Search Previous Year Questions

Solution :

Let assume that ages of Neha and Sneha 12 years before is x and 4x year respectively.

According to the question ,

After 3 years from now their ages will be :

\(\frac{x + 15}{4x + 15}\) = \(\frac{3}{7}\)

⇒ 7x + 105 = 12x + 45

⇒ 5x = 60

⇒ x = 12

Now ratio of their present ages :

⇒ (x + 12) : (4x + 12)

⇒ 24 : 60

⇒ 2 : 5

Hence the correct answer is "2 : 5"

Given

Distance = 300 km

Time = speed/3

Formula used

Time = Distance/Speed

Calculation

let the uniform speed is x km/h

Time = (300/x)

Time = x/3 hours

According to question

(300/x) = x/3

⇒ 300 × 3 = x²

⇒ 900 = x²

⇒ 30 = x

Time taken to cover the distance of 300 km = 30/3

⇒ 10 hours

∴ Time taken to cover distance of 300 km is 10 hours.

Shortcut Trick

Winning candidate = 65%

Losing candidate = 100% − 65% = 35%

Winning Margin = 65% − 35% = 30%

30% of total votes = 420

Total votes (100%) = (420 ÷ 30) × 100 = 1400

∴ The correct answer is 1400.

Alternate Method

Given:

Winner vote share = 65%

Winning margin = 420 votes

Formula Used:

Total Votes = (Winning Margin ÷ Percentage Difference) × 100

Winner (65%) Loser (35%)

Margin = 30% = 420 Total Votes (100%)

⇒ Let the total number of votes be T.

⇒ Votes obtained by the winner = 65% of T = 0.65T

⇒ Since no votes are invalid, Loser votes = 100% − 65% = 35% of T = 0.35T

⇒ Winning Margin = Winner votes − Loser votes

⇒ 420 = 0.65T − 0.35T

⇒ 420 = 0.30T

⇒ T = 420 ÷ 0.30

⇒ T = 42000 ÷ 30

⇒ T = 1400

∴ The correct answer is 1400.

Additional Information

Invalid Votes Concept

If x% votes are invalid, then the winner and loser percentages are calculated on the remaining (100−x)% valid votes.

Vote Casting Scenarios

Total Votes Polled = Total Registered Voters − Voters who did not cast their vote.

Winning Margin Calculation

The margin is always the absolute difference between the votes of the winner and the immediate runner-up: Margin = V₁ − V₂.

Shortcut Trick

A depreciation of 2% means the new value becomes 98% (or 49/50) of the previous year's value.

Present Value = Initial Value × Multiplying Factor²

⇒ Present Value = 362500 × (49 / 50) × (49 / 50)

⇒ Present Value = 145 × 2401 = 348145

∴ The correct answer is ₹348145.

Alternate Method

Given:

Value of the car 2 years ago (P) = ₹3,62,500

Rate of depreciation (R) = 2% per annum

Time (T) = 2 years

Formula Used:

Present Value = P × (1 − R / 100)^T

2 Years Ago ₹3,62,500

1 Year Ago ₹3,55,250

Present Value ?

−2%

−2%

Successive Depreciation over 2 years

Calculation:

⇒ Present Value = 362500 × (1 − 2 / 100)²

⇒ Present Value = 362500 × (98 / 100)²

⇒ Present Value = 362500 × (49 / 50) × (49 / 50)

⇒ Present Value = 362500 × 2401 / 2500

⇒ Present Value = 145 × 2401

⇒ Present Value = 348145

∴ The correct answer is ₹348145.

Additional Information

Depreciation Formula

When the value of an asset decreases uniformly by R% every year, the final value after T years is found using A = P × (1 − R/100)^T.

Successive Percentage Change

The effective net change of two successive percentage changes a% and b% is given by [a + b + (a × b) / 100]%. For two 2% depreciations, the net change is −2 − 2 + (4/100) = −3.96%.

Population Growth

If a value (like a town's population) increases at R% per annum, the new amount after T years follows the standard compound interest formula: A = P × (1 + R/100)^T.

Calculation:

⇒ (24 × 36 × 24 × 36) ÷ (2(\(\sqrt {1296 \div 2)} {)^2}\)

⇒ (24 × 36 × 24 × 36) ÷ (2 ×\(\sqrt {648}\) )²

 

⇒ (24 × 36 × 24 × 36) ÷ (4 × 648)

 

⇒ 288

 

∴ The correct answer is Option 2).

