UP Police Constable Re-Exam 2024 Official Paper (Held On: 31 Aug, 2024 Shift 2) (Previous Year Paper)

The logic followed here is:

Logic: Country known for a specific animal.

Here,

Elephant : Sri Lanka → Sri Lanka is known for its elephant population.

Similarly,

Kangaroo : Australia → Australia is known for its kangaroo population.

Hence, the correct answer is "Option 4".

Family Chart:

Given: Pointing to a photograph, Madhu said to her friend Krishna, "He is the only son of the mother of my father."

Let's break down the statement:

So, the person in the photograph is Madhu's father.

Therefore, Madhu is the 'Daughter' of the person in the photograph.

Hence, the correct answer is "Option 4".

The given series of letters is "TLSEEV".

Let's check each option:

Option 1) STEEL → Given letters  "TLSEEV" all required letters are present to give a meaningful word.

Option 2) LEAVE→ Given letters  "TLSEEV" "A" is missing to give a meaningful word.

Option 3) VESSEL→ Given letters  "TLSEEV" "S" is missing to give a meaningful word.

Option 4) TEASEL→ Given letters  "TLSEEV" "A" is missing to give a meaningful word.

Thus, Steel is the only word that can be given by the arrangement of given letters.

Hence, the correct answer is "Option 1".

Given Word: POTASSIUM

1. TOAST → Cannot be formed (Because in the given word there is only one 'O' and one 'T' whereas 'TOAST' has two 'T's and two 'O's)

2. POPPS → Cannot be formed (Because in the given word there is only one 'P' whereas it has three)

3) MASS → Can be formed

4. MOUSE → Cannot be formed (Because in the given word there is no 'E')

Hence, the correct answer is "Option 3".

The logic followed here is,

Logic: The entire figure undergoes a 180° rotation about the center of the hexagon.

And the internal indicator (dash) and external indicator circle move two steps along with it.

For,

Similarly, for

Hence, the correct answer is "Option 1".

The logic followed here is:

• 27 = 3³
• 125 = 5³
• 343 = 7³
• 512 = 8³
• 729 = 9³

All the numbers are perfect cubes.

However, 27, 125, 343, and 729 are cubes of odd numbers (3, 5, 7, and 9 respectively), while 512 is the cube of an even number (8).

Hence, the correct answer is "Option 2".

The logic followed here is:

Logic: (Square of 1st number) - 1 = 2nd number.

Now,

For, 7 : 48

→ (7²) - 1 = 49 - 1 = 48.

Similarly, for 12 : ?

→ (12²) - 1 = 144 - 1 = 143.

Hence, the related number is "Option 4".

Given: Initially facing North - East and turn 45 degrees to your  left.

Thus, If initially facing northeast and turn 45 degrees  left will be now facing North direction.

Hence, "Option 3" is the correct answer.

Given, you walk 5 km north and then turn 90 degrees to your left and walk another 5 km.

Then,

By Pythagoras theorem 

The distance between starting and final point is = (√ (5^2 + 5 ^2))

⇒ √ 50 ≈ 7 Km.

Hence the correct answer is "Option 4"

The logic followed here is,

Logic: All four small inner shapes are inverted, changing from a triangle to a diamond while maintaining their position and count.

For,

Similarly, 

Hence, the correct answer is "Option 2".

Given Equation: 9 Q 15 P 3 R 8 S 5 = ?

BODMAS Rule:

Decoding the given information:                                                      

Now replacing the signs from left to right using BODMAS Rule, we get:

⇒ 9 × 15 ÷ 3 + 8 - 5

⇒ 9 × 5 + 8 - 5

⇒ 45 + 8 - 5 =  48

Hence, the correct answer is "Option 4".

Shortcut Trick

First, evaluate (2 ? 3) → (2 + 3)² − (2 × 3) = 25 − 6 = 19

Second, evaluate (5 ≠ 3) → 5² − (5 × 3) + 3² = 25 − 15 + 9 = 19

Finally, evaluate the result (19 ≠ 19) → 19² − (19 × 19) + 19² = 361

∴ The correct answer is 361.

Alternate Method

Given:

⇒ m ≠ n = m² − mn + n²

⇒ m ? n = (m + n)² − mn

Calculation:

Step 1: Calculate the value of (2 ? 3)

⇒ Here m = 2 and n = 3

⇒ 2 ? 3 = (2 + 3)² − (2 × 3)

⇒ 2 ? 3 = 5² − 6

⇒ 2 ? 3 = 25 − 6 = 19

Step 2: Calculate the value of (5 ≠ 3)

⇒ Here m = 5 and n = 3

⇒ 5 ≠ 3 = 5² − (5 × 3) + 3²

⇒ 5 ≠ 3 = 25 − 15 + 9 = 19

Step 3: Calculate the overall expression (2 ? 3) ≠ (5 ≠ 3)

⇒ Substituting the derived values into the equation gives: 19 ≠ 19

⇒ Here m = 19 and n = 19

⇒ 19 ≠ 19 = 19² − (19 × 19) + 19²

⇒ 19 ≠ 19 = 361 − 361 + 361

⇒ 19 ≠ 19 = 361

∴ The correct answer is 361.

Additional Information

Algebraic Expansion

The formula (a + b)² = a² + 2ab + b² is a fundamental algebraic identity. Rearranging it allows for unique simplifications such as (a + b)² − ab = a² + ab + b².

Difference and Sum of Cubes

The given operators are closely related to the sum and difference of cubes identities: a³ + b³ = (a + b)(a² − ab + b²) and a³ − b³ = (a − b)(a² + ab + b²).

BODMAS Rule

When solving mathematical expressions with multiple brackets, always evaluate the innermost expressions first according to the standard order of operations.

The logic followed here is:

Logic: The first word is the playing area for the sport mentioned in the second word.

Here,

Diamond : Baseball → A Diamond is the playing area for Baseball.

Similarly,

Court : ?

A Court is a playing area for several sports. Let's check the options:

• Arena: An arena is a large enclosed area for sports or other entertainment.
• Squash: Squash is a racket sport played in a four-walled court.
• Ring: A ring is a playing area for boxing or wrestling.
• Rink: A rink is a playing area for ice skating or roller skating.

Among the given options, 'Squash' is a sport played on a 'Court'.

Hence, the correct answer is "Option 2".

The logic followed here is:

Logic: The first term is a mathematical constant or ratio associated with the second term.

Here,

Pi : Circle → Pi (π) is the ratio of a circle's circumference to its diameter, a fundamental constant associated with a Circle.

Similarly,

Phi : ?

Phi (ϕ) is another mathematical constant, known as the Golden Ratio. It appears in various natural and geometric contexts, often associated with aesthetic proportions.

Hence, the correct answer is "Option 2".

The diagram uses a Venn-like structure to show the number of people who take coffee, juice, and tea.

The part of the circle that is outside the rectangle (juice) and the triangle (tea) represents the individuals who drink only coffee.

According to the diagram, this value is,

⇒ 25 + 20 = 45

Hence, the correct answer is "Option 3".

Shortcut Trick

Students passed in at least one subject = Math + Chemistry − Both

⇒ Total passed = 70 + 60 − 20 = 110

Students who failed in both subjects = Total students − Total passed

⇒ Failed in both = 150 − 110 = 40

∴ The correct answer is 40.

Alternate Method

Given:

Total students in the class, n(∪) = 150

Students who passed in Mathematics, n(M) = 70

Students who passed in Chemistry, n(C) = 60

Students who passed in both subjects, n(M ∩ C) = 20

Total Students = 150

Math (70) Chemistry (60)

50 20 40

Failed Both = 40

Formula Used:

n(M ∪ C) = n(M) + n(C) − n(M ∩ C)

Number of students who failed in both = Total students − n(M ∪ C)

Calculations:

⇒ Students passed in at least one subject, n(M ∪ C) = 70 + 60 − 20

⇒ n(M ∪ C) = 130 − 20 = 110

⇒ Students who failed in both subjects = 150 − 110

⇒ Students who failed in both subjects = 40

∴ The correct answer is 40.

Additional Information

Union of Two Sets

The total number of elements in at least one of the two sets A and B is given by the formula: n(A ∪ B) = n(A) + n(B) − n(A ∩ B).

Exactly One Subject

To find the number of students who passed in exactly one subject, use the relation: n(A) + n(B) − 2 × n(A ∩ B).

De Morgan's Law

The complement of the union of two sets is the intersection of their complements: (A ∪ B)' = A' ∩ B'. In this context, it represents the students who failed in both subjects (i.e., elements outside both sets).

The logic followed here is,

Hence, the correct answer is "Option 1".

Given:

The logic followed here is.

For GARB : HEAR

For DROP:

'DROP' will be written as EVXF

Hence, the correct answer is "Option 2".

Given,

Statement:

Red-haired people love riding bikes.

Conclusions:

I. All people love riding bikes. - False (Because, the statement only provides information about "red-haired people". We cannot conclude anything about "all people" from this specific statement. The group of "red-haired people" is a subset of "all people", and the behavior of a subset does not define the behavior of the entire set).

II. Red-haired people love riding bikes only. - False (Because, the statement says "Red-haired people love riding bikes." This means riding bikes is "one thing" they love. It does not exclude the possibility that they also love other things, such as swimming, reading, or painting. The word 'only' makes this conclusion definitively false, as it imposes a restriction not present in the original statement).

So, Neither Conclusion I nor II follows.

Hence, the correct answer is "Option 2".

Shortcut Trick

Net change in sum = Correct value − Wrong value = 8.6 − 6.8 = +1.8

Net change in average = Net change ÷ Number of students

⇒ Net change in average = +1.8 ÷ 100 = +0.018

Correct average = Old average + Change in average = 5.8 + 0.018 = 5.818

∴ The correct answer is 5.818 marks.

Alternate Method

Given:

Total number of students = 100

Incorrect average marks = 5.8

Incorrect mark entered = 6.8

Correct mark = 8.6

Formula Used:

Correct Average = Incorrect Average + [(Correct Value − Incorrect Value) ÷ Total Students]

5.8 (Wrong)

5.818 (Correct)

+0.018 Shift

Sum correction = 8.6 - 6.8 = +1.8

Calculations:

⇒ Total incorrect sum of marks = 100 × 5.8 = 580

⇒ Total correct sum of marks = Incorrect sum − Wrong mark + Correct mark

⇒ Total correct sum = 580 − 6.8 + 8.6 = 581.8

⇒ Correct average = Total correct sum ÷ Number of students

⇒ Correct average = 581.8 ÷ 100 = 5.818

∴ The correct answer is 5.818 marks.

Additional Information

Weighted Average

When combining multiple groups with different averages, the combined overall average is computed as (n₁A₁ + n₂A₂) ÷ (n₁ + n₂), where 'n' represents the count and 'A' represents the average of the respective groups.

Impact of Arithmetic Operations

If every observation in a dataset is systematically increased, decreased, multiplied, or divided by a constant value 'k', the new average for the dataset naturally undergoes the exact same mathematical transformation.

Inclusion & Exclusion Rule

When a new individual joins a group, the updated average can be rapidly calculated using the formula: New Average = Old Average + [(New Value − Old Average) ÷ New Total Count].

Shortcut Trick

By using the direct Alligation method:

Ratio of Quantities = (Mean Price − Price of 2nd) : (Price of 1st − Mean Price)

Ratio = (40 − 28) : (48 − 40)

Ratio = 12 : 8 = 3 : 2

∴ The correct answer is 3 : 2.

Alternate Method

Given:

Price of first variety of sugar = ₹48 per kg

Price of second variety of sugar = ₹28 per kg

Mean price of the mixed sugar = ₹40 per kg

48

28

40

12

8

Type 1 (₹/kg) Type 2 (₹/kg) Mean Price Ratio = 12 : 8 = 3 : 2

Calculations:

⇒ Let the quantity of ₹48/kg sugar be x and ₹28/kg sugar be y.

