Subject Code: BCA 1030 Subject Name: Mathematics for IT
Unit 1: Set Theory1) What is a collection of objects?a) Classb)
Arrayc) Matrixd) Set2) A set denoted by ___________ letters.a)
Capital lettersb) Small lettersc) Numbersd) Any symbols3) The
elements of a set are denoted by ___________ letters.a) Capital
lettersb) Small lettersc) Numbersd) Any symbols4) If a is an
element of a set A, we say that ___________.a) a Ab) a Ac) a Ad) a
A5) How many types of representing a set?a) 2b) 3c) 4d) 56) The set
of all vowels in the English alphabets is ___________.a) {a ,e ,i
,o ,u}b) {e .a ,i ,u ,o}c) {i ,a ,o ,e ,u}d) All of the above7) {s
,c ,h ,o ,l} is the representation of a set in the ___________
form.a) Rosterb) Set builderc) Arrayd) General8) A= {x: x is a
letter of the word LITTLE}, the element of a set is ___________.a)
{L ,I ,T ,E}b) { L ,I ,T ,T ,L ,E }c) { L ,T ,I ,E }d) None of the
above9) A set which does not contain any element is called
___________.a) Empty setb) Null setc) Void setd) All of these10) A=
{Men in the world}, the element of a set is ___________.a) Empty
setb) Finite setc) Infinite setd) Null set11) Two sets A and B are
said to be equal if they have exactly the same elements then we
write ___________.a) Equal setb) Equivalent setc) Subsetd) Not
equal set12) If every element of a set A is also an element of a
set B, then A is called ___________.a) A Bb) A Bc) A Bd) A B13) The
collection of all subsets of a set A is called ___________.a) Power
set of Ab) Number set of Ac) Super set of Ad) Equivalent set of
A14) Standard formula for find the power set of given set is
___________.a) n2b) 2nc) 2n + 1d) 2n15) Power set is always contain
a ___________ set.a) Empty b) Nullc) Void d) All of the above16)
The graphical form of the set is ___________.a) Chartb) Graphc)
Venn diagramd) None of the above
17) U is the set of all elements of U which are not the elements
of A, is called ___________.a) Complement of a setb) Union of setc)
Intersection of setd) Super set18) Let U = {x: x is the employee of
marketing department}. Let A = {y: y is the employee of selling
& distribution department}, A is ___________.a) employee of
marketing departmentb) employee of selling & distribution
departmentc) employee of accounting departmentd) none of the
above19) if ___________ , then A and B are said to be disjoint
sets.a) A B = b) A B = c) A B = d) A B = 20) Let A = {x: x Z+}; B =
{x: x is a multiple of 7, x Z}, A B = ___________.a) {1, 3, 5 ,7
,9}b) {1, 5, 9, 11 21 ,49}c) {7, 14, 21, 28, ..}d) None of the
above21) If {x: x A and x B} then called ___________.a) A + Bb) A
Bc) A * Bd) A / B22) If X and Y are two sets such that n(X Y) =
100, n(X) = 30, n(X Y) = 50, then n(Y) = ___________.a) 50b) 20c)
120d) -12023) Find x and y if (x + 3, 10) = (1, x + 3y)a) 2, -4b)
4, -2c) -2, 4d) -4, 224) A set that is empty or consists of a
definite number of elements is called the ___________ set.a) Nullb)
Scalarc) Infinited) Finite25) The symbol of rational number is
___________.a) Qb) Nc) Zd) R26) If set A = {1, 2, 3, 4} and set B =
{3, 1, 4, 2), then the two sets are ___________.a) Disjointb)
Equalc) Equivalentd) Void
Unit 2: Mathematical Logic27) What is a symbol of conjunction is
___________.a) b) c) d) 28) What is a symbol of AND operation is
___________.a) b) c) d) 29) What is a symbol of disjunction is
___________.a) b) c) d) 30) What is a symbol of OR operation is
___________.a) b) c) d) 31) What is a symbol of negation is
___________.a) !b) c) d) ~
32) What is a symbol of NOT operation is ___________.a) !b) c)
d) ~33) F T = ___________.a) Fb) T34) F T = ___________.a) Tb) F35)
~ (p q) is equivalent to ___________.a) ~ p qb) P ~ qc) ~ p ~ qd) ~
p ~ q36) ~ (p q) is equivalent to ___________.a) ~ p qb) P ~ qc) ~
p ~ qd) ~ p ~ q37) If p is true and q is false, then p q is
___________.a) FALSEb) TRUE38) If p and q are both false, then p q
is ___________.a) FALSEb) TRUE39) If p is false and q is true, then
p q is ___________.a) FALSEb) TRUE40) If p and q are both true,
then p q is ___________.a) FALSEb) TRUE41) (~p) q is equivalent to
___________.a) p (~q)b) p qc) p qd) p q42) Truth value for ( p q )
( ~p) is ___________.a) Tautologiesb) Contradictionc) One true and
other falsed) One false and other true43) Truth value for ( p q ) (
~q) is ___________.a) Tautologiesb) Contradictionc) One true and
other falsed) One false and other true44) Truth value for ( p q ) (
~q) is ___________.a) Tautologiesb) Contradictionc) One true and
other falsed) One false and other true45) Truth value for ~ [(~ p)
