PYQs Based test 26: Engineering Mathematics

Given $f\left(z\right)=g\left(z\right)+h\left(z\right)$, where f, g, h are complex valued functions of a complex variable z. which one of the following statements is TRUE?

Let the probability density function of a random variable, $X$, be given as:

$fx\left(x\right)=\frac{3}{2}{e}^{-3x}u\left(x\right)+a{e}^{4x}u\left(-x\right)$

Where $u\left(x\right)$ is the unit step function.

Then the value of 'a' and $Prob\left\{X\le 0\right\}$ respectively, are

The maximum value attained by the function $f\left(x\right)=x\left(x-1\right)\left(x-2\right)$ in the interval [1, 2] is _____.

The Laplace Transform of is $f\left(t\right)=e^{2t}sin\left(5t\right)u\left(t\right)$

ax³ + bx² + cx + d is a polynomial on real x over real coefficients a, b, c, d wherein a ≠ 0. Which of the following statements is true?