Search Previous Year Questions

Preparing the family tree using the following symbols,

The family tree can be drawn based on the given information as shown below,

Here, we can see that M is the father of Q.

Hence, the correct answer is "Father".

Given:

Initial investment by A on 1^st January = ₹40,000

Initial investment by B on 1^st January = ₹60,000

Additional investment by A on 1^st March = ₹20,000

Withdrawal by B on 1^st June = ₹10,000

Total profit till 31^st December = ₹33,250

Formula Used:

Profit share = (Investment by partner × Time period) / Sum of (Investment × Time period for all partners)

Calculation:

Investment by A:

From 1^st Jan to 1^st Mar (2 months): ₹40,000

From 1^st Mar to 31^st Dec (10 months): ₹40,000 + ₹20,000 = ₹60,000

Investment by B:

From 1^st Jan to 1^st Jun (5 months): ₹60,000

From 1^st Jun to 31^st Dec (7 months): ₹60,000 - ₹10,000 = ₹50,000

Total investment by A:

₹40,000 × 2 + ₹60,000 × 10

⇒ ₹80,000 + ₹600,000

⇒ ₹680,000

Total investment by B:

₹60,000 × 5 + ₹50,000 × 7

⇒ ₹300,000 + ₹350,000

⇒ ₹650,000

Sum of investments:

₹680,000 + ₹650,000

⇒ ₹1,330,000

B's share in profit:

\(\left( \frac{\text{B's investment} \times \text{Total profit}}{\text{Total investment}} \right)\)

\(\left( \frac{650,000 \times 33,250}{1,330,000} \right)\)

⇒ \(\left( \frac{21,612,500}{1,330,000} \right)\)

⇒ ₹16,250

The share of B in the profit is ₹16,250.

The correct answer is Morarji Desai.

Key Points

• In 1967, Morarji Desai was designated as the Deputy Prime Minister of India.
• Morarji Desai served as Deputy Prime Minister under Prime Minister Indira Gandhi.
• He also held the position of Finance Minister during this time.
• Morarji Desai later became the Prime Minister of India in 1977.

Additional Information

• Chowdhry Charan Singh, Shri Jagjivan Ram, and Sardar Ballav Bhai Patel also held significant positions in the Indian government but were not designated as Deputy Prime Minister in 1967.
• Sardar Ballav Bhai Patel served as the first Deputy Prime Minister of India from 1947 to 1950.

The correct answer is Mandamus.

Key Points

• Mandamus is a writ issued by a higher court to compel a lower court or a government officer to perform mandatory or purely ministerial duties correctly.
• It ensures that public authorities fulfill their legal duties.
• It cannot be issued to compel a private individual or body.
• The term Mandamus means "We Command" in Latin.
• This writ is a powerful tool for judicial review of administrative actions.

Additional Information

• Certiorari is a writ issued by a higher court directing a lower court to send the record of a proceeding for review.
• Prohibition is a writ issued by a higher court to prevent a lower court from exceeding its jurisdiction.
• Habeas Corpus is a writ requiring a person under arrest to be brought before a judge or into court.

Given:

Speed of the train = 45 km/hr

Speed of the person = 5 km/hr

Time taken to cross the person = 18 seconds

Formula Used:

Length of the train (in metres) = Relative speed × Time

Calculation:

Relative speed = Speed of the train + Speed of the person

Relative speed = 45 km/hr + 5 km/hr

Relative speed = 50 km/hr

Convert relative speed to m/s:

Relative speed = 50 × (1000 / 3600) m/s

Relative speed = 50 × (5 / 18) m/s

Relative speed = 250 / 18 m/s

Relative speed = 125 / 9 m/s

Length of the train = Relative speed × Time

Length of the train = (125 / 9) × 18

Length of the train = 125 × 2

Length of the train = 250 metres

The length of the train is 250 metres.

The correct answer is Madras.

Key Points

• Annie Besant established the Home Rule League in Madras in 1916.
• The Home Rule League was an Indian political organization aimed at achieving self-governance and dominion status for India within the British Empire.
• The league played a crucial role in the Indian independence movement.
• Annie Besant was a prominent British socialist, theosophist, and supporter of Indian nationalism.
• The Home Rule League campaigned for the cause through public meetings, petitions, and extensive propaganda.

Additional Information

• Another Home Rule League was established by Bal Gangadhar Tilak in Pune around the same time.
• Both leagues worked in tandem to promote the idea of self-governance.
• The efforts of the Home Rule Leagues eventually led to greater political awareness and participation among Indians.
• This laid the groundwork for subsequent movements leading to India's independence in 1947.

