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PHYSICS JEE-MAIN (July-Attempt) 28 July (Shift-2) Paper Solution F. At m (AU) F = BIISInO r B= No 1R 2 CRIMET3 10.Dot D e Y= STRESS STRAIN

Consider the efﬁciency of carnot’s engine is given by

where and are

constants. If T is temperature, k is Boltzmann constant, is angular displacement and x has the dimensions of length. Then, choose the incorrect option

(A) Dimensions of is same as that of force.

Dimension of –1x is same as that of energy

Dimensions of –1 sin is same as that of

Dimensions of is same as that of .

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' 1.

= αβ loge βα ,

(B)

(C)

(D)

asina (t c & a k= G = E ⑭ M( 72" v lu) = pimension less 4: 1 logs (7) <B = 4 = H010+0 4 B=iLLIKIORCE IC = B

2. At time t = 0 a particle starts travelling from a height 7Z cm in a plane keeping z coordinate c o n s t a n t. At a n y i n s t a n t o f t i me i t ' s p o s i t i o n a l o n g t h e x a n d ŷ d i re c t i o n s a re deﬁn e d a s 3t a n d 5t3 respectively. At t=1s acceleration of the particle will be A & ⑭v I 273t[ 3 =5t3j, = = 74 2 C re==3, ry = = 15th, 0z ==o an = r=0, az=3 =30t3, az=d=o Quet =ax[+ cy 5+ a2 k 0f +30ty + 0 K anct t = lse qnet=0 + 305+0K a Quet = 30g

A pressure-pump has a horizontal tube of cross sectional area 10 cm2 for the outﬂow of water at a speed of 20 m/s. The force exerted on the vertical wall just in front of the tube which stops water horizontally ﬂowing out of the tube, is : (given: density of water = 1000 kg/m3]

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(A) 300 N (B) 500 N (C) 250 N (D) 400 N

↑ 3 V A=10cm, 5= 20m/sec S =103Kg/mP 7 Dt = m (DU). F=3 (A) (e) (0-0) S F SAG) (0). 3 A (0) (0). 8 Al" = MxxMx (2017 >400 N

4. A uniform metal chain of mass m and length 'L' passes over a massless and frictionless pulley. It is released from rest with a part of its length ‘l' is hanging on one side and rest of its length'L - l' is hanging on the other side of the pully. At a certain point of time, when l = L the acceleration of the chain is g. The value of x is _______."ke · = Mug -T = m. (82) 0 T mig = m, (81) 8 <I Add equation& & equation we I (e) <L-e). ② vT =M, -M2 (5)(m> m.) = (mytm.) my a + a T ↳81 ↓ Me 2 M2 -2 M = M, +M. 2 EC-e) -2Y1) ="FU +Yches 22-21221 =4th22041 = L = L=41zr=Y/:Ye Le = 4

5. A bullet of mass 200 g having initial kinetic energy 90 J is shot inside a long swimming pool as shown in the ﬁgure. If it's kinetic energy reduces to 40 J within 1 s. the minimum length of the pool, the bullet has to travel so that it completely comes to rest is : So, x = 4 => 905 = -me" 0= EX2. teo i TER : x30m/sec I 40 5 = me" ↑ 00L 40 = x200 x 18x0? m 200x183=0.2kg 8 MOX1o of-home in Of: uit a t 20 = 30-9 (1) = a =10M52 0= 0 + 2 a (s), 0 = 1603 " 2x10XS *S=30 = 45m

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6) Assume there are two identical simple pendulum clocks. Clock - 1 is placed on the earth and Clock - 2 is placed on a space station located at a height h above the earth surface. Clock - 1 and Clock - 2 operate at time periods 4 s and 6 s respectively. Then the value of h is –(consider radius of earth RF = 6400 km and g on earth 10 m/s2) (A) 1200 km (B) 1600 km (C) 3200 km (D) 4800 km

