Shortcut Trick

The exact value of the marked price (₹517) is a distractor and not needed to find the percentage.

Let the Cost Price (CP) be 100 units.

Marked Price (MP) is 30% above CP ⇒ MP = 130 units.

Profit is 2% on CP ⇒ Selling Price (SP) = 102 units.

Discount = MP − SP = 130 − 102 = 28 units.

Discount % = (28 ÷ 130) × 100 = 21.538% ≈ 21.54%.

∴ The correct answer is 21.54%.

Alternate Method

Given:

Marked Price (MP) = ₹517

Markup % = 30%

Profit % = 2%

Formula Used:

Discount % = [(MP − SP) ÷ MP] × 100

CP = 100a

SP = 102a

MP = 130a

+30% Markup

+2% Profit

Discount = 28a

Discount % = (28a ÷ 130a) × 100 ≈ 21.54%

Calculations:

⇒ Let Cost Price (CP) = 100a.

⇒ Marked Price (MP) = 100a + 30% of 100a = 130a.

⇒ Selling Price (SP) = 100a + 2% of 100a = 102a.

⇒ The given MP is ₹517. Thus, 130a = 517 ⇒ a = 517 ÷ 130.

⇒ Discount = MP − SP = 130a − 102a = 28a.

⇒ Discount % = (Discount ÷ MP) × 100

⇒ Discount % = (28a ÷ 130a) × 100

⇒ Discount % = (28 ÷ 130) × 100 = 280 ÷ 13

⇒ Discount % = 21.538... % ≈ 21.54%

(Note: The multiplier 'a' naturally cancels out, proving the exact marked price value is mathematically unnecessary.)

∴ The correct answer is 21.54%.

Additional Information

Direct Ratio Formula

The relationship between Cost Price (CP) and Marked Price (MP) can be established directly using the formula: CP ÷ MP = (100 − Discount %) ÷ (100 + Profit %).

Successive Discounts

When two successive discounts of a% and b% are given, the equivalent single discount is given by [a + b − (a × b) ÷ 100]%.

Markup Percentage

Markup is the amount added to the Cost Price to set the Marked Price. It is always calculated on the Cost Price: Markup % = [(MP − CP) ÷ CP] × 100.

Given:

Seven people, N, O, P, Q, R, S and T, are sitting in a straight line facing north.

Only two people are sitting to the left of R.

P is sitting to the immediate right of R and immediate left of S.

Q is sitting to the immediate left of O.

Q does not sit at an extreme end of the line. 

T is sitting at one of the ends of the line.

Thus, four people are sitting between O and N.

Hence, the correct answer is "Option 4".

The correct answer is Province.

Key Points

• The term 'Bhukti' in post-Gupta period referred to an administrative division or a province.
• Bhuktis were governed by officers known as 'Uparikas', who were appointed by the king.
• Each Bhukti consisted of multiple 'Vishayas' or districts, which were smaller administrative units.
• The Vishayas were managed by officers called 'Vishayapatis', who reported to the Uparikas of the Bhukti.
• Bhuktis were a key feature of the decentralized administrative structure during the post-Gupta era.

Additional Information

• Uparika: The head of a Bhukti, appointed by the king, who held administrative and judicial authority over the province.
• Vishaya: A sub-division of a Bhukti, equivalent to a district, managed by Vishayapatis.
• Post-Gupta Polity: This period saw a shift towards a more decentralized administrative system, with provinces playing a critical role in governance.
• Decentralization: The post-Gupta administration was characterized by a division of power between central and provincial authorities.
• Gupta Administration: The Gupta era laid the foundation for administrative units like Bhuktis and Vishayas, which continued in post-Gupta polity.

Shortcut Trick

Total Income is considered as 100%. If Expenditure is 45%, Saving is 100% − 45% = 55%.

We are given that 55% corresponds to ₹66,000.

1% → 66,000 ÷ 55 = 1,200

Total Income (100%) = 100 × 1,200 = 1,20,000

∴ The correct answer is ₹1,20,000.

Alternate Method

Total Income (100%)

Expenditure (45%)

Saving (55%) = ₹66,000

100% = ₹1,20,000

Given:

Kiran's expenditure = 45% of his income

Kiran's savings = ₹66,000

Formula Used:

Income = Expenditure + Savings

Calculations:

Let the total income of Kiran be 100%.

⇒ Savings % = Total Income % − Expenditure %

⇒ Savings % = 100% − 45% = 55%

According to the given condition,

⇒ 55% of Income = 66,000

⇒ 1% of Income = 66,000 ÷ 55

⇒ 1% of Income = 1,200

⇒ Total Income (100%) = 1,200 × 100 = 1,20,000

∴ The correct answer is ₹1,20,000.

Additional Information

Income & Expenditure Concept

Income is always the sum of Expenditure and Savings (Income = Expenditure + Savings). If Total Income is assumed to be 100%, then Expenditure % + Savings % = 100%.

Percentage Base Change

When any value is given as a percentage of the total, divide the value by its corresponding percentage to find the 1% value (base unit), then multiply by 100 to get the complete total.

Successive Percentage Change

If an amount undergoes successive changes of x% and y%, the net percentage change is given by the formula: Net Change % = x + y + (x × y) ÷ 100.

The logic followed in this pattern is based on alphabetical shifts between consecutive letters within each cluster.

For 'ECG':                    

For 'SQU':                     

For 'LJN':            

For 'POR':              

 

Thus, the letter-cluster that DOES NOT belong to that group is " POR".

Hence, the correct answer is "Option 4".

Shortcut Trick

Let total work for 1 hall be LCM(3, 7) = 21 units.

Combined efficiency of Varun and Ashish = 21 ÷ 3 = 7 units/day.

Varun's efficiency = 21 ÷ 7 = 3 units/day.

Ashish's efficiency = 7 − 3 = 4 units/day.

Time required for Ashish to paint 4 halls = (4 × 21) ÷ 4 = 21 days.

∴ The correct answer is 21 days.

Alternate Method

Given:

Time taken by Varun and Ashish together to paint 1 hall = 3 days

Time taken by Varun alone to paint 1 hall = 7 days

Formula Used:

Total Work = LCM of individual days

Efficiency = Total Work ÷ Time taken

Total Time = Total Work ÷ Efficiency

Calculations:

⇒ Efficiency of Ashish = Efficiency of (Varun + Ashish) − Efficiency of Varun

⇒ Efficiency of Ashish = 7 − 3 = 4 units/day

⇒ Total work to paint 4 such halls = 4 × 21 = 84 units

⇒ Time taken by Ashish alone to paint 4 halls = Total Work ÷ Efficiency of Ashish

⇒ Time taken by Ashish = 84 ÷ 4 = 21 days

∴ The correct answer is 21 days.

Additional Information

Pipes and Cisterns

Works exactly like Time & Work. Inlet pipes have positive efficiency, while outlet pipes (leaks) have negative efficiency.

Work and Wages

Wages are strictly distributed in the ratio of the total work done by each person. If they work for the same number of days, wages are distributed in the ratio of their efficiencies.

Alternate Days Work

When people work on alternate days, calculate the total work done in one complete cycle (e.g., 2 days for 2 people) and divide the total work by the cycle work to find the number of cycles required.

The correct answer is To measure the vertical temperature profile of the lunar regolith.

Key Points

• The Chandra's Surface Thermophysical Experiment (ChaSTE) is part of India's Chandrayaan-3 mission, specifically designed to study the Moon's surface.
• Its primary objective is to measure the vertical temperature profile of the lunar regolith (the Moon's surface layer composed of soil and loose material).
• ChaSTE uses a temperature probe equipped with 10 sensors to record thermal variations at different depths of the lunar surface.
• This data helps scientists understand the thermal behavior and properties of the lunar soil, which is critical for future lunar exploration and missions.
• The experiment focuses on the Moon's south pole region, which holds unique scientific significance due to its permanently shadowed areas and potential for water ice deposits.

Additional Information

• Lunar Regolith: It refers to the loose, unconsolidated material that covers the solid bedrock on the Moon's surface. It includes dust, soil, and broken rock fragments.
• South Pole Exploration: The Moon's south pole is of great interest because its craters are permanently shadowed, potentially preserving water ice and other volatiles.
• Thermal Properties: Understanding the thermal conductivity and heat capacity of the lunar regolith is crucial for designing equipment and habitats for future lunar missions.
• Chandrayaan-3 Mission: Chandrayaan-3 is India's third lunar exploration mission, developed by ISRO, aimed at demonstrating safe landing and conducting scientific experiments on the Moon's surface.
• Scientific Significance: The data from ChaSTE contributes to broader lunar studies, including surface composition, geological processes, and potential resource utilization for sustainable human presence on the Moon.

Shortcut Trick

Total Interest = Amount − Principal = 2280 − 1200 = 1080

Interest per year = 4% of 1200 = 48

Time = Total Interest ÷ Interest per year = 1080 ÷ 48 = 22.5 years

∴ The correct answer is 22.5 years.

Alternate Method

Principal ₹1200 Amount ₹2280

• SI = ₹1080 Rate = 4% p.a. Time = ? years

Given:

Principal (P) = ₹1,200

Amount (A) = ₹2,280

Rate of Interest (R) = 4% p.a.

Formula Used:

Simple Interest (SI) = A − P

SI = (P × R × T) ÷ 100

Calculation:

⇒ SI = 2280 − 1200 = ₹1,080

⇒ 1080 = (1200 × 4 × T) ÷ 100

⇒ 1080 = 48 × T

⇒ T = 1080 ÷ 48

⇒ T = 22.5 years

∴ The correct answer is 22.5 years.

Additional Information

Simple Interest vs Compound Interest

Simple Interest is calculated only on the principal amount, while Compound Interest is calculated on the principal as well as the accumulated interest from previous periods.

Compound Interest Formula

A = P × (1 + R/100)^T, where A is the Amount, P is Principal, R is Rate, and T is Time.

Rule of 72

It is a quick formula used to estimate the number of years required to double the invested money at a given annual fixed interest rate (Time ≈ 72 ÷ Rate).

Shortcut Trick

For two angles with a given sum and difference, Smaller angle = (Sum − Difference) ÷ 2.

The sum of supplementary angles is always 180°.

⇒ Smaller angle = (180° − 28°) ÷ 2

⇒ Smaller angle = 152° ÷ 2 = 76°

∴ The correct answer is 76°.

Alternate Method

Given:

The two angles are supplementary.

The larger angle is 28° more than the smaller angle.

Concept Used:

The sum of two supplementary angles is always 180°.

x x + 28°

Sum = 180° (Supplementary Angles)

Calculation:

Let the smaller angle be x.

⇒ Larger angle = x + 28°

According to the concept of supplementary angles:

⇒ x + (x + 28°) = 180°

⇒ 2x + 28° = 180°

⇒ 2x = 180° − 28°

⇒ 2x = 152°

⇒ x = 152° ÷ 2

⇒ x = 76°

∴ The correct answer is 76°.

Additional Information

Supplementary Angles

Two angles are supplementary if their measures add up to exactly 180°. They form a straight line when placed adjacent to each other.

Complementary Angles

Two angles are complementary if their combined sum equals exactly 90°, forming a right angle.

Linear Pair Axiom

If a ray stands on a straight line, then the sum of the two adjacent angles so formed is exactly 180°.

