GATE EE 2015 Question Paper (07-Feb-2015) (Shift 1)

A random variable $X$ has probability density function $f\left(x\right)$ as given below:

f≤ft( x ) = ≤ft\{ {*20c a + bx&for 0 < x < 1\\ 0&otherwise } .

If the expected value $E\left[X\right]=2/3$, then $P[X<0.5]$ is______.

If a continuous function f(x) does not have a root in the interval [a, b], then which one of the following statements is TRUE?

If the sum of the diagonal elements of a $2\times 2$ matrix is $-6$, then the maximum possible value of determinant of the matrix is__________.

Consider a function $\bar{f}=\frac{1}{r^2}\hat{r}$, where r is the distance from the origin and $\hat{r}$ is the unit vector in the radial direction. The divergence of the function over a sphere of radius R, which includes the origin, is

When the Wheatstone bridge shown is used to find value of resistance Rₓ, the galvanometer G indicates zero current when R₁ = 50 Ω, R₂ = 65 Ω & R₃ = 100 Ω. if R₃ is known with 5% tolerance on its nominal value of 100 Ω What is the range of Rₓ in ohms.