Test Series-8

### Instructions

A. Question paper format:
• The question paper consists of Physics Part. There are 5 sections.
• Section I contains 5 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which only one is correct.
• Section II contains 5 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which one or more is/are correct.
• Section III contains 2 questions. Each question has four statements (A, B, C and D) given in column I and four statements (p, q, r and s ) in Column II. Any given statement in Column I can have correct matching with one or more statement(s) given in Column II. For example, if for a given question, statement B matches with the statements given in q and r, then for that particular question, match B with q and r
• Section IV contains 2 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which only one is correct.
• Section V contains 6 questions. The answer to each of the questions is a single - digit integer, ranging from 0 to 9.

B. Marking scheme:
• For each question in Section I you will be awarded 2 marks for the correct answer and zero mark if question is not attempted.
• For each question in Section II, you will be awarded 3 marks for the correct choice(s) for the answer, and zero mark if question is not attempted.
• For each question in Section III, you will be awarded 5 marks for correct matching of each row in column 1 to the correct answer in column 2.
• For each question in Section IV, you will be awarded 4 marks for the correct answer and zero mark if question is not attempted.
• For each question in Section V you will be awarded 2 marks for the correct answer and zero mark if question is not attempted.

SECTION-I

Single Correct Choice Type

This section contains 5 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out which ONLY ONE is correct
1.What will be the equivalent resistance between A and D
• 40 ohm
• 30 ohm
• 20 ohm
• 10 ohm

2.The radius vector describing the position of the particle A relative to origin
r=t2i+(t-1)2j
Find the rectangular components of the average velocity in the time interval between t and t+Δt
• (Δt+2t),(Δt+2t-2)
• (Δt+2t),(Δt+2t+2)
• (Δt-2t),(Δt+2t+2)
• (Δt+2t),(Δt-2t+2)

3. A charged particle whose mass is 19.9*10-27 kg and charge is 1.6*10-19 C moves with a speed of 3*105 m/s at right angle to a magnetic field of .75 T. What is the force acting on the charge, centripetal acceleration and radius of the circle in which charged particle moves
• 3.6*10-14 N, 1.9*1012 m/s2, 49.9*10-3 m
• 3.0*10-14 N,1.81*1012 m/s2, 49.7*10-3 m
• 3.0*10-14 N,1.81*1012 m/s2, 40.7*10-3 m
• 3.6*10-14 N,1.81*1012 m/s2, 49.7*10-3 m

4. Three particles A,B,C each of mass m are placed at the corner of the equilateral triangle of side a. Find the potential energy of the system
• $\frac{-3G{m}^{2}}{a}$
• $\frac{-3G{m}^{2}}{\mathrm{2a}}$
• $\frac{-3G{m}^{2}}{\mathrm{3a}}$
• None of these

5.Two concentric coplanar circular loops made of wire with resistance per unit length 10-4 O/m have diameters .2 m and 2 m respectively. A time varying potential difference V=(4+2.5 t) V is applied to larger loop. Find the induced current in the small loop
• 1.25A
• 2 A
• 1 A
• 1.5 A

SECTION-II

Multiple Correct Choice Type
This section contains 5 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D) for its answer, out which ONE OR MORE is/are correct.
6.What is true for gravitional force
• work done between the two points does not depend on the path travell
• work done in a closed loop is zero
• W = - ΔU
• it is a conservative force

7. The displacement time equation for a particle in linear motion is given as $x=\frac{a}{b}\left(1-{e}^{-\mathrm{bt}}\right)$
• The velocity and acceleration of the particle at t=0 is a and –ab respectively
• The velocity will be decreasing as the time increases
• The displacement of the particle will fall between 0≤x≤a/b
• The maximum acceleration in the motion is –ab

8.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/ε0
• Flux crossing spherical surface for r > R is -2Q/ε0
• Flux crossing spherical surface for r < R is -Q/ε0

9.Let V, Vrms and Vp respectively denotes the mean speed, root mean square speed and most probable speed of the molecule in ideal monoatomic 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 )mVp2

10.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 < 0

SECTION-III

Matrix - Match Type
This section contains 2 questions. Each question contains statements given in two columns, which have to be matched. The statements in Column I are labeled A, B, C and D, while the statements in Column II are labeled p, q, r, s and t. Any given statement in Column I can have correct matching with ONE OR MORE statement(s) in Column II.

11.Three concentric shells A,B ,C of uniform density have masses M1 ,M2 and M3 respectively. There radii are R1,R2 and R3 respectively. R3 > R2 > R1
A particle of mass m is placed at placed at a distance d
 Column (A) ( it tells us about the location) Column (B) ( it tells us about the gravitational force experienced) a)R1 < d < R2 p) $\frac{G\left({M}_{1}+{M}_{2}+{M}_{3}\right)m}{{d}^{2}}$ b) d < R1 q) $\frac{G\left({M}_{1}+{M}_{2}\right)m}{{d}^{2}}$ c) R1 < R2 < d < R3 r) $\frac{G{M}_{1}}{{d}^{2}}$ 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)

12.Four circular coil( A,B,C,D) having radius r,2r,3r,4r having numbers of turns 4n,3n,2n,n and carrying the same same current are there.
 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)

SECTION-IV

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

13.The trajactory of the particle is
• y$=\mathrm{xa}\mathrm{sin}\left(\frac{\omega }{{u}_{0}}\right)$
• y$=x\mathrm{sin}\left(\frac{\mathrm{\omega a}}{{u}_{0}}\right)$
• $y=a\mathrm{sin}\left(\frac{\mathrm{\omega x}}{{u}_{0}}\right)$
• y$=a\mathrm{cos}\left(\frac{\mathrm{\omega x}}{{u}_{0}}\right)$

14.Find the radius vector of the object at t=3π/2ω
• -ai+$\left(\frac{3\pi {u}_{0}}{2\omega }\right)$j
• $\left(\frac{3\pi {u}_{0}}{2\omega }\right)$j
• ai+$\left(\frac{3\pi {u}_{0}}{2\omega }\right)$j
• ai-$\left(\frac{3\pi {u}_{0}}{2\omega }\right)$j

SECTION-V

This section contains 6 questions. The answer to each of the questions is a single digit integer, ranging from 0 to 10.
15.In Millikan's oil drop experiment ,a charged oil drop of mass 3.2X10-14 kg is held stationary between two parallel plates 6mm apart by applying a potential difference of 1200 V between them .How much excess electrons does the oil drop carry? Take g=10m/s2
• 7
• 8
• 9
• 10

16.A liquid is kept in a cylindrical vessel .When the vessel is rotated abouts its axis,the liquid rises at its sides.If the radius of the vessel is .05m 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=10m/s2 and π2=10
• 2 cm
• 8 cm
• 4 cm
• 1 cm

17.Two circular loops X and Y of radii Rx and Ry respectiviely 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

18.Two cylinerical rods of length L1 and L2,radii R1 and R2 have thermal conductivities K1 and K2 The ends of the rods are maintianed 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 K1/K2
• 8
• 2
• 1
• 4

19.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

20.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?
• 6m
• 8m
• 9m
• 1m