Download c-fr * i J=

UNIVERSITY OF CALICUT
SCHOOL OF DISTANCE EDUCATTON
,ts"A,
(
ECONOMICS
201J Ad mi ssion o nwo rd s )
l\,/
Semester
Core Course
OUANTTTATWE NIETHODS FOR ECONOMIC
ANAIYS$
Choose the correct Answer from the bracket.
E)(PONENTS
1.
Find the Value
(a)
2.
of
(b)
16
8
(c)
32
(d)
64
Find thevalueof (27)-aA
,.1
(a);
3;
23 x 21
@);
t.)
*
(d)
i
Find the nalue of (.001)%
(u)
(b).1
.001
(c)
.01
(d)
.0001
1a563/+s\-2/z
@16-r,
c-fr
(u) o/o,
5.
(b), /o,
The value of (-Z1s/z
(a)
Quontitotive Methods for
e*iii
"/o-,
(d) b/
i"
@ ,li.
'l-sz
G)
a*ty"ii
(c) y'ro
(d)
J=
o,
U
School of Distance Educotion
6.
36x7
ya + 4x6y is
(a)9x2y3
7.
(b)
9xy3
(c)
9y3x2
(d\ 9x1/eyt
(b)
6'
(c)
3'
(d)
(b)
2'
(c)
2'
(d) 4'
3 x 35 is equal to
es
(u)
3u
"t''
a,
'gl
(u)
/zis
equal to
8,
9.
100 is equal to
(a)
70.
If
10
x2= 1,
(a)
(b)
2
(b)
(a)
0
(d)
100
-2
(c)
0
(d)
1
is
x-
12. am x
(c)
x-2 isequal to
11. x^ x rtr
(a)
1
(b)
x- * "
(.)
r-"
(d)
x"
(d)
ao
ao is equal to
o'
(b) 0
(c) m
13.2-3isequalto
(u)8
16)%
(.)2
(d)3
74. 3t27t -g.-+4valueof ris
(a)7
Quonti.ative Mehods [or Economic
O)3
Ahd',js I I
(c)e
(d)s
(rt x xrs/z)
15.
ts ls
(a) x6
,'
(c) xs/z
(b)
r/,,
(c)
r'
(d)
(b) 4aa?b7
(c)
48a3b2
(d) +8arbs
(b) qn-"
(c) a-n
1u) ro%
(c)
ro%
(c)
1
(d) xa/s
/,, ,)'
(.' lxe
)'o
1.6.
r7
L/."
(a)
lxe
'/*"
)
r'
?
(6a3b
(6a3
b2))(8
b2
(8a4,bt) ls
17.
(a) ga72b1
14721bro
r1o
18.
am
=
an
rn is
mt
(a)
7e.
(a)
(b)
(d) a-+"
($"'o
10
lay
ro%
(d)
4
n. #isequarto
(a)2
(b)3
LOGARITI{MS
21.
logr 3 =
(a)
22.
3
ax
log6
(a)
gu o n d to ti u
"
u
(b)
logo
b
1
* o* 1* iiiiffi
9
(c)
1
(d)
0
a
(c)
b
(d)
0
is equal to
(b)
23.
log2 1 is
(a)
(b)
2
(.)
1
o
(d)
3
24. toe"(lt)=
(a) log" b
logJz
I
(a)
6
D
(b)
4
(a)
(d) -lo96 a
is
(c)
I
(d)
2
(b)
1
2
(c)
3
(d)
0
The characteristic of the logarithm of '0032 is
(a)
(b) -1
1
28. Antilogarithm of 2.4678 is
(b)
(a) 2e36
2e31
(c) -2
(d) -3
G)
(d)
2e3s
2e3o
Find the number of zeros in 3-2s immediately after the decimal point'
29.
(a)
30.
(b)
12
11
(c)
10
(d)
e
(c)
2
(d)
s
Find the logarithms of 125 to the base 5
(a)
(b)
3
1
31. Change into the logarithm lotm
(a) log5 216 =
32.
