PTU Punjab Technical University B-Tech May? 2019 Question Papers 1st Semester May Computer Science Engineering (CSE)
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Roll No.
Total No. of Pages : 03
Total No. of Questions : 18
B.Tech. (CSE/IT) (2018 Batch) (Sem.?1)
MATHEMATICS-I
Subject Code : BTAM-104-18
M.Code : 75362
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
1.
SECTION-A is COMPULSORY consisting of TEN questions carrying T WO marks
each.
2.
SECTION - B & C have FOUR questions each.
3.
Attempt any FIVE questions from SECTION B & C carrying EIGHT marks each.
4.
Select atleast T WO questions EACH from SECTION - B & C.
SECTION-A
1)
Can Rolle's theorem be applied to the function f (x) = 2 + (x ? 1)2/3, x [0, 2].
2)
Define beta function.
x cos x sin x
3)
Evaluate lim
2
x0
x sin x
x 3 2 y x 0
7
4)
Find the values of x, y, z, a which satisfy the relation
.
z 1
4a 6
3
2a
1 1
5)
Find adjoint of
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2
0
6)
Define basis of vector spaces.
7)
Give the statement of rank nullity theorem.
8)
Give any two properties of Eigen values.
9)
Define symmetric matrix with an example.
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2
1
10) Find sum and product of latent roots of the matrix
2 3
.
SECTION-B
11) a) Expand f (x) = sin?1x by Maclaurin's theorem.
a
x
x a
b) Evaluate lim
.
x
a
xa x a
1
1
12) a) Evaluate the integral
dx
in terms of gamma function.
4
0
1 x
b) Find maxima of f (x, y) = 2 (x2 ? y2) ? x4 + y4.
1 a
1
1
1
1
1
13) a) Prove that
1 1 b
1 abc 1
.
a
b
c
1
1 1 c
b) Solve the equations x +y + z = 1, x +2y + 3z = 6, x + 3y + 4z = 6 using Cramer's rule.
14) a) Are the vectors (2, 1, 1), (2, 0, ?1), (4, 2, 1) linearly dependent.
5
3
7
b) Find the rank o www.FirstRanker.com
f the matrix : 3 26
2
7
2 10
SECTION-C
2
0
1
15) Show that the matrix 5
1
0 satisfies the equation A3 ? 6A2 + 11A ? I = 0.
0
1
3
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x
x y
16) Let T : R3 R2 be the linear transformation defined by T y
, then find the
x z
z
matrix representation of T w.r.t. the ordered basis X = {(1, 0, 1), (1, 1, 0), (0, 1, 1)}T in R3
and Y = {(1, 0), (0, 1)}T in R2.
4
2
1
17) a) Is the matrix 6
3 4 orthogonal ?
2
1 0
1
2
3
b) Write the matrix 4
5
6 as the sum of symmetric and skew symmetric matrices.
7
8
9
1
2
2
18) Reduce the matrix
1
2
1 to the diagonal form.
1
1
0
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NOTE : Disclosure of Identity by writing Mobile No. or Making of passing request on any
page of Answer Sheet will lead to UMC against the Student.
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This post was last modified on 04 November 2019