q ] is ___________.a) Tautologiesb) Contradictionc) One true and
other falsed) One false and other true46) ~ [(~ p) q] is equivalent
to ___________.a) ~ p qb) P ~ qc) ~ p ~ qd) ~ p ~ q47) ~ [p (~q)]
is equivalent to ___________.a) ~ p qb) P ~ qc) ~ p ~ qd) ~ p ~
q48) Construction of ___________ is a method to determine whether a
given statement is a tautology or contradiction.a) Logicalb)
Sentencec) truth tabled) diagrams49) Two statements S1 and S2 are
said to be logically equivalent if they have the same ___________
for all logical possibilities.a) Valuesb) Parametersc) Answersd)
truth values50) Logic is the study of general patterns of
___________, without reference to particular ___________.a)
samples, eventsb) answers, situationc) reasoning, meaningd)
context, reasoning
Unit 3: Modern Algebra51) The image of an ordered pair (x, y)
under f is denoted by ___________.a) x f yb) y f xc) f x yd) f y
x52) The symbols +, x, 0, * are used in ___________ operation on a
set.a) Decimalb) Arithmeticc) Binaryd) None of these53) If Z is the
set of integers then usual ___________ operation on Z.a) Decimalb)
Additionc) Binaryd) None of these54) If Q is the set of rational
then usual ___________ operation on Q.a) Decimalb) Multiplicationc)
Binaryd) None of these55) If * is a binary operation on G then
___________ is an algebraic structure. a) (G, G)b) (*, *)c) (*,
G)d) (G, *)56) A/an ___________set with one or more binary
operations is called a/an ___________.a) empty, algebraic
structureb) non-empty, algebraic structurec) empty, groupd)
non-empty, group57) Addition modulo n of two integers a and b is
written as ___________.a) a n + bb) a n + b c) a + n bd) a + n b58)
Multiplication modulo n of two integers a and b is written as
___________.a) a n bb) a n bc) a n b d) a * n b59) A non-empty set
G is said to be a semi group w.r.t. the binary operation if the
___________ and ___________ axioms are satisfied.a) distributive,
identityb) closure, associativec) associative, commutatived)
commutative, distributive60) The identity element in a group is
___________.a) Finiteb) Infinitec) Uniqued) None of these
Unit 4: Trigonometry61) A ___________ is the angle subtended at
the center of a circle by an arc equal to the radius of the
circle.a) Radianb) Circular measurec) Both A and Bd) None of these
62) Radians are equal to ___________.a) 180ob) 227c) 90od) 3.1463)
5.9 radians = ___________ degree.a) 337b) 144.9c) 180d) 337.9064)
45o = ___________ radians.a) 0.1b) 0.78c) 0.5d) None of these65)
The basic knowledge of allied angles and compound angles is given
in ___________.a) Geometryb) Boolean algebrac) Trigonometricd) None
of these66) Length of an arc of a circle is equal to the
___________ of the radius of the circle and the angle in
___________ subtended at the center by the arc.a) product, degreeb)
sum, radianc) product, radiand) sum, degree67) A spaceship moves in
a circular orbit of radius 9000 km round the earth. How far does it
travel while sweeping an angle of 150o?a) 7500 kmb) 4000 kmc) 8000
kmd) 6500 km68) sec 30o tan 60o + sin 45o cosec 45o + cos 30o cot
60o = ___________. a) 5 2b) 2.5c) Both A and Bd) None of these69)
Tan 90o = ___________.a) 1b) 0c) d) -170) What is value of (2x -
3)(cosec2 3 sin2 4) = x tan2 ( 4) sec2 ( 6) 2a) (5/4)b) 4/5c) 5/4d)
(4/5)71) Cosec 1305o = ___________a) 2b) 1/2c) d) 172) Sin 135o +
cos 480o = ___________Sin 135o cos 120oa) 1b) 1/2c) d) 173) If sec
= 13/5 and 270o < < 360, the value of 2sin+ 3cos =
___________. 4sin + 9cosa) 3b) -3c) 0d) -174) Tan 15o =
___________a) 1b) 1/2 - 3c) d) 175) If sin A = -5/13, cos B = 4/5,
then cos (A + B) = ___________.a) 63 / 65b) -63 / 65c) 65 / 63d)
-65 / 6376) If A + B = / 4, then (1 + tan A)(1 + tan B) =
___________.a) 1b) 2c) 3d) 477) tan and cot are ___________ to each
other.a) Trigonometricb) Algebraicc) similard) reciprocal78) tan
(90o - ) = ___________a) cosb) sinc) cotd) cosec79) sin (180o + ) =
___________a) sinb) Sinc) Cosd) -cos80) Cot (180o - ) =
___________a) Cotb) Tanc) cotd) -tan81) If tan = 1/3 and tan = 1/7,
then 2 + = ___________a) / 2b) / 4c) / 3d) 82) 1 + tan2 (45o - ) =
___________1 tan2 (45o - )a) Cosecb) c) d) 83) Tan = ___________a)
Opposite side adjacent sideb) Adjacent side adjacent sidec)
Opposite side hypotenused) Adjacent side opposite side84) cosec =
___________a) Opposite side adjacent sideb) Adjacent side adjacent
sidec) Opposite side hypotenused) Hypotenuse opposite side85) Cos =
___________a) Opposite side adjacent sideb) Adjacent side
Hypotenusec) Opposite side hypotenused) Hypotenuse opposite side86)