(u)
(c) lo96 a
The characteristic of the logarithm of 83.2 is
26.
27.
(b) -log.
logr5
2lz
64
3
63 = 21'6
(b) log3 6 = 216
(c) lo963 = 216
(d)
G) r/z
(d)
log3 216
is equal to
b)
3lz
QEntitoaivc ethoits lor Economic Anolysis I I
2
=
6
EOUATION
33.
Find the value of rlr = 8
(b)
@)a
34. 7x - 27 - 3x +13 =
(a)
7+
If in the equation ar2
36.
simple
linear
@) r/z
2
6x -19 isequal to
o)1
2
(a)
(c)
8
f
(c)
bx + c =
(b)
0,
(d)
3
.s
b is zero, then the equation is called
pure quadratic
(c) generat quadratic (d)
The ss and dd curves for a commodity are known
to be gs = p _
I and qd =12/p.
Find the equation price.
(a)
37.
(b)
4
The quanti ty b2- 4ac is called
(a) roots
U.
b2-
kc
=
O,
(c)
2
_
(d)
6
s
of the quadratic equation.
(b) discriminmt (c) power
(d)
none
the roots are
(a)
real and. equal
(c)
irrational and unequal
o) rational
(d)
and unequal
unreal
39. Find thevalue of K for which x2_ 2 kx + gk _ 15
= 0 has equal roots.
(a)
o) 3,s
3,6
40. (x + 2)2 = x2+ 4x + 4 is known
(a)
41.
Sum of the roots of quadratic equation.
(^)
/,
b
q u o, ti a ti v
b) -b/o
"
u *h
ods
piiifr
ffi
s,3
(d)
(c)
both
(d)
5,6
as.
@) id.entity
equation
(c)
(r)
a/t
(d)
-a/r
are'
42. Product of the roots of quadratic equations
(a)
ct
lo
@')
(d) -c/a
(c) a/c
-'/"
PROGRISSIONS
Arithmetic ProEression
43.AseriesissaidtobeinArithmeticProgression,ifanytermofitisobtainedby
adding a constant number to its
term'
(c\ preceeding
(a) succeeding p) preceeding
-
and succeeding
(d)
none
The ntn term of an Arithmetic Progression'
(b) a+n(n-1)d
(d) a+(n-t)-d
(a) a+ (n-r)d
(c) o+(n-1)+d
45.
l2thterm of the series 9 + 13 + 77 + 27 + ... ... ....
(a)
(b)
s2
s3
(c)
(d)
sa
ss
,16. The sum of first n natural numbers'
(")ry
M.
(a)
(b) i6
13
(c)
5,
(d) none
the last term is 45, Sn=
18
(d)
e
s,3
(d)
s,6
The arithmetic mean between 8 and 14 is equal to
(a)
49.
+rl
(c) n(n + 1)2
The first term of an Arithmetic Progression is
n is equal to
(a)
48.
tu)
3,6
(b)
(c)
3,s
The nrh term of G.P. is
Tn-l
(b)
-n-t
=
qrordur;* U"*o* 1",
Economic Anatvsis
ll
(c)
arr-r
(d);
400,
50.
when r < 1, the sum of n terms of G.p. is
a(rn-l)
r-l
,r',
51.
(b)
++
The sum of infinite G.p.
(a)
52. C.M. between
(a)
none
8
(c)
16
(d)
2
120
(c)
e0
(d)
s4
18 and 162
(b)
22
SET
53.
(d)
16,&4,........
(b)
32
(c) both
TTilORY
Ina
set theory, the set of numberc1.,3, S,Z 9..... can be
represented by
A-{X: X is an odd integer} is a
method.
_
54.
55.
56.
(a)
Tabular Method
(b)
Rule method.
(c)
Roster method
(d)
Enumeration Method
Two sets A ={7,3,4,7) and B = {7,3,1, 4} are said to be
(a)
Equality
(c)
Null set
of
sets
s8.
