GATE EE 2014 Question Paper (02-Mar-2014) (Shift 1)

To evaluate the double integral $\underset{0}{\overset{8}{\int }}\left(\underset{\frac{y}{2}}{\overset{\left(\frac{y}{2}\right)+1}{\int }}\left(\frac{2x-y}{2}\right)dx\right)dy$ we make the substitution $u=\left(\frac{2x-y}{2}\right)$ and $v=\frac{y}{2}$. The integral will reduce to

Let X be a random variable with probability density function

f≤ft( x ) = ≤ft\{ {*20c 0.2, for ≤ft| x | ≤ 1\\ 0.1, for 1 < ≤ft| x | ≤ 4\\ 0, otherwise } .

The probability P(0.5 < X < 5) is _______.

The minimum value of the function f(x) = x³ – 3x² – 24 x + 100 in the interval [-3, 3] is

Assuming the diodes to be ideal in the figure, for the output to be clipped, the input voltage Vᵢ must be outside the range

The voltage across the capacitor, as shown in the figure, is expressed as vₜ(t) = A₁ sin (ω₁t – θ₁) + A₂ sin (ω₂t – θ₂)



The value of A₁ and A₂ respectively, are