Mathematics Tes...

A pair of dice is thrown. Find the probability of obtaining a sum of 8 or getting an even number on both the dice.

Evaluate: \(\int_{1}^{4}\left(5 x^{2}-8 x+5\right) d x\)

The equation of circle which passes through the origin and cuts off intercepts 5 and 6 from the positive parts of the \(x\) axis and \(y\) -axis respectively is \(\left(x-\frac{5}{2}\right)^{2}+(y-3)^{2}=\lambda\), where \(\lambda\) is:

In a quadrilateral \(PQRS , \overrightarrow{ PQ }=\overrightarrow{ a }, \overrightarrow{ QR }=\overrightarrow{ b }, \overrightarrow{ SP }=\overrightarrow{ a }-\overrightarrow{ b }\). \(M\) is the mid-point of \(QR\) and \(X\) is a point on \(SM\) such that \(SX =\frac{4}{5} SM\), then \(\overrightarrow{ PX }\) is:

The equations of the sides of a triangle are x - 3y = 0, 4x + 3y = 5 and 3x + y = 0. The line 3x - 4y = 0 passes through the _________ of the triangle.

\(A , B\) and \(C\) are three mutually exclusive and exhaustive events. \(P ( A )=2 P ( B )=6 P ( C )\), Find \(P ( B )\):

A plane passes through the point \((1,-2,3)\) and is parallel to the plane \(2 x-2 y+z=0 .\) The distance of the point \((-1,2,0)\) from the plane is:

Using principle of mathematical induction, prove that for \(n \in N\), \(3^{2 n+2}-8 n-9\) is:

Let \(\mathrm{f}:[-1,3] \rightarrow \mathrm{R}\) be defined as

\(f(x)=\left\{\begin{array}{cc} |x|+[x], & -1 \leq x<1 \\ x+|x|, & 1 \leq x<2 \\ x+[x], & 2 \leq x \leq 3 \end{array}\right.\)

where \([t]\) denotes the greatest integer less than or equal to \(t\). Then, \(\mathrm{f}\) is discontinuous at: