CBSE Questions for Class 11 Engineering Physics Motion In A Plane Quiz 12 - MCQExams.com

Two balls P and Q are at opposite ends of the diameter of a frictionless horizontal circular groove. P is projected along the groove and at the end of T second, it strikes ball Q. Let difference in their final velocities be proportional to the initial velocity of ball P and coefficient of proportionally is e then second strike occurs at

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  • $$\dfrac{2T}{e}$$
  • $$\dfrac{e}{2T}$$
  • $$2eT$$
  • $$Te$$
Is the claim of Mr.Kirkpatrick right?
  • yes
  • No
  • cannot say
  • may be correct or may be not
Find the magnitude of the angular acceleration of the cone.
129722_5a43c44dae394c988c95c61d3d926e9a.png
  • $$3.3\:rad/s^2$$
  • $$2.6\:rad/s^2$$
  • $$2.3\:rad/s^2$$
  • $$3.6\:rad/s^2$$
A projectile is required to hit a target whose coordinates relative horizontal and vertical axes through the point of projection are $$(\alpha,\beta)$$. If the gun velocity is $$\sqrt {2g \alpha}$$, it is impossible to hit the target if
  • $$\beta >\cfrac { 3 }{ 4 } \alpha $$
  • $$\beta \ge \cfrac { 3 }{ 4 } \alpha $$
  • $$\beta \le \cfrac { 3 }{ 4 } \alpha $$
  • $$\beta < \dfrac{ 3 }{ 4 } \alpha $$
A vector $$\displaystyle \overline{m}$$  of magnitude $$\displaystyle 2\sqrt{101}$$ in the direction of internal bisector of the angle between the vector $$\displaystyle \overline{b}=8\hat{i}-6\hat{j}-6\hat{k} \ and \ \overline{c}=4\hat{i}-3\hat{j}+4\hat{k}$$ is

167134.jpg
  • $$\displaystyle \frac{16\hat{i}-12\hat{j}+2\hat{k}}{5}$$
  • $$\displaystyle 16\hat{i}-12\hat{j}+2\hat{k}$$
  • $$\displaystyle \frac{-16\hat{i}+12\hat{j}+2\hat{k}}{5}$$
  • $$\displaystyle 16\hat{i}+12\hat{j}+2\hat{k}$$
Two particles projected from the same point with same speed $$u$$ at angles of projection $$\displaystyle \alpha $$ and $$\displaystyle \beta $$ strike the horizontal ground at the same point. If $$\displaystyle h_{1}$$ and $$\displaystyle h_{2}$$ are the maximum heights attained by the projectile, $$R$$ is the range for both $$\displaystyle t_{1}$$ and $$\displaystyle t_{2}$$ are their times of flights, respectively, then
  • $$\displaystyle \alpha +\beta =\frac{\pi }{2}$$
  • $$\displaystyle R=4\sqrt{h_{1}h_{2}}$$
  • $$\displaystyle \frac{t_{1}}{t_{2}}=\tan \alpha $$
  • $$\displaystyle \tan \alpha =\sqrt{\frac{h_{1}}{h_{2}}}$$
A racing car is travelling along a straight track at a constant velocity of $$40 m/s$$  A fixed TV camera is recording the event as shown in figure. In order to keep the car in view, in the position shown, the angular velocity of camera should be
218534_8c083f9db8de4f1a8f582003b5d6c0c9.png
  • $$3 $$ rad/s
  • $$2 $$ rad/s
  • $$4 $$ rad/s
  • $$1 $$ rad/s
A particle is projected at an angle of elevation $$\displaystyle \alpha $$ and after t second it appears to have an elevation of $$\displaystyle \beta $$ as seen from the point of projection. Find the initial velocity of projection.