Shortcut Trick

Speed of stream = [Distance ÷ 2] × [ (1 ÷ Downstream time) − (1 ÷ Upstream time) ]

⇒ Stream speed = (721 ÷ 2) × [ (1 ÷ 15) − (1 ÷ 42) ]

⇒ Stream speed = 360.5 × [ (42 − 15) ÷ (15 × 42) ]

⇒ Stream speed = 360.5 × (27 ÷ 630) = 360.5 × (3 ÷ 70)

⇒ Stream speed = 1081.5 ÷ 70 = 15.45 km/hr

∴ The correct answer is 15.45 km/hr.

Alternate Method

Given:

Distance (D) = 721 km | Upstream Time (T_u) = 42 hours | Downstream Time (T_d) = 15 hours

Formula Used:

Upstream Speed = Distance ÷ Upstream Time

Downstream Speed = Distance ÷ Downstream Time

Speed of stream = (Downstream Speed − Upstream Speed) ÷ 2

Stream Flow →Upstream: 721 km in 42 hrDownstream: 721 km in 15 hr

Calculations:

⇒ Downstream Speed = 721 ÷ 15 km/hr

⇒ Upstream Speed = 721 ÷ 42 = 103 ÷ 6 km/hr

⇒ Speed of stream = (Downstream Speed − Upstream Speed) ÷ 2

⇒ Speed of stream = (721 ÷ 15 − 103 ÷ 6) ÷ 2

⇒ Speed of stream = (1442 ÷ 30 − 515 ÷ 30) ÷ 2

⇒ Speed of stream = (927 ÷ 30) × (1 ÷ 2)

⇒ Speed of stream = 927 ÷ 60 = 15.45 km/hr

∴ The correct answer is 15.45 km/hr.

Additional Information

Speed of Boat in Still Water

It is calculated as the average of the downstream and upstream speeds: B = (Downstream Speed + Upstream Speed) ÷ 2

Downstream and Upstream Concepts

When a boat goes with the stream, Downstream Speed = Boat Speed + Stream Speed. When going against it, Upstream Speed = Boat Speed − Stream Speed.

Average Speed

If the boat travels equal distances upstream and downstream, the average speed for the whole journey is (2 × U × D) ÷ (U + D), where U and D are upstream and downstream speeds respectively.

The correct answer is Gondophernes.

Key Points

• The Takht-i-Bahi inscription is an important historical record that mentions Gondophernes, a Parthian ruler.
• Gondophernes was the founder of the Indo-Parthian Kingdom, ruling territories in present-day Afghanistan, Pakistan, and northern India during the 1st century CE.
• The inscription is associated with Buddhist monastic complexes in Takht-i-Bahi, located in present-day Pakistan.
• Historical sources suggest Gondophernes was contemporaneous with Saint Thomas, one of the apostles of Jesus Christ, who is believed to have traveled to India.
• Gondophernes' reign is notable for its cultural exchanges, particularly between Greek, Parthian, and Indian traditions.

Additional Information

• Takht-i-Bahi:
• A UNESCO World Heritage Site, Takht-i-Bahi is a Buddhist monastic complex dating back to the 1st century CE.
• It is located in the Mardan District of Khyber Pakhtunkhwa, Pakistan.
• The complex demonstrates significant Greco-Buddhist architectural influences.
• Indo-Parthian Kingdom:
• Gondophernes established the Indo-Parthian Kingdom after the decline of Greco-Bactrian and Indo-Greek rulers.
• The kingdom served as a cultural bridge between the Parthian Empire and Indian subcontinent.
• Parthian Empire:
• The Parthian Empire, also known as Arsacid Empire, existed in ancient Iran and surrounding regions from 247 BCE to 224 CE.
• It was known for its military prowess and cultural integration of Greek, Persian, and Central Asian traditions.
• Saint Thomas in India:
• According to Christian tradition, Saint Thomas traveled to India during Gondophernes’ reign to spread Christianity.
• He is believed to have established Christian communities in South India, particularly in Kerala.

The logic followed here is:

 

Thus, the missing term in the series is 65.

Hence, the correct answer is "Option 3";

Given:

Conditions:

(i) If the first element is a symbol and the last a number, the codes for these two (the first and the last elements) are to be interchanged.

(ii) If the first element is an odd number and the last an even number, the first and last elements are to be coded as ©

(iii) If both the second and third elements are perfect squares, the third element is to be coded as the code for the second element.

Given- 7 2 @ 1 3 &

Rule No. (i) This condition does not apply because the first element (7) is a number, not a symbol.

Rule No. (ii) This condition does not apply because while the first element (7) is an odd number, the last element (&) is a symbol, not an even number.

Rule No. (iii) This condition does not apply because neither the second element (2) nor the third element (@) are perfect squares.

So, the code for  7 2 @ 1 3 & is 

The code for 7 is W.

The code for 2 is A.

The code for @ is Z.

The code for 1 is R.

The code for 3 is T.

The code for & is M.

Thus, '7 2 @ 1 3 &' is code 'W A Z R T M'.

Hence, the correct answer is "Option 2".

BODMAS Rule:

Given the interchange rules:

• ‘+’ and ‘−’ are interchanged.
• ‘×’ and ‘÷’ are interchanged.

Now,

Given e×pression: 1125 × 45 ÷ 39 – 17 + 19

After replacing the symbols with their meanings:

⇒ 1125 ÷ 45 × 39 + 17 − 19

Perform operations according to BODMAS:

⇒ 1125 ÷ 45 × 39 + 17 − 19

⇒ 25 × 39 + 17 − 19

⇒ 975 + 17 − 19

⇒ 992 − 19

⇒ 973

Hence, the correct answer is "Option 4".

Shortcut Trick

Ratio of number of students in the two groups = 12 : 18 = 2 : 3.

Let the assumed average of the whole class be 60.

Deviation of the second group from the assumed average = 62 − 60 = +2.

Total net deviation = 3 × (+2) = +6.

Net average deviation = +6 ÷ (2 + 3) = +6 ÷ 5 = +1.2.

Overall Average = Assumed Average + Net average deviation = 60 + 1.2 = 61.2.

∴ The correct answer is 61.2 marks.

Alternate Method

Given:

Total students in the class = 30

Average score of 12 students = 60

Number of remaining students = 30 − 12 = 18

Average score of the remaining 18 students = 62

Formula Used:

Average = Total Sum of Observations ÷ Total Number of Observations

Avg: 60 n = 12 (Ratio 2)

Avg: 62 n = 18 (Ratio 3)

Overall Avg: 61.2

Distance ∝ 3 units

Distance ∝ 2 units

Calculations:

⇒ Total score of the first 12 students = 12 × 60 = 720

⇒ Total score of the remaining 18 students = 18 × 62 = 1116

⇒ Total score of all 30 students = 720 + 1116 = 1836

⇒ Average score of the class = 1836 ÷ 30

⇒ Average score of the class = 61.2

∴ The correct answer is 61.2 marks.

Additional Information

Weighted Average Method

When combining multiple groups, use the weighted average formula: A_w = (w₁x₁ + w₂x₂) ÷ (w₁ + w₂), where w represents the number of elements and x represents the average of each respective group.

Net Deviation Method

Instead of calculating large sums, pick an assumed average. Calculate the net deviation by multiplying the difference from the assumed average by the number of elements in that group, then distribute this deviation equally across the entire combined group.

Alligation Rule

The distance of the combined average from the individual group averages is inversely proportional to the ratio of their weights (number of entities). In this case, since weights are in ratio 2:3, distances are in ratio 3:2.

The correct answer is Article 43 B.

Key Points

• Article 43 B was added to the Directive Principles of State Policy (DPSP) by the 97th Constitutional Amendment Act, 2011.
• This Article aims to promote voluntary formation, autonomous functioning, democratic control, and professional management of cooperative societies.
• The 97th Constitutional Amendment Act recognizes cooperatives as an important economic vehicle for inclusive growth.
• It inserts the word "cooperatives" in Article 19(1)(c), ensuring the right to form cooperative societies as a fundamental right.
• Additionally, Article 43 B in Part IV of the Constitution emphasizes the state's role in promoting cooperatives.

Additional Information

• 97th Constitutional Amendment Act:
• It came into effect on 15 February 2012.
• The amendment added "cooperative societies" to the Constitution, recognizing their significance in economic development.
• It made provisions for the protection and regulation of cooperative societies under state law.
• Directive Principles of State Policy:
• These principles are enshrined in Part IV of the Indian Constitution.
• They are non-justiciable but serve as guidelines for the government in policy-making.
• The DPSPs aim to establish a welfare state, ensuring socio-economic justice.
• Cooperative Societies:
• Cooperatives are autonomous associations of persons united voluntarily to meet their common economic, social, and cultural needs.
• They are based on principles such as democratic control and equitable distribution of resources.
• In India, cooperatives play a crucial role in sectors like agriculture, banking, and housing.
• Part IV of the Constitution:
• Part IV of the Constitution deals with Directive Principles of State Policy.
• It includes Articles 36 to 51, focusing on principles to be followed by the state to ensure the welfare of citizens.
• Articles such as 38, 39, 41, and 43 highlight socio-economic goals like equal pay, living wages, and right to work.

The logic followed here is:

Logic: 1st number + 7 = 2nd number.

67 is related to 74

→ 67 + 7

→ 74 = 2nd number

13 is related to 20

→ 13 + 7

→ 20 = 2nd number

Similarly,

52 is related to 

→ 52 + 7

→ 59 = 2nd number

Hence, the correct answer is "Option 2".

The correct answer is 108.

Key Points

• India ranked 108 out of 193 countries in the Gender Inequality Index (GII) 2022, as reported by the United Nations Development Programme (UNDP).
• The Gender Inequality Index measures disparities in gender-based achievements across health, empowerment, and labor market participation.
• India's performance in the index reflects challenges in areas such as women’s participation in politics, workforce involvement, and reproductive health.
• The GII is part of the Human Development Report published by the UNDP, which serves as a global benchmark for assessing gender equality.
• India's ranking indicates ongoing efforts and room for improvement in addressing gender disparities in various sectors.

Additional Information

• Gender Inequality Index (GII):
• The GII was introduced in the Human Development Report 2010 to reflect the loss in human development due to inequality between genders.
• It focuses on three dimensions: reproductive health, empowerment, and labor market participation.
• Empowerment is measured through women’s participation in decision-making, including their presence in parliamentary roles and education levels.
• India’s Progress:
• India has made improvements in areas such as maternal health and education for women, but challenges remain in women’s representation in politics and workforce.
• Increasing focus on government initiatives like Beti Bachao Beti Padhao aims to address gender disparities.
• Global Trends:
• Countries with higher development indices generally score better on gender equality due to inclusive policies and social reforms.
• Nordic countries such as Iceland and Norway consistently rank among the top performers in the GII.
• Key Terminologies:
• Reproductive Health: Includes indicators like maternal mortality and adolescent birth rates.
• Empowerment: Refers to access to education and political representation.
• Labor Market Participation: Measures female participation in the workforce relative to men.

Given: A, B, C, D, E and F live on six different floors of the same building. The lowermost floor in the building is numbered 1, the floor above it, number 2 and so on till the topmost floor is numbered 6.

1. A lives on a floor which is a prime number.

2. The product of floors on which A and E live is 3.

The only two floor numbers whose product is 3 are 1 and 3. Since A lives on a prime number floor, A must live on floor 3, and E must live on floor 1.

3. Only 2 people live above B.

 

4. F lives immediately below C.

The only consecutive empty floors are 5 and 6. So C lives on Floor 6 and F lives on Floor 5.

The remaining person is D, who must live on the remaining empty floor, which is Floor 2.

 

Thus, two people live between D and F.

Hence, the correct answer is "Option 1".

The correct answer is Bhopal.