(d)
Singleton
(d)
none
The subset of every set
O) Equal Set
The set 0 is represented by
(a) singleton
(b) NuLl
(c)
Null set
(d)
none
(c)
Both
(d)
none
(c)
a
(d) -4
*\24i"
x-2
(a)
Qu a n
Equiualent sets
A set which contains only one element is called
(a) Null set
(c) Singleton
@) Equal set
. (a) Singleton
57.
@)
(b)
o
titatiye M e th o d s Io r Econ o-
ic
i o tyJlii
"
,\z
(a)
60.
,r*z
i"
(b)
32
A function is continuous
Lt
(a) x -.t a
d
4x4+ 3x3
(u) 4/s
62.
(u)
'b'
(r)
a/t
(d)3/+
The derivative of e:2 is
(b)
e2'
The minimum of the function y
Derivative of
If
7f,,
= 10 +
-2' "
@) 2x
lteddtlo
4x2
*
g is at
(c) x=4
(d)
None
of these
(c) 2x-3
(d)
N
one
of these
2r + 3r2 be the cost function then the srope of the average cost be
(a) 2+6x
Quantihdve
--
(d) 2x e'2
is
(b)
r
(c) Zex
(b) r=8
(d -x2
65.
of the above
ts
(a) x=0
64.
None
(d) None of the above
(b)a/z
e"
63.
(c) Both 'a' and
f inite quantity
bl. ,-+ _r ------;-:-:--1
(d)
if
f(x) = f(a) exist
(b) /(a)is
tt
(c) I
3e
Economtc
Ano,'l. tt
+ 3x2
(.)4+
a
(d) zxz
+
4x3
66.
The derivative of
(a) (x2
+
r2e'
2)e,
is
(b) (x,
rfy=li?,o
(a) 3x
! 2x)e,
(c)
x2e,
(d) (2x + L)ex
67.
68.
69.
(a)
(b)
!x-3
dx
ft y =
*the
(u)
(c) logex
(d)
t/",
(b) log x2
(c)
,
(d)r/*
(b)
(c) 3x-a
(d) 3x-2
(c) 2x2
(d)
N
one
of these
N
one
of these
-ax-z
derivative is
(a) o
72.
e'
is
(a) 3 x-a
7't.
(d)r/*
The derivative of Jogx
r log r
70.
612frxL/z
Derivative of ex is
xe'-L
(a)
r/rru/,
b)
b)1/z
lxbsxis
dx
r/*
73. xy=c2
@)
t + logx
(c)
llogx
(d)
G)
-'/y
(d)-Y/x
the derivative is
(u)Y/,
Quantiutive tlethods fot Econonic
(b)'/y
Anctysis I !
School of Distonce Education
74. A function
is said to be maximum at
r - a if
(a) /(a) is negative andf"(a) zero
(b) f(a) is zero andf "(a) is negative
(c) f(a) is zero and f " (a) is zerc
(d)
75.
/(a)
is negative
andf "(a) is negative
A function is said to be minimum
(u) f '=0 and f ">0
(b) f'=0 and f"<0
(c) f '>0 and f"=0
(d) f '<0andf "=0
76.
The function 2x2
(a)
77.
At
- 8x t
2 the
function -3xz
(a) maximum
78.
(c)
'
is equal to
(c)
2x
(b) e
-e
(u)
(b)
(c)
(d)
+
2
- (3 - r),
(c)
(b)
(d)
Negative
Non-positive
The function 3x3
(d)
p) minimum (c) Point of Inf lection (d) N one of the above
-3
Increasing function if and only if its derivatives on (a, b) is
(a)
80.
at'r'
+ lZ + 5 is
When Revenue is maximum if R = 3000
(u)
79.
minimum
(b) -8
4
t=
10 is
3x2
* x - 10 is
An increasing function
Decreasing function
Standard function
None of the above
Quanti.ative Methods lot Econonic Anolysis
ll
Non - N e gatioe
None ofthe above
(d)
3
81'
If the second derivative of a function/r) is positive then in the given
interval
the function is said to be
(a) Ino.easing @) Dec,reasing (c)
82.
