 9 × 3) ÷ 100

⇒ Interest received = 35 × 27 = ₹945

⇒ Net Gain/Loss = Interest Received − Interest Paid

⇒ Net Gain/Loss = 945 − 1050 = −₹105

⇒ Since the value is negative, it is a loss.

∴ The correct answer is ₹105 loss.

Additional Information

Simple Interest Concept

Simple Interest is calculated only on the Principal amount. The formula is SI = (P × R × T) / 100, where P is Principal, R is Rate per annum, and T is Time in years.

Effective Rate of Interest

The Effective Rate for a period is (R × T)%. Comparing effective rates (5% × 6 = 30% vs 9% × 3 = 27%) directly gives the profit or loss percentage on the principal.

Amount Formula

The total Amount (A) at the end of the period is the sum of Principal and Simple Interest: A = P + SI = P(1 + RT/100).

The correct answer is Barwani.

Key Points

• Bawangaja is a famous Jain pilgrim center in the Barwani district of Madhya Pradesh in India.
• Its main attraction is the world's second largest megalithic statue of Lord Rishabhadeva, the first Jain Tirthankara.
• The statue is 84 feet high.
• It was created early in the 12^th century.

Important Points

• The idol of Lord Adinatha is made in brown stone in Kayotsarga posture.
• The hands of idol are not joined with legs but are made separate.
• The structural art and style of this idol is unique.
• The various parts of idol are quite symmetrical.
• There is balanced depiction of all emotions like joy, mercy and separation on the face of this idol

The correct answer is Sodium azide.

• The driver-side airbag is a container containing about 50 grams of sodium azide.
• The passenger side container holds about 200 grams of sodium azide.
• Because vehicles change speed so quickly in an accident, airbags must inflate rapidly to reduce the risk of the occupant hitting the vehicle's interior.

Key Points

• The propellant used in most airbags is a combination of sodium azide (NaN₃) and potassium nitrate (KNO₃).
• When these two chemical compounds react, they burn rapidly and produce the nitrogen gas that fills the bag.

Additional Information

• Airbags are passive safety features designed to mitigate or prevent injuries among drivers and passengers in the event of a crash.
• Airbags provide added protection to seatbelts.
• For example, in higher-speed crashes, a seatbelt alone may not prevent a driver’s head from hitting the steering column.
• The deployment of an airbag protects the head and upper body of the driver and reduces some of the force exerted on the driver by the seatbelt.
• Airbags are useful whenever you experience a sudden reduction in speed.
• Airbag systems are composed of three basic parts: the bag itself, the inflator unit, and the crash sensor. The bag and inflator are contained together in the airbag module.
• Most often, the sensor is located in the passenger compartment of a vehicle and towards the front, so if a crash occurs it is quickly detected.

Least Possible Venn diagram:

Conclusions:

1. No lake is stream → Does not follow (it is possible but not definite)

This possibility can be shown using the below Venn diagram:

2. Some rivers are streams → Follows (According to statement 1 some streams are rivers so, some rivers are definitely "streams").

Here, Only conclusion 2 follows.

Hence, the correct answer is "Option 2".

Given:

\(\frac{36 \times 4+25}{13}=\frac{104}{?}\)

Concept:

Calculation:

According to the question,

⇒ \(\frac{36 \times 4+25}{13}=\frac{104}{?}\)

⇒ \(\frac{144+25}{13}=\frac{104}{?}\)

⇒ \(\frac{169}{13}=\frac{104}{?}\)

⇒ \(\frac{13}{1}=\frac{104}{?}\)

⇒ ? = 8

Therefore, "8" is the required answer.

correct answer is Kariz

Key Points

• Kariz
• A kareez is a combination below and above ground channel system used to bring water to a settlement or fields from a natural source, say an aquifer, mountain spring or lake.
• Many of the kareez / qanats are ancient and their history is intertwined with the history of Aryan lands. Importantly, the system was sustainable and did not exhaust underground aquifers.
• A jube is an above ground gutter (drain, ditch, or rain sewer). Frequently, communities that construct and use the kareez, also employ the jube as part of an urban water collection and management system.
• Jubes collect rain water in those areas with a significant enough amount of precipitation to cause a run-off. Water collected in this manner, while probably not suitable as drinking water is useful as irrigation water. In Persian, a spring is called sarab meaning the head or start of water or stream or cheshmeh.

