
Let A={1,2,3} and R={(1,1), (1,2), (2,1), (2,2), (3,3)} Show that R is
equivalence relation.
This question has 0 answers so far.


From a pack of 52 cards, two are drawn at random. What is the probability that one is a king and the other a queen?
This question has 1 answers so far.


a) Is H a subgraph of I shown in the following Figure? Explain it.
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(b) Show that the graphs are isomorphic.
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Find all paths of length 2 in the following graph G.
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Check the validity of the argument: Dr. Das buys a car, then he can go home in time. If he goes in time,
then his family will be happy.
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b) Define bipartite graphs. Verify whether following graph is bipartite or not.
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For what value of x, the matrix is singular.
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(a) Show that the relation is partial order relation on the set of natural numbers. (Where means less than or equal to).
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(a) Let f: be defined by
This question has 0 answers so far.


(b) Show that logically implies
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(a) Show that
This question has 1 answers so far.


(a) Express in factorial form and hence evaluate
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A grade school boy has 5 blue and 4 white marbles in his left pocket and 4 blue and 5 white marbles in his right pocket. If he transfer one
marble from his left pocket to right pocket, what is the probability of
bis then drawing a blue marble from his right pocket?
From a pack of 52 cards, two are drawn at random. What is the probability that one is a king and the other a queen?
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A can solve 75% of the problems and 3 can solve 70 of the problems. What is the probability that either A or B can solve problem
chosen at random?
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For all n>=1, let a recursive
function
f(n) be defined as Is f a well defined function?
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If p(x) and Q(x) are propositions, then prove that
Are (i) and (ii) tautologies?
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Consider a poset {(1,2,4,5,10,201.)} as described by Hasse diagram in
the following
Show that it is a lattice
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B) Let R be the set of real niamber and let is invertible ?
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Write short notes on PERT VS. CPM
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A bag contains four white and two black balls and a second bag contains three of each colour A bag is selected at random and a ball is then drawn at random from the bag choses. What is the probability that the ball drawn is white?
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Define normal distribution and hypergoometric distribution.
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Prove that every square matrix is uniquely expressible as the sum of asymmetric matrix and a skew symmetric matrix.
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Using properties without expanding prove that:
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Show that is continuous at x = 2.
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Show that function is maximum when x =
This question has 0 answers so far.


If the matrix is orthogonal, then find the values of a, b and c where matrix is
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Verify Cayley Hamilton theorem for the matrix Also, find
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Find eigen values and eigen vectors of the matrix
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Examine the following system of vectors for linearly dependence. If dependent, find the relation between them
X_{1} = (1,1, 1); X_{2} = (2, 1, 1); X_{3} = (3,0,2).
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Evaluate lim
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For what choice of 'a' and 'b' is the function continuous
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For what value of does the lim f(x) exists, where f(x) exists, where f is defined by the rule
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Discuss the nature of discontinuity at x = 0 of
This question has 0 answers so far.


Find all the asymptotes of y^{4}  2xy^{3} +2x^{3}y x^{4} 3x^{3 }+ 3x^{2}y + 3xy^{2}  3y^{3}  2x^{2} + 2y^{2}  1 = 0
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If and
This question has 0 answers so far.


If y = x then show that
This question has 0 answers so far.


If y = x then show that
This question has 0 answers so far.


Examine the function
for
maxima/minima
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Evaluate i)
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Evaluate ii)
This question has 0 answers so far.


Show that
This question has 0 answers so far.