cot = ___________a) Opposite side adjacent sideb) Adjacent side
Hypotenusec) Opposite side hypotenused) Adjacent side opposite
side87) Sin = ___________a) Opposite side adjacent sideb) Adjacent
side Hypotenusec) Opposite side hypotenused) Hypotenuse opposite
side88) sec = ___________a) Hypotenuse adjacent sideb) Adjacent
side Hypotenusec) Opposite side hypotenused) Hypotenuse opposite
side89) cosec2 - 1 = ___________a) Tan2b) Cot2c) Sec2d) Sin290)
Sin2 + cos2 = ___________a) Tan2b) Cot2c) 1d) 091) Tan2 sec2 =
___________a) sin2b) Cos2c) 1d) 092) 1 sin2 = ___________a) sin2b)
Cos2c) 1d) 093) 1 + cot2 = ___________a) sin2b) Cosec2c) 1d) 094) 1
+ tan2___________a) sin2b) Cosec2c) 1d) sec295) sec2 - 1 =
___________a) Tan2b) Cot2c) Sec2d) Sin296) 1 + cos2___________a)
sin2b) Cosec2c) 1d) sec297) sin A cos B + cos A sin B =
___________a) sin(A - B)b) cos(A + B)c) sin(A + B)d) cos(A - B)98)
cos A cos B + sin A sin B = ___________a) sin(A - B)b) cos(A + B)c)
sin(A + B)d) cos(A - B)99) cos A cos B sin A sin B = ___________a)
sin(A - B)b) cos(A + B)c) sin(A + B)d) cos(A - B)100) sin A cos B
cos A sin B = ___________a) sin(A - B)b) cos(A + B)c) sin(A + B)d)
cos(A - B)101) Tan A + tan B = ___________ 1 Tan A tan Ba) tan(A -
B)b) cot(A + B)c) tan(A + B)d) cot(A - B)102) tan A - tan B =
___________ 1 + tan A tan Ba) tan(A - B)b) cot(A + B)c) tan(A +
B)d) cot(A - B)103) 2sin A cos A = ___________a) Cos 2Ab) Sin 2Ac)
Sin Ad) cos A104) 2tan A = ___________ 1 tan2 Aa) Tan Ab) cot Ac)
cot 2Ad) tan 2A105) tan (180o + ) = ___________a) sinb) tanc)
-tand) sin106) cos (90o + ) = ___________a) sinb) Sinc) Cosd)
-cos107) sin (180o - ) = ___________a) sinb) Sinc) Cosd) -cos108)
sec (180o + ) = ___________a) sinb) Secc) sind) -sec109) sin (90o +
) = ___________a) sinb) Sinc) Cosd) -cos110) Cot A tan A =
___________a) 2 tan Ab) 2 cot Ac) 2 cot 2Ad) 2 tan 2A111) 1 cos 2A
= ___________ 1 + cos 2Aa) Tan2Ab) Tan 2Ac) Sin 2Ad) Sin2A112) Cot
A + tan A = ___________a) 2 sin Ab) 2 cosec 2Ac) 2 sin 2Ad) 2 cosec
A113) 2 tan A = ___________ 1 + tan2Aa) Tan2Ab) Tan 2Ac) Sin 2Ad)
Sin2A114) 1 tan2A = ___________ 1 + tan2Aa) Tan2Ab) Tan 2Ac) cos
2Ad) cos2A115) sec (90o + ) = ___________a) cosecb) cosecc) sind)
-sec116) cosec (180o + ) = ___________a) sinb) cosecc) sind)
-cosec117) sec (180o - ) = ___________a) sinb) Secc) sind) -sec118)
sin (90o - ) = ___________a) sinb) Sinc) Cosd) -cos119) cos (180o -
) = ___________a) sinb) Sinc) Cosd) -cos120) tan (180o - ) =
___________a) sinb) tanc) -tand) sin121) Cot (180o + ) =
___________a) Cotb) Tanc) cotd) -tan122) sec (90o + ) =
___________a) sinb) cosecc) sind) -cosec123) cosec (90o + ) =
___________a) sinb) secc) sind) -cosec124) cos (180o + ) =
___________a) sinb) Sinc) Cosd) -cos125) tan (90o + ) =
___________a) cotb) tanc) -tand) cot126) cosec (180o - ) =
___________a) sinb) cosecc) sind) -cosec127) Cot (90o - ) =
___________a) Cotb) Tanc) cotd) -tan128) cosec (90o - ) =
___________a) sinb) secc) sind) -cosec129) cos (90o - ) =
___________a) sinb) Sinc) Cosd) -cos130) Cot (90o + ) =
___________a) Cotb) Tanc) cotd) -tanUnit 5: Limits and
Continuity131) The numbers are represented as points on a
horizontal line called the ___________.a) Real axisb) Imaginary
axesc) X- axisd) Y- axis132) If a b, then | a b | is ___________.a)
Positiveb) Negativec) Zerod) Both (a) and (c)133) The distance
between a and b is defined as ___________a) a bb) | a b |c) b ad) |
b a | 134) A function of a ___________ is a function from N to R.a)
Integer numbersb) Discrete variablec) Continuous variabled) Real
numbers135) A function of a ___________ is a function from R to
R.a) Integer numbersb) Discrete variablec) Continuous variabled)
Real numbers136) The list given in ___________ is called a
sequence.a) (#)b) (&)c) ()d) (*)137) A sequence is said to be
convergent if it has a unique ___________ point.a) Markedb) Limitc)
Crossd) continuous138) The sequences that do not converge are
called ___________ sequences.a) Oscillatoryb) Cyclicc) Bisectedd)
periodic139) A constant sequence is ___________.a) Convergentb)
Divergentc) Scalard) regular140) If {xR | a < x < b}, then
interval is ___________a) (a, b)b) [a, b]c) [a, b)d) (a, b]141) If
{xR | a x b}, then interval is ___________a) (a, b)b) [a, b]c) [a,
b)d) (a, b]142) If {xR | a < x b}, then interval is
___________a) (a, b)b) [a, b]c) [a, b)d) (a, b]143) If {xR | a x
< b}, then interval is ___________a) (a, b)b) [a, b]c) [a, b)d)
(a, b]144) If {xR | a x}, then interval is ___________a) [a, )b)
(a, )c) (-, a]d) (-, a)145) If {xR | a < x}, then interval is
