Mathematics Tes...

The sum of an infinite geometric series with positive terms is 3 and the sum of the cubes of its terms is \(\frac{27}{19}\). Then the common ratio of this series is :

Let \(Z\) be the set of all integers, \(A=\left\{(x, y) \in Z \times Z:(x-2)^2+y^2 \leq 4\right\}\), \(B=\left\{(x, y) \in Z \times Z: x^2+y^2 \leq 4\right\}\) and

\(C=\left\{(x, y) \in Z \times Z:(x-2)^2+(y-2)^2 \leq 4\right\}\) If the total number of relation from \(A \cap B\) to \(A \cap B\) is \(2^p\) then the value of \(p\) is:

Evaluate the integral \(\int_{-1}^{1} \frac{5 x^{4}}{\sqrt{x^{5}+3}} d x\).

Find the value of \(\operatorname{det}(3 A )\) for the following matrix.

\(A=\left[\begin{array}{ccc}4 & 7 & 1 \\ -1 & 3 & 2 \\ -2 & 0 & 5\end{array}\right]\)

If \(A =\left[\begin{array}{rr}0 & - i \\ i & 0\end{array}\right]\) and \(B =\left[\begin{array}{rr}1 & 0 \\ 0 & -1\end{array}\right]\) are matrices, then \(AB + BA\) is:

Let \(f(x)=2 x^{3}+\frac{1}{x}\), then \(f'(1)\) is:

Find the area bounded by the curve \({y}=\sin {x}\) between \({x}=0\) and \({x}=2 \pi\).

If the distances of \(\mathrm{P}(x, y)\) from \(\mathrm{A}(4,1)\) and \(\mathrm{B}(-1,4)\) are equal, then which of the following is true?

\(\tan \left(2 \tan ^{-1}(\cos x)\right)\) is equal to?

Tickets numbered \(1\) to \(20\) are mixed up and then a ticket is drawn at random. What is the probability that the ticket drawn has a number which is a multiple of \(3\) or \(5\) ?