[Question Paper] Advanced SQL (Old Course) [April / 2015]
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The document is an advanced SQL examination paper from April 2015, consisting of various mathematical and computational problems divided into six questions. Candidates are required to attempt all of question 1 and any four from questions 2 to 6, with each question carrying equal marks. Topics covered include solving equations, interpolation, numerical methods, and estimating sales trends.
![A d v a n c e d S Q L
Q u e s t i o n P a p e r ( A p r i l – 2 0 1 5 ) [ O l d C o u r s e ]
1 | Page
M u m b a i B . S c . I T S t u d y
F a c e b o o k | T w i t t e r | I n s t a g r a m | G o o g l e + | Y o u T u b e
– Kamal T.
Time: 3 Hours Total Marks: 100
N.B.: (1) Questions No. 1 is Compulsory.
(2) Attempt any four questions from Q. No. 2 to 6.
(3) All questions carry equal marks.
Q.1 Attempt The Following Questions: (20 Marks)
(A) Using Gauss Jordon Method, Solve 𝑥 + 2𝑦 + 6𝑧 = 22, 3𝑥 + 4𝑦 + 𝑧 = 26, 6𝑥 − 𝑦 =
19.
(5)
(B) Find 𝑓(15) by Lagrange’s Interpolation formula also fit polynomial for the data: –
X 10 20 14 16
F(x) 0.25 0.2 0.15 0.1
(5)
Q.2 Attempt The Following Questions: (20 Marks)
(A) Using Tailor’s Series method the solution of
𝑑𝑦
𝑑𝑥
= 3𝑥 + 𝑦2
𝑎𝑛𝑑 𝑦 = 1, 𝑤ℎ𝑒𝑛 𝑥 = 0.
Find the value of y for x=0.1 correct up to 4 decimal places.
(5)
(B) Find the root of the equation 𝑓(𝑥) = 3𝑥 − cos 𝑥 − 1 = 0 by using Newton Raphson’s
Method with initial value 𝑥0 = 1.
(5)
Q.3 Attempt The Following Questions: (20 Marks)
(A)
Calculate up to 5 decimal places ∫ 𝑙𝑜𝑔 𝑒
5.2
4
𝑥𝑑𝑥 by using Simpon’s (
3
8
)
𝑡ℎ
rule taking 6
sub interval.
(5)
(B) Apply Euler’s modified method to solve
𝑑𝑦
𝑑𝑥
= 𝑥 + 3𝑦 subject to 𝑦(0) = 1 and hence
find an approximate value of y when x=1 taking h=0.2.
(5)
Q.4 Attempt The Following Questions: (20 Marks)
(A) Fit a straight line trend the following data estimate the sales for the year 2007.
Year 1998 1999 2000 2001 2002 2003 2004 2005
Sales in ‘000 RS 120 124 126 130 128 132 138 137
(5)
(B) Solve graphically:
Minimize 𝑧 = 600𝑥1 + 400𝑥2
Subject To 10𝑥1 + 𝑥2 ≥ 16
3𝑥1 + 𝑥2 ≥ 24
𝑥1 ≥ 0, 𝑥2 ≥ 0
(5)](https://image.slidesharecdn.com/sql-qpoldcourseapr-2015-170717052004/85/Question-Paper-Advanced-SQL-Old-Course-April-2015-1-320.jpg)
![A d v a n c e d S Q L
Q u e s t i o n P a p e r ( A p r i l – 2 0 1 5 ) [ O l d C o u r s e ]
2 | Page
M u m b a i B . S c . I T S t u d y
F a c e b o o k | T w i t t e r | I n s t a g r a m | G o o g l e + | Y o u T u b e
– Kamal T.
Q.5 Attempt The Following Questions: (20 Marks)
(A) Consider a table of values of the function 𝑓(𝑥) = 𝑥3
for 𝑥 = 0(2)10. Use Newton’s
Backward Interpolation Formula find (8.5)3
.
(5)
(B) Find a real root of the equation 𝑥3
− 2𝑥 − 5 = 0 by method of false position concept
to three decimal places.
(5)
Q.6 Attempt The Following Questions: (20 Marks)
(A) Using Trapezoidal Rule. Estimate approximately the area of the cross section of a river
80 meters wide. The depth d (in meters) at a distance x from one bank is given by the
following table:
x 0 10 20 30 40 50 60 70 80
d 0 4 7 9 12 15 14 8 3
(5)
(B) Suppose that you have the task of measuring the lengths of a bridge and river and
come up with 9999 and 9 cm respectively. If the true values are 10, 000 and 10 cm
respectively, compare:
(i) the error, and (ii) the percentage relative error in each case.
