The displacement time equation for a particle in linear motion is given as $x= \frac {a}{b} ( 1 - e^{-bt})$
  • The velocity and acceleration of the particle at t=0 is a and -ab respectively
  • The velocity will be decreasing as the time increasescorrect
  • The displacement of the particle will fall between 0≤x≤a/bcorrect
  • The maximum acceleration in the motion is -abcorrect
A point charge +Q is at the origin of a coordinates system . It is surrounded by a concentric uniform distribution of charge on a spherical shell at r=R for which the total charge is -2Q Which of the following is correct?
  • Flux crossing spherical surface for r < R is Q/ε0
  • Flux crossing spherical surface for r > R is -Q/ε0correct
  • Flux crossing spherical surface for r > R is -2Q/ε0
  • Flux crossing spherical surface for r < R is -Q/ε0
Let V, Vrms and Vp respectively denotes the mean speed, root mean square speed and most probable speed of the molecule in ideal mono-atomic gas at absolute temperature T. The mass of the molecule is m then
  • No molecule can have a speed greater the (2)1/2Vrms
  • No molecule can have a speed less the Vp / (2)1/2
  • Vp < V < Vrms
  • The average kinetic charge of a molecule (3/4 )mVp2correct
A thick slab extending from z=-b to z=+b carries a uniform current density K and direction of current is positive x axis. Which of the following is true
  • Magnetic field points in negative y axis for z > 0
  • Magnetic field points in negative y axis for z < 0
  • Magnetic field points in positive y axis for z > 0
  • Magnetic field points in positive y axis for z < 0correct
Match the columns
Column (A) ( it tells us about the location) Column (B) ( it tells us about the gravitational force experienced)
a)R1 < d < R2 p) $ \frac  {G ( M _1 + M_2 + M_3 ) m }{d^2}$
b) d < R1 q) $ \frac {G ( M_1 + M_2 ) m}{ d^2}$
c) R1 < R2 < d < R3 r) $ \frac {GM_1}{ d^2}$
d) R1 < R2 < R3 < d s) 0
  • A(p),B(q),C(r),D(s)
  • A(r),B(s),C(q),D(p)
  • A(p),B(r),C(q),D(s)
  • A(s),B(q),C(r),D(p)
Match the columns
Column (A) Column (B)
a)which coil will produce maximum Magnetic induction at the center p) A
b) which coil will produce minimum Magnetic induction at the center q) B
c) Which coil has maximum magnetic moment per turn r) C
d)Which coil has minimum magnetic moment per turn s) F
  • A(q),B(r),C(q),D(r)
  • A(p),B(s),C(p),D(s)
  • A(q),B(r),C(r),D(p)
  • A(p),B(s),C(s),D(p)
In Millikan's oil drop experiment ,a charged oil drop of mass 3.2 ×  10-14 kg is held stationary between two parallel plates 6 mm apart by applying a potential difference of 1200 V between them .How much excess electrons does the oil drop carry? Take g=10 m/s2
  • 7
  • 8
  • 9
  • 10
A liquid is kept in a cylindrical vessel .When the vessel is rotated about its axis,the liquid rises at its sides.If the radius of the vessel is .05 m and speed of the rotation is 2 rev/sec,The difference in the heights of the liquid at the center and at the sides of the vessel will be (take g=10 m/s2 and π2=10
  • 2 cm
  • 8 cm
  • 4 cm
  • 1 cm
Two circular loops X and Y of radii Rx and Ry respectively are made from a uniform wire .The ratio of their moments of inertia about axis passing through their centers and perpendicular to their planes is IY : IX=8:1,Then RY : RX
  • 2
  • 8
  • 4
  • 6
Two cylindrical rods of length L1 and L2,radii R1 and R2 have thermal conductivity K1 and K2 The ends of the rods are maintained at the same temperature difference .if L1 = 2L2 and R2 = 2R1, the rates of the heat flow will be same in the two rods provided K 1/ K2
  • 8
  • 2
  • 1
  • 4
The Potential Energy U in Joule of a particle of mass m=2 kg moving in the x-y plane is given by the formula $U=6x + 8y+5$ Here x and y are coordinates of the particle in meter The particle is at (4, 6) at t=0 and v0=0 i and j are the unit vectors across x and y axis respectively Find the acceleration of the particle
  • 9
  • 3
  • 4
  • 5
A ball is dropped from a height of 12 m. It loses 25% of its K.E. on striking the ground. Calculate the height to which it would bounce?
  • 6 m
  • 8 m
  • 9 m
  • 1 m
What is true for gravitational force
  • work done between the two points does not depend on the path travel
  • work done in a closed loop is zerocorrect
  • W = - ΔUcorrect
  • it is a conservative forcecorrect
A object is moving in a plane with velocity vector given by u=u0i+(ωacosωt)j Where i and j are unit vectors along x and y axes respectively . It is given at t=0, r=0 Where r is radius vector from origin The trajectory of the particle is
  • $y=xa sin ( \frac {\omega}{u_0})$
  • $y=x sin ( \frac {\omega a}{u_0})$
  • $y=a sin ( \frac {\omega x}{u_0})$
  • $y=a cos ( \frac {\omega x}{u_0})$
Find the radius vector of the object at t=3π/2ω
  • $-a\mathbf{i} + (\frac {2\pi u_0}{2 \omega})\mathbf{j}$
  • $ (\frac {2\pi u_0}{2 \omega})\mathbf{j}$
  • $a\mathbf{i} + (\frac {2\pi u_0}{2 \omega})\mathbf{j}$
  • $a\mathbf{i} - (\frac {2\pi u_0}{2 \omega})\mathbf{j}$
A heated object emits radiation which has maximum intensity at frequency m.Now if the temperature of the body is doubled,then the maximum intensity of radiation happens at the frequency
  • 4 m
  • 2 m
  • 1 m
  • .5 m
An electron of mass me initially at rest moves through a certain distance in a uniform electric field in time tA proton of mass mp also initially at rest ,takes time t2 to move through an equal distance in this uniform electric field.Neglect any effect of gravity. Which of the following equation is correct in this case
  • met22 -mpt12 =0
  • met12 -mpt22 =0
  • met2 -mpt1 =0
  • None of the above
In the visible region,the dispersive powers for crown and flint glass prism are ω1 and ω2 , and the mean angular deviation are d1 and d2 respectively. When the two prism are combined ,the condition of zero dispersion by the combination is
  • $(\omega _1 d_1)^2 + (\omega _2 d_2)^2 =0$
  • $(\omega _1 d_2) + (\omega _2 d_1) =0$
  • $(\omega _1 d_1) + (\omega _2 d_2) =0$
  • $\sqrt {\omega _1 d_1}+ \sqrt {\omega _2 d_2} =0$
A train sounds its whistle as it approaches and leaves a railroad crossing. An observer at the crossing measures a frequency of 219 hz as the train approaches and a frequency of 184 hz as the train leaves.The speed of the sound is 340 m/s. Find the speed of the train and frequency of its whistle
  • 26.5 m/s, 200 hz
  • 29.5 m/s, 150 hz
  • 29.5 m/s, 200 hz
  • 29.5 m/s, 250 hz
A larger wooden wheel of radius R and moment of inertia 'I' is mounted on an axle so as to rotate freely. A bullet of mass m and speed v is shot tangential to the wheel and strikes its edge ,lodging in the rim. If the wheel were originally at rest. What will be angular velocity after the collision
  • $ \frac {mvr}{mR^2 + I}$
  • $ \frac {mR^2}{mvr + I}$
  • $ \frac {mR^2}{mvr +2 I}$
  • None of the above
0 h : 0 m : 1 s