MP Police Constable : (4 Dec 2025) Memory-Based Paper (Previous Year Paper)

The Correct Answer is ​New Delhi.

In News

• Global Technology Summit 2025 to begin in New Delhi with theme ‘Sambhavna’.

Key Points

• Event Overview:
• The 9^th edition of the Global Technology Summit (GTS) 2025 will be held in New Delhi.
• The theme for this year's summit is "Sambhavna", meaning possibilities.
• The summit will explore how emerging technologies can:
• Drive inclusive growth.
• Strengthen digital governance.
• Deepen cross-border partnerships.
• Summit Details:
• The event will last for three days.
• It will feature over 40 public sessions, including:
• Keynote addresses.
• Ministerial conversations.
• Expert panels.
• Strategic discussions.
• Global Participation:
• More than 150 speakers from over 40 countries will join discussions.
• The summit will cover the pressing tech challenges and opportunities of today.
• Youth Engagement:
• The GTS Young Ambassadors program will amplify the voices of the next generation.
• Students and young professionals from across India will contribute to discussions on:
• Digital futures.
• Responsible AI.
• Global tech norms.

Given :

Given

Statement:

D @ N @ H & Y @ F % V

So,

• D @ N → D is the daughter of N.

• N @ H → N is the daughter of H.

• H & Y → H is the husband of Y.

• Y @ F → Y is the daughter of F.

• F % V → F is the wife of V.

​

Thus, according to the final family tree Y is the maternal grandmother i.e mother's mother of D.

Hence, "Mother’s mother" is the correct answer.

Given 

X took a loan = Rs 12500 

Formula used 

Simple Interest = principal × Rate × time/100 

Calculation 

Rate of interest = Time = x 

⇒ 18000 = 12500 × x²/100 

⇒ x² = 144

x = 12%

∴ The rate of Interest is 12 percent

The Correct Answer is Mumbai.

In News

• The first World Audio Visual & Entertainment Summit (WAVES), a milestone event for the Media & Entertainment (M&E) sector, will be hosted by the Government of India in Mumbai, Maharashtra, from May 1 to 4, 2025.

Key Points

• WAVES 2025 is the first edition of the World Audio Visual & Entertainment Summit and will take place from May 1-4, 2025 at the Jio World Convention Centre & Jio World Gardens in Mumbai.
• The summit focuses on four key pillars:
• Broadcasting & Infotainment
• AVGC-XR (Animation, Visual Effects, Gaming and Comics, Extended Reality)
• Digital Media & Innovation
• Films
• WAVES is designed to bring together leaders, creators, and technologists to showcase the future of India's Media & Entertainment (M&E) sector.
• Animation Filmmakers Competition is a key initiative under the AVGC-XR pillar and provides a platform for creators to showcase their talent.
• Ministry of Information & Broadcasting has partnered with Dancing Atoms, a leading force in animation, to launch this competition.
• The competition offers mentorship, masterclasses, and the opportunity to pitch to industry leaders.
• The event aims to connect the global M&E industry with the Indian M&E sector and its talent.

Analyzing the given arguments

1. Yes, it leads to more wastage.

At least in schools they should promote children to fountain pens or ones they can refill. → Yes, it is a strong argument. Use of 'use and throw pens' should be minimized, it is not eco friendly. 2. No, there are so many pens available, why should it be used less. → It is not a strong argument. Availability of variety of pens or bulk quantity does not mean that it should be used. It should not be used if it creates more wastage.

Hence, Only argument 1 is correct.

Shortcut Trick

For inverse proportion: P₁ × Q₁ = P₂ × Q₂

Product must remain constant: 10 × 6 = 60

Now, 15 × Q = 60

Q = 60 ÷ 15 = 4

∴ The correct option is B.

Alternate Method

Given:

Initial P (P₁) = 10

Initial Q (Q₁) = 6

New P (P₂) = 15

Formula Used:

In inverse proportion, P ∝ 1/Q ⇒ P × Q = k (Constant)

Case 1
P = 10
Q = 6

→

Case 2
P = 15
Q = ?

Product (P × Q) remains Constant = 60

Calculations:

⇒ P₁ × Q₁ = k

⇒ 10 × 6 = 60

⇒ Now, P₂ × Q₂ = 60

⇒ 15 × Q₂ = 60

⇒ Q₂ = 60 ÷ 15

⇒ Q₂ = 4

∴ The correct option is B.

Additional Information

Direct Proportion

Two quantities are in direct proportion if an increase in one leads to a proportional increase in the other (y/x = k or y₁/x₁ = y₂/x₂).

Inverse Proportion

Two quantities are in inverse proportion if an increase in one leads to a proportional decrease in the other (xy = k or x₁y₁ = x₂y₂).

Proportionality Constant

The value k is known as the constant of proportionality, which relates the two variables in any state of the relationship.

The correct answer is "Women in Peacekeeping: A Global South Perspective"

In News

• India is hosting the first-ever Conference for Women Peacekeepers in New Delhi from February 24-25, 2025.
• The theme is "Women in Peacekeeping: A Global South Perspective".

Key Points

• Organized by MEA, Ministry of Defence, and Centre for United Nations Peacekeeping (CUNPK).
• Women peacekeepers from 35 Troop Contributing Countries (TCCs) in the Global South will participate.
• UN representatives Jean-Pierre Lacroix and Christian Saunders will attend.
• President Droupadi Murmu will meet the participating women peacekeepers.
• Discussions will focus on technology in peacekeeping, training, and regional collaboration.
• India has contributed over 200,000 personnel to UN peacekeeping across 49 missions.
• Indian soldiers are recognized globally for their dedication in conflict zones.

The logic followed here is:

Hence, "Option 2" is the correct answer.

Alternate Method

Given:

A man goes from point A to B with the speed of 25 km/hr

The man comes from point B to A with the speed of 4 km/hr

Total time to cover whole journey = 5 hrs 48 minutes.

Formula:

Speed = distance/time

1 hr = 60 min

Calculation:

5 hrs 48 min = (5 + 48/60) hr = (5 + 4/5) = 29/5 hr

Let distance between A and B be x km, then

According to the question,

x/25 + x/4 = 29/5

⇒ (4x + 25x)/100 = 29/5

⇒ 29x/100 = 29/5

⇒ x = 29/5 × 100/29

⇒ x = 20

∴ Distance between A and B is 20 km.

The Correct Answer is ​Kālachakra – People, Peace and Planet.

In News

• PM Modi to to inaugurate 10^th edition of Raisina Dialogue in New Delhi.

