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Given:

Amount for elder daughter (A_elder) = ₹38,000

Amount for younger daughter (A_younger) = ₹38,000

Rate of interest (r) = 15%

Time for elder daughter (t_elder) = 18 - 12 = 6 years

Time for younger daughter (t_younger) = 18 - current age

Extra amount for elder daughter = ₹4,800

Formula used:

A = P\((1+\frac{r}{100})^t\)

Where,

P = Principal

A = Amount

r = Rate of interest

t = Time

Calculation:

For elder daughter:

38,000 = P_elder\((1+\frac{15}{100})^6\)

⇒ 38,000 = P_elder\((1+0.15)^6\)

⇒ 38,000 = P_elder(1.15)⁶

⇒ 38,000 = P_elder × 2.313

⇒ P_elder = \( \dfrac{38,000}{2.313} \)

⇒ P_elder ≈ ₹16,425

For younger daughter:

P_younger = P_elder - ₹4,800

⇒ P_younger = 16,425 - 4,800

⇒ P_younger ≈ ₹11,625

∴ The amount he kept for his younger daughter is ₹11,625.

The correct answer is Mahatma Gandhi.

Key Points

• Mahatma Gandhi represented the Indian National Congress in the Second Round Table Conference.
• The Second Round Table Conference was held in London from September to December 1931.
• Gandhi was the sole representative of the Indian National Congress, as the Congress had decided to boycott the conference initially but later sent Gandhi as their representative.

Additional Information

• The First Round Table Conference was held in London from November 1930 to January 1931 and was boycotted by the Indian National Congress.
• The Third Round Table Conference took place from November to December 1932, but by this time, the Congress had again boycotted the conference.
• The Round Table Conferences were a series of conferences organized by the British Government to discuss constitutional reforms in India.

Given:

Percentage of voters who restrained from voting = 25%

Percentage of invalid votes = 2%

Percentage of votes won by the candidate = 75%

Votes won by the candidate = 9261

Formula Used:

Total voters = Total votes cast / (1 - Percentage of voters who restrained from voting)

Valid votes = Total votes cast × (1 - Percentage of invalid votes)

Votes won by the candidate = Valid votes × Percentage of votes won by the candidate

Calculation:

Let the total number of voters be V.

Total votes cast = V × (1 - 0.25) = 0.75V

Valid votes = 0.75V × (1 - 0.02) = 0.75V × 0.98 = 0.735V

Votes won by the candidate = 0.735V × 0.75

⇒ 0.735V × 0.75 = 9261

⇒ 0.55125V = 9261

⇒ V = (9261)/(0.55125)

⇒ V = 16800

The total number of voters was 16800.

The logic followed here is: 

Logic: Along the row → Third number = (First number + Second number) × 2 + Second number

Let's check each row as per the logic,

Third row:

→ 59 = (13 + 11) × 2 + 11

→ 59 = 24 × 2 + 11

→ 59 = 48 + 11

Second row: 

→ 69 = (9 + 17) × 2 + 17

→ 69 = 26 × 2 + 17

→ 69 = 52 + 17

First row:

→ 49 = (? + 13) × 2 + 13

→ 49 = 2 × ? + 26 + 13

→ 49 = 2 × ? + 39

→ 10 = 2 × ? 

→ 10/2 = ?

→ 5 = ?

Hence, the correct answer is "5".

The correct answer is Narmada.

Key Points

• The Sardar Sarovar Multi-purpose Project is situated on the Narmada River.
• The Narmada River is one of the major rivers in India that flows westwards over a length of approximately 1,312 kilometers (815 miles).
• It originates from the Amarkantak Plateau in Madhya Pradesh.
• The project aims to provide water for irrigation, hydroelectric power generation, and drinking purposes.
• The Sardar Sarovar Dam is one of the largest dams constructed on the Narmada River.