⇒ Total cost of the mixture = 48x + 28y

⇒ Total quantity of the mixture = x + y

⇒ Mean price of the mixture = (48x + 28y) ÷ (x + y)

⇒ 40 = (48x + 28y) ÷ (x + y)

⇒ 40(x + y) = 48x + 28y

⇒ 40x + 40y = 48x + 28y

⇒ 40y − 28y = 48x − 40x

⇒ 12y = 8x

⇒ x / y = 12 / 8

⇒ x : y = 3 : 2

∴ The correct answer is 3 : 2.

Additional Information

Alligation Rule

The rule of alligation enables us to easily find the ratio in which two ingredients at different given prices must be mixed to produce a required mean price. The ratio is given directly by the cross-differences.

Weighted Average Concept

When quantities are mixed in a specific ratio n₁ : n₂, the average value of the mixture is calculated as A = (n₁A₁ + n₂A₂) ÷ (n₁ + n₂).

Shortcut Trick

Downstream Speed = Speed in still water + Speed of current = 10 + 5 = 15 km/hr

Time taken = Distance ÷ Downstream Speed = 60 ÷ 15 = 4 hours

∴ The correct answer is 4 hours.

Alternate Method

Current (v) = 5 km/hr

Boy

u = 10 km/hr

Distance = 60 km Downstream Speed = u + v = 15 km/hr

Given:

Speed of boy in still water (u) = 10 km/hr

Speed of current (v) = 5 km/hr

Distance to travel downstream (D) = 60 km

Formula Used:

Downstream Speed = Speed of boy + Speed of current

Time = Distance ÷ Speed

Calculations:

⇒ Downstream Speed = 10 + 5 = 15 km/hr

⇒ Time taken = 60 ÷ 15

⇒ Time = 4 hours

∴ The correct answer is 4 hours.

Additional Information

Upstream Speed

When swimming against the flow of the river, the net speed decreases. It is calculated as Upstream Speed = u − v.

Speed in Still Water

If the downstream speed (D) and upstream speed (U) are given directly, the speed of the person or boat in still water is: u = (D + U) ÷ 2.

Speed of Stream

If the downstream speed (D) and upstream speed (U) are given, the speed of the current or stream is: v = (D − U) ÷ 2.

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'.

Shortcut Trick

Let the total capital be 9 units.

A's investment = 1/3 of 9 = 3 units.

B's investment = 1/3 of the remaining 6 units = 2 units.

C's investment = Remaining units = 9 − 3 − 2 = 4 units.

Difference in C and B's profit = [(4 − 2) ÷ (3 + 2 + 4)] × 4050 = (2 ÷ 9) × 4050 = ₹900.

∴ The correct answer is ₹900.

Alternate Method

Given:

A invests 33¹⁄₃% of the total capital.

B invests 33¹⁄₃% of the remaining capital.

C invests the remaining capital.

Total profit at the end of the year = ₹4050.

Formula Used:

When the time period is identical for all partners, Profit Ratio = Capital Ratio.

A: 3 parts

B: 2 parts

C: 4 parts

Total Capital / Profit = 9 parts = ₹4050

Difference (C − B) = 2 parts

Calculations:

⇒ Let total capital = 1 unit

⇒ A's capital = 33¹⁄₃% of 1 = 1/3

⇒ Remaining capital = 1 − 1/3 = 2/3

⇒ B's capital = 33¹⁄₃% of 2/3 = 1/3 × 2/3 = 2/9

⇒ C's capital = Remaining capital = 2/3 − 2/9 = 4/9

⇒ Profit Ratio A : B : C = 1/3 : 2/9 : 4/9 = 3 : 2 : 4

⇒ Total profit parts = 3 + 2 + 4 = 9 parts

⇒ 9 parts = ₹4050

⇒ 1 part = 4050 ÷ 9 = ₹450

⇒ Difference between C's profit and B's profit = 4 parts − 2 parts = 2 parts

⇒ Value of 2 parts = 2 × 450 = ₹900

∴ The correct answer is ₹900.

Additional Information

Partnership Profit Ratio

When partners invest capital for different periods, the profit ratio is the product of capital and time: Profit Ratio = Capital × Time.

Sleeping vs Active Partner

An active partner usually receives a fixed salary or a specific percentage of the total profit for managing the business, and the remaining profit is distributed based on the capital invested.

Fraction Equivalents

Memorising percentage to fraction equivalents significantly accelerates exam calculations. For example: 33¹⁄₃% = 1/3, 16²⁄₃% = 1/6, and 66²⁄₃% = 2/3.

Shortcut Trick

Let initial CP = 100, initial SP = S.

New CP = 2 × 100 = 200; New SP = 3S.

Profit = 65% ⇒ 3S = 1.65 × 200 = 330.

S = 110.

Original Profit % = (110 − 100) / 100 = 0.1.

∴ The correct option is B.

Alternate Method

Given: Selling price is tripled and cost price is doubled, profit becomes 65%.

Formula Used: Selling Price (SP) = CP × (1 + Profit % / 100)

Old CP: x

Old SP: y

New CP: 2x

New SP: 3y

Profit = 65%

Let original CP be x and original SP be y.

⇒ New CP = 2x

⇒ New SP = 3y

⇒ New SP = New CP × (1 + 65/100)

⇒ 3y = 2x × 1.65

⇒ 3y = 3.3x

⇒ y = 1.1x

⇒ Profit = y − x = 1.1x − x = 0.1x

⇒ Profit % = (0.1x / x) × 100 = 10%

⇒ In decimal form, Profit = 0.1.

∴ The correct option is B.

Additional Information

Profit Percentage

Profit % = [(SP − CP) / CP] × 100. It is always calculated on the Cost Price unless specified otherwise.

Selling Price and Multiplier

If Profit is p%, then SP = CP × (100 + p)/100. For example, a 65% profit means SP = 1.65 × CP.

Decimal Representation

Profit percentages can be expressed as decimals: 10% = 0.1, 25% = 0.25, and 100% = 1.0.

Shortcut Trick

Make all decimals have the same number of decimal places by adding zeroes: 0.70, 0.35, 1.05.

Treat them as whole numbers by ignoring the decimal point: 70, 35, 105.

Find the LCM of 70, 35, and 105 ⇒ LCM(70, 105) = 35 × 6 = 210.

Place the decimal point back after two places from the right ⇒ 2.10 = 2.1.

∴ The correct answer is 2.1.

Alternate Method

Given:

Decimals: 0.7, 0.35, 1.05

Formula Used:

LCM of fractions = (LCM of Numerators) ÷ (HCF of Denominators)

Calculations:

⇒ Convert decimals to fractions: 0.7 = 7/10, 0.35 = 35/100, 1.05 = 105/100

⇒ Simplify the fractions to their lowest terms:

⇒ 7/10 = 7/10

⇒ 35/100 = 7/20

⇒ 105/100 = 21/20

⇒ Numerators are 7, 7, 21.

⇒ LCM of (7, 7, 21) = 21

⇒ Denominators are 10, 20, 20.

⇒ HCF of (10, 20, 20) = 10

⇒ LCM of given fractions = 21 ÷ 10 = 2.1

∴ The correct answer is 2.1.

Additional Information

HCF of Fractions

The HCF of fractions is calculated as (HCF of Numerators) ÷ (LCM of Denominators).

Product of Numbers Rule

For any two numbers A and B, the product of the numbers is equal to the product of their LCM and HCF (A × B = LCM × HCF).

LCM and HCF of Decimals (Equal Places Method)

Convert all decimals to the same number of decimal places by adding zeroes. Treat them as whole numbers to find the LCM or HCF, then place the decimal point in the result at the original position.

Shortcut Trick

Sum of reciprocals of two numbers = Sum of numbers ÷ Product of numbers

Product of numbers = HCF × LCM

⇒ Sum of reciprocals = 25 ÷ (3 × 105)

⇒ Sum of reciprocals = 25 / 315 = 5 / 63

∴ The correct answer is 5/63.

Alternate Method

Given:

Sum of two numbers (a + b) = 25

HCF = 3

LCM = 105

Formula Used:

Product of two numbers (a × b) = HCF × LCM

Sum of reciprocals = 1/a + 1/b = (a + b) / (a × b)

Calculations:

⇒ Product of the two numbers = 3 × 105 = 315

⇒ Sum of reciprocals = (a + b) / (a × b)

⇒ Sum of reciprocals = 25 / 315

⇒ Dividing numerator and denominator by 5

⇒ Sum of reciprocals = 5 / 63

∴ The correct answer is 5/63.

Additional Information

Product of Two Numbers

For any two numbers, the product of the numbers is always equal to the product of their HCF and LCM (Product = HCF × LCM).

Co-prime Numbers

Two numbers are considered co-prime if their HCF is 1. For such numbers, their LCM is exactly equal to the product of the two numbers.

HCF and LCM of Fractions

HCF of fractions = (HCF of numerators) ÷ (LCM of denominators). Similarly, LCM of fractions = (LCM of numerators) ÷ (HCF of denominators).

Shortcut Trick

The effective compound interest rate for two successive years can be calculated using the successive percentage formula: X + Y + (X × Y) ÷ 100.

Effective Rate = 4 + 5 + (4 × 5) ÷ 100 = 9 + 0.2 = 9.2%.

Total Amount = (100% + 9.2%) of the Principal = 109.2% of ₹25,000.

Amount = (109.2 ÷ 100) × 25000 = 109.2 × 250 = ₹27,300.

∴ The correct answer is ₹27,300.

Alternate Method

Given:

Principal (P) = ₹25,000

Rate of interest for the 1^st year (R₁) = 4% per annum

Rate of interest for the 2^nd year (R₂) = 5% per annum

Time (T) = 2 years

Formula Used:

Amount (A) = P × (1 + R₁/100) × (1 + R₂/100)

₹25000 Start

• 4%

₹26000 Year 1

• 5%

₹27300 Year 2

Calculations:

⇒ Amount = 25000 × (1 + 4/100) × (1 + 5/100)

⇒ Amount = 25000 × (104/100) × (105/100)

⇒ Amount = 25000 × (26/25) × (21/20)

⇒ Amount = 25000 × (546/500)

⇒ Amount = 50 × 546

⇒ Amount = 27300

∴ The correct answer is ₹27,300.

Additional Information

Effective CI Rate for 2 Years

If the rate of interest is the same R% per annum for 2 years, the effective compound interest rate is (2R + R² ÷ 100)%.

Difference Between CI and SI

The difference between Compound Interest and Simple Interest for 2 years on a principal P at rate R% is given by the formula: Difference = P × (R ÷ 100)².

Rule of 72

To estimate the number of years required to double the invested money at a given compound annual interest rate R%, divide 72 by the interest rate (i.e., Years ≈ 72 ÷ R).

Shortcut Trick

The speed of the current is directly calculated as half the difference between the downstream and upstream speeds.

Speed of current = (Downstream Speed − Upstream Speed) ÷ 2

Speed of current = (22 − 18) ÷ 2

Speed of current = 4 ÷ 2 = 2 km/hr

∴ The correct answer is 2 km/hr.

Alternate Method

Downstream = 22 km/hr

Upstream = 18 km/hr

Diff = 4

Current = Diff ÷ 2 = 2 km/hr

Given:

Speed of boat downstream (along the current) = 22 km/hr

Speed of boat upstream (against the current) = 18 km/hr

Formula Used:

Let the speed of the boat in still water be x km/hr and the speed of the current be y km/hr.

