Jee Mains + Adv most important Question

PART-I (PHYSICS)
SECTION-1
One or More Than One Correct Type Questions
1. A source is moving across a circle given by the
equation x2 + y2 = R2 , with constant speed
330 (A) VB = 12 V
v= m/s , in anti-clockwise sense. A detector
6 3 (B) VB = 14 V
is at rest at point ( 2R,0) w.r.t. the centre of the (C) If R = 10 Ω, then voltmeter resistance = 20 Ω
(D) Potential difference between P and Q is 8 V
circle. If the frequency emitted by the source is f
and the speed of sound, C = 330 m/s . Then SECTION-2
Single Correct Type Questions
(A) the position of the source when the detector
4. A straight wire segment AB of length a whose end
records the maximum frequency A is placed at a perpendicular distance a from an
 3R R  coplanar infinitely long straight wire as shown in
+ ,− 
the figure. Angle θ is 30°. Find the magnetic force
 2 2
(B) the co-ordinate of the source when the on wire segment AB if it is also given a current I.
Both the wires are in xy plane.
detector records minimum frequency is
( 0, R )
(C) the minimum frequency recorded by the
6 3
detector is f
+6 3
(D) the maximum frequency recorded by the
(A)
0 I 2  2 + 3   1 ˆ ˆj 
6 3 ln   i+
detector is f 2  2   3 
6 3−
0 I 2  2 + 3  ˆ ˆ

(B) ln 
2  2 
 i+j ( )
2. A thin glass plate of thickness t = ,  being the
3
0 I 2  2 + 3 
wavelength of incident light and refractive index (C) ln 
2  2 
 ( 3iˆ + ˆj )
 = 1.5 , is placed in front of lower slit (between
(D) None of these
the lower slit and the screen) in Young's double
slit experiment. If the intensity at a point on the 5. The graph of alternating emf versus time is shown
screen equidistant from the slits (i.e. central point in the figure. The RMS value of this alternating
of the screen) is found to be I, then emf in the first cycle will be
V
(A) Intensity at the same point before
3I V0
introduction of glass plate was
2 3T/4 t
(B) Intensity at the same point before 0 T/4T/2 T
4I –V0
introduction of glass plate was
3
(C) Central maximum will be in the lower half of
V0
screen after introduction of glass plate (A)
3
(D) Fringe width remains unchanged on
V
introduction of glass plate (B) 0
2
4V0
3. The circuit shown consists of three identical (C)
5
resistances R and three identical voltmeters A, B
5V0
and C. If the voltmeter A reads VA = 22 V and the (D)
8
third voltmeter C reads VC = 8 V, then

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, 6. Consider a solid insulating sphere (of relative 11. A block attached to a spring is placed on a
permittivity one) of radius R having a spherically horizontal frictionless table as shown, another
symmetric charge distribution. The charge density block of same mass m and velocity v0 moves
varies as  = 0 r2 (0 is a constant and r is
towards the other. The time for which spring
measured from centre). Consider two points A and
B at distances x and y respectively (x < R, y > R) m
remains compressed is 2 where K is spring
from the centre. If magnitude of electric fields at CK
points A and B are equal, then constant. Find the value of C.
(A) x2y = R3 (B) x3y2 = R5 m K
2 3
(C) x y = R 5
(D) x4y = R5 v0 m

7. Three identical point masses are placed at the
vertices of an equilateral triangle and joined 12. A cylindrical long wire of radius R carries current
through identical springs of spring constant K. I0 uniformly distributed in its cross-sectional
The system is placed on an smooth table. If the
surface. The pressure developed due to magnetic
masses are displaced slightly along arrows as
shown in figure, then period of their oscillation R
force in wire at distance from its axis is given
will be 2
n0 I 02
by . Find value of n.
162 R 2

13. A projectile is projected to hit a target whose
coordinates are (4, 3), where point of projection is
origin and y-axis is along vertical. If the minimum
velocity of projection is 2 g, then the value of
m m
(A) 2 (B) 2 α is
k 3k
m m
(C) 2 (D) 2 SECTION-4
2k 5k
Matrix Match Type Questions
SECTION-3 14. An electron in a hydrogen atom makes a transition
Non-Negative Integer Type Questions n1 → n2, where n1 and n2 are the principal
8. A particle of mass 0.2 kg is moving in one quantum numbers of the two states. Assume Bohr
dimension under a force that delivers a constant model to be valid.
power 0.5 W to the particle. If the initial speed (in List-I List-II
ms–1) of the particle is zero, the speed (in ms–1)
I The electron emits an P n1 = 2, n2 = 1
after 5 s is
energy of 2.55 eV

9. In a long cylindrical metal wire of radius r and of II Time period of the Q n1= 4, n2 = 2
resistivity , a current of strength I flows in electron in the initial
uniform distribution. The wire has constant state is eight times that in
surface temperature T0. The temperature of the the final state.
wire on its axis of symmetry is given by
III Speed of electron R n1 = 5, n2 = 3
I 2 become two times
T = T0 + 2 2  . Here K is thermal
 r K
IV Radius of orbit of S n1= 6, n2 = 3
conductivity of wire. Find 4λ.
electron becomes 4.77Å
10. A small rigid object carries positive and negative T n1=8, n2 = 4
charges +4 C and –4 C. It is oriented so that the
positive charge has coordinates (–1.2 mm, 1.1 I II III IV
mm) and negative charge has coordinates (1.4 (A) Q P,Q P,Q R
mm, –1.3 mm). The object is kept in an electric (B) Q P,QS P,R,S,T S
field of (2500iˆ − 5000 ˆj )N / C . If the magnitude (C) Q P,Q,S,T P,Q,S,T R,S
of torque (in N-m) acting on the dipole is k × 7, (D) Q P,Q,R,S,T P,Q,R,S,T S
then find the value of k.
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