Key Points

• The 24º latitude passes closest to the capital city of Bhopal, which is the capital of the Indian state of Madhya Pradesh.
• Bhopal is situated at approximately 23.25° N latitude and 77.41° E longitude, making it the closest to the 24º N latitude line among the given options.
• Other state capitals mentioned in the options, such as Patna, Raipur, and Dispur, are located farther away from the 24º latitude line.
• Madhya Pradesh lies in central India, making it geographically closer to the Tropic of Cancer, which is at 23.5º N latitude.

Additional Information

• Tropic of Cancer:
• The Tropic of Cancer is an imaginary line located at 23.5º N latitude, marking the northernmost point where the sun can appear directly overhead during the June solstice.
• It passes through eight states in India: Gujarat, Rajasthan, Madhya Pradesh, Chhattisgarh, Jharkhand, West Bengal, Tripura, and Mizoram.
• Bhopal's Significance:
• Bhopal is known as the "City of Lakes" due to its numerous natural and artificial lakes.
• It is one of the greenest cities in India and serves as the administrative headquarters of Madhya Pradesh.
• Latitude:
• Latitude is a geographic coordinate that specifies the north-south position of a point on the Earth's surface.
• Lines of latitude are often referred to as parallels and run horizontally around the globe.
• Geographical Importance of Madhya Pradesh:
• Madhya Pradesh is referred to as the "Heart of India" due to its central location.
• The state is rich in cultural heritage and biodiversity, hosting several UNESCO World Heritage Sites and wildlife reserves.

The logic followed here is:

Option 1)  # = FDG, % = MLG

Does not follow the same logic.

Option 2)  # = FJH, % = MHU

Does not follow the same logic.

Option 3) # = EGC, % = NPL

Follow the same logic.

Option 4) # = DEG, % = NIU

Does not follow the same logic.

Hence, the correct answer is "Option 3".

Conditions:

(i) If the first element is a symbol and the last a number, the codes for these two (the first and the last elements) are to be interchanged.

(ii) If the first element is an odd number and the last an even number, the first and last elements are to be coded as ©

(iii) If both the second and third elements are perfect squares, the third element is to be coded as the code for the second element.

Given- 5 & 3 @ 7 % 2

The first element is 5 (an odd number).

The last element is 2 (an even number).

The second element is & (a symbol, not a perfect square).

The third element is 3 (not a perfect square).

Rule No. (i): This condition does not apply because the first element (5) is a number, not a symbol.

Rule No. (ii): This condition applies because the first element (5) is an odd number and the last element (2) is an even number. So, the first and last elements will be coded as ©.

Rule No. (iii): This condition does not apply because neither the second element (&) nor the third element (3) are perfect squares.

Based on the applicable rule (ii), the first and last elements are coded as ©.

The code for & is M.

The code for 3 is D.

The code for @ is Z.

The code for 7 is W.

The code for % is P.

Thus, '5 & 3 @ 7 % 2' is coded as → © M D Z W P ©.

Hence, the correct answer is "Option 4".

Conditions:

(i) If the first element is a symbol and the last a number, the codes for these two (the first and the last elements) are to be interchanged.

(ii) If the first element is an odd number and the last an even number, the first and last elements are to be coded as ©

(iii) If both the second and third elements are perfect squares, the third element is to be coded as the code for the second element.

Given- 7 2 4 @ 5

The first element is 7 (an odd number).

The last element is 5 (an odd number).

The second element is 2 (not a perfect square).

The third element is 4 (a perfect square, 2*2=4).

Rule No. (i): This condition does not apply because the first element (7) is a number, not a symbol.

Rule No. (ii): This condition does not apply because the last element (5) is an odd number, not an even number.

Rule No. (iii): This condition does not apply because the second element (2) is not a perfect square, even though the third element (4) is.

Since none of the given conditions apply, the codes for the respective number/symbol are to be followed directly as given in the table.

The code for 7 is P.

The code for 2 is T.

The code for 4 is B.

The code for @ is F.

The code for 5 is J.

Thus, '7 2 4 @ 5' is coded as → P T B F J.

Hence, the correct answer is "Option 3".

The correct answer is 90%.

Key Points

• As of April 2025, 90% of the India-UK Free Trade Agreement (FTA) has been finalized, marking significant progress in negotiations.
• The India-UK FTA is aimed at enhancing trade relations by reducing tariffs, increasing market access, and fostering economic cooperation.
• Both nations are working towards concluding the deal to boost bilateral trade, which currently stands at over £34 billion annually.
• The agreement covers key sectors such as technology, pharmaceuticals, automobiles, and financial services.
• The finalization of the agreement is expected to strengthen ties and contribute to mutual economic growth.

Additional Information

• Free Trade Agreement (FTA):
• FTA is a pact between two or more nations to reduce or eliminate trade barriers such as tariffs and quotas.
• It aims to promote free flow of goods and services between member countries.
• India's Trade Policy:
• India actively pursues FTAs to enhance its global trade footprint and attract foreign investments.
• Major FTAs include agreements with ASEAN, Japan, South Korea, and the UAE.
• UK's Post-Brexit Trade Strategy:
• After exiting the EU, the UK has focused on establishing FTAs with countries worldwide, including India.
• This strategy is designed to mitigate economic impacts post-Brexit and expand trade opportunities.
• Economic Impact of FTA:
• FTAs can lead to increased exports, job creation, and lower costs for consumers due to reduced tariffs.
• They also foster innovation and global competitiveness among domestic industries.

The correct answer is JMM, Barhait.

Key Points

• The Chief Minister of Jharkhand after the 2024 Assembly elections is Hemant Soren.
• Hemant Soren is a member of the Jharkhand Mukti Morcha (JMM), a regional political party focused on the rights of tribal communities and the development of Jharkhand.
• He represents the Barhait constituency, which is located in the Sahebganj district of Jharkhand.
• The JMM-led coalition government, which includes the Indian National Congress (INC) and the Rashtriya Janata Dal (RJD), emerged victorious in the state assembly elections.
• Hemant Soren has served as the Chief Minister of Jharkhand since 2019, and his leadership continued following the 2024 elections.

Additional Information

• Jharkhand Mukti Morcha (JMM):
• Founded by Shibu Soren, the JMM is a key political party advocating for the socio-economic development of tribal communities in Jharkhand.
• It played a pivotal role in the creation of the state of Jharkhand in 2000.
• Barhait Constituency:
• Barhait is a reserved constituency for Scheduled Tribes (ST) and holds significant importance for tribal representation in Jharkhand's state assembly.
• Hemant Soren has been elected from Barhait multiple times, showcasing strong public support in the region.
• Key Issues in Jharkhand Politics:
• Land rights, tribal welfare, education, healthcare, and industrial development remain the core focus areas.
• The JMM government emphasizes preserving tribal culture and providing employment opportunities in rural areas.
• Coalition Politics in Jharkhand:
• Jharkhand has a history of coalition governments due to the fragmented political landscape.
• The JMM-led coalition government in 2024 reflects the party's ability to build alliances and address diverse political challenges.

The correct answer is Raja Ram Mohan Roy.

Key Points

• Raja Ram Mohan Roy was a key social reformer in India during the 19th century.
• He strongly advocated for progressive reforms, including the promotion of inter-caste and inter-religious marriages.
• Roy was instrumental in the abolition of Sati and worked towards improving women's rights, aligning with his broader reformist agenda.
• He founded the Brahmo Samaj in 1828, which championed social and religious reforms and encouraged egalitarian values.
• His efforts laid the foundation for modern Indian society by promoting rationalism, equality, and universal human rights.

Additional Information

• Inter-caste and inter-religious marriages: These marriages are a union between individuals from different castes or religions, challenging traditional norms and promoting social integration.
• Brahmo Samaj: A socio-religious reform movement founded by Raja Ram Mohan Roy. It emphasized monotheism, rational thought, and rejection of caste discrimination.
• Sati: A historical practice in which a widow was immolated on her husband's funeral pyre. Raja Ram Mohan Roy was pivotal in its abolition through legislation in 1829.
• Social reform in British India: Reform movements during the colonial period aimed at addressing societal issues such as caste hierarchy, gender inequality, and religious orthodoxy.
• Legacy: Raja Ram Mohan Roy is regarded as the "Father of Modern India" for his efforts in modernizing Indian society and promoting progressive ideals.

The correct answer is Raja Rammohan Roy.

Key Points

• Raja Rammohan Roy founded the Vedanta College in Calcutta in 1825 to promote a blend of Indian traditional learning and modern Western education.
• He aimed to integrate the teachings of Vedanta philosophy with scientific and rational education.
• The college emphasized learning English, science, mathematics, and other contemporary subjects alongside traditional Indian scriptures.
• Raja Rammohan Roy is widely regarded as the father of modern Indian Renaissance for his progressive social and educational reforms.
• His educational initiatives were instrumental in laying the foundation for the spread of modern education in India.

Additional Information

• Brahmo Samaj: Rammohan Roy founded the Brahmo Samaj in 1828, which was a reformist movement promoting monotheism, equality, and social reform.
• Educational Reforms: He also played a significant role in advocating for the abolishment of the traditional Sanskrit-based education system and supported modern scientific learning.
• Sati Abolition: Rammohan Roy was a pioneer in the movement to abolish the practice of Sati and worked with the British government to pass the Regulation XVII in 1829 banning it.
• Journalism Contributions: He published newspapers like Sambad Kaumudi to advocate for social and political reforms, including freedom of the press.
• Legacy: Rammohan Roy's contributions to education, social reforms, and religious reformation earned him the title of the "Father of the Indian Renaissance."

Given:

Total number of students in the row = 73

Gita's position = 16th from the left end.

Sunita's position = 21st to the right of Gita.

Total persons = (Rank from Left) + (Rank from Right) - 1

Find Sunita's position from the left end:

Sunita's position from the left = Gita's position from left + 21

= 16 + 21

= 37th.

Now, we can find Sunita's position from the right end using her rank from the left and the total number of students:

Sunita's position from the right = Total students - (Sunita's rank from left) + 1

= 73 - 37 + 1

= 36 + 1

= 37th.

Hence, the correct answer is "Option 1".

Shortcut Trick

Apply the BODMAS rule directly to solve the expression in sequence:

127 − 7 × (17 + 6) + 93

⇒ 127 − 7 × 23 + 93

⇒ 127 − 161 + 93

⇒ 220 − 161 = 59

∴ The correct answer is 59.

Alternate Method

Given:

Expression: 127 − 7 × (17 + 6) + 93

Formula Used:

BODMAS rule: Brackets → Orders → Division → Multiplication → Addition → Subtraction.

Calculation:

⇒ First, solve the values inside the brackets:

⇒ 17 + 6 = 23

⇒ The expression becomes: 127 − 7 × 23 + 93

⇒ Next, perform the multiplication:

⇒ 7 × 23 = 161

⇒ The expression updates to: 127 − 161 + 93

⇒ Group the positive numbers together before subtracting:

⇒ (127 + 93) − 161

⇒ 220 − 161

⇒ 59

∴ The correct answer is 59.

Additional Information

BODMAS Rule

It specifies the sequence of operations: Brackets, Orders (powers/roots), Division, Multiplication, Addition, and Subtraction. Addition and Subtraction have the same priority and can generally be performed from left to right.

Bracket Types and Priority

When nested brackets are present, solve them from innermost to outermost: Line brackets (vinculum) first, Round brackets ( ) second, Curly brackets { } third, and Square brackets [ ] last.

Sign Rules in Simplification

Multiplying numbers of the same sign gives a positive result (− × − = +). Multiplying numbers of different signs gives a negative result (+ × − = −).

