JEE(MAIN) 2015 TEST PAPER WITH SOLUTION (HELD ON SATURDAY 04 th APRIL, 2015) PART A PHYSICS

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1 1. Distance of the centre of mass of a solid uniform cone from its vertex is. f the radius of its base is and its height is h then is equal to :- 5h 8 () h 4 h 4 for solid cone c.m. is h 4 so h h 4 h 4 () h 8 h 4 from base. A red LED emits light at.1 watt uniformly around it. The amplitude of the electric field of the light at a distance of 1 m from the diode is: V/m () 7.75 V/m () 1.7 V/m.45 V/m av 1 E E JEE(MAN) 15 TET PAPE WTH OLUTON (HELD ON ATUDAY 4 th APL, 15) PAT A PHY P 4r c P 4 r On putting value we get.45 v/m. ODE-D. A pendulum made of a uniform wire of cross sectional area A has time period T. When an additional mass M is added to its bob, the time period changes to T M. f the Young's modulus of the material of the wire is Y then 1 is equal Y to :- (g gravitational acceleration) TM 1 T T () 1 T M () Ans. () T T M T T M T L g T M F A Y L L A Mg A Mg A 1 Mg Mg 1 A L L g L FL AY Putting () in ()......()...() solving the equation we get the value of 1 Y as TM T A 1 mg JEE (Main + Advanced) Leader ourse (Target-16) for X Passed / Appeared students tart on 15th April 15 (English / Hindi Medium) and JEE (Main) Leader ourse (Target-16) for X Passed / Appeared students tart on 15th April 15 (English / Hindi Medium) at Kota entre only. 1

2 JEE(MAN) For a simple pendulum, a graph is plotted between its kinetic energy (KE) and potential energy (PE) against its displacement d. Which one of the following represents these correctly? (graphs are schematic and not drawn to scale) E KE d 5. A train is moving on a straight track with speed ms 1. t is blowing its whistle at the frequency of 1 H. The percentage change in the frequency heard by a person standing near the track as the train passes him is (speed of sound ms 1 ) close to :- 18% () 4% () 6% 1% f' v f v v () () E E E PE PE KE PE PE KE KE KE 1 m [A d ], downward parabola PE 1 m d, upward parabola. KE PE d d f" v f v v f" v v f ' v v f" f ' 1 f ' v v v v 1 v 1 v v v v v v 1 ~ 1% 6. When 5V potential difference is applied across a wire of length.1 m, the drift speed of electrons is ms 1. f the electron density in the wire is m, the resistivity of the material is close to : m () m () m m Ans. () V i V nev d (neav d) A V nev d On putting values are got the answer m JEE (Main + Advanced) Leader ourse (Target-16) for X Passed / Appeared students tart on 15th April 15 (English / Hindi Medium) and JEE (Main) Leader ourse (Target-16) for X Passed / Appeared students tart on 15th April 15 (English / Hindi Medium) at Kota entre only.

3 ODE-D 7. 6V P L V Two long current carrying thin wires, both with current, are held by the insulating threads of length L and are in equilibrium as shown in the figure, with threads making an angle '' with the vertical. f wires have mass per unit length then the value of is :- (g gravitational acceleration) () tan gl tan µ () sin µ r gl µ cos µ sin f g gl tan µ sin gl µ cos where f is force per unit length(i) µ g tan sin on solving sin g µ cos Q n the circuit shown, the current in the 1 resistor is :-.1 A, from Q to P ().1 A, from P to Q () 1. A, from P to Q A E 6V P Q V V i E.1 from +ve to ve Q to P 9. Assuming human pupil to have a radius of.5cm and a comfortable viewing distance of 5cm, the minimum separation between two objects that human eye can resolve at 5 nm wavelength is :- 1 µm () µm () 1 µm µm d 1. d d d d d µm JEE (Main + Advanced) Leader ourse (Target-16) for X Passed / Appeared students tart on 15th April 15 (English / Hindi Medium) and JEE (Main) Leader ourse (Target-16) for X Passed / Appeared students tart on 15th April 15 (English / Hindi Medium) at Kota entre only.

