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Recent questions in Mathematics
Questions
>>
EAMCET
>>
Mathematics
If
∫
e
x
(
1
−
sin
x
1
−
cos
x
)
d
x
−
f
(
x
)
+
c
o
n
s
t
a
n
t
then
f
(
x
)
=
jeemain
eamcet
math
2008
q71
asked
Oct 18, 2013
by
meena.p
0
answers
If
z
=
sec
−
1
(
x
4
+
y
4
−
8
x
2
y
2
x
2
+
y
2
)
then
x
d
z
d
x
+
y
d
z
d
y
=
jeemain
eamcet
math
2008
q70
asked
Oct 18, 2013
by
meena.p
1
answer
The length of the sub tangent at (2,2) to the curve
x
5
=
2
y
4
is :
jeemain
eamcet
math
2008
q69
asked
Oct 18, 2013
by
meena.p
1
answer
If m and M respectively denote the minimum and maximum of
f
(
x
)
=
(
x
−
1
)
2
+
3
for
x
∈
[
−
3
,
1
]
then the ordered pair
(
n
,
M
)
-
jeemain
eamcet
math
2008
q68
asked
Oct 18, 2013
by
meena.p
1
answer
The angle between the curves
y
2
=
4
x
+
4
and
y
2
=
36
(
9
−
x
)
is
jeemain
eamcet
math
2008
q67
asked
Oct 18, 2013
by
meena.p
1
answer
The equation to the normal to the curve
y
4
=
a
x
3
at
(
a
,
a
)
is
jeemain
eamcet
math
2008
q66
asked
Oct 17, 2013
by
meena.p
1
answer
If
y
=
sin
(
log
e
x
)
then
x
2
d
2
y
d
x
2
+
x
d
y
d
x
=
jeemain
eamcet
math
2008
q65
asked
Oct 17, 2013
by
meena.p
1
answer
If
x
−
a
{
cos
θ
+
log
tan
(
θ
2
)
}
and
y
=
a
sin
θ
then
d
y
d
x
=
jeemain
eamcet
math
2008
q64
asked
Oct 17, 2013
by
meena.p
1
answer
If
f
(
2
)
=
4
and
f
′
(
2
)
=
1
, then
lim
x
→
2
x
f
(
2
)
−
2
f
(
x
)
x
−
2
=
jeemain
eamcet
math
2008
q63
asked
Oct 17, 2013
by
meena.p
1
answer
If
f
:
ℜ
is defined by
f
(
x
)
=
{
cos
3
x
−
cos
x
x
2
f
o
r
x
≠
0
λ
f
o
r
x
=
0
.
and if f is continuous at
x
=
0
,
then
λ
=
jeemain
eamcet
math
2008
q62
asked
Oct 17, 2013
by
meena.p
1
answer
If
f
:
ℜ
→
ℜ
is defined by
f
(
x
)
=
[
x
−
3
]
+
|
x
−
4
|
for
x
∈
ℜ
then
lim
x
→
3
−
f
(
x
)
=
jeemain
eamcet
math
2008
q61
asked
Oct 17, 2013
by
meena.p
1
answer
lim
x
→
0
(
1
−
e
x
)
sin
x
x
2
+
x
3
=
jeemain
eamcet
math
2008
q60
asked
Oct 17, 2013
by
meena.p
1
answer
The radius of the circle with the polar equation
r
2
−
8
r
(
√
3
cos
θ
+
sin
θ
)
+
15
−
0
is
jeemain
eamcet
math
2008
q59
asked
Oct 17, 2013
by
meena.p
1
answer
The distance between the foci of the hyperbola
x
2
−
3
y
2
−
4
x
−
6
y
−
11
=
0
is
jeemain
eamcet
math
2008
q58
asked
Oct 17, 2013
by
meena.p
1
answer
For an ellipse with eccentricity
1
2
the center is at the orgin. If one directrix is
x
=
4
, then the equation of the ellipse is
jeemain
eamcet
math
2008
q57
asked
Oct 17, 2013
by
meena.p
1
answer
If
2
x
+
3
y
+
12
=
0
and
x
−
y
+
4
λ
=
0
are conjugate with respect to the parabola
y
2
=
8
x
then
λ
=
jeemain
eamcet
math
2008
q56
asked
Oct 17, 2013
by
meena.p
1
answer
If
θ
is the angle between the tangents from
(
−
1
,
0
)
to the circle
x
2
+
y
2
−
5
x
+
4
y
−
2
=
0
, then
θ
jeemain
eamcet
math
2008
q55
asked
Oct 17, 2013
by
meena.p
1
answer
The inverse of the point (1,2) with respect to the circle
x
2
+
y
2
−
4
x
−
6
y
+
9
=
0
, is
jeemain
eamcet
math
2008
q54
asked
Oct 17, 2013
by
meena.p
1
answer
If the lines
2
x
−
3
y
=
5
and
3
x
−
4
y
=
7
are two diameters of a circle of radius 7, then the equation of the circle is
jeemain
eamcet
math
2008
q53
asked
Oct 17, 2013
by
meena.p
1
answer
The angle between the lines whose direction cosines are
(
√
3
4
,
1
4
,
√
3
2
)
and
(
√
3
4
,
1
4
,
−
√
3
2
)
is
jeemain
eamcet
math
2008
q52
asked
Oct 17, 2013
by
meena.p
1
answer
In
Δ
A
B
C
the mid-points of the sides AB,BC and CA are respectively
(
l
,
0
,
0
)
,
(
0
,
m
,
0
)
and
(
0
,
0
,
n
)
.