The correct answer is Ethanol

• Ethanol is an active ingredient in all alcoholic drinks.

Key Points

• Ethanol is a member of a class of organic compounds that are given the general name alcohol.
• Its molecular formula is C2H5OH.
• It is also called ethyl alcohol.
• Ethanol is also the intoxicating ingredient of many alcoholic beverages such as beer, wine, and distilled spirits.
• As an industrial chemical it is used as a solvent, in the synthesis of other organic chemicals, and as an additive for automotive gasoline.

Additional Information

• Pentane is an organic compound that is a clear colorless liquid. It is an alkane with five carbon atoms.
• Butane is an alkane with the formula C₄H₁₀. It is a colorless gas with a faint petroleum-like odor.
• Propane is a flammable hydrocarbon gas. It is commonly used for fuel in heating, cooking, hot water and vehicles.

1. R, N, O, W, Q and C are sitting around a circular table facing the center.
2. R is sitting to the immediate left of W, who is facing O, O is sitting to the immediate left of N.
3. C is not an immediate neighbor of W.

The final arrangement will be as shown below:

W is sitting to the left of Q.

Hence, ‘W’ is the correct answer.

Confusion PointsHere W is facing O, not R.

Concept of ‘who/ which’ and ‘and’

i) The description after the word ‘who/which’ in any sentence always describes the person named just before the word ‘who/ which'.

ii) The description after the word ‘and’ is always given for the person whose name is given at the starting of the sentence.

Given:

Ratio of the cost of 5 bananas and 4 apples is equal to the cost of 3 bananas and 7 apples.

Calculation:

Let the cost of one banana = x

Cost of one apple = y

∴ 5x + 4y = 3x + 7y

⇒ 2x = 3y

x/y = 3/2

∴ The ratio of the price of banana and an apple is 3 : 2.

The correct answer is Tawa.

Key Points

• The largest road bridge of Madhya Pradesh is located across the Tawa river.
• The bridge is situated on Babai-Hoshangabad road.
• Tawa river is a tributary of the Narmada river.
• It is the longest tributary of the Narmada river.
• It is merging with Narmada in the Hoshangabad district.
• Tawa River rises in the Satpura Range of Betul.
• Bori Reserve forest is situated on the banks of the Tawa river.

Additional Information

• Narmada is the largest west flowing peninsular river in India.
• It flows between the Deccan plateau and the Malwa plateau.
• It flows through a rift valley between Vindhya and Satpura ranges.
• Kanha national park is situated on the banks of the Narmada river.
• Tapti is the second-largest west-flowing peninsular river in India.
• Tapti is known as the 'hand made of Narmada'.
• The Ukai dam is built across the Tapti river.
• Chambal is a tributary of the River Yamuna.
• The Rana Pratap Sagar Dam is built on the Chambal river.

The correct answer is Na₂O.

Key Points

• Neutral oxides are said to be oxides that do not show any properties of acids and bases.
• Neutral oxide is an oxide that does not react in the presence of any acid or base.
• Let us see other examples of the neutral oxides such as
• CO
• N₂O
• NO
• MnO₂
• H₂O

Important Points

• Sodium Oxide having a chemical formula of Na₂O, is a metal oxide.
• It is also known as an alkali metal oxide as it comprises two sodium and one Oxygen atoms.

Additional Information

• Acidic Oxide:
• It is said to be the oxides when reacted with the water molecule will give acids.
• Basic Oxide:
• It is said to be the oxides when reacted with water molecules will give bases.
• Amphoteric Oxide:
• It is said to be the oxides that can react as acid as well as bases.

