GATE EE 2015 Question Paper (07-Feb-2015) (Shift 2)

The volume enclosed by the surface $f\left(x,y\right)=e^x$ over the triangle bounded by the line $x=y;x=0;y=1$ in the xy plane is ________.

Two coins R and S are tossed. The 4 joint events $H_R{H}_S,T_R{T}_S,H_R{T}_S,T_R{H}_S$ have probabilities 0.28, 0.18, 0.30, 0.24, respectively, where H represents head and T represents tail. Which one of the following is TRUE?

A differential equation $\frac{di}{dt}-0.2i=0$ is applicable over $-10<t<10$. If $i\left(4\right)=10$, then $i\left(-5\right)$ is _______.

Consider a signal defined by

x≤ft( t ) = ≤ft\{ {*20c {e^~j10t}&for≤ft| t | ≤ 1\\ 0&for≤ft| t | > 1 } .

Its Fourier Transform is

The coils of a wattmeter have resistances 0.01 Ω and 1000 Ω ; their inductances may be neglected The wattmeter is connected as shown in figure, to measure the power consumed by a load, which draws 25A at power factor 0.8. The voltage across the load terminals is 30 V. The percentage error on the wattmeter reading is –