(d)
Convex
Concave
The differential Coefficient of the dependent variabre with
respect to one of the
independent variabres keeping the other independent variabre
is constant is
called
(a)
(c)
Simple derivotive
Partial derivative
(b)
(d)
Total derivative
Cross derivative
BASIC MATRD( AIGEBRA
A triangular matrix is the one in which
a. All the diagonal elements are zero
b. All the elements above or below the diagonal are zero
c. All diagonal elements are non-zero
d. All
the elements are unity
84. If A = AT, the A is called
a. Square matrix
b. Skew symmetric
85.
c. Orthogonal matrix
d. Symmetric Matrix
matrix
When the determinant of a matrix is zero, the matrix is called
a.
Singular
c. Null
b. Non singular
85. Given A
d. Identity
is 2x2 matrix and B is 2x3, the matrix AB
a.2x2
b.2x3
will be
c.3x3
d.3x2
87. If the two rows or columns are identical or proportional
, the determinant is
a. One
b.
Infinity
88. The transpose of a matrix of minors
a.
Adjoint
b. Cofactor
Quontitative Me,hodslor Econonic Anatysis
c.
Undefined
d. Zero
Determinat
d. Inverse
is called
c.
89. tu{-l=
a.A -.
90.
=A-1A
b.
A-1
c.
I
d.
None of the above
For a matrix minor M12=-34, then the cofactor C12
a. 34
b.
will be
'17
c. -34
d.0
91..
The linear form AX= B implies that
a. X= A-1B
b.
c.
X=B-1A
X=AB
d.
X=BA-1
92. The determinant is defined only for
a. Row matrix
b. Column matrix
c. Square matrix
d. Null matrix
.
93. Matrix B is called Skew symmetric
a.
b.
if
B=BT
c.
B=-BT
B=B2
d.
None of the above
94. If the turo matrices are of the order mm and nxp, then AB will of the dimension
a.
b.
c.
Pxn
mxP
95. If A=AZ the matrix A is known
a. Symmetric
b. Skew SYmmetric
d.
nxp
mxn
as
. c. IdemPotent
d. Triangular
95. If AxA
= A, then the matrix A is
a. Nil potent
b. Symmetric
97'
c.
d.
Triangular
Identity
If the determinant of a matrix is found out to be -65, the determinant
of its
transpose is
a. -65
b. 65
c.
32.5
d.
Cannot say
98. A square matrix in which all the diagonal elements are
equal and non_diagonal
elements are zero is called
a. Diagonal matrix
b. Scalar matrix
99.
The determinant of 3x3 matrix is called
a. First order determinant
b.
Second order determinant
c.
d.
c.
d.
Triangular matrix
Unit matrix
Third order determinant
Fourth order determinant
100.
A matrix with equal number of rows and column is called
a. Square matrix
c. Column matrix
b. Row matrix
d. Null matrix
101.
A diagonal matrix with each of the diagonal elements is
unity is
a. Vector
c. Diagonal matrix
b. Square rirahix
d. Identity matrix
-102.
If in
it
a square
matrix, all the elements below the leading diagonal is zero,
is
a. Lower triangular matrix
b. Upper triangular matrix
c.
d.
Identity metrix
Null matrix
103. The maximum number of linearly independent rows
or columns
matrix is called
a. Determinant
b. Trace
Quontitative Methods
lot Econonic
Anolysis
c.
d.
It
Rank
Minor
in
the
104.
The determinant of the triangular matrix is the product of
a.
b.
c.
Rows
Columns
d.
Rows and columns
Diagonals
105. Minor with the prescribed sign is called
c.
a. Inverse
b. Cofactor
106.
d.
Determinant
Adjoint
The transpose of the cofactor matrix is
a.
b.
c.
Cofactor
Rank
Inverse
d. Adjoint
1.07. For a square matrix, inverse exists if and only if it is
a.
b.