② TIGS 1 E = 6S 5G T=2T "g 8 = =>i 8oti = n = 5n = =4R+ h =6R 4h= z R. 2: R = 6o = 3200km

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7. Consider a cylindrical tank of radius lm is ﬁlled with water. The top surface of water is at 15 m from the bottom of the cylinder. There is a hole on the wall of cylinder at a height of 5 m from the bottom. A force of 5 x 105N is applied an the top surface of water using a piston. The speed of ifﬂux from the hole will be : (given atmospheric pressure PA = 1.01×105 Pa, density of water w = 1000 kg/m3 and gravitational acceleration g = 10 m/s2) (A) 11.6 m/s (B) 10.8 m/s (C) 17.8 m/s (D) 14.4 m/s

⑭ ↓ ⑭ pyh 15x105N Yom 15 m ·F.Iin ①+ 3ghy + 190, " O+5ghc H/80" 5x10" + 18x 10x10 +0 = 101x105O+X100o 02= 17Sm/sec

8. A vessel contains 14 g of nitrogen gas at a temperature of 27°C. The amount of heat to be transferred to the gas to double the r.m.s speed of its molecules will be : Take R = 8.32 J mol-1k-1. (A) 2229 J (B) 5616 J (C) 9360 J (D) 13.104 J Of 307, OCF = go=?: H T =44 R 0.32 Jm/molkHeat supplied & = 21 Sr AT T = 300K xERX (T. -T.. T2 =4x300 =1200K. x x832 x (1200-300) = 93605

A slab of dielectric constant K has the same cross-sectional area as the plates of a parallel plate capacitor and thickness 3 d, where d is the separation of the plates. The capacitance of the 4 capacitor when the slab is inserted between the plates will be: (Given Co = capacitance of capacitor with air as medium between plates.)

n ⑭ > v awith aid K Co= EA c = FGCFT.TH = GO A x *, & (P-+ =) FoM z = GKAAN 5T(IAT =3) So

10. A uniform electric field E = (8m/e) V/m is created between two parallel plates of length 1 m as shown in figure, (where m = mass of electron and e = charge of electron). An electron enters the field symmetrically between the plates with a speed of 2 m/s. The angle of the deviation () of the path of the electron as it comes out of the field will be _______. Use = 2 M/sea R = 0 5 = Ut + 1 act"V 1 = 2 (t) t0 - += =0.5sec HF =0, ly = Uy+ayt =ly =0 + (t) VI =em(er) (t) =0 (t)=0x0.5 I = 4MS Vy tano Use = 1 = 2 10) Ve 2 0: rail (h)

11. Given below are two statements : Statement I: A uniform wire of resistance 80 is cut into four equal parts. These parts are now connected in parallel. The equivalent resistance of the combination will be 5. Statement II: Two resistances 2R and 3R are connected in parallel in a electric circuit. The value of thermal energy developed in 3R and 2R will be in the ratio 3:2. In the light of the above statements, choose the most appropriate answer from the option given below (A) Both statement I and statement II are correct (B) Both statement I and statement II are incorrect (C) Statement I is correct but statement II is incorrect (D) Statement I is incorrect but statement II is correct I & v ATETHCNTin a parts each part 30-ohm - ↓ + ottot to ZOnReg 20 I Zon A con Reg Lo*Reg.5-ohm ee 2 On STATEN ONT 2 TheThermal energy ↳ O O Incorrect H= "CH) = HC CORRECT -Rs = 1 = E

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12. A

triangular shaped wire carrying 10 A current is placed in a uniform magnetic ﬁeld of 0.5 T, as shown in ﬁgure. The magnetic force on segment CD is (Given BC = CD = BD = 5 cm.)

