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The correct answer is option 4, i.e. 'bizzare'.

Apart from the word 'Bizzare', the other words are correctly spelt.

The correct spelling of the word 'Bizzare' is 'Bizarre'.

Let us look at the meaning of the given words:

• Colleague : a person with whom one works in a profession or business
• Conscious : aware of and responding to one's surroundings
• Usually : under normal conditions; generally
• Bizarre : very strange or unusual

Here the correct answer is Pursue a course of action that will most likely be futile.

Key Points

• The idiom "Barking up the wrong tree" means to make a mistake or to be mistaken about something, especially when accusing or blaming someone.
• It implies that someone is directing their efforts in the wrong direction and will not achieve the desired result.
• For example:
• If you think I stole your wallet, you're barking up the wrong tree. I was in a meeting when it went missing.
• Tom thought he could win the game by attacking the weakest player, but he was barking up the wrong tree.
• Thus, the correct answer is Option 1.

Additional Information

• The word "futile" means ineffective, useless, or having no practical value. It describes a situation or action that is pointless and unlikely to succeed.
• Example sentence: Despite his efforts to repair the old car, it was a futile attempt as the vehicle was beyond repair.

Shortcut Trick

Profit Ratio = (Capital_A × Time_A) : (Capital_B × Time_B)

Ratio = (75 × 12) : (80 × 7) = 900 : 560 = 45 : 28

Total Ratio = 45 + 28 = 73 units

73 units = ₹4,08,800 ⇒ 1 unit = ₹5,600

A’s share = 45 × 5,600 = ₹2,52,000

B’s share = 28 × 5,600 = ₹1,56,800

∴ The correct answer is ₹2,52,000 and ₹1,56,800.

Alternate Method

Given:

Investment of A = ₹75,000

Investment of B = ₹80,000

Time period of A = 12 months

Time period of B = 12 − 5 = 7 months

Total Profit = ₹4,08,800

Formula Used:

Profit Ratio = (Investment₁ × Time₁) : (Investment₂ × Time₂)

Partner A ₹75,000 × 12 m

Partner B ₹80,000 × 7 m

Ratio = 45 : 28

Calculations:

⇒ Profit share of A : Profit share of B = (75,000 × 12) : (80,000 × 7)

⇒ Ratio = 9,00,000 : 5,60,000

⇒ Ratio = 90 : 56 = 45 : 28

⇒ Total profit units = 45 + 28 = 73

⇒ Share of A = (45 ÷ 73) × 4,08,800

⇒ Share of A = 45 × 5,600 = ₹2,52,000

⇒ Share of B = (28 ÷ 73) × 4,08,800

⇒ Share of B = 28 × 5,600 = ₹1,56,800

∴ The correct answer is ₹2,52,000 and ₹1,56,800.

Additional Information

Partnership Profit Distribution

Profit is always distributed in the ratio of the product of Capital and Time (P = C × T).

Active vs Sleeping Partner

An active partner manages the business and may receive a salary before the remaining profit is shared according to the investment ratio.

Variable Investment

If investment changes during the period, use the sum of (Investment × Duration) for each interval: (C₁t₁ + C₂t₂ + ...).

Shortcut Trick

Ratio of Expenditure to Savings = 3 : 1 (since 200% more means 1 + 2 = 3 parts).

Using weighted average for Income change: [(3 × −6%) + (1 × 26%)] ÷ (3 + 1)

Net Change = (−18% + 26%) ÷ 4 = 8% ÷ 4 = 2%.

In decimal form, 2% = 2 ÷ 100 = 0.02.

∴ The correct answer is 0.02.

Alternate Method

Given:

Expenditure of Sudha = Savings + 200% of Savings

Expenditure decrease = 6% | Savings increase = 26%

Formula: Income = Expenditure + Savings

⇒ Let Savings = 100

⇒ Expenditure = 100 + 200 = 300

⇒ Total Income = 300 + 100 = 400

⇒ New Expenditure = 300 − (6% of 300) = 300 − 18 = 282

⇒ New Savings = 100 + (26% of 100) = 100 + 26 = 126

⇒ New Income = 282 + 126 = 408

⇒ Increase in Income = 408 − 400 = 8

⇒ Percentage Increase = (8 ÷ 400) × 100 = 2%

⇒ Decimal representation = 2 ÷ 100 = 0.02

∴ The correct answer is 0.02.

Additional Information

Income Expenditure Relation

Total Income is always the sum of Expenditure and Savings (Income = E + S).

Weighted Average Method

When a total value is composed of multiple parts, the overall percentage change is the sum of (part ratio × part change) divided by the total ratio.

Percentage Change Formula

Percentage Change = [(Final Value − Initial Value) ÷ Initial Value] × 100.

Shortcut Trick

The difference between the last and first number is directly proportional to the difference in the averages of their respective groups.

Last Number − First Number = Number of terms × (Average of last group − Average of first group)

19 − First Number = 3 × (16 − 15)

19 − First Number = 3

First Number = 19 − 3 = 16

∴ The correct answer is 16.

Alternate Method

Given:

Average of the first three numbers = 15

Average of the last three numbers = 16

The last number = 19

Sum = 15 × 3 = 45

a

b + c

b + c

d = 19

Sum = 16 × 3 = 48

Formula Used:

Sum of observations = Average × Number of observations

Calculations:

Let the four numbers in sequence be a, b, c, and d.