Non-singular
Singular
c.
Null
d.
Cannot say
FI'NCTIONS AND GRAPHS
108. A
is a value that may change
set of operations
within the scope of a given problem or
-
(a) constant
(b) variable
function
(d) exponent
(c)
109. Given
y = f (x) 'y' is called a
variable and
variable.
(a) independent, dependent
(b) variable, constant
-
variable
(d) dependent, independent
(c) constant,
110. In u = f (xl.'r/
(a)
is called
output, input
(b) variable, constant
(c)
input, output
(d) constant variable
Quand&,dvc
N.ahodshr E..,,,onb Arfrod/l
lt
and
'r'
is called
'x' is called
an
111. .
represents a response, behaviour,
wishes to predict or explain.
or outcome that the
researcher
(a) independent variable
(b) function
(c) equation
(d) dependent variable
1-12.
variable is a factor that is not itself under study but
affects the
measurement of the study variables or the examination
of thJir relaU."rf,ipr.
(a) Exogenous
(b) Endogenous
-(c) Extraneous
(d) Dependent
113. If a term cohsists of only variables, its coefficient is
(a) 1
(b) does not exist
(.) o
(d) unknown
114. Expressions consisting of a real number or of a coefficient
times one or more
variables raised to the power of a positive integer are
called .....
(a) polynomials
(b) monomials
(c) functions
(d) equations
115. In a variable expressions
5a + 3b, ,a, and ,b,
are_
5 and 3 are and+ is an
(a) variables, constants, operator
(b) constants, variables, operator
(c) operator, variables, constants
(d) variables, operator, constants
116' A
is an equation for which any x that can
will- yield exactly one y out of the equation
(a) monomial
(b) polynomial
(c) function
(d) operator
Quantitotive Methods lor
t"ono-i, l,nAyri"
t
1
be prugged into the equation
plot a graph of a function, as
independent variable on the _
variable on the _
axis.
117. Tci
a
matter
axis of
of convention, we plot the
a graph, and the dependent
(a) horizontal, vertical
(b) vertical, horizontal
(c) vertical or horizontal
(d) vertical and horizontal
118.
take the form y = a + qr
(a) Power
(b) Quadratic
(c) Linear
-functions
(d) Exponential
"179.
functions take the form y = a + kxp
-(a) Power
(b) Quadratic
(c) Linear
(d) Exponential
-120.
If the relation between two variables x and y is expressed in the form t(x,y)=O,
'
where x cannot be expressed as a function of y, oiy .unoot be expressed
as a
function of x, is called _
function.
(a) Quadratic
(b)
function
implicit
explicit
(d) Linear function
(c)
The graph of
is such that the two ends of the graph will be
directed towards the same side.
(a) odd
(b) implicit
(c)
-function
power
(d) even
122. A function/x) has an inverse function if and only if
f(x) is
(a) one-to-one
(b) one-to-many
(c) many-to-one
(d) one-to-two
Quantitative Methods lor Econonic Atlotysis
II
123. In the rectangular coordinate system
This notation is called
(a) cartesian
the coordinates of the origin are (e0).
product
(b) ordered pair
(c) Determinant
(d) None of these
124. In the rectangular coordinate system, in quadrant IV, x is
always.
and y is
always_
(a) negative, positive
(b) negative, negative
(c) positive, negative
(d) positive, positive
125. The distance formula
can be obtained by creating a triangle and
using the
Pythagorean Theorem to find the length of the "
(a) arc
(b) slope
(c) graph
(d) hypotenuse
125'
The
is an ordered pair formed by finding the
average of the x-varues
and the average of the y-values of thu gire., po"ints
-
(a) arc
(b) slope
(c)
midpoint
(d) hypotenuse
-127.
The
_of
a
line measures the change in y (Ay) divided
by change in x (Ax).
(a) stope
(b) arc
(c) hypotenuse
(d) midpoint
128.