Downstream Speed (D) = x + y

Upstream Speed (U) = x − y

By subtracting both equations: y = (D − U) ÷ 2

Calculations:

⇒ D = 22 km/hr

⇒ U = 18 km/hr

⇒ y = (22 − 18) ÷ 2

⇒ y = 4 ÷ 2

⇒ y = 2 km/hr

∴ The correct answer is 2 km/hr.

Additional Information

Speed of Boat in Still Water

It is the speed of the boat when the water is entirely stationary. Calculated using the formula: (Downstream Speed + Upstream Speed) ÷ 2.

Downstream Speed

When the boat travels in the same direction as the flow of the stream, the speeds are combined together. Formula: Speed of Boat + Speed of Current.

Upstream Speed

When the boat travels in the opposite direction against the flow of the stream, the effective speed is reduced. Formula: Speed of Boat − Speed of Current.

Shortcut Trick

We can use the successive percentage change formula directly for mark-up and discount:

Overall Profit/Loss % = a + b + (a × b) / 100

Here, mark-up (a) = +120% and discount (b) = −10%.

⇒ Profit % = 120 − 10 + (120 × −10) / 100

⇒ Profit % = 110 − 12 = 98%

∴ The correct answer is 98%.

Alternate Method

Given:

Mark-up percentage = 120% above CP

Discount percentage = 10% on MP

Formula Used:

MP = CP × (1 + Mark-up% / 100)

SP = MP × (1 − Discount% / 100)

Profit % = [(SP − CP) / CP] × 100

Mark-up: +120%

Profit %

−10% Disc.

CP = 100

SP = 198

MP = 220

Profit = SP − CP = 198 − 100 = 98 Profit % = 98%

Calculations:

⇒ Let the Cost Price (CP) of the book be 100 units.

⇒ Marked Price (MP) = 100 + (120% of 100) = 100 + 120 = 220 units

⇒ The shopkeeper gives a 10% discount on the Marked Price.

⇒ Discount = 10% of 220 = (10 / 100) × 220 = 22 units

⇒ Selling Price (SP) = MP − Discount = 220 − 22 = 198 units

⇒ Profit = SP − CP = 198 − 100 = 98 units

⇒ Profit % = (98 / 100) × 100 = 98%

∴ The correct answer is 98%.

Additional Information

Marked Price & Discount

Marked Price (MP) is the price printed or tagged on an item. Discount is always calculated on the Marked Price, not the Cost Price. The basic rule is: SP = MP × (1 − D / 100).

Successive Discounts

When a seller gives two continuous discounts of x% and y%, the effective single discount is calculated as [x + y − (x × y)/100]%. It is always less than the simple sum of the two discounts.

Direct Relation Formula

A very useful ratio connecting all four terms (Cost Price, Marked Price, Profit %, and Discount %) directly is: CP / MP = (100 − Discount%) / (100 + Profit%). This saves calculation time in complex sums.

Shortcut Trick

The direct relation between Marked Price (MP), Cost Price (CP), Profit% (P), and Discount% (D) is:

⇒ MP ÷ CP = (100 + P%) ÷ (100 − D%)

⇒ MP ÷ 6400 = (100 + 25) ÷ (100 − 20)

⇒ MP ÷ 6400 = 125 ÷ 80 = 25 ÷ 16

⇒ MP = 6400 × (25 ÷ 16) = 10000

∴ The correct answer is ₹10,000.

Alternate Method

Given:

Cost Price (CP) = ₹6,400

Profit = 25%

Discount = 20%

Formula Used:

Selling Price (SP) = CP × (100 + Profit%) ÷ 100

Marked Price (MP) = SP × 100 ÷ (100 − Discount%)

CP ₹6,400

SP ₹8,000

MP ₹10,000

+25% Profit

−20% Discount

CP × 1.25 = SP = MP × 0.80

Calculations:

⇒ SP = 6400 × (100 + 25) ÷ 100

⇒ SP = 6400 × 1.25

⇒ SP = ₹8,000

⇒ The Selling Price (SP) is obtained after allowing a 20% discount on the Marked Price (MP).

⇒ SP = MP × (100 − 20) ÷ 100

⇒ 8000 = MP × 0.80

⇒ MP = 8000 ÷ 0.80

⇒ MP = 10000

∴ The correct answer is ₹10,000.

Additional Information

Marked Price & Discount

Discount is always calculated on the Marked Price (MP) unless specified otherwise. Formula: Selling Price = MP × (100 − D%) ÷ 100.

Successive Discounts

If two successive discounts of a% and b% are given, the equivalent single discount percentage is (a + b − a × b ÷ 100)%.

Dishonest Dealer Concept

When a dealer pretends to sell goods at CP but uses false weights to cheat customers, the actual Profit% is calculated as [Error ÷ (True Weight − Error)] × 100.

Shortcut Trick

Formula: Time (T) = [(n − 1) ÷ R] × 100, where n is the number of times the amount becomes.

Given: The amount is tripled, so n = 3, and Rate (R) = 25%.

T = [(3 − 1) ÷ 25] × 100

T = (2 ÷ 25) × 100 = 2 × 4 = 8

∴ The correct answer is 8 years.

Alternate Method

Given:

Rate (R) = 25% per annum

Final Amount (A) = 3 × Principal

Formula Used:

Simple Interest (SI) = (P × R × T) ÷ 100

Amount (A) = P + SI

t = 0 Principal = P t = T Amount = 3P

SI = 3P − P = 2P Rate = 25% p.a.

Calculations:

⇒ Let the Principal be P.

⇒ The amount is tripled, so Amount (A) = 3P.

⇒ Simple Interest (SI) = A − P = 3P − P = 2P

⇒ Substitute these values into the Simple Interest formula:

⇒ 2P = (P × 25 × T) ÷ 100

⇒ 2 = 25T ÷ 100

⇒ 2 = T ÷ 4

⇒ T = 2 × 4 = 8 years

∴ The correct answer is 8 years.

Additional Information

Simple Interest vs Compound Interest

Simple Interest is calculated only on the principal amount, whereas Compound Interest is calculated on the principal along with the accumulated interest from previous periods.

Finding Rate of Interest Directly

If an amount becomes n times of itself in T years at simple interest, the rate can be determined using the formula: R = [(n − 1) ÷ T] × 100.

Rule of 72

It is a quick shortcut used to find the approximate time required to double an investment at a given compound interest rate: T ≈ 72 ÷ R.

Shortcut Trick

Total work = LCM of 24 and 16 = 48 units.

Efficiency of C = 2 units/day and Efficiency of D = 3 units/day.

If D had not left 4 days before completion, he would have done an additional 4 × 3 = 12 units of work.

Total hypothetical work = 48 + 12 = 60 units.

Total days taken for completion = Total hypothetical work ÷ Combined Efficiency = 60 ÷ (2 + 3) = 12 days.

∴ The correct answer is 12 days.

Alternate Method

Given:

C can complete the work in 24 days.

D can complete the work in 16 days.

D left the work 4 days before its completion.

Calculations:

Let the total number of days taken to complete the work be x.

⇒ C worked for all x days.

⇒ D worked for (x − 4) days.

⇒ Total work done by C = Efficiency × Days = 2 × x = 2x units

⇒ Total work done by D = Efficiency × Days = 3 × (x − 4) = 3x − 12 units

⇒ Total Work = Work done by C + Work done by D

⇒ 2x + (3x − 12) = 48

⇒ 5x − 12 = 48

⇒ 5x = 60

⇒ x = 12

∴ The correct answer is 12 days.

Additional Information

Leaving Work Before Completion

If a person leaves 'n' days before completion, imagine they stayed and completed 'n' more days of work. Add this extra work to the total work and divide by total combined efficiency to easily get the total duration.

Total Work Concept

In Time and Work problems, Total Work is generally assumed as the Least Common Multiple (LCM) of the given time durations to make efficiency calculations integer-based.

Work Efficiency

Efficiency is inversely proportional to time. A person taking fewer days to complete a task has higher working efficiency.

Shortcut Trick

Let SP of 1 orange = 1 unit ⇒ Total SP = 110 units, Profit = 22 units.

Cost Price (CP) = Total SP − Profit = 110 − 22 = 88 units.

Profit % = (Profit ÷ CP) × 100 = (22 ÷ 88) × 100 = 25%.

∴ The correct answer is 25%.

Alternate Method

Given:

Total oranges sold = 110

Profit made = Selling Price of 22 oranges

Formula Used:

Profit = SP − CP

Profit % = (Profit ÷ CP) × 100

CP = 88 units

SP = 110 units

• 22 units Profit

Profit % = (22 ÷ 88) × 100 = 25%

Calculations:

⇒ Let the Selling Price (SP) of 1 orange be ₹1.

⇒ Total SP of 110 oranges = 110 × ₹1 = ₹110

⇒ Profit earned by shopkeeper = SP of 22 oranges = 22 × ₹1 = ₹22

⇒ We know that Cost Price (CP) = Selling Price − Profit

⇒ CP of 110 oranges = 110 − 22 = ₹88

⇒ Profit % = (Profit ÷ CP) × 100

⇒ Profit % = (22 ÷ 88) × 100

⇒ Profit % = (1 ÷ 4) × 100

⇒ Profit % = 25%

∴ The correct answer is 25%.

Additional Information

Profit and Loss Basics

When Selling Price (SP) > Cost Price (CP), there is a profit. Profit = SP − CP. Conversely, Loss = CP − SP.

Calculation Base

Profit and Loss percentages are always calculated on the Cost Price (CP) unless explicitly stated otherwise. Profit % = (Profit ÷ CP) × 100.

Marked Price & Discount

Discount is always offered on the Marked Price (MP). Selling Price = MP − Discount. Discount % = (Discount ÷ MP) × 100.

Shortcut Trick

3M × 16 = 6F × 16 ⇒ M/F = 2/1 (Efficiency ratio)

Total work = 3 × 2 × 16 = 96 units.

Efficiency of 12M + 8F = 12(2) + 8(1) = 32 units/day.

Required days = 96 ÷ 32 = 3 days.

∴ The correct answer is 3 days.

Alternate Method

Given:

3 Males complete the work in 16 days.

6 Females complete the work in 16 days.

Calculations:

⇒ Time taken by 1 Male to complete the work = 16 × 3 = 48 days

⇒ Time taken by 1 Female to complete the work = 16 × 6 = 96 days

⇒ Combined efficiency of 12 Males and 8 Females = 12 × 2 + 8 × 1 = 24 + 8 = 32 units/day

⇒ Required days = Total Work ÷ Combined efficiency

⇒ Required days = 96 ÷ 32 = 3 days

∴ The correct answer is 3 days.

Additional Information

Work Equivalence Formula

M₁D₁H₁ / W₁ = M₂D₂H₂ / W₂, where M is the number of people, D is days, H is hours, and W is work done.

Total Work Concept

Total work is the product of the number of workers, their individual efficiency, and the time taken to complete the task.

Combined Efficiency

When multiple individuals or groups work together, their combined efficiency is simply the sum of their individual unit-day efficiencies.

Pipes & Cisterns Analogy

Time and Work concepts directly map to Pipes and Cisterns, where efficiency is replaced by the filling or emptying rate of the pipes.

Shortcut Trick

Initial ratio = 1 : 2 (difference is 1)

Final ratio = 5 : 7 (difference is 2)

Multiply the initial ratio by 2 to equalize the differences between parts: 2 : 4

Increase in ratio parts = 5 − 2 = 3 parts for both numbers.

Since 21 is added to both, 3 parts = 21 ⇒ 1 part = 7.

Initial numbers are 2 parts and 4 parts ⇒ 2 × 7 = 14 and 4 × 7 = 28.

∴ The correct answer is 14, 28.

Alternate Method

Ratio Change Analysis Initial Values x 2x

+21 +21

Final Ratio 5 : 7

Given:

The initial ratio of two numbers = 1 : 2

Number added to both = 21

The final ratio = 5 : 7

Calculation:

Let the two initial numbers be x and 2x.