___________a) [a, )b) (a, )c) (-, a]d) (-, a)146) If {xR | x a},
then interval is ___________a) [a, )b) (a, )c) (-, a]d) (-, a)147)
If {xR | x > a}, then interval is ___________a) [a, )b) (a, )c)
(-, a]d) (-, a)148) If {R}, then interval is ___________a) [a, )b)
(a, )c) (,]d) (-, )149) The open interval is denoted by
___________.a) [ ]b) ( )c) { }d) < >150) The close interval
is denoted by ___________.a) [ ]b) ( )c) { }d) < >151) If {xR
| | x - 5 | < 6}, then interval is ___________a) (1, 11)b) [1,
11)c) (1, 11]d) [1, 11]152) lt (10 5x) = ___________ x2a) 10b) 5c)
0d) -5153) lt x2 5x + 6 = ___________ x2 x - 2a) -1b) -2c) 0d)
2154) lt x3 1 = ___________ x x - 1a) -1b) -3c) 0d) 3155) lt x - 1
= ___________ x3 x2 - 1a) 4b) 1 / 4c) 0d) 2156) lt x2 + 2x + 1 =
___________ x3 x2 - 3x + 2a) -1b) -2c) 8d) 2157) lt 1 = ___________
x1 a) 1 / b) 5c) d) 1
Unit 6: Differentiation158) The process of finding a derivative
is called ___________.a) Calculusb) Differentiationc) Limits &
continuityd) None of these159) If f(x) = 4x 3, then f (3) =
___________.a) 8b) 0c) 1d) 4160) If f(x) = x3 & c = 2, then f
(x) = ___________.a) 3b) 12c) 4d) 8161) If f(x) = ex & c=log 3,
then f (x) = ___________.a) e log 3b) exc) 3d) log 3162) If f(x) =
log x & c=log log 2, then f (x) = ___________.a) 1 / log log
2b) log log 2c) log 2d) none of these163) lt sin x = ___________ x0
xa) 1b) Sin xc) xd) 0164) lt 1 cos x = ___________ x0 xa) 1b) Sin
xc) xd) 0165) If f(x) = sin x & c = 3 / 2, then f (x) =
___________a) -1b) 0c) 1d) 166) If f(x) = cos x & c = / 4, then
f (x) = ___________a) -1/ b) 0c) 1/ d)
167) If f(x) = sin x & c = , then f (x) = ___________a) -1b)
0c) 1d) 168) If f(x) = cos x & c =0, then f (x) = ___________a)
-1b) 0c) 1d) 169) If f has a derivative at c, then f is ___________
at c.a) Discontinuousb) Differentiationc) Limitd) continuous170) If
f(x) = 1/x, then f(x) = ___________a) -1/x2b) -1/xc) X2d) x2 171)
If f(x) = , then f(x) = ___________a) b) 1/x2c) d) - 172) If f(x) =
ax, then f(x) = ___________a) ax b) ax log e ac) x log ad) none of
the above173) If f(x) = ex, then f(x) = ___________a) ex b) ex log
e ac) x log ad) none of the above174) If f(x) = log x, then f(x) =
___________a) Log xb) ax log e ac) x log ad) 1/x
175) If f(x) = sin x, then f(x) = ___________a) Sin xb) sin xc)
cos xd) cos x176) If f(x) = cos x, then f(x) = ___________a) Sin
xb) sin xc) cos xd) cos x177) If f(x) = tan x, then f(x) =
___________a) Sec2 xb) sin x/cos xc) cos2 xd) sec2 x178) If f(x) =
cot x, then f(x) = ___________a) cosec2 xb) sin x/cos xc) cos x/tan
xd) cosec2 x179) If f(x) = sec x, then f(x) = ___________a) Sec2
xb) 1/sin xc) Sec x tan xd) 1/cos x180) If f(x) = cosec x, then
f(x) = ___________a) cosec2 xb) 1/sin xc) -cosec x cot xd) 1/cos
x181) If f(x) = sin-1 x, then f(x) = ___________a) 1/2b) 1/sin xc)
-1/2d) none of the above182) If f(x) = sin-1 x, then f(x) =
___________a) 1/2b) 1/sin xc) -1/2d) none of the above
183) If f(x) = tan-1 x, then f(x) = ___________a) 1/2b) 1/1+x2c)
-1/2d) -1/1+x2184) If f(x) = cot-1 x, then f(x) = ___________a)
1/2b) 1/1+x2c) -1/2d) -1/1+x2185) If f(x) = sec-1 x, then f(x) =
___________a) 1/|x|x2 - 1b) 1/1+x2c) -1/|x|x2 - 1d) -1/1+x2186) If
f(x) = cosec-1 x, then f(x) = ___________a) 1/|x|x2 - 1b) 1/1+x2c)
-1/|x|x2 - 1d) -1/1+x2187) (g f) (x) is ___________ equal to( f
g)(x)a) not alwaysb) sometimesc) alwaysd) never188) The
mathematician Gottfried Wilhelm Van Leibniz used the symbol
___________ for f(x)a) dx/dyb) dyc) dy/dxd) dx189) Issac Newton and
Leibniz are the two mathematician who developed ___________.a)
Differentiation b) Calculusc) Integrationd) None of these190) Let y
= f(u) and u = g(x) be two differentiable functions, then according
to ___________ = a) Differentiation ruleb) Chain rulec) Division
ruled) Multiplication rule191) If we evaluate dx / dy by using only
the definition and not the ___________, then we call this
differentiation from first principles.a) Definitionb) Variablesc)
known formulasd) limit192) If f(x) = log (2x + 3), then f(x) =
___________.a) 1/(2x + 3)b) 2x + 3c) 2/(2x + 3)d) None of the
above193) If f(x) = 3a / 4x5, then f(x) = ___________.a) -15a/x6b)
-15a/x5c) 15a/x6d) 15a/x5194) If f(x) = sin x + cos x, then f(x) =
___________. Cos x a) Sec2 xb) sin x/cos xc) cos2 xd) sec2 x195) If
f(x) = sin 3x, then f(x) = ___________.a) Sin xb) 3 cos 3xc) 3 sin
3xd) -3 sin 3x196) If f(x) = e5x + 3, then f(x) = ___________.a)
exb) 5exc) 5ex + 3d) None of the above197) If x = 2sin t and y =
cos 2t, then f(x) = ___________.a) -2 sin tb) 2 sin tc) 2 sin 2td)
