Explanation : 

Three persons A B C

It will be minimum in case of 3B4A2C10 arrangement.
Digits represent number of person between them/ahead/behind

Explanation : 

Five friends p q x y z purchased some notebooks

Now, let’s analyze the given information:

1. Z purchased 8 notebooks more than X did.
Z = X + 8
2. P and Q together purchased 21 notebooks.
P + Q = 21
3. Q purchased 5 notebooks less than P did.
Q = P – 5
4. X and Y together purchased 28 notebooks.
X + Y = 28
5. P purchased 5 notebooks more than X did.
P = X + 5

Now we have a system of 5 linear equations with 5 unknowns. Let’s solve the system step by step:
Step 1: Substitute equation (3) into equation (2):
P + (P – 5) = 21
2P – 5 = 21
2P = 26
P = 13
Step 2: Substitute the value of P from step 1 into equation (5):
13 = X + 5
X = 8
Step 3: Substitute the value of X from step 2 into equation (1):
Z = 8 + 8
Z = 16
Step 4: Substitute the value of X from step 2 into equation (4):
8 + Y = 28
Y = 20
Step 5: Substitute the value of P from step 1 into equation (3):
Q = 13 – 5
Q = 8

Now we have the number of notebooks purchased by each friend:
P = 13, Q = 8, X = 8, Y = 20, Z = 16

The total number of notebooks is:
Total notebooks = P + Q + X + Y + Z = 13 + 8 + 8 + 20 + 16 = 65

Since each notebook is priced at 40, the total cost of all notebooks is:
Total cost = Total notebooks * Price per notebook = 65 * 40 = 2600

The total cost of all the notebooks is 2600.

Explanation : 

Is Z brother of X?

Statement 1:
X is the brother of Y, and Y is the brother of Z.
But we do not know whether Z is a male or a female. So, we cannot say whether Z is the brother or sister of X.

Statement 2:
X, Y, and Z are siblings. It tells us nothing much. Here, also gender of Z is not known. So, Z can be either brother or sister of X.
Even if we combine the two statements, we cannot answer the given questions.

Explanation : 
From Statement-1 we know that some doctors are teachers.
From Statement-2 we know that all teachers are engineers.
Combining these two statements we can conclude that some doctors are engineers.
From Statement-3 we know that all engineers are scientists.

Therefore, combining this with the previous conclusion, we can conclude that some scientists are doctors (Conclusion-I).
Since only some doctors are engineers (not all), Conclusion-II is incorrect. However, since some doctors are engineers, Conclusion-III is correct.

Explanation : 

Counting distinct non-zero digit combinations in the decimal form 0.XY

The number of numbers of the form 0.XY, where X and Y are distinct non-zero digits, can be found by counting the number of possibilities for X and Y, and then multiplying them together.

There are 9 choices for X (all digits except 0), and once X is chosen, there are 8 choices for Y (all digits except the chosen value of X).
Therefore, the total number of numbers of the form 0.XY is:
9 × 8 = 72

Therefore, the answer is (a) 72.

Explanation : 

Possibilities of three consecutive integers whose sum equals their product.

Let’s assume the three consecutive integers to be n-1, n, and n+1.
Their sum would be (n-1) + n + (n+1) = 3n
Their product would be (n-1)n(n+1) = n^3 – n
As per the question, their sum is equal to their product, so we can equate them:
3n = n^3 – n

Rearranging the equation:
n^3 – 4n = 0
n(n^2 – 4) = 0

n = 0 or n = ±2

Explanation : 

There are 9 cups placed on a table

Case 1: When we have 3 coffee cups in one row, 2 coffee cups in another row, and 1 coffee cup in the remaining row (3!).

For row having 3 coffee cups arrangement can be done in only one way.
For row having 2 coffee cups arrangement can be done in three ways.
For row having 1 coffee cup arrangement can be done in three ways.

Total arrangements for case 1 = 3! × 1 × 3 × 3 = 54.

Case 2: When we have 2 coffee cups in each row (1).
Each row has 2 coffee cups arrangement can be done in three ways.
Total arrangements for case 2 = 1 × 3 × 3 × 3 = 27

So, total arrangement for given conditions = 54 + 27 = 81.

Hence, the correct answer is an option(4) i.e., 81.

Explanation : 

To form a password, we need one non-zero digit, one vowel (in capital), and one consonant (in capital).

The password must start with a vowel and end with a consonant. Therefore, the password format will be Vowel-Digit-Consonant.

There are 5 vowels in the English alphabet (A, E, I, O, U).
There are 21 consonants in the English alphabet (the remaining letters after excluding the vowels).
There are 9 non-zero digits (1, 2, 3, 4, 5, 6, 7, 8, 9).

For each position in the password, we can use the number of available options for that specific position. So, to calculate the total number of possible passwords, we can multiply the available options for each position:

Total passwords = Number of vowels × Number of non-zero digits × Number of consonants
Total passwords = 5 × 9 × 21

Total passwords = 945

Thus, 945 such passwords can be generated (option c).

Explanation : 

Sum of all 3-digit numbers formed by distinct non-zero digits (A, B, C)

Let’s consider all possible 3-digit numbers formed by A, B and C without repetition: ABC, ACB, BAC, BCA, CAB and CBA. The sum of these numbers is x = ABC + ACB + BAC + BCA + CAB + CBA.

We can rewrite x as: x = 100A + 10B + C + 100A + 10C + B + 100B + 10A + C + 100B+10C+A+100C+10A+B+100C+10B+A.

By grouping the terms we get: x = (222)(A+B+C). Since A,B,C are distinct non-zero digits the minimum value for A+B+C is when A=1,B=2,C=3 so the minimum value for x is (222)(1+2+3)=1332. Therefore statement 1 is correct.

Statement 2: The 3-digit greatest value of x is 888: False, as the least value of x is 1332.

Explanation : 

A pie chart gives the expenditure

The total angle in a pie chart is 360°. The sum of the angles for items B, C, D and E is 90° + 50° + 45° + 75° = 260°. Therefore, the angle for item A is 360° – 260° = 100°.

Since the total angle in a pie chart represents 100%, each degree represents 100/360 = (5/18)%. Therefore, the percentage of expenditure on item A is (5/18) * 100 = (500/18)% ≈ (250/9)%.

So the correct answer is d. (250/9).