  • $$\displaystyle v= \frac{gt\cos \beta }{2\sin \left ( \alpha -\beta \right )}$$
  • $$\displaystyle v= \frac{2gt\cos \beta }{\sin \left ( \alpha -\beta \right )}$$
  • $$\displaystyle v= \frac{gt\cos \beta }{\sin \left ( \alpha +\beta \right )}$$
  • $$\displaystyle v= \frac{2gt\cos \beta }{\sin \left ( \alpha +\beta \right )}$$
At a height of $$15\ m$$ from ground velocity of a projectile $$\displaystyle \vec{v}= \left ( 10\hat{i}+10\hat{j} \right )$$ and  ($$g = 10\ ms^{-2}$$ )
  • particle was projected at an angle of $$\displaystyle 45^{\circ}$$ with horizontal
  • time of flight of projectile is $$4\ s$$
  • horizontal range of projectile is $$100\ m$$
  • maximum height of projectile form ground is $$20\ m$$
A projectile of mass m is fired into a liquid at an angle $$\displaystyle \theta _{0}$$ with an initial velocity $$\displaystyle v _{0}$$ as shown. If the liquid develops a frictional or drag resistance on the projectile which is proportional to its velocity, i.e., F= -kv where k is a positive constant, determine the x and y components of its velocity at any instant. Also find the maximum distance $$\displaystyle x_{max}$$ that it travels?

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  • $$\displaystyle v_{x}=v_{0}\cos \theta _{0}e^{-kt/m},v_{y}=\frac{m}{k}\left [ \frac{k}{m}v_{0}\sin\theta _{0}+g^{-\frac{kt}{m}}-g \right ]X_{m}=\frac{mv\cos\theta}{k}$$
  • $$\displaystyle v_{x}=v_{0}\cos \theta _{0}e^{-2kt/m},v_{y}=\frac{m}{k}\left [ \frac{k}{m}v_{0}\sin\theta _{0}+g^{-\frac{kt}{m}}-g \right ]X_{m}=\frac{mv\cos\theta}{2k}$$
  • $$\displaystyle v_{x}=v_{0}\cos \theta _{0}e^{-kt/m},v_{y}=\frac{m}{k}\left [ \frac{k}{m}v_{0}\sin\theta _{0}+g^{-\frac{2kt}{m}}-g \right ]X_{m}=\frac{mv\cos\theta}{k}$$
  • $$\displaystyle v_{x}=v_{0}\cos \theta _{0}e^{-kt/m},v_{y}=\frac{m}{k}\left [ \frac{k}{m}v_{0}\sin\theta _{0}+g^{-\frac{kt}{m}}-g \right ]X_{m}=\frac{mv\cos\theta}{4k}$$
A particle is moving in a circle of radius $$R$$ in such a way that at any instant the normal and tangential component of its acceleration are equal. If its speed at $$t=0$$ is $$\displaystyle v_{0}.$$ The time taken to complete the first revolution is
  • $$\displaystyle \frac{R}{v_{0}}$$
  • $$\displaystyle \frac{R}{v_{0}}e^{-2\pi }$$
  • $$\displaystyle \frac{R}{v_{0}}\left ( 1-e^{-2\pi } \right )$$
  • $$\displaystyle \frac{R}{v_{0}}\left ( 1+e^{-2\pi } \right )$$
Between $$t=30\;s\;and\;t=40/s$$, the merry-g-round
281309_ad4ecf9d254646cbbdac23e1d543d265.png
  • rotates clockwise, at a constant rate
  • rotates clockwise, and slows down
  • rotates counterwise, at a constant rate
  • rotates counterclockwise, and slows down
If the equation for the displacement of a particle moving on a circular path is given by $$(\theta)=2t^3+0.5$$, where $$\theta$$ is in radians and $$t$$ in seconds, then the angular velocity of the particle after $$2s$$ from its start is
  • $$\;8\;rad/s$$
  • $$\;12\;rad/s$$
  • $$\;24\;rad/s$$
  • $$\;36\;rad/s$$
In one second, a particle goes from point A to point B moving in a semicircle. Find the magnitude of the average velocity.
251203_4ff4707aaccd4c3f9556284601405ed2.png
  • 1 m/s
  • 2 m/s
  • 0.5 m/s
  • None of the above
Between $$t=0\;and\;t=10\;s$$, about how many revolutions (approx) does the merry-go-round complete?
281306_93919dbb2b4041c7a09264f9f04bae1c.png
  • $$\;1$$
  • $$\;2$$
  • $$\;3$$
  • $$\;4$$
Between $$t=10\;s\;and\;t=20\;s$$, the merry-go-round.