2 cos t198) If x = a( + sin and y = a(1 - cos), then f(x) =
___________.a) Tan b) Cot c) Cot /2d) Tan /2 199) If f(x) = x 1/x,
then f(x) = ___________.a) 1 1/xb) x 1c) 1 1/x2d) none of the
above200) If x = a sec and y = b tan, then f(x) = ___________.a)
cosec b) b/a cosec c) a/b cosecd) a/b tan
Unit 7: Integrations201) The process of summation is generalized
by ___________.a) differential equationb) trigonometryc)
integrationd) differentiation202) The derivative of a function
remains the same if a ___________ is added to it.a) Functionb)
Constantc) Variabled) value203) k dx = ___________a) Kx + cb) K +
cc) X + cd) None of the above204) x dx = ___________a) 1b) X + cc)
X2 + cd) X2 / 2 + c205) 1 / x dx = ___________a) 1b) 1/x + cc) log
x + cd) None of the above206) ex dx = ___________a) ex + cb) exc)
log x + cd) 1207) sin x dx = ___________a) Sin x + cb) cos x + cc)
Cos x + cd) sin x + c208) cos x dx = ___________a) Sin x + cb) cos
x + cc) Cos x + cd) sin x + c209) sec2 x dx = ___________a) Sec x +
cb) cos x + cc) Tan x + cd) sec x tan x + c210) cosec2 x dx =
___________a) Sin x + cb) cot x + cc) tan x + cd) sin x + c211) sec
x tan x dx = ___________a) sec x tan x + cb) sec x + cc) Cos x +
cd) sec x + c212) cosec x cot x dx = ___________a) cosec x + cb)
sin x + cc) -cosec x + cd) sin x + c213) dx = ___________ 1 + x2a)
tan-1 x + cb) 1 / 1 + x2 + cc) tan x + cd) none of the above
214) dx = ___________ 2a) sin x + cb) 1 / 2 + cc) sin-1 x + cd)
none of the above215) dx = ___________ x2 - 1a) log x2 1 + cb) log
(x + x2 - 1) + cc) log x + cd) none of the above216) dx =
___________ x x2 - 1a) sec-1 x + cb) cosec-1 x + cc) both (a) &
(b)d) none of the above217) x-4 dx = ___________a) 1 / x3 + cb) -1
/ x4 + cc) -1 / 3x3 + cd) None of the above218) sin (A + B) + sin
(A - B) dx = ___________a) 2 sin A cos Bb) 2 cos A sin Bc) 2 cos A
cos Bd) 2 sin A sin B219) sin (A + B) - sin (A - B) dx =
___________a) 2 sin A cos Bb) 2 cos A sin Bc) 2 cos A cos Bd) 2 sin
A sin B220) cos (A + B) - cos (A - B) dx = ___________a) 2 sin A
cos Bb) 2 cos A sin Bc) 2 cos A cos Bd) 2 sin A sin B221) cos (A +
B) - cos (A - B) dx = ___________a) 2 sin A cos Bb) 2 cos A sin Bc)
2 cos A cos Bd) 2 sin A sin B222) etan-1 x dx = ___________ 1 +
x2a) tan-1 x + cb) ex + cc) etan-1 x + cd) none of the above223) x2
dx = ___________ 1 + x6a) 1/3 tan-1 x3 + cb) x2 + cc) 1/1 + x6 +
cd) none of the above224) tan x dx = ___________a) sin x / cos x +
cb) sec x + cc) 1/1+x2 + cd) log sec x + c 225) sec x dx =
___________a) 1 / cos x + cb) sec x + cc) 1/1+x2 + cd) log (sec x +
tan x) + c 226) dx = ___________ x2 + a2a) 1 / tan-1(x2 + a2) + cb)
1 / a tan-1(x/a) + c c) tan(x/a) + cd) none of the above 227) dx =
___________ x2 - a2a) 1 / log(x2 - a2) + cb) 1 / 2a log(x-a/x+a) +
c c) tan(x/a) + cd) none of the above 228) dx = ___________ a2 -
x2a) 1 / tan-1(x2 + a2) + cb) 1 / a tan-1(x/a) + c c) 1 / 2a
log(a+x/a-x) + c d) none of the above 229) dx = ___________ a2 -
x2a) 1 / tan-1(x2 + a2) + cb) sin-1(x/a) + c c) 1 / 2a log(a+x/a-x)
+ c d) none of the above
Unit 8: Differential Equations230) The order of a differential
equation is the order of the highest ___________ appearing in it.a)
Derivativeb) Functionc) Variabled) constant231) An ordinary
differential equation is that in which all the differential
coefficients have ___________ independent variable.a) One b) Two or
morec) Zerod) None of the above232) An partial differential
equation is that in which all the differential coefficients have
___________ independent variable.a) One b) Two or morec) Zerod)
None of the above233) The degree of a differential equation is the
order of the highest ___________ occurring in it.a) Derivativeb)
Functionc) Variabled) constant234) Every geometrical or physical
problem when translated into ___________ gives rise to a
differential equationa) differential equationb) functionsc) venn
diagramsd) mathematical symbols235) A solution of a differential
equation is a relation between the ___________.a) Derivativeb)
Functionc) Variabled) constant236) All the differential
coefficients have reference to a ___________ independent variable
in ___________.a) multiple, partial differential equationb) single,
partial differential equationc) multiple, ordinary differential
equationd) single, ordinary differential equation237) The standard
form of a linear equation of the first order is known as
___________.a) Leibnitzs equationb) Bernoullis equationc) Cramers
equationd) None of the above238) A differential equation is said to
be linear if the different variables and its differential