4 JEE(MAN) An inductor (L. H) and a resistor (.15 k) are connected in series to a battery of 15V EMF in a circuit shown below. The key K 1 has been kept closed for a long time. Then at t, K 1 is opened and key K is closed simultaneously. At t 1ms, the current in the circuit will be (e 5 15) :- 11. An L circuit is equivalent to a damped pendulum. n an L circuit the capacitor is charged to Q and then connected to the L and as shown below :- L.H.15k 15V K K ma ().67 ma () 1 ma 67 ma Ans. () Decay of current e 15 e 15 1 e 1 t L f a student plots graphs of the square of maximum charge (Q Max) on the capacitor with time (t) for two different values L 1 and L (L 1 > L ) of L then which of the following represents this graph correctly? (plots are schematic and not drawn to scale) () () Q Max Q Max Q Max L L 1 Q (For both L and L ) 1 L L 1 t t t ma Q Max L 1 L t Ans. () JEE (Main + Advanced) Leader ourse (Target-16) for X Passed / Appeared students tart on 15th April 15 (English / Hindi Medium) and JEE (Main) Leader ourse (Target-16) for X Passed / Appeared students tart on 15th April 15 (English / Hindi Medium) at Kota entre only. 4

5 As damping is happening its amplitude would vary as Q harge ODE-D The oscillations decay exponentially and will be proportional to e t where depends inversely on L. o as inductance increases decay becomes slower for L 1 L 1. n the given circuit, charge Q on the µf capacitor changes as is varied from 1µF to µf. Q as a function of '' is given properly by : (figures are drawn schematically and are not to scale) :- Q harge 1µF harge E µf 1µF µf () Q Q eq 1µF harge E Q 1µF E 1 Q /when 1µF E Q /when µf E dq d 1 d d E µf µf Q eq. E E 1 4 E 1 E 6E 6E 1E () Q 1µF µf JEE (Main + Advanced) Leader ourse (Target-16) for X Passed / Appeared students tart on 15th April 15 (English / Hindi Medium) and JEE (Main) Leader ourse (Target-16) for X Passed / Appeared students tart on 15th April 15 (English / Hindi Medium) at Kota entre only. 5

6 JEE(MAN) From a solid sphere of mass M and radius a cube of maximum possible volume is cut. Moment of inertia of cube about an axis passing through its centre and perpendicular to one of its faces is:- g T g T g 11 1 g () 4M 9 M a () 4M M 16 Let mass and side of cube be M' and a M' M 4 a Moment of nertia of cube M 'a 6 a M a 4M a The period of oscillation of a simple pendulum L is T. Measured value of L is. cm g known to 1 mm accuracy and time for 1 oscillations of the pendulum is found to be 9s using a wrist watch of 1s resolution. The accuracy in the determination of g is : 1% () 5% () % % T g g 1.7% % g 15. On a hot summer night, the refractive index of air is smallest near the ground and increases with height from the ground. When a light beam is directed horiontally, the Huygens' principle leads us to conclude that as it travels, the light beam : bends downwards () bends upwards () becomes narrower goes horiontally without any deflection Ans. () Normal µ µ 1 µ increases > 1 light bends towards normal light beam bends upwards (as µwith height) 16. A single of 5 kh frequency is amplitude modulated on a carrier wave of frequency MH. The frequencies of the resultant signal is/are - 5 kh, kh and 1995 kh () kh and 1995 kh () MH only 5 kh and 1995 kh Frequency present after modulation f c, f c ± f s KH, 5 KH and 1995 KH 17. A solid body of constant heat capacity 1 J / g 4 T JEE (Main + Advanced) Leader ourse (Target-16) for X Passed / Appeared students tart on 15th April 15 (English / Hindi Medium) and JEE (Main) Leader ourse (Target-16) for X Passed / Appeared students tart on 15th April 15 (English / Hindi Medium) at Kota entre only. 6

