Question

Which of the following could be the set of programs to be operated on the first day of a month?

• A. T, U, R, V, S
• B. U, Q, S, T, W
• C. V, Q, R, T, S
• D. Q, S, R, V, U
• A. R cannot be operated at fourth place.
• B. Q cannot be operated at third place.
• C. P cannot be operated at third place.
• D. T cannot be operated at third place.
• A. T
• B. S
• C. Q
• D. U
• A. 12
• B. 8
• C. 4
• D. 16
• A. 14B
• B. 12C
• C. 10C
• D. 16C

Answer 1

The Correct Option is A

T, U, R, V, S is correct because it adheres to all the given conditions without violating any rules.
The correct option is (A): T, U, R, V, S

Answer 2

If R is in the fourth position, V would have to follow R, but V can only be placed in the fifth position, violating the rule that either S or U must be the last program. Therefore, R cannot be in the fourth position because it would force V to occupy the fifth position, which is not allowed.
The correct option is (A): R cannot be operated at fourth place.

Answer 3

If R is operated at the third place, let's analyze each option:
T: There is no direct restriction between R and T in the given conditions, so T could potentially be the second program.
S: There is no restriction that prevents S from being the second program, so it could be second.
Q: If Q is operated, T must be operated after Q. Since R is already in the third place, T cannot follow Q directly, violating the condition. Therefore, Q cannot be second in this case.
U: There are no direct restrictions between R and U, so U could be the second program.
The correct option is (C): Q

Answer 4

To determine the missing character in the matrix, we will analyze the pattern established by the first three elements in each column, which are multiplied together to yield the fourth element
Examine the first column. The elements are:
First element: 6
Second element: 5
Third element: 4
We calculate the fourth element:
\(6\times5\times\times4=120\)
Next, we analyze the second column. The elements are:
First element: 6
Second element: 7
Third element: 3
We calculate the fourth element:
\(6\times7\times3=126\)
Now, we need to find the unknown number in the third column. The elemts are:
First element: 8
Second element: 5
Third element: x
We set up the equation based on the established pattern:
\(8\times5\times1=320\)
Simplify the equation:
\(40x=320\)
Solving for \(x\):
\(x=\frac{320}{40}=8\)
Thus, the missing character is 8.
The correct option is (B): 8

Answer 5

In each column, out of the letters A, B and C, each of these must appear once. Along the diagonals, the sum of two numbers is equal to the third number.
The missing number will be (7+9) i.e. 16 and the letter will be C.
Hence, the answer is 16C.
The correct option is (D): 16C