(A) 0.126 N (B) 0.312 N (C) 0.216 N (D) 0.245 N

C vi N s 1600 10f_A B b = B = 0.5T = 10 A Force oN <D F=BISInQ of B ↳ I x = 10x0.5x5x 15x Sin600 -0216N

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13. The magnetic ﬁeld at the center of current carrying circular loop is B1. The magnetic ﬁeld at a distance of √3 times radius of the given circular loop from the center on its axis is B2. The value of B1/B2 will be (A) 9:4 (B) 12: √15 (C) 8:1 (D) 5: √3

y ⑭ Br = MO ( sense of 2 R. a loop) BC = No 1RY 2 SRCT3F MoiRR2)3x MOR = to 2(4RE) 3 = 1 ? Bg!--

14. A transformer operating at primary voltage 8 kV and secondary voltage 160 V serves a load of 80 kW. Assuming the transformer to be ideal with purely resistive load and working on unity power factor, the loads in the primary and secondary circuit would be (A) 800 and 1.06 (C) 800 and 0.32 oh m⑭ o (B) 10n and 500 ohm ⑭ (D) 100 m and 500-ohm VO=OKV, LOAD = 80x18 Watt Primary loadRi = " O = (Ox183): =800-0hm. 80 x 103 Secondary load &r = 11oos=032-ohm

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15. Sun light falls normally on a surface of area 36 cm2 and exerts an average force of 7.2 x 10-9N within a time period of 20 minutes. Considering a case of complete absorption, the energy ﬂux of incident light is (A) 25.92 x 102 W/cm2 (C) 6.0 W/cm2 (B) 8.64 x 10–6 W/cm2. (D) 0.06 W/cm2

9& AA = 36cm" F=72x189N, t=20x60 sec F. Dt =m C 0. F = & -> 36x 18"m" " * = freeinprox-boorrm-irmieveF5x108 +00me36

16. The power of a lens (biconvex) is 1.25m-1 in particular medium. Refractive index of the lens is 1.5 and radii of curvature are 20 cm and 40 cm respectively. The refractive index of surrounding medium: (A)1.0 (B) 9 (C) 3 (D) 4 723 5 = CoMn-1) (*-E) 0: f = 5 = $5100cm = (-1) (o Fho) = Fortoan 60 <m R = 20 B40cm o (F-1)C") -= (-1) (T) 2 - 1.5 =+1 = ? M. ICE

17. Two streams of photons, possessing energies equal to ﬁve and ten times the work function of metal are incident on the metal surface successively. The ratio of maximum velocities of the photoelectron emitted, in the two cases respectively, will be (A)1:2 (B)1:3 (C)2:3 (D)3:2 E = NO + 1m Umar 5 Wo =Notmeinal 10wo: not me man 4 Wo= tmotman 900 McmanO -- oumae on=

Radioactive sample left after 15 min

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18. A radioactive sample decays 7/8 times its original quantity in 15 minutes. The half life of the sample is (A) 5 min (B) 7.5 min (C) 15 min (D) 30 min

Do Y= /8 H No (t) h o =No (t)" - n=3 Total time = 2 (T) 15= 3 (T) T = 5 men

19. An n.p.n transistor with current gain = 100 in common emitter configuration is shown in figure. The output voltage of the amplifier will be ⑭ * = 100 => Voltage gain AV = B to V = 10ox to 1000= VI No 1000x1X153 I vot

transmitter, using modulating signal of frequency

required for transmission

frequency deviation modulating frequency

has a deviation ratio of 10. The

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20. A FM Broad cast

20kHz

Bandwidth

is: (A) 220 kHz (B) 180 kHz (C) 360 kHz (D) 440 kHz

Modulating frequency = 20KHz = -> Deviation ratio

=If = 10 Af = (0) 20). = 200KH2 Band width=2(f + Df) = 2 (20 +200) KH2 = 440KH2.