281307_6dacc854725e483e81c6f7f4425d0749.png
  • rotates clockwise, at a constant rate
  • rotates clockwise, and slows down
  • rotates counterwise, at a constant rate
  • rotates counterclockwise, and slows, down
Single Correct Answer Type
The path of a projectile is given by the equation $$y=ax-bx^2$$, where $$a$$ and $$b$$ are constants and $$x$$ and $$y$$ are respectively horizontal and vertical distances of projectile from the point of projection. The maximum height attained by the projectile and the angle of projection are respectively:
  • $$\displaystyle\frac{2a^2}{b}$$,  $$ \tan^{-1}(a)$$
  • $$\displaystyle\frac{b^2}{2a}$$, $$\tan^{-1}(b)$$
  • $$\displaystyle\frac{a^2}{b}$$, $$ \tan^{-1}(2b)$$
  • $$\displaystyle\frac{a^2}{4b}$$, $$\tan^{-1}(a)$$
Consider two children riding on the merry-go-round Child 1 sits near the edge, child 2 sits closer to the centre.
Let $$v_1\;and\;v_2$$ denote the linear speed of child 1 and child 2, respectively. Which of the following is true?
281310_0184842bfe104d4fb19cf1def898930c.png
  • $$v_1>v_2$$
  • $$v_1=v_2$$
  • $$v_1\,<\,v_2$$
  • (4) we cannot determine which is true, without more information
The velocity of a car travelling on a straight road is $$3.5km{ h }^{ -1 }$$ at an instant of time. Now travelling with uniform acceleration for $$10s$$ the velocity becomes exactly double. If the wheel radius of the car is $$25cm$$, then which of the following is the closest to the number of revolutions that the wheel makes during this $$10s$$?
  • $$84$$
  • $$95$$
  • $$126$$
  • $$135$$
Equation of parabolic trajectory of a projectile can be given by:
  • $$\dfrac{sin\theta}{cos\theta}x - \dfrac{gx^2}{sin^2\theta+cos^2\theta + cos2\theta}$$
  • $$\dfrac{sin\theta}{cos\theta}x - \dfrac{gx^2}{u^2(sin^2\theta+cos^2\theta + cos2\theta)}$$
  • $$\dfrac{sin\theta}{cos\theta}x - \dfrac{gx^2}{2u^2(sin^2\theta+cos^2\theta + cos2\theta)}$$
  • $$\dfrac{sin\theta}{cos\theta}x - \dfrac{gx^2}{u^3(sin^2\theta+cos^2\theta + cos2\theta)}$$
Two billiard balls are rolling on a flat table. One has velocity components $$V_x = 1  \ m/s, V_y\,=\, \sqrt{3}\,  \ m/s$$ and the other has component $$V_x \,=\, 2 \ m/s\,$$ and $$\, V_y\,=\, 2 \  m/s$$. If both the balls start moving from the same point the angle between their path is:
  • $$60^{\circ}$$
  • $$45^{\circ}$$
  • $$22.5^{\circ}$$
  • $$15^{\circ}$$
A particle of mass $$10\  g$$ moves along a circle of radius $$6.4\  cm$$ with a constant tangential acceleration. What is the magnitude of this acceleration if the kinetic energy of the particle becomes equal to $$8 \times {10}^{-4} J$$ by the end of the second revolution after the beginning of the motion?
  • $$0.1\  {m}/{{s}^{2}}$$
  • $$0.15\  {m}/{{s}^{2}}$$
  • $$0.18\  {m}/{{s}^{2}}$$
  • $$0.2 \ {m}/{{s}^{2}}$$
A plane flying horizontally at a height of 1500 m with a velocity of $$200ms^{-1}$$ passes directly overhead an antiaircraft gun. Then the angle with the horizontal at which the gun should be fired for the shell with a muzzle velocity of 400 $$ms^{-1}$$ to hit the plane is:
  • $$90^{\circ}$$
  • $$60^{\circ}$$
  • $$30^{\circ}$$
  • $$45^{\circ}$$
It is possible to project a particle with a given velocity in two possible ways so as to make them pass through a point P at a horizontal distance $$r$$ from the point of projection. If $$t_1$$ and $$t_2$$ are times taken to reach this point in two possible ways, then the product $$t_1t_2$$ is proportional to:
  • $$\displaystyle\frac{1}{r}$$
  • $$r$$
  • $$r^2$$
  • $$\displaystyle\frac{1}{r^2}$$
The x and y co-ordinates of a particle is x = Asin($$\omega{t}$$) and y = Asin($$\omega{t} +\frac{\pi}{2}$$) . Then the motion of the particle is ( x and y are in the directions shown in the fgure )
760723_958837acd0a44abe9101dfbd8ed1c873.png
  • Circular anticlockwise
  • Circular clockwise
  • Elliptical clockwise
  • Rectilinear
If $$\vec{A} = 3 \hat{i} - 2 \hat{j} + \hat{k}, \vec{B} = \hat{i} - 3 \hat{j} + 5 \hat{k}\  and\ \vec {C} = 2 \hat{i} + \hat {j} - 4 \hat{k}$$ form a right angled triangle then out of the following which one is satisfied?
