Mathematics Tes...

Find the equation of the plane passing through the line of intersection of planes \(x+y\) \(+z=6\) and \(2 x+3 y+4 z+5=0\) and passing through the point (1,1,1).

If \(P=\left[\begin{array}{cc}1 & 0 \\ 1 / 2 & 1\end{array}\right]\), then \(P^{50}\) is:

For all \(n \in N\), \(\left(n^{2}+n\right)\) is:

Find the value of \(\cos \left(3015^{\circ}\right)\):

From a pack of \(52\) cards, two cards are drawn together at random. What is the probability of both the cards being kings?

Find the equation of a line having a slope of \(-2\) and passes through the intersection if \(2 x-y=1\) and \(x+ 2 y = 3\).

Let \(\mathrm{f}(\mathrm{x})\) be a polynomial of degree 4 having extreme values at \(\mathrm{x}=1\) and \(x=2\). If \(\lim _{x \rightarrow 0}\left(\frac{f(x)}{x^2}+1\right)=3\) then \(f(-1)\) is equal to:

If \(a, b, c\) are real numbers, then the value of the determinant \(\left|\begin{array}{ccc}1-a & a-b-c & b+c \\ 1-b & b-c-a & c+a \\ 1-c & c-a-b & a+b\end{array}\right|\) is:

Find the sum of the series whose nth term is:

n(n+1)(n+4)