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The correct answer is Mizoram.

Key Points

• Anthurium festival of Mizoram is one of the most popular festivals celebrated in the state.
• This festival is celebrated to promote tourism.
• The Anthurium Festival is organized annually by the Tourism Department in collaboration with the Horticulture Department.
• The Chapchar Kut is also regarded as the most popular spring festival for the people of the state.
• This festival is a public holiday in the state.
• Traditional bamboo dance - Cheraw and other dances were performed at the main event, attracting thousands of people.
• Mizoram:
• State Animal - Sumatran serow.
• State Bird - Mrs. Hume's pheasant.
• National Parks - Murlen National Park, Phawngpui National Park.

Additional Information

• Festivals of Assam:
• ​Bihu is the harvest festival of Assam.
• Bihu marks the end of the harvesting season.
• Bihu is a set of three important Assamese festivals.
• Rongali or Bohag Bihu in April.
• Kongali or Kati Bihu in October.
• Bhogali or Magh Bihu in January.
• Festivals of Manipur:
• ​Lai Haraoba.
• Kang Festival.
• Sangai Festival.
• Kut Festival.
• Cheiraoba Festival
• Festivals of Nagaland:
• ​Hornbill Festival.
• Sekrenyi.
• Tsukheneye.
• Aoleang.
• Naknyulem

Given:

25 ÷ 5 × 2 + 25 - 11 = 24

Calculation:

By option Method:

Option I: After interchanging 11, 24

⇒ 25 ÷ 5 × 2 + 25 - 24 = 11

⇒ 5 × 2 + 25 - 24

⇒ 10 + 1

⇒ 11 = 11

This is correct the equation.

Option II: After interchanging  2, 5

⇒ 25 ÷ 2 × 5 + 25 - 11 = 24

⇒ 12.5 x 5 + 25 -11 = 24

⇒ 76.5  ≠ 24

This is not correct the equation.

Option III: After interchanging 5, 25

⇒ 25 ÷ 25 × 2 + 5 - 11 = 24

⇒ 1 × 2 + 5 - 11 = 24

⇒ - 5 ≠ 11

This is not correct the equation.

Option IV: After interchanging 24, 25

⇒ 25 ÷ 5 × 2 + 24 - 11 = 25

⇒ 5 × 2 + 24 -11 = 25

⇒ 23 ≠ 25

This is not correct the equation.

∴ Interchanges (11,24) would make the given equation correct.

The correct answer is Sindhi.

Key Points

• The Sindhi language was added to the list of languages in the Indian Constitution by the 21^st Amendment in 1967.
• It was added to the 8^th schedule by the 21^st Amendment Act of 1967.

Additional Information

• There are 22 languages that have been recognized in the eighth schedule of the Indian constitution.
• Part XVII of the Indian constitution deals with the official languages of India from articles 343 to 351.
• Originally, only 14 languages were mentioned and later, after several amendments, the other languages were added.
• The Sindhi language was added to the 8^th schedule by the 21^st Amendment Act of 1967.
• Konkani, Manipuri and Nepali were added by the 71^st Amendment Act of 1992.
• Bodo, Dongri, Maithili and Santhali were added by the 92^nd Amendment Act of 2003.
• Of all the 22 official languages the Hindi language is spoken by most of Indians.

Shortcut Trick

Product of LCM and HCF = Product of the two numbers.

Product = 48 and Difference = 13.

Check options: 3 × 16 = 48 and 16 − 3 = 13. This satisfies both conditions.

∴ The correct answer is 3 and 16.

Alternate Method

Given:

LCM × HCF = 48

Difference (x − y) = 13

Formula Used:

Product of two numbers = LCM × HCF

Calculations:

⇒ Let the numbers be x and y.

⇒ x × y = 48

⇒ x − y = 13 ⇒ x = 13 + y

⇒ (13 + y) × y = 48

⇒ y² + 13y − 48 = 0

⇒ y² + 16y − 3y − 48 = 0

⇒ y(y + 16) − 3(y + 16) = 0

⇒ (y − 3)(y + 16) = 0

⇒ y = 3 (since numbers are positive)

⇒ x = 13 + 3 = 16

∴ The correct answer is 3 and 16.

Additional Information

Fundamental Property of HCF and LCM

For any two positive integers a and b, HCF(a, b) × LCM(a, b) = a × b.

HCF as a Factor

The HCF of two or more numbers is always a factor of their LCM.

Co-prime Numbers

If two numbers are co-prime, their HCF is 1 and their LCM is equal to the product of the numbers.

Shortcut Trick

Work done by Rani in 1 day (6 hours) = 6 ÷ 3 = 2 gowns.

Work done by Padma in 1 day (6 hours) = 6 ÷ 2 = 3 gowns.

Alternate days cycle (2 days): 2 + 3 = 5 gowns.

In 10 cycles (20 days), work done = 10 × 5 = 50 gowns.

Remaining 2 gowns are stitched by Rani on the 21^st day.

∴ The correct answer is 21 days.

Alternate Method

Given:

Time taken by Rani per gown = 3 hours.

Time taken by Padma per gown = 2 hours.

Daily working hours = 6 hours.

Total gowns to be stitched = 52 gowns.

Calculations:

⇒ Day 1 (Rani) = 2 gowns.

