An occasion coordinator is arranging a program for a gathering of 20 individuals who need to set out on a touring trip. Because of space imperative at the offices to be visited the association segment the gathering into five non-void subgroups.the number of individuals in the subgroup may change starting with one subgroup then onto the next.

(1) the number of various parcels are there for the coordinator ?

(2) what number diverse parcel are there if the subsequent subgroup is comprised of 4 individuals ?.

(3) what number diverse parcel are there if the fouth subgroup is comprised of 6 individuals ?

(4) what number diverse segment are there if the second and fouth subgroups have 4 and 6 individuals separately ?

(5) The coordinator picks a parcel of individuals at arbitrary .Find the likelihood that the quantity of individuals in the second and fouth subgroups of the picked segment are not 4 and 6 separately.

2. Find the general solution of each of the following partial differential equations. (a) dur + buy + cu = 0, a #0, b and c are numerical constants. (b) y'us - ry'uy = cru, c # 0 is a constant, y > 0. (c) us + (x + y)uy = zu. (d) rus - yuy +ylu = y?. (e) rus + yuy = u, 1 / 0. (f ) rustyruy = (x+y)u, x / 0 and y # 0. (g) 3us + 4uy + 14(x + y)u = Gre-(Ity)? (h) rustuy = ru.Circuit #J: Wien Robinson Active Notch Filter . The advantage of this filter is that the passband gain A can be adjusted without changing the value of Q, unlike the active twin-t filter. Figure 7 shows the circuit diagram for this Mter. The frequency-dependent portion is composed of the parallel and trim RC combinations between the two op-amps Figure 7 Wien Robinson action witch fiber . Equation 11 gives the transfer function for this circuit H (s) = with the additional variables defined as IT = . The filter parameters of the center frequency in. gain A, and quality factor O are ghen by Equations 14, 15, and 16: 1341 A=-(2) Suppose that an LTI has an impulse response given by h (n ) = 4(-1) (1/2-4) [8(n - 2k) (a) Sketch h(n). Is this filter an IIR or an FIR filter? Find the difference equation of the filter. (b) Determine whether the filter is stable and/or causal. (c) Find the output of the filter, y(n), for an input given by r(n) = u(n)u(-n + 5). (e) Plot the frequency response (magnitude and phase) over the range 0 S w S 7. What type of filter is this