Mathematics Tes...

\(100\) cards are numbered from \(1\) to \(100\). Find the probability of getting a prime number.

If \(5 \theta\) and \(4 \theta\) are acute angles satisfying sin \(5 \theta=\cos 4 \theta\), then \(2 \sin 3 \theta-\sqrt{3} \tan 3 \theta\) is equal to:

Find the value of \(I=\int_{1}^{2} \frac{\log x}{x^{2}}\):

The point of intersection of diagonals of a square ABCD is at the origin and one of its vertices is at A(4, 2). What is the equation of the diagonal BD?

If \(a_{1}, a_{2}, a_{3},=t_{9}, a_{9}\) are in GP, then what is the value of the following determinant?

\(\left|\begin{array}{lll}\ln a_{1} & \ln a_{2} & \ln a_{3} \\ \ln a_{4} & \ln a_{5} & \ln a_{6} \\ \ln a_{7} & \ln a_{8} & \ln a_{9}\end{array}\right|\)

Find the coefficients of the term independent of \(x\) in the expansion of \(\left(\frac{x^{3 / 2}-1}{x+1+x^{1 / 2}}-\frac{x^{3 / 2}+1}{x+1-x^{1 / 2}}\right)^{5}\).

Find the angle between the lines \( \vec{r}=3 i+2 j-4 k+\lambda(i+2 j+2 k) \) and \(\vec{r}=(5 j-2 k)+\mu(3 i+2 j+6 k)\).

Find the smallest positive integer value of \(\mathrm{k}\) for which quadratic equation \(\sqrt{3} \mathrm{x}^{2}-\sqrt{2} \mathrm{kx}+2 \sqrt{3}=0\), will have distinct real roots ?

If \(\mathrm{f}(\mathrm{x})=\frac{\sin \mathrm{x}}{\mathrm{x}},\) where \(\mathrm{x} \in \mathrm{R},\) is to be continuous at \(\mathrm{x}=0,\) then the value of the function at \(x=0\).