of 48
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1.
If
3
is the root of the equation
:
2
-
Bx
+
k
= 0,
then what is ;the
value.of
k?
a)
1
-15
. b)
9
c).
15
d)
24
I
I
I
·
2.
Two
straight lines x
3y
2 = j
and
2 x 6 y 6 = 0
1
I
a) never intersect
I
b) intersect at a single point
I
'
c) intersect at infinite number of
points
I
d)
intersect
at
more
than
one
I
point
but finite number of
points)
3. If
(a,
0), (0, b),
1, 1) are
collinear,
what is a+ ab equal to?
j
I
a)
2
b)
1
c) 0
d)
-1
P A Q N A ~ Z N G U / 6 6 A
2
4. If
5.
6.
A = [ ~ and B = ~
,
then
which
of
the
following is1 re
correct?
1.
AB
is defined
.
2.
BA is
defined
3.
AB=BA
•
Select
the
correct
answer using the
code
given below
:
Code:
a)
1
only
b)
2
only
c)
1 and 2
only
d)
1, 2 and 3
Using
the
digits 1,
2,
3, 4 and 5
only
once, how
many
numbers greater
than
41000 can be formed?
a)
41
b)
48
c) 50
d) 55
If
an
angle
a
is divided into two parts
A and B
such that
A
-
B
= and
tanA: t anB=2: 1
then
what
is
sinx equal to?
a)
3sina
b)
2sina)
3
c)
sin
a)
I 3
d)
2sina
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•
~
L
wft'fl(UI x
-
x
+ k =
0
'liT
l\'h
'@
3 t,
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7 A man
standing
on the bank of a
river observes that the
angle
of
elevation
of the top of a tree just on
the opposite bank is
60 . The
angle
of elevation is 30
from
a point at a
distance y metres from the bank.
What
is
the height
of
the
tree?
a) y metres
{b)
2y metres
../3y
c) metres
2
d) metres
8.
If P Q,
R
are three non-collinear
points, then what
is
Qn R
equal
to?
a) Null set
b) {P}
c)
{P
Q R}
{d) {Q R}
9 A, B,
C,
D and E are coplanar
points·
and three of them lie in a straigh(
line.
What
is the maximum number
of triangles that can
be
drawn with
these points as their vertices?
a)
5
b)
9
c) 10
d) 12
P-AQNA-L-ZNGU/66A
4
.
10 The vector
a lies in
the
plane
of \
...
...
vectors
b and
c Which one of
the
following is orre t ?
_ _ _
{a) · b x c) = 0
....
... _
{b) a · b x c ) = 1
... ...
...
c) a · b x c) = -1
...
...
_
d)
a ·
b x
c =
3
11 What is the
projection
of the
vector
1-
2)
+
k
on the vector
41-4}
+
7k
?
-./5
a) 2
{b)
c)
19
9
-./5
4
{d)
11
3
12 Which one of the following
statements is correct?
a)
sin
2
30 ,
sin
2
45 , sin
2
60
are
in GP
b) co s
2
30 ,
co s
2
45 , co s
2
60
are
in GP
c) cot
2
30 , co t
2
45 , cot
2
60 are
in
AP
d) tan
2
30 , tan
2
45 ,
tan
2
60 are
in
GP
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7.
mil il;
fof;;rit ~
1% 'Of
~
'li\uT 60 i I fof;;rit U y
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13.
If sum of
squares
of the
roots
of the
equation
x
+k x b = 0
is
2b,
what
is
k
equal to ?
a)
1
b) b
c)
b
d)
0
14 If one
root of the
equation
ax
+ bx +
c
= 0 a;< 0
is
reciprocal
of
the other
root,
then
which
one•
of
the following is correct ?
b) b = c
c) a= c
d) b
= 0
15. f w is
the
imaginary
cube
root of
unity, then
what
is 2- w+2w
2
)
27
equal
to?
a)
3
27
w
P-AQNA-L-ZNGU/66A
6
16
What is the modulus of
1 1
?
