Search Previous Year Questions

Given:

 

The first 30 natural numbers are 1, 2, 3, 4, ..., 30.

 

Concept:

 

The sum of an arithmetic series is the number of terms in the series times the average of the first and last terms.

 

Formula:

 

Sn = n/2(a + l)

 

where:

 

Sn is the sum of the series

 

n is the number of terms in the series

 

a is the first term in the series

 

l is the last term in the series

 

Solution:

 

Define the variables:

 

n = 30 (number of terms)

 

a = 1 (first term)

 

l = 30 (last term)

 

Substitute the values in the formula:

 

Sn = n/2(a + l) = 30/2(1 + 30) = 30/2 × 31 = 465

 

Therefore, The sum of the first 30 natural numbers is 465.

The correct answer is Bipin Chandra Pal.

Key Points

• The author of 'The Soul of India' is Bipin Chandra Pal.
• Bipin Chandra Pal (1858-1932) was a renowned freedom fighter, journalist, writer, and orator from India.
• He is often referred to as the 'Father of Revolutionary Thoughts' in India and was among the triumvirate, referred to as "Lal-Bal-Pal," of key leaders of the Indian Independence movement against British colonial rule during the early 20^th century.
• The triad comprised Lala Lajpat Rai (Lal), Bal Gangadhar Tilak (Bal), and Bipin Chandra Pal (Pal).
• 'The Soul of India' is one of his most notable works and is considered a significant contribution to Indian philosophical and political thought.
• In this book, Pal discusses the spiritual and cultural roots of India, its history, its civilization, and the future path that the nation was to follow.
• He critiques both British imperialism and the narrow-mindedness of some sections of Indian society.

Symbol for family tree: 

Rita is the aunt of Nikhil. 

Hence Option 3 is the correct answer.

The correct answer is South America.

Key Points

• The most arid place on Earth is situated in South America. Specifically, it is the Atacama Desert.
• The Atacama Desert is located along the Pacific coast of northern Chile and is considered the driest non-polar desert in the world.
• Its aridity is the result of a constant temperature inversion due to the cold offshore Humboldt Current and the Andes Mountains.
• The average rainfall in the Chilean region of the Atacama is just 1 millimeter (0.04 inches) per year.
• Some weather stations in the Atacama have never received rain.
• Its soil composition has been likened to that of Mars, and the region is often used as a testing site for Mars rovers.

Additional Information

• Africa: The Sahara Desert in Africa is the largest hot desert in the world but not the most arid. While extremely dry, some regions of the Sahara receive more periodic rainfall than the Atacama.
• Asia: This continent includes the Arabian and Gobi deserts. While these are indeed arid regions, they are not as arid as the Atacama in South America.
• Australia: This continent features several deserts, including the Great Victoria and Simpson deserts. Although these regions are characterized by low rainfall and high temperatures, they do receive more moisture than the Atacama.

Given:

 

First Discount: 10%

 

Second Discount: 20%

 

Concept:

 

The concept used here is successive discounts. When discounts are applied successively, they are multiplied together, but one minus the discount rate

 

Solution:

 

Let's assume the original price to be 100 for simplicity of calculations.

 

First discount is applied: ⇒ New price = Original price × (1 - First discount rate)

 

⇒ New price = 100 × (1 - 0.10) = 90

 

Then the second discount is applied on the new price: ⇒ Final price = New price × (1 - Second discount rate)

 

⇒ Final price = 90 × (1 - 0.20) = 72

 

Calculate equivalent total discount: The equivalent total discount is the difference between the original price and final price divided by the original price:

 

⇒ Equivalent total discount = (Original price - Final price) ÷ Original price × 100%

 

⇒ Equivalent total discount = (100 - 72) ÷ 100 × 100% = 28%

 

Hence, applying a 10% discount followed by a 20% discount is equivalent to a total discount of 28%.

The opposite sides are given below:

Note:- Two opposite faces are never seen together or adjacent to each other.

In figure (1):  

None of the opposite faces are seen together nor they are adjacent to each other. Thus this cube can be made.

