Download PTU B-Tech CSE-IT 2020 Dec 1st Sem 75362 Mathematics I Question Paper

Download PTU (I.K.Gujral Punjab Technical University (IKGPTU)) B-Tech (Bachelor of Technology) (CSE-IT)- Computer Science Engineering -Information Technology 2020 December 1st Sem 75362 Mathematics I Previous Question Paper

Roll No.
Total No. of Pages : 02
Total No. of Questions : 08
B.Tech. (CSE / IT) (2018 & Onwards) (Sem.?1)
MATHEMATICS-I
Subject Code : BTAM-104-18
M.Code : 75362
Time : 2 Hrs. Max. Marks : 30
INST RUCT IONS T O CANDIDAT ES :
1 .
Attempt any FIVE question (s), ea ch que stion c arrie s 6 ma rks .
1)
a) Expand f (x) = esin x upto the term containing x4.
b) Show that f (x) = sin x (1 + cos x) has a maximum at x = /3.
2
2
x
y
2)
a) Find the volume of the solid generated by revolving
1, a b about the
2
2
a
b
major axis.
b) Using Gamma function evaluate
x exp ( 3
x ) dx
.
0
5 4
1
2
3 2
3)
a) If A
, B
and C
, then show that (AB)C = A(BC).
1
1
1
3
1 4
b) Solve the equations using Cramer rule 2x + 3y + 4z = 11, x + 5y + 7z = 15, 3x + 11y +
13z = 25.
8
1 4
4)
a) Find the rank of the matrix 4
4
7 .
1
8
4
b) Solve using Gauss elimination method x ? y + 2z = 3, x + 2y + 3z = 5, 3x ? 4y?5z = ?13.
5)
a) Express v = (2, ?5, 3) in R3 as a linear combination of vectors u1 = (1, ?3, 2),
u2 = (2, 4, ?1), u3 = (1, ?5, 7).
b) Determine whether the vectors u1 = 2t2 + 4t ? 3 and u2 = 4t2 + 8t ? 6 are linearly
dependent?
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6)
a) Suppose the mapping F : R2 R2 is defined by F (x, y) = (x + y, x).
Using the properties of matrices, show that F is a linear mapping.
b) Find the dimension and a basis of the subspace W of P3 (t) spanned by
u = t3 + 2t2 ? 3t + 4, v = 2t3 + 5t2 ? 4t + 7, w = t3 + 4t2 + t + 2.
1 4
7)
Find the characteristic equation of the matrix
and hence compute A?1.
2 3
5
3
7
8)
Reduce the matrix 3 26
2 to the diagonal form.
7
2 10
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