⇒ According to the problem: (x + 21) ÷ (2x + 21) = 5 ÷ 7

⇒ By cross-multiplying the equation:

⇒ 7 × (x + 21) = 5 × (2x + 21)

⇒ 7x + 147 = 10x + 105

⇒ 10x − 7x = 147 − 105

⇒ 3x = 42

⇒ x = 14

The first number = x = 14

The second number = 2x = 2 × 14 = 28

∴ The correct answer is 14, 28.

Additional Information

Cross-Multiplication Method

When a ratio a : b changes to c : d by adding quantities x and y respectively, then the initial value of 1 unit can be found directly using the formula (xd − yc) ÷ (ad − bc).

Compound Ratio

The compound ratio of two ratios a : b and c : d is defined as the product of the antecedent and consequent terms given by (a × c) : (b × d).

Duplicate & Triplicate Ratio

The duplicate ratio of a : b is a² : b², and the triplicate ratio of a : b is given by a³ : b³.

Shortcut Trick

Let the total number of voters be 100%, so the votes cast = 100% − 8% = 92%.

The winner's share is 48% of the total voters ⇒ Loser's share = 92% − 48% = 44%.

Winning margin in percentage = 48% − 44% = 4%.

Since 4% → 110 votes ⇒ 100% → (110 ÷ 4) × 100 = 2750.

∴ The correct answer is 2750 voters.

Alternate Method

Given:

⇒ Percentage of voters who did not cast votes = 8%

⇒ Percentage of total votes obtained by winner = 48%

⇒ Winning margin = 110 votes

Formula Used:

⇒ Total Votes = Votes Not Cast + Votes Cast

⇒ Votes Cast = Winner's Votes + Loser's Votes

Total Voters (100%)

Not Cast (8%)

Votes Cast (92%)

Winner (48%)

Loser (44%)

Difference = 48% − 44% = 4% → 110 Votes

Calculations:

⇒ Let the total number of voters be x.

⇒ Number of voters who did not cast their vote = 8% of x = 0.08x

⇒ Number of votes cast = x − 0.08x = 0.92x

⇒ Number of votes the winner got = 48% of x = 0.48x

⇒ Number of votes the loser got = 0.92x − 0.48x = 0.44x

⇒ Difference in votes between winner and loser = 0.48x − 0.44x = 0.04x

⇒ Given, the winning margin is 110 votes.

⇒ 0.04x = 110

⇒ x = 110 ÷ 0.04

⇒ x = (110 × 100) ÷ 4

⇒ x = 2750

∴ The correct answer is 2750 voters.

Additional Information

Election Base Concept

In an election, the total voting list is always treated as the base value of 100%. If a percentage is explicitly given as 'of total voters', it directly maps to this 100% base regardless of how many votes were actually cast or were invalid.

Valid vs Invalid Votes

Total votes cast = Valid votes + Invalid votes. The distribution of votes among candidates is done only on valid votes unless specified otherwise in the question.

Percentage Difference Method

The winning margin is always calculated as the difference in percentages between the winner and the nearest rival multiplied by the base vote count. Equating this difference directly to the numerical given value acts as the fastest solving route.

Shortcut Trick

Ratio of amount (Raised : Remaining) = 75% : 25% = 3 : 1

Ratio of people (Solicited : Remaining) = 60% : 40% = 3 : 2

Ratio of Average = (Amount ÷ People) = (3 ÷ 3) : (1 ÷ 2) = 1 : 0.5 = 2 : 1

Since 2 units of average corresponds to ₹600, 1 unit = 600 ÷ 2 = ₹300.

∴ The correct answer is ₹300.

Alternate Method

Given:

Amount raised = 75%, Remaining amount needed = 25%

People solicited = 60%, Remaining people = 40%

Average donation from solicited people = ₹600

Amount Needed:

Raised: 75% (3 parts) Rem: 25% (1) People Solicited:

Solicited: 60% (3 parts) Rem: 40% (2 parts) Avg = 3 parts / 3 parts = 1 unit → ₹600 Avg = 1 part / 2 parts = 0.5 unit → ₹300

Formula Used:

Total Amount = Number of People × Average Donation

Calculations:

⇒ Let the total number of people be P and total amount needed be A.

⇒ Amount raised = 75% of A = 0.75A

⇒ People solicited = 60% of P = 0.6P

⇒ Average donation of solicited people = 0.75A ÷ 0.6P = 1.25(A/P) = 600

⇒ A/P = 600 ÷ 1.25 = 480

⇒ Remaining amount to be raised = 25% of A = 0.25A

⇒ Remaining people to be solicited = 40% of P = 0.4P

⇒ Average donation needed from remaining people = 0.25A ÷ 0.4P = 0.625(A/P)

⇒ Substitute the value of (A/P) = 480

⇒ Average donation = 0.625 × 480 = 300

∴ The correct answer is ₹300.

Additional Information

Weighted Average

When a group is divided into two parts, the overall average is given by: Combined Average = (n₁x₁ + n₂x₂) ÷ (n₁ + n₂)

Proportionality in Averages

Average is directly proportional to the total amount and inversely proportional to the number of people. Ratio of Averages = Ratio of Amounts × Inverse Ratio of People.

Fractional Equivalent

Converting percentages to fractions simplifies ratio calculations. 75% = 3/4, 25% = 1/4, 60% = 3/5, 40% = 2/5.

The logic followed here is'

Hence, the correct answer is "Option 4".

Family Chart:

Given: Pointing to a woman, Ashok said, "Her granddaughter is the only daughter of my brother".

Let's break down the statement from Ashok's perspective:

​

So, the woman is Ashok's 'Mother'.

Hence, the correct answer is "Option 3".

Family Chart:

Given: Dhanesh said, "This girl is the wife of the grandson of my mother."

Let's break down the statement,

​

Therefore, Dhanesh is the 'Father-in-law' to the girl.

Hence, the correct answer is "Option 4".

The logic followed here is,

Hence, the correct answer is "Option 4".

The correct mirror image of the image is,

Hence, the correct answer is "Option 3".

The logic followed here is,

In Figures 1, 3, and 4, the star is located in one of the corners of the outer square and is in the region between the outer and inner square (the frame).

In Figure 2, the star is located inside the inner square.

Therefore, Figure 2 is the odd one out because the star's position is different from the pattern established by the other three figures.

Hence, the correct answer is "Option 1".

The logic followed here is:

• 169 = 13²
• 216 = 6³
• 343 = 7³
• 512 = 8³

All the numbers except 169 are perfect cubes.

169 is a perfect square, while 216, 343, and 512 are perfect cubes.

Hence, the dissimilar number is "Option 1".

The logic followed here is,

Thus, the missing number in the series is "127".

Hence, the correct answer is "Option 4".

The logic followed here is:

• Hornbill: A type of bird known for its large beak, capable of flight.
• Ostrich: A large, flightless bird native to Africa.
• Kiwi: A small, flightless bird native to New Zealand.
• Emu: A large, flightless bird native to Australia.

Among the given options, Ostrich, Kiwi, and Emu are all flightless birds.

However, the Hornbill is a bird that can fly.

Hence, the word that is different from the rest is "Option 1".

The criteria set for selecting faculty members in a School and the fulfillment status for Sudha Ranjan.

Analysis:

Sudha Ranjan satisfies criteria a (Age), b (Experience), and d (Interview Marks).

She fails criteria c, as she has only 56% in her Postgraduate degree (MCA), while the requirement is minimum 60%.

None of the special conditions (e, f, g) apply for the failure of the minimum marks in the Postgraduate degree.

Since the candidate does not satisfy all the basic eligibility criteria and no special clause covers this specific failure, the candidate is not to be selected as a faculty member.

Hence, the correct answer is "Option 1".

The logic followed here is:

• 1331 = 11³
• 1728 = 12³
• 2197 = 13³
• 2744 = 14³
• 3365 = Not a perfect cube (15³ = 3375)

All the numbers except 3365 are perfect cubes of consecutive integers (11, 12, 13, 14). However, 3365 is not a perfect cube.

Hence, the odd one out is "Option 3".

The number of triangles in the given figure is,

So, the number of triangles in the figure is 9.

Hence, the correct answer is "Option 3".

Shortcut Trick

The sum of the first n natural numbers is directly calculated using the formula n × (n + 1) ÷ 2.

Here, the number of terms n = 24.

Sum = 24 × (24 + 1) ÷ 2

Sum = 24 × 25 ÷ 2 = 12 × 25 = 300.

∴ The correct answer is 300.

Alternate Method

Given:

The sequence of the first 24 natural numbers is 1, 2, 3, ..., 24.

This sequence forms an Arithmetic Progression (A.P.).

Formula Used:

Sum of an Arithmetic Progression = n ÷ 2 × (a + l)

Where n = total number of terms, a = first term, and l = last term.

Calculations:

⇒ For this progression, n = 24, a = 1, and l = 24.

⇒ Sum = 24 ÷ 2 × (1 + 24)

⇒ Sum = 12 × 25

⇒ Sum = 300

∴ The correct answer is 300.

Additional Information

Sum of First n Odd Natural Numbers

The sum of the first n odd natural numbers is always equal to n².

Sum of First n Even Natural Numbers

The sum of the first n even natural numbers is equal to n(n + 1).

Sum of Squares of First n Natural Numbers

The sum of the squares of the first n natural numbers is given by n(n + 1)(2n + 1) ÷ 6.

Sum of Cubes of First n Natural Numbers

The sum of the cubes of the first n natural numbers is given by [n(n + 1) ÷ 2]².

Shortcut Trick

Ratio of boys to girls = 3 : 1

Total ratio parts = 3 + 1 = 4

The total number of children must be completely divisible by 4 (since children cannot be in fractions).

Among the given options (24, 40, 20, 22), only 22 is not divisible by 4.

∴ The correct answer is 22.

Alternate Method

Given:

The number of boys in the classroom is three times the number of girls.

Formula Used:

Total children = Number of boys + Number of girls

Boys (3x) Girls (1x)

Total Children = 4x (Must be a multiple of 4)

Calculations:

⇒ Let the number of girls in the classroom be x.

⇒ Number of boys = 3x

⇒ Total number of children = 3x + x = 4x

⇒ Since x represents the number of girls, it must be a positive integer. Consequently, the total number of children must be a multiple of 4.

Let's check the given options by dividing each by 4:

⇒ 24 ÷ 4 = 6 → (Whole number, possible)

⇒ 40 ÷ 4 = 10 → (Whole number, possible)

⇒ 20 ÷ 4 = 5 → (Whole number, possible)

⇒ 22 ÷ 4 = 5.5 → (Decimal value, not possible)

⇒ Since 22 yields a fractional number of children, it cannot represent the total number of children in the class.

∴ The correct answer is 22.

Additional Information

Divisibility in Ratios

When identical or indivisible items (such as people, cars, or animals) are divided into a ratio a : b, the total number of those items must always be a perfect multiple of the sum of the ratio parts (a + b).

Compound Ratio

For two independent ratios a : b and c : d, their compound ratio is formed by multiplying their respective parts together, resulting in ac : bd.

Proportion Rule

An equality between two differing ratios is known as a proportion. If a : b = c : d, then the product of the extreme terms equals the product of the mean terms (ad = bc).

The number of triangles in the figure is,

So, the total number of triangles in the figure is 28.

Hence, the correct answer is "Option 4".

The logic followed here is,

Logic: The figure is rotated 90° in each subsequent figure.

Hence, the correct answer is "Option 2".

Shortcut Trick

When a plane slices a cube perpendicular to its main body diagonal, the shape of the cross-section changes based on the cut's position.

If the slice is made close to a vertex, it forms an equilateral triangle.