coefficients occur in ___________.a) Multiplicationb) Additionc)
first degreed) first order239) Leibnitzs linear equation is
___________.a) dy/dx + Py = Qb) dy/dx + Py = Qync) d2x/dt2 + n2x =
0d) none of the above240) Bernoullis linear equation is
___________.a) dy/dx + Py = Qb) dy/dx + Py = Qync) d2x/dt2 + n2x =
0d) none of the above241) A differential equation of the form M(x,
y)dx + N(x, y)dy = 0, is said to be exact if the solution is
___________.a) u(x, y) = Nb) u(x, y) = cc) u(x, y) = 0d) u(x, y) =
M242) Every geometrical or physical problem when translated into
___________ gives rise to a differential equation.a) Functionsb)
truth tablesc) mathematical symbolsd) venn diagrams
Unit 9: Complex Numbers243) What is the value of (i) in complex
number?a) 1b) -1c) d) 244) If z = (x, y) is a complex number then x
is called the ___________ part and y is called the ___________ part
of the complex number.a) Real, imaginaryb) Imaginary, realc) Real,
reald) Imaginary, imaginary245) For every (x, y) C, ___________ is
the additive inverse of (x, y).a) (-x, -y)b) (x, -y)c) 0d) (-x,
y)246) ___________ C is the multiplicative inverse of (x, y).a) x /
x2+y2 , y / x2+y2b) x / x2+y2 ,- y / x2+y2c) -x / x2+y2 , y /
x2+y2d) -x / x2+y2 , -y / x2+y2247) What is the value of (i2) in
complex number?a) 1b) -1c) d) 248) What is the value of (i7) in
complex number?a) 1b) -1c) id) -i249) If z = x + iy be a complex
number. Then the complex number ___________ is called the complex
conjugate.a) -x - iyb) -x + iyc) x - iyd) x + iy250) If z = -5 -
10i be a complex number. Then the complex number ___________ is
called the complex conjugate.a) -5 - 10ib) -5 + 10ic) 5 - 10id) 5 +
10i251) The product of complex number and its conjugate is a
___________ numbera) realb) complexc) imaginaryd) integer252) | z |
is ___________ a non-negative real number.a) Sometimesb) Neverc)
not alwaysd) always253) The plane whose points are represented by
complex numbers is called a/an ___________.a) Real planeb)
Imaginary planec) Argand planed) Euler plane254) ___________ of a
complex number z is denoted by ___________.a) Modulus, z.b)
Conjugate, z.c) Conjugate, |z|d) Distance, z255) r (cos, i sin),
This form of a complex number is called the ___________form.a)
Polarb) Trigonometricc) Both (a) and (b)d) None of these256) The
distance between the points z1 and z2 are ___________.a) | z1 z2
|b) | z2 z1 |c) Both (a) and (b)d) None of these257) If sincosthen
___________a) / 3b) / 2c) 2 / 3d) 5 / 3
258) If sincosthen ___________a) / 3b) / 2c) -2 / 3d) 5 / 3259)
eix = cosx + i sinx, This is called ___________.a) Eulers formulab)
Trigonometric formulac) exponential formd) None of the above260) r
e^i , This is called ___________.a) Eulers formulab) Trigonometric
formulac) exponential formd) None of the above261) (cos + i sin )n
= cos n + i sin n, This is called ___________.a) Eulers formulab)
Trigonometric formulac) exponential formd) De Moivres Theorem262) a
is a non-zero complex number and n, is a positive integer then z is
called the nth root of ___________.a) ab) zc) azd) za263) The cube
roots of unity are 1, , , then 1+ + 2 = ___________.a) 1b) 0c) d)
2
Unit 10: Matrices and Determinants264) We can have a zero matrix
of ___________ order.a) Zerob) Onec) Twod) any265) Two matrices A
and B are equal if its ___________ of rows of A and B are the
same.a) Determinantb) Numberc) Elementsd) cofactor266) A square
matrix is ___________ matrix if only the entries on the diagonal
are nonzero and other entries are 0s.a) Squareb) Zeroc) Diagonald)
scalar267) A diagonal matrix having the same number along the
diagonal is called a ___________.a) Squareb) Diagonalc) Scalard)
Zero268) If A and B are two matrices then AB is defined only when
the number of columns of A = number of ___________ of B.a) Rowsb)
Columnsc) Both (a) and (b)d) None of the above269) A m n matrix is
said to be a ___________ matrix when ___________.a) zero, m=0b)
zero, n=0c) diagonal, m = nd) square, m = n270) A/an ___________ is
a ___________ array of numbers .a) equation, sequentialb) equation,
rectangularc) matrix, diagonald) matrix, rectangular271) Let A, B,
C be 3 matrices, where (AB) C = A(BC) defines ___________.a) Left
distributive lawb) Right distributive lawc) Commutative lawd)
Associative law272) Let A, B, C be 3 matrices, where A(B + C) = AB
+ AC defines ___________.a) Left distributive lawb) Right
distributive lawc) Commutative lawd) Associative law273) Let A, B,
C be 3 matrices, where (B + C)A = BA + CA defines ___________.a)