Evaluate
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Obtain the reduction formula for .Also evaluate
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Define (i) ogives
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Define (ii) histogram
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Define (iii) relation between mean, median and mode.
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Karl Pearson's coefficient of skewness of a distribution is 0.32, its standard deviation is 6.5 and mean is 29 6, find the mode of the
distribution .
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A contractor employs three types of workers  male, female and children. To a male worker he pays Rs. 200 per day to a female
worker Rs. 150 per day and to a child worker Rs. 85 per day. What is
the average wage per day paid by the contractor?
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Find the two lines of regression and coefficient of correlation for the data given below:
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Obtain the dual of the following Linear Programming Problem:
Maximize z = 7x_{1 }+ 5x_{2} Subject to constraints:
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Find the missing frequencies for the class intervals using the following data of 150 students given that the mean marks is 65.
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Compute quartile deviation from the following data:
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Suppose that samples of Polythene bags from two Manufacture, A and B are tested by a Prospective buyer for bursting pressure, with the
following results:
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The mean of 5 observations is 4,4 and variance is 8.24. If three of the five observation are 1, 2 and 6. Find the other two.
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Calculate the correlation coefficient from the following data:
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Ten Participants in a Context are ranked by three judges as follows:
Calculate the rank correlation coefficient and also discuss which pair of
judges has similar taste.
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Calculate (i) two regression lines,(ii) two regression coefficient and(iii) coefficient of correlation from the following data:
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Two random variables have the regression equations 3x+2y26 = 0
L 6x+y31 = O Calculate
(i) Mean value of X and Y.
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Two random variables have the regression equations 3x+2y26 = 0
L 6x+y31 = O Calculate
(ii) The coefficient of Correlation
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Two random variables have the regression equations 3x+2y26 = 0
L 6x+y31 = O Calculate
(iii)If var(x) = 25, find standard deviation of x from the data given above.
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Write the dual of the following primal problems and also find its optimal solution using simplex method
Min z = 8x_{1} + 9x_{2 } Sub to Constraints:
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Solve the following linear programming problem by Graphical Method: Max 5x_{1}  4x_{2} Subject to constraints:
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A branch of PNB has only one typist. Since the typing work varies in length, the mean service rate 8 letters/hr. The letters arrive at a rate of
5/hr during the entire 8 hr work day. If the type write is valued 1.50/
Rs. per hour, determine: (i) The equipment utilization
This question has 0 answers so far.


The average system time
A branch of PNB has only one typist. Since the typing work varies in length, the mean service rate 8 letters/hr. The letters arrive at a rate of
5/hr during the entire 8 hr work day. If the type write is valued 1.50/
Rs. per hour, determine: ii) The Percent time that an arriving letter has to wait.
This question has 0 answers so far.


The
The average system time
A branch of PNB has only one typist. Since the typing work varies in length, the mean service rate 8 letters/hr. The letters arrive at a rate of
5/hr during the entire 8 hr work day. If the type write is valued 1.50/
Rs. per hour, determine: (iii) The average system time
This question has 0 answers so far.


The
The average system time
A branch of PNB has only one typist. Since the typing work varies in length, the mean service rate 8 letters/hr. The letters arrive at a rate of
5/hr during the entire 8 hr work day. If the type write is valued 1.50/
Rs. per hour, determine: (iv) The average cost due to waiting on the part of the type writer
This question has 0 answers so far.


Given the following data, determine the least cost allocation of the available machines to five jobs
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Solve the following transportation problem and test for optimality to find optimal solution by MODI method
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Let A = {1, 2, 3) and B = {a, b, c). Let R = {(1.b)(1.c)(3.b)}. Find the domain and range of the relation. Determine ..
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Let D denote the set of all positive divisors of the positive integer n. Determine and represent it by Hasse Diagram.
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Define isomorphic and Hamilton Graphs with example.
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Let f, g, be functions from N to N (set of natural numbers) for such that f(n) = n + 1, g(n) = 2n. Find fog and gof.
This question has 0 answers so far.


Define Tautology and contradictions,
This question has 0 answers so far.


Show that the relation of parallel lines in the set of lines on a plane is an equivalence relation.
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Choose any two statements p and q as you like. Draw the truth table for and
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Consider the graph G (V, E) where v consists of Four vertices A, B, C,D and E of five edges where represent this undirected graph
diagrammatically. Determine the degree of each vertex.
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Let f be a mapping from R to R such that f(x) = 2x + 3. Show that f is invertible and find its inverse.
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.If n (A) = 40, n(B) = 30, = 20. Then find
This question has 0 answers so far.