⇒ Day 2 (Padma) = 3 gowns.

⇒ Total gowns in 2 days = 2 + 3 = 5 gowns.

⇒ Total cycles of 2 days needed = 52 ÷ 5 = 10 cycles with 2 gowns remainder.

⇒ Days for 10 cycles = 10 × 2 = 20 days.

⇒ Gowns completed in 20 days = 10 × 5 = 50 gowns.

⇒ Remaining gowns = 52 − 50 = 2 gowns.

⇒ On 21^st day, Rani stitches the remaining 2 gowns (since her capacity is 2 gowns/day).

⇒ Total time = 20 + 1 = 21 days.

∴ The correct answer is 21 days.

Additional Information

Alternate Day Work

In alternate work, tasks are solved in cycles. If A and B work alternately, 1 cycle = 2 days, and work done per cycle = Efficiency(A) + Efficiency(B).

Work and Efficiency

Efficiency is inversely proportional to time. Total Work = Efficiency × Time. In this problem, efficiency is converted to gowns per day based on a 6-hour shift.

Shortcut Trick

Sum of ages 3 years ago = 26 − (3 × 2) = 20 years.

Ratio of Kishore to Sarala (3 years ago) = 3 : 2.

Total units = 3 + 2 = 5 units → 20 years.

1 unit = 4 years ∴ Sarala's age (3 years ago) = 2 × 4 = 8 years.

Present age of Sarala = 8 + 3 = 11 years.

∴ The correct answer is 11 years.

Alternate Method

Given: Sum of Sarala (S) and Kishore (K) is 26. 3 years ago, K was 3/2 of S.

Formula: Ratio = Age₁ / Age₂

⇒ Let Sarala's present age be S.

⇒ Kishore's present age K = 26 − S.

⇒ 3 years ago: (K − 3) = 3/2 × (S − 3).

⇒ (26 − S − 3) = 3/2 × (S − 3).

⇒ 2 × (23 − S) = 3 × (S − 3).

⇒ 46 − 2S = 3S − 9.

⇒ 5S = 55.

⇒ S = 11.

∴ The correct answer is 11 years.

Additional Information

Age Sum Property

If the sum of ages of 'n' persons is S now, then 't' years ago, the sum was S − (n × t).

Ratio of Ages

The difference between the ages of two people remains constant regardless of the number of years passed.

Linear Equations

For age problems, always define variables based on the Present Age to avoid calculation errors in final steps.

The logic is follows here is as,

Hence, 'option 3' is the correct answer.

The correct answer is Ministry of Minority Affairs.

Key Points

• The revised PMJVK will be implemented in all districts of the country including all the Aspirational Districts.
• The projects under PMJVK will be proposed in any area where the concentration of the minority population is more than 25% in the catchment area (15 KM radius).
• The revised PMJVK has been approved by the Government for continuation over the 15^th Finance Commission Cycle i.e., during FY 2021-22 to 2025-26.
• PMJVK will support the State/UTs in creating infrastructure to improve the quality of life of people and reduce the imbalances in the identified minority concentration areas to be at par with the rest of the country.

Additional Information

• The Cabinet Committee on Economic Affairs chaired by Prime Minister Narendra Modi on May 2, 2018, approved the proposal for renaming and restructuring of the Multi-sectoral Development Programme (MsDP) as Pradhan Mantri Jan Vikas Karyakram (PMJVK).
• The restructured program would provide better socio-economic infrastructure facilities to the minority communities, particularly in the field of education, health & skill development.
• The area to be covered under PMJVK would be 57% more as compared to the existing MsDP.
• The MsDP covered 196 districts of the country whereas PMJVK will cover 308 districts of the country.

Given:

x = 18% of 200

Calculation:

⇒x = 18% of 200

⇒ x = \(200 \times {18 \over 100}\)

⇒ x = 36

The value of x is 36.

Shortcut Trick

Let the cost of production be x.

Final Price = x × (112 ÷ 100) × (115 ÷ 100) × (120 ÷ 100) = 15,456.

x × (28 ÷ 25) × (23 ÷ 20) × (6 ÷ 5) = 15,456.

x = (15,456 × 25 × 20 × 5) ÷ (28 × 23 × 6).

x = 10,000.

∴ The correct answer is ₹10,000.

Alternate Method

Given: Retail Price = ₹15,456, Manufacturer Gain = 12%, Wholesale Gain = 15%, Retailer Gain = 20%. Formulas: SP = CP × (100 + P%) ÷ 100.

⇒ Let Cost of Production = C. ⇒ Price after Manufacturer = C × 1.12. ⇒ Price after Wholesaler = (C × 1.12) × 1.15. ⇒ Price after Retailer (Retail Price) = (C × 1.12 × 1.15) × 1.20 = 15,456. ⇒ C × 1.5456 = 15,456. ⇒ C = 15,456 ÷ 1.5456 = 10,000.

∴ The correct answer is ₹10,000.

Additional Information

Successive Percentage Changes

When a value changes by a%, then b%, then c% successively, the Effective Multiplier is (1 + a/100) × (1 + b/100) × (1 + c/100).

Chain Rule in Profit and Loss

In a chain of transactions, the Selling Price for one becomes the Cost Price for the next buyer in the sequence.