Engineering Mathematics
Q23.
If a random variable X has a Poisson distribution with mean 5, then the expectation E[(X+2)^{2}] equals ______________.Q25.
Let f(x)=x^{-(1/3)} and A denote the area of the region bounded by f(x) and the x-axis, when x varies from -1 to 1. Which of the following statements is/are TRUE? I) f is continuous in [-1,1] II) f is not bounded in [-1,1] III) f is nonzero and finiteQ28.
The function f(x)=x sin x satisfies the following equation: f''(x)+f(x)+tcos x=0. The value of t is______.Q29.
Let the function f(\theta)=\begin{vmatrix} sin\theta & cos\theta & tan\theta \\ sin(\frac{\pi}{6}) & cos(\frac{\pi}{6}) & tan(\frac{\pi}{6})\\ sin(\frac{\pi}{3})& cos(\frac{\pi}{3}) & tan(\frac{\pi}{3}) \end{vmatrix} where \theta \in [\frac{\pi}{6},\frac{\pi}{3}] and f'(\theta ) denote the derivative of f with respect to \theta . Which of the following statements is/are TRUE? (I) There existrs \theta \in (\frac{\pi}{6},\frac{\pi}{3}) such that f'(\theta )=0 (I) There existrs \theta \in (\frac{\pi}{6},\frac{\pi}{3}) such that f'(\theta )\neq 0Q30.
What is the least value of the function f(x) = 2x^{2}-8x-3 in the interval [0, 5]?