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SCHOOL OF DISTANCE EDUCATION - UNIVERSITY OF CALICUT MULTIPLE CHOICE QUESTIONS

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SCHOOL OF DISTANCE EDUCATION - UNIVERSITY OF CALICUT MULTIPLE CHOICE QUESTIONS
School Of Distance Education
SCHOOL OF DISTANCE EDUCATION - UNIVERSITY OF CALICUT
B.Sc DEGREE PROGRAMME MATHEMATICS (CORE COURSE)
SIXTH SEMESTER - THEORY OF EQUATIONS & FUZZY SETS
MULTIPLE CHOICE QUESTIONS
Module- I
(1) The number of real zeros of the polynomial function x 2  1 is:
A)1
B) 0
C) 2
D) None of these.
(2) A polynomial equation in x of degree n always have:
A ) n distinct roots
B) n real roots
C) n complex roots
D) None of these
(3) If  2  3 i is a root of the polynomial equation p ( x )  0 , then another root is:
A) 2  3 i
B) 2  3 i
C)  2  3i
D) 3  2 i
3
(4) A zero of the polynomial x  2 x  i equals:
A ) i
B) 1
C) 1  i
D) None of these.
(5) If  is an r  multiple root of f ( x )  0 , then which of the following polynomial has  as an
(r  1)  multiple root ?
A ) f 2 ( x)  0
B) f / ( x)  0
1
x
D) f ( x )  0
C) f ( )  0
(6) If  ,  are the roots of ax 2  bx  c  0 , then    equals:
A)
b
a
B)
c
a
C)
a
b
D)
b
a
(7) If  ,  ,  are the roots of x 3  px 2  qx  r  0 , then      equals:
A)
p
q
B)  p
C) q
D)  q
1 1 1
  equals:
  
q
q
p
q
A)
B)
C)
D)
r
r
r
p
1
1
1
(9) If  ,  ,  are the roots of x 3  px 2  qx  r  0 , then
equals:


  
p
p
p
q
A)
B)
C)
D)
r
r
r
q
3
(10) A polynomial equation whose roots are 3 times those of the equation 2 x  5 x 2  7  0 is:
A) 3 x 3  15 x 2  21  0
B) 2 x 3  15 x 2  189  0
C) 2 x 3  15 x 2  189  0
D) None of these
(11) If  is a root of a reciprocal equation f ( x )  0 , then another root of f ( x )  0 is:
1
1
1
A)
B) 2
C) 
D)