The correct answer is Heroism and praises of kings and their deeds.

Key Points

• Purananuru and Patirruppattu are part of the Sangam literature's Ettuttokai collection, which predominantly focuses on the external (puram) aspects of life.
• The primary theme of these anthologies is heroism, with a significant emphasis on praising the valor and deeds of Tamil kings, chieftains, and warriors.
• Purananuru, in particular, provides a vivid account of the political landscape, battles, and the ideals of kingship in ancient Tamil society.
• Patirruppattu is a series of ten poems that specifically extol the virtues and exploits of the Chera kings, one of the prominent dynasties of Tamilakam.
• These works serve as a historical record, offering insight into the socio-political and military aspects of early Tamil civilization.

Additional Information

• Sangam Literature: Sangam literature is a body of ancient Tamil texts composed between 300 BCE and 300 CE, divided into two categories: Aham (love and personal life) and Puram (public life, heroism, and war).
• Ettuttokai: Ettuttokai, meaning "Eight Anthologies," is one of the two major collections of Sangam literature. It includes works like Purananuru, Patirruppattu, and others.
• Puram Concept: The Puram genre focuses on themes like valor, philanthropy, ethics of war, and the life of warriors and kings, contrasting with the Aham genre, which deals with love and emotions.
• Historical Significance: These texts are invaluable for understanding the political structures, cultural practices, and military traditions of ancient Tamilakam (modern Tamil Nadu and Kerala).
• Key Dynasties: The Sangam works frequently mention three major Tamil dynasties: the Cholas, Cheras, and Pandyas, highlighting their contributions to warfare, governance, and culture.

Key Points

• The Climate Change Performance Index (CCPI) evaluates 63 countries responsible for over 90% of global greenhouse gas emissions.
• The CCPI is published annually by Germanwatch, NewClimate Institute, and Climate Action Network International.
• It assesses countries based on four categories: Greenhouse Gas Emissions, Renewable Energy, Energy Use, and Climate Policy.
• The index is designed to highlight efforts and gaps in combating climate change among the world's major emitters.
• The CCPI aims to increase transparency in international climate politics and serves as a tool to press governments into enhancing climate action.

Additional Information

• The CCPI uses a scoring system where countries are ranked on their performance in mitigating climate change, with high performers categorized as "Very High" and low performers as "Very Low."
• The CCPI includes indicators such as the Paris Agreement targets to evaluate countries' progress toward limiting global warming to below 2°C.
• The index is widely recognized as an independent monitoring tool that holds countries accountable for their climate commitments.
• Top-performing countries often include Scandinavian nations due to their strong climate policies and renewable energy adoption.
• Countries like Saudi Arabia, Russia, and Iran typically rank low due to insufficient climate action and high fossil fuel dependency.

The given venn diagram is:

Thus, 9 person who are chefs and also teachers but not lawyers.

Hence, the correct answer is "Option 1".

Shortcut Trick

If two quadratic equations a₁x² + b₁x + c₁ = 0 and a₂x² + b₂x + c₂ = 0 have both roots common, their coefficients are strictly proportional.

a₁/a₂ = b₁/b₂ = c₁/c₂

2/3 = K/4 = 8/12

Taking 2/3 = K/4 ⇒ K = (2 × 4) / 3 = 8/3

∴ The correct answer is 8/3.

Alternate Method

Given:

Equation 1: 2x² + Kx + 8 = 0

Equation 2: 3x² + 4x + 12 = 0

Formula Used:

For two quadratic equations to have both roots in common, the ratio of their corresponding coefficients must be equal:

a₁/a₂ = b₁/b₂ = c₁/c₂

Calculations:

⇒ a₁ = 2, b₁ = K, c₁ = 8

⇒ a₂ = 3, b₂ = 4, c₂ = 12

⇒ 2/3 = K/4 = 8/12

⇒ Simplifying the constant ratio: 8/12 = 2/3

⇒ 2/3 = K/4 = 2/3

⇒ K/4 = 2/3

⇒ K = (2 × 4) / 3

⇒ K = 8/3

∴ The correct answer is 8/3.

Additional Information

Condition for One Common Root

If only one root is common between a₁x² + b₁x + c₁ = 0 and a₂x² + b₂x + c₂ = 0, the condition is (a₁b₂ − a₂b₁)(b₁c₂ − b₂c₁) = (c₁a₂ − c₂a₁)².

Sum and Product of Roots

For a quadratic equation ax² + bx + c = 0, the sum of roots is −b/a and the product of roots is c/a.

Nature of Roots

Determined by the discriminant D = b² − 4ac. If D > 0, roots are real and distinct. If D = 0, roots are real and equal. If D < 0, roots are imaginary.

Given:

P, Q, R, S, T, U and V are sitting around a circular table facing the centre.

Only two people sit between T and S when counted from the right of T.

S sits to the immediate right of Q.

Only three people sit between V and Q when counted from the right of Q.

 U sits to the immediate right of R. 

Thus, 2 people sit between Q and U when counted from the right of Q.

Hence, the correct answer is "Option 2".

The correct answer is 5.4.

Key Points

• The 6th Annual Employment-Unemployment Survey (2016-17) by the Labour Bureau reported the overall unemployment rate in India as 5.4% (0.054).
• The survey highlighted a higher unemployment rate among women (8.7%) compared to men (4.0%).
• Rural unemployment stood at 5.1%, while urban unemployment was slightly higher at 5.8%.
• The survey aimed to provide detailed insights into employment patterns, labor force participation, and unemployment trends across various demographics.
• The report is considered a critical source for policymaking in addressing employment challenges in India.

Additional Information

• Unemployment Rate:
• It refers to the percentage of individuals in the labor force who are unable to find jobs despite actively seeking work.
• Unemployment is categorized into types such as structural, frictional, cyclical, and seasonal unemployment.
• Labour Bureau Surveys:
• The Labour Bureau, under the Ministry of Labour and Employment, conducts these surveys to assess employment and unemployment trends in India.
• The surveys are critical in identifying challenges in the labor market and formulating evidence-based policies.
• Periodic Labour Force Survey (PLFS):
• Since 2017-18, the PLFS by the National Statistical Office (NSO) has replaced the Labour Bureau surveys for better and more frequent labor market data.
• PLFS provides quarterly estimates for urban areas and annual estimates for both rural and urban regions.
• Labor Force Participation Rate (LFPR):
• It is the percentage of the working-age population that is either employed or actively seeking employment.
• India's LFPR has historically been low, particularly for women, due to various social, economic, and cultural factors.
• Policy Interventions:
• The Indian government has launched schemes like MGNREGA, Skill India, and Start-Up India to address unemployment and enhance skill development.
• These initiatives aim to provide employment opportunities and promote entrepreneurship among the youth.

Given: Seven boxes, A, B, C, D, E, F and G, are kept one over the other but not necessarily in the same order.

1. No box is kept above F.

This means F is the topmost box (Position 7).

2. Only three boxes are kept between F and B.

3. D is kept immediately above B.

 

4. Only one box is kept between G and D.

Let's consider two cases:

Case 1: G is at 2

Case 2: G is at 6

 

5. Only four boxes are kept between G and C.

Consider Case 1 (G is at 2): If G is at 2, and there are 4 boxes between G and C, then C must be at 7 However, F is already at 7. So, Case 1 is not possible.

Consider Case 2 (G is at 6): If G is at 6, and there are 4 boxes between G and C, then C must be at 1 (6 - 4 - 1 = 1).

6. A is kept in some place above E.

 

Thus, there are 3 boxes kept below D.

Hence, the correct answer is "Option 1".

The correct answer is To protect Fundamental Rights.

Key Points

• Article 32 of the Indian Constitution provides the right to Constitutional Remedies, empowering the Supreme Court to issue writs for the enforcement of Fundamental Rights.
• Writs under Article 32 include Habeas Corpus, Mandamus, Prohibition, Quo Warranto, and Certiorari, ensuring the protection of Fundamental Rights.
• Dr. B.R. Ambedkar described Article 32 as the "heart and soul" of the Constitution, emphasizing its significance in safeguarding citizens' rights.
• Only the Supreme Court can issue writs under Article 32, while High Courts can issue writs under Article 226 for broader purposes, including legal rights.
• Article 32 is considered a cornerstone of the judiciary's role in maintaining checks and balances in India's democratic framework.

Additional Information

• Fundamental Rights: These are guaranteed under Part III of the Indian Constitution and include rights such as the Right to Equality, Right to Freedom, Right to Freedom of Religion, Cultural and Educational Rights, and Right to Constitutional Remedies.
• Types of Writs:
• Habeas Corpus: To release a person unlawfully detained.
• Mandamus: To compel a public authority to perform its legal duty.
• Prohibition: To prevent lower courts from exceeding their jurisdiction.
• Quo Warranto: To challenge the legality of a person's claim to a public office.
• Certiorari: To transfer a case from lower courts to higher courts for review.
• Directive Principles of State Policy: Mentioned under Part IV of the Constitution, these are non-justiciable guidelines for the government to ensure social and economic welfare.
• Judicial Review: Under Article 13, the judiciary has the power to invalidate laws that violate Fundamental Rights, ensuring their supremacy.
• Comparison with Article 226: Article 226 allows High Courts to issue writs not only for Fundamental Rights but also for legal rights, making its scope broader than Article 32.

Shortcut Trick

Using the special symmetric identity: (Ax − By)² + (Bx + Ay)² = (A² + B²)(x² + y²)

Here A = 2, B = 5 ⇒ (2x − 5y)² + (5x + 2y)² = (2² + 5²)(x² + y²) = 29x² + 29y²

The third term is a standard difference of squares: (2x + 5y)(2x − 5y) = 4x² − 25y²

Adding them together: 29x² + 29y² + 4x² − 25y² = 33x² + 4y²

∴ The correct answer is 33x² + 4y².

Alternate Method

Given:

(2x − 5y)² + (5x + 2y)² + (2x + 5y)(2x − 5y)

Formula Used:

⇒ (a − b)² = a² − 2ab + b²

⇒ (a + b)² = a² + 2ab + b²

⇒ (a + b)(a − b) = a² − b²

Calculations:

⇒ First term: (2x − 5y)² = (2x)² − 2 × (2x) × (5y) + (5y)² = 4x² − 20xy + 25y²

⇒ Second term: (5x + 2y)² = (5x)² + 2 × (5x) × (2y) + (2y)² = 25x² + 20xy + 4y²

⇒ Third term: (2x + 5y)(2x − 5y) = (2x)² − (5y)² = 4x² − 25y²

⇒ Add all three terms together:

⇒ (4x² − 20xy + 25y²) + (25x² + 20xy + 4y²) + (4x² − 25y²)

⇒ Grouping the like terms:

⇒ (4x² + 25x² + 4x²) + (−20xy + 20xy) + (25y² + 4y² − 25y²)

⇒ 33x² + 0 + 4y²

⇒ 33x² + 4y²

∴ The correct answer is 33x² + 4y².

Additional Information

Basic Algebraic Identities

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

Difference of Squares

The product of the sum and difference of the same two terms equals the difference of their squares: (a + b)(a − b) = a² − b²

Symmetric Sum of Squares Identity

An important shortcut to directly solve crossed-coefficient questions without full expansion: (Ax − By)² + (Bx + Ay)² = (A² + B²)(x² + y²)

The correct answer is Rajasthan.

