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Guru Gobind Singh Indraprastha Vishwavidyalaya 2009-2nd Year B.C.A Computer Application Mathematics-IV, Fourth Semester, End Term , Year , , - Question Paper

Tuesday, 28 May 2013 01:25Web

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(ft a parabola of second degree to the foMowing data:- (6.5)

X	1.0	1 s	2.0	2.5	3.0 I
y_	i.i_	h?	2 6	2.0	2;?.]

box content 12 butbs out oI which 3 are defective If 3 Bulbe are drawn at random from the box, find the expected nunber of detective bulbe drawn. (9)

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ind the polynomial of lowest degree that can be fitted for the following data:* (6.5)

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[x 7 3 ; 2 1 jjwf 3 '12TH

IS -21

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Using Newton Raphson method obtain a formula to calculate square root of a natural number N' and hence evaluate -Jit. (6)

07 (a) Using bisection method determine the real root of the equation < - 9i * I * 0 whose root lies between x>2 and x*4. (6.5)

(b)G<ve sin45-0.7071, iSQ = 0.7660. siaJJ'= 0.8192. su>60 0.8660. Find the value of in 52*. (6)

y UNIT-tV

09 (rfSolve by wing Gauss EVninafion method Sx-y-2142, x-3y-z-30, 2x-y-5 (6.5)

JfiiCalculate the approximate value of f'sfaixt&r by Simpson's 1/3* rule using

11 ontnatee. (6)

06 (a)Evaluate j(ifax-iog,x+<')byu$Trapezoidal rule. (6.5)

(b) Fnd f (5) for the polynomial of lowest degree f(x) whie*i satisfies the following set of rw*nber*. 0.7, 26.63.124.215. 342. 511. (6)

End Term Examination

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01 (i)A bag contains 4 white and 2 black bate and a second bag contains three of 'S each colour. A bag is selected at random and a bail is then drawn at random

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/fremi (W Thf \/ heads

i the bag chosen What is the probability that the ball drawn Is white?

i Three unbiased coins are tossed together Find the probability of getting (i) all heads and (U) atieaat 2 heads.

OO Determine the mode of binomial distribution if n*50 Pl/6.. it) Using Poisson Distribution find the probability that the ace of spade will be _v/ drawn from a pack of well shuffled cards atleaat one in 104 consecutive trails W^-Using usual notations prove that A*E^a'2Ei.

What are the errors in trapezoidal rule and Simpsons one-third rule?

(ayfn how many ways can 12 balloons be distnbuted at a Birthday party among

10 children?

<X) The regression coefficient of X on Y is 3.2 and that of Y on X a 0.8. Is this tement correct? Jusbfy your answer.

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"A die is ttrown at random What a the expectation of the number on it? Also find E(X^J).

0} If X and Y are two independent variables then prove that Cov(XY)=0 (2.5x1025)

UNtT-l

02 MTbne ums A. B and C contain red and black baits Ums A contains 4 red and

pr

3 black bads, um B contains $ red and 4 Mack bals and um C contains 4 red end 4 black balls One ball is drawn from each of theee ums, what la the robabtlity that the 3 balls drawn consists of 2 red and 1 black balls. (6.6) (bvlf A and B are two events then prove that P{A) + P{8)-P{Ar\B) (6)

Q3 (a) There are 2 bags A and 8. Bag A contains 'P white and 2 black balls and bag

6 contains 2 while and P' black balls. One of the 2 bags is selected at random and 2 balls drawn are white and the probability that the bag A was used to draw the baits ts 6/7 Find the value of V (6.6)

(b) If "m' things are to be (Sstrtbuted among a' men and 'b' women show that the probabftty that the number of things received by men is odd and is given by

m

UMIT.II

04 (a) A normal distnoution has 75 as mean Fmd its standard deviation if 25% of area under the curve fies to the right of 60 (6.6)

(b) Two judges in a beauty competition rank the 12 entries as folows-