(5)](https://image.slidesharecdn.com/sql-qpoldcourseapr-2015-170717052004/85/Question-Paper-Advanced-SQL-Old-Course-April-2015-2-320.jpg)
[Question Paper] Advanced SQL (Old Course) [April / 2015]
- 1. A d v a n c e d S Q L Q u e s t i o n P a p e r ( A p r i l – 2 0 1 5 ) [ O l d C o u r s e ] 1 | Page M u m b a i B . S c . I T S t u d y F a c e b o o k | T w i t t e r | I n s t a g r a m | G o o g l e + | Y o u T u b e – Kamal T. Time: 3 Hours Total Marks: 100 N.B.: (1) Questions No. 1 is Compulsory. (2) Attempt any four questions from Q. No. 2 to 6. (3) All questions carry equal marks. Q.1 Attempt The Following Questions: (20 Marks) (A) Using Gauss Jordon Method, Solve 𝑥 + 2𝑦 + 6𝑧 = 22, 3𝑥 + 4𝑦 + 𝑧 = 26, 6𝑥 − 𝑦 = 19. (5) (B) Find 𝑓(15) by Lagrange’s Interpolation formula also fit polynomial for the data: – X 10 20 14 16 F(x) 0.25 0.2 0.15 0.1 (5) Q.2 Attempt The Following Questions: (20 Marks) (A) Using Tailor’s Series method the solution of 𝑑𝑦 𝑑𝑥 = 3𝑥 + 𝑦2 𝑎𝑛𝑑 𝑦 = 1, 𝑤ℎ𝑒𝑛 𝑥 = 0. Find the value of y for x=0.1 correct up to 4 decimal places. (5) (B) Find the root of the equation 𝑓(𝑥) = 3𝑥 − cos 𝑥 − 1 = 0 by using Newton Raphson’s Method with initial value 𝑥0 = 1. (5) Q.3 Attempt The Following Questions: (20 Marks) (A) Calculate up to 5 decimal places ∫ 𝑙𝑜𝑔 𝑒 5.2 4 𝑥𝑑𝑥 by using Simpon’s ( 3 8 ) 𝑡ℎ rule taking 6 sub interval. (5) (B) Apply Euler’s modified method to solve 𝑑𝑦 𝑑𝑥 = 𝑥 + 3𝑦 subject to 𝑦(0) = 1 and hence find an approximate value of y when x=1 taking h=0.2. (5) Q.4 Attempt The Following Questions: (20 Marks) (A) Fit a straight line trend the following data estimate the sales for the year 2007. Year 1998 1999 2000 2001 2002 2003 2004 2005 Sales in ‘000 RS 120 124 126 130 128 132 138 137 (5) (B) Solve graphically: Minimize 𝑧 = 600𝑥1 + 400𝑥2 Subject To 10𝑥1 + 𝑥2 ≥ 16 3𝑥1 + 𝑥2 ≥ 24 𝑥1 ≥ 0, 𝑥2 ≥ 0 (5)
- 2. A d v a n c e d S Q L Q u e s t i o n P a p e r ( A p r i l – 2 0 1 5 ) [ O l d C o u r s e ] 2 | Page M u m b a i B . S c . I T S t u d y F a c e b o o k | T w i t t e r | I n s t a g r a m | G o o g l e + | Y o u T u b e – Kamal T. Q.5 Attempt The Following Questions: (20 Marks) (A) Consider a table of values of the function 𝑓(𝑥) = 𝑥3 for 𝑥 = 0(2)10. Use Newton’s Backward Interpolation Formula find (8.5)3 . (5) (B) Find a real root of the equation 𝑥3 − 2𝑥 − 5 = 0 by method of false position concept to three decimal places. (5) Q.6 Attempt The Following Questions: (20 Marks) (A) Using Trapezoidal Rule. Estimate approximately the area of the cross section of a river 80 meters wide. The depth d (in meters) at a distance x from one bank is given by the following table: x 0 10 20 30 40 50 60 70 80 d 0 4 7 9 12 15 14 8 3 (5) (B) Suppose that you have the task of measuring the lengths of a bridge and river and come up with 9999 and 9 cm respectively. If the true values are 10, 000 and 10 cm respectively, compare: (i) the error, and (ii) the percentage relative error in each case. (5)