  • $$ \vec{A} = \vec{B} + \vec{C}\ and\ A^2 = B^2 + C^2$$
  • $$ \vec{A} = \vec{B} + \vec{C}\ and\ B^2 = A^2 + C^2$$
  • $$ \vec{B} = \vec{A} + \vec{C}\ and\ B^2 = A^2 + C^2$$
  • $$ \vec{B} = \vec{A} + \vec{C}\ and\ A^2 = B^2 + C^2$$
A particle is projected in such a way that it follows a curved path with constant acceleration $$\vec{a}$$. For finite interval of motion. Which of the following option(s) may be correct: $$\vec{u}=$$ initial velocity, $$\vec{a}=$$ acceleration of particle, $$\vec{v}=$$ instant velocity for $$t > 0$$.
  • $$|\vec{a}\times \vec{u}|\neq 0$$
  • $$|\vec{a}\times \vec{v}|\neq 0$$
  • $$|\vec{u}\times \vec{v}|\neq 0$$
  • $$\vec{u}\cdot \vec{v}=0$$
A stone tied to a string of length $$L$$ is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed $$u$$. Determine the magnitude of the change in its velocity as it reaches a position where the string is horizontal is:
  • $$\sqrt { { u }^{ 2 }-2gL } $$
  • $$\sqrt { 2gL } $$
  • $$\sqrt { { u }^{ 2 }-gL } $$
  • $$\sqrt { 2\left( { u }^{ 2 }-2gL \right) } $$
Two particles are projected simultaneously from the same point, with the same speed, in the same vertical plane, and at different angles with the horizontal in a uniform gravitational field acting vertically downwards. A frame of the other particle, as observed from this frame, is $$\vec { r }$$. Which of the following statements is correct?
  • $$\vec { r }$$ is a constant vector.
  • $$\vec { r }$$ changes in magnitude as well as direction with time.
  • The magnitude of $$\vec { r }$$ increases linearly with time; its direction does not change.
  • The magnitude of $$\vec { r }$$ increases linearly with time; its direction changes.
In the adjacent figure, a uniform disc of mass $$2m$$ and radius $$l/2$$ is lying at rest on a smooth horizontal surface. A particle $$'A'$$ of mass $$m$$ is connected to a light string of length $$l$$, whose other end is attached to the circumference of the disc. Initially string is just taut and tangential to the disc, particle $$A$$ is at rest. In the same horizontal plane another particle $$B$$ of some mass $$m$$ moving with velocity $$v_{0}$$ perpendicular to string collides elastically with $$A$$. Just after impact which of the following statements will be true
806106_88350e91a4ab4be9b02b4a9960e206f6.png
  • Tension in the string is $$\dfrac {2mv_{0}^{2}}{5l}$$
  • Acceleration of the centre of the disc is $$\dfrac {v_{0}^{2}}{5l}$$
  • Tension in the string is $$\dfrac {mv_{0}^{2}}{5l}$$
  • Acceleration of the centre of the disc is $$\dfrac {2v_{0}^{2}}{5l}$$
A pulley $$1m$$ in diameter rotating at $$600 r.p.m.$$ is brought to rest in $$80\ s$$. By constant force of friction on its shaft. How many revolutions does it moves?
  • $$200$$
  • $$400$$
  • $$600$$
  • $$500$$
Two paper screens $$A$$ and $$B$$ are separated by $$150\ m$$. A bullet pierces $$A$$ and $$B$$. The hole in $$B$$ is $$15\ cm$$ below the hole is $$A$$. If the bullet is travelling horizontally at the time of hitting $$A$$, then the velocity of the bullet at $$A$$ is $$(g = 10\ ms^{-2})$$.