Let A = {1,2,5,6), B = {2,5,7), C = (1,3,5,7,9). Verify (A x B) {A X C} = A x B x C}.
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Let N = {1,2,3,........), denote the set of all positive integers and A = {, 3 < x < 12), B = {, x is even, x < 15). Find
This question has 0 answers so far.


If R is an equivalence relation in a set A. Then prove that is also equivalence relation.
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In a lattice, prove that
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In a lattice, prove that
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Define complemented lattice, also find the complement (if exists) of all elements of
This question has 0 answers so far.


Let A = {1,2,3,4,6,8,9, 12, 18, 24} be equipped with relation x divides y.Draw the Hasse diagram.
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Let G be an undirected graph with m vertices, sayDefine the adjacent matrix A of G. Consider the undirected graph G
with 5 vertices shown in the following diagram.
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Draw the directed graph for the following incident matrix. Also find the degree of all vertex.
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Show that the two graphs shown in the figure are Isomorphic.
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Show that the two graphs shown in the figure are Isomorphic.
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Prove that the union of two graphs will be a graph such that.
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Prove that the union of two graphs will be a graph such that.
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By means of truth tables, justify that the conditional statement "If p then q" is logically equivalent to the statement "Not p or q".
This question has 0 answers so far.


Define a proposition. Let p and q be propositions and denote compound proposition, "if p then q" Draw the truth table for the
compound proposition Let p: you try, and q: you will succeed.
Justify the truth table for
This question has 0 answers so far.


Verify Demorgan's laws for propositions. And also prove that.
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Consider the following: P: Today is Tuesday, Q: It is raining, R: It is cold. Write in simple sentence the meaning of
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Consider the following: P: Today is Tuesday, Q: It is raining, R: It is cold. Write in simple sentence the meaning of .
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(b) to show that
This question has 0 answers so far.


(c) Find the domain and range of the function f(x) =
This question has 0 answers so far.


(d) Define Tautology and Contradiction.
This question has 0 answers so far.


(e) By means of truth table, prove that
This question has 0 answers so far.


(f) If , then find
for all
This question has 0 answers so far.


(g) Verify Demorgan's laws for universal set U = {1, 2, 3, 4, 5, 6, 7),A = {4, 1, 2, 5) and B = {1, 2, 4, 6).
This question has 0 answers so far.


(h) Define Distributed & Complemented Lattice.
This question has 0 answers so far.


(f) Define POSET with example.
This question has 0 answers so far.


(a) R is an equivalence relation in a set A, then prove that is also and quivalence relation.
This question has 0 answers so far.


(b) Let U = {a,b,c,d,e), A = {a,b,d} and B = {b,d,e). Find (i) (ii) (iii) BA (iv) (v)
This question has 0 answers so far.


(b) Define the relation congruence modulo m." Show that it is and quivalence relation in set of integers.
This question has 0 answers so far.


(a) Let be a lattice, then prove that for every element a,b (i) (ii) (iii)
This question has 0 answers so far.


(b) Prove that every finite lattice L is bounded.
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(a) Find the complements of each element in D_{42}
This question has 0 answers so far.


(b) Let R be the relation of divisibility on set A. Draw the Hasse diagram of poset relation R where A = 2, 4, 8, 16, 32).
This question has 0 answers so far.


(a) Find the chromatic number of the graph given below using the WelchPowell algorithm.
This question has 0 answers so far.


(a) Draw a 3regular graph with 6 vertices.
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(b) Prove that the degree of any vertex in a simple graph of n vertices cannot exceed n  1.
This question has 0 answers so far.


(a) Prove that is a tautology.
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(a) Prove that
This question has 0 answers so far.


(b) Prove that
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(b) Estimate the missing term in the following table
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(c) A random variable x has the following probability function
find the value of k.
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(d) If a random variable has a Poisson distribution such that P(1)  P(2),find the mean of the distribution.
This question has 0 answers so far.


