Mathematics Tes...

The principal value of \(\tan ^{-1}(-\sqrt{3})+2 \sec ^{-1}\left(\frac{2}{\sqrt{3}}\right)\) is:

Find the area bounded by the line \(y=3-x\), the parabola \(y=x^{2}-9\) and \(x \geq-4, y \geq 0\).

The set of all \(\alpha \in \mathbf{R},\) for which \(\mathrm{w}=\frac{1+(1-8 \alpha) z}{1-z}\) is a purely imaginary number, for all \(z \in\) C satisfying \(|z|=1\) and \(\operatorname{Re} z \neq 1\), is:

If \(x=3\), find the other 2 roots of \(\left|\begin{array}{ccc}x & 2 & 3 \\ 1 & x & 1 \\ 3 & 2 & x\end{array}\right|=0\)

If \(\vec{a}, \vec{b}\) and \(\vec{c}\) are coplanar, then what is \((2 \vec{a} \times 3 \vec{b}) \cdot 4 \vec{c}+(5 \vec{b} \times 3 \vec{c}) \cdot 6 \vec{a}\) equal to?

If n^th terms of two A.P.’s are 3n + 8 and 7n + 15, then the ratio of their 12^th terms will be:

The equation of the line which passes through \( (1, 2)\) and is parallel to the line passing through \( (3, 4)\) and \( (4, 5)\), is:

Find the equation of the plane passing through the point \((1, 0, 1)\) and perpendicular to the planes \(2x + 3y - z = 2\) and \(x - y + 2z = 1\).

\(2  \times 4^{2n+1}+3^{3 n+1}\) is divisible by: (for all \(n \in N\) )

How many two-digit numbers are divisible by 4?