The words 'solving the immediate problems of today rather than on trying to solve the anticipated problems' tells us that more priority should be given to current problems. This makes assumption I implicit. However, it is not stated the future problems should not be solved at all. This makes assumption II invalid.

Since, 12, 16, k, 28, 32, 35, 39, 47, 53 are in ascending order

So, the value of k must be in between 16 to 28

∴ The value of k is 27 from option

The correct answer is Narmada.

• Narmada is the largest river in Madhya Pradesh.
• Madhya Pradesh falls in five major river basins.
• The northern part of the state falls within the Ganges Basin where the Betwa, Chambal, and Son flow.
• Narmada river mainly flows in Madhya Pradesh and the Gujarat state of India.
• It is also known as the "Life Line of Madhya Pradesh and Gujarat" for its huge contribution to the state of Madhya Pradesh and Gujarat in many ways.
• Narmada rises from Amarkantak Plateau in Anuppur district Madhya Pradesh.

​

• About Madhya Pradesh:
• Chief Minister -  Dr. Mohan Yadav
• Governor - Mangubhai C. Patel (July 2021)
• Capital - Bhopal
• Total Districts - 52 districts
• Literacy Rate - 69.32%
• Largest district - Chhindwara
• Smallest district - Niwari

The correct answer is Just before it touches the ground.

Key Points

• When an object reaches the ground it has its maximum value of kinetic energy just before touching the ground.
• Since kinetic energy + potential energy = Constant, so on reaching the ground, the potential energy of an object becomes zero.
• So eventually, the kinetic energy on reaching the ground becomes maximum.

Additional Information

• Kinetic energy is the work needed to accelerate a body of a given mass from rest to its stated velocity.
• K.E. = \(1\over2\) mv², where, m= mass of the body, v= velocity of the given group.
• Potential energy is stored energy that depends upon the relative position of various system parts.
• P.E. = mg h, where, m= mass of the body, g= gravitational acceleration, h= height.
• When the stone was at top of the roof it has P.E. = maximum, K.E.= zero. Because the stone was in idle condition so velocity, v=0, K.E.=0.
• Just after the stone is dropped, P.E. is started reducing, and the velocity is increasing, which in turn increases its K.E.
• When the stone is just halfway, K.E. and P.E. just become half of their actual values.
• When the stone touches the ground, its velocity v=0, so K.E. =0, and P.E. again get restored to its original value.
• The law of conservation of energy states that energy can neither be created nor destroyed, it transforms from one form to another.
• So in the course of the stone dropped from the roof of a house to its reaches at the ground, K.E. and P.E. transform between each other.
• But every time, K.E. + P.E. = Total energy = Constant must be maintained.

Prime numbers starting from the reverse order i.e. 47, 43, 41, 37, and 31 are subtracted from each number.

Hence, the correct answer is "1".

Mistake Points

Note: Here the pattern is, prime numbers in reverse from 47 is used and subtracted from the given number to get the answer.

Another pattern is being followed in the given series -4, -2 pattern but the option according to that pattern is not available in the question.

So, the correct answer is "1".

Important Points

What is a prime number?

Prime numbers are numbers that have only 2 factors: 1 and themselves.

For example, the first 5 prime numbers are 2, 3, 5, 7, and 11.

Given:

Volume of the cone = \(\frac{128}{3} \pi\)

Height of the cone (h) = 2 × radius of the cone (r)

Formula Used:

Volume of cone = \(\frac{1}{3} \pi r^2 h\)

Slant height (l) of the cone = \( √{r^2 + h^2} \)

Calculation:

We know, Volume of cone = \(\frac{1}{3} \pi r^2 h\)

Given volume is \(\frac{128}{3} \pi\), so:

\(\frac{1}{3} \pi r^2 h = \frac{128}{3} \pi\)

⇒ \(\pi r^2 h = 128 \pi\)

⇒ \(r^2 h = 128\)

Since h = 2r:

⇒ \(r^2 (2r) = 128\)

⇒ \(2r^3 = 128\)

⇒ \(r^3 = 64\)

⇒ \(r = \sqrt[3]{64}\)

⇒ \(r = 4\)

Now, h = 2r = 2 × 4 = 8

Slant height (l) = \( \sqrt{r^2 + h^2} \)

⇒ \( \sqrt{4^2 + 8^2} \)

⇒ \( \sqrt{16 + 64} \)

⇒ \( \sqrt{80} \)

The slant height of the cone is √80

The correct answer is Indore.

