Download PTU (I.K. Gujral Punjab Technical University Jalandhar (IKGPTU) ) BE/BTech CSE/IT (Computer Science And Engineering/ Information Technology) 2020 March 3rd Sem BTAM 302 Mathematics Iii Previous Question Paper
1 | M-70808 (S2)-841
Roll No. Total No. of Pages : 03
Total No. of Questions : 18
B.Tech.(CSE/IT) (2012 to 2017)
(Sem.?3)
MATHEMATICS ? III
Subject Code : BTAM-302
M.Code : 70808
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks
each.
2. SECTION-B contains FIVE questions carrying FIVE marks each and students
have to attempt any FOUR questions.
3. SECTION-C contains THREE questions carrying TEN marks each and students
have to attempt any TWO questions.
SECTION-A
Answer briefly :
1. Write Euler?s formula of Fourier series.
2. Define Laplace transforms.
3. Define the Homogeneous partial differential equations.
4. Define analytic functions and write its Cauchy-Riemann equations.
5. Define Binomial and Poisson distributors.
6. Define Null and Alternative hypothesis.
7. What is the difference between Euler?s and Runge-Kutta methods for solving the
differential equations?
8. Write the difference between chi-square and t-distributions.
9. Write the Laplace transform of t
2
sin 2t
10. Define eigen value.
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1 | M-70808 (S2)-841
Roll No. Total No. of Pages : 03
Total No. of Questions : 18
B.Tech.(CSE/IT) (2012 to 2017)
(Sem.?3)
MATHEMATICS ? III
Subject Code : BTAM-302
M.Code : 70808
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks
each.
2. SECTION-B contains FIVE questions carrying FIVE marks each and students
have to attempt any FOUR questions.
3. SECTION-C contains THREE questions carrying TEN marks each and students
have to attempt any TWO questions.
SECTION-A
Answer briefly :
1. Write Euler?s formula of Fourier series.
2. Define Laplace transforms.
3. Define the Homogeneous partial differential equations.
4. Define analytic functions and write its Cauchy-Riemann equations.
5. Define Binomial and Poisson distributors.
6. Define Null and Alternative hypothesis.
7. What is the difference between Euler?s and Runge-Kutta methods for solving the
differential equations?
8. Write the difference between chi-square and t-distributions.
9. Write the Laplace transform of t
2
sin 2t
10. Define eigen value.
2 | M-70808 (S2)-841
SECTION-B
11. Express f (x) = x as a half-range cosine series in 0 < x < 2.
12. Using the Laplace transform, evaluate
3
0
sin
t
te t dt
?
?
?
13. Solve the following equation
3 3 3
3 2 2
4 4 0
z z z
x x y x y
? ? ?
? ? ?
? ? ? ? ?
14. a) Service calls come to a maintenance center, according to a Poisson process and, on
the average, 2.7 calls come per minute. Find the probability that (a) no more than 4
calls come in any minute ; (b) fewer than 2 calls came in any minute.
b) Find the value of c such that P (|X? 25| < c) = 0.9544 where X ~ N (25, 36). Given
that P (Z < ? 2) = 0.0228 and P (Z < ? 1.69) = 0.0456, Z being a standard normal
variate.
15. A survey of 240 families with 4 children each revealed the following distribution :
No. of boys 4 3 2 1 0
No. of families 10 55 105 58 12
Is the result consistent with the hypothesis that male and female births are equally
probable? Use chi-square value for 4 & 5 d.f. at 5%level of significance is 9.49 & 11.07
respectively.
SECTION-C
16. Prove that the function f (z) define by
3 3
2 2
(1 ) (1 )
( )
x i y i
f z
x y
? ? ?
?
?
, z ? 0 and f (0) = 0 is
continuous and the Cauchy-Riemann equations are satisfied at the origin, yet f ? (0) does
not exist.
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1 | M-70808 (S2)-841
Roll No. Total No. of Pages : 03
Total No. of Questions : 18
B.Tech.(CSE/IT) (2012 to 2017)
(Sem.?3)
MATHEMATICS ? III
Subject Code : BTAM-302
M.Code : 70808
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks
each.
2. SECTION-B contains FIVE questions carrying FIVE marks each and students
have to attempt any FOUR questions.
3. SECTION-C contains THREE questions carrying TEN marks each and students
have to attempt any TWO questions.
SECTION-A
Answer briefly :
1. Write Euler?s formula of Fourier series.
2. Define Laplace transforms.
3. Define the Homogeneous partial differential equations.
4. Define analytic functions and write its Cauchy-Riemann equations.
5. Define Binomial and Poisson distributors.
6. Define Null and Alternative hypothesis.
7. What is the difference between Euler?s and Runge-Kutta methods for solving the
differential equations?
8. Write the difference between chi-square and t-distributions.
9. Write the Laplace transform of t
2
sin 2t
10. Define eigen value.
2 | M-70808 (S2)-841
SECTION-B
11. Express f (x) = x as a half-range cosine series in 0 < x < 2.
12. Using the Laplace transform, evaluate
3
0
sin
t
te t dt
?
?
?
13. Solve the following equation
3 3 3
3 2 2
4 4 0
z z z
x x y x y
? ? ?
? ? ?
? ? ? ? ?
14. a) Service calls come to a maintenance center, according to a Poisson process and, on
the average, 2.7 calls come per minute. Find the probability that (a) no more than 4
calls come in any minute ; (b) fewer than 2 calls came in any minute.
b) Find the value of c such that P (|X? 25| < c) = 0.9544 where X ~ N (25, 36). Given
that P (Z < ? 2) = 0.0228 and P (Z < ? 1.69) = 0.0456, Z being a standard normal
variate.
15. A survey of 240 families with 4 children each revealed the following distribution :
No. of boys 4 3 2 1 0
No. of families 10 55 105 58 12
Is the result consistent with the hypothesis that male and female births are equally
probable? Use chi-square value for 4 & 5 d.f. at 5%level of significance is 9.49 & 11.07
respectively.
SECTION-C
16. Prove that the function f (z) define by
3 3
2 2
(1 ) (1 )
( )
x i y i
f z
x y
? ? ?
?
?
, z ? 0 and f (0) = 0 is
continuous and the Cauchy-Riemann equations are satisfied at the origin, yet f ? (0) does
not exist.
3 | M-70808 (S2)-841
17. Determine the largest eigen value and the corresponding eigen vector of the matrix
2 1 0
1 2 1
0 1 2
? ? ?
? ?
? ?
? ?
? ? ?
? ?
using the power method. Take [1, 0, 0]
T
as initial eigen vector.
18. a) Using Euler?s method, find an approximate value of y corresponding to x = 0.5 given
that
dy
x y
dx
? ? , and y = 1, where x = 0. Use step size 0.1
b) Apply Gauss elimination method to solve the equations
x + 4y ? z = ? 5
x + y ? 6z = ? 12
3x ? y ? z = 4.
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 21 March 2020