Key Points

• Rajasthan is a landlocked state located in the northwestern part of India and does not have a coastline.
• It is bordered by Punjab, Haryana, Uttar Pradesh, Madhya Pradesh, and Gujarat, along with an international border with Pakistan.
• States with coastlines in India include Odisha, Andhra Pradesh, and Gujarat, among others, as they are adjacent to the Bay of Bengal or Arabian Sea.
• Rajasthan is known for its desert landscape, particularly the Thar Desert, which significantly influences its geography and climate.
• As a landlocked state, Rajasthan relies on other states for access to ports and maritime trade.

Additional Information

• India's Coastline: India has a vast coastline of approximately 7,517 kilometers, with states like Gujarat, Maharashtra, Goa, Karnataka, Kerala, Tamil Nadu, Andhra Pradesh, Odisha, and West Bengal having coastal access.
• Landlocked States: Apart from Rajasthan, other landlocked states in India include Haryana, Madhya Pradesh, Uttar Pradesh, Bihar, and others that lack direct access to the sea.
• Thar Desert: Covering much of Rajasthan, the Thar Desert is the world's 17th largest desert and the 9th largest subtropical desert.
• Importance of Coastlines: Coastal states significantly contribute to India's economy through trade, fishing, and tourism, as they have access to ports and maritime routes.
• Geographical Diversity: India showcases diverse geography, including mountains, plains, plateaus, deserts, and coastal regions, which influence the lifestyle and economic activities of its population.

Decoding symbols:

Given: M + N × O ÷ P – Q

M + N → M is the mother of N. (M is Female)

N × O → N is the wife of O. (N is Female, O is Male)

O ÷ P → O is the father of P. (O is Male, P's gender is unknown)

P – Q → P is the brother of Q. (P is Male, Q's gender is unknown)

Based on the decoded relationships, here is the Family Tree Representation:

Thus, M is the mother's mother of Q.

Hence, the correct answer is "Option 4".

The correct answer is To apply consistent formatting, fonts, and layouts to all slides.

Key Points

• The Slide Master is a feature in MS PowerPoint used to ensure uniform design and formatting across all slides in a presentation.
• It allows users to customize elements like fonts, colors, backgrounds, and placeholders, which are then applied globally to all slides.
• The Slide Master streamlines the process of maintaining consistency in layouts for titles, content, and other elements.
• Users can also create custom slide layouts within the Slide Master to suit specific design needs.
• Any changes made in the Slide Master affect all slides linked to that master, saving time and effort in editing individual slides.

Additional Information

• Slide Master Terminology:
• Master Slide: The main slide that controls the design and layout for all associated slides.
• Layouts: Specific slide designs controlled by the master slide, including placeholders for text and images.
• Consistency in Design:
• Ensures presentations look professional and cohesive, especially in business or academic settings.
• Time Efficiency:
• Reduces the need to format individual slides, as changes in the Slide Master are applied universally.
• Advanced Customization:
• Users can add logos, watermarks, or other branding elements to all slides using the Slide Master.
• Accessing Slide Master:
• Located under the View tab in the MS PowerPoint ribbon.

The logic followed here is:                                                                

Thus, the missing term in the series is 676.

Hence, the correct answer is "Option 1";

Shortcut Trick

Remaining distance = 1 − 2/3 = 1/3 of total distance

Remaining time = 1 − 5/7 = 2/7 of total time

Remaining distance = 519 × 1/3 = 173 km

Remaining time = 7 × 2/7 = 2 hours

Required speed = 173 ÷ 2 = 86.5 km/hr

∴ The correct answer is 86.5 km/hr.

Alternate Method

Given:

Total distance = 519 km

Total time = 7 hours

Part 1 (2/3) 346 km 5 hr

Part 2 (1/3) 173 km 2 hr

Total Distance = 519 km, Total Time = 7 hr

Formula Used:

Speed = Distance ÷ Time

Calculations:

⇒ Distance covered initially = 519 × 2/3 = 346 km

⇒ Time taken initially = 7 × 5/7 = 5 hours

⇒ Remaining distance = 519 − 346 = 173 km

⇒ Remaining time = 7 − 5 = 2 hours

⇒ Speed for remaining distance = 173 ÷ 2

⇒ Required speed = 86.5 km/hr

∴ The correct answer is 86.5 km/hr.

Additional Information

Average Speed

It is defined as the total distance traveled divided by the total time taken. Average Speed = Total Distance ÷ Total Time.

Relative Speed

When two objects move in the same direction, their relative speed is the difference of their individual speeds (S₁ − S₂). When moving in opposite directions, it is the sum of their speeds (S₁ + S₂).

Conversion of Units

To convert speed from km/hr to m/s, multiply by 5/18. To convert from m/s to km/hr, multiply by 18/5.

Shortcut Trick

For an odd number of observations (n = 11), the median is simply the exact middle value when sorted.

We only need to find the 6^th smallest number without sorting the entire sequence.

Identifying smallest to 6^th term: 11, 18, 27, 30, 34, 35.

The 6^th value is 35.

∴ The correct answer is 35.

Alternate Method

Given:

Observations: 76, 83, 30, 11, 81, 52, 18, 34, 84, 35, 27

Total number of observations (n) = 11

Formula Used:

When the number of observations (n) is odd, Median = ((n + 1) ÷ 2)^th observation

Calculations:

⇒ First, arrange the given observations in ascending order:

⇒ 11, 18, 27, 30, 34, 35, 52, 76, 81, 83, 84

Data arranged in Ascending Order

11

18

27

30

34

35

52

76

81

83

84

Median = 6th Term

⇒ Total number of observations (n) = 11, which is an odd number.

⇒ Median = ((11 + 1) ÷ 2)^th observation

⇒ Median = (12 ÷ 2)^th observation

⇒ Median = 6^th observation

⇒ From the sorted data, the 6^th observation is 35.

∴ The correct answer is 35.

Additional Information

Mean

The arithmetic average of a dataset. Mean = Sum of all observations ÷ Total number of observations.

Median for Even 'n'

If the number of observations 'n' is even, Median = Average of the (n ÷ 2)^th and ((n ÷ 2) + 1)^th terms after sorting the data in ascending order.

Mode

The value that appears most frequently in a dataset. A dataset may have one mode, multiple modes, or no mode at all.

Range

The total spread or difference between the highest and lowest values in a dataset. Range = Maximum value − Minimum value.

Shortcut Trick

Total capacity of the tank = LCM(18, 20) = 180 units.

Efficiency of Pipe A = +10 units/min and Efficiency of Pipe B = −9 units/min.

Tank filled by Pipe A in the first 6 minutes = 6 × 10 = 60 units.

Remaining capacity to fill = 180 − 60 = 120 units.

Time to fill remaining part = 120 ÷ (10 − 9) = 120 minutes.

∴ The correct answer is 120 minutes.

Alternate Method

Given:

⇒ Time taken by Pipe A to fill the tank = 18 minutes

⇒ Time taken by Pipe B to empty the tank = 20 minutes

⇒ Time for which only Pipe A was operated initially = 6 minutes

Formula Used:

⇒ Total Work = LCM of individual time taken

⇒ Efficiency = Total Work ÷ Time

⇒ Time Required = Remaining Work ÷ Net Combined Efficiency

Calculations:

⇒ In the first 6 minutes, work done by Pipe A = 6 × 10 = 60 units.

⇒ Remaining capacity to be filled = 180 − 60 = 120 units.

⇒ After 6 minutes, both pipes A and B are open together.

⇒ Net efficiency of both pipes combined = 10 + (−9) = +1 unit/min.

⇒ Time required to fill the remaining capacity = 120 units ÷ 1 unit/min = 120 minutes.

∴ The correct answer is 120 minutes.

Additional Information

Pipes and Cisterns Net Efficiency

When a filling pipe (time x) and an emptying pipe (time y) run together, the net part filled per hour is (1/x − 1/y), provided the filling rate is higher than the emptying rate.

Concept of Leakage

A leakage at the bottom of a tank acts exactly like an emptying pipe. It continuously reduces the effective efficiency of the filling pipes, thereby increasing the total time required to completely fill the tank.

Alternating Pipes Method

When filling and emptying pipes are opened in alternate turns, compute the net work done in a full cycle (e.g., 2 hours). Special care must be taken towards the end, as the tank might become completely filled before the next emptying cycle begins.

The correct answer is 115.

Key Points

• In February 2025, Muthoot Finance received approval from the Reserve Bank of India (RBI) to open 115 new branches across the country.
• This strategic expansion aims to strengthen Muthoot Finance's presence in the gold loan market, a key segment in India's financial sector.
• The approval aligns with Muthoot Finance's vision to broaden its reach, especially in rural and semi-urban areas, to cater to the growing demand for gold loans.
• Muthoot Finance is the largest gold financing company in India, with a market share of over 20% in the organized gold loan market.
• The new branches will enhance access to financial services, including gold loans, insurance, and money transfer services, among underserved populations.

Additional Information

• Gold Loan Market in India:
• India is one of the largest consumers of gold globally, with households holding over 25,000 tons of gold, making gold loans a popular financial product.
• Gold loans are secured loans where borrowers pledge their gold jewelry or ornaments as collateral.
• The organized gold loan market in India is dominated by NBFCs like Muthoot Finance and Manappuram Finance, along with banks.
• Muthoot Finance Overview:
• Muthoot Finance Limited is a leading Non-Banking Financial Company (NBFC) in India, founded in 1939.
• It specializes in gold loans, money transfer services, investment products, and insurance services.
• With a vast network of branches, Muthoot Finance primarily caters to rural and semi-urban customers.
• RBI's Role in Branch Approvals:
• The Reserve Bank of India regulates NBFCs and approves their expansion plans, ensuring adherence to financial and operational guidelines.
• Branch expansions are approved based on factors such as financial health, compliance history, and market demand.
• Impact of Branch Expansion:
• Branch expansions improve financial inclusion by providing easier access to loans and other financial services in underbanked areas.
• They also contribute to employment generation and support regional economic growth.

Shortcut Trick

We know that 18³ = 5832 and 10⁴ = 10000.

Given expression = (18 ÷ 10) × (5 ÷ 24) × 78

⇒ (18 × 5 × 78) ÷ (10 × 24)

⇒ (90 ÷ 240) × 78 = (3 ÷ 8) × 78

⇒ 234 ÷ 8 = 29.25

∴ The correct answer is 29.25.

Alternate Method

Given:

Expression: (³√5832 ÷ ⁴√10000) × (5 ÷ 24) × 78

Calculation:

⇒ First, find the cube root of 5832.

⇒ 10³ = 1000 and 20³ = 8000, so the cube root is strictly between 10 and 20.

⇒ Since 8³ = 512 (ends in 2), the cube root of 5832 must be 18.

⇒ Next, find the fourth root of 10000.

⇒ 10000 = 10 × 10 × 10 × 10 = 10⁴, so ⁴√10000 = 10.

⇒ Substitute the root values into the given expression:

⇒ (18 ÷ 10) × (5 ÷ 24) × 78

⇒ (9 ÷ 5) × (5 ÷ 24) × 78

⇒ (9 ÷ 24) × 78

⇒ (3 ÷ 8) × 78

⇒ 234 ÷ 8 = 117 ÷ 4

⇒ 29.25

∴ The correct answer is 29.25.

Additional Information

BODMAS Rule

Always solve mathematical expressions in the exact sequence: Brackets, Orders (powers/roots), Division, Multiplication, Addition, and Subtraction.

Finding Cube Roots Trick

For a perfect cube, look at the last digit. If it ends in 2, its cube root ends in 8. Then strike off the last three digits and find the nearest smaller perfect cube for the remaining prefix number.

Fourth Roots

A fourth root is simply the square root of a square root. For example, ⁴√10000 = √(√10000) = √100 = 10.