In News

• Indore is set to establish India's first PPP Green Waste Processing Plant under the Swachh Bharat Mission-Urban.

Key Points

• Indore's plant will process green waste and convert it into valuable resources like sawdust, wooden pellets, and eco-friendly materials.
• The facility, spanning 55,000 square feet in Bicholi Hapsi, will recycle tree branches and leaves.
• The Indore Municipal Corporation (IMC) will earn approx. Rs 3,000 per tonne in royalty for supplying wood and branches.
• Astronomical Industries Private Limited, in partnership with IMC, will oversee the plant’s operations and waste transformation.

Additional Information

• Swachh Bharat Mission-Urban
• Launched in - 2014
• Aim - To achieve Garbage-Free Cities and improve waste management.
• Wooden Pellets
• Produced from processed green waste.
• Used as an eco-friendly alternative to coal in power plants like NTPC.
• Composting Initiative
• IMC is promoting composting through specially designed pits in municipal gardens.
• Other private firms have established additional waste processing plants in Sirpur.
• Air Quality Index (AQI) Improvement
• The initiative will help reduce air pollution by preventing waste burning.
• Promotes sustainability and cleaner urban living conditions.

The correct answer is Tungsten.

• An electric bulb has a filament made of Tungsten.

Key Points

• Tungsten has the highest melting point i.e.  3,410°C.
• Hence, it is used as the filament of an electric bulb.
• Argon is used in electric bulbs to prevent corrosion of its tungsten filament. Since it doesn't react with tungsten, it stops the filament from burning away in the presence of oxygen.
• Hence, which results in increased light bulb life.
• In the electric bulb, electric energy is converted into light energy.
• Tungsten:
• Symbol: W
• Atomic number: 74
• Atomic mass: 183.84 u

According to BODMAS

49 - 4 ÷ 120 × 8 + 100 = ?

Interchanging the signs -

⇒ 49 + 4 x 120 ÷ 8 - 100 = ?

⇒ 49 + 4 x 15 - 100 = x

⇒ 49 + 60 - 100 = x

⇒ 109 - 100 = 9

So, 9 will come in place of question mark.

Hence the correct answer is "Option 4".

tan θ tan 5θ = 1

tan 5θ = 1/tan θ 

tan 5θ = cot θ 

tan 5θ  = tan (90°- θ)

so 5θ  = 90° - θ 

so,  θ + 5θ = 90°

6θ = 90°

2θ = 30°

Sin 2θ = sin 30° = 1/2

• Tansen served in the court of Badshah Akbar in the early 16^th century.
• He was one of the nine navratnas in Akbar's court.
• His real name was Ramtanu Pande
• Some his greatest works in ragas are Durbari Kanada, Miyan Ki Todi and Miyan Ki Malhar.

The correct answer is Boron, silicon, antimony.

 Key Points

• Metalloids:-
• These are elements that have properties similar to both metals and non-metals. In some of their properties, they show similarity with metals and in others with non-metals.
• They are hence placed in between metals and non-metals.
• Metalloids can also be called semimetals.
• They are found in groups 13, 14, 15, 16 and 17 of the p-block.
• Metalloids include Boron, Silicon, Germanium, Arsenic, Antimony, Tellurium and Polonium.
• Total elements are 118 out of which 91 are metals, 7 are metalloids, and 20 are non-metals.
• In the modern periodic table, metalloids are in Right of the periodic table

Given: D & C N E ^ & G ^ Y % % @ G Y & I & * H K Z

Now, 

vowels are there that are immediately followed by a symbol.