(e) For a normally distributed variable with mean 1 and S.D 3, find the probability that
This question has 0 answers so far.


(f) If X and Y are independent binomial variables such that Xb(5, 1/2), (7, 1/2). Find P [X+Y=3).
This question has 0 answers so far.


(g) Find the Lagrange interpolating polynomial that fit the following data values.
Also interpolate at x=1.5
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(h) Events A and B are such that
This question has 0 answers so far.


(i) The expected value of a random variable x is 2 and its variance is 1.Find the variance of 3x+4.
This question has 1 answers so far.


(i) if two regression coefficients are 0.8 and 0.2. What would be the value of coefficient of correlation?
This question has 0 answers so far.


(a) A bag containts 40 tickets numbered 1,2,3,.,40 of which four are drawn at random and arranged in ascending order Find
the probability of t_{3} being 25.
This question has 1 answers so far.


(b) The probability that Nirmal will solve a problem is 2/3 and the probability that Satyajit will solve it is What is the probability that
(i) the problem will be solved (b) neither can solve it.
This question has 1 answers so far.


(a) The content of three urns are: 1 white, 2 red, 3 green balls; 2 white, 1 red, 1 green balls and 4 white, 5 red, 3 green balls. Two balls are
drawn from an urn chosen at random. These are found to be one
white and one green. Find the probability that the balls so drawn
come from the third urn.
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(b) For what value of n is
This question has 0 answers so far.


(a) of the moment generating function of normal distribution is
This question has 0 answers so far.


(b) Calculate the coefficient of rank correlation from the following.
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(a) Find and variance for the following distribution.
This question has 0 answers so far.


(b) From the given data obtain the two regression equations using the method of least square.
This question has 0 answers so far.


(b) Using NewtonRaphson method evaluate to two decimal figures, the root of the equation e^{x} = 3x, lying between 0 and 1.
This question has 0 answers so far.


(a) Use Newton's interpolating formulae to find y when x =1.85 and x=2.4 from the data.
This question has 0 answers so far.


(b) Find a root of x^{3}5x+3 = 0, by NewtonRaphson method.
This question has 0 answers so far.


(a) Solve by Jacobi's Method 4x + y + 32 = 17
x + 5y + z = 14 2xy + 8z = 12
This question has 0 answers so far.


(b) Given that Find and at and
This question has 0 answers so far.


(a) Apply LU Method to solve the equations 3x+2y+7z =4, 2x+3y+z=5, 3x+4y+z=7
This question has 0 answers so far.


(b) Calculate the value of
by simpson' s 1/3 rule using 1 1 ordinals.
This question has 0 answers so far.


A coin is tossed three times. What is the probability of occurrence of head and tail alternately?
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Find the value of so that the following function is a probability density function
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Find the value of so that the following function is a probability density function
This question has 0 answers so far.


For any positive integers r and n>r, prove that
This question has 0 answers so far.


Using Lagrange's interpolation find the interpolation polynomial for the function y(x) for the given values below.
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Find two successive approximation of a real roots of the equation by using Bisection method.
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A fire insurance company has 3,840 policyholders. If the probability is 1/1200 that any one of the policyholders will file atleast one claim in any given year. Find the mean of the distribution.
This question has 0 answers so far.


Prove that for any two events A and B
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A coin is tossed until a a head appears. What is the expectation of the number of tosses?
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A coin is tossed until a a head appears. What is the expectation of the number of tosses?
This question has 0 answers so far.


A perfect cube die is a large number of times in a set of 8. The occurrence of 5 or 6 is called a success. What is probability of exactly 3 success?
This question has 0 answers so far.


Cut of (2n+1) tickets consecutively numbered, three are draws at random. What is the probability that the numbers on them are in arithmetic progression (A. P.)?
This question has 0 answers so far.


Find the probability that at most 5 defective fuses will be found in a box of 200 fuses if experience show that 2% of such fuses are
defective.
This question has 0 answers so far.


