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This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 12701. |
A body projected vertically from the earth reaches a height equal to earth.s radius before returning to the earth. The power exerted by the gravitational force is greatest |
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Answer» at the highest POSITION of the body Just before hitting the earth `theta = 0^@` . Hence, the power exerted by the gravitation force is greatest at the instant just before the body hits the earth. |
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| 12702. |
A rope of negligible mass is wound round a hollow cylinder of mass 5 kg and radius 0.40m. What is the linear acceleration of the cylinder if the rope is pulled with a force of 30N ? |
Answer» SOLUTION : `tau=Iprop=FR` where `|=MR^2=3xx0.4^2=0.48kgm^2` `tau=30xx0.4=12.0Nm` `prop=tau/I=`(12)/(0.48)=25rads^(-2)` `a=rprop` i.e `a=0.4xx25=10.0ms^(-1)` |
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| 12703. |
Comparatively, which of the following has lesser value than others? |
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Answer» STATIC FRICTION |
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| 12704. |
Check the correctness of the following equation by the method of dimensions (i) v^(2)=u^(2)+2gs (ii) s=ut+1/2"gt"^(2) (iii) v=u+"gt" |
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Answer» Solution :(i) `v^(2)=u^(2)+2gs` Dimensional formula of `v^(2)` is `[LT^(-1)]^(2)` that of `u^(2)` is `[LT^(-1)]^(2)` and gs is `[LT^(-1)]^(2)` and gs is `[LT^(-2)][L]=[L^(2)T^(-2)]` substituting in the equation `L^(2)T^(-2)=L^(2)T^(-2)+L^(2)T^(-2)` Each term on both sides of the equation has the same DIMENSIONS. So the equation is DIMENSIONALLY CORRECT. (ii) `s=ut+1/2"GT"^(2)` Dimensional formula of s is `[L]`, that of ut is `[LT^(-1)][T]=[L]` and that of `1/2"gt"^(2)` is `[LT^(-2)][T^(2)]=[L]` Substituting the dimensions in the given equations `[L]=[LT^(-1)][T]+[LT^(-2)][T^(2)]` `[L]=[L]+[L]` Eac term on both sides of the equation has the same dimensions. So the equation is dimensionally correct (III) `v=u+"gt"` Dimensional formula of v,u and gt are `[LT^(-1)],[LT^(-1)]` and `[LT^(-2)][T]` respectively. Substituting in the given equation `[LT^(-1)]=[LT^(-1)]+[LT^(-2)][T]` `=[LT^(-1)]+[LT^(-1)]` Each on both sides of equation has the same dimensions. So the equation is dimensionally correct. |
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| 12705. |
Define the center of mass of a body. |
| Answer» Solution :The CENTER of mass of a body is defined as a POINT where the entire mass of the body APPEARS to be CONCENTRATED | |
| 12706. |
The equation of a wave is y = 20 sin(100pit-0.08pix)cm.The frequency of the wave is |
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Answer» 50 Hz |
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| 12707. |
A body initially at rest is moving with uniform acceleration a .Its velocity after n seconds is v.The displacement of the body in last 2s is |
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Answer» `(2V(N-1))/(n)` |
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| 12708. |
When a spring is compressed by 3cm, the potential energy stored in it is U. When it is compressed further by 3 cm, the increase in potential energy is, |
| Answer» Answer :D | |
| 12709. |
If a simple pendulum has significant amplitude (up to a factor of 1/e of original) only in the period between t = 0 s to 1 = T sec, then T may be called the average life of the pendulum. When the spherical bob of the pendulum of mass 1kg suffers a retardation (due to viscous drag) proportional to into velocity with .b. as the constant of proportionality, the average life time of pendulum is (assuming damping is small) in seconds |
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Answer» `(0.693)/(B)` |
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| 12710. |
The lengths of two bodies measured by a metre scale are l_1=(20_-^+0.5)cmand l_2=(15_-^+0.2)cm Calculate: Sum of these lengths |
| Answer» SOLUTION :`(35_-^+0.7)CM` | |
| 12711. |
What is the relation between escape and orbital velocity? |
| Answer» SOLUTION :`V_(E)=(SQRT2).V_(0)` | |
| 12712. |
A cylinder of fixed capacity 67.2 litres containshelium gas at STP. The amount of heat needed to rise the temperature of the gas in the cylinder by 20^(@)C is (R = 8.31 "Jmol"^(-1)K^(-1)) |
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Answer» 748J |
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| 12713. |
Two particles of equal mass move in a circle of radius r under the action of their mutual gravitational attraction . Find the speed of each particle if its mass is m. |
Answer» Solution : The particle will ALWAYS remain diametrically OPPOSITE , so that the force on each particle will be directed along the radius. When each particle is describing a CIRCULAR orbit, the gravitational force on one of the PARTICLES must be equal to the necessary centripetal force , `(mV^2)/r =(Gmm)/((2r)^2)"" i.e V = sqrt((Gm)/r)` |
