Download PTU (I.K. Gujral Punjab Technical University Jalandhar (IKGPTU) B.Sc (Non-Medical) 2020 March Previous Question Papers
Roll No. Total No. of Pages : 02
Total No. of Questions : 09
B.Sc. (Non Medical) (2018 Batch) (Sem.?2)
THEORY OF EQUATIONS
Subject Code : BSNM-206-18
M.Code : 76304
Time : 3 Hrs. Max. Marks : 50
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of TEN questions carrying ONE 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
1) Write briefly :
(a) What do you mean by rate of convergence?
(b) What is the nature of convergence of Newton?s method?
(c) Define floating point number.
(d) If there is only one change in sign in f (x), then how many positive root (s) will
f (x)have?
(e) Find the absolute error if the number X= 0.00545828 is truncated to three decimal
digits.
(f) Without actual division, find the remainder when x
3
+ 6x
2
? 5x + 3 is divided by x + 2.
(g) Form an equation whose roots are the roots of the equation x
4
?3x
2
+ 7x ? 1 = 0 with
their signs changed.
(h) Find the roots of the equation x
3
?12x
2
+ 44x ? 48 = 0, given that the roots are in A.P.
(i) Use synthetic division to compute f (5) where f (x) = x
5
? 4x
4
? 7x
3
+ 11x ? 13.
(j) Show that x
3
+3x + 2 = 0 has two non-real roots.
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1 | M-76304 (S105)-2629
Roll No. Total No. of Pages : 02
Total No. of Questions : 09
B.Sc. (Non Medical) (2018 Batch) (Sem.?2)
THEORY OF EQUATIONS
Subject Code : BSNM-206-18
M.Code : 76304
Time : 3 Hrs. Max. Marks : 50
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of TEN questions carrying ONE 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
1) Write briefly :
(a) What do you mean by rate of convergence?
(b) What is the nature of convergence of Newton?s method?
(c) Define floating point number.
(d) If there is only one change in sign in f (x), then how many positive root (s) will
f (x)have?
(e) Find the absolute error if the number X= 0.00545828 is truncated to three decimal
digits.
(f) Without actual division, find the remainder when x
3
+ 6x
2
? 5x + 3 is divided by x + 2.
(g) Form an equation whose roots are the roots of the equation x
4
?3x
2
+ 7x ? 1 = 0 with
their signs changed.
(h) Find the roots of the equation x
3
?12x
2
+ 44x ? 48 = 0, given that the roots are in A.P.
(i) Use synthetic division to compute f (5) where f (x) = x
5
? 4x
4
? 7x
3
+ 11x ? 13.
(j) Show that x
3
+3x + 2 = 0 has two non-real roots.
2 | M-76304 (S105)-2629
SECTION-B
2. Discuss various types of errors and their sources.
3. Solve x
3
? 27x + 54 = 0 using Cardan?s method.
4. Solve x
4
+ 15x
3
+ 70x
2
+ 120x + 64 = 0 when the roots are in G.P.
5. Find the iterative formula or finding
3
N , where N is a real number, using Newton-
Raphson formula. Hence evaluate
3
28 .
6. Find the equation whose roots exceed by 2 the roots of the equation
4x
4
+ 32x
3
+ 83x
2
+ 76x + 21 = 0. Hence find the roots of the equation.
SECTION-C
7. Solve the equation x
4
+ 12x
3
+ 54x
2
+ 96x + 40 = 0 by Ferrari?s method.
8. (a) Show that the equation 2x
7
+ 3x
4
+ 3x + k = 0 has at least four imaginary roots for all
values of k.
(b) If the product of two roots of x
4
+ px
3
+ qx
2
+ rx + s = 0 is equal to the product of the
other two. then show that r
2
= p
2
s.
9. (a) Find a root of the equation x
3
? 2x ? 5 = 0 using secant method correct to three places
of decimal.
(b) Use the iteration method to find a root of the equation x
3
+ x
2
? 100 = 0, correct to
four decimal places.
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 02 April 2020