The correct answer is NH₄Cl.

Key Points

• NH₄Cl (Ammonium chloride) is a salt of a weak base (NH₃) and a strong acid (HCl), making its aqueous solution slightly acidic due to hydrolysis.
• In water, NH₄Cl dissociates into NH₄⁺ and Cl⁻ ions. The NH₄⁺ ion undergoes hydrolysis to form NH₃ and H⁺ ions, increasing the acidity.
• The Cl⁻ ion does not hydrolyze because it is the conjugate base of a strong acid (HCl) and remains inert in the solution.
• The pH of an NH₄Cl solution is typically less than 7, confirming its acidic nature.
• Other options like Na₂CO₃ and CH₃COONa are basic, while NH₄CH₃COO is nearly neutral due to the balance between its acidic and basic components.

Additional Information

• Hydrolysis: It is the reaction of a salt with water to form an acidic or basic solution depending on the strength of the parent acid and base.
• Ammonium Ion (NH₄⁺): It is a weak acid that hydrolyzes in water, releasing H⁺ ions and contributing to the solution's acidity.
• Conjugate Acid-Base Pair: NH₄⁺ is the conjugate acid of the weak base NH₃, while Cl⁻ is the conjugate base of the strong acid HCl.
• pH of Salts: The pH of a salt solution depends on the hydrolysis of its ions. Salts of strong acids and weak bases are acidic, while salts of strong bases and weak acids are basic.
• Non-Hydrolyzing Ions: Ions like Cl⁻, derived from strong acids, do not hydrolyze and do not affect the solution's pH.

Shortcut Trick

Let Rahul's age be 3 units and his daughter's age be 1 unit.

After 8 years, Rahul's age is 2 times her age plus 5 years.

Equating directly: 3 units + 8 = 2 × (1 unit + 8) + 5

3 units + 8 = 2 units + 21 ⇒ 1 unit = 13

Rahul's present age = 3 units = 3 × 13 = 39 years.

∴ The correct answer is 39 years.

Alternate Method

Given:

⇒ Rahul's age is three times his daughter's age.

⇒ After 8 years, his age will be 5 years more than twice the age of his daughter.

Present Rahul = 3x Daughter = x

• 8 years

Future (+8 yrs) Rahul = 3x + 8 Daughter = x + 8

Condition: 3x + 8 = 2(x + 8) + 5

Calculations:

⇒ Let the present age of the daughter be x years.

⇒ Present age of Rahul = 3x

⇒ Age of daughter after 8 years = x + 8

⇒ Age of Rahul after 8 years = 3x + 8

⇒ According to the condition: 3x + 8 = 2 × (x + 8) + 5

⇒ 3x + 8 = 2x + 16 + 5

⇒ 3x + 8 = 2x + 21

⇒ 3x − 2x = 21 − 8

⇒ x = 13

⇒ Daughter's present age = 13 years

⇒ Rahul's present age = 3x = 3 × 13 = 39 years

∴ The correct answer is 39 years.

Additional Information

Constant Age Difference

The absolute difference in ages between any two individuals always remains exactly the same, regardless of how many years pass backward or forward.

Cross-Multiplication Trick

When comparing ages represented as initial and final ratios over a fixed period of time, cross-multiplying the ratios simplifies finding the base value of 1 ratio unit rapidly.

Average Age Expansion

If the average age of a group of n persons is A, then after k years, the new average age logically becomes exactly A + k without recalculating individual totals.

Shortcut Trick

Since the selling price is the same for both, we can use the ratio method to equate SP units:

5% Profit = +1/20 ⇒ CP : SP = 20 : 21

30% Loss = −3/10 ⇒ CP : SP = 10 : 7 ⇒ Multiply by 3 to equate SP ⇒ 30 : 21

Total CP = 20 + 30 = 50 units | Total SP = 21 + 21 = 42 units

Loss % = (50 − 42) ÷ 50 × 100 = 8 ÷ 50 × 100 = 16%

∴ The correct answer is 16%.

Alternate Method

Given:

Selling price (SP) of each dryer = ₹63,000

Profit on first dryer = 5% | Loss on second dryer = 30%

Formula Used:

CP = (SP × 100) ÷ (100 ± Profit/Loss %)

Loss % = (Loss ÷ Total CP) × 100

Dryer 1 (5% Profit) CP: 60,000 → SP: 63,000

Dryer 2 (30% Loss) CP: 90,000 → SP: 63,000

Overall Transaction Total CP: ₹150k | Total SP: ₹126k Net Loss: 16%

Calculations:

⇒ CP of first dryer = (63,000 × 100) ÷ 105 = ₹60,000

⇒ CP of second dryer = (63,000 × 100) ÷ 70 = ₹90,000

⇒ Total CP = 60,000 + 90,000 = ₹1,50,000

⇒ Total SP = 63,000 + 63,000 = ₹1,26,000

⇒ Total Loss = 1,50,000 − 1,26,000 = ₹24,000

⇒ Loss % = (24,000 ÷ 1,50,000) × 100 = 16%

∴ The correct answer is 16%.

Additional Information

Same SP with Same Profit & Loss %

When two articles are sold at the same price, one at a profit of x% and the other at a loss of x%, there is always an overall net loss equal to (x² ÷ 100)%.

Successive Profit/Loss

If an article goes through multiple % changes (x and y), the net effect is given by x + y + (xy ÷ 100), where loss is taken as negative and profit as positive.

Dishonest Dealer

Profit % = (True Weight − False Weight) ÷ False Weight × 100.

The correct answer is West Bengal to Tamil Nadu.

Key Points

• The Eastern Coastal Plains of India extend from West Bengal in the north to Tamil Nadu in the south, running along the eastern coastline of India.
• They are bordered by the Bay of Bengal on the east and the Eastern Ghats on the west.
• The plains are divided into two sub-regions: the Utkal Plains in Odisha and the Coromandel Coast in Andhra Pradesh and Tamil Nadu.
• These plains are characterized by several major rivers like the Ganga, Mahanadi, Godavari, Krishna, and Kaveri, which form fertile deltas in this region.
• The region supports intensive agriculture, particularly of crops like rice, coconut, and sugarcane, due to the availability of fertile alluvial soil.

Additional Information

• Eastern Coastal Plains:
• These are wide, flat plains formed by the depositional activity of rivers.
• They are broader and more fertile compared to the Western Coastal Plains of India.
• Major Deltas:
• The region is home to some of the largest deltas in the world, such as the Sundarbans Delta (Ganges-Brahmaputra Delta) and the Godavari-Krishna Delta.
• Climate:
• The Eastern Coastal Plains experience a tropical monsoon climate with high humidity and significant rainfall, especially during the northeast monsoon season.
• Ports and Harbors:
• Major ports like Chennai, Visakhapatnam, and Paradip are located along the Eastern Coastal Plains, playing a significant role in trade and commerce.
• Biodiversity:
• The region includes ecologically significant areas such as the Sundarbans Mangrove Forests, which are home to the Royal Bengal Tiger and other endangered species.

Shortcut Trick To find the value x added to a, b, c, and d to make them proportional, use the direct formula: x = (bc − ad) ÷ ((a + d) − (b + c)). x = (15 × 21 − 30 × 11) ÷ ((30 + 11) − (15 + 21)) = (315 − 330) ÷ (41 − 36) = −15 ÷ 5 = −3. Given 6x : y :: y : (3x − 9), it means y is the mean proportional between 6x and (3x − 9). y2 = 6x(3x − 9) = 6(−3) × (3(−3) − 9) = (−18) × (−18) = 324. Since y > 0, we take the positive square root, giving y = 18. ∴ The correct answer is 18.

Alternate Method Given: Numbers: 30, 15, 21, and 11. If x is added, they become proportional. 6x, y, and (3x − 9) are in continuous proportion where y > 0. Formula Used: For a proportion a : b :: c : d, the product of extremes equals the product of means (ad = bc).

30 + x

:

15 + x

::

21 + x

:

11 + x

27

:

12

::

18

:

8

Both ratios simplify to 9 : 4 (when x = −3)

Calculations: ⇒ (30 + x) ÷ (15 + x) = (21 + x) ÷ (11 + x) ⇒ (30 + x)(11 + x) = (15 + x)(21 + x) ⇒ 330 + 41x + x2 = 315 + 36x + x2 ⇒ 41x − 36x = 315 − 330 ⇒ 5x = −15 ⇒ x = −3 Now, substituting x = −3 in the given continuous proportion 6x : y :: y : (3x − 9): ⇒ 6(−3) : y :: y : (3(−3) − 9) ⇒ −18 : y :: y : −18 ⇒ y2 = (−18) × (−18) ⇒ y2 = 324 ⇒ y = 18 (since it is given that y > 0) ∴ The correct answer is 18.

Additional Information Proportion Rule If four numbers a, b, c, d are in proportion, they satisfy a : b :: c : d, which translates algebraically to the rule: Product of Extremes = Product of Means (ad = bc). Mean Proportional The mean proportional 'y' between two numbers 'A' and 'B' is defined by A : y :: y : B, yielding the fundamental formula y2 = AB. Proportion Balancing Shortcut To find a value x added to a, b, c, and d to make them proportional without forming quadratic equations, simply use: x = (bc − ad) ÷ ((a + d) − (b + c)).

The given numbers are: 614, 457, 249, 625, 150.

The highest number in the list is 625.

The second digit of 625 is 2.

The lowest number in the list is 150.

The second digit of 150 is 5.

Subtract the second digit of the highest number (2) from the second digit of the lowest number (5).

Resultant = 5 - 2 = 3.

Thus, the resultant is 3.

Hence, the correct answer is "Option 4".

Given:

Option 1) MU - KH

Option 2) HL - JN

Option 3) SW - UY

Option 4) NR - PT

Option 1 follows a different pattern of making it the odd one out.

Hence, the correct answer is "Option 1".

The correct answer is 1817.

Key Points

• The Paika Rebellion of 1817 was led by Bakshi Jagabandhu Bidyadhar, the military chief of the Khurda Kingdom, in Odisha.
• It was a significant uprising against the British East India Company’s land revenue policies, which caused widespread discontent among the Paikas and other sections of society.
• The rebellion began in Khurda and rapidly spread to other regions of Odisha, involving a broad coalition of peasants, zamindars, and tribal groups.
• The British imposed exploitative taxes, disrupted traditional land rights, and confiscated the hereditary estates of many zamindars, fueling the revolt.
• The Paikas, traditional militia of Odisha, were primarily affected as their role in the Khurda kingdom was marginalized due to British administrative reforms.

Additional Information

• Who were the Paikas?
• The Paikas were the traditional landed militia of Odisha who rendered military service to the kings of the Khurda Kingdom in exchange for land grants.
• Their hereditary land tenures were known as "jagir," which the British abolished, reducing them to poverty.
• Impact of British Revenue Policies:
• The introduction of Permanent Settlement in Bengal and parts of Odisha disrupted the traditional agrarian system.
• The British confiscated lands and auctioned them off to new landlords, alienating the Paikas and local zamindars.
• Key Events of the Rebellion:
• The rebellion began in March 1817, with the Paikas attacking British establishments and burning government buildings.
• It was suppressed by September 1817, as the British used superior military technology and administrative measures.
• Legacy of the Paika Rebellion:
• The Paika Rebellion is often regarded as a precursor to India's First War of Independence in 1857.
• In 2017, the Government of India commemorated the 200th anniversary of the rebellion, recognizing its historical significance.

Shortcut Trick

Let the numbers be 5x and 3x.