Key Points

• The 10^th edition of the Raisina Dialogue will be inaugurated by Prime Minister Narendra Modi in New Delhi.
• Christopher Luxon, Prime Minister of New Zealand, will be the Chief Guest and deliver the keynote address.
• The theme of this year's dialogue is "Kālachakra – People, Peace and Planet".
• The Raisina Dialogue will run for three days from March 17 to 19, 2025.
• The event will cover six thematic pillars:
• Politics Interrupted: Shifting Sands and Rising Tides
• Resolving the Green Trilemma: Who, Where, and How
• Digital Planet: Agents, Agencies and Absences
• Powerplay: The New Global Game of Influence
• Global Governance 2.0: Reforming International Institutions
• The Future of Conflict: Redefining War and Peace
• Around 125 countries are expected to participate in the dialogue.
• The Raisina Dialogue is India’s premier conference focused on geopolitics and geoeconomics.

The given series is as follows.

Hence, the correct answer is 45Y10.

Given:

A train travelling from Mumbai to Goa covered the first 420 km at a speed of 60 km/h and then covered the remaining 195 km at a speed of 65 km/h. 

Concept used:

Distance = Speed × Time

Calculation:

Time taken to cover 1^st 420 km is 420 / 60 = 7 hr

Time taken to cover  195 km is  195 / 65 = 3 hr

Total distance is 420 + 195 = 615 km

Total time taken is 7 + 3 = 10 hr

So average speed is 615 /10 = 61.5 km/h

∴ The correct option is 2

The correct answer is Shaping Future Governments

In News

• World Government Summit (WGS) 2025 opened in Dubai with the theme "Shaping Future Governments" and will run until February 14.

Key Points

• The summit has record international participation, including heads of state, government officials, global institutions, and experts discussing governance trends and critical sectors.
• Key forums include the Future of Work Forum, Government Experience Exchange Forum, Government Services Forum, Artificial Intelligence Forum, Future of Education Forum, Future of Mobility Forum, and Gender Balance Forum.
• India’s Union Environment Minister Bhupender Yadav participated in sessions like the High-Level Roundtable on the Future of Mobility and XDG 2045 Ministerial Roundtable.
• Yadav stressed two primary needs for developing countries:
• Capacity building in clean technology, electric vehicles, and climate-resilient infrastructure.
• Securing financial resources to achieve SDGs with a focus on combating climate change and protecting the environment.
• He highlighted Mission LiFE (Lifestyle for Environment), introduced by PM Narendra Modi, promoting a pro-planet lifestyle with sustainability at individual, community, and national levels.
• India remains committed to green growth through initiatives like afforestation, sustainable agriculture, and developing green infrastructure.
• Haitham Al Ghais, Secretary-General of OPEC, discussed the oil sector's investment requirements, predicting a cumulative investment of $17.4 trillion between 2024 and 2050**, averaging **$640 billion annually.
• $14.2 trillion** for **exploration and production** (around **$525 billion annually).
• $1.9 trillion for refining and manufacturing.
• $1.3 trillion for transportation and storage.
• The summit continues to serve as a global platform to discuss governance, innovation, and sustainable development for shaping the future.

The table of alphabet place value:

The pattern followed here is:

AMOUNT : QWYKXJ

Similarly,

MARKET : '?'

Hence, the correct answer is "EIONXA".

Shortcut Trick

The difference between the Selling Price and Cost Price is the Profit.

Profit = 26% of Cost Price ⇒ 26 units = Rs. 143

Selling Price = 100% (CP) + 26% (Profit) = 126 units

Selling Price = (143 ÷ 26) × 126 = 11 × 63 = 693

∴ The correct answer is Rs. 693.

Alternate Method

Given:

Difference between Cost Price (CP) and Selling Price (SP) = Profit = Rs. 143

Profit percentage = 26%

Cost Price (100%) Profit (26%) Rs. 143 Selling Price (126%) = Rs. 693 Profit and Loss Visualisation

Formula Used:

Profit = (Profit% ÷ 100) × CP

SP = CP + Profit

Calculations:

⇒ 143 = (26 ÷ 100) × CP

⇒ CP = (143 × 100) ÷ 26

⇒ CP = 11 × 50

⇒ CP = Rs. 550

⇒ SP = CP + Profit

⇒ SP = 550 + 143

⇒ SP = Rs. 693

∴ The correct answer is Rs. 693.

Additional Information

Profit and Loss Basics

Profit occurs when the Selling Price (SP) is greater than the Cost Price (CP). Thus, Profit = SP − CP. Conversely, a loss happens when CP is greater than SP.

Profit Percentage Base

Profit and loss percentages are always calculated on the Cost Price (CP) unless the question specifically mentions calculating it on the Selling Price. Formula: Profit% = (Profit ÷ CP) × 100.

Direct Selling Price Formula

When the cost price and profit percentage are known, the selling price can be directly calculated using the multiplier formula: SP = CP × (100 + Profit%) ÷ 100.

The Correct Answer is “BIMSTEC – Prosperous, Resilient and Open”.

In News

• PM Modi to visit Thailand for BIMSTEC summit.

Key Points

• Prime Minister Narendra Modi will embark on a two-day visit to Thailand.
• This will be the Prime Minister’s third visit to Thailand after 2016 and 2019.
• The theme of the 6^th BIMSTEC Summit, to be held this Friday, is “BIMSTEC – Prosperous, Resilient and Open.”
• The Bangkok Vision 2030 will be adopted at the Summit, and the Report of the BIMSTEC Eminent Persons’ Group will also be endorsed.
• Following the BIMSTEC Summit, Prime Minister Modi will travel to Sri Lanka from the 4^th to the 6^th of April for a state visit at the invitation of Sri Lankan President Anura Kumara Disanayake.

The given word is

TEACHERMATE

Now, check from the options which word cannot be formed using the given word.

1) RACTAER

⇒ TEACHERMATE

The word RACTAER cannot be formed from the given word because in TEACHERMATE only one R is present but in RACTAER there are two R.

So, RACTAER can not be formed from TEACHERMATE.

2) EATMEAR

⇒ TEACHERMATE

The word EATMEAR can be formed from the given word.

3) EARTAHM

⇒ TEACHERMATE

The word EARTAHM can be formed from the given word.

4) REAMACH

⇒ TEACHERMATE

The word REAMACH can be formed from the given word.

Therefore, the word that cannot be formed from the given word is RACTAER.

Hence, the correct answer is RACTAER.

Given:

A person borrowed some money on simple interest. After 4 years. he returned \(\frac{9}{5}\) of the money to the lender.

Formula used:

Simple interest = P × R × T / 100 [ P = principal, R = rate of interest, T = time]

Calculation:

Let,R = rate of interest 

Principa is = P

The simple interest got by the person is  

⇒ 9P/5 - P = 4P/5

As per the formula,

⇒ 4P/5 = P × 4 × R / 100

⇒ R = 20%

∴ The correct option is 4

The correct answer is Azerbaijan.

Key Points

• The COP29 Declaration on Enhanced Climate Action in Tourism was launched by the COP29 Presidency under Azerbaijan's leadership.
• This was the first time tourism was included in the UN Climate Change COP agenda, with the declaration aiming to transform the tourism sector into a climate-resilient, low-carbon industry.
• Azerbaijan's role in advocating for tourism's inclusion in climate discussions was a significant milestone, supporting sustainable practices in the tourism sector.
• Azerbaijan's commitment is evident in its partnership with the World Travel and Tourism Council and in promoting initiatives like Sustainable Aviation Fuel (SAF) in the tourism sector.

