iit jee mathematics 2004
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IIT JEE Mathematics 2004TRANSCRIPT
IIT JEE -2004
MATHEMATICS- SOLVED PAPER - I
SECTION – I (Total Marks : 28)
Single Correct Answer Type This section contains 28 multiple choice questions. Each question has four choices (A), (B), (C)
and (D) out of which ONLY ONE is correct.
01If is a complex cube root of unity, the least value of for which is
a. 6
b. 5
c. 3
d. 2
Problem
1 n N
Problem 02If the function Is differentiable and strictly increasing in a neighborhood of
then is equal to
a. -1
b. 0
c. 1
d. 3/2
2
0lim
0x
f x f x
f x f
0,f
Problem03Two tangents are drawn from point (1, 4) to the parabola Angle between
these tangents is
a.
b.
c.
d. / 2
/ 3
/ 4
/ 6
Problem04If x is the first term of an infinite G.P., whose sum is 10, then?
a.
b.
c.
d.
10x
10 10x
5 5x
0 10x
Problem05Area of the triangle formed by the angle bisectors of the pair of line
and the line (in square units is)
a. 1
b. 2
c. 3
d. 4
2 2 2 1 0x y y 3x y
Problem06In common chord of the circle C with centre at (2, 1,) and radius r and the
circle is a diameter of the second circle: then value of r is
a. 3
b. 2
c. 3/2
d. 1
Problem07If then b is equal to
a. 2i
b. I
c. 2i – j + 7k
d. 2i – k
a=i+j+k, a× b=1and a x b = j-k,
Problem08A unit vector coplanar with 2i + j + k and i – j +k and orthogonal to 5i + 2j +
6k
a. Is
b.
c.
d. 12 2
3i j k
17 2 2
57i j k
16
37i k
13
10j k
Problem09The value of for which the system of equations
has no solution is
a. -3
b. -2
c. 0
d. 3
4 , 2 4 0,2 2x y z x x y z x y z
Problem10If then
a. Has no local minima
b. Has no local maxima
c. Is strictly increasing on R
d. Is strictly decreasing on R
20 ,b c 3 2f x x bx cx d
Problem11Let be a function of x satisfying the relation then at
= 0
a. 0
b. 1/3
c. 1
d. 2
y x log 2 ,x y xy 'y x
Problem12If and = 125, then is equal to
a.
b. 3
c. 4
d. 5
2
2A
3A
1
Problem13If and then k lies in the interval
a.
b.
c.
d.
,n r N 313 ,n
r rC k C
3, 3
2,
3,
3,2
n 1
Problem14Let If Roll’s theorem can be applied to f on [0,
1], then
value of can be
a. -1
b. -1/2
c. 0
d. 1/2
log if 0
0 if 0
x x xf x
x
Problem15If, for t > 0 the define integral then is equal
a.
b.
c.
d.
4
25f
2
5
0
2,
5
txf x dx t
2
5
2
5
2
5
2
5
Problem16If a, b, c are the sides of a triangle such that a: b: c = 1: 2, then ratio
A: B: C is equal to
a. 3: 2: 1
b. 3: 1: 2
c. 1: 2: 3
d. 1: 3: 2
3
Problem17If the quadratic expression then
a.
b.
c.
d. 5a
5a
5 2a 2 3a
2 2 3 10 0x ax a ,x R
Problem18Locus of the mid-points of the segments which are tangents to the ellipse
and which are intercepted between the coordinate axes is
a.
b.
c.
d.2 2
1 11
2 4x y
2 2
1 11
3 4x y
2 21 11
4 2x y
2 21 11
2 4x y
Problem19If and are acute angle such that then
lies in
a.
b.
c.
d. None of these
1 1sin , cos ,
2 3a b
,3 2
2,
2 3
2 2,
3 3
Problem20 Let and then will be an invertible function if x lies in
a.
b.
c.
d.
2 1f x x sin cos ,g x x x f g x
0,3 / 2
0, / 2
4 /, / 4
2, /0
Problem21Out of first 100 natural numbers, three numbers are chosen without
replacement. The probability that all these numbers are divisible both by
2 and 3 is
a. 4/11
b. 4/55
c. 4/33
d. 4/1155
Problem22Two lines and intersect at a point if k is
equal to
a. 2/9
b. 1/2
c. 9/2
d. 1/6
3
1 2
x y kz
1 1 1
2 3 4
x y z
Problem23If area lying between the curves and is 1 square
unit, then a is equal to
a.
b.
c.
d.
3
1
3
1
2
1
3
2x ay2y ax
Problem24If one root of the equation is 1 square of the other,
then p and q satisfy the relation
a.
b.
c.
d.
2 0x px q
3 23 1 0p q p q
3 23 1 0p q p q
3 23 1 0p q p q
3 23 1 0p q p q
Problem25The definite integral is equal to satisfy the relation
a. 1
b.
c.
d.
1
0
1
1
xdxx
1
2 2
12
Problem26If satisfies the differential equation
then is equal to
a. 1
b. 2/3
c. 1/3
d. 5/3
/ 2y 2 sin 1 cos 0, 0 1dy
x y x ydx
y y x
Problem27The point of contact of the line and the hyperbola is
a.
b.
c.
d.
2 6 2x y 2 22 4x y
4, 6
6,1
1 3,
6 2
1 1,
2 6
Problem28Value of x for is
a. -1/2
b. 0
c. 1/2
d. 1