The correct answer is Total internal reflection.

Key Points

• Mirage is an example of total internal reflection.
• Total internal reflection occurs when a wave hits a medium boundary at an angle larger than a particular critical angle with respect to the normal to the surface.
• Mirages are optical phenomena where light rays bend to produce a displaced image of distant objects or the sky.
• This bending of light usually occurs due to the temperature gradient in the atmosphere.

Additional Information

• Refraction is the bending of light as it passes from one medium to another.
• A spectrum is a range of different colors produced when light is dispersed by a prism.
• Reflection is the bouncing back of light from a surface.
• Mirage involves the bending of light rays due to total internal reflection, resulting in optical illusions.

Shortcut Trick

Separate the integer and fractional parts to calculate rapidly.

Integers: 12 + 10 − 7 − 1 = 14

Fractions: 1/3 + 5/6 − 2/3 − 4/7 = −1/3 + 5/6 − 4/7 = 3/6 − 4/7 = −1/14

Combine parts: 14 − 1/14 = 13 + (14/14 − 1/14) = 13 13/14

∴ The correct answer is 13 13/14.

Alternate Method

Given:

12 1/3 + 10 5/6 − 7 2/3 − 1 4/7

Calculations:

⇒ Converting mixed fractions to improper fractions:

⇒ 37/3 + 65/6 − 23/3 − 11/7

⇒ Grouping terms with denominator 3:

⇒ (37/3 − 23/3) + 65/6 − 11/7

⇒ 14/3 + 65/6 − 11/7

⇒ Taking LCM of 3 and 6, which is 6:

⇒ (28 + 65)/6 − 11/7

⇒ 93/6 − 11/7

⇒ Simplifying the fraction:

⇒ 31/2 − 11/7

⇒ Taking LCM of 2 and 7, which is 14:

⇒ (31 × 7 − 11 × 2) / 14

⇒ (217 − 22) / 14

⇒ 195 / 14

⇒ 13 13/14

∴ The correct answer is 13 13/14.

Additional Information

Mixed Fractions

A mixed fraction represents the sum of a whole number and a proper fraction. It can be split into two parts for easier addition and subtraction: A B/C = A + B/C.

BODMAS Rule

It dictates the correct order of mathematical operations: Brackets, Orders, Division/Multiplication, and Addition/Subtraction. Operations of the same rank are solved from left to right.

LCM for Fractions

When adding or subtracting fractions with different denominators, always find the Least Common Multiple (LCM) of the denominators to create equivalent fractions.

The correct answer is Laterite Soil.

Key Points

• Laterite soil is ideal for coffee plantation.
• Laterite soils are rich in iron and aluminum, which are beneficial for coffee plants.
• These soils are well-drained, which is a crucial requirement for coffee cultivation.
• Laterite soil is commonly found in regions with a high amount of rainfall, which suits the water needs of coffee plants.

Additional Information

• Red soil is also used for coffee cultivation but is not as ideal as laterite soil.
• Alluvial soil is more suited for crops like rice, wheat, and sugarcane.
• Black soil is ideal for cotton cultivation due to its moisture-retentive capacity.

Given:

Amount after 1 year (A₁) = Rs. 5,500

Amount after 3 years (A₃) = Rs. 6,655

Formula Used:

Compound Interest Formula: \(A = P \left(1 + \frac{r}{100}\right)^n\)

Calculation:

Let the principal amount be P and the rate of interest be r%.

From the given data, we have:

A₁ = \(P \left(1 + \frac{r}{100}\right)^1\)

5,500 = \(P \left(1 + \frac{r}{100}\right) \)

A₃ = \(P \left(1 + \frac{r}{100}\right)^3\)

6,655 = \(P \left(1 + \frac{r}{100}\right)^3 \)

Dividing the two equations:

\(\frac{A_3}{A_1} = \left(1 + \frac{r}{100}\right)^3 / \left(1 + \frac{r}{100}\right)\)

\(\frac{6,655}{5,500} = \left(1 + \frac{r}{100}\right)^2\)

⇒ \(\frac{6655}{5500} = \left(1 + \frac{r}{100}\right)^2\)

⇒ \(\frac{6655}{5500} = 1.21\)

⇒ \(\left(1 + \frac{r}{100}\right)^2 = 1.21\)

⇒ \(1 + \frac{r}{100} = \sqrt{1.21}\)

⇒ \(1 + \frac{r}{100} = 1.1\)

⇒ \( \frac{r}{100} = 0.1\)

⇒ r = 10%

The rate of interest is 10%.