Additional Information

• The COP29 presidency in Azerbaijan marked the historic inclusion of tourism in climate discussions, aiming for a low-carbon and climate-resilient tourism sector.
• Azerbaijan’s involvement is part of a broader strategy to promote sustainable tourism, with a roadmap guiding the industry towards emission reduction across all tourism subsectors, from accommodation to aviation.
• The inclusion of tourism in COP29 aligns with global climate goals, and efforts like the Net Zero Roadmap and Sustainable Aviation Fuel (SAF) are key to reducing the sector's carbon footprint.
• The declaration aims to tackle global sustainability issues by transforming tourism into a responsible industry, reducing its environmental impact, and enhancing economic development through sustainable practices.

• Given:

Mr. Thaddeus D’Souza

Flat No. 816, ‘C’ Wing,

Trinity Housing Society,

Gymkhana Road, Virar West,

Thane, Maharashtra

• To find: Exactly same address

Explanation:

• As can be seen in the above table, only option 1 is exactly same as the given address.

Hence, option 1 is the correct answer.

Mistake Points

• The question is about finding the same address.
• DO NOT try to find a different address.
• Among the given options, options 2, 3, and 4 have mistakes in the address.
• Only option 1 does not have any error.

Given:

Increase in population = 8%

Present population = 40,000

Formula used:

New population = Present population × [(100 + increase %)/100]ⁿ

Where, n → Number of years

Calculation:

New population = 40,000 × [(100 + 8)/100]²

⇒ 40,000 × (108/100) × (108/100)

⇒ 4 × 108 × 108

⇒ 46656

∴ The population of the village after 2 years is 46656

The Correct Answer is ​Brasilia, Brazil.

In News

• Union Minister Shivraj Singh Chouhan to attend 15^th BRICS Agriculture Ministers Meeting at Brasilia, Brazil.

Key Points

• Shivraj Singh Chouhan, Union Minister for Agriculture & Farmers' Welfare and Rural Development, is leading the Indian delegation to the 15^th BRICS Agriculture Ministers' Meeting (AMM) in Brasilia, Brazil on April 17, 2025.
• The theme of the 15^th BRICS AMM is “Promoting Inclusive and Sustainable Agriculture through Cooperation, Innovation, and Equitable Trade among BRICS Countries”.
• Agriculture Ministers and senior officials from BRICS countries, including:
• Brazil, Russia, India, China, South Africa, and others like Saudi Arabia, Egypt, UAE, Ethiopia, Indonesia, Iran are expected to attend.
• During the visit, Chouhan will hold bilateral meetings with key Brazilian counterparts:
• Carlos Henrique Baqueta Fávaro, Minister of Agriculture and Livestock
• Luiz Paulo Teixeira, Minister of Agrarian Development and Family Farming
• Focus of meetings will be on enhancing India-Brazil collaboration in agriculture, agri-technology, rural development, and food security.

Bodmas Table:

 

Given: 812 + 58 – 65 + 26 – 2 = ?

After substitution the symbols:

812 ÷ 58 × 65 ÷ 26 × 2 = ?

⇒ 14 × 2.5 × 2 = ?

⇒ 70.

Hence, the correct answer is "70".

Given:

Speed while going to college = 5 km/h.

Speed while returning = 4 km/h.

Total time taken = 9 hours.

Formula Used:

Distance = Speed × Time.

For combined trips with different speeds, use the relationship between distance, speed, and time to set up an equation.

Calculation:

Let the distance between the village and the college be d kilometers.

Time taken to go to college = d / 5 hours.

Time taken to return = d / 4 hours.

Total time for both trips = Time to go + Time to return = 9 hours.

Setting up the equation:

(d / 5) + (d / 4) = 9

To solve for d, find a common denominator and solve the equation:

(4d + 5d) / 20 = 9

9d = 180

d = 180 / 9

d = 20 kilometers.

Therefore, the distance between the village and the college is 20 kilometers.

The correct answer is Wetlands for Life.

In News

• The International Film Festival and Forum on Environment and Wildlife, Vatavaran, was inaugurated with the theme "Wetlands for Life."

Key Points

• The festival aims to raise awareness and promote the conservation of wetlands.
• Around 6% of Indians depend on wetlands for their livelihoods, highlighting their importance.
• The event encourages discussions on significant environmental issues.
• Bilateral cooperation between India and Germany has been successful in wetland conservation.

Additional Information

• Wetlands
• Ecological systems that provide numerous benefits including water purification, flood control, and habitat for wildlife.
• Support livelihoods for millions of people through fishing, agriculture, and tourism.
• Vatavaran
• An international film festival focusing on environmental and wildlife issues.
• Uses film as a medium to engage the public and raise awareness about conservation efforts.

Option 1) Shoot the criminal's leg so that he can't run any further and you can catch him.  (Incorrect): Shooting an unarmed, fleeing suspect violates police guidelines on proportional force. Leg shots are not a safe alternative; they carry a high risk of hitting the femoral artery, which can cause fatal bleeding or permanent injury.

​Option 2 Take down the criminal and claim it under an encounter.(Incorrect): Using deadly force (torso shots) is illegal when there is no immediate threat to life. Fleeing to evade arrest does not justify execution.

Option 3 Follow the criminal until you catch him. (Incorrect): Leaving the van unattended violates procedure. Chasing without informing the control room leaves you isolated and without backup.

Option 4 Call the headquarters and inform them of his escape. (Correct): This balances immediate action with proper protocol. It secures the van, initiates a foot chase, and instantly uses the police radio network to cordon off the open field for a safe, non-lethal recapture.

Hence, the correct answer is "Option 4".

Shortcut Trick

Direct formula for height when TSA, length (l), and breadth (b) are given:

Height = (TSA ÷ 2 − l × b) ÷ (l + b)

Height = (4200 ÷ 2 − 15 × 16) ÷ (15 + 16)

Height = (2100 − 240) ÷ 31 = 1860 ÷ 31 = 60

∴ The correct answer is 60 cm.

Alternate Method

Given:

Total Surface Area (TSA) = 4200 cm²

Length (l) = 15 cm

Breadth (b) = 16 cm

Formula Used:

TSA of a cuboid = 2(l × b + b × h + h × l)

Calculations:

⇒ 4200 = 2(15 × 16 + 16 × h + h × 15)

⇒ 2100 = 240 + 16h + 15h

⇒ 2100 = 240 + 31h

⇒ 31h = 2100 − 240

⇒ 31h = 1860

⇒ h = 1860 ÷ 31 = 60

∴ The correct answer is 60 cm.