1
3i
1 3i
a)
3
5
{b)
9
25
c)
3
25
d)
5
3
17
Let
M be the set of
men and
R is a
relation
is
son
or defined on M
Then R is
a) an equivalence relation
b) a symmetric relation only
{c)
a
transitive relation
only
d) None
of the above
18. What is the locus of
the point
which
is
at a
distance
8 units to the
left
of y-axis ?
a) x
= 8
c)
x
= -8
d) y
=
8
f)
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• 13. \1tfl'h(Oi x
2
+ k x b = 0 i t >@ it
'fliT ""
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19 The
number 10101111
in binary
system
is
represented in decimal
system by which one
of
the
following
numbers?
a) 157
b)
175
c) 571
d)
751
20 There
are 4
letters
and 4 directed
envelopes.
These 4 letters
are
ran
domly inserted into the
4 envelopes.
What
is
the
probability
that the
letters
are inserted into the
corresponding
envelopes?
a) 11/12
b)
23/24
c)
1/24
d) None of
the
above
21
The average daily income of workers
of a factory including that of t he
owner
is
I
110.
However, if the
income of
the
owner
is excluded,
the average
daily
income
of
the
remaining 9
workers
is
I 76. What
is the daily income of
the
ownerr
a) I 300
b) I
316
c) I 322
d) I
416
P-AQNA-L-ZNGU
/66A
8
22. If
A,
B, Care non-empty
sets s u c h .
that
A
n
C =
then what is
(Ax B n(Cx B equal to?
a) Ax C
b)
Ax
B
c) Bx C
d)
23. If
A
{4n + 21 n is a natural number}
and
B = {3n I n
is a
natural
number},
then what
is A n B equal
to
?
a)
{12n
2
+
6n
1
n
is
a
natural
number}
b) { 24n- 12 I n is
a
natural
number}
c) { 60n + 30
I
n is a natural
number}
d) {12n-61n
is a
natural
number}
24.
If
the matrix
A [ ~
]
is such that
A
2
=
I, then
which one
of
the
following is correct?
a) a =
0,
J3 =
I or
a =
I
J3 =
0
b) a
= 0, J3 I
or a
0, J3 = I
c)
a
=
I
J3 0
or a
I J3 =0
d) a
¢ 0, 13 ¢ 0
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19. ~ 3 l l t f f i \ 14>l
i l ~ r m ?
a)
11/12
b) 23/24
c) 1/24
21. fomt
it
q;
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25.
What is
the sum of
the focal
distances of a point of
an ellipse
x2 y2
-+-=1?
a2
b2
a) a
b) b
c) a
{d) 2b
26.
What is the degree
of
the following
differential
equation?
{a)
1
b) 2
c)
3
d)
4
27.
What
is the sum of
~ - - - · ..
?
~
a)
2
{b)
2
c)
~
3
d)
P AQNA L ZNGU/66A
10
28. What does the differential equation
:
ydy x=a
dx
where a is a constant)
represent?
a)
A
set of
circles
having
centre
on the
y-axis
b) A set of circles
having centre
on
the x axis
c)
A set of ellipses
d) A pair of straight
lines
29.
If
30.
such that A
2
= B, then what is the
value of a
a) 1
b)
c) 2
d) 4
What
is
the value
of
n if
P 15,
n -
1
: P 16, 2) = 3 : 4 ?
a)
10
b)
12
c)
14
d) 15
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27.
a) a
b)
b
c) a
d) 2b
a)
1
b) 2
c)
3
d)
4
.,[3
1 I
+ - + - +
... 'iT >itTJ
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12/48
31.
What is
the value of
the
determinant
x 1
x + 2 x + 4
x 3 x + 5
x+8
?
x+7
x 10
x
14
a) x
+2
b) x
+2
c)
2
d)
-2
32
Consider
the
following statements in
respect of the function
f x )=x
3
-1 ,
xe[-1 , 1
1.
f x) is increasing
in
[-
1, 1
2. f x) has no
root
in
-
1, 1
Which of the
statements
above
is/ are correct?
a) 1
only
b) 2
only
c)
Both
1 and 2
d)
Neither
1 nor 2
P-AQNA-L-ZNGU/66A
• I
g1ven
12
33.