As the plane moves toward the exact center of the cube, it begins to intersect more faces.

At the very center of the cube, the perpendicular plane symmetrically slices through exactly 6 faces.

Since the plane cuts 6 sides evenly, the resulting maximum cross-section is a perfect regular Hexagon.

∴ The correct answer is Hexagon.

Alternate Method

Given:

⇒ A cube is sliced by a plane perpendicular to one of its body diagonals.

Body Diagonal Hexagonal Cross-Section

Concept Used:

⇒ Let the side of the cube be a. We can position the cube in a 3D coordinate system with vertices ranging from (0, 0, 0) to (a, a, a).

⇒ The main body diagonal connects the origin (0, 0, 0) to the opposite furthest vertex (a, a, a).

⇒ A 3D plane that is perpendicular to this body diagonal will have the linear equation: x + y + z = k.

Calculation:

⇒ To determine the shape, we must locate where this plane intersects the outer edges of the cube.

⇒ The largest possible slice occurs when the plane passes directly through the midpoint of the diagonal, giving us k = 1.5a.

⇒ Substituting k = 1.5a, the plane x + y + z = 1.5a cuts through exactly 6 of the 12 edges of the cube.

⇒ The intersection coordinates on the edges are: (a, 0.5a, 0), (0.5a, a, 0), (0, a, 0.5a), (0, 0.5a, a), (0.5a, 0, a), and (a, 0, 0.5a).

⇒ Connecting these six intersecting midpoints creates a perfectly symmetrical, closed 6-sided polygon.

⇒ Because all edge lengths and angles of this polygon are identical, the final cross-section is a regular hexagon.

∴ The correct answer is Hexagon.

Additional Information

Triangular Cross-section

If a cube is sliced by a plane passing near a vertex and cutting through three adjacent intersecting edges, the resulting cross-section shape is an equilateral triangle.

Rectangular Cross-section

If the slicing plane passes completely through two parallel and diagonally opposite edges of the cube, the resulting cross-section is a rectangle with an area equal to a²√2.

Body Diagonal Length

The body diagonal represents the maximum distance inside a cube. For a cube having side length 'a', the body diagonal is calculated directly as a√3.

The logic followed here is:

Logic: The first organ performs the function described by the second word.

Here,

Heart : Circulate → The Heart's primary function is to Circulate blood throughout the body.

Similarly,

Lungs : Breathe

The primary function of the Lungs is to facilitate respiration, which is to Breathe (taking in oxygen and expelling carbon dioxide).

• Breathe: The main function of the lungs.
• Digest: Function of the digestive system (e.g., stomach, intestines).
• Excrete: Function of the excretory system (e.g., kidneys, skin).
• Vision: Function of the eyes.

Hence, the correct answer is "Option 1".

Given: Three streets X, Y, and Z are being compared based on how busy they are.

Street X is not the busiest.

Street Y is busier than street Z.

The final order of busyness (from busiest to least busy) is:

Y > Z/X

Therefore, the busiest street is Y.

Hence, the correct option is "Option 3".

‘चरण कमल बन्दौ हरि राई' में अलंकार है - रूपक

Key Points

• (इस पंक्ति में चरणों की तुलना कमल से की गई है, यहां चरणों को कमल के समान बताया गया है, इस तरह रूपक अलंकार का प्रयोग हुआ है।)
• जब एक वस्तु पर दूसरी वस्तु का आरोप किया जाये अर्थात् जब एक वस्तु को दूसरी वस्तु का रूप दिया जाये तो रूपक अलंकार कहलाता है।
• उदाहरण-
• पायो जी मैंने राम रतन धन पायो।
• (यहाँ पर राम रतन को ही धन बता दिया गया है।)

Additional Information 

उत् + हार के योग से शब्द बनेगा - उद्धार

Key Points 

• 'उद्धार' का संधि विच्छेद करने पर 'उत्' + 'हार' होगा। यहाँ व्यंजन संधि है।
• नियम - जब त् का मिलन ह् से हो तो त् को द् और ह् को ध् में बदल दिया जाता है।
• त् या द् के साथ ज या झ का मिलन होता है तब त् या द् की जगह पर ज् बन जाता है।
• उदाहरण - ​
• उत् + हरण = उद्धरण, तत् + हित = तद्धित, सत् + जन = सज्जन, जगत् + जीवन = जगज्जीवन आदि।

अन्य विकल्प -

• 'आहार' का अर्थ - भोजन, खाना।
• 'उतार' का अर्थ - उतरने की क्रिया, उतराई।
• 'उदार' का अर्थ - दाता, दानशील, महान्।

Additional Informationव्यंजन संधि - 

• जब संधि करते समय व्यंजन के साथ स्वर या कोई व्यंजन के मिलने से जो रूप में परिवर्तन होता है, उसे ही व्यंजन संधि कहते हैं।​

उदाहरण - 

• दिक् + गज = दिग्गज
• वाक् + ईश = वागीश
• उत् + नति =  उन्नति
• सत् + आशय = सदाशय आदि।

‘जिसके हृदय में ममता नहीं है' वाक्यांश के लिए एक शब्द होगा - निर्मम

Key Points

• ‘जिसके हृदय में ममता नहीं है' वाक्यांश के लिए एक शब्द होगा - निर्मम
• वाक्यांश के लिए उपयुक्त शब्द - अनेक शब्दों के लिए एक शब्द को प्रयुक्त करना ही वाक्यांश के लिए एक शब्द कहलाता है।

अन्य विकल्प -

Additional Information   कुछ महत्वपूर्ण वाक्यांश के लिए एक शब्द -

'हजारों लोगों ने उसे देखा है' - वाक्य में विशेषण है - हजारों

Key Points

• वाक्य - हजारों लोगों ने उसे देखा है (वाक्य में 'लोगों' विशेष्य शब्द और 'हजारों' विशेषण शब्द होगा।)
• संज्ञा अथवा सर्वनाम शब्दों की विशेषता (गुण, दोष, संख्या, परिमाण आदि) बताने वाले शब्द 'विशेषण' कहलाते हैं।
• जैसे- बड़ा, काला, लम्बा, दयालु, भारी, सुंदर, कायर, एक, दो, वीर पुरुष, गोरा, अच्छा, बुरा, मीठा, खट्टा, आदि।
• जैसे- कौआ काला होता है।

अन्य विकल्प-

• विशेष्य शब्द - 'लोगों'
• क्रिया शब्द - 'देखा'
• सर्वनाम शब्द - 'उसे'

Additional Information विशेष्य-

• जिस संज्ञा और सर्वनाम की विशेषता बताई जाती है, उसे विशेष्य कहते हैं।
• जैसे- बालक चतुर है। (वाक्य में 'बालक' विशेष्य शब्द और 'चतुर' विशेषण शब्द होगा।)

क्रिया:-

• जिस शब्द के द्वारा किसी कार्य के करने या होने का बोध होता है उसे क्रिया कहा जाता है।
• जैसे- पीना, पढ़ना, लिखना, दौड़ना, चलना, जाना आदि।​
• अन्वित पढ़ रहा है।

सर्वनाम:-

• जो शब्द संज्ञा शब्दों के स्थान पर प्रयोग किए जाते हैं, वे सर्वनाम कहलाते हैं।
• हिंदी में मूलतः सर्वनाम 11 प्रकार के होते है - मै, तू, आप, यह, वह, जो, सो, कौन, क्या, कोई, कुछ आदि।
• जैसे- तुम कौन हो?

'नाग' का अनेकार्थी शब्द है - हाथी

Key Points

• 'नाग' के अनेकार्थी शब्द - हाथी, पर्वत, बादल, साँप।
• अनेकार्थी शब्द - ऐसे शब्द, जिनके अनेक अर्थ होते है, अनेकार्थी शब्द कहलाते है।

अन्य विकल्प -

Additional Informationकुछ अन्य महत्वपूर्ण अनेकार्थक शब्द:-

'पूस की रात' (कहानी) के रचयिता हैं - प्रेमचंद

Key Pointsपूस की रात-

• रचनाकार - प्रेमचंद
• विधा - कहानी
• प्रकाशन वर्ष - 1930 ई.
• मुख्य पात्र - हल्कू किसान, उसकी पत्नी मुन्नी, सहना जो कर्ज वसूलने आता है।
• विषय - एक किसान "हल्कू "की कठिनाई चित्रित किया गया है।

Important Pointsप्रेमचंद-

• जन्म- 1880 - 1936 ई.
• भारत के उपन्यास सम्राट माने जाते हैं।
• प्रेमचंद का वास्तविक नाम धनपत राय श्रीवास्तव था।
• कहानी-
• बड़े घर की बेटी (1910)
• नमक का दरोगा (1913)
• सज्जनता का दण्ड (1916)
• पंच परमेश्वर (1916)
• आप बीती (1923)
• शतरंज के खिलाड़ी (1925) आदि।

Additional Informationशिवपूजन सहाय-

• जन्म- 1893 -1963 ई.
• हिन्दी के प्रसिद्ध उपन्यासकार, कहानीकार, सम्पादक और पत्रकार थे।
• कहानी**-संग्रह-** 
• विभूति (1926 ई.)

जयंशकर प्रसाद-

• जन्म- 1889-1937 ई.
• हिन्दी कवि, नाटककार, कहानीकार, उपन्यासकार तथा निबन्ध-लेखक थे।
• कहानी-संग्रह-
• छाया (1912 ई.)
• प्रतिध्वनि (1926 ई.)
• आकाशदीप (1929 ई.)
• आँधी (1931 ई.)
• इन्द्रजाल (1936 ई.) आदि।

सूर्यकान्‍त त्र‍िपाठी निराला-

• जन्म- 1896 -1961 ई.
• हिन्दी के छायावादी कवियों में कई दृष्टियों से विशेष महत्त्वपूर्ण हैं।
• निराला जी एक कवि, उपन्यासकार, निबन्धकार और कहानीकार थे।
• कहानी संग्रह-
• लिली (1934 ई.)
• सखी (1935 ई.)
• सुकुल की बीवी (1941 ई.)
• चतुरी चमार (1945 ई.)
• देवी (1948 ई.) आदि।

‘आदि - आदी’ शब्द-युग्म का सही अर्थ है - आरंभ - अभ्यस्त

Key Points

• 'आदि' (आरंभ) - 'आदी' (अभ्यस्त)
• शब्द युग्म - ऐसे शब्द जिनका उच्चारण प्राय: समान होता है किन्तु उनके अर्थ भिन्न होते हैं, शब्द युग्म कहलाते हैं।

अन्य विकल्प-

Additional Information कुछ महत्वपूर्ण शब्द युग्म और उनके अर्थ -

‘साखी' का मूल तत्सम शब्द है - साक्षी

Key Points

• 'साक्षी' एक तत्सम शब्द है, जबकि इसका तद्भव शब्द 'साखी' होगा।
• तत्सम - जिन शब्दों को संस्कृत से बिना किसी परिवर्तन के ले लिया जाता है, उन्हें तत्सम शब्द कहते हैं। 
• जैसे- अक्षि, कूप, गृह आदि।
• तद्भव - जिन शब्दों में समय और परिस्थितियों के कारण कुछ परिवर्तन होने से जो शब्द बने हैं, उन्हें तद्भव कहते हैं। 
• जैसे- आँख, कुआँ, घर आदि।​

अन्य विकल्प-​

Additional Information 

वाक्य का शुद्ध रूप होगा- बच्चे को फल काटकर खिलाओ।

Key Points

• शुद्ध वाक्य - बच्चे को फल काटकर खिलाओ।
• वाक्य में लिंग, वचन, पुरुष, काल, कारक आदि का क्रिया के साथ ठीक-ठीक मेल हो, उसे शुद्ध वाक्य कहते है।
• पदों के उचित क्रम में न होने पर उसके भाव या अर्थ में स्पष्टता नहीं रहती और इसे वाक्य की पदक्रम संबंधी अशुद्धियाँ कहा जाता है।