In figure (2):

 Here the shaded potion cannot be adjacent to the doted side. The doted side should be opposite to the shaded side. Hence this cube cannot be formed.

In figure (3): 

None of the opposite faces are seen together nor they are adjacent to each other. Thus this cube can be made.

In figure (4): 

None of the opposite faces are seen together nor they are adjacent to each other. Thus, this cube can be made.

Hence the correct answer is Option 2: 1, 3 and 4 only

Mistake Points

Cube will form with these sides. Yes, it is confusing because there have three empty sides. In this type of question, you should focus on the possible case. We should ignore the empty sides which are opposite to symbols and try to form a dice with the other empty side.

Given:

 

Simple interest rate: 6 1/4% per annum

 

Concept:

 

The formula for simple interest is I = PRT/100, where 'I' is the interest, 'P' is the principal amount, 'R' is the rate of interest, and 'T' is the time in years. In this problem, the interest equals to the principal as money doubles itself.

 

Solution:

 

Let the principal (P) be 1 unit (for simplicity), hence the interest (I) at the end of the period is also 1 unit (because the money doubles).

 

Convert the rate of interest to a decimal: R = 6.25 / 100 = 0.0625.

 

Substituting I, P and R into the formula and solving for T:

 

⇒ 1 = 1 × 0.0625 × T ⇒ T = 1 / 0.0625 ⇒ T = 16

 

Hence, the time required to double the sum of money at 6 1/4% simple interest per annum is 16 years.

Given:

 

Total number of mobile phones: 80

 

The average price of all mobile phones: Rs. 30,000

 

Average price with highest and lowest phones sold out: Rs. 29,500

 

Cost of the highest price mobile: Rs. 80,000

 

Concept:

 

The total cost of the items is the product of the average cost and the number of items. The average price is calculated without the highest and lowest items by subtracting their cost from the total cost and dividing by the new number of items.

 

Solution:

 

First, we calculate the total cost of all 80 mobile phones

 

⇒ Total cost = Average price × Total number

 

⇒ Total cost = Rs. 30,000 × 80 = Rs. 2,400,000

 

Secondly, we calculate the total cost of the 78 mobile phones after selling the highest and lowest price phones

 

⇒ New Total cost = New Average price × New Total number ⇒ New Total cost = Rs. 29,500 × 78 = Rs. 2,301,000

 

To find out the cost of lowest the mobile, we subtract the cost of the highest price mobile and the total cost of the 78 phones from the total cost of all 80 phones

 

⇒ Cost of lowest price phone = Total cost - New Total cost - Cost of highest price phone

 

⇒ Cost of lowest price phone = Rs. 2,400,000 - Rs. 2,301,000 - Rs. 80,000 = Rs. 19,000

 

Therefore, the cost of the lowest price mobile phone is Rs. 19,000.

The correct answer is Jahangir.

Key Points

• On 18 September 1615, English diplomat Sir Thomas Roe arrived at the Surat port as the ambassador of the English King James I to Mughal Emperor Jahangir’s court.
• He stayed in the Mughal court for three years from 1615 to 1618.
• The East India Company received the royal charter to trade with India from the British monarch Elizabeth I in 1600.
• Their envoy William Hawkins had visited Jahangir in 1608.

The correct answer is Tea.

Key Points

• India earns most of its foreign currency from the Tea sector.
• India is one of the world's largest producers of tea, and it exports a significant portion of its production. Famous for its Darjeeling and Assam teas, India's tea industry constitutes a substantial part of the agriculture-based export economy.
• The processed tea is shipped to countries all around the world, contributing a significant amount to India's foreign exchange earnings.
• That being said, it's important to remember that while tea, spices, jute, and tobacco are all significant agricultural exports from India, they do not represent the sectors that earn the most foreign exchange for the country as a whole.
• There are other sectors such as information technology services, petroleum products, textiles, gems and jewelry, which account for a more substantial share of India's export earnings.
• Therefore, based on the options provided, 'Tea' is the correct answer but in a broader context and a larger frame, sectors like IT services and petroleum products earn more foreign exchange for India.