Gujarat University 2009-1st Year B.C.A Computer Application Advanced Mathematics - Question Paper
(b) Answer the following questions (any two):
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(I) IfA
is true or not.
is given then verify (A + B)2 - A2 + B2
(2) Define Addition of matrices. If A
.2 5 B "[ 4
matrix C such that 2C = A * B.
(3) Solve the differential equation cos(x - y)dy dx.
(c) Solve the differential equation (any one) r
(1) (e* + l)cos x dx+ eysinj: dy = 0
I
3. (a) Answer the following questions :
Define Break Even point.
OR
If f: R -> R, fl;*) * 2x + 1 and g: R -+ R. g(*) *= x + k, k e R and fog gof then find k.
(b) Answer the following questions :
A Pan drive making company finds that the production cost of each Pan drive is Rs. 30 and the fixed cost is Rs. 18,000. If each tin can be sold for Rs. 50 determine (i) the cost function (ii) the revenue function (iii) the break even point.
OR
If f(*)log . then prove that f = 2-fl
(c) Answer the following questions (any five): 10
(1) Find out the equation of line parallel to 2x- 3y - 5 = 0 and passing through the point (4, 5).
(2) Find out area of the triangle whose vertices arc (2, 3), (5,7), (-3. 4).
(3) Find out the co-ordinates of a point which divides line joining the points (5, 2) and (7,9) in ratio 2 : 7.
2019-B 2
(4) Show that (-2,-I), (1, 0), (4, 3) and (1,2) arc vertices of a parallelogram.
(5) Show that the points (-1, 1), (3,-2) and (-5,4) are collinear.
(6) Find out angle between lines 3x + 2y-11 =0 and 2x + y+J2 = 0.
(7) What will be the value of x if the distance between (x,-4) and (-8,2) be 10?
4. (a) Answer the following questions (any five): 5
(1) Define Finite set.
(2) If n(A) ** 2 and n(B) *= 3 is given, what will be the no. of elements in P(AxB)?
(3) Write down the set in set builder form A= {* N/x4- ) 0).
(4) Write down distributive properties or D' Morgans laws for sets. t (5) Define One - One function.
(6) Find out range of a function f: {1,2) R, fit*)-** 1 (b) Answer the following questions (any three): 9
(1) If A = {1, 2, 4, 5}, B = {2, 3, 5, 6} and C = {4. 5, 6. 7}, then verify following results:
(i) An(BnC) = (AnB)riC
(ii) Au(BnC) = (AuB)n(AuC)
(2) If A = {1,2,3}, B = {51 andC = {7} then verify following results :
(i) A x <B n C) (A x B) r (A x C)
(ii) A x (B U C) - (A x B) U (A x C)
(3) In a survey of 100 students it was found that 50 used the college library, 40 had their own and 30 borrowed books, 20 used both college library and their own, 15 borrowed books and used their own books, whereas 10 used borrowed books and college ..library. Assuming that all students use cither college library books or their own or borrowed books, find the number of students using all three sources. And if the number of students using no book at all. is 10 and the number of students using all three is 20, show that the information is inconsistent.
(4) Find out inverse of f: R -* R, fpc) = 2x + 1 if exists.
2019-B 3 P.T.O.
5. (a) Answer the following questions (any two): 4
(1) Discuss the continuity of ffr)
lim 10*-5*+ 2*- 1
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(2) Evaluate
(3) Evaluate
*-0 x2
lim i'' lVn + 4 n-> i, ' nj
(b) Answer the following questions (any five):
10
(1) Evaluate J* sin x dr using integration by parts.
(2) Evaluate j(x_1)\x_2) d*
1
(3) Evaluate
o
2
(4) Evaluate J cos!0.xdx.
(5) Find the area bounded region by the curve y = x2 + 4, jr-axis, x - 3 and
x = 5.
(6) If fixed cost for producing x units of an item is Rs. 1,000 and marginal cost function is 200 - 20* - 0.2*2. Find total cost of company.
Time : 3 Hours] .(Max. Marks : 70
1. (a) Answer ihe following questions (any five): 5
(1) What is derivative of sin x?
(2) What is derivative of a* ?
(3) find out derivative of Y = ,
(4) Find out derivative of y =x sin* lira x a
(5)
.r a x - a lirn eir~cx
X->0 X '.........
(7) Define continuous function.
i
(b) Answer the following questions (any th ree) :
(1) Find ifyx** is given.
(2) Find out Minimum and Maximum value of a function ffr) * j1 - 6x + 13 if exists.
(3) If Y ~(x + a/i +.V2) then prove thai (I + ;r) y2 + xy{ - m2y = 0
(4) Find derivatives of following functions:
(ii) y = log(sin x)
(a) Answer the following questions (any three):
()) Define Square matrix, Symmetric matrix.
(2) Define degree of the differential equation. Find out degree of the differential equation = *+ y
(3) Define generalsoiution of a differential equation. And show that y = cos ax is the solution of the differential equation y2 + a2y * 0.
(4) Give an example of two matrices such that A * 0, B * 0 but AB = 0.
20I9-B 1 P.T
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| Earning: Approval pending. |
