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Testpapers of Andhra University BCA - Mathematics

Answer any FIVE questions and all questions carry equal marks

a. Find the derivative of tan(2x+3)

b. A circular plate expands, when heated, from a radius of 5 cms.to 5.06 cms. Find the approximate increase in its area.

c. Trace the graph of the function y2=x2(a2-x2)

d. Find the equation of the circle passing through (0,0),(1,0) and directrix. 2.

a. Find the equation to the parabola whose focus is (1,-1) and directrix 3x+4y+2=0

b. Find the area of the circle x2+y2=a3 by the method of integration.

c. Integrate the following functions

(i) ex(tanx+sec2x)

(ii) 2x/1+x4 d. Evalute integral from -1 to 1 dx/1+x2 3.

a. Show that the vectors (1,2,1),(2,1,0) and (1,-1,2) form a basis of R3

b. Let F be the field of Complex numbers and

T:F3 -> F3 be defined by T(x1,x2,x3) = (x1-x2+2x3,2x1+x2-x3,-x1-2x2) Show that T is a linear transformation. Describe the null space of T.4.

a. Find the characteristic roots and characteristic vectors of the matrix

| 0 1 0 | A= | 0 0 1 | | -12 -20 -9 | b.

Solve the system of equations:

2x+3y+z=2; x+2y-z=6; 3x+z=2 by Cramer's rule 5.

a. If A and B are similar linear transformations on a vector space V, show that A2 and B2 are similar

b.Let T be the linear operator on R3 defined by

T(x1,x2,x3) = (3x1+x2,-2x1+x2,-x1+2x2+4x3) Prove that T is inevitable and find formula for T-1 6.

a. Calculate mean, median and mode of the following frequency distribution. Class 0-9 10-19 20-29 30-39 40-49 50-59 Frequency 13 38 67 76 22 4 b.

A Problem in mathematics is given to three students A,B and C whose chances of solving it are ½,1/3 and ¼ respectively. What is the probability that the problem is solved. 7.

a.Fit a straight line to the following data

X : 1 2 3 4 6 8 Y : 2.4 3 3.6 4 5 6b.

The two regression equations of the variables x and y are x=19.13-0.87y and y=11.64-0.50x.Find (i) mean of x's ,(ii) mean of y's and (iii) Correlation coefficient between x and y. 8.

a. If A, B, C are sets prove that

(i) (A-B) U (B-A) = (AUB)- (AÇB)

(ii) A U (B Ç C)=(AUB) Ç (AUC)

b.

Define reflexive,symmetric and transitive relations.Give examples for

(i) A relation which is reflexive and symmetric but not transitive

(ii) A relation which is reflexive and transitive but not symmetric 9.

a.For any two elements a nd b of a Boolean algebra,show that a £ b if and only if b' £ a'.

b. If A={2,3,4},B={1,2} and C={4,5,6} find

( I ) A + B (ii) B + C and (iii) A+B+C

c. For any three elements a,b and c in a Boolean algebra,show that

(a Ç b Ç c) U (b Ç c) = (b Ç c) 10.

a.Define a distributive lattice and prove that every chain is a distributive lattice.

b.Show that, in a lattice, a £ b < c Þ a Å b = b-c

c.Show that in a complemented lattice with more than one element, no element is it's own compliment.

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