Additional Information

Volume of a Cuboid

The space occupied by the cuboid is calculated as: Volume = l × b × h

Lateral Surface Area

The area of the four side walls excluding top and bottom: LSA = 2h(l + b)

Length of Diagonal

The longest rod that can be placed inside a cuboid: Diagonal = √(l² + b² + h²)

Number of Days from 02/04/2021 to 22/05/2021

Number of Days from 02/04/2021 to 02/05/2021 → 30 (Count from 03/04/2021)

Number of Days from 02/05/2021 to 22/05/2021 → 20 (Count from 03/05/2021)

Number of weeks → 50 days = 7 weeks and 1 day.

So, 21^st of next month is Friday, and 22^nd of the next month is Saturday.

Hence, Saturday is the correct answer.

Shortcut Trick

Volume of Sphere = Volume of Cylinder (Wire)

4/3 × π × r_s³ = π × r_w² × h

4/3 × 6 × 6 × 6 = 8 × 8 × h

4 × 2 × 36 = 64 × h ⇒ 288 = 64 × h

h = 288 ÷ 64 = 4.5 cm

∴ The correct answer is 4.5 cm.

Alternate Method

Given:

Radius of Copper Sphere (r_s) = 6 cm

Radius of Wire (r_w) = 8 cm

Formula Used:

Volume of Sphere = 4/3 × π × r³

Volume of Cylinder = π × r² × h

Calculations:

⇒ Volume of Sphere = 4/3 × π × (6)³

⇒ Volume of Sphere = 4/3 × π × 216 = 288π cm³

⇒ Volume of Wire = π × (8)² × h = 64πh cm³

⇒ Since the sphere is melted to form a wire, their volumes are equal.

⇒ 288π = 64πh

⇒ h = 288 ÷ 64

⇒ h = 4.5 cm

∴ The correct answer is 4.5 cm.

Additional Information

Conservation of Volume

When a solid is melted and recast into another shape, the total volume remains constant, provided there is no wastage.

Surface Area of Sphere

The total surface area of a sphere is given by the formula 4 × π × r².

Cylinder Properties

For a cylinder, the Curved Surface Area (CSA) is 2πrh and the Total Surface Area (TSA) is 2πr(r + h).

The correct answer is option 3) i.e. Bihar.

• This folk dance is performed to please the god of rain, Indra.
• Young ladies and girls of the district perform this dance while offering prayers to the god for good rain and a good crop.
• Some of the other folk dances of Bihar are Jat-Jatin, Kajari, Sohar-Khilouna, Jhumeri, etc.

Let's check each option:

Given, equation: 96 * 21 * 65 * 8 * 2 * 335

1. 96 + 21 - 65 × 8 ÷ 2 = 335 

⇒ L.H.S = 96 + 21 - 65 × 8 ÷ 2

⇒ L.H.S = 96 + 21 - 65 × 4

⇒ L.H.S = 96 + 21 - 260

⇒ L.H.S = 117 - 260

⇒ L.H.S = -143

⇒R.H.S = 335

⇒ L.H.S ≠ R.H.S

2. 96 + 21 × 65 - 8 = 2 ÷ 335 

⇒ L.H.S = 96 + 21 × 65 - 8 

⇒ L.H.S = 96 + 1365 - 8

⇒ L.H.S = 1461 - 8 

⇒ L.H.S = 1453

⇒ R.H.S = 2 ÷ 335

⇒ R.H.S = 0.0060

⇒ L.H.S ≠ R.H.S

3. 96 × 21 + 65 - 8 ÷ 2 = 335

⇒ L.H.S = 96 × 21 + 65 - 8 ÷ 2 

⇒ L.H.S = 96 × 21 + 65 - 4

⇒ L.H.S = 2016 + 65 - 4

⇒ L.H.S = 2081 - 4

⇒ L.H.S = 2077

⇒ R.H.S = 335

⇒ L.H.S ≠ R.HS

4. 96 - 21 + 65 × 8 ÷ 2 = 335

⇒ L.H.S = 96 - 21 + 65 × 8 ÷ 2

⇒ L.H.S = 96 - 21 + 65 × 4

⇒ L.H.S = 96 - 21 + 260

⇒ L.H.S = 356 - 21

⇒ L.H.S = 335

⇒ R.H.S = 335

⇒ L.H.S = R.H.S

 Hence, the correct answer is option 4.

Given:

Area of the shaded region = 17,248 cm2

Sum of radius of concentric circle = 98 cm

Concept:

Area of the shaded region is the difference of the areas of the bigger circle and the smaller circle.

Formula used

Area of circle = \(\pi r^2\)

Calculation:

∵ Area of the shaded region = \(\pi R^2\) - \(\pi r^2\)

⇒ 17,248 = \(\pi (R^2 - r^2)\)

⇒ 17,248 = \(\pi (R - r)(R + r)\)

⇒ 17,248 = \(\pi (R - r) × 98\)

⇒ 17,248 = 22/7 × (R - r) × 98

⇒ R - r = (17,248 × 7)/(22 × 98)

⇒ R - r = 56 cm

∴ R + r + R - r = 98 + 56

⇒ 2R = 154 cm

⇒ R = 77 cm

∴ r = 98 - R

= 98 - 77 

= 21 cm

The correct answer is option 2.

In News

• The Maharashtra government has recently reclaimed the iconic sword of Raghuji Bhosale I, a legendary Maratha warrior and founder of the Nagpur Bhonsle dynasty.

Key Points

• Raghuji Bhosale I (1695–1755) was an important commander in the Maratha army during Chhatrapati Shahu Maharaj's reign. Hence, Option 2 is correct.
• He was bestowed the title ‘Senasahibsubha’ by Chhatrapati Shahu Maharaj in recognition of his bravery and military prowess.
• He played a major role in expanding Maratha influence to Bengal, Odisha, Chhattisgarh, and South India.

Additional Information

• The Nagpur Bhonsle dynasty, founded by Raghuji Bhosale I, became one of the key ruling Maratha families alongside the Peshwas, Holkars, Gaikwads, and Scindias.
• The region under the Nagpur Bhosales was rich in iron and copper, which contributed to their reputation for high-quality weapon craftsmanship.

The logic followed here is:

From option 1:-

Add 4 in 1^st letter we get 2^nd letter, add 7 in 2^nd letter we get 3^rd letter, subtract 4 in 3^rd letter we get 4^th letter.

From option 2:-

Add 4 in 1^st letter we get 2^nd letter, add 11 in 2^nd letter we get 3^rd letter, subtract 4 in 3^rd letter we get 4^th letter.

From option 3:-

Add 4 in 1^st letter we get 2^nd letter, add 7 in 2^nd letter we get 3^rd letter, subtract 4 in 3^rd letter we get 4^th letter.

From option 4:-

Add 4 in 1^st letter we get 2^nd letter, add 7 in 2^nd letter we get 3^rd letter, subtract 4 in 3^rd letter we get 4^th letter.

Option 2 is different from other.

Hence, "option 2" is the correct answer.

Given:

The ratio of the present ages of Rani and Rohan is 3 ∶ 4.

After 3 years their ratio = 4 ∶ 5.