The correct answer is: Option 4 i.e. manage.

Key Points

• The word "squander" means to waste something, especially money or time, in a reckless and foolish manner. (अपव्यय करना)
• Example: He squandered all his savings on gambling.
• "Manage" refers to the act of handling or controlling something with skill and efficiency. (प्रबंधन करना)
• Example: She manages her finances very wisely.
• Hence, we can infer that the opposite of 'squander' is 'manage'.

Therefore, the correct answer is: Option 4 i.e. manage.

Additional Information

Here are the other options explained along with their Hindi meanings and example sentences:

• Fritter away (बरबाद करना): To waste time, money, or energy on trifling matters.
• Example: He frittered away his inheritance on unnecessary luxuries.
• Splurge (फिजूलखर्ची करना): To spend money freely or extravagantly.
• Example: She decided to splurge on a new dress for the party.
• Squabble (झगड़ा करना): To engage in a petty quarrel.
• Example: The siblings often squabble over trivial matters.

The correct answer is Option (1) i.e., are.

Key Points

• The question is inquiring about a plan, which is ongoing or future-oriented.
• Therefore, the present continuous tense, "are planning" is used.
• "Are" is the correct auxiliary verb to use with "you" in forming present continuous questions.

Therefore, the correct answer is- "When are you planning to start the project?"

Additional Information

• "Is" and "was" do not align with the second-person pronoun "you."
• "Will" would suggest a simple future inquiry without the ongoing aspect that "planning" conveys.

The correct answer is "Dull."

Key Points

• "Blunt" means (used about a knife, pencil, tool, etc.) without a sharp edge or point. ((चाक़ू आदि) कुंद, भोथरा)
• Example: That knife is blunt.
• Synonym of "blunt" is "dull."
• "Dull" means lacking sharpness or intensity. (तीक्ष्णता या तीव्रता का अभाव)
• Example: The pencil was so dull that it couldn't even make a mark on the paper.
• The correct answer is Option 2.

Additional Information

• Option 1, "Cheerful", means happy and optimistic. (प्रसन्‍न, प्रमुदित; हँसमुख)
• Option 3, "Valiant", means brave and courageous. (साहसी और निर्भीक)
• Option 4, "Sharp", means having a thin edge or point. (तेज़ धार या नोंक वाला, धारदार या नोकदार; जो आसानी से किसी वस्‍तु को काट दे या उसमें छेद कर दे, पैना, तीक्ष्‍ण)

The correct answer is option 3), i.e., 'loud.'

Key Points 

• Let's look at the meaning of the words given in the options:

• According to the context of the sentence, the word "cackle" refers to loud, harsh, and shrill laughter or cry. In the given sentence, the witch made a loud noise as she turned the boy into a beast.
• According to the above-mentioned points, the most appropriate word to fill in the blank is "loud."
• Therefore, the correct answer is Option 3.
• Another example:
• The loud music made him feel totally uninhibited.

 

Complete Sentence: The crowing witch released a loud cackle as she turned the boy into a beast.

The correct answer is 'A notice'.

Key Points

• A notice: A piece of paper or a sign giving information, a warning, etc. that is put where everyone can read it.
• E.g.- There’s a notice on the board saying that the meeting has been cancelled.

Hence, the correct answer is 'A notice'.

Additional Information

• An office order: An order issued by the employer or the authority or senior employees.
• ​ E.g.- Vivek is afraid of an office order for the act he has done.
• ​A note sheet: A brief summary or record in writing
• ​E.g.- He has a habit of making a note sheet.
• ​A report: To give people information about what you have seen, heard, done, etc.
• ​E.g.- Several people reported having seen the boy.

Important Points

• A notice: This is a written announcement or warning publicly displayed. Its purpose is to inform people about something - it might present news, instructions, warnings, schedules, or any kind of general information to an audience.
• A report: A report is a detailed account or statement of a particular matter prepared after thorough investigation or examination.
• Reports are typically not used for public display of information, but rather for in-depth analysis of specific issues.

Therefore, when referring to a displayed sheet giving news or information, the term "notice" is the most accurate choice.