The largest value
of
•
x
3
- 3x
2
- 12x +
5
for
-2
; x ; 2
occurs when
a)
X=
-2
b)
X=
-1
c)
x = 2
d)
x=O
34 What is
r dx
0
1+2sin
2
x
equal to?
a)
b)
c)
1t
../3
d)
2rr
../3
35.
If
5 and 7 are the roots of the
equation
X 4 5
7 X 7
=
0
5 8
X
then
what
is
the third
root?
a)
-12
b)
9
c) 13
d)
14
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x 1 x 2 x 4
x 3 x 5 x 8
x 7
x+lO x 14
a) x
+2
c)
2
d) -2
32
f(x)
= x
3
- 1,
x E
1,
1] iii fii I I
it
f.i"1R1fula
'R :
1. f(x), [- 1, 1] it
< Prr:
t I
2. f ( x ) l i l ~ W f ( - 1 , 1)it 'ft tl
a)
1
b)
~
c) 13ft\ 2
~
P AQNA L ZNGU
/66A
13
I
33 '-2,;; x,;; 2
~
2x
3
3x
2
:
i2x + 5
liT 31f'q
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36
In
a
GP
of
positive
terms, any term
is equal to
one-third of the
sum
of
next two terms. What is
the
common ratio
of
the GP?
.Jl3
+ 1
a)
2
.Jl3-
1
b)
2
c)
.Jl3
+
1
3
d) .Jl3
37
If( l+tan8)(l+tancp)=2,
then what
is
8 cp equal
to
?
a) 30•
b) 45°
c)
60•
fd
go·
38 If
f(x) is
an
even function,
then
what is
J ~ J c o s x)
x
equal to?
a) 0
b)
g
f(cos x)
x
c) Jg f(cosx)dx
d)
1
P-AQNA-L-ZNGU/66A
14
39.
What is the value of k for
which
th
system
of
equations kx 2y = 5
and
3x y
= 1
has
no solution?
a)
0
b)
3
c) 6
d) 15
40 In how many ways
can
6 girls be
seated in 2 empty chairs?
a)
10
{b)
15
c)
24
d) 30
41
What is
the
value
of
a) 3
b) 2
c) 1
d) 0
42 Which
term
of
the series
is
-128?
a)
9th
b) lOth
c) 11th
d)
12th
1 1
4
2
1
...
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, • 36. 'Gl
)
{ O j -
1
f.'ri >r<
kx
+
2y =
5
om 3x
+
y =1' 'liT
~ ~ m i '
a)
0
b)
3
c) 6
d)
15
I
40 6
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43
Wha
t
is
the
number
of
or
dered pairs
of non
-zero
positiv
e
integers
x
i
y
such tha
t y s; 4 ?
a) 4
b) 5
c) 6
{d) 8
I
44
In
the binary
system of n
u m ~ r s
let
= 00 111
and
b
= 0 111 0, then
in
deci
mal system what
is b}
e
qual
to?
a
)
b) 2
c)
d) 5
45
f
1 1
1 1
-
- --=-
b
a b e
c
then a,
b, c are in
a)
P
b)
G
P
c)
P
d) No
ne of
t
he above
P-AQNA
-lr-ZNGU/66
A
I 16
46
W
hat
is
the
middle
term
in
t
h
expansion
of
1 - ~ r
?
a)
35x
4
b)
I7x
5
8
c)
35x
5
d)
None
of the
above
47.
What is
the sum of the roots
of the
e
quation
a
)
2--/3
b) 2 13
c) 7
-4-/3
d) 4
48
W
hat
is
the total n
umber
of
combi
nations o
f n different
things
taken
1 2
3
... ,
at
a time
b)
2
2n+l
c)
2 -I
d
)
2
1
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••
tfl 43. i t
;r; lrn :rtiJ
x,
Y
ofi\
f''T + y :5 4 it?