Calculation:

Let the present age of Rani be 3x

And the present age of Rohan be 4x

Then, \({3x + 3 \over 4x + 3} = {4\over 5}\) 

⇒ 15x + 15 = 16x + 12

⇒ x = 3

Present age of Rani = 3x = 3 × 3 = 9

Her age after 24 years = 9 + 24 = 33 years

And the present age of Rohan = 4x = 4 × 3 = 12

His age after 24 years = 12 + 24 = 36 years

The ratio of their ages after 24 years = 33: 36 

⇒ 11: 12

Hence, the correct answer is 11: 12.

Alternate Method

⇒ (4 × 4) units - (5 × 3) units = (5 × 3) - (3 × 4)  

⇒ 16 units - 15 units = 15 - 12 

⇒ 1 unit = 3

Thus, the present age of Rani ⇒ 3 × 3 = 9 years

Her age after 24 years ⇒ 9 + 24 = 33 years

And the present age of Rohan ⇒ 4 × 3 = 12 years 

His age after 24 years ⇒ 12 + 24 = 36

The ratio of their ages after 24 years ⇒ 33: 36 = 11: 12

Hence, the correct answer is 11: 12.

The correct answer is lysosomes.

Key Points

• Lysosomes
• These are membrane bound vesicular structures formed by the process of packaging in the golgi apparatus.
• The isolated lysosomal vesicles have been found to be very rich in almost all types of hydrolytic enzymes (hydrolases – lipases, proteases, carbohydrases) optimally active at the acidic pH.
• These enzymes are capable of digesting carbohydrates, proteins, lipids, and nucleic acids.

Important Points

• Vacuoles
• The vacuole is the membrane-bound space found in the cytoplasm.
• It contains water, sap, excretory product and other materials not useful for the cell.
• The vacuole is bound by a single membrane called tonoplast.
• In plant cells, the vacuoles can occupy up to 90% of the volume of the cell.
• Mitochondria
• It is sausage-shaped or cylindrical having a diameter of 0.2-1.0µm (average 0.5µm) and length 1.0-4.1µm.
• It is called the powerhouse of the cell.
• Each mitochondrion is a double membrane-bound structure with the outer membrane and the inner membrane dividing its lumen distinctly into two aqueous compartments.
• The outer compartment and the inner compartment.
• The inner compartment is filled with a dense homogeneous substance called the matrix.
• The outer membrane forms the continuous limiting boundary of the organelle.
• Ribosomes
• Ribosomes are made up of RNA and proteins.
• The ribosomes, which are present in all active cells, are the sites of protein manufacture.
• In prokaryotes, ribosomes are associated with the plasma membrane of the cell.

Given:

Alert : Vigilant: : Dissipate:?

Alert: Vigilant →

Alert → An attitude of vigilance, readiness, or caution, as before an expected attack.

Similarly,

Dissipate: ? →

Dissipate → To spend or use wastefully or extravagantly; squander.

Here**, '**Dissipate: Squander' is correct as per the given information.

Hence, the correct answer is "Squander".

Shortcut Trick

Total capacity of bucket = LCM(4, 5) = 20 units.

Filling efficiency = 20 ÷ 4 = 5 units/min.

Net efficiency (Fill − Hole) = 20 ÷ 5 = 4 units/min.

Hole efficiency = 5 − 4 = 1 unit/min.

Time to empty = 20 ÷ 1 = 20 min.

∴ The correct answer is 20 min.

Alternate Method

Given: Time taken to fill = 4 min, Time taken with hole = 5 min.

Formula Used: Total Work = Efficiency × Time | Efficiency of Hole = Pipe efficiency − Net efficiency.

⇒ Let the total capacity of the bucket be the LCM of 4 and 5.

⇒ Total Capacity = 20 units.

⇒ Efficiency of the filling pipe = 20 ÷ 4 = 5 units/min.

⇒ Combined efficiency of pipe and hole = 20 ÷ 5 = 4 units/min.

⇒ Efficiency of the hole = 5 − 4 = 1 unit/min (Outflow).

⇒ Time required by the hole to empty the full bucket = Total Capacity ÷ Hole Efficiency

⇒ Time = 20 ÷ 1 = 20 min.

∴ The correct answer is 20 min.

Additional Information

Inlet and Outlet Pipes

Inlet pipes add water (positive efficiency) and outlet pipes (leaks/holes) remove water (negative efficiency).

Direct Formula for Leakage

If a pipe fills in X hours and with a leak it takes Y hours, the leak empties the tank in (X × Y) ÷ (Y − X) hours.

Work and Time Relation

Efficiency is inversely proportional to time taken when the total work (tank capacity) remains constant.

The correct answer is option 1.

Key Points

• The Harappans are believed to have worshipped a proto-Shiva figure, identified as "Pashupati" based on certain seals. Hence, option 1 is correct.
• Important Fact: The Pashupati seal found at Mohenjo-daro is one of the most iconic Harappan artifacts, showing a figure surrounded by animals.

Option(1) is correct.

Argument I: Yes, we should not show bias to particular sports items: We should respect all games, every sports item has its importance, So Argument I is strong,

Argument II: No, we should choose a few and concentrate only on them so that we can excel in them: We should give equal importance to every sport so Argument II is not strong.

Hence, the correct answer is an option(1)i.e., Argument I is strong.

Given:

Expense for groceries = 12% × income

Expense for medicines = 8% × income

Expense for school fee = 20% × income

Remaining income = Rs.36000

Calculation:

Total expenses = 12 + 8 + 20 = 40%

According to the question:

⇒ 60% = 36000

⇒ 100% =  {36000 × 100}/60

Income of the person = 60000

∴ The correct answer is 60000.

The correct answer is 1398.

• In 1398, Timur ruler of Central Asia invaded India aiming to destroy Hindu kings and rulers.

Key Points

• He attacked the Delhi Sultanate which Muhammad Shah Tughlaq of the Tughlaq dynasty was ruling.
• His victory in Delhi demonstrated his destructive qualities.
• His journey started from Samarkand; crossing the Sindh river and entered Punjab.
• He is remembered as the epitome of cruelty.
• He brutally looted the villages through which he passed, killing people and dishonoring women so the people got their daughters and sisters married at very early ages.

BODMAS Table:

Given equation: 42 + 16 ÷ 7 - 36 × 16 = 76

Let's check each option by interchanging the signs,

1) + and -

→ 42 - 16 ÷ 7 + 36 × 16 = 76

→ 42 - 2.29 + 36 × 16 = 76

→ 42 - 2.29 + 576 = 76

→ 618 - 2.29 = 76

→ 615.71 ≠ 76

→ LHS ≠ RHS.

2) ÷ and ×

→ 42 + 16 × 7 - 36 ÷ 16 = 76

→ 42 + 16 × 7 - 2.25 = 76

→ 42 + 112 - 2.25 = 76

→ 154 - 2.25 = 76

→ 151.75 ≠ 76

→ LHS ≠ RHS.