Then
A
B
2
+
B
C
2
+
C
A
2
l
2
+
m
2
+
n
2
=
jeemain
eamcet
math
2008
q51
asked
Oct 17, 2013
by
meena.p
1
answer
A pair of perpendicular straight lines passes through the origin and also through the point of intersection of the curve
x
2
+
y
2
=
4
with
x
+
y
=
a
. The set containing the value of 'a' is
jeemain
eamcet
math
2008
q50
asked
Oct 17, 2013
by
meena.p
1
answer
The value of
λ
such that
λ
x
2
−
10
x
y
+
12
y
2
+
5
x
−
16
y
−
3
=
0
represents a pair of straight lines, is
jeemain
eamcet
math
2008
q49
asked
Oct 17, 2013
by
meena.p
1
answer
The value of k such that the lines
2
x
−
3
y
+
k
=
0
,
3
x
−
4
y
−
13
=
0
and
8
x
−
11
y
−
33
=
0
are concurrent , is
jeemain
eamcet
math
2008
q48
asked
Oct 17, 2013
by
meena.p
1
answer
If l,m,n are in arithmetic progression, then the straight line
l
x
+
m
y
+
n
=
0
will pass through the point
jeemain
eamcet
math
2008
q47
asked
Oct 17, 2013
by
meena.p
1
answer
The transformed equation of
3
x
2
+
3
y
2
,
2
x
y
=
2
when the coordinate axes are rotated through an angle of
45
∘
is
jeemain
eamcet
math
2008
q46
asked
Oct 17, 2013
by
meena.p
1
answer
If the sum of the distances of a point P from two perpendicular lines in a plane is 1, then the locus of P is a
jeemain
eamcet
math
2008
q45
asked
Oct 17, 2013
by
meena.p
1
answer
If X is a Poisson variate such that
P
(
X
−
1
)
−
P
(
X
=
2
)
,
then
P
(
X
=
4
)
=
jeemain
eamcet
math
2008
q44
asked
Oct 17, 2013
by
meena.p
1
answer
The distribution of a random variable X is given below:
jeemain
eamcet
math
2008
q43
asked
Oct 17, 2013
by
meena.p
1
answer
For
k
=
1
,
2
,
3
the box
B
k
contains k red balls and
(
k
+
1
)
white balls. Let
P
(
B
1
)
−
1
2
,
P
(
B
2
)
−
1
3
and
P
(
B
3
)
=
1
6
. A box is selected at random and a ball is drawn from it . If a red ball is drawn, then the probability that it has come from box
B
2
is
jeemain
eamcet
math
2008
q42
asked
Oct 17, 2013
by
meena.p
0
answers
Let S be the sample space of the random experiment of throwing simultaneously two unbiased dice with six faces ( numbered 1 to 6) and let
E
k
=
{
(
a
,
b
)
∈
S
:
a
b
=
k
}
f
o
r
k
≤
1
. If
p
k
=
P
(
F
k
)
f
o
r
k
≤
1
then the correct, among the following , is
jeemain
eamcet
math
2008
q41
asked
Oct 17, 2013
by
meena.p
1
answer
If A and B are independent events of a random experiment such that
P
(
A
∩
B
)
=
1
6
and
P
(
ˉ
A
∩
ˉ
B
)
=
1
3
,
then
P
(
A
)
=
(Here
ˉ
E
is the complement of the event E)
jeemain
eamcet
math
2008
q40
asked
Oct 17, 2013
by
meena.p
1
answer
Let
ˉ
a
be a unit vector,
ˉ
b
=
2
ˉ
i
+
ˉ
j
−
ˉ
k
and
ˉ
c
=
ˉ
i
+
3
ˉ
k
. The maximum value of
[
ˉ
a
ˉ
b
ˉ
c
]
is
jeemain
eamcet
math
2008
q39
asked
Oct 17, 2013
by
meena.p
1
answer
If
ˉ
a
=
ˉ
i
+
ˉ
j
+
ˉ
k
,
ˉ
b
=
ˉ
i
−
ˉ
j
+
ˉ
k
,
ˉ
c
=
ˉ
i
+
ˉ
j
−
ˉ
k
and
ˉ
d
=
ˉ
i
−
ˉ
j
−
ˉ
k
,