So, Needed pattern is: Vowels - Symbol.

D & C N E ^ & G ^ Y % % @ G Y & I & * H K Z

There are Two Vowels that are immediately followed by a symbol.

Hence, the correct answer is 'Option 2'.

Given:

Average of the first three numbers = 24

Average of the last three numbers = 29

Last number = 33

Formula Used:

Sum of the first three numbers = Average × 3

Sum of the last three numbers = Average × 3

Sum of the last three numbers = Second number + Third number + Last number

Calculation:

Sum of the first three numbers = 24 × 3

Sum of the first three numbers = 72

Sum of the last three numbers = 29 × 3

Sum of the last three numbers = 87

Sum of the last three numbers = Second number + Third number + 33

87 = Second number + Third number + 33

Second number + Third number = 87 - 33

Second number + Third number = 54

Sum of the first three numbers = First number + Second number + Third number

72 = First number + 54

⇒ First number = 72 - 54

⇒ First number = 18

The first number is 18.

The correct answer is Bhil.

Key Points

• The Bhagoria Festival is celebrated by the tribal people of Madhya Pradesh.
• Tribes who participate include the Bhil, Bhilala, and Pateliya.
• The festival takes place in the Badwani, Dhar, Alirajpur, Khargone, and Jhabua districts of Madhya Pradesh.
• It has agricultural significance and coincides with the end of harvesting crops.
• It is celebrated for seven days in the month of March.

THE BHILS OF MADHYA PRADESH

• According to the 2011 Census of India, Bhil is the most populous tribe in M.P. with a total population of 4,618,068.
• The Bhils are inhabitants of the Dhar, Jhabua, Khargone, and Ratlam districts of Madhya Pradesh.
• The rich cultural tradition of the Bhils of Madhya Pradesh is manifest in their rituals, songs and dances, their community deities, tattoos, myths, and lore.
• Their homes reveal an innate sense of aesthetics.
• Walls are plastered every year and decorated with clay relief work, mittichitra, and paintings.

Additional Information 

The correct answer is To prepare Proteins.

Key Points

• Plants Proteins-
• All plants absorb nitrogen as NO₃ (nitrate ion) from the soil.
• These are then converted to ammonium ions to combine into amino acids and eventually convert into proteins.

​​

Additional Information

• ​Plants Sugar -
• Plants form sugars during the process of photosynthesis.
• The food prepared by the leaves is in the form of simple sugars, called 'glucose'.
• This glucose is sent to other parts of the plant and excess glucose is stored as 'starch' in the leaves of the plant.
• Glucose and starch belong to the group of carbohydrates.​
• Plants Cellulose-
• It is a type of carbohydrate in plants.
• The walls of plant cells are made up of cellulose.
• Cellulose is an organic compound with a chemical formula (C₆H₁₀O₅)_n.
• ​Fat is made up of elements of carbon, hydrogen, oxygen.

The logic is:

841 : 29 → 29² : 29

Similarly,

484 : ? → 22² : 22

Hence, ‘22’ is the correct answer.

Given:

The average of 50 numbers = 23.

Each number is multiplied by 13.

Formula used:

New average = Old average × Multiplier

Calculation:

Old average = 23

Multiplier = 13

⇒ New average = 23 × 13

⇒ New average = 299

∴ The new average is 299.

The correct answer is Earthquakes.

Key Points

• An Earthquake is caused by the forces originating in the interior of the earth. These internal forces are called endogenetic forces.
• The magnitude of an earthquake is measured by the Richter scale.
• The place of origin of the Earthquake is called Focus.
• The place on the ground surface which is perpendicular to the focus is called Epicentre.
• Seismology is the special branch of geology that deals with the study of Earthquakes.
• Shadow zones are zones where earthquakes do not occur or rarely occur.
• Earthquake-prone areas of the country have been identified on the basis of scientific inputs relating to seismicity, earthquakes that occurred in the past, and the tectonic setup of the region.
• Based on these inputs India has been grouped into four seismic zones, viz. Zone II, III, IV, and V.
• The Geological Survey of India (GSI) first published the seismic zoning map of the country in the year 1935.