3) × and +

→ 42 × 16 ÷ 7 - 36 + 16 = 76

→ 96 - 36 + 16 = 76

→ 112 – 36 = 76

→ 76 = 76

→ LHS = RHS.

4) ÷ and +

→ 42 ÷ 16 + 7 - 36 × 16 = 76

→ 2.625 + 7 - 36 × 16 = 76

→ 2.625 + 7 - 576 = 76

→ 9.625 - 576 = 76

→ -566.375 ≠ 76

→ LHS ≠ RHS.

Here, we can see that only 'Option 3' satisfies the equation.

Hence, the correct answer is "Option 3".

Shortcut Trick

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

Given sec θ + tan θ = 5, then sec θ − tan θ = 1/5.

Subtracting the two equations: 2 tan θ = 5 − 1/5 = 24/5.

⇒ tan θ = 12/5.

∴ The correct answer is 12/5.

Alternate Method

Given: sec θ + tan θ = 5

Formula Used: sec² θ − tan² θ = 1

⇒ (sec θ + tan θ)(sec θ − tan θ) = 1

⇒ 5 × (sec θ − tan θ) = 1

⇒ sec θ − tan θ = 1/5

Let sec θ + tan θ = 5 be Equation (1) and sec θ − tan θ = 0.2 be Equation (2).

Subtracting Eq(2) from Eq(1):

⇒ (sec θ + tan θ) − (sec θ − tan θ) = 5 − 1/5

⇒ 2 tan θ = 24/5

⇒ tan θ = 24 / (5 × 2)

⇒ tan θ = 12/5

∴ The correct answer is 12/5.

Additional Information

Trigonometric Identity

The identity 1 + tan² θ = sec² θ is a fundamental relation derived from the Pythagorean theorem.

Cosecant and Cotangent Identity

Similarly, cosec² θ − cot² θ = 1. If cosec θ + cot θ = x, then cosec θ − cot θ = 1/x.

Pythagorean Triplets

In this case, since tan θ = 12/5 (P/B), the hypotenuse H is √(12² + 5²) = 13. Thus (5, 12, 13) is the triplet.

The correct answer is cytokinesis

Key Points

• Cytokinesis is the process during cell division where the cytoplasm of a parental cell is divided between two daughter cells.
• The formation of the phragmoplast occurs during cytokinesis in plant cells.
• The phragmoplast is a structure that serves as a scaffold for cell plate assembly and subsequent formation of a new cell wall separating the two daughter cells.
• It is essential for the successful completion of cell division in plants, ensuring that each daughter cell receives the necessary cellular components.

Additional Information

• Cell division consists of two main processes: mitosis (karyokinesis) and cytokinesis.
• Mitosis is the division of the nucleus, whereas cytokinesis is the division of the cytoplasm.
• In animal cells, cytokinesis occurs through the formation of a cleavage furrow that pinches the cell into two.
• In plant cells, the phragmoplast guides the formation of a cell plate, which eventually develops into a separating cell wall.
• The G0 phase is a resting phase where the cell is not actively preparing to divide.
• The S phase is the part of the cell cycle where DNA replication occurs.

The correct answer is "option(3)".

 

• Qualities projected in this situation: (Effective Intelligence, Social Adaptability, Group Influencing Ability, Determination and Power of Expression)

Key Points 

 Checklist for attempting SRT Questions:

1. Read the question and options carefully

2. Look for an option that is optimistic, realistic, and reflects officer-like qualities.

3. Do not skip any questions.

4. Relegate the negative sentences and choose the most logical option among the remaining. As time is an important factor, your thinking ability should be swift.

5. Read quickly and be logical.

Additional Information

Given : 

\(\rm \left(3y-\frac{3}{y}\right)=5 \)

Formula Used : 

(a - b)² = a² + b² - 2ab

Calculation : 

⇒ y - 1/y = 5/3

⇒ y² + 1/y² - 2 = 25/9

⇒ y² + 1/y² = 25/9 + 2

⇒ y2 + 1/y2 = (25 +18)/9

⇒ y2 + 1/y2 = 43/9

∴ The correct answer is 43/9.

The correct answer is homologous. 

Concept:

• Organic evolution: Evolution is the very gradual process of development of living beings from single-celled organisms to organisms with complex structured organs performing different metabolic processes.
• The discovery of analogous organs and homologous organs are evidence for the process of evolution.

Analogous organs:

• These are defined as the organs of different animals having different structures but perform the same functions.
• Examples:
• Wings of insects and birds.
• Sweet potatoes and potatoes.
• The tailfin of a lobster and the flukes of a whale.

Homologous organs:

• These are defined as the organs of different animals having similar structures but differ in their functions.
• Examples:
• Forelimbs of frog, man, and the flippers of the whale.
• The arm of a human and the leg of dogs, bulls.
• A bat's wing and a whale's flipper.
• The leg of a dog and the flipper of a dolphin or whale.

​

 

​These similarities in the organs laid down the formation of the theory of evolution. 

Explanation:

• The wings of the bat and flippers of whales are having similar structures.
• But bats use it for flying while whales use it for swimming in the sea.
• This change happens due to their different habitat and environment.
• The organs get evolved according to the need.
• But, the common structure in organs can clearly be seen.

So, the correct option is homologous.

 

Note:

Multiple of 400 years i.e. 800, 1200, 1600, 2000 have 0 odd days.

Calculating leap year: For Finding the number of leap year (1 - 99) years, divide the number of years by 4 and the quotient will be the number of leap years.

Code for weekdays:

​

2012 = we find out the odd days (the nearest leap century year + the nearest century year + completing year) = 2000 + 11 year + year 2012

• In 2000 year the odd days = 0
• In 11 years, odd days = 2 leap year & 9 normal year
• 2 leap year = 4 odd day
• 9 normal year = 9 odd day ÷ 7 = 2 odd days
• Odd days in 1 January to 22 February:
• In 2012, the number of days up to 22 February = 31 (Jan) + 22 (Feb) = 53 / 7 = 4 odd days.
• Total = 0 + 4 + 2 + 4 = 10 days = 3 odd day
• 3 is the code for Wednesday.

Hence, Wednesday​ is the correct answer.

Given:

Speed of the car = 80 km/hr

Time taken to complete the journey = 9 hours

Speed of the car for the same distance = 60 km/hr

Formula Used:

Distance = Speed × Time

Time = Distance / Speed

Calculation:

Distance travelled = 80 km/hr × 9 hrs

Distance travelled = 720 km

Time required to travel 720 km at 60 km/hr

⇒ Time = 720 km / 60 km/hr

⇒ Time = 12 hours

The correct answer is option 3.

The correct answer is Mohammad Bin Tughlaq.