The four attendants A, B, C and D of a company are supposed to wash the windshield of each customer's car. A, who service 20% of all
cars, fails to wash the windshield one time in 20; B, who services 60%
of all cars, fails to wash the windshield one time in 10: C, who
services 15% of all cars, fails to wash the windshield one time in 10,
and D, who services 5% of all cars, fails to wash the windshield one
time in 20. If a customer complains later that his windshield was not
washed, what is the probability that his car was serviced by A?
This question has 0 answers so far.


Out of 3n consecutive number 3 numbers are selected at random. What is the probability that their sum is divisible by 3?
This question has 0 answers so far.


Prove that the Binomial distribution reduces to Poisson distribution under the conditions that the number of trial n is very large and the
probability of success p is small such that , a constant.
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If X is normally distributed with mean 2 and variance. Find
This question has 0 answers so far.


Find the moment generating function of Binomial distribution of random variable X. Hence find its mean and variance.
This question has 0 answers so far.


It has been claimed that in 60% of all solar heat installations utility bill reduced by atleast onethird. Accordingly, what are the
probability that the utility bill will be reduced by at least onethird in
four of five installation.
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It has been claimed that in 60% of all solar heat installations utility bill reduced by atleast onethird. Accordingly, what are the
probability that the utility bill will be reduced by at least four of five installation?
This question has 0 answers so far.


Find a real root of the equation correct to 3 decimal places using method of False position.
This question has 0 answers so far.


From the following table of value of x and f(x).
Determine the value of (0.23) and (0.29).
This question has 0 answers so far.


Find a real root of the equation using NewtonRaphson method with an accuracy of 10^3.
This question has 0 answers so far.


Give the table of values
Evaluate using Lagrange's interpolation and estimate the error.
This question has 0 answers so far.


Consider the system of equations:
Find the inverse of the coefficient matrix of the above system of
equations by Gauss Jordan method.
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A rocket is launched from the ground. Its acceleration a(t) measured in every 5 seconds is tabulated below.
Find the velocity of the rocket at t = 30 second using Simpson's 1/3 rule.
This question has 1 answers so far.


Solve the system of equations:
Using LU decomposition method.
This question has 0 answers so far.


Solve the system of equations:
Using LU decomposition method.
This question has 0 answers so far.


From the following table find the value of dy/dx and d^2y/dx^2 at the point x=1.5.
This question has 0 answers so far.


From the following table find the value of dy/dx and d^2y/dx^2 at the point x=1.5.
This question has 0 answers so far.


(a) Evaluate the determinant of the matrix (b) Use Cramer's rule to sole the system of equations
x+y+z+ 1 = 0; ax + by + cz + d = 0; a^{2}x+ b^{2}y + c^{2} z+ d^{2 }= 0 (c) Find the maximum value of y=(1/x)^{2} (d) Evaluate (e) Evaluate lim, (ex^{1/x}+1), if it exists.
This question has 0 answers so far.


(a) Show that the vectors x_{1} =(1, 2, 4), x2 = (2,1,3), x3 = (0,1,2) and x_{4}= (3,7,2)
dependent and find the relation between them. (b) Find the eigen values and eigen vectors of A =
This question has 0 answers so far.


(a) Given A = find adj (A) by using CayleyHamilton theorem. (b) Find the rank of the matrix A =
This question has 0 answers so far.


(a) Discuss the continuity of the function
f(x) = (b) Solve
This question has 0 answers so far.


(a) Discuss the continuity of
the function (b) Evaluate
This question has 0 answers so far.


(a) Verify Lagrange's Mean value Theorem for
(b) Expand logx in powers of (x1) by Taylor's theorem and hence find the value of loge (1.1).
This question has 0 answers so far.


a if y = and calculate yn(O).
blind all the asymptotes of the curve
y^{3} + 4xy^{2} + 4x^{2} y + 5y^{2} + 15xy + 10x^{2}  2x + 1 = 0
This question has 0 answers so far.