​

Additional Information

The logic followed here is:

1) Movement of the uppermost symbols: Left uppermost symbol shifted one step left bottom side and the right uppermost symbol shifted one step left uppermost side.

2) Movement of the leftmost bottom symbol: The symbol shifted one step right side of the bottom.

3) Movement of the right bottom symbol and appearance of the new symbol.

Hence, the correct answer is "Option 4".

Given:

Two dice are thrown.

Concept:

The number of ways in which a sum of 7 can be obtained from two dice.

Solution:

To get a sum of 7, the possible combinations are (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1).

There are 6 ways in which two dice can be thrown, so the probability of getting a sum of 7 is 6/36 or 1/6.

Therefore, the number of ways in which the sum can be 7 is 6.

Therefore, the answer is option 3.

The correct answer is Madhya Pradesh.

• Jawara dance is related to Madhya Pradesh state.

Key Points

• Jawara Dance:
• It is a folk dance of Madhya Pradesh.
• It is mainly performed in the Bundelkhand region among the peasant community.
• It is also known as harvest dance.
• Both male and female participate in the Jawara dance.
• Other folk dances of Madhya Pradesh are Matki, Aada, Khada Nach, Phulpati, Grida Dance, Selalarki, Selabhadoni, Maanch.

Additional Information

The correct answer is Option 3: Dive into the river and take him to the shore.

• Qualities Projected in this situation:  (Effective Intelligence, Sense of responsibility, Courage, and Speed of decision making).

Key Points

• Checklist for attempting SRT questions:

1. Read the question and options carefully.
2. Look for options that are realistic, optimistic, and reflect officer-like qualities.
3. Do not skip any situation.
4. Relegate the negative sentences and choose the most logical option among the remaining. As time is an important factor, hence your thinking ability should be swift.
5. React quickly and be logical.

Additional Information

Officer qualities:

Given:

The ratio of two numbers = 3:4

The HCF of the two numbers = 4

Formula used:

LCM × HCF = Product of the numbers

If the numbers are in the ratio a:b, then the numbers can be written as:

First number = a × HCF

Second number = b × HCF

LCM = Product of the numbers / HCF

Calculation:

First number = 3 × 4 = 12

Second number = 4 × 4 = 16

Product of the numbers = 12 × 16 = 192

⇒ LCM = 192 / 4

⇒ LCM = 48

∴ The correct answer is option (4).

The correct answer is Gautamiputra Satakarni.

• Gautamiputra Satakarni holds the title 'Sathavahanavamsa Prathishtapanakaraka'.

Important Points

• Gautamiputra Satakarni was one of the greatest rulers of the Satavahana Dynasty.
• He was the 23^rd king of the Satavahana dynasty.
• Titles: Ekabhramana,Dakshina Samudradheeshwara,DwijakulaVardhana ,Eka Surudu.
• The Salivahana Saka started during his era.

Additional Information

• Yajnasri Satakarni:
• He holds the title Trisamudradhipathi.
• Sivasri Satakarni was the first king in the Satavahana dynasty who printed the coins in two languages namely Prakrit and Tamil.
• Vasishtaputra Pulomavi:
• He was the son of Gautamiputra Satakarni.
• He holds the title Navanagara Swamy and Andhrapatheshwara.

