Model Question Paper Maths Government Science College Bangalore University : www.gscblr.kar.nic.in

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Bangalore University
Government Science College
I Semester B.Sc/B.A. Examination, Nov/Dec 2005
(Semester Scheme)
MATHEMATICS (Paper-I)
Time: 3 Hours
Max.Marks:90

Model Question List : http://gscblr.kar.nic.in/Exam_Papers.html
Model Question Paper : http://gscblr.kar.nic.in/files/Maths.doc

Instructions:
1) Answer all questions.
2) Answer should be written completely either in English or in Kannada.

1. Answer any fifteen of the following: (2x15=30)
1) Write the negation of V x [P (x) ? q(x)].
2) Find T [P (x)], if P(x): x2-3x+2=0, the replacement set is z.
3) Define an equivalence relation.
4) If f: Q?Q is defined by f(x)=3x+1, Vx€Q, then show that f is onto.
5) Find the nth derivative of Cx/2, Sin 2x.
6) Find the nth derivative of Sin3 2x.
7) If z=xy, then find ?2z/?x ?y
8) If y2=4ax, find dy/dx using partial differentiation.
9) If u=x3-2x2y+3xy2+y3, prove that x ?u/?x+y ?u/?y=3u.
10 If u=2x-3y8, v=5x+4y, show that ? (u,v)/ ? (x,y)=23.
11) Evaluate ?dx/ (1+x2)7/2
12) Evaluate ?p2Sin 4x cos3x dx.
13) Find the direction cosines of the joining (2,-3, 6) and (3, -1,-6).
14) Show that the line x-1/-1= y+1/1=z/1 lies on the plane x-y+2z=2.
15) Find the equation of a plane passing through (2,3, 4) and perpendicular to the vector ^i+^j+^k.