Product of numbers = LCM × HCF ⇒ 15x² = 135 ⇒ x² = 9 ⇒ x = 3.

HCF = x = 3, and LCM = 15x = 45.

Sum of reciprocals = 1/45 + 1/3 = (1 + 15) / 45 = 16/45.

∴ The correct answer is 16/45.

Alternate Method

Given:

Ratio of two numbers = 5 : 3

Product of their LCM and HCF = 135

Formula Used:

Product of two numbers = LCM × HCF

Ratio = 5 : 3 Numbers: 5x, 3x

LCM × HCF = 135 15x² = 135 → x = 3

HCF = x = 3 LCM = 15x = 45

Sum of Reciprocals 1/45 + 1/3 = 16/45

Calculations:

⇒ Let the numbers be 5x and 3x.

⇒ Product of numbers = 5x × 3x = 15x²

⇒ 15x² = 135

⇒ x² = 9 ⇒ x = 3

⇒ The numbers are 5(3) = 15 and 3(3) = 9.

⇒ HCF of 15 and 9 = 3

⇒ LCM of 15 and 9 = 45

⇒ Sum of reciprocals = 1/LCM + 1/HCF

⇒ Sum = 1/45 + 1/3 = (1 + 15) / 45 = 16/45

∴ The correct answer is 16/45.

Additional Information

LCM & HCF Relation

For any two numbers a and b, the product of the numbers is equal to the product of their LCM and HCF. (a × b = LCM × HCF).

Co-prime Factors

If two numbers are given in a ratio p : q (where p and q are co-prime), and their HCF is x, then the numbers are px and qx, and their LCM is pqx.

Reciprocals Trick

The sum of reciprocals of two numbers a and b is given directly by (a + b) ÷ (a × b).

Shortcut Trick

Given tan θ = 15/8, which represents the ratio of Height to Base.

Height ratio = 15 parts → 30 m

Multiplier = 30 ÷ 15 = 2

Base distance = 8 parts × 2 = 16 m

∴ The correct answer is 16 m.

Alternate Method

Given:

Height of the top of the ladder from the ground (Perpendicular) = 30 m

Angle made by the ladder with the ground = θ

tan θ = 15/8

θ 30 m Wall d = ? Ground Ladder

Formula Used:

tan θ = Perpendicular ÷ Base

Calculations:

⇒ tan θ = Height of the wall ÷ Distance of foot from wall

⇒ 15/8 = 30 ÷ Distance

⇒ Distance × 15 = 30 × 8

⇒ Distance = 240 ÷ 15

⇒ Distance = 16 m

∴ The correct answer is 16 m.

Additional Information

Trigonometric Ratios in Right Triangles

For an acute angle θ, the primary ratios are: sin θ = Perpendicular ÷ Hypotenuse, cos θ = Base ÷ Hypotenuse, and tan θ = Perpendicular ÷ Base.

Pythagorean Triplets

Sets of three integers that naturally satisfy the Pythagorean theorem (H² = P² + B²). Common triplets include (3, 4, 5), (5, 12, 13), and (8, 15, 17).

Angle of Elevation

The angle formed by the line of sight with the horizontal plane when viewing an object located above the observer's level.

Shortcut Trick According to the empirical formula: Mean = (3 × Median − Mode) ÷ 2 ⇒ Mean = (3 × 88 − 28.4) ÷ 2 ⇒ Mean = (264 − 28.4) ÷ 2 ⇒ Mean = 235.6 ÷ 2 = 117.8 ∴ The correct answer is 117.8.

Alternate Method Given: Mode = 28.4 Median = 88 Formula Used: Karl Pearson's Empirical Formula: Mode = 3 × Median − 2 × Mean

Mode 28.4

Median 88

Mean 117.8

Mode = 3 × Median − 2 × Mean Positively Skewed (Mean > Median > Mode)

Calculations: ⇒ 28.4 = 3 × 88 − 2 × Mean ⇒ 28.4 = 264 − 2 × Mean ⇒ 2 × Mean = 264 − 28.4 ⇒ 2 × Mean = 235.6 ⇒ Mean = 235.6 ÷ 2 ⇒ Mean = 117.8 ∴ The correct answer is 117.8.

Additional Information Empirical Relationship in Statistics For a moderately skewed distribution, the relationship between Mean, Median, and Mode is given by the empirical formula: Mode = 3 × Median − 2 × Mean. Symmetrical Distribution In a perfectly symmetrical or normal distribution, all three measures of central tendency are equal: Mean = Median = Mode. Positively Skewed Distribution The distribution tail is longer on the right side. The measures follow the order: Mean > Median > Mode. Negatively Skewed Distribution The distribution tail is longer on the left side. The measures follow the order: Mean < Median < Mode.

The correct answer is Windows 10.

Key Points

• Windows 10 is a widely used operating system developed by Microsoft for personal computers, laptops, and tablets.
• It was officially released on July 29, 2015, and has since become one of the most popular desktop operating systems globally.
• Windows 10 introduced features like the Start Menu, Cortana (AI assistant), and Microsoft Edge browser, providing a seamless user experience.
• The operating system supports various software applications and provides compatibility for hardware devices, making it suitable for both professional and personal use.
• Windows 10 receives regular updates from Microsoft to ensure better performance, security, and new features.

Additional Information

• Operating System (OS):
• An operating system is system software that manages hardware and software resources and provides services for computer programs.
• Examples of popular desktop operating systems include Windows, macOS, and Linux.
• Microsoft Word:
• Microsoft Word is a word processing software developed by Microsoft, not an operating system.
• It is commonly used for creating and editing text documents.
• Google Chrome:
• Google Chrome is a web browser developed by Google, not an operating system.
• It is used for accessing websites and browsing the internet.
• Adobe Photoshop:
• Adobe Photoshop is a graphic design and photo editing software developed by Adobe Systems, not an operating system.
• It is used for tasks such as editing images and creating digital artwork.
• Windows 11:
• The latest version of Microsoft's operating system, Windows 11, was launched on October 5, 2021.
• It introduced a redesigned user interface and enhanced productivity tools while maintaining compatibility with Windows 10 applications.

Shortcut Trick

For three numbers in continuous proportion, Mean Proportion² = First Term × Third Term

⇒ 260² = x × 338

⇒ x = (260 × 260) ÷ 338

⇒ x = 67600 ÷ 338 = 200

∴ The correct answer is 200.

Alternate Method

Given:

Mean proportion = 260

First term = x

Third term = 338

x

:

260

::

260

:

338

Mean Proportion

Continuous Proportion

Formula Used:

Mean Proportion = √(First term × Third term)

Calculations:

⇒ 260 = √(x × 338)

Squaring both sides:

⇒ 260² = x × 338

⇒ 67600 = 338x

⇒ x = 67600 ÷ 338

⇒ x = 200

∴ The correct answer is 200.

Additional Information

Mean Proportion

If b is the mean proportion between a and c, then b = √(a × c).

Third Proportion

If a : b :: b : c, then c is called the third proportion. Formula: c = b² ÷ a.

Fourth Proportion

If a : b :: c : d, then d is called the fourth proportion. Formula: d = (b × c) ÷ a.

Compound Ratio

The compound ratio of a : b and c : d is defined as (a × c) : (b × d).

Shortcut Trick

Use the successive percentage change formula: Net % change = a + b + (a × b) ÷ 100

Here, a = −15% (reduction) and b = +10% (raise)

Net change = −15 + 10 + (−15 × 10) ÷ 100

Net change = −5 − 1.5 = −6.5%

The negative sign indicates an overall decrease of 6.5%.

∴ The correct answer is 6.5%.

Alternate Method

Given:

Reduction in salary = 15%

Subsequent raise in salary = 10%

Calculations:

Initial 100

Reduced 85

Final 93.5

−15%

+10%

Net Change: −6.5%

⇒ Let the initial salary of Salil be 100 units.

⇒ Salary after 15% reduction = 100 − (15% of 100) = 100 − 15 = 85 units.

⇒ Subsequent 10% raise on the new salary = 85 + (10% of 85) = 85 + 8.5 = 93.5 units.

⇒ Net decrease in salary = Initial salary − Final salary = 100 − 93.5 = 6.5 units.

⇒ Percentage decrease = (Net decrease ÷ Initial salary) × 100

⇒ Percentage decrease = (6.5 ÷ 100) × 100 = 6.5%.

∴ The correct answer is 6.5%.

Additional Information

Successive Percentage Change

When a value undergoes multiple percentage changes sequentially, the net effect is given by: a + b + (a × b) ÷ 100. Always use a positive sign for increments/profit and a negative sign for decrements/loss.

Multiplying Factor Method

Final Value = Initial Value × (1 ± r₁ ÷ 100) × (1 ± r₂ ÷ 100). For this question: Final = Initial × 0.85 × 1.10 = Initial × 0.935, directly showing a 6.5% drop.

Base Value Concept

In successive percentage problems, every subsequent change is applied to the newly obtained intermediate value, never on the original base value.

BODMAS Rule:

According to the question, the symbol meanings are:

Now,

Given e×pression: 32 ÷ 14 + 16 – 8 × 4 = ?

After replacing the symbols with their new meanings:

⇒ 32 + 14 − 16 × 8 ÷ 4

Perform operations according to BODMAS/PEMDAS:

⇒ 32 + 14 − 16 × 8 ÷ 4

⇒ 32 + 14 − 128 ÷ 4

⇒ 32 + 14 − 32

⇒ 46 − 32

⇒ 14

Hence, the correct answer is "Option 1".

The logic followed here is:

Thus, 'LPT' will be the next in the series.

Hence, the correct answer is "Option 2".

The correct answer is 100.

Key Points

• The Smart Cities Mission was launched by the Government of India on 25 June 2015 under the Ministry of Housing and Urban Affairs.
• Initially, 100 cities were selected to be developed as part of the mission.
• The mission aims to improve urban infrastructure and provide better quality of life through sustainable and inclusive development.
• The cities were selected through a competitive process known as the Smart Cities Challenge.
• The total planned investment for the mission is estimated at ₹2.05 lakh crore, covering projects like affordable housing, urban mobility, and IT connectivity.

Additional Information

• Smart Cities Mission Objectives:
• The mission focuses on area-based development such as retrofitting, redevelopment, and greenfield projects.
• It emphasizes smart solutions like smart meters, intelligent traffic management, and e-governance.
• Selection Process:
• The cities were selected through a three-stage competition involving state governments, urban local bodies, and central government evaluation.
• Only cities that meet specified criteria are granted funding under the mission.
• Implementation:
• Each selected city sets up a Special Purpose Vehicle (SPV) for implementation, with support from government and private partners.
• The SPV is responsible for planning, appraising, and executing projects under the mission.
• Progress:
• As of 2023, over 7,000 projects have been tendered, with many nearing completion across various cities.
• Key focus areas include urban mobility, affordable housing, and green energy initiatives.

The logic followed here is:

Option 1)  # = DQU, % = XHA

Does not follow same logic.

Option 2)  # = FTS, % = XHA

Does not follow same logic.

Option 3) # = XHA, % = ZKY

Follow the same logic.

Option 4)  # = ZKY, % = FTS

Does not follow same logic.

Hence, the correct answer is "Option 3".

The correct answer is Town Area Committee.

Key Points

• A Town Area Committee is a semi-municipal authority responsible for administering small towns with limited municipal functions.
• It typically manages essential services such as street lighting, drainage, and sanitation in areas that are not large enough to require a full-fledged municipal corporation.
• These committees are constituted by the State Governments and operate under their supervision.
• Unlike municipal corporations, a Town Area Committee has limited jurisdiction and fewer responsibilities.
• The members of the committee can be either elected, nominated, or both, depending on state regulations.