अन्य विकल्प -

• बच्चे को काटकर फल खिलाओ। **(**पदक्रम संबंधी अशुद्धियाँ)
• काटकर फल बच्चे को खिलाओ। (पदक्रम संबंधी अशुद्धियाँ)
• फल बच्चे को काटकर खिलाओ। (पदक्रम संबंधी अशुद्धियाँ)

Additional Information पदक्रम संबंधी अशुद्धियाँ - 

प्रत्यक्ष के द्वारा अप्रत्यक्ष का चमत्कारपूर्ण वर्णन अनुमान अलंकार का लक्षण है। 

Key Points

• प्रत्यक्ष के द्वारा पर अप्रत्यक्ष की कल्पना या अनुमान करना ही अनुमान अलंकार होता है,यह एक तर्क न्यायमूलक अलंकार है।
• उदाहरण -
• मोहि करत कत बावरी, किये दूराव दुरै न।
• कहे देत रंग राति के, रँग निचुरत से नैन॥ - बिहारीलाल
• (यहाँ लाल आँखें देखकर रात की रति-केलि का अनुमान हो रहा है। 'रंग निचुरत से नैन' साधन है जिसके द्वारा 'रति के रंग' साध्य का अनुमान होता है।)

Additional Information 

“पेड़ से कई आम गिरे” में कारक का प्रयोग हुआ है - अपादान कारक

Key Points

• वाक्य - पेड़ से कई आम गिरे। (वाक्य में पेड़ से कई आम गिरे (अलगाव) की बात की जा रही है।)
• यहाँ से विभक्ति चिन्ह का प्रयोग किया जा रहा है, अतः यह उदाहरण अपादान कारक के अंतर्गत आएगा।
• जब संज्ञा या सर्वनाम के किसी रूप से किन्हीं दो वस्तुओं के अलग होने का बोध होता है, तब वहां अपादान कारक होता है।
• अपादान कारक का भी विभक्ति चिन्ह से होता है। 
• उदाहरण - दूल्हा घोड़े से गिर पड़ा। चूहा बिल से बाहर निकला।

Confusion Points करण और अपादान कारक में अंतर:-

• करण और अपादान दोनों ही कारकों में ‘से’ चिन्ह का प्रयोग होता है।
• परन्तु अर्थ के आधार पर दोनों में अंतर होता है।
• करण कारक में जहाँ पर ‘से’ का प्रयोग साधन के लिए होता है
• वहीं पर अपादान कारक में अलग होने के लिए किया जाता है।

Important Points हिन्दी में आठ कारक’ हैं -

Additional Information 

शब्द स्त्रीलिंग और पुल्लिंग दोनों है - हार

आयोग द्वारा इस प्रश्न का उत्तर वार दिया गया है, हमने इसका उत्तर हार माना है, निचे हार संबंधित उदाहरण भी दिए गए है, अंतिम उत्तर कुंजी यदि कोई परिवर्तन आता है, तो यहां भी कर दिया जाएगा।

Key Points

• स्त्रीलिंग और पुल्लिंग दोनों है - 'हार'
• जैसे - सुनीता में नया हार ले लिया। (पुल्लिंग)
• जैसे - विपक्ष की हार हो गयी। **(**स्त्रीलिंग)
• स्त्रीलिंग - शब्द के जिस रूप से व्यक्ति या वस्तु की स्त्री जाति का बोध होता है, उसे स्त्रीलिंग कहते हैं।
• जैसे - माता, लड़की, भेड़, गाय, बंदरिया, मछली, बुढ़िया, शेरनी, नारी, रानी, राजकुमारी, बहन आदि।
• पुल्लिंग - शब्द के जिस रूप से पुरुष जाति का बोध होता है, उसे पुल्लिंग कहते हैं।
• जैसे- बकरा, घोड़ा, लड़का, आदमी, शेर, हाथी, भेड़िया, बन्दर, बालक, शिशु, राजा, राजकुमार आदि।

अन्य विकल्प-

Additional Informationलिंग दो प्रकार के होते हैं-

1. पुल्लिंग
2. स्त्रीलिंग

"खटिया सेना" मुहावरे का सही अर्थ है - बीमार होना

Key Points

• "खटिया सेना" का अर्थ - बीमार होना। वाक्य प्रयोग - माला की माँ बुखार के कारण "खटिया सेती है"।
• मुहावरा - ऐसे वाक्यांश, जो सामान्य अर्थ का बोध न कराकर किसी विलक्षण अर्थ को प्रकट करते है, उसे मुहावरा कहते है।
• उदाहरण के लिए - पगड़ी रखना- इज्जत बचाना। वाक्य प्रयोग - हल्दी घाटी में झाला सरदार ने राजपूतों की "पगड़ी रख ली"।

अन्य विकल्प-

Additional Information 

वाक्य सकर्मक क्रिया वाला है - सतीश ने केले खरीदे।

Key Points

• वाक्य - सतीश ने केले खरीदे।
• (वाक्य में 'खरीदे' क्रिया का प्रभाव 'सतीश' (कर्ता) पर न पड़कर 'केले' पर पड़ रहा है। यहाँ पर 'केले' कर्म हैं, अत: यह सकर्मक क्रिया के उदाहरण है।)

अन्य विकल्प -

• हरीश बस पर चढ़ गया।
• राजू सदा रोता रहता है।
• कैलाश छत से गिर पड़ा।
• (वाक्य में कर्म का अभाव है तथा 'चढ़ गया, रोता रहता, गिर पड़ा' (क्रिया) का प्रभाव
• 'हरीश, राजू, कैलाश' (कर्ता) पर पड़ रहा है, अत: यह अकर्मक क्रिया उदाहरण है।)

Important Points क्रिया के भेद -

• कर्म के आधार पर क्रिया के दो भेद होते हैं।

1. सकर्मक क्रिया
2. अकर्मक क्रिया

Additional Information 

‘प्रत्युप्तन्नमति' शब्द में प्रयुक्त उपसर्ग है - प्रति

Key Points

• प्रति + उत्पन्न + मति = प्रत्युप्तन्नमति
• 'प्रति' उपसर्ग, 'उत्पन्न' मूलशब्द और 'मति' प्रत्यय
• 'प्रत्युप्तन्नमति' का अर्थ - जो तुरंत ही कोई उपयुक्त बात या काम सोच ले।

Important Points 

• उपसर्ग शब्द के शुरू में जुड़ता है।

Additional Information कुछ महत्वपूर्ण उपसर्ग शब्द:-​

• प्रति (प्रत्येक) - प्रतिदिन, प्रत्येक, प्रतिकूल, प्रतिहिंसा, प्रतिरूप।
• प्र (आगे) - प्रदान, प्रबल, प्रयोग, प्रसार, प्रहार, प्रयत्न।
• अनु (पीछे) - अनुचर, अनुकरण, अनुकूल, अनुनाद, अनुभव।
• निर् (बिना) - निराकार, निरादर, नीरोग, नीरस, निरीह, निरक्षर।
• उप (सहायक) - उपभोग, उपवन, उपमन्त्री, उपयोग, उपनाम, उपहार।
• सम् (अच्छी तरह) - सन्तोष, संगठन,संलग्न, संकल्प, संशय, संरक्षा।
• अनु (पीछे) - अनुचर, अनुकरण, अनुकूल, अनुनाद, अनुभव।

'सप्तर्षि' में समास है - द्विगु

Key Points

• 'सप्तर्षि' में 'द्विगु' समास है। इसका समास विग्रह होगा- सात ऋषियों का समाहार।
• वह समास जिसका पहला पद संख्यावाचक विशेषण होता है तथा समस्तपद किसी समूह या फिर किसी समाहार का बोध करता है तो वह द्विगु समास कहलाता है।
• उदाहरण -
• नवरात्र = नौ रात्रियों का समूह
• ​अष्टसिद्धि = आठ सिद्धियों का समाहार

Important Pointsसमास के भेद-

1. तत्पुरुष समास
2. कर्मधारय समास
3. द्विगु समास
4. द्वन्द्व समास
5. बहुव्रीहि समास
6. अव्ययीभाव समास​

Additional Information

'विशिष्ट' का विलोम शब्द है - सामान्य

Key Points

• 'विशिष्ट' शब्द का विलोम शब्द 'सामान्य' होगा।
• 'विशिष्ट' का अर्थ - जिसमें किसी प्रकार की विशेषता हो, विशेषतायुक्त।
• 'सामान्य' का अर्थ - मामूली, साधारण।
• विलोम - एक-दूसरे के विपरीत या उल्टा अर्थ देने वाले शब्दों को, विलोम शब्द कहते है।

अन्य विकल्प-

Additional Information कुछ अन्य महत्वपूर्ण विलोम शब्द -

'देखा गया हो' क्रिया के पक्ष का उदाहरण है - संभाव्य वर्तमान।

संभाव्य वर्तमान- इससे वर्तमान काल में काम के पूरा होने की संभावना रहती है। डॉ. वासुदेवनंदन प्रसाद के अनुसार यह संभाव्य वर्तमान का उदाहरण है।

Key Points

• 'देखा गया हो' - क्रिया के संभाव्य वर्तमान पक्ष का उदाहरण है।
• संभाव्य वर्तमान- क्रिया के जिस रूप से वर्तमान काल में कार्य के होने की केवल संभावना या अनिश्चितता का बोध हो।
• उदाहरण- शायद उसने देखा हो।

Additional Information

‘मुक्तिबोध' के लिए जैनेन्द्र कुमार को साहित्य अकादमी पुरस्कार से सम्मानित किया गया था। 

Key Points

• 'मुक्तिबोध' हिन्दी के विख्यात साहित्यकार जैनेन्द्र कुमार द्वारा रचित एक उपन्यास है
• जिसके लिये उन्हें सन् 1966 में साहित्य अकादमी पुरस्कार से सम्मानित किया गया।
• जैनेन्द्र कुमार को भारत सरकार द्वारा सन 1971 में पद्म भूषण सम्मान प्रदान किया गया था।
• जैनेन्द्र कुमार (1905 - 1988) हिन्दी साहित्य के प्रसिद्ध मनोवैज्ञानिक कथाकार, उपन्यासकार तथा निबंधकार थे।
• उपन्यास - 'परख' (1929), 'सुनीता' (1935), 'त्यागपत्र' (1937), 'कल्याणी' (1939), 'विवर्त' (1953), 'सुखदा' (1953), 'व्यतीत' (1953), 'जयवर्धन' (1956) आदि।

अन्य विकल्प-

Additional Informationसाहित्य अकादमी द्वारा सम्मानित किये गये हिन्दी साहित्यकारों की सूची इस प्रकार है -

"(गुरु) ने प्रसन्न होकर मुझे एक मंत्र दिया।" कोष्ठक में दिए गए शब्द का वचन बदलने के बाद होगा - गुरुजन

Key Points

• 'गुरु' एक एकवचन शब्द है जिसका बहुवचन शब्द 'गुरुजन' है।

Important Points

Additional Information 

संस्कृत के ऐसे शब्द जिन्हें हम ज्यों का त्यों प्रयोग में लाते है, वे तत्सम कहलाते है। 

Key Points

• तत्सम - जिन शब्दों को संस्कृत से बिना किसी परिवर्तन के ले लिया जाता है, उन्हें तत्सम शब्द कहते हैं।
• जैसे - ​दुग्ध, पुष्प, आम्र, रात्रि, उष्ट्र, अर्द्ध, ग्राम, निंद्रा आदि।
• तद्भव - जिन शब्दों में समय और परिस्थितियों के कारण कुछ परिवर्तन होने से जो शब्द बने हैं, उन्हें तद्भव कहते हैं।
• जैसे - दूध, फूल, आम, रात, ऊँट, आधा, गाँव, नींद आदि।​