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| 12714. |
A body is just supported at the face of a cart moving at an acceleration. The acceleration of the cart so that the body does not slide |
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Answer» Independent of MASS of the body |
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| 12715. |
If the pitch of the sound of a source appears to drop by 10%to a moving person, then determine the velocity of motion of the person. Velocity of sound = 330 ms ^(-1). |
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Answer» SOLUTION :APPARENT FREQ. `v.=((v-v_(0))/v)v or (v.)/v=900/1000=9/10,v=330ms^(-1) therefore 9/10=330-v_(0)=9/10**330=297 v_(0)=330-297=(33M)/s.` |
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| 12716. |
Zeroth law of thermodynamics represents concept of temperature state of thermal equilibrium of a system that heat is a form of energy |
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Answer» a, B are CORRECT |
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| 12717. |
The potential energy of a body of mass m is given by U = px + qy + rz. The magnitude of acceleration of the body will be |
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Answer» `(p + q + R)/(m)` |
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| 12718. |
The shadow of a tower standing on a level plane is found to be 50m longer when sun's altitude is 30^@ then when it is 60^@. Find the height of tower. |
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Answer» 40.3m |
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| 12719. |
The centreof mass of a systemof particlesdoes not dependon |
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Answer» massesof the PARTICLES |
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| 12720. |
A vessel of capacity V=101 contains m_(0)=2g of nitrogen molecules at 27^(@)C. Calculate the time in which half of it will escape into a vacuum through a hole of area s=1cm^(2). You may take barc=c_("rms") |
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| 12721. |
A water pipe has aninternal diameter of 10 cm . Water flows through it at the rate of 20//sec. The water jet strikes normally on a wall and falls dead. Find the force on the wall . |
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| 12722. |
A bat emits ultrasonic sound of frequency 1000 kHz in air. If the sound meets a water surface, what is the wavelength of (a) the reflected sound, (b) the transmitted sound ? Speed of sound in air is 340 ms ^(-1) and in water 1486 ms ^(-1). |
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Answer» Solution :(i) Here sound wave reflected from water surface is travelling in air. If its wavelength is `lamda _(a)` and velocity of sound in air is `v _(a)` then, `v _(a) = F lamda_(a) implies lamda _(a)=(v _(a))/(f )` `= (340)/(100xx 10 ^(3)) =3.4 xx 10^(-3) m` (ii) Here, after the sound wave is INCIDENT on the water surface, partially it gets reflected and partially it enters into water medium. Even after change in the medium, frequency of sound wave remains same (because it is source dependent and here source of sound remain same). HENCE, if wavelength of sound wave in water medium is `lamda_(W)` and velocity of sound in water is `v _(W) ` then, `v _(W) = f lamda _(W) implies lamda _(W) = (v _(W))/(f)` `=(1486)/(100 xx 10 ^(3)) = 1.49 xx 10 ^(-2) m` |
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| 12723. |
Sameer and Rameez went to Thirupathi during holidy time. They found more crowd even though they have to wait to see God, in queue. Went the crowd started to move, the place was so hot and temperature does not fall. Every one was sweating and got caught in this congested situation. Why it is hot whenever we are in a crowd? (i) What is internal energy of a system. Give an expression? |
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Answer» Solution :WHEREVER there is crowd, we can feel the HOTNESS of air. This is because in the crowded region, people who are moving may have a chance to collide with each other, and also with the atoms or molecules present in that region due to this COLLISION heat energy is released, which forms as a disturbance and spreads from a particle to particle. Any congested room will have this effect mostly. It's just the Brownian motion of the molecules, based on the kinetic theory of gases. (ii) Relatin between `C_(P)&C_(V)`: `C_(P)` - Molar SPECIFIC heat capacity of a gas at constant pressure. `C_(V)` - Molar specific heat capacity of a gas at constant volume. Where, `Rrarr` Gas constant `C_(P)-C_(V)=R`. |
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| 12724. |
The resultant of two vectors of magnitudes (P+Q) and (P-Q) is sqrt(P^(2) + Q^(2)). THn the angle between the vectors is |
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Answer» `cos^(-1) [(-(P^(2) + Q^(2)))/(2(P^(2) - Q^(2)))]` |