Additional Information

• The Narmada River flows through the states of Madhya Pradesh, Maharashtra, and Gujarat before draining into the Arabian Sea.
• The river is considered sacred by Hindus and is often referred to as the "Life Line of Gujarat and Madhya Pradesh."
• The Sardar Sarovar Project is part of the Narmada Valley Development Plan, which includes multiple dams and canals to harness the river's potential.
• The project has been both praised for its benefits and criticized for its environmental and social impacts.

Given:

First day savings = ₹1

Second day savings = ₹2

Third day savings = ₹4

Fourth day savings = ₹8

Number of days = 12

Formula used:

The savings form a geometric series with the first term (a) = 1 and common ratio (r) = 2.

The sum of the first n terms of a geometric series is given by:

S_n = a(1 - rⁿ) / (1 - r)

Calculation:

For 12 days:

a = 1, r = 2, n = 12

S₁₂ = 1 × (1 - 2¹²) / (1 - 2)

⇒ S₁₂ = (1 - 4096) / (-1)

⇒ S₁₂ = -4095 / (-1)

⇒ S₁₂ = 4095

∴ The total savings in 12 days is ₹4095.

The correct answer is Gurusikhar.

Key Points

• Gurusikhar is the highest peak of the Aravalli range.
• The peak is located in Mount Abu, Rajasthan, and it rises to a height of about 1,722 meters (5,650 feet) above sea level.
• It offers a panoramic view of the surrounding area and is a popular tourist destination.
• The Aravalli range is one of the oldest mountain ranges in India, stretching approximately 800 km from Gujarat to Delhi.
• Mount Abu is the only hill station in the state of Rajasthan and is known for its cool climate and lush green surroundings.

Additional Information

• Dodabeta is the highest peak of the Nilgiri Hills in Tamil Nadu.
• Gorgaburu is a peak in the Ajodhya Hills of West Bengal.
• Panchmari is a hill station in Madhya Pradesh, but not a peak in the Aravalli range.

Given:

Perimeter of the rectangular field = 20 cm

Area of the rectangular field = 24 sq cm

Formula used:

Perimeter of rectangle = 2(length + breadth)

Area of rectangle = length × breadth

Calculation:

Let the length be L and the breadth be B.

From the perimeter:

2(L + B) = 20

⇒ L + B = 10

From the area:

L × B = 24

We have two equations:

1. L + B = 10
2. L × B = 24

Substitute B = 10 - L into the area equation:

L(10 - L) = 24

⇒ 10L - L² = 24

⇒ L² - 10L + 24 = 0

Solving the quadratic equation:

L = \(\dfrac{10 ± \sqrt{(10)^2 - 4×1×24}}{2×1}\)

⇒ L = \(\dfrac{10 ± \sqrt{100 - 96}}{2}\)

⇒ L = \(\dfrac{10 ± \sqrt{4}}{2}\)

⇒ L = \( \dfrac{10 ± 2}{2}\)

So, L = 6 or L = 4

If L = 6, then B = 4

If L = 4, then B = 6

The difference between length and breadth:

⇒ |L - B| = |6 - 4| = 2

∴ The difference of length and breadth of the field is 2 cm.

The mirror image of the given figure is shown below,

Hence, the correct answer is "Option 1".

The correct answer is Gopal Krishna Gokhale.

Key Points

• Gopal Krishna Gokhale was a prominent Indian political leader and a social reformer during the Indian independence movement.
• He founded the 'Servants of India Society' in 1905. 
• The objective of the society was to train and raise a group of selfless and dedicated individuals to serve India and promote social and human welfare.
• Gokhale was a senior leader of the Indian National Congress and was known for his moderate views and advocacy for constitutional methods of agitation.
• He played a significant role in the Indian National Congress and was a mentor to Mahatma Gandhi.

Additional Information

• The 'Servants of India Society' worked in the fields of education, healthcare, and rural development.
• It aimed to promote Indian nationhood and to serve the underprivileged sections of society.
• Gopal Krishna Gokhale believed in the principles of non-violence and constitutional means to achieve political goals.
• He was also associated with the Deccan Education Society and Fergusson College in Pune.
• His efforts laid the foundation for various social reforms in India.