List of top Bioinformatics Questions on Mathematics

If a matrix \(A=\dfrac{1}{3}\begin{bmatrix}1& 2& 2\\2& 1&-2-2& 2&-1\end{bmatrix}\), then

Find the Laplace transform of \(f(t)=\sin 2t \sin 3t\).

Match List-I with List-II. List-I: A. Poisson distribution \(P(x=r)\), B. Mean \((\mu)\), C. Standard deviation \((\sigma)\), D. Binomial distribution.

Match List-I with List-II. List-I: A. \(e^{at}\), B. \(\cos at\), C. \(\sin at\), D. \(\cosh at\).

Match List-I with List-II. List-I: A. If A is an invertible matrix then, B. If A is orthogonal matrix then, C. \((A-\lambda I)\) is a matrix, D. The rank of unit matrix of order n. List-II: I. \(|A|=\pm 1\), II. \(|A|\ne 0\), III. is \(n\), IV. Characteristic.

Determine the order and degree of the following differential equation: \(\left(\dfrac{d^2y}{dx^2}\right)^3 + \sqrt{1+\left(\dfrac{dy}{dx}\right)^2=0.\)}

\(\displaystyle \int_{0}^{\pi} \sin x \, dx = ?\)