Key Points

• Abdullah Shah Changal is one of many Muslim saints who was associated with the Dhar district of Madhya Pradesh.
• He came to the city as religious preaching teachers during the reign of Muslim rulers, especially the reign of the Malwa Sultans in the 15^th and 16^th centuries.
• Muhammad Bin Tughlaq issued copper coins instead of silver ones.
• Tughlaq's silver coin was named Adi.
• He started the circulation of copper and brass coins as the token currency which had the same value as gold or silver coins in 1330-32 CE.
• In 1330, after his unsuccessful campaign in Devagiri, he issued a token currency.

Additional Information

Important Points

The logic followed here is:

Logic: Taste association.

Here,

Sugar : Sweet → Sugar is associated with Sweet taste.

Similarly,

Habanero : Spicy → Habanero is associated with Spicy taste.

Hence, the correct answer is "Option 4".

Calculation:

Let, the total time required in days = m

⇒ \(\dfrac{1}{m}\) = \(\dfrac{1}{8} + \dfrac{1}{16} + \dfrac{1}{12}\)

⇒ \(\dfrac{1}{m}\) = \(\dfrac{6 + 3 + 4}{48}\) = \(\dfrac{13}{48}\)

⇒ Half work time = \(\dfrac{m}{2} = \dfrac{48}{13 \times 2}\)

⇒ Required Time = 1\(\dfrac{11}{13}\) days

∴ The Half work completion would require 1\(\dfrac{11}{13}\) days.

Alternate Method 

 

In the question, it is asked that → If all three work together, then in how many days HALF OF THE WORK will be completed?

 

Let the total work be 48 units (LCM of 8, 16 and 12)

 

Thus, Half Work = 24 units

 

⇒ Efficiency of Ram = 48/8 = 6 units/day

 

⇒ Efficiency of Rahim = 48/16 = 3 units/day

 

⇒ Efficiency of Shyam = 48/12 = 4 units/day

 

Their combined efficiency = 13

 

Thus the time required = 24/13 = \(1 \frac{11}{13}\) days

The correct answer is only c.​

Key Points

• Tantya Bhil was born in 1842 in East Nimar (Khandwa district), Madhya Pradesh.
• He was also affectionately called by the name of Tantya Mama.
• He participated in the great revolt of 1857 at the age of 15.
• He was excellent in Guerilla warfare.
• He was known as Robin hood of India.
• He was arrested by the British because of the betrayal of some trusted people.
• He was hanged on 4 December 1889.

The number of days between 5 June and 11 December is (25 + 31 + 31 + 30 + 31 + 30 +11) = 189 days.

A day repeats itself on the seventh day.

Thus, no. of weeks = 189 ÷ 7 = 27 weeks.

Hence, Tushar's birthday is on Monday.

Given:

\(\left( 2 \frac{4}{5} \times 5 \frac{1}{7} \times 4 \frac{1}{6} \right) \div \frac{2}{3}\)

Calculation:

\(\left( 2 \frac{4}{5} \times 5 \frac{1}{7} \times 4 \frac{1}{6} \right) \div \frac{2}{3}\)

⇒ (14/5 × 36/7 × 25/6) × 3/2

⇒ 60 × 3/2 = 90

∴ ? = 90

The correct answer is Jasprit Bumrah.

In News

• L&T Finance Ltd. names Jasprit Bumrah as their brand ambassador.

Key Points

• Jasprit Bumrah, an iconic Indian cricketer, has been appointed as the brand ambassador for L&T Finance Ltd. (LTF).
• The partnership aims to boost brand visibility through ATL and BTL marketing campaigns.
• Bumrah’s disciplined and relatable nature makes him an ideal representative for LTF, aligning with their core values of excellence and customer-centricity.
• LTF is a leading NBFC providing financial services across rural and urban India, with a significant market presence.

Additional Information

• L&T Finance Ltd. (LTF)
• Founded in - 1994
• HQ - Mumbai
• ​RISE Worldwide
• Facilitator of Bumrah's partnership with LTF
• Specializes in brand extension and value creation

When evaluating the strengths of the arguments related to debarring individuals with higher educational qualifications from seeking jobs than the optimum requirements, we consider the relevance, direct impact, and principles involved in employment rights and workplace dynamics.

Arguments I. The argument that it will further aggravate the problem of educated unemployment is strong. Barring overly qualified individuals does not solve the root causes of unemployment and restricts the job market further, making it a pertinent issue worth considering.

Arguments II. Claiming it creates complexes among employees and affects work adversely is a more subjective argument. While workplace dynamics and employee morale are important, the assumption that higher qualifications automatically lead to negative outcomes is not universally valid. This argument can be considered weaker as it generalizes the impact without accounting for variable organizational cultures and individual differences.

Arguments III. The argument that debarring individuals goes against the basic rights of the individuals is strong. Employment should ideally be based on merit and fit for the role, and restricting opportunities based on qualifications above a certain level can be seen as discriminatory, thus impacting fundamental rights to work.

Arguments IV. Asserting that this practice will increase productivity is a weak argument without specific context. Productivity is influenced by many factors, including but not limited to educational qualifications. It presupposes that individuals with higher qualifications do not contribute to or may hamper productivity, which is not necessarily true across different jobs and industries.

Note:- Therefore, the strong arguments are those recognizing the potential infringement on basic rights and highlighting broader societal implications (Only I and III). Hence, if choosing based on the given options where none reflect this exact combination, the closest would be acknowledging individual rights as a stronger principle:

Only III is strong.

Hence, the correct answer is "Only III is strong".

Shortcut Trick 

MP = Rs. 2200

Discount % = 14%

⇒ 100 unit = Rs. 2200

⇒ 1 unit = Rs. 22

Now, Real SP = 86 × 22 = Rs. 1892

∴ The selling price of the machine is Rs. 1892.

Alternate Method

Given:

MP = Rs. 2200

Discount % = 14%

Formula:

SP = MP - Discount

Discount % = Discount/MP × 100

Calculation:

Let, Discount = D

According to the question,

⇒ 14 = D/2200 × 100

⇒ 14/100 = D/2200

⇒ D = 14/100 × 2200

⇒ D = 14 × 22 = Rs. 308

Now, SP = 2200 - 308 = Rs.1892

∴ The selling price of the machine is Rs. 1892.

The correct answer is Sir Cyril Radcliffe.

Key Points

• After the partition of India on 17 August 1947, the "Radcliffe Line" became the border between India and Pakistan.
• The line was determined by the Border Commission headed by Sir Cyril Radcliffe.

Additional Information

• The Cripps Mission of 1942 was led by Sir Stafford Cripps alone, aiming to gain Indian support during World War II.

The Cabinet Mission of 1946 included Pethick Lawrence, Stafford Cripps, and A.V. Alexander, and was focused on planning for the Indian independence.

1) Ratels → EXTRATERRESTRIAL → can be formed

2. Rational → EXTRATERRESTRIAL → cannot be formed because O and N are missing.

3) Tarsier → EXTRATERRESTRIAL → can be formed

4) Steatite → EXTRATERRESTRIAL → can be formed

Rational cannot be formed from the letters of the given word.

Hence, **"**Rational" is the correct answer.

Shortcut Trick

Total failed in at least one subject = Failed in Maths + Failed in Science − Failed in Both

⇒ Total failed % = 25% + 35% − 15% = 45%

⇒ Passed in both subjects = 100% − Total failed %

⇒ Passed in both subjects = 100% − 45% = 55%

∴ The correct answer is 55%.

Alternate Method

Given:

Percentage of students who failed in Maths, n(M) = 25%

Percentage of students who failed in Science, n(S) = 35%

Percentage of students who failed in both, n(M ∩ S) = 15%

Universal Set (100%)

Maths (25%)
Science (35%)

10%
15%
20%

Passed Both Subjects = 55%

Formula Used:

n(A ∪ B) = n(A) + n(B) − n(A ∩ B)

Percentage passed in both = 100% − n(A ∪ B)

Calculations:

⇒ Total percentage of students who failed in at least one subject = n(M ∪ S)

⇒ n(M ∪ S) = n(M) + n(S) − n(M ∩ S)

⇒ n(M ∪ S) = 25% + 35% − 15%

⇒ n(M ∪ S) = 60% − 15% = 45%

⇒ Percentage of students who passed in both subjects = 100% − n(M ∪ S)

⇒ Percentage of students who passed in both subjects = 100% − 45% = 55%

∴ The correct answer is 55%.

Additional Information

Union of Two Sets

The formula for finding the total number of distinct elements in two overlapping sets is n(A ∪ B) = n(A) + n(B) − n(A ∩ B).

De Morgan's Laws

The complement of the union of two sets is equal to the intersection of their complements: (A ∪ B)' = A' ∩ B'. In this context, students who did not fail any subject (A ∪ B)' are exactly those who passed both (A' ∩ B').

Union of Three Sets

For three sets, the extended principle of inclusion-exclusion applies: n(A ∪ B ∪ C) = n(A) + n(B) + n(C) − n(A ∩ B) − n(B ∩ C) − n(A ∩ C) + n(A ∩ B ∩ C).

The correct answer is Narmada River.

• Hoshangabad is located on the south bank of the Narmada River.
• Hoshangabad also known as Narmadapuram.

Key Points

• Hoshangabad is named after Hoshang Shah, the first ruler of Malwa.
• It was part of the Nerbudda (Narmada) Division of the Central Provinces and Berar, which became the state of Madhya Bharat (later Madhya Pradesh) after India's independence in 1947.
• The city is famous for its beautiful ghats along the banks of the Narmada river, Sethani ghat is a major attraction.
• It is about 7 km downstream from the confluence of Tawa and Narmada rivers.
• Hoshangabad has an average literacy rate of 87.01%.
• Male literacy is 91.79%, and Female literacy is 81.79%.
• The economy largely depends on agriculture.
• Hoshangabad is one of the largest producers of Soya Bean.

Pattern is as follows:

5² + 12² = 13²

Adding square of 1^st and 3^rd term gives square of 2^nd term.

15² + 13² ≠ 19²

6² + 8² = 10²

11² + 9² ≠ 15²

13² + 11² ≠ 17²

Hence (6, 10, 8) is the answer.

Given:

Travelled equal distance at 10 km/hr, 20 km/hr, and 6 km/hr speeds

Total time = 19 minutes = 19/60 hours

Formula used: 

Time = Distance/Speed

Calculation:

Let the equal distance be 'x' km

⇒ (x/10) + (x/20) + (x/6) = 19/60

⇒ 19x/60 = 19/60

∴ x = 1

∵ Apurva travels 3 equal distance (x) at different speeds,

Total distance = 3x 

⇒ 3 × 1 = 3 km

The correct answer is Stomata.

Key Points

• Stomata are small openings found on the surface of leaves.
• They play a crucial role in gas exchange, allowing plants to take in carbon dioxide and release oxygen.
• Stomata are also involved in the process of transpiration, which is the loss of water vapor from plants to the atmosphere.
• Each stoma is flanked by two specialized cells known as guard cells that control its opening and closing.
• The opening and closing of stomata help in maintaining water balance and regulating photosynthesis in plants.

 Additional Information

• Vascular bundle
• Vascular bundles are part of the plant's transport system.
• They consist of xylem and phloem tissues, which are responsible for the transport of water, nutrients, and food throughout the plant.
• Vascular bundles are found in the stem, roots, and leaves of plants but are not specific to the epidermis of a leaf.
• Chlorenchyma
• Chlorenchyma is a type of parenchyma tissue in plants that contains chloroplasts.
• It is involved in the process of photosynthesis and is typically found in the mesophyll of leaves.
• Aerenchyma
• Aerenchyma is a type of parenchyma tissue with large air spaces.
• It helps in providing buoyancy and facilitating the exchange of gases in aquatic plants.

We know that: 

In an ordinary year, there are 365 days and on dividing 365 by 7,

• We get remainder = 1 so this extra one day is taken as odd day.

Similarly, in an leap year, there are 366 days and on dividing 366 by 7,

• we get remainder = 2 so this extra two days is taken as odd days.

Thus, the remainder, which we get after dividing the number of days by 7 is considered as odd days.

Given 10^th May of a given year is Monday.

Number of days in month of May = 31 days

Number of days in month of June = 30 days

Number of days in month of July = 31 days

Number of days from 10^th May to 11^th July of the same year = 21 + 30 + 11

∴ Number of days from 10^th May to 11^th July of the same year = 62

The number of odd days from 10^th May to 11^th July = 6

∴ On 10^th May of a given year, it was Monday + 6 = Sunday.

∴ Here, 'Sunday' is day of the week on 11^th July of the same year.

Hence, the correct answer is "Sunday".

Given:

Rate of interest (R) = 10%

Time Duration (N) = 2 years

CI - SI = Rs. 500

Formula Use:

Compound Interest (CI) = P \(({1 + {R\over100}})^N\) - P

Simple Interest (SI) = \({P × N × R} \over 100\)

Where,

P be the Principal

N be the Time Duration

R be the Rate of interest

Calculation:

We have,

CI - SI = Rs. 500

⇒ 500 = P \(({1 + {R\over100}})^N\) - P - \({P × N × R} \over 100\)

⇒ 500 = P [\(({1 + {R\over100}})^N\) - 1 - \({N × R} \over 100\)]

⇒ 500 = P [\(({1 + {10\over100}})^2\) - 1 - \({2 × 10} \over 100\)]

⇒ 500 = P [\(({ {11\over10}})^2\) - 1 - \(1\over5\)]

⇒ 500 = P [\(121\over100\) - 1 - \(1\over5\)]

⇒ 500 = 0.01P

⇒ P = Rs. 50000

∴ The value of principal is Rs. 50000.

Alternate Method

Formula used

(SI - CI) for 2 years = P(R/100)2

P = Principal

R = Rate

Calculation

SI - CI = P(R/100)2

⇒ 500 = P(10/100)2

⇒ 500 = P(1/100)

⇒ P = 50000

∴ The value of principal is Rs. 50000.