Explanation

We know:

81 = 3⁴  

So,  

log₃ 81 = log₃ (3⁴) = 4

Explanation

R = xS⁴  

When S = 5, R = 6  

So,  

6 = x × (5)⁴ = x × 625  

⇒ x = 6 / 625

Now find R when S = 8:  

R = (6 / 625) × (8)⁴ = (6 / 625) × 4096  

= 24576 / 625 = 39.3216

Explanation

In a Geometric Progression, the nth term is given by:

Tn​=a×r^n−1

Where:

• a = first term

• r = common ratio

• n = term number

Explanation

0.005 × 10,000 = 50
So the question becomes: 50 is what percent of 50?

50/50​×100=100%

Explanation

Surface area of a cube = 6 × (side)²

=6×32=6×9=54 cm²

Explanation

a³ + b³ = (a + b)³ – 3ab(a + b)  

= 13³ – 3 × 37.2671 × 13  

= 2197 – (3 × 37.2671 × 13)  

= 2197 – 1454.4265 ≈ 742.57

Explanation

With parallelization across different staff, the tasks can be efficiently pipelined.

Given the schedule:

1. Typist takes 2 hours per document.

2. Proofreader takes 1 hour per document.

3. Signer takes 0.5 hours per document.

The pipeline schedule shows:

After Doc 1 is typed (2 hours), it moves to proofreading, and Doc 2 starts typing.

By the time Doc 3 is done typing (6 hours total for typing 3 documents), Doc 1 would have been signed (3.5 hours total for Doc 1 to be signed after starting typing).

The critical path here is determined by the longest sequence in the pipeline, which is typing (6 hours for 3 documents).

Given the pipelined schedule provided:

The last document (Doc 3) finishes signing at 4.5 hours.

Explanation

Given:

1. R is above P

2. Q is below T

3. S is above R but below T

From (3), the order for S, R, and T is:

T > S > R (in terms of position from top to bottom)

Given R is above P, and S is above R:

T > S > R > P

Given Q is below T, and the above order:

T > S > R > P > Q or T > S > R > P with Q possibly at the very bottom if not directly below one of these.

The order that satisfies all conditions with T at the top is:

T > S > R > P > Q

The file at the top is T.

Explanation

Let’s solve the seating arrangement step by step:

Given:

A is sitting directly opposite D → So, A and D are facing each other.

B is seated to the immediate right of A → So we need to determine directions first.

Assume the employees are seated clockwise around the circular table.

Step-by-Step Placement:

Place A at the top (12 o'clock position).

Since B is to the immediate right of A, in clockwise direction, B is at the 1 o'clock position.

D is directly opposite A → So D is at 6 o'clock position (bottom).

Now, we need to find who is to the immediate left of D.

That position aligns with F if we place the rest logically.

Explanation

The rule says Audit must come after Legal, but Admin can appear anywhere in the sequence.

Admin - Legal - Audit follows this rule correctly, making it a valid sequence.