A 0000MAT101121904 Pages: 3

Reg No.: Name:
APJ ABDUL KALAM TECHNOLOGICAL UNIVERSITY

B.Tech 51 (Special Improvement) Examination January 2021 (2019 scheme)

Course Code: MAT101
Course Name: LINEAR ALGEBRA AND CALCULUS
(2019-Scheme)

Max. Marks: 100 Duration: 3 Hours
PARTA
Answer all questions, each carries 3 marks.
1 1 -1 0 (3)
Determine the rank of the matrix 4 = |1 3 -1
5 3 -2
2 What kind of conic section is represented by the quadratic form (3)

2 2 ⋅⋅ ⋅
⊽∍∊∣−⊦∊∍∊∎∍∁≳−⊦⊽↙⊺≳−−⊋⊖⊖⊺⊺⋮⋯⊱∱∘⋯∥↥⋯↧∘∁⇣⋯∘⋯∁∂⊔∘↾⋯⋅

Find the derivative of ഥി with respect to t along the 4)

path x = ५12, y=2at.

4 Let f(x, 9) = J3x+2y 29, find the slope of the surface z= f(x,y) in the 4)
y -direction at the point (2, 5).
5 aaa (3)
Evaluate | | [ (ट +xz+ xy)dxdydz
000
6 Use polar co-ordinates to evaluate (3)

1 പി 3

ர [ (2 + 32 | 2
-| 0

7 ௦௦ 1 (3)
Test the convergence of 2೨. നി
k=1(2k +3

8 ௦௦ 1 (3)
Examine whether the series convergence or not >.

६-1 (In(k 1)"

9 ⋅ ⋅ ∙ 1 (3)
Find the Maclaurin series of i up to third degree term.

10 Find the Fourier Half Range sine series of f(x)=x in,O
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