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[QUOTE=ijt.dolora@gmail.com;267929][B][U]Name of the Organaisation [/U][/B]: MIT College of Engineering - Pune (mitcoe.ac.in)
[B][U]Type of Announcement [/U][/B]: Engineering Mathematics –I
[B][U]Home Page [/U][/B]: [URL]http://www.mitcoe.ac.in/[/URL]
[CENTER][B]Engineering Mathematics –I[/B]
[/CENTER]
[B][U]Instruction to candidate [/U][/B]:
1. Attempt Q. No. 1or 2, Q. No. 3 or 4.
2. Neat diagrams must be drawn whenever necessary.
3. Figures to the right indicate full marks.
4. Use of non programmable electronic pocket calculator, Mollies charts, stream Tables and statistical tables are allowed.

[B][U]Do Either or Nor Options [/U][/B]:
1. The Vertices of the triangle ABC are 1+2i, 4-2i, 1-6i. Prove that ABC is isosceles triangle and find the lengths of the sides.
2. Find the Eigen values and corresponding Eigen vectors of the matrix 
3. For what values of K the equations (4)
x+y+z=1
x+2y+4z=K
x+4y+10z=K[FONT=&quot]²[/FONT] are consistent and in each case find solution
4. Given sin h (1.5) = 2.1293, cos h (1.5) = 2.3524. Calculate approximately the value of cos h (1.505) by Taylor’s theorem
5. Find nth derivative of y = x/x[FONT=&quot]²+a[/FONT][FONT=&quot]²[/FONT]
6. if u = x[FONT=&quot]²[/FONT] + y[FONT=&quot]²[/FONT] where x = r sin[FONT=&quot]θ[/FONT] + cos[FONT=&quot]θ[/FONT] and y = r cos[FONT=&quot]θ [/FONT] calculate [FONT=&quot][FONT=&quot]ⱷu/[/FONT][/FONT][FONT=&quot][FONT=&quot][FONT=&quot]ⱷv[/FONT][/FONT] [/FONT] and [FONT=&quot]ⱷu/[/FONT][FONT=&quot]ⱷv[/FONT]
7. Discuss the maxima and minima of f (x, y ) = x[FONT=&quot] ³[/FONT]+ xy[FONT=&quot]²[/FONT]+21x – 12x[FONT=&quot]²[/FONT]-2y[FONT=&quot]²[/FONT].
8. Show that the stationary values of a[FONT=&quot]³[/FONT]x+b[FONT=&quot]³[/FONT]y+c[FONT=&quot]³[/FONT]z is given by x = a+b+c/a, y= a+b+c/b,z=a+b+c/c where  1/x+1/y+1/z= 1
9. If Z= 2xy-3xy , x increases at the rate of 2cm/sec as it passes through 3 cm. show that if y is passing through y=1 cm , y must decreases at the rate 32/15 cm/sec in order that z shall remain constant.

[B][U]See more questions download here [/U][/B]: [URL="http://www.mitcoe.ac.in/downloads/cees/Final%20FE%20Qp.pdf"]www.mitcoe.ac.in/downloads/cees/Final%20FE%20Qp.pdf[/URL][/QUOTE]

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