a) 4
b)
5
c)
6
d)
8
44
~ m m t l oli\
~ o n j
l:rR fif;
a ; 00111
3fn:
b 01110, (OI I
2
-.J3)x
2
- 7 -4.J3)x + 2 +
. J3 ;
0
1
i t
@ l
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49. One of
the
roots of
the quadratic
equation
ax
2
+ bx + c = 0, a 0 is
positive and
the other root is
negative. The condition
for
this to
happen is I
a) a >
0, b
>
0, c
>
0
b)
a>
0, b < 0,
c >
0
c) a
< 0,
b
> 0,
c
< 0
d)
a< 0,
c
> 0
50. f
the solution
of
the
differential
equation
dy
ax 3
=
dx 2y+ f
represents a circle, then what
is
the
value of
a? 1
a) 2
b)
1
c) -2
d)
1
I
I
51.
f A
B,
Care
in AP
and
b:
c = J3:
.J2
then what is
the
value of sin C?
a) 1
1
b)
J3
c) J3
1
d)
.J2
P A Q N ~ L Z N G U / 6 6 A
18
52. The points with position
vectors
101
+ 3 , 121- 5 , a +
11
are
collinear,
if the value
of
a is
a) 8
b) 4
{c) 8
d) 12
53. What is
the
sine
of
angle between
the
vectors i +
2
+3k and - +2] + 3k?
a) ff
b) .ff3
7
c)
13
.J7
d)
None
of
the
above
54. If
. .
1
1
1
)
Slfl ln
5
COS =
then what
is
x equal to?
a) 0
b)
1
c)
4
5
1
d) 5
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•
. 49
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55 What
is
l o g a + ~ a + 1)+log(
1
)
a ~ a 1
equal
to?
(a)
1
b)
0
{c)
2
{d) I
2
56.
5
books
are
to be
chosen
from a lot
of
I
0
books. If
m
is
the number bf
ways of choice when one
s p e i f i ~ d
book is always included and
n
is
the
number of ways of choice
when
a
specified book is always exclude
d,
then which one
of
the
following
is
correct?
(a) m
>
n
(b) m = n
c)
m
=
n I
(d) m = n 2
57 Which one
of
the
following ' is
correct
in respect of
the
function
f(x)
=)xi+ x
?
(a) f(x) is
not continuous at
x
=
0
(b)
f(x)
is
differentiable
at
x
=•0
c) f(x) is
continuous
but not
differentiable
at
x
= 0
(d) None of
the
above
P-AQNA-J...-ZNGU/66A
20
•
8.
What
is
the
condition
that
one rooto
the
equation ax
+ bx + c =
0,
a
0
should
be double
the
other?
(a) 2a
2
=
bc
(b)
2b
2 =
ac
c) 2c
2
= ab
(d) None of
the
above
59. Consider the
following with regard to
a relation
R
on a
set
of real
numbers defined by
xRy
if and
only if 3x
+ 4 y = 5 :
I
0
R
I
2.
IR_ _
2
3.
~ ~
3
4
Which
of
the above are
correct?
(a) I
and
2 only
(b) I and
3
only
c) 2
and 3
only
(d)
I,
2
and
3
60. The function
f(x)
=
k sin
x
+_ _sin
3x
3
has maximum
value
at
x =
Z: What
3
is
the value
of
k
?
(a) 3
b)
I
3
c) 2
(d)
I
2
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•••
55.
l o g ( a + ~ a
+1)+log(
1
J
liT
a ~ a 1
1lR q
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61
Wha
t is
J in-
1
co
sx) dx
e
qual
to
?
X1l
x
a)
-
- -
k
2
2
1
t
x
(
b) -
-
k
2
2
X1
l x
(c
)
---
-
kx
2
2
1t
x
d) --
-
k
2
2
where k
is
a
consta nt
of
n t e g r a t i
6
2. f
a
and
3
are
the
ro
ots
of
th
e
equa
tion
4 x
2
+
3x
+ 7
0,
then
w
hat
is the
v
alue
of
a
-
2
+
3 -2 ?
a)
47/
49
b
) 49/4
7
(c)
4
7/49
d) 4
9/4
7
6
3. W
hat
is
t
he
eq ua
tion o
f th
e l
ine
p
assi
ng
thro
ugh
(2
, -
3 )
an
d
para
llel
to y-a
xis?
a) y
3
(b)
y 2
(
c)
x 2
d
) X ~
-
3
P-A
QNA
-L-
ZNG
U/66
A
22
64.
