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Recent questions in 2003
Questions
>>
JEEMAIN and NEET
>>
JEEMAIN PAST PAPERS
>>
2003
A body travels a distance
s
in
t
seconds. It starts from rest and ends at rest. In the first part of the journey, it moves with constant acceleration
f
and in the second part with constant retardation
r
. The value of
t
is given by:
jeemain
math
past papers
2003
225
asked
Dec 11, 2018
by
pady_1
0
answers
Two stones are projected from the top of a cliff
h
metres high, with the same speed
u
so as to hit the ground at the same spot. If one of the stones is projected horizontally and the other is projected at an angle
θ
to the horizontal, then
tan
θ
equals :
jeemain
math
past papers
2003
224
asked
Dec 11, 2018
by
pady_1
0
answers
Two particles start simultaneously from the same point and move along two straight lines, one with uniform velocity
→
u
and the other from rest with uniform acceleration
→
f
. Let
α
be the angle between their directions of motion. The relative velocity of the second particle w.r.t. the first is least after a time :
jeemain
math
past papers
2003
223
asked
Dec 11, 2018
by
pady_1
0
answers
A couple is of momen
→
G
and the force forming the couple is
→
P
. If
→
P
is turned through a right angle, the moment of the couple thus formed is
→
H
. If instead, the forcce
→
P
is turned through an angle
α
, then the moment of couple becomes :
jeemain
math
past papers
2003
222
asked
Dec 11, 2018
by
pady_1
0
answers
Let
R
1
and
R
2
respectively be the maximum ranges up and down an inclined plane and
R
be the maximum range on the horizontal plane. Then
R
1
,
R
,
R
2
are in :
jeemain
math
past papers
2003
221
asked
Dec 11, 2018
by
pady_1
0
answers
The resultant of forces
→
P
and
→
Q
is
→
R
. If
→
Q
is doubled, then
→
R
is doubled. If the direction of
→
Q
is reversed, then
→
R
is again doubled, then
p
2
:
Q
2
:
R
2
is :
jeemain
math
past papers
2003
220
asked
Dec 11, 2018
by
pady_1
0
answers
The mean and variance of a random variable
X
having a binomial distribution are 4 and 2 respectively, then
P
(
X
=
1
)
is :
jeemain
math
past papers
2003
219
asked
Dec 11, 2018
by
pady_1
0
answers
Events A, B, C are mutually exclusive events such that
P
(
A
)
=
3
x
+
1
3
,
P
(
B
)
=
1
−
x
4
and
P
(
C
)
=
1
−
2
x
2
. The set of possible values of
x
are in the interval :
jeemain
math
past papers
2003
218
asked
Dec 11, 2018
by
pady_1
0
answers
Five horses are in a race. Mr. A selects two of the horses at random and bets on them. The probabiliy that Mr. A selected the winning horse, is :
jeemain
math
past papers
2003
217
asked
Dec 11, 2018
by
pady_1
0
answers
In an experiment with 15 observations on
x
, the following results were available <br>
∑
x
2
=
2830
,
∑
x
=
170
<br> One observation that was 20, was found to be wrong and was replaced by the correct value 30. Then the corrected variance is :
jeemain
math
past papers
2003
216
asked
Dec 11, 2018
by
pady_1
0
answers
The median of a set of 9 distinct observations is 20.5. If each of the largest 4 observations of the set is increased by 2, then the median of the new set :
jeemain
math
past papers
2003
215
asked
Dec 11, 2018
by
pady_1
0
answers
A particle acted on by constant forces
4
ˆ
i
+
ˆ
j
−
3
ˆ
k
and
3
ˆ
i
+
ˆ
j
−
ˆ
k
is displaced from the point
ˆ
i
+
2
ˆ
j
+
3
ˆ
k
to the point
5
ˆ
i
+
4
ˆ
j
+
ˆ
k
. The total work done by the forces is :
jeemain
math
past papers
2003
213
asked
Dec 11, 2018
by
pady_1
0
answers
The vectors
→
A
B
=
3
ˆ
i
+
4
ˆ
k
, and
→
A
C
=
5
ˆ
i
−
2
ˆ
j
+
4
ˆ
k
are the sides of a triangle
A
B
C
. The length of the median through
A
is :
jeemain
math
past papers
2003
212
asked
Dec 11, 2018
by
pady_1
0
answers
Consider points A, B, C and D with position vectors
7
ˆ
i
−
4
ˆ
j
+
7
ˆ
k
,
ˆ
i
−
6
ˆ
j
+
10
ˆ
k
,
−
ˆ
i
−
3
ˆ
j
+
4
ˆ
k
and
5
ˆ
i
−
ˆ
j
+
5
ˆ
k
respectively. Then ABCD is a :
jeemain
math
past papers
2003
211
asked
Dec 11, 2018
by
pady_1
0
answers
If
→
u
,
→
v
and
→
w
are three non-coplanar vectors, then
(
→
u
+
→
v
−
→
w
)
.
