Mathematics Tes...

If log 2 = 0.3010 and log 3 = 0.4771, the value of log₅ 512 is:

If $A=\left[\begin{array}{cc}1& 1\\ 4& 5\end{array}\right]$ and $B=\left[\begin{array}{cc}1& 0\\ 4& 5\end{array}\right]$ then evaluate $AB$.

What is sin 105° + cos 105° equal to?

What is the sum of all two-digit numbers which when divided by 3 leave 2 as the remainder?

The value of $x + x\left(x^x\right)$ when x = 2 is:

What is the greatest integer among the following by which the number 5⁵ + 7⁵ is divisible? 

The third term of a geometric progression (GP) is $3$. What is the product of the first five terms?

If $\cos \alpha +\cos \beta +\cos \gamma =0$, where $0<\alpha \le \pi /2$ and $0<\gamma \le \pi /2$, then what is the value of $\sin \alpha +\sin \beta +\sin \gamma$?

What is the equation of the plane passing through the points (–2, 6, –6), (–3, 10, –9) and (–5, 0, –6)? 

If $A+\frac{1}{A}=5$ then find the value of $A^4+\frac{1}{A^4}$.