Explanation : 
From the information given in the question, we can deduce that Q is the grandmother of T. So the correct answer is b. Q is the grandmother of T.

Here’s how we can figure it out: R is the spouse of Q and P’s daughter is T. Since R’s son is P thus d. T is the granddaughter of Q

Explanation : 

Two friends X and Y start running

After running together for 50 meters in the same direction and reaching a point, X turns right and runs 60 meters while Y turns left and runs 40 meters.

This means that they are now 100 meters apart from each other on a straight line (60 + 40 = 100).

Then X turns left and runs 50 meters and stops while Y turns right and runs 50 meters and then stops.

Since both X and Y ran in the same direction for the same distance (50 meters), their distance from each other remains unchanged at 100 meters.

Explanation : 

Deciphering the representation of ‘LUCKNOW’ after reversing the order of English alphabet letters.

The English alphabet has 26 letters. If we assign a numerical value to each letter based on its position in the alphabet (A=1, B=2, C=3 and so on), then we can find the reverse of each letter by subtracting its value from 27. This is because when the order of the alphabet is reversed, the first letter (A) becomes the last (Z), the second letter (B) becomes the second last (Y) and so on.

For example: L is the 12th letter in the alphabet. To find its reverse, we subtract its value from 27: 27-12=15. The 15th letter in the alphabet is O. So L becomes O when reversed.

Using this method we can find that: L -> O U -> F C -> X K -> P N -> M O -> L W -> D

So LUCKNOW becomes OFXPMLD when reversed using this method.

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.