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| 12725. |
For a system to be in equlibrium the torques acting on it must balance. This is true only if the torques are taken about |
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Answer» the CENTRE of the system |
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| 12726. |
A uniform wire of length 20 cm is bent into a circle, It is placed gently on the surface of water of surface tension 0.07Nm^(-1). The extra force than its weight required to pull it out of the water is |
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Answer» 0.014N |
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| 12727. |
A girl in a swing is 2.5 m above ground at the maximum height and at 1.5 m above the ground at the lowest point. Her maximum velocity in the swing is (g = 10 ms^(-2)) |
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Answer» `5sqrt(2) ms^(-1)` `:.` Total energy `, E_1 = mgh_1 + 0 = mgh_1` At the lowest point, `v = ?, h_2 = 1.5 m` `:. ` Total energy , `E_2 = mgh_2 + 1/2 mv^2` According to the law of CONSERVATION of MECHANICAL energy `E_1 = E_2` `:. mgh_1 = 1/2 mv^2 + mgh_2 " or " v^2 = 2g (h_1 - h_2)` Or `v = sqrt(2h(h_1 - h_2)) = sqrt(2 XX 10 xx (2.5 - 1.5)) = 2sqrt(5) ms^(-1)`. |
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| 12728. |
The velocity of a listener who is moving away from a stationary source of sound such that the listener notices 5% apparent decrease in frequency of sound is (Velocity of sound in air =340m//s) |
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Answer» `12.5ms^(-1)` |
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| 12729. |
Which of the following is having same dimensional formula? |
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Answer» TENSION and surface tension |
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| 12730. |
Referring to figure of previous question let DeltaU_(1) and DeltaU_(2) be the changes in internal energy of the system in the processes A and B. Then |
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Answer» `DeltaU_(1)gt DeltaU_(2)` |
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| 12731. |
Define radius of gyration. What is the purpose of defining it ? |
| Answer» SOLUTION :It HELPS us to FIND the Mi. of IRREGULAR bodies | |
| 12732. |
A planet in a distant solar system is 10 times more massive than the earth and its radius is 10 times smaller. Given that the escape velocity from the earth is 11 kms^(-1) ,the escape velocity from the surface of the planet would bex xx 11 km/s. Find x. |
| Answer» SOLUTION :The high PRESSURE AIR in the cycle TUBE undergoes an adiabatic EXPANSION, which produces cooling. | |
| 12733. |
The energy of a loaded wire is E. In doubling the load, what is the energy stored in the wire ? |
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Answer» |
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| 12734. |
Two billiard balls of the same size (radius r) and same mass are in contact on a billiard table. A third ball alsoof the same size and mass strike them symmetrically and remains at rest after the impact. The coefficient of restitution between the balls is |
Answer» Solution : `sin THETA = (r )/(2r) = (1)/(2) , therefore theta = 30^(@)` From conservation of linear momentum `m U = 2mvcos30^(@)ORV=(u)/(sqrt(3))` `"Now" " " E = ("relative velocity of separation")/("relative velocity of approach")` in common normal direction Hence, `e=(v)/(ucos30^(@))=(u//sqrt(3))/(usqrt(3)//2)=(2)/(3)` |
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| 12735. |
If a rubber ball is taken down to a 100 m deep lake its volume is decreased by 0.1%. If g = 10 m//sec^(2). Then the bulk modulus of elasticity is |
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Answer» `10^(9)Pa` |
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| 12736. |
The fundamental mode of vibration of a stretched string is shown belown Let the fundamental frequency is 45 hz and the length of wire is 87.5 cmif the linear density of wire is 4xx10^(-2)kg m find the tension in the string. |
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Answer» SOLUTION :`v_0` = 45Hz, L = `87xx10^-2m`,`lemda` = `4xx10^-2` V = `1/2l sqrtT/m`.T = 248N |
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| 12737. |
A light anda heavy body have same K.E., which of the two have more momentum and why ? |
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| 12738. |
The two specific heat capacities of a gas are measured as C_(P)=(12.28+0.2) units and C_(V)=(3.97+0.3) units, if the value of gas constant R is 8.31 pm 0 . x units, the vaslue of x is (Relation : C_(P)-C_(V)=R) |
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| 12739. |
A stone is projected from the ground with a velocity of 14 ms^(-1) one second later it clears a wall 2 m high. The range of projection is (g=10ms^(-2)) |
