Explanation : 

Cubical vessel of side 1 m

Calculating Volume of a Cube
Side length = 1 meter
Volume formula = side length³
Volume = 1 × 1 × 1 = 1 cubic meter

Converting to Milliliters:
1 cubic meter = 1000 liters
1 liter = 1000 milliliters

Final Calculation:
Total milliliters = 1000 × 1000
= 1,000,000 milliliters

Answer: (d) 1,000,000 milliliters

Explanation : 

Sum & Product of Consecutive Integers

Problem Part 1 – Five Consecutive Integers
Let’s say the first integer is x.
The next four numbers are: x+1, x+2, x+3, and x+4
The sum of these five numbers is 5x + 10
If this sum equals 100, then:
5x + 10 = 100
Solving for x: x = 18
Therefore, the five consecutive integers are: 18, 19, 20, 21, 22

Problem Part 2 – Numbers 1, 2, and 3
Sum: 1 + 2 + 3 = 6
Product: 1 × 2 × 3 = 6

Conclusion:
Both statements are correct since:
1. We found five consecutive integers that sum to 100
2. For numbers 1, 2, and 3, their sum equals their product

Explanation : 

Numbers greater than 30000, using 22333 as digits

Given:
– Digits available: 2,2,3,3,3 (two 2’s and three 3’s)
– Number must be > 30000
– First digit must be 3

Step 1: Organize possible cases
Case 1: First two digits are 33
Remaining digits: 2,2,3
Possible arrangements:
1. 33223
2. 33232
3. 33322

Case 2: First digit 3, second digit 2
Remaining digits: 2,3,3
Possible arrangements:
4. 32233
5. 32323
6. 32332

Step 2: List all numbers in ascending order
1. 32233
2. 32323
3. 32332
4. 33223
5. 33232
6. 33322

Answer: 6 distinct numbers can be formed (Option b is correct)

Explanation : 

Chess Board Consecutive Squares Chosen

Given:
– Chess board has 2 diagonals with 8 squares each
– Need to select 6 consecutive squares
– These 6 squares must be consecutive along a diagonal

Step 1: Analyze one diagonal
– Diagonal has 8 squares
– Need to select 6 consecutive squares
– Think of 6 squares as one block
– This block can slide along diagonal

Step 2: Calculate possible positions on first diagonal
– 8 squares total, need 6 consecutive
– First position: squares 1-6
– Second position: squares 2-7
– Third position: squares 3-8
Total positions on first diagonal = 3

Step 3: Calculate possible positions on second diagonal
– Same calculation as first diagonal
– 3 possible positions
Total positions on second diagonal = 3

Step 4: Calculate total number of ways
– First diagonal: 3 ways
– Second diagonal: 3 ways
Total ways = 3 + 3 = 6

Explanation : 

Best Method- Check All option
15873 × 7 = 111111

Explanation : 

Price of an article is decreased & increased by 20, 25

Given:
– Original price = P
– First change: 20% decrease
– Second change: 25% increase

Step 1: Calculate price after 20% decrease
– Decrease amount = 20% of P = 0.2P
– New price = P – 0.2P
– New price = 0.8P

Step 2: Calculate final price after 25% increase
– Increase amount = 25% of 0.8P = 0.25(0.8P) = 0.2P
– Final price = 0.8P + 0.2P
– Final price = 1P

Step 3: Calculate net percentage change
– Original price = P
– Final price = P
– Net change = (Final price – Original price)/Original price × 100
– Net change = (P – P)/P × 100
– Net change = 0%

Explanation : 

The difference between 2 digit number and the number obtained is 54

Given:
– Original number = 10x + y (where x is tens digit, y is units digit)
– New number after interchanging = 10y + x
– Difference between these numbers = 54

Step 1: Write equation for the difference
(10x + y) – (10y + x) = 54

Step 2: Simplify left side
10x + y – 10y – x = 54
9x – 9y = 54

Step 3: Further simplify
9(x – y) = 54
x – y = 6

Step 4: Analyze what we know
– Difference between tens and units digit is 6
– Since it’s a 2-digit number:
* x must be from 1 to 9
* y must be from 0 to 9
* x must be greater than y by 6

Step 5: Find possible digit pairs
Since x – y = 6:
– If y = 0, x = 6
– If y = 1, x = 7
– If y = 2, x = 8
– If y = 3, x = 9

Analysis:

1. Statement 1 (about sum of digits) is incorrect
– Multiple pairs of digits satisfy x – y = 6
– Each pair would give different sums
– Examples: 6+0=6, 7+1=8, 8+2=10, 9+3=12

2. Statement 2 (about difference of digits) is correct
– We proved x – y = 6
– This is a definite value

Answer: Statement 1 is incorrect and Statement 2 is correct.

Explanation : 

Pie Chart Analysis

A pie chart represents 100% of the data as a full circle with 360 degrees. In this case, proteins correspond to 16% and water corresponds to 70%, so the other dry elements correspond to 100% – 16% – 70% = 14%. Since p represents the sum of proteins and other dry elements, p = 16% + 14% = 30%.

Since p represents 30% of the data, the central angle of the sector representing p on the pie diagram is (30/100) * 360 = 108 degrees.

Explanation : 

Biology Class at High School Population Growth Model

Given:
– Initial population (2021) = 50 animals
– Population doubles every 12 years
– Need formula for population P after n years

Step 1: Identify Growth Type
– Not linear growth (population doesn’t increase by fixed amount)
– Population multiplies by 2 at fixed intervals
– This indicates exponential growth

Step 2: Basic Exponential Growth Formula
P = Initial Value × (growth factor)^(time/interval)

Step 3: Identify Components
– Initial Value = 50
– Growth factor = 2 (doubles)
– Time = n years
– Interval = 12 years

Step 4: Analyze Options
a) P = 12 + 50n
Incorrect: Shows linear growth

b) P = 50 + 12n
Incorrect: Shows linear growth

c) P = 50(2)^12n
Incorrect: Time interval ratio is wrong

d) P = 50(2)^(n/12)
Correct: Shows proper exponential growth

Step 5: Verify Option D
After 0 years: P = 50(2)^0 = 50 (correct initial population)
After 12 years: P = 50(2)^1 = 100 (population doubles)
After 24 years: P = 50(2)^2 = 200 (doubles again)

Answer: The correct formula is P = 50(2)^(n/12)
This formula accurately represents population doubling every 12 years from an initial value of 50 animals.

Explanation : 

Problem: Finding when petrol and diesel prices are equal ?

Given:
– 2021 is non leap year
– Petrol price formula: 80 + 0.1m (where m = 1 to 100, constant thereafter)
– Diesel price formula: 69 + 0.15n (for any value of n)

Step 1: Set up equation for equal prices
80 + 0.1m = 69 + 0.15n

Step 2: Solve for n in terms of m
80 + 0.1m = 69 + 0.15n
0.1m – 0.15n = -11
-0.15n = -11 – 0.1m
n = (2m + 220)/3

Step 3: Find n when m = 100
n = (2(100) + 220)/3
n = (200 + 220)/3
n = 420/3
n = 140

Answer: The prices of petrol and diesel are equal on the 140th day of 2021, which is May 20th.