Wh
at is
th
e s
et of
p
oints
x
,
})• •
sa t
is fy i
ng the
e
quat
io ns
x 2
+ y
2
4
and
x
y ~ 2
?
a)
{ 2, 0), -2 , 0) ,
0,
2)}
b) { 0
, 2),
0,
-2)
}
(c
) { 0,
2),
2,
0)}
d)
{
2, 0),
-2,
0),
0 ,
2
),
0 ,
-2)}
65.
C
ons
ider th
e
fo
llow
ing
state
men
ts :
I. T
he i
nve r
se of
a
s
quar
e m
atrix
,
i
f
t
ex
is ts
s uniq
ue.
2
.
f
and
B
a
re
sing
ular
m
at r
ices of
or
der n
then
B
is a
lso a
s
in gu
la r m
atri
x of
or e
r n
W
hic
h of
th
e state
men
ts
g
iven
ab
ove
is I
are
corr
ect?
a
) 1 o
nly
b
) 2
on
ly
(c)
B
oth
1
and
2
d
) Ne
ither
1
nor 2
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X1l x2
a) - - - k
2 2
1t
x2
b) - - k
2 . 2
X1l x2
c)
---- kx
2 2
1t x2
d)
--- k
2 2
62.
~ \ 1 ~ i i f i { O i 4x
2
+3x +7 = 0 '@
a 31i\ J t i t (a -2 + J -2)
'1>1
l R 'l'IT
t?
a) 47/49
b)
49/47
c) 47/49
d) -49/47
63. (2, - 3) i t 11
X
y = 2 qi \
~ ~ m (x, IJ '1>1
'l'IT t? i
a)
{(2,
0),
(-2,
0),
(0,
2)}
b) {(0, 2),
(0,
-2))
c) {( 0, 2), (2,
0 }
I
I
d) {(2, 0), (-2, 0), (0, 2), (0,
- 2)}
i
I
L
' - ~ - : J :
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66
Wha
t is
th e
an g
le be
twe
en
th e
li n
es
whos
e di
recti
on
co
sine
s
a
re
prop
or ti
onal
to 2
,
3
, 4
an
d
1,
-2 ,
1 re
spec
tive l
y?
a
) 90
°
b)
6
0°
c
) 45
°
d)
30
°
67.
W
ha t
i
s
th e
val
ue o
f
for
whi
ch
th
e f
o l low
ing
f
unct
ion f
x)
is
co
ntin
uous
for al l
x?
{x
3
-3x
2
f
or
x
1
f x) =
x
~ 1
2
for
x=1
a)
3
{
b)
2
c)
1
d)
-1
68 If
p
q
,
r are
ra
tiona
l nu
mbe
rs, the
n
the
roots
o
f th
e e
quat
ion
are
a
) co
mple
x
b)
p
ure
im a
gina
ry
c) ir r
at io n
al
d)
ratio
nal
P-A
QNA
-L-
ZNG
U/66
A
2
4
•
9. If
A
{
1, 2,
5, 6}
and B
{
1, 2, 3
} •
7
0
the
n
w
hat
is
Ax
B n
Bx
A
equ
al to?
a
) {
1, 1
). 2
, 1).
6,
1). 3
, 2
}
b
) { 1,
1).
1, 2)
. 2,
1).
2, 2)}
c
) { 1 ,
1) .
2 ,2)
}
d)
{
1, 1
). 1
, 2).
2,
5), 2
, 6
))
W
hat
i
s
th e
di ff
eren
tial
equ
atio
n of
a
ll
p
arab
olas
who
se
ax e
s are
p
aral
lel to
y-a x
is?
wh
ere c
is
a
cons
tant.
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••
66 ff.l
~ m
4i't
~ ~
(2, 3, 4)
:;m
(1,
-2
1)
~
jiill1 1:
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For the
next
five
5)
items
that
follow :
The students
of a class are offered three
languages (Hindi, English
and
French).
