Mathematics Tes...

If \(A\) and \(B\) are two events such that \(P ( A \cup B )\)= \(\frac{5}{6}\) , \(P ( A \cap B )\) = \(\frac{1} {3}\), \(P ( B )\) = \(\frac{1}2\), then the events \(A\) and \(B\) are:

The point(s) on the curve \(y=x^3-11 x+5\) at which the tangent is \(y=x-11\) is/are:

If \(\alpha\) and \(\beta\) are the roots of the equation \(x^{2}+p x+q=0\), then the value of \((\alpha+\beta) x-\left(\frac{\alpha^{2}+\beta^{2}}{2}\right) x^{2}+\left(\frac{\alpha^{3}+\beta^{3}}{3}\right) x^{3}+\ldots\), is:

If \({ }^{{n}} {P}_{{r}}=2760,{ }^{{n}} {C}_{{r}}=23\), then the value of \({r}\) is:

The mean of \(8\) observations is \(25\). The \(7\) observations are \(30, 24, 27, 22, 18, 26, 32\). What is the \(8\)th observation?

If \(\omega \neq 1\) is a cube root of unity, then \(A=\left[\begin{array}{ccc}1+2 \omega^{100}+\omega^{200} & \omega^{2} & 1 \\ 1 & 1+2 \omega^{100}+\omega^{200} & \omega \\ \omega & \omega^{2} & 2+\omega^{100}+2 \omega^{200}\end{array}\right]\)

Consider the following Linear Programming Problem (LPP):

Maximize Z = 3x₁ + 2x₂ Subject to       

x₁ ≤ 4

x₂ ≤ 6

3x₁ + 2x₂ ≤ 18

x₁ ≥ 0, x₂ ≥ 0

If \(|x|<-5\) then the value of \(x\) lies in the interval:

In the following trigonometry expression, find the value of (MN).

\(\frac{(1+\cos x)}{(1-\sin x)}(\sin x+\cos x-1)^{2}=M \sin ^{N} x\)

What is the number of possible values of k for which the line joining the points (k, 1,3) and (1,-2, k+1) also passes through the point (15,2,-4)?