(8) If  ,  ,  are the roots of x 3  px 2  qx  r  0 , then
Theory of Equations & Fuzzy Sets
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School Of Distance Education
(12) The equation x 3  2 x  3  0 has:
A) one positive real root
B) one negative real root
C) three real roots
D) None of these
10
6
(13) Greatest possible number of real roots of x  10 x  5 x 3  x  4  0 is :
A) 6
B) 5
C) 10
D) None of these
5
2
(14) How many real roots are there for the equation x  6 x  4 x  5  0 ?
A) 5
B) 1
C) 3
D) 0
(15) In any polynomial equation f ( x )  0 , the number of real positive roots cannot exceed the
number of changes in the signs of the coefficients of the terms in f (x ), and the number of real
negative roots cannot exceed the number of changes in the signs of the coefficients of :
A)  f (x )
B) f (  x )
C)  f (  x )
D) None of these
(16) Given that a polynomial p ( x )  0 cannot be solved algebraically in terms of a finite number
of additions, subtractions, multiplications, divisions, and root extractions. Then possible degree
of p (x ) is:
A) 3
B) 4
C) 5
D) None of these
5  2 is given by _____
A) x  14 x  9  0
B) x  14 x 2  9  0
C) x 4  14 x  9  0
D) x 4  14 x 2  9  0
(18) If 3 is a double root of the equation 8 x 3  47 x 2  66 x  9  0 , the third root is:
1
1
A)
B)
C) 8
D)  8
8
8
(19) If f ( x )  0 is a reciprocal equation of first type and odd degree, then which of the
(17) The equation with rational coefficients, one of whose roots is
4
2
4
following is always a root?
.
A) x  1
B) x  0
C) x  i
D) x  1
4
3
(20) Given that the product of two roots of the equation x  2 x  25 x 2  26 x  120  0 is 8.
The roots are __________________
8
3
C)  4,  2,  3,  5
A ) 4, 2, 8,
1. B
8. A
15. B
2. D
9. B
16. C
Theory of Equations & Fuzzy Sets
3. C
10. B
17. A
B) 4, 2,  3,  5
D) None of these.
Answer Key
Module – I
4. A
5. B
11. D
12. B
18. A
19. D
6. D
13. A
20. B
7. C
14. C
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School Of Distance Education
SCHOOL OF DISTANCE EDUCATION - UNIVERSITY OF CALICUT
B.Sc DEGREE PROGRAMME MATHEMATICS (CORE COURSE)
SIXTH SEMESTER
THEORY OF EQUATIONS & FUZZY SETS
MODULE II: FUZZY SET THEORY : OBJECTIVE TYPE QUESTIONS WITH ANSWER KEY.
1. Let ⊂ be a crisp set. Then the Law of Excluded Middle is ----a)
∪ =
b) =
c) ∪ =
d) ∪ =
2. Generalizations of ordinary fuzzy sets which involve fuzzy sets defined within a universal set whose
elements are ordinary fuzzy sets constitute a --------fuzzy set.
a) Level 1
b) Level 2
3) Level 3
4) Level 4
3. Let h(A) denote the height of a fuzzy set A. A is called a normal fuzzy set if
a) h(A)=0
b)h(A)=1
c)h(A)<1
d)h(A)> 1
4. Let A be a fuzzy set. Then 1-cut of A is usually called
a) Support of A
b) height of A c) Core of A
d) cut of A
5. The cut of the complement of a fuzzy set A is always same as the complement of the
a) Strong cut of A b)strong cut of
c) Strong ( − ) cut of A d) Strong (1- ) cut of A c
6. The boundary condition satisfied by the standard fuzzy complement is
a) c(0)=1 and c(1)=1 b) c(0)=0 and c(1)=1 c)c(0)=0 and c(1)=0
d) c(0)=1 and c(1)=0
7. Involutive property of the standard fuzzy complement c, for each a∈ [ , ] is ---a) c(c(a))=c(a)
b) c(c(a))= 1
c) c(c(a))=0
d) c(c(a))=a
8. Each fuzzy complement has at most ------equilibrium.
a) 1 b)2
c) 3
d) None of these
9. Yager Class of fuzzy complement is defined as
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
( )=( − )
a)
b) ( ) = ( − ) c) ( ) = ( − ) d) None
Equilibrium of a fuzzy complement c is a solution of the equation
a) c(a)-a=1
b) c(a)-a=2
c) c(a)=2a
d)c(a)-a=0
For a∈ [ , ], the boundary condition for the t-norm function i is
a) i(a,1)=0
b)i(a,0)=a
c) i(a,1)=a
d) i(a,0)= 1
For standard fuzzy intersection, which of the following hold?
a) i(a,b)=min(a,b)
b)i(a,b)=ab
c)i(a,b)=a-b
d)None
Example of an idempotent t-norm is
a) Algebraic Product b) Bounded Difference c) Drastic intersection d) Standard intersection
The most adequate choice for an upper bound for the drastic intersection is
a) i(a,b)
b) min(a,b)
c) a
d) All the three options given.
The boundary condition for a t-conorm u is
a) U(a,1)=0 b) u(a,0)=0
c) u(a,0)=a
d) None
The super idempotency condition for a t-conorm is
a) U(a,a)>1 b) u(a,a)=1
c)u(a,a)<1
d) None
For t-conorm algebraic sum, u(a,b) is defined as
a) Max(a,b) b) a+b-ab
c) min(1,a+b) d) None
Equilibrium value for the standard fuzzy complement is ----a) 0 b) 0.5 c) 1
d) 0.4
The set Q of rational numbers is
a) Countably finite
b) Countably infinite c) Uncountably infinite d) None.
A continuous super idempotent t- conorm is called ----a) Strictly Archimedean
b) Archimedean
c) t-norm
d) None.
Theory of Equations & Fuzzy Sets
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School Of Distance Education
Answers:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
A
B
B
C
C
D
D
A
C
D
C
A
D
A
C
A
B
B
B
B
Theory of Equations & Fuzzy Sets
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