15
students
learn all the three languages
whereas 28 students do
not
learn
any
language. The
number
of
students
learning
,
Hindi and
English
but
not French
is twice;
the number of students learning Hindi and,
French
but
not English. The number
of
students learning
English
and French
but
not
Hindi
is
thrice the number of
students
learning
Hindi
and French but
not
English. 23 students
learn
only Hindi
and
17
students
learn only English. The
total number of students
learning
French
is 46 and the total number of students
learning
only
French
is
11.
71
How
many
students
learn
precisely
two languages?
a)
b)
40
c) 30
d)
13
I
72
How
many students
learn at
least
two languages?
a)
15
b)
30
c) 45
d)
55
P-AQNA-J.r.ZNGU
/66A
26
73 What
is
the
total
strength
of
the
class?
a} 124
b) 100
c) 96
d) 66
74 How many
students
learn
English
and
French?
a) 30
b) 43
c) 45
d)
73
75
How
many
students learn at least
one
language?
a)
45
b) 51
c)
96
d) None
of
the
above
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P AQNA L ZNGU/66A
27
[ P
T
0
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76.
If
I = i tann xdx
n o
then
what is
In + In_
equal to?
a) 1 /n
{b) 1/ n-1)
c) nf n-1)
d) 1/ n-2)
77. What is
the
equation of
the
line
joining
the
origin
with
the
point
of
,
intersection of the lines 4x + 3y =
12 ,
and 3x+4y=
12?
78
{a)
X
y I
b) y
I
c) 3y=4x
d)
X y
If
the
sum
of the squares of the
distances of the
point (x,
y)
from
the points
(a, 0)
and -a,
0)
is 2b
2
,
then
which one of
the following
is
correct
P AQNA L ZNGU/66A
28
79
If
f(x)
= 2x,
then what
is f (x)
equal to?
{a
2x ln2)
2
b) x(x -1)2x-
2
c)
2X I
(ln2)
d)
2x(log
10
2)
2
80
In
an examination, there are
3
multiple-choice
questions
and each
question
has
4
choices. f
a
student
randomly
selects an
answer for all
the
three questions, what
is the
probability that the
student will
not
answer all the three questions
correctly?
a) 1/64
b)
63/64
c)
1/12
d)
11/12
81 What is
the
geometric mean of
the
data 2,
4, 8,
16,
32
?
a) 2
b) 4
c)
8
d) 16
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··
76 ~
•
~ t a n n x d x
n
0
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82
What is the cumulative
frequency
85 What is
curve of
statistical data
commonly
called?
lim
a x l - ~ a +1
x . ~
a)
Cartogram
equal
to?
a)
1
b)
-
Histogram
2
c)
Ogive
b)
c)
2
d) Pictogram
d) 0
86
What is
83.
If
A and
Bare two mutually
exclusive
JsinJX
x
events,
then what
is
P AB)
equal
to?
X
equal to?
a)
0
cosJX
a)
+c
2
b)
P A)
P B)
2cosJX c
b)
c)
P A) P B)
c)
cosJX
+c
2
d)
P A)P B
IA)
d) -2cosJX
+c
where cis a constant of
integration.
84
If x ;s in8 cos8 and y;s in8.cos8,
then
what
is the
value
of
87. Which one of the following is
the
unit
vector
perpendicular
to
the
x
4
-4 x
2
y- 2x
2
+4y
2
4y 1?
vectors 41 2] and -31 2} ?
a)
1 J
J2
a)
0
b)
1 -
J
b) 1
J2
c) 2
c) k
d)
1 ] k
d)
None of the
above
.[3
P-AQNA-L-ZNGU/66A
30
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82.
:j J
l +]
I
a)
./2
I
'
a) 0
l ]
I
b)
i
./2
I
{b) 1
I
c)
k
c) 2
d)
l+]+k
d)
it t 'It ../3
P-AQNA-lr-ZNGU/66A
31
[P. T.
0.