  • $$100\sqrt {3}ms^{-1}$$
  • $$200\sqrt {3}ms^{-1}$$
  • $$300\sqrt {3}ms^{-1}$$
  • $$500\sqrt {3}ms^{-1}$$
Two particles are thrown simultaneously from points $$A$$ and $$B$$ with velocities $${ u }_{ 1 } = 2\ { ms }^{ -1 }$$ and $${ u }_{ 2 } = 14\ { ms }^{ -1 }$$, respectively, as shown in Fig
The direction (angle) with horizontal at which $$B$$ will appear to move as seen from $$A$$ is
  • $$37^{}$$
  • $$53^{}$$
  • $$15^{}$$
  • $$90^{}$$
A particle of mass $$2 kg$$ moves with an initial velocity of $$\bar { v } =4\hat { i } +4\hat { j } m{ s }^{ -1 }$$. A constant force of $$\bar { F } =20\hat { j } N$$ is applied on the particle. Initially, the particle when its y-coordinate again becomes zero is given by
  • $$1.2 m$$
  • $$4.8 m $$
  • $$6.0 m $$
  • $$3.2 m$$
Two particles $$P$$ and $$Q$$ projected simultaneously away from each other from a point $$A$$ as shown in the figure. The velocity of $$P$$ relative to $$Q$$ in $$m { s }^{ -1 }$$ at the instant when the motion of $$P$$ is horizontal is
980944_8913991f3b5d43298cdb9337d74fd60b.png
  • $$10\sqrt { 4-\sqrt { 3 } }$$
  • $$ 20\sqrt { 4-\sqrt { 3 } }$$
  • $$ 10\sqrt { 4+\sqrt { 3 } }$$
  • $$ 20\sqrt { 4+\sqrt { 3 } } $$
The point from where a ball is projected is taken as the origin of the coordinates axes. The $$x$$ and $$y$$ components of its displacement are given by $$x = 6t$$ and $$y = 8t - 5t^{2}$$. What is the velocity of projection?
  • $$6 \ ms^{-1}$$
  • $$8 \ ms^{-1}$$
  • $$10 \ ms^{-1}$$
  • $$14 \ ms^{-1}$$
Which of the following statements is/are correct (figure)?
981369_ad05956c584d4a43ab19c0559dc1c5e6.JPG
  • The sign of the x-component of $$\vec{d}_{1}$$ is positive and that of $$\vec{d}_{2}$$ is negative.
  • The signs of the y-components of $$\vec{d}_{1}$$ and $$\vec{d}_{2}$$ are positive and negative, respectively.
  • The signs of the x- and y-components of $$\vec{d}_{1}$$ + $$\vec{d}_{2}$$ are positive.
  • None of these.
a particle of mass $$2 kg$$ moves with an initial velocity of $$(4\hat { i } +2\hat { i } ) m{ s }^{ -1 }$$ on the x-y plane. A force $$F=(2\hat { i } +8\hat { j } )N$$ acts on the particle. The initial position of the particle is $$(2 m, 3 m)$$. Then for $$ y=3 m$$,
  • Possible value for x is only $$x=2 m$$
  • Possible value of x is not only $$x=2 m$$, but there exists some other value of x also
  • Time taken is $$2 s$$
  • All of the above
A uniform disc of mass $$M$$ and radius $$R$$ is mounted on an axle supported in frictionless bearings. A light cord is wrapped around the rim of the disc and a steady downward pull $$T$$ is exerted on the cord. The tangential acceleration of a point on the rim is
  • $$\cfrac { T }{ M } $$
  • $$\cfrac { MR }{ T } $$
  • $$\cfrac { 2T }{ MR } $$
  • $$\cfrac { MR }{ 2T } $$
A particle is projected at an angle of elevation $$\alpha$$ and after $$t$$ second, it appears to have an angle of elevation $$\beta$$ as seen from the point of projection. The initial velocity will be
  • $$\dfrac { gt }{ 2\sin { \left( \alpha -\beta \right) } }$$
  • $$\dfrac { gt\cos { \beta } }{ 2\sin { \left( \alpha -\beta \right) } }$$
  • $$\dfrac { \sin { \left( \alpha -\beta \right) } }{ 2gt }$$
  • $$\dfrac { 2\sin { \left( \alpha -\beta \right) } }{ gt\cos { \beta } }$$
A disc rotates about its axis with a constant angular acceleration of $$4$$ rad$$/s^2$$. Find the radius tangential accelerations of a particle at a distance of $$1$$ cm from the axis at the end of the second after the disc starts rotating.
