Show that any tree with exactly two vertices of degree 1 is a path
See Answer →Prove or disprove the following statement. If m divides , then m divides
also.
Consider the propositions ‘2+3 = 5’ and ’The Sun rises in the West’.
i) Write the disjunction of the statements and give its truth value.
ii) Write the conjunction of the statements and give its truth value.
iii) Write the exclusive disjunction of the statements and give its truth value.
See Answer →Every 3-colourable graph is 4-colourable
See Answer →If a graph is isomorphic to its complement, then it has odd number of vertices.
See Answer →If g(x) is the generating function for { }, then
is the generating function for the sequence
where
The generating function of the sequence {1,2,3,4,...,n...} is (1−z) −2 .
See Answer →an = an 2 +n,a1 = 0, where n is a power of 2, is a linear recurrence relation
See Answer →Every bipartite graph with odd number of vertices is non-hamiltonian.
See Answer →K4,4 is non-planar
See Answer →The generating function associated with a sequence can never be a polynomial.
See Answer →The number of onto functions from {1,2,3,4,5,6} to {a,b, c,d} is 4!S 4 6 .
See Answer →‘x 2 +y 2 −3 is not dividible by 4.’ is mathematical statement.
See Answer →The differential equations
model a disease spread by contact, where S is the number of susceptibles, I is the number of infectives, β is the contact rate, γ is the removal rate and λ is the birth rate of susceptible
(i) Identify which term in the RHS of each differential equation arises from the birth of susceptibles.
(ii) Discuss the model given by the above two differential equations.
See Answer →Suppose the quarterly sales for a particular make of a car in Delhi were 2682, 2462 and 3012, respectively. From the past data prior to these three data points, a straight line was to fit. The value on the line corresponding to the last observed time is 2988 and the slope is 80. Use exponential smoothing based upon the three observations given above to forecast sales for the quarterly period following these observations, using α = β = 0 ⋅ .
See Answer →A model corresponding to the cooperative interaction between two species x and y is given by
Find all the equilibrium points of the system and discuss the stability of the system at these points
See Answer →The mean arrival rate to a service centre is 3 per hour. The mean service time is found to be 10 minutes foe service. Assuming Poisson arrival and exponential service time, find
(i) the utilisation factor for this service facility,
(ii) the probability of two units in the system,
(iii) the expected number of units in the system, and
(iv) the expected time in hours that a customer has to spend in the system
See Answer →Give one example each from the real world for the following, along with justification, for your example:
(i) A non-linear model
(ii) A stochastic model
(iii) A linear, deterministic model
See Answer →A short run cost function for an entrepreneur is Determine the price at which the entrepreneur cases production in an ideal market. Also, derive the supply function
Consider the upward motion of a particle under gravity with a velocity of projection u0 and resistance . 2 mkv Show that the velocity V at time t and distance x from the point of projection are related as
See Answer →