The Logic here is as follows:

[(1^st Number)3 + (3^rd number)3] ÷ 2 = 2^nd Number

In (5, 728, 11)

[(1^st Number)3 + (3^rd number)3] ÷ 2 = 2^nd Number

(53 + 113) ÷ 2

= (125 + 1331) ÷ 2

= 1456 ÷ 2

= 728 = 2^nd Number

Now check the all options,

Option (1) (7, 244, 5)

[(1^st Number)3 + (3^rd number)3] ÷ 2 = 2^nd Number

(73 + 53) ÷ 2

= (343 + 125) ÷ 2

= 468 ÷ 2

= 234 ≠ 2^nd Number

Option (2) (3, 269, 8)

[(1^st Number)3 + (3^rd number)3] ÷ 2 = 2^nd Number

(33 + 83) ÷ 2

= (27 + 512) ÷ 2

= 539 ÷ 2

= 269.5 ≠ 2^nd Number

Option (3) (2, 121, 6)

[(1^st Number)3 + (3^rd number)3] ÷ 2 = 2^nd Number

(23 + 63) ÷ 2

= (8 + 216) ÷ 2

= 224 ÷ 2

= 112 ≠ 2^nd Number

Option (4) (3, 185, 7)

[(1^st Number)3 + (3^rd number)3] ÷ 2 = 2^nd Number

(33 + 73) ÷ 2

= (27 + 343) ÷ 2

= 370 ÷ 2

= 185 = 2^nd Number

Hence, the correct answer is "(3, 185, 7)".

Given:

Radius of the spherical ball (r) = 14 cm

Rate of painting = Rs. 10 per cm²

Formula Used:

Surface Area of Sphere = 4πr²

Cost of Painting = Surface Area × Rate

Calculation:

Surface Area of Sphere = 4πr²

⇒ Surface Area = 4 × (22/7) × 14²

⇒ Surface Area = 4 × (22/7) × 196

⇒ Surface Area = 4 × 22 × 28

⇒ Surface Area = 2464 cm²

Cost of Painting = 2464 × 10 = 24640

The cost of painting the spherical ball is Rs. 24,640.

The correct answer is Himachal Pradesh.

Key Points

• Phulaich festival is one of the festivals of Himachal Pradesh which is held in September.
• Villagers play drums and celebrate this festival on a larger basis and go to the mountains to collect Ladra flowers.
• This festival is celebrated in Kinnaur, the festival is organized to remember those who have passed away.
• This festival is celebrated on the juncture of 16^th day of the Hindu month of Bhadrapada (August and September), the season for the flowering of wildflowers in the upper hilly areas.

Additional Information

• Various Festivals of other states
• Uttar Pradesh - Ganga Dussehra, Krishna Janmashtami, Ram Navami, Shab-e-Barat.
• Madhya Pradesh - Lokrang, Kalidas Samaroh.
• Andhra Pradesh - Ugadi, Deccan Festival, Lumbini Festival.

As per the given information, the sitting arrangement is as follows:

1. E is B's neighbour, who is at the far end.

Case:1

Case:2

2. Between E and F is G and D is Third from the southern end.
3. C is directly to the right of D and the remaining A is in the end.

Here, if C switches place with G, then C receives the third position from the northern end.

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

Shortcut Trick

If x − 1/x = k, then x² + 1/x² = k² + 2.

In this problem, k = 8.

⇒ x² + 1/x² = 8² + 2 = 64 + 2 = 66.

∴ The correct answer is 66.

Alternate Method

Given:

x − 1/x = 8

Formula Used:

(a − b)² = a² + b² − 2ab

Calculations:

Squaring both sides of the given equation:

⇒ (x − 1/x)² = 8²

⇒ x² + (1/x)² − 2 × x × (1/x) = 64

⇒ x² + 1/x² − 2 = 64

⇒ x² + 1/x² = 64 + 2

⇒ x² + 1/x² = 66

∴ The correct answer is 66.

Additional Information

Positive Sign Identity

If x + 1/x = k, then x² + 1/x² = k² − 2.

Cubic Relation

If x − 1/x = k, then x³ − 1/x³ = k³ + 3k.

Square Conversion

(x + 1/x)² = (x − 1/x)² + 4.

Power Four Relation

If x² + 1/x² = m, then x⁴ + 1/x⁴ = m² − 2.