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Answer» `45^(@)` |
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| 12740. |
A girl in a swing is 2.5 m above ground at the maximum height and at 1.5 m above the ground at the lowest point, Her maximum velocity in the swing is (g = 10 ms^(-2)) |
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Answer» `5sqrt(2) MS^(-1)` |
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| 12741. |
The substance whichshowsparticallyno ealstic after effect is |
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Answer» copper |
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| 12742. |
A bomb at rest explodes into two pieces of masses 1 kg and 2 kg. If the velocity of the lighter piece is 200 ms^(-1), find the velocity of the heavier piece. |
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Answer» |
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| 12743. |
A body of mass 0.5 kg travels in a straight line with velocity v = kx^(3//2) where k = 5 m^(-1//2) s^(-1) What is the work done by the net force during its displacement from x = 0 to x = 2 m? |
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Answer» 25 J ACCELERATION, `a = (dv)/(dt) = (dv)/(DX)(dx)/(dt) = v (dv)/(dx)` As `v^2 = k^2 x^3 :. 2v (dv)/(dx) = 3k^2 x^2 :. a = 3/2 k^2 x^2` Force, `F = ma = 3/2 mk^2 [(x^3)/(3)]_(0)^(2) = 3/2 xx 0.5 xx 5^2 xx 8/3 = 50 J` |
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| 12744. |
(a) You are given a thread and a metre scale. How will you estiate the diameter of the thread ?(b) A screw gauge has pitch of 1.0 mm and 200 division on thecircular scale. Do you think it is possiblel to increase the accuracy of the gauge arbitrarily by increasing the number of division on the circular scale ? (c ) The mean diameter of a thin brass rod is to be measured by vernier callipers. Why is a set of 100 measurements of the diameter expected to yield a more reliable estimate then a set 5 measurements only? |
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Answer» Solution :(a) The diameter of a thred is so small that it cannot be measurd using a metre scale. We wind a number of turns of the thread on the meter scale so that the turns are CLOSELY toching one another. Measure the length (I) of the winding on the scale which contains n number of turns :. Diameter of thred = `(I)/(n)` (b) As least count=` ("pithc")/("number of divisions on circular scale")` :. theoretically SPEAKING least count decreases on increasing the number of divisions on the ciruclar scale. HENCE, accuracy would increase. Practically it may not be possible to take the reading precisely due to LOW resoulation of human eye. (c ) A large number of observaions (say, 100) will given more reliable result then smaller number of observations (say 5). This is bacuse of probability of making a positive random error of certain magnitude is equal to that of making a negative randow error of the same magnitude. Therefore, when number of observations is large, randow error are likely to cancel and the result may be morel reliable. |
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| 12745. |
A bird moves in such a way that it has a displacement of 12 m towards east, 5 m towards north and 9 m vertically upwards. Find the magnitude of its displacement. |
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Answer» `5 SQRT2 m` |
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| 12746. |
It substance of T temperature is kept in surrounding of T temperature, then give the net rate of loss of radlation energy. |
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Answer» SOLUTION :`H=3sigmaA(T^(4)-T_(S)^(4))` Where e = EMISSIVITY, A = AREA, `SIGMA=` Stefan-Boltzmaan CONSTANT. and `TgtT_(S)` |
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| 12747. |
Density of water is maximum at the temperature of ………………. . |
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Answer» `32^(@)F` `(F-32)/(9)=(C )/(5)=(4)/(5) rArr F=39.2^(@)F` |
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| 12748. |
The angle of projection for a projectile to covermaximum range is : |
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Answer» `30^(@)` `(u^(2))/(g) SIN 2 theta = (u^(2))/(g) ` . `sin 2 theta = 1` `:. 2 theta = 90^(@)` `theta = 45^(@)` |
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| 12749. |
An incandescent light bulb has a tungsten filament that is heated to a temperatur'e 3 xx 10^(3)K when an electric current passes through it. If the surface area of the filament is approximately 10^(-4) m^(2) and it has an emissivity of 0.32, the power radiated by the bulb is |
| Answer» ANSWER :A | |
| 12750. |
A ball impines directly upon another ball at rest and is itself brough to rest by the impact. If half of initial kinetic energy is destroyed in the collision, the coefficient of restitution is |
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Answer» 0.3 |
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