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convergent.

Module 11
Answer any two questions, each carries 5 marks.

2

ಈರಿ

0 10 If u = ‏رو عر‎ (ल 2tan 8 find (5)

11 5 5 85 ರಿಂ
Let z = ‏و‎ ,x = r ८959, y =r 57718, use chain rule to evaluate i and ಸ್ಥಾ

(5)
೩೫7 =2and@= 5

12 A rectangular box open at the top is to have volume 3223. Find the
dimensions of the box requiring least material for its construction.

Module 111

(5)

Answer any two questions, each carries 5 marks.

13 Suppose that a particle moves along a circular helix in 3-space so that its
position vector at time t is r(t ) = 40057217 4sin ‏وغج‎ + ६ Find the distance

(5)

travelled and the displacement of the particle during the time interval
12225,

14 Suppose that the position vector of a particle moving in a plane
5
7 = 12/2८ द + ‏رارع‎ ६ 0.1൩ the minimum speed of the particle and locate (5)
when it has minimum speed?

15 Find the parametric equation of the tangent line to the curve
x=cost,y=sint,z=f where { = to and use this result to find the parametric (5)

equation of the tangent line to the point where t =z.

Module 1V
Answer any two questions, each carries 5 marks.

16 Evaluate Sp y dA where R is the region in the first quadrant enclosed (5)
between the circle - + y* = 25 and the linex+ y= 5.

Evaluate 1 1 ನ 7 (5)

18 Evaluate [കര്‍ where V is the volume of the tetrahedron bounded by the 5)
7۷

17

plane x=0,y=0,2=Ox+y+z=a.
Module V

Answer any three questions, each carries 5 marks.
19 Find the scalar potential of ह = (24 + z9i+ ८2 + 3८22 (5)
20 Find the work done byF(x, - (८2 + y7)i— xj along the curve

८2 \ y? , (5)
:x° + +~ = 1 counter clockwise from (1,0) to (0,1).

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