Q.1
##### 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
Q.2
##### 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
Q.3
##### 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
Q.4
##### 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
Q.5
##### 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)
Q.6
##### 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)
Q.7
• 7
• 8
• 9
• 10
Q.8
• 2 cm
• 8 cm
• 4 cm
• 1 cm
Q.9
• 2
• 8
• 4
• 6
Q.10
• 8
• 2
• 1
• 4
Q.11
• 9
• 3
• 4
• 5
Q.12
• 6 m
• 8 m
• 9 m
• 1 m
Q.13
##### 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
Q.14
##### 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
• $y=xa sin ( \frac {\omega}{u_0})$
• $y=x sin ( \frac {\omega a}{u_0})$
• $y=a sin ( \frac {\omega x}{u_0})$
• $y=a cos ( \frac {\omega x}{u_0})$
Q.15
##### Find the radius vector of the object at t=3π/2ω
• $-a\mathbf{i} + (\frac {2\pi u_0}{2 \omega})\mathbf{j}$
• $(\frac {2\pi u_0}{2 \omega})\mathbf{j}$
• $a\mathbf{i} + (\frac {2\pi u_0}{2 \omega})\mathbf{j}$
• $a\mathbf{i} - (\frac {2\pi u_0}{2 \omega})\mathbf{j}$
Q.16
• 4 m
• 2 m
• 1 m
• .5 m
Q.17
##### 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
Q.18
##### 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
• $(\omega _1 d_1)^2 + (\omega _2 d_2)^2 =0$
• $(\omega _1 d_2) + (\omega _2 d_1) =0$
• $(\omega _1 d_1) + (\omega _2 d_2) =0$
• $\sqrt {\omega _1 d_1}+ \sqrt {\omega _2 d_2} =0$
Q.19
##### 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
Q.20
##### 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