Explanation :

Minimum number & maximum of points of intersection of a square and circle

Statement 1 is incorrect. The minimum number of points of intersection between a square and a circle can be 0 if the circle is entirely inside or outside the square.

Statement 2 is correct. The maximum number of points of intersection between a square and a circle is 8. This can happen when the circle passes through all four corners of the square and intersects each side once.

So only statement 2 is correct. Therefore, the correct answer is indeed (b) 2 only.

Explanation : 

Digit n > 3 is divisible by 3

Since n is divisible by 3 but not divisible by 6, it means that n must be an odd multiple of 3. Let’s take n=9 as an example.

(a) 2n = 2 * 9 = 18 which is not divisible by 4

(b) 3n = 3 * 9 = 27 which is not divisible by 4

(c) 2n +4 = (2 *9) +4 =22 which is not divisible by 4

(d) 3n +1 = (3 *9)+1=28 which is divisible by 4

So the correct answer is (d) 3n+1.

Explanation :

PROBLEM: Find the final ratio of liquids A and B after two replacements

STEP 1: After First Replacement
– Liquid A = 16 litres
– Liquid B = 4 litres
– Total = 20 litres
– Ratio of A to total = 16/20 = 4/5

STEP 2: Second Replacement
– 4 litres mixture removed
– Liquid A removed = 4 × 4/5 = 3.2 litres
– Liquid A remaining = 16 – 3.2 = 12.8 litres
– Liquid B = 20 – 12.8 = 7.2 litres

STEP 3: Final Ratio
12.8:7.2 simplifies to 16:9

ANSWER: The final ratio of liquid A to liquid B is 16:9

Explanation : 

PROBLEM: Find percentage of married adults in population

GIVEN:
– 40% men are married
– 30% women are married
– Each marriage has one man and one woman

SOLUTION:
Let M = number of men
W = number of women

1. Since married men = married women:
0.4M = 0.3W
W = (4/3)M

2. Total Population N = M + W = M + (4/3)M = (7/3)M

3. Total married adults = 0.4M + 0.3W
= 0.4M + 0.3(4/3)M
= 0.8M

4. Percentage = (0.8M)/(7/3)M = (0.8 × 3)/7 = 2.4/7
= 240/7%
≈ 34.29%

ANSWER: 240/7% or approximately 34.29%

Explanation : 

acpq: besu:: mngi: @

PATTERN: ACPQ → BESU
Letter Shifts:
– 1st letter: +1
– 2nd letter: +2
– 3rd letter: +3
– 4th letter: +4

Starting Word: MNGI
Applying shifts:
M + 1 = N
N + 2 = P
G + 3 = J
I + 4 = M

ANSWER: NPJM

Explanation : 

ghi=1578 def=912 abc= ?

ALPHABETS TO NUMBERS:
ABC = 123
DEF = 456
GHI = 789

DOUBLING THE NUMBERS:
ABC: 123 × 2 = 246
DEF: 456 × 2 = 912
GHI: 789 × 2 = 1578

Pattern: Each three-letter group when doubled gives the result shown on the right side.

Explanation : 

If 1 litre of water weighs 1kg ….

GIVEN CONVERSIONS:
1. Volume Conversion:
– 1 cubic millimeter = 10^-6 liters
– 1 liter = 10^6 cubic millimeters

2. Weight-Volume Relationship:
– 1000 grams (1 kg) = 10^6 cubic millimeters

CALCULATION:
1. To find volume for 0.1 grams:
– If 1000 grams = 10^6 cubic millimeters
– Then 1 gram = 10^3 cubic millimeters
– Therefore, 0.1 grams = 10^2 cubic millimeters
– 0.1 grams = 100 cubic millimeters

Explanation : 

C is younger than D

From statement S1 we know that C is younger than D but older than A and B. So the order of their ages is: D > C > A and B.

From statement S3 we know that A is older than B. Combining this information with statement S1, we get the order of their ages as: D > C > A > B.

So from statements S1 and S3 together, we can conclude that B is the youngest among A, B, C and D

Explanation : 

Digit n > 3 is divisible by 3

Since n is divisible by 3 but not divisible by 6, it means that n must be an odd multiple of 3. Let’s take n=9 as an example.

(a) 2n = 2 * 9 = 18 which is not divisible by 4

(b) 3n = 3 * 9 = 27 which is not divisible by 4

(c) 2n +4 = (2 *9) +4 =22 which is not divisible by 4

(d) 3n +1 = (3 *9)+1=28 which is divisible by 4

So the correct answer is (d) 3n+1.

Explanation : 

Let’s solve this step by step:

PROBLEM: Finding which fraction has minimum change when s is added to both numerator and denominator

ORIGINAL FRACTIONS:
2/3, 3/4, 4/5, 5/6

NEW FRACTIONS AFTER ADDING s:
(2 + s)/(3 + s)
(3 + s)/(4 + s)
(4 + s)/(5 + s)
(5 + s)/(6 + s)

CHANGES IN VALUE:
|2/3 – (2 + s)/(3 + s)|
|3/4 – (3 + s)/(4 + s)|
|4/5 – (4 + s)/(5 + s)|
|5/6 – (5 + s)/(6 + s)|

ANALYSIS:
1. When s becomes very large:
– The numerator terms (2,3,4,5) become negligible
– The denominator terms (3,4,5,6) become negligible
– All fractions approach s/s = 1

2. Original values:
2/3 ≈ 0.667
3/4 = 0.750
4/5 = 0.800
5/6 ≈ 0.833

3. Since all fractions approach 1:
– The fraction closest to 1 will have minimum change
– 5/6 is closest to 1 among all given fractions

CONCLUSION: The fraction 5/6 will have the minimum change in value when s is added to both numerator and denominator.