Question : If a number K = 42 × 25 × 54 × 135 is divisible by 3^a, then find the maximum value of a.

Option 1: 6

Option 2: 7

Option 3: 4

Option 4: 5

Question : If $a^{3}+\frac{1}{a^{3}}=2$, then the value of $\frac{a^{2}+1}{a}$ is ($a$ is a positive number):

Option 1: 1

Option 2: 2

Option 3: 3

Option 4: 4

Question : The positive square root of
[0.6 × 0.6 × 0.6 + 0.4 × 0.4 × 0.4 + 3 × 0.6 × 0.4 (0.6 + 0.4)] is equal to:

Option 1: 2.1736

Option 2: 1

Option 3: 0.21736

Option 4: 0.072

Question : If $\sin A = \frac{4}{5}$, then what is the value of $\sin^2 A$?

Option 1: $\frac{26}{25}$

Option 2: $\frac{36}{25}$

Option 3: $\frac{48}{25}$

Option 4: $\frac{16}{25}$

Question : If $(4a + \frac{5}{a} + 5)=14$, what is the value of $(16a^2+ \frac{25}{a^2})$?

Option 1: 25

Option 2: 36

Option 3: 41

Option 4: 40