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88 Consider
the
following statements in
respect
of
the vectors
__
__
u
1
; (I,
2,
3
),
u
2
;
(2, 3, I),
u3;
(I,
3,
2)
and u4;
(4,
6,
2)
I .
u
is parallel
to
u4
2. u2
is parallel
to u4
3. u2 is parallel to u
Which of the statements given
above is/ are correct?
a) I only
b) 2
c)
3
only
d)
I
and
3
89 The line mx + ny I passes through
the points (I, 2)
and
(2, 1). What is
the value
of m?
a) I
b)
3
I
c)
2
d) I
3
90 What is
the
solution
set
for
the
equation x
4
-26x
2
25 ; 0?
a)
{ -
5, -
1, 1,
5}
b)
{-5,
-1}
c) {1, 5)
d) { - 5,
0, 1, 5}
P-AQNA-1.-ZNGU/66A
32
For
the
next
four
4)
items that
follow :
.
ABC is
a
triangle right angled at B The
.
hypotenuse
AC) is four times
the
· perpendicular
BD)
drawn to it from the
opposite vertex
and
D <
DC
91
What is one
of the
acute angles
of the
triangle?
a)
15•
bJ
3o•
c)
45•
d)
None of
the
above
92. What is angle
ABD?
a) 15•
bJ
3o•
c) 45•
d)
None of
the
above
93
What is AD DC equal
to?
a) 7- 2J3) : 1
b)
7 -4J3 : I
c) 1 : 2
d) None of
the
above
••
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··
88. u
=
(1,
2,
3), i
2
=
(2,
3, 1),
u
= (1, 3,
2) 3itt
i
4
= (4,
6, 2)
ifi
q
f.il•"lfeifl ld ' ~ 'R
f
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94
What
is tan(A - C)
equal
to ?
a}
0
{b) 1
c)
2
d) None of the above
95
What is the radius of the
sphere
x
2
2
z
2
x y z= 0?
a)
J¥
b)
~
c)
d)
1
-
3
96
An
experiment
consists
of flipping•a
coin and
then
flipping it a
second
time if
head
occurs.
If
a tail
occurs
'
on the
first flip,
then
a six-faced die
'
s
tossed once.
Assuming
that the
outcomes
are equally likely, what
is
the probability of
getting
one head
and one tail?
a) 114
b) 1136
c) 116
d)
118
P-AQNA-L-ZNGU/66A
4
97. If, in
general,
the value of
sinA
is
known, but the value of A
is
not
known,
then
how
many
values of
tan(A 12
can
be calculated ?
a) 1
b) 2
c) 3
d)
4
98 Consider the following :
l
cosec-
1
~ ) =
~
2. sec-
1
~ ) =
Which of the above is I are correct?
a) 1 only
b)
2
only
c) Both 1 and 2
d) Neither 1 nor 2
99 Consider the
following
statements
with regard
to
correlation
coefficient
r
between
random
variables
x
and y
:
l
r =
1
or -1
means there
is a
linear relation between x and
y
2. - I ; r ; I and r
2
is a measure
of the linear relationship
between the variables.
Which
of
the statements given
above is I
are correct ?
a) I
only
b) 2 only
c)
Both
I and 2
d)
Neither I
nor
2
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•••
94. tan(A - C)
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100. I f the values of a set are measured
in em, what will be
the unit of
variance?
a)
em
c) cm
3
d) No unit
101. A
box
contains 6 distinct dolls.
From
this
box,
three
dolls
are
randomly selected one by one
with replacement.
What
is
the
probability of selecting 3
distinct
dolls?
a)
5/54
b)
12/25
c) 1/20
d) 5/9
102. For
the equation
ax
by
2hxy 2gx 2fy c; 0
where a * 0 to represent a circle
the condition will
be
a) a ;
b and
c ;
0
b)
f
;
g
and h ;
0
c)
a
; b and h ; 0
d) f ; g and
c
; 0
P-AQNA-L-ZNGU/66A
36
103. If
A
and
B are events
·such that
P AuB);0-5 , P B) ;0 -8 and
P
A
I B) ; 0-4, then what is P A
n
B)
equal to?
a)
0·
08
b)
0·02
c)
0 · 8
d)
0·2
104.