  • $$0.16 m/s$$
  • $$1 m/s$$
  • $$3 m/s$$
  • $$10 m/s$$
A disc of mass $$m$$, radius $$R$$ is set rolling with angular velocity $$\omega$$, up on a rough inclined plane of inclination $$30$$ to the horizontal and is in rolling motion always. The distance it will move up on the inclined plane will be:
  • $$\dfrac{3}{4} \dfrac{R^2 \omega^2}{g}$$
  • $$\dfrac{3}{2} \dfrac{R^2 \omega^2}{g}$$
  • $$\dfrac{3R^2 \omega^2}{g}$$
  • $$\dfrac{9}{8} \dfrac{R^2 \omega^2}{g}$$
A wheel is making Revolution about axis with uniform angular acceleration, Starting from rest, it reaches $$100\ rev/sec$$ in $$4\ seconds$$. Find the angular rotated during these four seconds.
  • $$200 \pi rad/sec$$
  • $$400 \pi rad/sec$$
  • $$600 \pi rad/sec$$
  • $$800 \pi rad/sec$$
A positive charge moving along the positive x-direction with a speed v traces a non-linear trajectory OA in the x-y plane after passing O as shown in the figure. The combination of electric $$(\vec{E})$$ and magnetic field $$(\vec{B})$$ fields that would lead to the trajectory OA is (a, b,. c are non-zero positive constants).
1012706_df198f2829614253941473d7910a7fc2.jpg
  • $$\vec{E}=0; \vec{B}=a\hat{i}+c\hat{k}$$
  • $$\vec{E}=a\hat{i}; \vec{B}=b\hat{j}+c\hat{k}$$
  • $$\vec{E}=0; \vec{B}=b\hat{j}+c\hat{k}$$
  • $$\vec{E}=a\hat{i}; \vec{B}=b\hat{j}-c\hat{k}$$
A conducting circular loop of radius r carries a constant current ii. It is placed in a uniform magnetic field $$\vec{B_0}$$ such that $$\vec{B_0}$$ is perpendicular to the plane of the loop. The magnetic force acting on the loop is?
  • ir $$B_0$$
  • $$2\pi$$ ir $$B_0$$
  • Zero
  • $$\pi$$ is $$B_0$$
You throw a ball which a launch velocity of $$\vec {v}=(3\hat {i}+4\hat {j})\ m/s$$ the maximum height attaind by the body is ?
  • $$0.8m$$
  • $$0.2 m$$
  • $$2.3m$$
  • $$5.3m$$
A particle is moving along a circle such that it completes one revolution in 40 seconds. In 2 minutes 20 seconds, the ratio$$\frac{{\left| {displacment} \right|}}{{dis\tan ce}}$$ is
  • 0
  • 1/7
  • 2/4
  • 1/11
Two particles A and B of equal masses have velocities $$\vec{V_a} = 4\hat{i}$$ and $$\vec{V_B} = 4\hat{jm}$$. The particles move with accelerations $$\vec{a_A} =(-5\hat{i}+5\hat{j})ms^2$$  respectively. while the acceleration of other part is zero.the center of mass of two particles move in a path of
  • a straight line
  • a parabola
  • a circle
  • an ellipse
Consider the x-axis as representing east, the y-axis as north and z-axis as vertically upwards. Give the vector representing each of the following points.
  • 5 m north east and 2 m up
  • 4 m south east and 3 m up
  • 2 m north west and 4 m up
  • 3 m south east and 5 m up
If $$R$$ and $$H$$ are the horizontal range and maximum height attained by a projectile, than its speed of projection is:
  • $$\sqrt{2gR+\dfrac{4R^{2}}{gH}}$$
  • $$\sqrt{2gH+\dfrac{R^{2}g}{8H}}$$
  • $$\sqrt{2gH+\dfrac{8H}{Rg}}$$
  • $$\sqrt{2gH+\dfrac{R^{2}}{H}}$$
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