Additional Information

• Municipal Corporation:
• A municipal corporation is an urban local government body responsible for the governance of large cities with populations exceeding a specific threshold (e.g., 1 lakh or more).
• It handles diverse functions such as waste management, public transportation, and urban planning.
• Special Purpose Agencies:
• These are autonomous bodies created to manage specific functions like water supply, transportation, or housing in urban areas.
• They operate independently of the municipal government.
• Port Trust:
• A Port Trust is a specialized body responsible for managing and maintaining ports and their associated facilities.
• It primarily focuses on trade and maritime operations rather than urban governance.
• Urban Local Self-Government:
• Urban local self-government refers to the institutions that govern cities and towns, ensuring the provision of essential services and infrastructure.
• Examples include municipal corporations, municipalities, town area committees, and notified area councils.

The correct answer is Vimana.

Key Points

• In South Indian temple architecture, the term Vimana refers to the pyramidal or stepped structure built directly above the sanctum (garbhagriha).
• The Vimana is often elaborately decorated with intricate carvings, sculptures, and ornamental details, showcasing the artistic skill of ancient Indian craftsmen.
• This feature is a distinguishing aspect of Dravidian temple architecture, commonly seen in temples of Tamil Nadu, Andhra Pradesh, Karnataka, and Kerala.
• The Vimana serves not only as an architectural feature but also as a symbolic representation of the sacred Mount Meru, believed to be the center of the universe in Hindu cosmology.
• Famous examples of Vimanas can be seen in temples like the Brihadeeswarar Temple in Thanjavur and the Meenakshi Temple in Madurai.

Additional Information

• Adhisthana:
• The Adhisthana is the base or platform on which the temple structure is built. It provides stability and often contains ornamental moldings.
• Jagati:
• The Jagati refers to a raised platform that surrounds the temple, often used for circumambulation (pradakshina) by devotees.
• Mandapa:
• A Mandapa is a pillared hall or pavilion in a temple, used for congregational purposes, rituals, and ceremonies. It is often located in front of the sanctum.
• South Indian Temple Architecture:
• South Indian temples are primarily built in the Dravidian architectural style, characterized by towering gopurams (gateway towers), Vimanas, and intricate carvings.
• The temple layout often includes key components like the Garbhagriha (sanctum), Vimana, Mandapa, and Prakara (enclosure walls).

Shortcut Trick

The sum of two supplementary angles is always 180°.

Smaller angle = (Sum of angles − Difference) ÷ 2

Smaller angle = (180° − 50°) ÷ 2

Smaller angle = 130° ÷ 2 = 65°

∴ The correct answer is 65°.

Alternate Method

Given:

Two angles are supplementary.

The larger angle is 50° more than the smaller angle.

Formula Used:

Sum of supplementary angles = 180°

x

x + 50°

180°

Calculations:

Let the smaller angle be x.

⇒ Larger angle = x + 50°

⇒ x + (x + 50°) = 180°

⇒ 2x + 50° = 180°

⇒ 2x = 180° − 50°

⇒ 2x = 130°

⇒ x = 130° ÷ 2

⇒ x = 65°

∴ The correct answer is 65°.

Additional Information

Supplementary Angles

Two angles whose sum is exactly 180°. When placed adjacent to each other, they form a straight line.

Complementary Angles

Two angles whose sum is exactly 90°. For example, 40° and 50° form a complementary pair.

Adjacent Angles

Angles that share a common vertex and a common boundary side, but have no overlapping interior area.

Vertically Opposite Angles

When two straight lines intersect, the non-adjacent opposite angles formed are always equal.

The logic followed in this pattern is a consistent alphabetical shift of -3 for each letter.

For 'FARM' related to 'CXOJ':

For 'FRESH' related to 'COBPE':

Applying the same logic to 'RICH':

Thus, RICH is related to OFZE.

Hence, the correct answer is "Option 1".

The logic followed here is:

Option 1) # = GCH, % = TPU

Follow same logic.

Option 2) # = FDH, % = NHU

Does not follow the same logic.

Option 3) # = UPS, % = RPV

Does not follow the same logic.

Option 4) # = DCV, % = NHY

Does not follow the same logic.

Hence, the correct answer is "Option 1".

Given:

Fardeen starts from point A and drives 13 km towards west.

He then takes a left turn, drives 7 km, turns right and drives 6 km.

He then takes a left turn and drives 8 km. He takes a final left turn, drives 19 km and stops at point P. 

Thus, Fardeen has to drive 15km north to reach point A.

Hence, the correct answer is "Option 3".

The correct answer is 0.64%.

Key Points

• India's expenditure on Research and Development (R&D) as a percentage of GDP stands at 0.64%, as per the Economic Survey 2024-25.
• This figure has remained relatively stagnant over the years, reflecting the need for increased investment in innovation and technology.
• India's R&D spending is significantly lower compared to global averages; countries like the USA and China spend around 2-3% of their GDP on R&D.
• Government funding constitutes the majority of R&D expenditure in India, with limited contributions from the private sector.
• The low R&D spending impacts India's global competitiveness in technological advancements and innovation.

Additional Information

• Global Comparison:
• Countries like South Korea and Israel invest over 4% of their GDP in R&D, showcasing their emphasis on innovation-driven growth.
• India's R&D Landscape:
• Key sectors include pharmaceuticals, information technology, and space research, led by organizations like ISRO, DRDO, and CSIR.
• Private Sector Participation:
• India's private sector contribution to R&D is relatively low, accounting for approximately 36% of total R&D expenditure.
• Policy Recommendations:
• Experts suggest increasing public-private partnerships and incentivizing private sector investment in R&D to boost innovation.
• Innovation Index:
• India ranks 40th in the Global Innovation Index 2023, highlighting the scope for improvement in research and innovation capabilities.

The correct answer is Burning wood.

Key Points

• Burning wood is a chemical change because it involves the transformation of wood into new substances such as carbon dioxide, water vapor, ash, and heat energy.
• During burning, a chemical reaction known as combustion occurs, where wood reacts with oxygen to produce energy and byproducts.
• The process is irreversible, meaning the original wood cannot be recovered after burning, which is a hallmark of a chemical change.
• New chemical bonds are formed, and old bonds are broken during the process, indicating a change in the chemical composition of the material.
• Other examples of chemical changes include rusting of iron, cooking food, and souring of milk.

Additional Information

• Chemical Change: A process where one or more substances are transformed into new substances with different chemical properties. Examples include burning, rusting, and fermentation.
• Physical Change: A change in the state, shape, or size of a material without altering its chemical composition. Examples include melting ice, boiling water, and cutting paper.
• Combustion: A high-temperature exothermic reaction between a fuel (e.g., wood) and an oxidant (e.g., oxygen) that produces energy (heat and light) and byproducts like carbon dioxide and water.
• Irreversibility: Chemical changes are often irreversible, meaning the original substances cannot be restored. This is a key distinction from physical changes, which are usually reversible.
• Indicators of a Chemical Change: Common signs include color change, formation of a precipitate, emission of gas, change in temperature, and production of light or sound.

The correct answer is Graphic Card.

Key Points

• The Central Processing Unit (CPU) primarily consists of three main components: Arithmetic Logic Unit (ALU), Control Unit (CU), and Registers. These work together to process data and execute instructions.
• A Graphic Card is a separate hardware component designed to handle the rendering of images, videos, and 3D graphics, and is not a part of the CPU.
• The Arithmetic Logic Unit (ALU) is responsible for performing arithmetic and logical operations within the CPU.
• The Control Unit (CU) directs the flow of data within the CPU, coordinating the activities of other components.
• Registers are small storage locations within the CPU that hold data, instructions, and addresses temporarily during computation.

Additional Information

• Central Processing Unit (CPU): Often referred to as the "brain" of the computer, the CPU performs all processing tasks and executes instructions from programs.
• Graphic Card: Also known as a GPU (Graphics Processing Unit), it is optimized for rendering images and videos. It is essential for tasks such as gaming, video editing, and 3D modeling, but operates independently of the CPU.
• Registers: These are high-speed storage units located inside the CPU. Examples include the accumulator, instruction register, and program counter.
• Control Unit (CU): The CU interprets instructions from programs and directs the operation of the CPU and other components such as memory and I/O devices.
• ALU (Arithmetic Logic Unit): Performs mathematical calculations (addition, subtraction, multiplication, division) and logical operations (AND, OR, NOT) within the CPU.

Given: (Left) 401 418 733 283 902 (Right)

The highest number is: 902

The second digit of the highest number is: 0

And, 

The lowest number is: 283

The third digit of the lowest number is: 3

So, the addition of the second digit of the highest number and the third digit of the lowest number is:

→ 0 + 3 = 3.

The correct answer is "Option 4".

The correct answer is Option 4.

Key Points

• The Digital Agriculture Mission was launched with the aim to modernize the agriculture sector by leveraging digital technologies.
• It involves the creation of Digital Public Infrastructure, including AgriStack and Comprehensive Soil Fertility Maps, to enhance precision farming and decision-making for farmers.
• AgriStack is not managed solely by the Central Government but involves collaboration with private entities and state governments for its development and implementation.
• One of the key objectives of the mission is to provide digital services like credit, insurance, and advisory through authenticated data, ensuring better access and transparency for farmers.

Additional Information

• AgriStack: A digital ecosystem initiative that integrates data from various agriculture-related sources to provide farmers with actionable insights. It includes land records, weather data, and crop patterns.
• Comprehensive Soil Fertility Maps: These maps provide detailed information on soil health, helping farmers optimize fertilizer use and improve crop yields sustainably.
• Digital Public Infrastructure: Refers to shared platforms and tools that can be used by private and public entities for delivering agricultural services and solutions.
• Farmer Authentication: The use of Aadhaar and other digital tools ensures that only genuine farmers benefit from the schemes and services under the mission.
• Precision Agriculture: The use of technology and data-driven approaches under the Digital Agriculture Mission helps reduce input costs and improve productivity while minimizing environmental impact.

Key Points

• K Sanjay Murthy assumed charge as the Comptroller General of India in November 2024.
• The Comptroller General of India is responsible for overseeing the financial accountability and auditing of government expenditures.
• K Sanjay Murthy has a distinguished career in public administration, holding various important positions in the government prior to this appointment.
• The role of Comptroller General of India is crucial for ensuring transparency and efficiency in the management of public funds.
• K Sanjay Murthy was selected for this position due to his extensive experience in financial management and governance.

Additional Information

• Comptroller and Auditor General (CAG):
• The Comptroller and Auditor General (CAG) of India is an authority established under Article 148 of the Constitution of India.
• The CAG audits all receipts and expenditures of the Government of India and the state governments, including those of bodies and authorities substantially financed by the government.
• The CAG's reports are submitted to the President and Governors, who then present them to the respective legislatures.
• The position is considered vital for ensuring accountability and transparency in the financial administration of the government.
• Government Financial Oversight:
• Financial oversight ensures that government funds are allocated and spent effectively and in accordance with legal and policy frameworks.
• This involves auditing government expenditures, reviewing financial statements, and identifying irregularities or inefficiencies.
• Public Accountability:
• Public accountability is a cornerstone of good governance, requiring transparency in financial and administrative operations.
• Institutions like the Comptroller General of India play a critical role in maintaining this accountability.
• Auditing Standards:
• Auditing standards are guidelines for conducting audits to ensure accuracy, reliability, and fairness in financial reporting.
• In India, these standards are governed by the CAG and aligned with international best practices.