Sum of the first three numbers (a + b + c):

⇒ a + b + c = 15 × 3 = 45     --- (Equation 1)

Sum of the last three numbers (b + c + d):

⇒ b + c + d = 16 × 3 = 48     --- (Equation 2)

Subtracting Equation 1 from Equation 2 to eliminate the common terms (b + c):

⇒ (b + c + d) − (a + b + c) = 48 − 45

⇒ d − a = 3

We are given that the last number (d) is 19. Substituting this value into the equation:

⇒ 19 − a = 3

⇒ a = 19 − 3

⇒ a = 16

∴ The correct answer is 16.

Additional Information

Basic Average Formula

The average of a set of numbers is calculated by dividing the sum of all observations by the total number of observations.

Overlapping Averages Rule

If the sum of a sequence is calculated in overlapping parts, the difference between the sums of the parts equals the difference between the non-overlapping extreme terms.

Effect of Change on Average

If every observation in a dataset is increased or decreased by a constant value 'k', the new average of the dataset also increases or decreases by exactly 'k'.

Let 137 be x

& 133 be y

$\begin{array}{l} \therefore ;;\frac{{137 \times 137 + 137 \times 133 + 133 \times 133}}{{137 \times 137 \times 137 - 133 \times 133 \times 133}}\ = ;\frac{{a \times a + a \times b + b \times b}}{{a \times a \times a - b \times b \times b}}\ = ;\frac{{{a^2} + ab + {b^2}}}{{{a^3} - {b^3}}}\ = ;\frac{{{a^2} + ab + {b^2}}}{{\left( {a - b} \right)\left( {{a^2} + ab + {b^2}} \right)}}\ = ;\frac{1}{{a - b}}\ = ;\frac{1}{{137 - 133}} \end{array}$

=  1/4

'आँख का अंधा नाम नयनसुख' मुहावरे का अर्थ है -'नाम के विपरीत आचरण होना'।

अन्य विकल्प असंगत हैं। अतः विकल्प 2 सही उत्तर है। 

Key Points 

• 'आँख का अँधा नाम नयनसुख ' का अर्थ 'नाम के विपरीत आचरण होना' है।
• वाक्य प्रयोग- हमारे पड़ोसी का नाम तो करोड़ीमल है परन्तु पाई-पाई के मोहताज हैं,
• इसे ही आँख का अँधा नाम नयनसुख कहा जाता है।
• मुहावरे- मूहावरा अरबी भाषा का शब्द है, जिसका अर्थ है- बातचीत करना या उत्तर देना।
• जब कोई वाक्यांश अपने सामान्य अर्थ को छोड़कर विशेष अर्थ में रूढ़ हो जाता है, उसे मुहावरा कहते है।
• अन्य विकल्प-

Additional Information

• 'लोकोक्ति’ शब्द ‘लोक + उक्ति’ शब्दों से मिलकर बना है जिसका अर्थ है- लोक में प्रचलित उक्ति या कथन’।
• जब कोई पूरा कथन किसी प्रसंग विशेष में उद्धत किया जाता है तो लोकोक्ति कहलाता है।
• लोकोक्ति को कहावत भी कहते है।

Given:

A sum of money doubles itself in 7 years at simple interest.

Concept used:

S.I = (P × T × R)/100

Calculation:

According to the question,

P = (P × 7 × R)/100

⇒ 1 = 7R/100

⇒ R = 100/7

Now,

4P = (P × T × 100)/(7 × 100)

⇒ 28P = PT

⇒ 28 = T

So, time = 28 years

∴ The required answer is 28 years.

The correct answer is: Option 1 i.e. To do something carefully.

Key Points

• The idiom "Dot the I's and cross the T's" means to pay attention to every small detail in a task. (हर छोटे से छोटे विवरण पर ध्यान देना)
• Example: Before submitting the report, make sure to dot the I's and cross the T's.
• "To do something carefully" refers to performing a task with great precision and attention to detail. (सावधानीपूर्वक कुछ करना)
• Example: She always does her homework carefully to avoid any mistakes.

Therefore, the correct answer is: To do something carefully.

Additional Information

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

• To make a bad situation worse (खराब स्थिति को और खराब करना): To take actions that exacerbate an already negative situation.
• Example: His careless remarks only made a bad situation worse.
• To have no standard of beauty (सौंदर्य का कोई मानक नहीं होना): To not adhere to conventional standards of beauty.
• Example: Art is subjective, and sometimes it seems to have no standard of beauty.
• To complain about something (किसी चीज के बारे में शिकायत करना): To express dissatisfaction or annoyance about something.
• Example: She tends to complain about the smallest inconveniences.

'दिनकर' का पर्यायवाची है- सूर्य

सूर्य के अन्य पर्यायवाची-  मार्तण्ड, सूरज, पतंग, रवि, अंशुमाली, भास्कर, दिनकर, आदित्य, मरीची, तरणि, दिनकर, भानु, सविता, दिवाकर, प्रभाकर, आदित्य, हंस, अर्क, दिनेश आदि। 

Key Points अन्य विकल्प-

Additional Information

• पर्यायवाची- ऐसे शब्द जिनके अर्थ समान हों, पर्यायवाची शब्द कहलाते हैं।