Additional Information विदेशज:- 

• जो शब्द विदेशी भाषा के हैं, परंतु हिंदी में उन शब्दों का प्रचलन हो रहा है, ऐसे शब्द विदेशज शब्द कहे जाते हैं।
• विदेशी शब्द अरबी, फारसी, तुर्की, अंग्रेजी इत्यादि भाषाओं से लिए गए है। ​
• जैसे - डॉक्टर, दुकान, लीची, डॉक्टर, तोप, चश्मा, फकीर आदि।

देशज:-

• वे शब्द जिनकी उत्पत्ति का श्रोत ज्ञात न हो और लेकिन भाषा में उनका प्रचलन भरपूर हो, देशज शब्दों की श्रेणी में आते हैं, 
• जैसे - लोटा, कटोरा, डोंगा, डिबिया, खिचड़ी, खिड़की, पगड़ी, चिड़िया, जूता, तेंदुआ, फुनगी, कलाई आदि।

'मीन' का पर्यायवाची शब्द मत्स्य है। 

Key Points

• 'मीन' का पर्यायवाची शब्द मत्स्य है।
• 'मीन' के सभी पर्यायवाची शब्द - मछली, मत्स्य, झख, जलजीवन, सफरी, झष, जलीय जीव।
• पर्यायवाची - जो शब्द समान अर्थ के कारण किसी दूसरे शब्द की जगह ले लेते हैं, उन्हें पर्यायवाची शब्द कहते हैं।

अन्य विकल्प -

Additional Information कुछ महत्वपूर्ण पर्यायवाची शब्द  -

‘सर्प’, ‘मेघ’, ‘हरिण’ शब्द के अनेकार्थी हैं - सारंग

Key Points

• 'सर्प, मेघ, हरिण' सारंग शब्द के अनेकार्थी हैं।
• 'सारंग' के अन्य अनेकार्थी शब्द - कोयल, चातक, मोर, हंस, बाज, सिंह, घोङा, सोना, भौंरा आदि।
• अनेकार्थी शब्द - ऐसे शब्द, जिनके अनेक अर्थ होते है, अनेकार्थी शब्द कहलाते है।

अन्य विकल्प -

• 'नारंग' का अर्थ - नारंगी का पेड़ और फल।
• 'षडंग' का अर्थ - शिक्षा, व्याकरण, छंद, कल्प, निरुक्त्त और ज्योतिष ये छ: वेदांग।
• 'शारंग' शब्द में वर्तनी सम्बन्धित त्रुटि है।

Additional Information  कुछ प्रमुख अनेकार्थी शब्द:-

'अरे ! जरा इधर तो आ' में से अव्यय है- विस्मयादिबोधक

Key Points

• 'अरे ! जरा इधर तो आ' अव्यय शब्द : (अरे! इस वाक्य में विस्मयादिबोधक चिन्ह (!) लगेगा।)
• जिन अव्यय शब्दों से हर्ष, शोक, विस्मय, ग्लानी, लज्जा, घर्णा, दुःख, आश्चर्य आदि के भाव का पता चलता है, उन्हें विस्मयादिबोधक अव्यय कहते हैं।
• जहाँ पर अरे!, हाय!, शबाश!, ओह!, वाह!, हाँ!, वाह!, हैं!, ऐ!, क्या!, ओहो, अहा!, उफ, हा-हा!आदि आते हैं।
• जैसे - अरे! तुम यहाँ कैसे?

Additional Information

जिसमें कोई पद प्रधान नहीं होता तथा अन्य अर्थ प्रधान होता है, वहाँ बहुव्रीहि समास होता है।

Key Points

• जिस समास में प्रथम पद एवं द्वितीय पद दोनों की प्रधानता न हो बल्कि कोई तीसरा पद की प्रधानता हो, उसे बहुव्रीहि समास कहते हैं।
• जैसे - 
• नीलकंठ - नीला है कंठ जिसका अर्थात शिव जी
• चक्रधर - चक्र को धारण करने वाला अर्थात विष्णु जी

Important Pointsसमास के भेद-

1. तत्पुरुष समास
2. कर्मधारय समास
3. द्विगु समास
4. द्वन्द्व समास
5. बहुव्रीहि समास
6. अव्ययीभाव समास​

Additional Information 

हिंदी वर्णमाला में स्वरों की कुल संख्या है- 13

Key Points

• हिंदी वर्णमाला स्वर और व्यंजन से मिलकर बनती है। हिंदी में वर्णों (स्वर और व्यंजन) की कुल संख्या 52 है,
• जिसमें 13 कुल स्वर (11 स्वर + 2 अयोगवाह), 33 मूल व्यंजन, 2 उत्क्षिप्त व्यंजन और 4 संयुक्ताक्षर होते हैं।
• स्वर- वे ध्वनियाँ जो स्वतंत्र रूप से बोली जाए, परन्तु जिनका प्रयोग स्वतंत्र रूप से न होकर मात्राओं के रूप में हो, स्वर कहलाते है।
• हिन्दी में मूल रूप से स्वरों की संख्या 11 है (अ, आ, इ, ई, उ, ऊ, ऋ, ए, ऐ, ओ, औ), परन्तु अयोगवाह (ं, ः) को शामिल करने पर इनकी कुल संख्या 13 हो जाती है।

Additional Informationव्यंजन:-

• स्पर्श व्यंजन इन्हें पाँच वर्गों में रखा गया है और हर वर्ग में पाँच-पाँच व्यंजन हैं। हर वर्ग का नाम पहले वर्ग के अनुसार रखा गया है।
• क वर्ग- क् ख् ग् घ् ड़् ( कंठव्य व्यंजन )
• च वर्ग- च् छ् ज् झ् ञ् ( तालव्य व्यंजन )
• ट वर्ग- ट् ठ् ड् ढ् ण् (ड़् ढ्) ( मूर्धन्य व्यंजन )
• त वर्ग- त् थ् द् ध् न् ( दन्त्य व्यंजन )
• प वर्ग- प् फ् ब् भ् म्  ( ओष्ठव्य व्यंजन )
• उत्क्षिप्त व्यंजन - ड़ और ढ़।
• अयोगवाह - 2 (ं) और (ः)
• अंतःस्थ- य् र् ल् व्
• ऊष्म- श् ष् स् ह्
• संयुक्त व्यंजन - क्ष, त्र, ज्ञ, श्र

साहित्य अकादमी पुरस्कार प्राप्त निराला की साहित्य साधना की कृति है - रामविलास शर्मा

Key Points

• हिन्दी के विख्यात साहित्यकार रामविलास शर्मा ने निराला की साहित्य साधना (1969) नाम की जीवनी लिखी है,
• जिसके लिए उन्हें साल 1970 में साहित्य अकादमी पुरस्कार से सम्मानित किया गया था।
• डॉ॰ रामविलास शर्मा (1912- 2000) आधुनिक हिन्दी साहित्य के सुप्रसिद्ध आलोचक, निबंधकार, विचारक एवं कवि थे।
• रामविलास शर्मा जी की समीक्षा कृतियों में विशेष उल्लेखनीय हैं-
• 'प्रेमचन्द ��र उनका युग' (1953), 'निराला' (1946 ई.),'भारतेन्दु हरिश्चन्द्र' (1954 ई.),
• 'प्रगति और परम्परा' (1954 ई.), 'भाषा साहित्य और संस्कृति' (1954 ई.), 'भाषा और समाज' (1961 ई.)।

Additional Informationसाहित्य अकादमी द्वारा सम्मानित किये गये हिन्दी साहित्यकारों की सूची इस प्रकार है -

'अघ' शब्द का समभिन्नार्थक है - पाप

Key Points

• 'अघ' (पाप) - 'अर्घ' (मूल्य)
• अन्य सभी विकल्पों से सही अर्थ का बोध नहीं हो रहा है।
• ऐसे शब्द जो पढ़ने और सुनने में लगभग एक-से लगते हैं, परंतु अर्थ की दृष्टि से भिन्न्न होते हैं, समभिन्नार्थक शब्द कहलाते हैं।

अन्य विकल्प -​

Additional Information समभिन्नार्थक शब्द और उनके अर्थ -

शुद्ध वाक्य होगा - श्रीकृष्ण के अनेक नाम हैं।

दिए गए विकल्पों में केवल विकल्प 1 व्याकरण की दृष्टि से शुद्ध है। अन्य विकल्पों में लिंग, वचन एवं शब्द चयन संबंधी अशुद्धियाँ हैं।

Key Points

• शुद्ध वाक्य - श्रीकृष्ण के अनेक नाम हैं।
• वाक्य में लिंग, वचन, पुरुष, काल, कारक आदि का क्रिया के साथ ठीक-ठीक मेल हो उसे शुद्ध वाक्य कहते है।

अन्य विकल्प-

Additional Information पदक्रम व शब्द-अर्थ संबंध संबंधी अशुद्धियाँ -

'ऊँट के मुँह में जीरा' मुहावरे का अर्थ है - बहुत अधिक खाने वाले को बहुत कम देना।

Key Points

• 'ऊँट के मुँह में जीरा' का अर्थ - बहुत अधिक खाने वाले को बहुत कम देना ।
• वाक्य प्रयोग - महावत ने हाथी को खाने के लिए दो गन्ने दिये और वह उसके लिए **"**ऊँट के मुँह में जीरा" सिद्ध हुआ।
• मुहावरा - ऐसे वाक्यांश, जो सामान्य अर्थ का बोध न कराकर किसी विलक्षण अर्थ को प्रकट करते है, उसे मुहावरा कहते है।
• जैसे : 'पगड़ी रखना' का अर्थ- इज्जत बचाना।, वाक्य प्रयोग - हल्दीघाटी में झाला सरदार ने राजपूतों की "पगड़ी रख ली"।

Additional Information 

‘शास्त्रप्रवीण महाविद्यालय में पीताम्बर धारण करने आते हैं।' इस वाक्य में तत्पुरुष समास पद में है - शास्त्रप्रवीण

Key Points

• 'शास्त्रप्रवीण' का समास विग्रह - शास्त्र में प्रवीण, 'शास्त्रप्रवीण' में तत्पुरुष समास है।
• समास का वह रूप जिसमें द्वितीय पद या उत्तर पद प्रधान अर्थात प्रथम पद गौण हो, उसे तत्पुरुष समास कहते हैं।
• इस समास में आने वाले कारक चिन्हों को, से, के लिए, से, का/के/की, में, पर आदि का लोप होता है।
• जैसे - नीतिकुशल = नीति में कुशल। गुणहीन = गुण से हीन

अन्य विकल्प -

• महाविद्यालय = महान है जो विद्यालय (कर्मधारय समास)
• गिरिधर = गिरि को धारण करने वाला है जो अर्थात् कृष्ण जी।  - बहुव्रीहि समास
• पीतांबर = पीत (पीला) है अंबर (वस्त्र) जिसका अर्थात (श्रीकृष्ण जी) - बहुव्रीहि समास
• पीतांबर = पीत (पीला) है जो अंबर (वस्त्र) - कर्मधारय समास

Additional Information

'हस्ती' शब्द का समभिन्नार्थक है - अस्तित्व।

Key Points

• 'हस्ती' का अर्थ - 'अस्तित्व'
• अन्य सभी विकल्पों से सही अर्थ का बोध नहीं हो रहा है।

अन्य विकल्प -​

Additional Information कुछ प्रमुख सम भिन्नार्थक शब्द:-

छत्रसाल बुन्देला ने जिस समय मुग़लों का सामना किया, उस समय उनके पास थे - पाँच सवार और पच्चीस पैदल