[
(
→
u
−
→
v
)
×
(
→
v
−
→
w
)
]
equals :
jeemain
math
past papers
2003
210
asked
Dec 11, 2018
by
pady_1
0
answers
→
a
,
→
b
,
→
c
are three vectors, such that
→
a
+
→
b
+
→
c
=
→
0
,
|
→
a
|
=
1
,
|
→
b
|
=
2
,
|
→
c
|
=
3
, then
→
a
.
→
b
+
→
b
.
→
c
+
→
c
.
→
a
is equal to :
jeemain
math
past papers
2003
209
asked
Dec 11, 2018
by
pady_1
0
answers
Two systems of rectangular axes have the same origin. If a plane cuts them at distances
a
,
b
,
c
and
a
′
,
b
′
,
c
′
from the origin, then :
jeemain
math
past papers
2003
208
asked
Dec 11, 2018
by
pady_1
0
answers
The shortest distance from the plane
12
x
+
4
y
+
3
z
=
327
to the sphere
x
2
+
y
2
+
z
2
+
4
x
−
2
y
−
6
z
=
155
is :
jeemain
math
past papers
2003
207
asked
Dec 11, 2018
by
pady_1
0
answers
The two lines
x
=
a
y
+
b
,
z
=
c
y
+
d
and
x
=
a
′
y
+
b
′
,
z
=
c
′
y
+
d
′
will be perpendicular, if and only if :
jeemain
math
past papers
2003
206
asked
Dec 11, 2018
by
pady_1
0
answers
The lines
x
−
2
1
=
y
−
3
1
=
z
−
4
−
k
and
x
−
1
k
=
y
−
4
2
=
z
−
5
1
are coplanar if :
jeemain
math
past papers
2003
205
asked
Dec 11, 2018
by
pady_1
0
answers
The radius of the circle in which the sphere
x
2
+
y
2
+
z
2
+
2
x
−
2
y
−
4
z
−
19
=
0
is cut by the plane
x
+
2
y
+
2
z
+
7
=
0
is :
jeemain
math
past papers
2003
204
asked
Dec 11, 2018
by
pady_1
0
answers
A tetrahedron has vertices at
O
(
0
,
0
,
0
)
,
A
(
1
,
2
,
1
)
,
B
(
2
,
1
,
3
)
and
C
(
−
1
,
1
,
2
)
. Then the angle between the faces
O
A
B
and
A
B
C
will be :
jeemain
math
past papers
2003
203
asked
Dec 11, 2018
by
pady_1
0
answers
The foci of the ellipse
x
2
16
+
y
2
b
2
=
1
and the hyperbola
x
2
144
−
y
2
81
=
1
25
coincide. Then the value of
b
2
is :
jeemain
math
past papers
2003
202
asked
Dec 11, 2018
by
pady_1
1
answer
The normal at the point
(
b
t
2
1
,
2
b
t
1
)
on a parabola meets the parabola again in the point
(
b
t
2
2
,
2
b
t
2
)
then :
jeemain
math
past papers
2003
201
asked
Dec 11, 2018
by
pady_1
1
answer
The lines
2
x
−
3
y
=
5
and
3
x
−
4
y
=
7
are diameters of a circle having area as
154
s
q
.