Left distributive lawb) Right distributive lawc) Commutative lawd)
Associative law274) A square matrix A is invertible (or non
singular) if there exists a square matrix B such that
___________.a) AB = BA = Inb) BA = AB = Inc) Both (a) and (b)d)
None of the above275) If B is called the inverse of A then it is
denoted by ___________.a) A-1b) 1 / Ac) B-1d) 1 / B276) | A | is
called a ___________ of order n matrix.a) Modeb) Determinantc) Both
(a) and (b)d) None of the above277) The determinant of matrix A = 0
2 3 1 4 7 2 0 4 a) 0b) 4c) -4d) None of the above278) If |A| = 0,
the matrix a is called ___________.a) invertibleb) singularc)
non-singulard) non-invertible279) A matrix is invertible if and
only if it is ___________.a) invertibleb) singularc) non-singulard)
non-invertible280) Solve a system of n linear equations in n
variables using determinants. The method is provided by
___________.a) Cramers Ruleb) Eulers formulac) De Moivres Theoremd)
None of the aboveUnit 11: Infinite Series281) Infinite series u1 +
u2 + u3 + + un + .., which can be written as ___________.a) nb) c)
nd) All of the above282) Sequence of partial sums is denoted by
___________.a) Snb) Spc) Ssd) S283) A series is called ___________
if the sequence of its partial sums has a finite limit,a)
Divergenceb) Convergencec) Infinited) None of the above284) If a
sequence of its partial sums has no finite limit, then the series
is called ___________.a) Divergenceb) Convergencec) Infinited) None
of the above285) The series 1 + 2 + 3 + + n + + in ___________.a)
Divergenceb) Convergencec) Infinited) None of the above286) The
series Sn = 1 1 + 1 1 + .. is called ___________.a) Divergenceb)
Convergencec) Infinited) oscillatory287) A positive term series
diverges to ___________, according as its sequence of partial sums
is bounded or not.a) 0b) 1c) d) 288) The Binomial series is
absolutely convergent if ___________.a) | x | < 1b) | x | >
1c) | x | = 1d) | x | 1289) The logarithmic series convergent if
___________.a) 1 > x > -1b) -1 < x < 1c) Both (a) and
(b)d) None of the above290) A series is called ___________ if the
sequence of its partial sums has a ___________ limit.a) convergent,
infiniteb) convergent, finitec) divergent, constantd) divergent,
finite
Unit 12: Probability291) An ___________ is a process that
generates well-defined outcomes.a) Experimentb) Trialc) sample
spaced) throw292) When we perform an experiment we call it a
___________.a) Experimentb) Trialc) sample spaced) throw293) In
probability, 0 and 1 represents ___________ and ___________.a)
impossibility, certaintyb) certainty, impossibilityc) occurrence,
failured) yes, no294) ___________ is one and only one outcome among
the several well defined outcomes.a) Experimentb) Trialc) sample
spaced) throw295) If tossing of two coins, then the probability are
___________.a) 2b) 3c) 4d) 6
296) If Roll of two dice, then the probability are
___________.a) 12b) 32c) 24d) 36297) Plays a test cricket match,
then the probability are ___________.a) Winb) Defeatc) Drawd) All
of the above298) The ___________ for an experiment is the set of
all possible outcomes.a) Experimentb) Trialc) sample spaced)
throw299) An event in an experiment is a subset of the
___________.a) Experimentb) Trialc) sample spaced) throw300) A
single outcome is called an ___________.a) Experimentb) Elementary
eventc) sample spaced) throw301) The classical probability is also
called ___________.a) Mathematical probabilityb) Priori
probabilityc) Statistical probabilityd) Both (a) and (b)302) In
___________ approach, the experiment is repeated a number of times
to define the probability of an event.a) Statistical probabilityb)
Priori probabilityc) Subjective probabilityd) Classical
probability303) A bag contains 3 red balls, 4 green balls and 5
blue balls. The probability of choosing 2 red balls, 1 green ball
and one blue ball are ___________.a) 4 / 33b) 1 / 33c) 4 / 99d) 1 /
99304) The statistical probability is also called ___________.a)
Mathematical probabilityb) Priori probabilityc) empirical
probabilityd) Both (a) and (b)305) The subjective probability is
also called ___________.a) Bayesian probabilityb) Priori
probabilityc) empirical probabilityd) Both (a) and (c)306) In
___________ approach, the experiment that can be performed only
once or only few times.a) Statistical probabilityb) Priori
probabilityc) Subjective probabilityd) Classical probability307) A
ball is drawn from a bag containing 10 black and 7 white balls, the
probability that it is white are ___________.a) 17 / 7b) 7 / 17c) 7
/ 19d) 19 / 7308) If two dice are rolled & the sum is greater