Key Points

• गद्यांश के अनुसार-
• ​शिवाजी ने एक ज़मींदार और बीजापुरधीश के नौकर के पुत्र होकर चक्रवर्ती राज्य स्थापित करने की
• इच्छा को पूर्ण-सा कर दिखाया और छत्रसाल बुन्देला ने जिस समय मुग़लों का सामना करने का साहस किया
• उस समय उनके पास केवल पाँच सवार और पच्चीस पैदल थे।
• इसी सेना से इस महानुभाव ने दिल्ली का सामना करने की हिम्मत की और मरते समय
• अपने उत्तराधिकारियों के लिए दो करोड़ वार्षिक मुनाफे का स्वतंत्र राज्य छोड़ा।

Additional Information

• पच्चीस सवार और पाँच पैदल
• ​गद्यांश में 'पच्चीस सवार और पाँच पैदल' की चर्चा कही भी नहीं की गयी है।
• दो सवार और पाँच पैदल
• ​​गद्यांश में **'**दो सवार और पाँच पैदल' की चर्चा कही भी नहीं की गयी है।
• पच्चीस सवार और दो पैदल​
• ​गद्यांश में 'पच्चीस सवार और दो पैदल' की चर्चा कही भी नहीं की गयी है।

भूषण का प्रिय काव्य रस था - वीर

Key Points

• गद्यांश के अनुसार- 
• इसी सेना से इस महानुभाव ने दिल्ली का सामना करने की हिम्मत की और मरते समय
• अपने उत्तराधिकारियों के लिए दो करोड़ वार्षिक मुनाफे का स्वतंत्र राज्य छोड़ा।
• छत्रपति शिवाजी की प्रशस्ति में लिखे गए दो काव्य ग्रंथ हैं -
• शिवा बावनी और शिवराज भूषण। इस पाठ बोधन में भूषण वीर काव्य रस दर्शाया गया है।

Additional Information

महाकवि भूषण दरबारी कवि थे, उनके आश्रयदाता राजा का नाम शिवाजी था।

Key Points

• गद्यांश के अनुसार-
• ​शिवाजी और छत्रसाल से महानुभावों के पवित्र चरित्रों को वर्णन करने वालों की जितनी प्रशंसा की जाए थोड़ी है।
• शिवाजी ने एक ज़मींदार और बीजापुरधीश के नौकर के पुत्र होकर चक्रवर्ती राज्य स्थापित करने की
• इच्छा को पूर्ण-सा कर दिखाया।

Additional Information

• वीर सिंह जूदेव -
• ​गद्यांश में 'वीर सिंह जूदेव' की चर्चा नहीं की गयी है।
• छत्रसाल -
• छत्रसाल बुन्देला ने जिस समय मुग़लों का सामना करने का साहस किया उस समय उनके पास केवल पाँच सवार और पच्चीस पैदल थे।​
• औरंगज़ेब -​
• ​गद्यांश में 'औरंगज़ेब' की चर्चा नहीं की गयी है।

छत्रपति शिवाजी की प्रशस्ति में लिखे गए दो काव्य ग्रंथों के नाम हैं - शिवा बावनी, शिवराज भूषण

Key Points

• गद्यांश के अनुसार-
• इसी सेना से इस महानुभाव ने दिल्ली का सामना करने की हिम्मत की और मरते समय
• अपने उत्तराधिकारियों के लिए दो करोड़ वार्षिक मुनाफे का स्वतंत्र राज्य छोड़ा।
• छत्रपति शिवाजी की प्रशस्ति में लिखे गए दो काव्य ग्रंथ हैं - शिवा बावनी और शिवराज भूषण।
• इस पाठ बोधन में भूषण वीर काव्य रस दर्शाया गया है।

Additional Information

• शिवा चरित, शिवा विलास
• ​गद्यांश में **'**शिवा चरित, शिवा विलास' की चर्चा कही भी नहीं की गयी है।
• शिव कथा, शिवा विक्रम
• ​​गद्यांश में **'**शिव कथा, शिवा विक्रम' की चर्चा कही भी नहीं की गयी है।
• ​शिवा वैभव, शिवा चिन्तन
• ​​गद्यांश में **'**​शिवा वैभव, शिवा चिन्तन' की चर्चा कही भी नहीं की गयी है।

इस गद्यांश का सार्थक शीर्षक हो सकता है - भूषण की बुद्धिमत्ता

Key Points

• गद्यांश के अनुसार-
• ​भूषण महाराज ने विषय और विशेषतः नायक चुनने में बड़ी बुद्धिमत्ता से काम लिया है।
• शिवाजी और छत्रसाल से महानुभावों के पवित्र चरित्रों को वर्णन करने वालों की जितनी प्रशंसा की जाए थोड़ी है।

Additional Information

• भूषण का काव्यनायक चयन
• ​गद्यांश में 'भूषण का काव्यनायक चयन' से उचित सार्थक शीर्षक का बोध नही हो रहा है।
• भूषण विवेक​
• ​गद्यांश में 'भूषण विवेक' से उचित सार्थक शीर्षक का बोध नही हो रहा है।
• भूषण की कला​
• ​गद्यांश में 'भूषण की कला' से उचित सार्थक शीर्षक का बोध नही हो रहा है।

The logic followed here is,

So, the dissimilar number is 178.

Hence, the correct answer is "Option 1".

Shortcut Trick

Relative speed (same direction) = 80 − 44 = 36 km/hr.

Speed in m/s = 36 × (5 / 18) = 10 m/s.

Combined length = Relative speed × Time.

Combined length = 10 × 40 = 400 m.

∴ The correct answer is 400 m.

Alternate Method

Train 1

80 km/hr

Train 2

44 km/hr

Relative Speed = 80 - 44 = 36 km/hr Time = 40 sec

Given:

Speed of first train (S₁) = 80 km/hr

Speed of second train (S₂) = 44 km/hr

Time taken to cross (T) = 40 seconds

Formula Used:

Relative Speed (same direction) = S₁ − S₂

Distance = Speed × Time

Calculations:

⇒ Relative Speed = 80 − 44 = 36 km/hr

⇒ Convert km/hr to m/s: 36 × (5 / 18) = 10 m/s

⇒ Distance covered = Relative speed × Time

⇒ Distance covered = 10 × 40 = 400 m

⇒ The distance covered to cross each other completely is equal to the combined length of both trains.

∴ The correct answer is 400 m.

Additional Information

Relative Speed

When two bodies move in the same direction, Relative Speed = S₁ − S₂. When they move in opposite directions, Relative Speed = S₁ + S₂.

Unit Conversions

To convert km/hr to m/s, multiply the value by (5 / 18). To convert m/s to km/hr, multiply by (18 / 5).

Trains Crossing a Pole or Point

When a train crosses a stationary pole or a standing man, the distance covered is exactly equal to the length of the train itself.

The logic followed here is,

Hence, the correct answer is "Option 2".

Given:

Total quantity at Shop A = 1200 kg

Total quantity at Shop B = 1000 kg

Prices per kg: Mango = ₹30, Apple = ₹40, Orange = ₹20, Other fruits = ₹15, Guava = ₹18

Formula used:

Total price = (Percentage of fruit / 100) × Total quantity × Price per kg

Calculation:

Total price at Shop A = (24/100 × 1200 × 30) + (16/100 × 1200 × 40) + (20/100 × 1200 × 20) + (30/100 × 1200 × 15) + (10/100 × 1200 × 18)

Total price at Shop A = ₹31,320

Total price at Shop B = (24/100 × 1000 × 30) + (14/100 × 1000 × 40) + (20/100 × 1000 × 20) + (26/100 × 1000 × 15) + (16/100 × 1000 × 18)

Total price at Shop B = ₹20,940

⇒ Combined total price = ₹31,320 + ₹20,940 = ₹52,260

∴ The combined price of all fruits at Shop A and Shop B is ₹52,260.

Shortcut Trick Ratio of speeds of Car and Train = 100 : 175 = 4 : 7 Ratio of travel time (inverse of speed) = 7 : 4 Difference in time ratio = 7 − 4 = 3 units = 18 minutes (stoppage time) ⇒ 1 unit = 6 minutes ⇒ Time taken by car (7 units) = 42 minutes = 7/10 hours ⇒ Speed of car = Distance ÷ Time = 70 ÷ (7/10) = 100 kmph ∴ The correct answer is 100 kmph.

Alternate Method Given: Distance = 70 km The train travels 75% faster than the car. Stoppage time of the train = 18 minutes = 18/60 hours = 3/10 hours. Formula Used: Time = Distance ÷ Speed

Point A Point B

Distance = 70 km

Train (Stops 18 mins) Speed = 1.75v | Travel Time = t - 18m

Car (No stops) Speed = v | Travel Time = t

Calculations: ⇒ Let the speed of the car be v kmph. ⇒ Speed of the train = v + 75% of v = 1.75v = 7v/4 kmph ⇒ Time taken by car = Distance ÷ Speed = 70/v hours ⇒ Active travel time of train = 70 ÷ (7v/4) = 40/v hours ⇒ Since both start and arrive simultaneously, the car's travel time equals the train's active travel time plus its stoppage time. ⇒ 70/v = 40/v + 3/10 ⇒ 70/v − 40/v = 3/10 ⇒ 30/v = 3/10 ⇒ 3v = 300 ⇒ v = 100 kmph ∴ The correct answer is 100 kmph.

Additional Information Time Difference Formula When two objects cover the same distance D with speeds S1 and S2 (where S1 > S2) and the time difference is Δt: D = (S1 × S2) ÷ (S1 − S2) × Δt Relative Speed When moving in the same direction, Relative Speed = S1 − S2. When moving in opposite directions, Relative Speed = S1 + S2. Average Speed If an object covers two equal distances at speeds S1 and S2, its Average Speed = (2 × S1 × S2) ÷ (S1 + S2).

Given Equation: [(C × D) + (F × J)]/D

BODMAS Rule:

Decoding the given information:

Now replacing the alphabets with their corresponding digits:

⇒ [(2 × 3) + (5 × 9)] / 3

Applying BODMAS Rule, first solve the operations inside the brackets:

⇒ [2 × 3 + 5 × 9] / 3

⇒ [6 + 45] / 3

⇒ 51 / 3 = 17

Hence, the correct answer is "Option 2".

Decoding symbols for Family Tree:

Step-by-step Relationship Analysis:

• U is the daughter of Z.
• X is the brother of U.
• V is the son of X.
• Y is the daughter-in-law of Z. Z is the parent of X. A daughter-in-law of Z must be the wife of Z's son X.

Consolidated Family Structure :

V is the son of X. Y is the wife of X.

Thus, Y is the mother of V.

Hence, the correct answer is "Option 2".

Given:- A person walks from 12 o'clock to 9 o'clock then from 9 o'clock to 6 o'clock, and finally from 6 o'clock to 3 o'clock

So, the person is finally facing in the North direction.

Hence, The correct answer is option 3.

The logic followed here is,

For, 95474 is written as GCBEB

Now, apply this logic to 73453:

Hence, the correct answer is "Option 1".

The logic followed here is:

Logic: The first term is a common name for an element, and the second term is its chemical symbol.

Here,

Iron : Fe → Iron is the common name for the element with the chemical symbol Fe (Ferrum).

Similarly,

Silver : ?

Silver is the common name for the element with the chemical symbol Ag (Argentum).

Hence, the correct answer is "Option 4".

The logic followed here is:

Logic: The first term is an instrument used to measure the second term.

Here,

Barometer : Air pressure → A Barometer is an instrument used to measure Air pressure.

Similarly,

Anemometer : ?

An Anemometer is an instrument used to measure Wind speed.

Hence, the correct answer is "Option 1".