IIT-JEE 2011 - Career Point

A
90V
S
2C
B
Q
R
(A) 15 V (B) 30 V (C) 45 V (D) 60 V
C
2C
5. A long straight wire along the z-axis carries a
current I in the negative z direction. The magnetic
vector field → B at a point having coordinates (x, y)
in the z = 0 plane is -
µ ⎛ ⎞
0I
(A) ⎜
yî − xĵ
⎟
µ ⎛ ⎞
0I
(B) ⎜
xî + yĵ
⎟
π
2 2
2
⎝ x + y
2 2
⎠ 2π
⎝ x + y ⎠
µ ⎛ ⎞
0I
(C) ⎜
xĵ−
yî
⎟
µ ⎛ ⎞
0I
(D) ⎜
xî − yĵ
⎟
π
2 2
2
⎝ x + y
2 2
⎠ 2π
⎝ x + y ⎠
6. Two coils, X and Y, are linked such that emf E is
induced in Y when the current in X is changing at
⎛ dI ⎞
the rate I • ⎜ = ⎟ . If a current I 0 is now made to
⎝ dt ⎠
flow through Y, the flux linked with X will be -
•
⎛
(A) EI 0 I (B)
⎟ ⎟ ⎞
⎜ E
I0
⎜ •
⎝ I ⎠
•
(C) (E I)
I 0
(D)
C
I
E
P
•
0 I
7. In the circuit shown, A is joined to B for a long
time, and then A is joined to C. The total heat
produced in R is -
R
Questions 9 to 12 are multiple choice questions. Each
questions has four choices (A), (B), (C) and (D), out of
which MULTIPLE (ONE OR MORE) is correct.
9. Two objects have life times given by t 1 and t 2 . if t is
the life time of an object lying midway between
these two times on the logarithmic scale then -
(A) log 10 (t) = 2
1 [log10 (t 1 ) + log 10 (t 2 )]
t t 2
(B) t =
2
(C) t = t 1 t 2
1 1 ⎛ 1
(D) = t 2 ⎜ +
⎝ t
1 +
1 t 2
1 ⎞
⎟
⎠
10. The position of a particle traveling along x-axis is
given by x t = t 3 – 9t 2 + 6t where x t is in cm and t is
in second Then -
(A) the body comes to rest firstly at (3 – 7 ) s and
then at (3 + 7 ) s
(B) the total displacement of the particle in
traveling from the first zero of velocity to the
second zero of velocity is zero
(C) the total displacement of the particle in
traveling from the first zero of velocity to the
second zero of velocity is – 74 cm.
(D) the particle reverses its velocity at (3 – 7 ) s
and then at (3 + 7 ) s and has a negative
velocity for (3 – 7 ) < t < (3 + 7 )
11. A projectile is fired upward with velocity v 0 at an
angle θ and strikes a point P(x, y) on the roof of the
building (as shown). Then,
y
Roof
(A)
(C)
LE
R
LE
4R
2
2
2
2
+
2L
E
–
2R
(B)
A
LE
2R
2
2
2
LE
(D)
8R 2
8. In a transformer, N P and N S are 1000 and 3000
respectively. If the primary is connected across 80
V A.C., the potential difference across each turn of
the secondary will be -
(A) 240 V
(B) 0.24 V
(C) 0.9 V
(D) 0.08 V
C
B
h
θ
v 0
P(x,y)
(A) the projectile hits the roof in minimum time if
π
θ + α = . 2
(B) the projectile hits the roof in minimum time if
π
θ + α = . 4
(C) the minimum time taken by the projectile to hit
2
2
v0
− v0
− 2gh cos α
the roof is t min =
.
g cosα
(D) the projectile never reaches the roof for
v 0 < 2 gh cosα
α
x
XtraEdge for IIT-JEE 50
MAY 2010