7 is being heated by keeping it in contact with reservoirs in two ways - (i) equentially keeping in contact with reservoirs such that each reservoir supplies same amount of heat. (ii) equentially keeping in contact with 8 reservoirs such that each reservoir supplies same amount of heat. n both the cases body is brought from initial temperature 1 to final temperature. Entropy change of the body in the two cases respectively is - ln, ln () ln, 8ln () ln, 4ln ln, ln T dt nc T1 T dt 1 1 n 1 T dt 1 n 1 T 18. onsider a spherical shell of radius at temperature T. The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume U u T 4 V and pressure p 1 U V. f the shell now undergoes an adiabatic expansion the relation between T and is - T 1 1 () T () T e T e P 1 U V P T 4 using PV nt 1 V T ODE-D 19. Two stones are thrown up simultaneously from the edge of a cliff 4 m high with initial speed of 1 m/s and 4 m/s respectively. Which of the following graph best represents the time variation of relative position of the second stone with respect to the first? (Assume stones do not rebound after hitting the ground and neglect air resistance, take g 1 m/s ) (The figure are schematic and not drawn to scale) () () (y y )m 1 (y y )m 1 (y y )m 1 t (y y )m 1 For particle 1 A m 1m/s t(s) t(s) t(s) t(s) T 1 JEE (Main + Advanced) Leader ourse (Target-16) for X Passed / Appeared students tart on 15th April 15 (English / Hindi Medium) and JEE (Main) Leader ourse (Target-16) for X Passed / Appeared students tart on 15th April 15 (English / Hindi Medium) at Kota entre only. 7

8 JEE(MAN) t gt 5t 1t 4 t 1 8 sec For particle A 4 4t gt 4m/s 5t 4t 4 t 1 sec for < t < 8 sec a rel straight line x-t graph for 8 < t < 1 sec a rel g downward parabola for t > 1 sec oth particles comes to rest. A uniformally charged solid sphere of radius has potential V (measured with respect to ) on its surface. For this sphere the equipotential surfaces with potentials V 5V V,, 4 4 and have radius 1,, and 4 respectively. Then 1 and < ( 4 ) () < 4 () 1 and > ( 4 ) 1 and ( 1 ) > ( 4 ) Ans. (1 or ) for r < kq & for r > V r kq at r V kq at r V V 1 V 4 kq r V 5 for V V 4 for V V 4 for V V 4 kq r 5 kq. 4 kq kq 4 4 kq kq Monochromatic light is incident on a glass prism of angle A. f the refractive index of the material of the prism is µ, a ray, incident at an angle, on the face A would get transmitted through the face A of the prism provided : A cos µ sin A sin µ () cos µ sin A sin µ () sin µ sin A sin µ sin µ sin A sin Ans. () µ JEE (Main + Advanced) Leader ourse (Target-16) for X Passed / Appeared students tart on 15th April 15 (English / Hindi Medium) and JEE (Main) Leader ourse (Target-16) for X Passed / Appeared students tart on 15th April 15 (English / Hindi Medium) at Kota entre only. 8

9 ODE-D For all light to come out from face A angle of emergence e 9 Apply nell's Law at face A µ sin r 1 sin e 1 r sin 1 µ (if e 9) (d) x y 1 r 1 A sin 1 ( r µ 1 + r A) Apply nell's law at face A 1 sin µsin(r 1 ) sin µ sin(a-sin µ for all light transmitted through A, e < > sin µ sin(a-sin µ. A rectangular loop of sides 1 cm and 5 cm carrying a current of 1 A is place in different orientations as shown in the figures below : (a) (b) x x y y f there is a uniform magnetic field of. T in the positive direction, in which orientations the loop would be in (i) stable equilibrium and (ii) unstable equilibrium? (b) and (d), respectively () (b) and (c), respectively () (a) and (b), respectively (a) and (c), respectively For stable equilibrium M For unstable equilibrium magnetic field M magnetic moment. Two coaxial solenoids of different radii carry current in the same direction. Let F1 be the magnetic force on the inner solenoid due to the outer one and F be the magnetic force on the outer solenoid due to the inner one. Then : F1 is radially inwards and F () F1 is radially outwards and F () F1 F F1 is radially inwards and F is radially outwards. Ans. () (c) x y 1 JEE (Main + Advanced) Leader ourse (Target-16) for X Passed / Appeared students tart on 15th April 15 (English / Hindi Medium) and JEE (Main) Leader ourse (Target-16) for X Passed / Appeared students tart on 15th April 15 (English / Hindi Medium) at Kota entre only. 9