Consider the
following
relations
among the angles a, f3 y made by a
vector
with
the
coordinate axes
1.
cos2a +cos2f3+cos2y; I
2. sin
2
a +sin
2
f3 +
sin
2
y ; 1
Which
of the above
is/ are
correct?
a)
I
only
b) 2 only
c)
Both
1
and
2
d)
Neither
1 nor 2
105. Which one of the following points lies
on
the
plane 2x + y 6 z ; 21?
a) 3, 2 2)
b)
3, 7, 1
c) 1,
2,
3)
d) 2, 1, -1
··
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••
100
~
mf\ ~ i t ; l1R em
ii
.rn orffi
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106
What is the acute
angle
between
the planes
x
+ y+2z =
3
and
- 2 x y - z = 11?
a) n
I
5
b)
1t
14
c) n I
6
dJ
n 13
107 What is the area bounded by the
curves
y
= e ,
y
= e-
and
the
straight line
x
= 1?
108
a) e
+ _. :l
square units
e;
b)
square
units
c)
e +
2)
square
units
d) e
- ~ -
2)
square units
hat
are the
points
of
intersection
of
the curve 4x
2
- 9y
2
=
1
with its
conjugate
axis?
a) (112, 0) and (-112, 0
b) (0, 2)
and
(0,
-2)
c)
(0, 3)
and
(0,
-3)
d) No
such points exist
P-AQNA-L-ZNGU/66A
38
109
What is
the
locus
of a
point
which
moves equidistant from the
coordinate axes?
a) x ± y = 0
b) X
+2y
=
0
c)
2x
+ y = 0
d) None of the above
110
What is
111
equal to?
a) xe + c
d) 2xe +c
where cis
a
constant of
integration.
Let
p,
q, r, s
be
respectively the
magnitudes of the vectors 31- 2],
21
+ 2] + k, 41-] +
k, 21
+ 2] +
3k
Which one of the following is
correct
a} r > s >
q
>
p
b) s > r > p > q
c) r
>
s >
p
>
q
d) s >
r
>
q
>
p
••
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106
109
f.tfuol;
31cl B
"WfR ~
~
x +y +
2z 3 3ffi
-2x +y
z 11
q ; J ~ ~ < F n i ?
iii [ O
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112 In a triangle
ABC,
if c = 2
A
1200
a
= ..[6 then what is equal to ?
113
a) ·
30°
c)
600
lass
Interoal
1 5 6 10
11 15 16 20
Frequency
3 6 5
Consider the following statements
in respect of the above frequency
distribution :
I The median is contained in the
modal class.
2. The distribution
is
bell shaped.
Which of the
above
statements
is
I are correct?
a) I only
b)
2
only
c) Both I and 2
d)
Neither I
nor
2
P AQNA L ZNGU/66A 40
For the next tw
21 items that
follow :
Tlie following table gives the continuous
f r ~ q u e n y
distribution
of a continuous
variable
X
:
lass Interval
0 10
10 20 20 30
30 40 40 50
Frequency
5
10
20
5 10
114 What is the median of the above
frequency distribution?
a)
23
b) 24
c) 25
d)
26
115 What is the mean of the
above
frequency distribution?
a) 25
b) 26
c) 27
d) 28
•
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112 ABC
il, ~ c
=
2, A 120°,
a
../6, m
~
< mf(
113
a)
300
c) 600
q t f ~
1-5
6-10 11-15
16-20
UIHI GIIHU
3
7
6
5
f f i \ fu
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~ · 1 1 6 .
l f u ~
[ 2 x
1
= 1
3 - x
-1
-3
~ ~ > A U f t 4
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SP CE FOR ROUGH WORK
I·
P AQNA L ZNGU/66A
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SP CE FOR ROUGH WORK
P AQNA L ZNGU/66A
5
•
[ P
T
·
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SP CE FOR ROUGH
WOR
P AQNA L ZNGU 66A
6
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~
~
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--
--
--
--
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--
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--
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--
--
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--
--
--
~ ~
il
oft
m
:
P
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S
2 ~
~ g
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< n
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ih 3
00
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"
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lTG,
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i T
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fiAT
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itif
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rn
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rrm ~
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IT ~
'lit, 3
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it •
>
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ll-'l'l ~ m
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