then observe the following lists:
jeemain
eamcet
math
2008
q38
asked
Oct 17, 2013
by
meena.p
1
answer
If the position vector of
A
,
B
and
C
are respectively
2
ˉ
i
−
ˉ
j
+
ˉ
k
,
ˉ
i
−
3
ˉ
j
−
5
ˉ
k
and
3
ˉ
i
−
4
ˉ
j
−
4
ˉ
k
, then
cos
2
A
=
jeemain
eamcet
math
2008
q37
asked
Oct 17, 2013
by
meena.p
1
answer
If the points with position vectors
60
ˉ
i
+
3
ˉ
j
,
40
ˉ
i
−
80
ˉ
j
and
a
ˉ
i
−
52
ˉ
j
are collinear, then
a
=
jeemain
eamcet
math
2008
q36
asked
Oct 17, 2013
by
meena.p
1
answer
The position vectors of P and Q are respectively
ˉ
a
and
ˉ
b
. If R is a point on
↔
P
Q
such that
→
P
R
=
5
→
P
Q
,
then the position vector of R is :
jeemain
eamcet
math
2008
q35
asked
Oct 17, 2013
by
meena.p
1
answer
From the top of a hill the angles of depression of the top and the bottom of a pillar are
α
and
β
respectively. The height (in meters) of the pillar is
jeemain
eamcet
math
2008
q34
asked
Oct 17, 2013
by
meena.p
1
answer
In a triangle , if
r
1
=
2
r
2
=
3
r
3
, then
a
b
+
b
c
+
c
a
=
jeemain
eamcet
math
2008
q33
asked
Oct 17, 2013
by
meena.p
1
answer
Observe the following statements :(I) In
Δ
A
B
C
,
b
cos
2
C
2
+
c
cos
2
B
2
=
s
(II) In
Δ
A
B
C
,
cot
A
2
=
b
+
c
2
=>
B
=
90
∘
Which of the following is correct?
jeemain
eamcet
math
2008
q32
asked
Oct 17, 2013
by
meena.p
1
answer
If
Δ
A
B
C
if
1
b
+
c
+
1
c
+
a
=
3
a
+
b
+
c
then
C
=
jeemain
eamcet
math
2008
q31
asked
Oct 17, 2013
by
meena.p
1
answer
1
+
tan
h
x
2
1
−
tan
h
x
2
=
jeemain
eamcet
math
2008
q30
asked
Oct 17, 2013
by
meena.p
1
answer
If
sin
−
1
(
3
x
)
+
sin
−
1
(
4
x
)
=
π
2
then
x
=
jeemain
eamcet
math
2008
q29
asked
Oct 17, 2013
by
meena.p
1
answer
{
x
∈
ℜ
:
cos
2
x
+
2
cos
2
x
=
2
}
=
jeemain
eamcet
math
2008
q28
asked
Oct 17, 2013
by
meena.p
1
answer
If
α
+
β
+
γ
=
2
θ
, then
c
o
s
θ
+
cos
(
θ
−
α
)
+
cos
(
θ
−
β
)
+
cos
(
θ
−
γ
)
=
jeemain
eamcet
math
2008
q27
asked
Oct 17, 2013
by
meena.p
1
answer
If
tan
θ
+
tan
(
θ
+
π
3
)
+
tan
(
θ
+
2
π
3
)
=
3
,then which of the following is equal to 1?
jeemain
eamcet
math
2008
q26
asked
Oct 17, 2013
by
meena.p
0
answers
If
A
=
35
∘
,
B
=
15
∘
and
C
=
40
∘
, then
t
a
n
A
.
tan
B
+
tan
B
.
tan
C
+
tan
C
.
tan
A
=
jeemain
eamcet
math
2008
q25
asked
Oct 17, 2013
by
meena.p
1
answer
√
2
−
c
o
s
e
c
20
∘
−
sec
20
∘
=
jeemain
eamcet
math
2008
q24
asked
Oct 17, 2013
by
meena.p
1
answer
If
m
1
,
m
2
,
m
3
and
m
4
respectively denote the moduli of the complex numbers
1
+
4
i
,
3
+
i
,
1
−
i
,
and
2
−
3
i
,
then the correct one, among the following is
jeemain
eamcet
math
2008
q23
asked
Oct 17, 2013
by
meena.p
1
answer
If
Ω
is a complex cube root of unity, then
sin
{
(
ω
10
+
ω
23
)
π
−
π
4
}
=
jeemain
eamcet
math
2008
q22
asked
Oct 17, 2013
by
meena.p
1
answer
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