(a) Prove that(m,n) = (b) (1)Evaluate (ii) Evaluare
This question has 0 answers so far.


(a} If I_{n }=_{ } xdx ,show that (b) Evaluate
This question has 0 answers so far.


Let A= (1,2,3.9.181}. Consider the partial order of divisibility on A. Draw the Hasse diagram of the poset (A, <=)
This question has 0 answers so far.


Construct the truth table to determine whether each of the following is a tautology, or an absurdity?
This question has 0 answers so far.


Show that Pvq = qvp,  (Pvq) = ~p^ ~q
This question has 0 answers so far.


Let Find
This question has 0 answers so far.


Show that the graph G_{1 }=( V_{1'}E_{1} ) and G_{2}=(V_{2,}E_{2}) , are isomorphic
This question has 0 answers so far.


b) Let be a lattice shown in the following figure where L  (a,b,c,d,e,f,g). Define an algebraic system on A
This question has 0 answers so far.


a) IN Q 6a, consider the following subset of Lattice i) S2.4.10.20) ii) S14,5,10,20,) iii) S 11.2.5,10) Determine whether the above subset of the lattice is a sublattice.
This question has 0 answers so far.


b) Define distributed and complemented lattices In Q 6a, find the component the element 4, Is the lattice given in Q6a complemented lattice.
This question has 0 answers so far.


b) Prove the following
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a) Let A  BR the set of real numbers.
: Let be given by the
formula f(x)4x^{5}1 and let g  be given by
Show that f is bijection and g is also bejection.
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The following data which is the number of tonnes shipped weekly across the Pacific by a shipping company.
398, 412, 560, 476, 544, 690, 587, 600, 613, 457, 504, 477, 530, 641,
359, 566, 452, 633, 474, 499, 580, 606, 344, 455, 505, 396, 347, 441,
390, 632, 400, 582.
Assume these data represent an entire population. Find the population
mean and the population standard deviation.
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The following data are numbers of colour television sets manufactured per day at a given plant: 15, 16, 18, 19, 14, 12, 22, 23, 25, 20, 32, 17,
34, 25, 40, 41. Draw a frequency polygon and an ogive for these data.
This question has 0 answers so far.


Given the set of data 4, 8, 9, 8, 6, 5, 7, 5, 8, find each of the following sample statistics: (i) Mean (ii) Median (iii)Mode (iv) Midrange
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The following table shows the average weights for given heights in a population of men.
(a) The relationship between the variables is modelled by the regression
equation yax+b. Write down the value of a and of b.
(b) Use this relationship to estimate the weight of a man whose height is
177 cm.
(c) Find the correlation coefficient.
This question has 0 answers so far.


For the data X and Y given below:
(i)Find Spearman's rank correlation coefficient. (ii)Find the regression line (iii)Find the coefficient of determination for the regression line fit.
This question has 0 answers so far.


Correlation and Causality are one and the same. Critically comment.
This question has 0 answers so far.


(a) Maximize subject to
Using the Simplex method
This question has 0 answers so far.


Explain the concept of duality in context to linear programming problems.
This question has 0 answers so far.


Define and explain (1) pessimistic time (2) Optimistic time
This question has 0 answers so far.


The project activities, precedence relationships and durations are described in the table. The critical path of the project is
This question has 0 answers so far.


A trucking company has a contract to move 115 truckloads of sand per week between three sandwashing plants W,X and Y, and three
destinations, A,B and C. Cost and volume information is given below.
Compute the optimal transportation cost and the transportation plan
This question has 0 answers so far.


A head of department has four lecturers to assign to pure maths (1),mechanics (2), statistics (3) and Quantitative techniques (4). All of the
teachers have taught the courses in the past and have been evaluated
with a score from 0 to 100. The scores are shown in the table below.
The head of department wishes to know the optimal assignment of teachers to courses that will maximize the overall total score. Give the
optimal assignment of teachers and courses / papers as well as the
optimal score.
This question has 0 answers so far.