than 9 then the probability are ___________.a) 1 / 36b) 36c) 6d) 1
/ 6 309) The probability that a 60 year old man to be alive for 5
years is 0.80 and the same probability for a 55 year old woman is
0.85. Find the probability that a couple of ages 60 and 50
respectively will be alive for the next 5 years.a) 0.80b) 0.85c)
0.68d) 0.86310) When events A, B, C are mutually independent, then
the events A and B are ___________.a) Dependentb) Independentc)
Outcomesd) mutually dependent
311) Bayes theorem is used for revising ___________ on the basis
of new information.a) Numbersb) Datac) Probabilityd) Equation312)
The revised probabilities are called ___________.a) posteriori
probabilityb) Priori probabilityc) Subjective probabilityd)
Classical probability
Unit 13: Basic Statistics313) The ___________ of a set of data
gives an indication of the amount of dispersion, or the scatter, of
members of the set from the measure of central tendency.a) central
tendencyb) standard deviationc) geometric meand) harmonic mean314)
A simple comparison of frequency distribution is made by comparing
their measures of ___________.a) central tendencyb) standard
deviationc) geometric meand) harmonic mean315) ___________ of a set
of values is obtained by dividing the sum of the values by the
number of values in the set.a) Arithmetic Meanb) Geometric Meanc)
Harmonic Meand) Median316) Heights of six students are 163, 173,
168, 156, 162 and 165 cms, the arithmetic mean is ___________.a)
170 cmsb) 165 cmsc) 164.5 cmsd) 166.5 cms317) Algebraic sum of the
deviations of a set of values from their arithmetic mean is
___________.a) 1b) c) -1d) 0318) Sum of the squared deviations of a
set of values is ___________ when deviations are taken around the
arithmetic mean.a) Maximumb) Minimumc) 0d) None of the above319)
The mean of marks scored by 30 girls of a class is 44%. The mean
for 50 boys is 42%. The mean for the whole class is ___________. a)
44%b) 42%c) 42.75%d) None of the above320) ___________ of a set of
values is the middle most value when they are arranged in the
ascending order of magnitude.a) Arithmetic Meanb) Geometric Meanc)
Harmonic Meand) Median321) No. of children per couple: 2, 0, 5, 2,
5 , 1, 0, 0, 3, 4, 2, 1, 1, 2, 3, 0, 1, 2, 7, 2, 2, 1, 3, 4, 1. The
median is ___________.a) 2 children per coupleb) 5 children per
couplec) 1 children per coupled) 3 children per couple322)
___________ is the value which has the highest frequency.a)
Arithmetic Meanb) Geometric Meanc) Moded) Median323) Median of a
set of values is the middle most value when they are arranged in
the ___________ order of magnitude.a) Calculativeb) Ascendingc)
Descendingd) average324) Frequency distributions have only one
value with highest frequency. Such frequency distributions are
called as ___________.a) Unimodalb) Multimodalc) Bimodald) None of
the above325) Frequency distribution, there is more than one value
with highest frequency, Such frequency distributions are called as
___________.a) Unimodalb) Multimodalc) Bimodald) None of the
above326) Frequency distribution, there is two value with highest
frequency, Such frequency distributions are called as
___________.a) Unimodalb) Multimodalc) Bimodald) None of the
above327) ___________ is the root mean square deviation of the
values from their arithmetic mean.a) central tendencyb) standard
deviationc) geometric meand) harmonic mean328) Symbol of standard
deviation is ___________.a) b) c) d) 329) Standard deviation is the
positive square root of ___________.a) Meanb) Modec) Covarianced)
variance330) ___________ is the best absolute measure of
dispersiona) central tendencyb) standard deviationc) geometric
meand) harmonic mean331) The coefficient of variation represents
the ratio of the ___________ to the ___________.a) median, meanb)
median, modec) standard deviation, meand) mean, standard
deviation332) While comparing two or more groups, the group which
has less coefficient of variation is ___________.a) more
consistentb) less homogeneousc) less uniformd) more variable333)
Coefficient of variation is the more widely used relative measure
of ___________ and the best measure of ___________.a) Standard
deviation, meanb) Mean, standard deviationc) Central tendency,
dispersiond) Dispersion, central tendency334) ___________ is the
mean square deviation of the values from their arithmetic mean.a)
Standard deviationb) Coefficient of variationc) Varianced) Central
tendency335) Standard deviation is used in ___________.a) Biologyb)
Educationc) Psychologyd) All of the above1
