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Internal Assesment Test - Il CMR, .. . .. ~. .. , -.-~_........ . - ----.--.-- - T"'-"-'---'-"'-'" _ _-:
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CMRINSTITUTE OFTEClINOLOGY
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ibstance after 40
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2·If u=x+y+z, uv=y+z, uvw=z,then find 8(x,y,z).
8(u, v, w)
If u = Sin-Il( '\+ 2Yg + 3~) then find =, + YUy + zu z :
X + Y +z(b) dy 3Solve -=xy -xy.
dx
3(a)
4(a)
Find the largest Eigen value & corresponding Eigen vector 0
(b)using Rayleigh's power method. Perform 3 Iterations.J f a substance cools from 370K to 330K in 10 Minutes. Whenof the surrounding air is 290K. Find the temperature of the siMinutes.Show the linear transformation YI = 2x, + x2 + x) , Y2 = XI + X2 + 2X3 '
Y3 ::::;XI - 2x) is regular hence find inverse transform.Solve the system of equations using Gauss Seidel method 3x + 20 Y - z = -] 8,2x - 3y + 20z = 25, 20x + y - 2z ::::;17 . Perform 3 Iterations.Find the orthogonal trajectories of the family of cardioids r = a (1 + Cos(B)) ,where' a' is the parameter.
Reduce the matrix A ::::;I-19 71 to diagonal form.1-42 16- -
Solve (x2 + y3 +6xylx+ y2 x dy = O.
Solve the system of equations using Gauss Elimination method X + 2y + z::::; 3,2x+3y+3z = 10, 3x- y+3z::::; 13.
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Course Outcomes
~-.-.. -._..,.... ._ ..._- .- _.-I Apply nth derivate to obtain Taylor andf Maclaurin's series of a given function.
CO I: Evaluate the radius of curvature forcartesian, parametric polar and pedale uation.
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Apply partial derivatives to calculate rates of!~CO.2: change of multivariate fU. nctions. Evaluate
I definite Integrals.- - -'rAnalyze position;-~eloCltY:arid acceleration
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, EvnlunLc curl and divergence of a vector ,~ tII C04' valued functions which has various I 'I' I'
I 2 ·3 - l -1. -:.-!- ~_~_~_~_~a_~~~;~_in_e_'I:tri~~ty,_mag_~e~sm ~~.~_ _. .. -1-... :I
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: I Solve first order ordinary DifferentialI C05: I ~~~~i~Og~Sand model Newton's law of 2 I 3 ,- I- 1- I - J _=_tl I I __I'
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-1_" I-_-~ .I COG: ! solving systems of linear equations used inI ! the different areas of Linear Al ebra.
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KEYWORDS
L4
LS
summarize, describe, interpret, contrast, predict, associate, distinguish. estimate, differentiate, discuss, extendApply, demonStrate, calculate, complete, 'illustrate, show, solve, examine, modify:-.:e"ite; change, classifY,"ex eriment, discover.
List, define, tell, describe, identify, show, label, collect, examine, tabulate, quote, name, who, when, where, etc,
! Analyze, separate, order, explain, connect, classify, arrange, divide, compare, select, explain, infer.- "ASSess, cleCi"de;-;:ank, grade, tesl,-measure:-i-ecol11l11end;-convince, select, judge, explain, discriminate, support,
conclude, com are, summarize.
POI Engineering knowledge; P02 . Problem analysis; P03 " Design/development OJSOII;~iOIlS; IP04 " Conduct investigations of complex problems; POS " Modern tool usage; POG - The Engineer and society; 1'07- !Environment and sustainabllity; P08 Ethics; P09 Individual and team work; IPO 10" Communication; PO 11 - Project management and finance; PO 12 - Life-long learning I
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