u
n
i
t
. Then the equation of the circle is :
jeemain
math
past papers
2003
200
asked
Dec 11, 2018
by
pady_1
1
answer
If the two circles
(
x
−
1
)
2
+
(
y
−
3
)
2
=
r
2
and
x
2
+
y
2
−
8
x
+
2
y
+
8
=
0
intersect in two distinct points, then :
jeemain
math
past papers
2003
199
asked
Dec 11, 2018
by
pady_1
0
answers
A square of side
a
lies above the
x
-axis and has one vertex at the origin. The side passing through the origin makes an angle
α
(
0
<
α
<
π
4
)
with the positive direction of
x
-axis. The equation of its diagonal not passing through the origin is :
jeemain
math
past papers
2003
198
asked
Dec 11, 2018
by
pady_1
1
answer
If the pair of straight line
x
2
−
2
p
x
y
−
y
2
=
0
and
x
2
−
2
q
x
y
−
y
2
=
0
be such that each pair bisects the angle between the other pair, then :
jeemain
math
past papers
2003
197
asked
Dec 11, 2018
by
pady_1
0
answers
Locus of centroid of the triangle whose vertices are
(
a
cos
t
,
a
sin
t
)
,
(
b
sin
t
,
−
b
cos
t
)
and
(
1
,
0
)
where
t
is a parameter, is :
jeemain
math
past papers
2003
196
asked
Dec 11, 2018
by
pady_1
0
answers
If the equation of the locus of a point equidistant from the points
(
a
1
,
b
1
)
and
(
a
2
,
b
2
)
is
(
a
1
−
a
2
)
x
+
(
b
1
−
b
2
)
y
+
c
=
0
, then the value of
′
C
′
is :
jeemain
math
past papers
2003
195
asked
Dec 11, 2018
by
pady_1
0
answers
The solution of the differential equation
(
1
+
y
2
)
+
(
x
−
e
tan
−
1
y
)
d
y
d
x
=
0
is :
jeemain
math
past papers
2003
194
asked
Dec 11, 2018
by
pady_1
0
answers
The degree and order of the differential equation of the family of all parabolas whose axis is
x
-axis, are respectively :
jeemain
math
past papers
2003
193
asked
Dec 11, 2018
by
pady_1
0
answers
Let
f
(
x
)
be a function satisfying
f
′
(
x
)
=
f
(
x
)
with
f
(
0
)
=
1
and
g
(
x
)
be a function that satisfies
f
(
x
)
+
g
(
x
)
=
x
2
. Then the value of the integral
∫
1
0
f
(
x
)
g
(
x
)
d
x
is :
jeemain
math
past papers
2003
192
asked
Dec 11, 2018
by
pady_1
0
answers
The area of the region bounded by the curves
y
=
|
x
−
1
|
and
y
=
3
−
|
x
|
is :
jeemain
math
past papers
2003
191
asked
Dec 11, 2018
by
pady_1
0
answers
Let
d
d
x
F
(
x
)
=
(
e
sin
x
x
)
,
x
>
0
<br> If
∫
4
1
3
x
e
sin
x
3
d
x
=
F
(
k
)
−
F
(
1
)
, <br> then one of the possible values of
k
, is
jeemain
math
past papers
2003
190
asked
Dec 11, 2018
by
pady_1
0
answers
lim
n
→
∞
1
+
2
4
+
3
4
+
.
.
.
+
n
4
n
5
−
lim
n
→
∞
1
+
2
3
+
3
3
+
.
.
.
.