The
_the
absolute value of the slope, the
(a) steeper, greater
(b) $eater, steeper
(c)
greater, flatter
(d) lesser, steeper
Qu o n ti to ti v e
M e th o ds Fo r e, o"
oiiirr,fi ii
_the
line.
129. The slope of a vertical line (for example
for which Ax = 0, is
a
perfectly inelastic demand curve),
(a) o
(b) 1
(c) -1
(d) undefined
130. The
(a)
x
is the point where your line crosses the x-axis.
ihtercept
-
(b) slope
(c) arc
(d) quadrant
A
is a relation (usually an equation) in which no two ordered pairs have
same
x<oordinate when graphed.
the
-
(a) graph
@) quadratic
(c) function
equation
(d) linear equation
Point-slope refers to a method for
(a) a
graphing
equation on an x-y axis.
linear
(b) a quadratic
linear
(d) a cubic
(c) a non
-
School oI Dtstance Edu
ANSWERKEY
1.
(a)
16
n. (a) maximum
78. (d) 3
79. (b) Non-Negative
80. (a) An increasing function
81. (c) convex
82. (c) Partial derivative
83 (b) All the elements above or
2. G)r/u
3.
4'
5.
6.
' 7.
.7
@)"/o,
(a).\E3Z
p) 9xy3
(d) 3u
(b)
below the diagonal are zero
8.
9.
10.
11.
12.
28
(b) 1
(d) 1
(b) :-*"
(a) a-
&1
85
86
8Z
88
(b) 2x3
13.
1u)
8e
(") I
-t4.
%
(a)
(c)
7
15. (u) ,u
76. @) 1/r"
77. @) 48a?b7
18. (b) a--"
19. (a) 10
20. (a) 2
21.. (c) 1
22. (a) 1
23. (c) 0
24. (b) log" D
25. (a)6
26. (a)1
27. (d)3
Quontitotive l,lethodsfor Econonic Ahab,sis
L
90
91
92
93
94
95
96
97
98
99
(d) symmetric Mahix
(a) Singular
(d) Zero
(b) cofactor
(a) 34
(a) X= A-1B
(c) Square Matrix
(c) B=-BT
(b) Mxp
(c)
Idempotent
(d) Identity
(a) -6s
(a) Diagonal matrix
(c) Third order determinant
100 (a) Square matrix
101 (d) Identity matrix
102 (b) Upper triangular
103 (c) Rank
t
t
matrix
22
28.
(a)2936
1&
(d) Diagonals
29.
(b) 11
(b) Cofactor
30.
(a) 3
31-
(a) logu2l6=3
32.
(b)3/z
105
106
107
108
JJ.
(c) 2
109
(d) dependent, independent
34.
(a) 2
110.
(a) output,
35.
(b) Pure Quadratic
111. (d) dependent variable
36.
(a) 4
112.
(c) Extraneous
J/.
(b) discriminant
113
(u)
38.
(a) real and equal
114.
(b) monomials
39.
(c) s,3
(a) variables, constants, operator
40.
(b) identity
41..
(b) b/"
115
776
777
42.
(u)
118
43.
(b) preceeding
119
(a) Power
u.
(a) a+ (n-1)d
120.
(b)
45.
(b) s3
nfn+1)
- ---:------(al
121. (d) even
46.
'/a
(b)
49.
(c)
s0.
s1.
52.
53.
54.
55.
56.
(a) Non-singular
(b) variable
input
1
(c) function
(a) horizontal, vertical
(d) Exponential
implicit
-122. (a) one-to-one
2
47.
48.
(d) Adioint
"123
(b) ordered pair
Da.
@)
125.
(d) hypotenuse
126.
(c)
(a) 32
127.
(a) slope
(d) s4
128.
(b) greater, steeper
(b) Rule Method
129. (d) undefined
(a) Equality of sets
130.
(a) intercept
(c) Singleton
131.
(c) function
132.
(a) a linear
16
(a) 11
1u)
ar"-1
g!#
(c) Null set
Quontitotive Mehods lor Economic Anollsis
ll
positive, negative
midpoint