10 JEE(MAN)-15 Field due to solenoid outside the solenoid is ero f1 Due to action reaction f or solenoid behave as magnetic dipole Md f dx d field of 1 is uniform dx f 4. A particle of mass m moving in the x direction with speed is hit by another particle of mass m moving in the y direction with speed. f the collisions perfectly inelastic, the percentage loss in the energy during the collision is close to : 56 % () 6% () 44% 5% efore collison y m v v m 1 1 Kinetic energy m(v) m(v) mv After collison Applying momentum conservation for inelastic collision mvj ˆ mvi ˆ m v 8 v f v 9 1 4mv Kf m v f K i Kf 5mv / 5 % K 56% K mv 9 i f x 5. onsider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion, the average time of collision between molecules increases as V q, where V is the volume of the gas. The value of q is :- JEE (Main + Advanced) Leader ourse (Target-16) for X Passed / Appeared students tart on 15th April 15 (English / Hindi Medium) and JEE (Main) Leader ourse (Target-16) for X Passed / Appeared students tart on 15th April 15 (English / Hindi Medium) at Kota entre only. 1 p v 1 () 5 6 Volume v avg 1 V 1 T For adiabatic process T V 1 V T comparing 1 1 1/ V () q 6. From a solid sphere of mass M and radius, a spherical portion of radius is removed, as shown in the figure. Taking gravitational potential V at r, the potential at the centre of the cavity thus formed is : (G gravitational constant) () GM GM () GM GM

11 y principle of superosition GM G M V GM GM GM 8 8 ODE-D 8. A long cylindrical shell carries positive surface charge in the upper half and negative surface charge in the lower half. The electric field lines around the cylinder will look like figure given in : (figures are schematic and not drawn to scale) F 7. A Given in the figure are two blocks A and of weight N and 1 N, respectively. These are being pressed against a wall by a force F as shown. f the coefficient of friction between the blocks is.1 and between block and the wall is.15, the frictional force applied by the wall on block is :- 1 N () 15 N () 1 N 8 N F A f 1 f for equllibrrium of A f 1 for equllibrrium of f f f 1 N f () () Ans. () t behaves as a dipole JEE (Main + Advanced) Leader ourse (Target-16) for X Passed / Appeared students tart on 15th April 15 (English / Hindi Medium) and JEE (Main) Leader ourse (Target-16) for X Passed / Appeared students tart on 15th April 15 (English / Hindi Medium) at Kota entre only. 11

12 JEE(MAN) As an electron makes a transition from an excited state to the ground state of a hydrogen - like atom/ion : kinetic energy decreases, potential energy increases but total energy remains same () kinetic energy and total energy decrease but potential energy increases () its kinetic energy increases but potential energy and total energy decreases kinetic energy, potential energy and total energy decrease Ans. () K U T 1.6 n as n decreases k increases 7. n 1.6 n as n decrease U & T decrease. Match List- (Fundament Experiment) with List- (its conclusion) and select the correct option from the choices given below the list : (A) () () List- Franck-Hert Experiment. Photo-electric experiment Davison-Germer Experiment (i) (iii) (iiii) (iv) List- Particle nature of light Discrete energy levels of atom Wave nature of electroc tructure of atom A-ii, -i, -iii () A-iv, -iii, -ii () A-i, -iv, -iii A-ii, -iv, -iii elf Explanatory/Theory (A) Franck-Hert experiment explains disrete energy levels of atom () Photo-electric experiment explain particle nature of light () Davison Germer experiment explain wave nature of electron. JEE (Main + Advanced) Leader ourse (Target-16) for X Passed / Appeared students tart on 15th April 15 (English / Hindi Medium) and JEE (Main) Leader ourse (Target-16) for X Passed / Appeared students tart on 15th April 15 (English / Hindi Medium) at Kota entre only. 1

J E E (M ain)-2015 PAPER 1 CHEMISTRY, MATHEMATICS & PHYSICS. Important Instructions:

J E E (M ain)-2015 PAPER 1 CHEMISTRY, MATHEMATICS & PHYSICS. Important Instructions: Note: For the benefit of the students, specially the aspiring ones, the question of JEE(Main), 05 are also given in this booklet. Keeping the interest of students studying in class XI, the questions based