+
n
3
n
5
is :
jeemain
math
past papers
2003
189
asked
Dec 11, 2018
by
pady_1
0
answers
The value of the integral
I
=
∫
1
0
x
(
1
−
x
)
n
d
x
is :
jeemain
math
past papers
2003
188
asked
Dec 11, 2018
by
pady_1
0
answers
The value of
lim
x
→
0
∫
x
2
0
sec
2
t
d
t
x
sin
x
is :
jeemain
math
past papers
2003
187
asked
Dec 11, 2018
by
pady_1
0
answers
If
f
(
a
+
b
−
x
)
=
f
(
x
)
, then
∫
b
a
x
f
(
x
)
d
x
is equal to :
jeemain
math
past papers
2003
186
asked
Dec 11, 2018
by
pady_1
0
answers
If
f
(
y
)
=
e
y
,
g
(
y
)
=
y
;
y
>
0
and
F
(
t
)
=
∫
t
0
f
(
t
−
y
)
g
(
y
)
d
y
, then :
jeemain
math
past papers
2003
185
asked
Dec 11, 2018
by
pady_1
0
answers
If the function
f
(
x
)
=
2
x
3
−
9
a
x
2
+
12
a
2
x
+
1
, where
a
>
0
, attains its maximum and minimum at
p
and
q
respectively such that
p
2
=
q
, then
a
equals :
jeemain
math
past papers
2003
184
asked
Dec 11, 2018
by
pady_1
0
answers
If
f
(
x
)
=
{
x
e
−
[
1
|
x
|
−
1
x
]
,
x
≠
0
then
f
(
x
)
is :
0
x
=
0
jeemain
math
past papers
2003
183
asked
Dec 11, 2018
by
pady_1
0
answers
The function
f
(
x
)
=
log
(
x
+
√
x
2
+
1
)
, is :
jeemain
math
past papers
2003
182
asked
Dec 11, 2018
by
pady_1
0
answers
If
f
n
(
a
)
,
g
n
(
a
)
exist and are not equal for some
n
. Further is
f
(
a
)
=
g
(
a
)
=
k
and
lim
x
→
a
f
(
a
)
g
(
x
)
−
f
(
a
)
−
g
(
a
)
f
(
x
)
+
g
(
a
)
g
(
x
)
−
f
(
x
)
=
4
, then the value of
k
is equal to :
jeemain
math
past papers
2003
181
asked
Dec 11, 2018
by
pady_1
0
answers
If
lim
x
→
0
log
(
3
+
x
)
−
log
(
3
−
x
)
x
=
k
, the value of
k
is :
jeemain
math
past papers
2003
180
asked
Dec 11, 2018
by
pady_1
0
answers
lim
x
→
π
2
[
1
−
tan
(
x
2
)
]
[
1
−
sin
x
]
[
1
+
tan
(
x
2
)
]
[
π
−
2
x
]
3
is :
jeemain
math
past papers
2003
179
asked
Dec 11, 2018
by
pady_1
0
answers
Domain of definition of the function
f
(
x
)
=
3
4
−
x
2
+
log
10
(
x
3
−
x
)
, is :
jeemain
math
past papers
2003
178
asked
Dec 11, 2018
by
pady_1
0
answers
If
f
(
x
)
=
x
n
, then the value of
f
(
1
)
−
f
′
(
1
)
1
!
+
f
″
is :
jeemain
math
past papers
2003
177
asked
Dec 11, 2018
by
pady_1
0
answers
If
f : R \to R
satisfies
f(x+y) = f(x) + f(y)
, for all
x, \; y \in R
and
f(1) = 7
, then
\displaystyle\sum_{r=1}^{n} f(r)
is :
jeemain
math
past papers
2003
176
asked
Dec 11, 2018
by
pady_1
0
answers
The real number
x
when added to its inverse gives the minimum value of the sum at
x
equals to :
jeemain
math
past papers
2003
175
asked
Dec 11, 2018
by
pady_1
0
answers
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