21. A ball is thrown vertically upwards with a velocity of 19.6 ms-1 from the top of a tower. The ball strikes the ground after 6 s. The height from the ground up to which the ball can rise will be (k) m. The value of k is ____. (use g = 9.8 m/s2) Sol. 392

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Section - B

15) Da- 19.6x6 = 1/ (9.0) (6) " it 21964 6-49x3610. -> 50.0 mt a 10) F (19.6)> 2(9.8) 22 22 = (19.6) (56) a I FOUCL C = 19.6m 41tRn = 15 58.8+ 19.6 = K/5 k=392,

22. The distance of centre of mass from end A of a one dimensional rod (AB) having mass density = 0 (1 x2) kg/m and length L (in meter) is 3L m. The value of is___. (where x is the distance from end A) D-e)-* ⑳ m. # am B am-5:toce,it isa Siso (I) am K) -" 3C3J. "So (n.) are 1.33 (2- () C 0

23. A string of area of cross-section 4 mm2 and length 0.5 m is connected with a rigid body of mass 2 kg. The body is rotated in a vertical circular path of radius 0.5 m. The body acquires a speed of 5 m/s at the bottom of the circular path. Strain produced in the string when the body is at the bottom of the circle is _______×10-5 (use young's modulus 1011 N/m2 and g = 10 m/s2) B 5 30 & Aly M Y= TRESS STRAIN STRAIN-seess. St. F = tr"Hing = I5E"+2x10 I - ION 5m/s STRAIN= #5 Tol mg -> 30 x 155

pressure

observed

24. At a certain temperature, the degrees of freedom per molecule for gas is 8. The gas performs 150 J of work when it expands under constant pressure. The amount of heat absorbed by the gas will be _______ J.750 Degree of freedom = 8 W.A by the gas 1505 at contact

Heat

by gas=? * R = c + DU. = URAT+ GURAT URDT = 15 = 150 + 3x150 Q. =750]

25. The potential energy of a particle of mass 4 kg in motion along the x-axis is given by U = 4(1 - cos 4x) J. The time period of the particle for small oscillation (sin ≃ ) is (π) s. The value of K is _____. )s. v = 4(1-Josase) Took ⑦--dVe-f 4 (I-cosmm) 3 In 42 1 42 = = 16 Sin 42 F x10 (42) = m (A). ↑ 16Xa (r)) m <pr) #* = no " = W =4. F: =I=TK.K=2.

26. An electrical bulb rated 220 V, 100 W. is connected in series with another bulb rated 220 V, 60 W. If the voltage across combination is 220 V, the power consumed by the 100 W bulb will be about _______ W.14 R. = = (2207 " 100 &2-1220is Reg = Pot Ry F1 tea = (220)" (Too+ Yo). 220x 600 (2203" x 16 = (920)" (ot10) =10 X1c -> <2203"x16 600 Power consumed by 100w. P: 12R, = x) Y (0)"_14 watt

For the given circuit the current through battery of 6 V just after closing the switch 'S' will be _____

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ductrFr well act

as a opencircuit

27.

Jess

L F = 5 = 1Amp

28. An object 'o' is placed at a distance of 100 cm in front of a concave mirror of radius of curvature 200 cm as shown in the ﬁgure. The object starts moving towards the mirror at a speed 2 cm/s. The position of the image from the mirror after 10 s will be at ______ cm.400 R = 200<m. No = 2 C M/s position of object after loses v 100- distance covered 100- 2x10 = 00cm f = 1 = 200 =100km U =-00km, F = =100km =+ **=1-Y = Uf = (=00) +10 80x100 0 = 400cm

In an experiment with a convex lens. The plot of the image distance (') against the object distance (') measured from the focus gives a curve ' '=225. If all the distances are measured in cm. The magnitude of the focal length of the lens is ______ cm.

per f

Physics tab

experiment

29.

Sol. 15 ⑭ ⑭ sug u'l = 225 As

= I "

225

= 15Sm.

30. In an experiment to ﬁnd acceleration due to gravity (g) using simple pendulum, time period of 0.5 s is measured from time of 100 oscillation with a watch of 1 sec resolution. If measured value of length is 10 cm known to 1 mm accuracy. The accuracy in the determination of g is found to be x %. The value of x is _______. 5 T= ITT Eg DS: Dt += (o) - o x2 (55700). to +100 : fr 4 x 100 FX1W =5%.

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