Mathematics Tes...

A fair coin is tossed independently four times. The probability of the event "the number of times heads show up is more than the number of times tails show up" is:

\(\left(\begin{array}{ll}2 & 3 \\ 4 & 1\end{array}\right) \times\left(\begin{array}{cc}5 & -2 \\ -3 & 1\end{array}\right)=\left(\begin{array}{cc}1 & -1 \\ 17 & \lambda\end{array}\right)\)  then what is λ equal to?

The area in the first quadrant bounded by,

\(y=4 x^{2}, x=0, y=1\) and \(y=4\) is:

If \(y=\frac{12 \tan x-4 \tan ^{3} x}{9-27 \tan ^{2} x}\), then find \(\frac{d^{2} y}{d x^{2}}\).

Find the middle terms in the expansion of \(\left(2 \mathrm{x}+\frac{1}{\mathrm{x}}\right)^{8}\).

Two cards are drawn at random and without replacement from a pack of \(52\) playing cards. Find the probability that both the cards are black:

Find the equation of the plane which is at a distance of \(\frac{1}{ 3}\) unit from the origin and \(\hat{i}+2 \hat{j}+2 \hat{k}\) is the normal vector from the origin to the plane?

If A={1, 2, 4}, B={2, 4, 5}, C={2, 5}, then (A-C)×(B-C) is equal to:

An equilateral triangle is inscribed in the parabola \(y^2=4 a x\), where one vertex is at the vertex of the parabola. Find the length of the side of the triangle.

The mean of six numbers is 47. If one number is excluded, their mean becomes 41. The excluded number is: