SAMPLE TEST - 3. Time Allotted: 3 Hours Maximum Marks: 360

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1 FIITJEE - JEE (Main) SAMPLE TEST - Time Allotted: Hours Maimum Marks: 60 Do not open this Test Booklet until you are asked to do so. Please read the instructions carefully. You are allotted 5 minutes specifically for this purpose. Important Instructions:. Immediately fill in the particulars on this page of the Test Booklet with Blue / Black Ball Point Pen. Use of pencil is strictly prohibited.. The Answer Sheet is kept inside this Test Booklet. When you are directed to open the Test Booklet, take out the Answer Sheet and fill in the particulars carefully.. The test is of hours duration. 4. The Test Booklet consists of 90 questions. The maimum marks are There are three sections in the question paper I, II, III consisting of Physics, Chemistry and Mathematics having 0 questions in each section of equal weightage. Each question is allotted 4 (four) marks for correct response. 6. Candidates will be awarded marks as stated above in instruction No.5 for correct response of each question. ¼ (one fourth) marks will be deducted for indicating incorrect response of each question. No deduction from the total score will be made if no response is indicated for an item in the answer sheet. 7. There is only one correct response for each question. Filling up more than one response in any question will be treated as wrong response and marks for wrong response will be deducted accordingly as per instruction 6 above. 8. Use Blue / Black Ball Point Pen only for writing particulars / marking responses on Side- and Side- of the Answer Sheet. Use of pencil is strictly prohibited. 9. No candidate is allowed to carry any tetual material, printed or written, bits of papers, pager, mobile phone, any electronic device, etc. ecept the Admit Card inside the eamination hall / room. 0. On completion of the test, the candidate must hand over the Answer Sheet to the Invigilator on duty in the Room / Hall. However, the candidates are allowed to take away this Test Booklet with them.. Do not fold or make any stray marks on the Answer Sheet. Name of the Candidate (in Capital Letters) : Enrolment Number : Batch : Date of Eamination : FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -006, Ph , , Fa 6594

2 JEE-MAIN -SAMPLE TEST --PCM- Useful Data Chemistry: Gas Constant R = 8.4 J K mol = 0.08 Lit atm K mol =.987 Cal K mol Avogadro's Number N a = Planck s Constant h = Js = erg.s Faraday = Coulomb calorie = 4. Joule amu = kg ev = J Atomic No : H=, D=, Li=, Na=, K=9, Rb=7, Cs=55, F=9, Ca=0, He=, O=8, Au=79. Atomic Masses: He=4, Mg=4, C=, O=6, N=4, P=, Br=80, Cu=6.5, Fe=56, Mn=55, Si = 8 Pb=07, u=97, Ag=08, F=9, H=, Cl=5.5 Useful Data Physics: Acceleration due to gravity g = 0 m / s FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -006, Ph , , Fa 6594

3 JEE-MAIN -SAMPLE TEST --PCM- Section I (Physics). If L, R, C, V respectively represent inductance, resistance, capacitance and potential difference, L then the dimensions of are the same as those of RCV Current Current Charge Charge A body starting from rest with acceleration which varies with time t according as At B where A and B are the constants. The velocity of the particle after time t is: At At Bt A Bt Bt Bt At. A particle starts from origin at t = 0 and moves in the y plane with a constant acceleration 6 m/s in y-direction. The equation of motion is y, then its velocity component along - direction at = is (in m/s) 6 4. From the surface of a certain planet a body is projected with a certain velocity at a certain angle from the horizontal surface. The horizontal and vertical displacements and y are given by 0 t and y 0t t where t is the time in second and and y are in meter. The magnitude and direction of the velocity of projection are: 0 ms - at 0 0 from the horizontal 0 ms - at 60 0 from the horizontal 0 ms - at 60 0 from the horizontal 0 ms - at 0 0 from the horizontal 5. From the top of a tower of height 40m, a ball is projected upwards with a speed of 0 ms - at an angle of 0 0 to the horizontal. If g 0 ms, after how long will the ball hit the ground? s s s 4 s 6. A particle is moving in a circle of radius R. At t = 0 its speed is zero and during its motion speed varies as v s where s is the distance travelled. The angle made by acceleration vector with radial direction after one revolution. tan 4 7. The displacement of a particle at any instant is related to its velocity as v 9. Its acceleration and initial velocity are: unit and unit unit and 9 unit 9 unit and unit unit and 9 unit 8. A body is moving down a long inclined plane of angle of inclination. The coefficient of friction between the body and the plane varies as 0.5, where is the distance moved down the plane. The body will have the maimum velocity when it has travelled a distance given by tan tan cot cot FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -006, Ph , , Fa 6594

4 JEE-MAIN -SAMPLE TEST --PCM-4 9. At the instant t = 0 a force F kt k is a constant acts on a small body of mass m resting on a smooth horizontal surface. The time, when body leaves the surface is: mgk sin k sin / mg mg sin / k mg / k sin m F 0. If the potential energy of a gas molecule is M N U, r 6 r M and N being positive constants, then the potential energy at equilibrium must be: zero M / 4N N / 4M MN / 4. A body is moving up an inclined plane of angle with an initial kinetic energy E. The coefficient of friction between the plane and the body is. The work done against friction before the body comes to rest is cos E cos sin E cos E cos cos sin E cos cos sin. A body P strikes another body Q of mass that is p times that of body P and moving with a velocity that is q of the velocity of body P. If body P comes to rest, the coefficient of restitution is p q p q p q q p p q p q p q p q. A solid cylinder is rolling without slipping down an incline of inclination. Minimum coefficient of friction so that the cylinder does not slip on the incline is tan tan tan tan 4. A circular portion of diameter R is cut out from a uniform circular disc of mass M and radius R as shown in Fig. The moment of inertia of the remaining (shaded) portion of the disc about an ais passing through the centre O of the disc and perpendicular to its plane is 5 A MR B 7 6 MR C MR D 8 MR R O R Cut out circular portion 5. The centres of a ring of mass m and a sphere of mass M of equal m M radius R, are at a distance 8R apart as shown in Fig The force of attraction between the ring and the sphere is GmM GmM 7 R 8 Rh GmM 9R GmM 9 9R R A 8R R B FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -006, Ph , , Fa 6594

5 JEE-MAIN -SAMPLE TEST --PCM-5 6. The magnitude of gravitational force on a particle of mass m placed at a distance from the rod of mass M and length l as shown in the figure is: GMm GMm l l l GMm l GMm l l 7. Water from a tap emerges vertically downwards with an initial speed of ms -. The crosssectional area of top is 0-4 m. Assume that the pressure is constant throughout the stream of water and that the flow is steady. The cross-sectional area of the stream 0.5 m below the top is (take g = 0ms - ) m 0 m 5 0 m 0 m 8. One end of a thermally insulated rod is kept at a temperature T and the other at T. The rod is composed of two sections of lengths l and l and thermal conductivities k and k respectively. The temperature at the interface of the section is k l T k l T / k l k l k l T k l T / k l k l A B C k l T k l T / k l k l D k l T k l T / k l k l l T T l k k 9. A body cools from C to C in 5s. How long will it take to cool from C to C? Assume the temperature of the surroundings to be C and Newton s law of cooling to be valid..5s 0 s 0 s 5 s 0. In the following figures, the block of mass m is slightly displaced from its mean position. The ratio of time periods of oscillations in Fig(i) and Fig(ii) is: : : : : k k (i) m (ii) k k m. Third overtone of a closed organ pipe is in unison with fourth harmonic of an open organ pipe. Find the ratio of lengths of the pipes: : : 4 5 : 6 7 : 8. Two point charges q and q (q /) are placed at points A(0, ) and B(,0) as shown in the figure. The electric field vector at point P(,) makes an angle with the -ais, then the angle is: tan tan tan 4 tan 0 q y * A * B O * q P, l. Three point charges 4 q, Q and q are placed in straight line of length l at points distant 0,, l respectively. If the net force on charge q is zero, the magnitude of the force on charge 4q is q l 0 q l 0 FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -006, Ph , , Fa 6594 q l 0 4q l 0

6 JEE-MAIN -SAMPLE TEST --PCM-6 4. The capacitance of a sphere of radius R is increased times when it enclosed by an earthed sphere of radius R. The ratio R /R is 4 5. The network shown in the following figure is part of a circuit. What is the potential difference V V. When current I is 5A and is decreasing at a rate of 0 A / s? 5 V 5 V B A 0 V zero A I 5V 5H B 6. A particle of mass m and charge q moves with a constant velocity v along the positive direction. It enters a region containing a uniform magnetic field B directed along the negative z direction, etending from a to b. The minimum value of v required so that the particle can just enter the region > b is qbb / m qb a B / m qab / m qb a B / m 7. A square loop is placed in a uniform magnetic field B as shown in figure. The power needed to pull it out of the field with a constant velocity v is proportional to / v v v v / B Loop v 8. An observer can see through a pin-hole the top end of a thin rod of height h, placed as shown in the figure. The beaker height is h and its radius h. when the beaker is filled with a liquid up to a height h, he can see the lower end of the rod. Then the refractive inde of the liquid is: A 5 B 5 C D h h h h 9. A U shaped wire is placed in front of a concave mirror of radius of curvature 0 cm as shown in the figure. The total length of the image of the wire ABCD is nearly:.5 cm 6 cm.5 cm 5 cm 5cm A D B C 0cm 0 cm 0. Interference pattern is obtained with two coherent light sources of intensity ratio n. In the I I ma min interference pattern, the ratio will be I I n n ma n n min n n n n space for rough work FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -006, Ph , , Fa 6594

7 JEE-MAIN -SAMPLE TEST --PCM-7 Section II (Chemistry). For a hypothetical reaction AB B ; g g AB g H kj More AB could be produced by using a catalyst removing some of B increasing the temperature increasing the pressure. The pk b of CN is 4.7. The ph of solution prepared by miing.5 mole of KCN and.5 moles of HCN in water and making the total volume upto 500 ml, is The ph of a solution of weak base at half neutralization with strong base is 8, K b for base is HBr and HI reduce sulphuric acid, HCl can reduce KMnO 4 and HF can reduce H SO 4 KMnO 4 K Cr O 7 None of these 5. The correct IUPAC name of the compound given below is: H C 4-Ethyl--methyloctane, -Dimethylheptane -Methyl-4-ethyloctane 5-Ethyl-6-methyloctance. 6. The transition metal ion with least magnetic moment has the electronic configuration d d d d 7. Potassium ferricyanide on ionization produces ions ions 5 ions 4 ions 8. Arrange the following free radicals in order of stability: Benzyl (I), Allyl (II), Methyl (III), Vinyl (IV) IV > III > II > I I > II > III > IV I > III > IV > II IV > III > I > II 9. A hydrocarbon A with molecular mass 84 gives a single monochloride but four dichlorides on photochemical chlorination. The hydrocarbon A is Cyclopentane Cycloheane, -Dimethylbutane Methyl cyclopentane 0. What would be the epected formula of a compound which is formed of element X containing electrons in the valence shell and element Y contains 7 electrons in the valence shell? X Y XY XY X Y 6. If one million atoms of silver weight.79 0 g, the gram atomic mass of silver is 07 g 07. g 07.8 g 08. g FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -006, Ph , , Fa 6594

8 JEE-MAIN -SAMPLE TEST --PCM-8. H O can act as reducing as well as oidising agent. In its reaction with NH OH and KIO 4, H O is acting as Oidising agent, reducing agent Reducing agent, oidising agent Oidising agent, oidising agent Reducing agent, reducing agent. The blue colour developed when Lassaigne s etract is heated with fresh FeSO 4 in presence of alkali, cooled and acidified with dil. H SO 4 indicates. and is due to the formation of N, Fe FeCN N, Na 4 Fe CN S, Na 4 FeCN NOS 5 N S, Fe CNS 8a 4. If the critical temperature of the gas be TC and T B is the Boyle s temperature, then which 7Rb of the following, is the correct relation between T C and T B? TC TB TC TB TC TB TC TB The composition of a sample of wustite is Fe0.9 O. What is the percentage of iron present as Fe? 5% 5% 5% 45% 6. The uncertainty in the position of a dust particle with mass equal to mg (if uncertainty in its 0 velocity is ms ) is: o 9.58 A 958 o A 9.58 nm None. 7. Which of the following has highest bond dissociation energy? O O O O Given, that the abundance of isotopes Fe, 56 Fe and 57 Fe are 5%, 90% and 5% respectively, the atomic mass of Fe is The volume strength of.5 N H O solution is Which of the following has the maimum number of atoms? 4 g of C() 56 g of Fe(56) 7 g of Al(7) 08 g of Ag(08). An aqueous solution of 6. g oalic acid dihydrate (H C O 4.H O ) is made upto 50 ml. The volume of 0. N NaOH required to completely neutralize 0 ml of this solution is 40 ml 0 ml 0 ml 4ml. In the standardization of Na S O using KCrO 7 by iodometry, the equivalent weight of KCrO 7 is: molecular weight molecular weight molecular weight 6 molecular weight. What volume of CO at STP will evolve when gm of CaCO reacts with ecess of dil HCl? 4 ml ml 58 ml 448 ml FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -006, Ph , , Fa 6594

9 JEE-MAIN -SAMPLE TEST --PCM-9 4. The vapour pressure of benzene at 80 K is 40 mbar. When urea is mied at the same temperature, the vapour pressure falls by 8 mbar. The mole fraction of benzene in the solution is Ammonia gas is passed into water, yielding a solution of density 0.9 g/cm and containing 8.6% NH by weight. The mass of NH per cc of the solution is 0.7 g/cm 0.4 g/cm 0.5 g/cm 0.68 g/cm 6. A sample of NaHCO + Na CO required 0 ml of HCl using phenolphthalein as indicator and 5 ml more is required if methyl orange is used as indicator. Then molar ratio of NaHCO to Na CO is 4 7. Br H H acetone NaI Product. The product of the reaction is: C H 5 I H H H I H I H I C H H H C H 5 C H 5 C H 5 C H 5 8. Rank the following in order of decreasing rate of solvolysis with aq. ethanol. H C Br H C C Br H C CH CH CHMe Br () () () > > > > > > > > 9. In each of the following groups, which is the strongest nucleophile? (I) In MeOH () CHO () O () Me S (II) In DMF () OH () H O () O O H I, ; II, I, ; II, I, ; II, I, ; II, 0. Which of the following statement is correct regarding the rate of hydrolysis of the compounds () and (y) by S N reaction? Br O Br () (y) reacts faster than y Both and y reacts at the same rate y reacts faster than Neither nor y reacts pace for rough work FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -006, Ph , , Fa 6594

10 JEE-MAIN -SAMPLE TEST --PCM-0. Range of function f Section III (Mathematics) [-, ] [0, /) is [ Where {} represent fractional part of ],. If 0 0 < < 90 0, cos = 0, then value of log 0 sin + log 0 cos + log 0 tan is 0 - None of these, ( ). The function f()=[] cos discontinuous. at all at no (Where [] denotes the greatest integer function) is at all integer points at which is not integer 4. Suppose a, b, c are in A.P and a, b, c are in G.P. If a < b < c and a + b + c = /, then value of a is 5. If tan tan y = a and + y = then tan and tan y satisfy the equation, 6 ( a) a 0 ( a) a 0 a a ( ) 0 ( a) a 0 6. Let f ( ) = f ( P) then is equal to f ( P ) f ( P ) P f P f P f P 7. The points (, y ), (, y ), (, y ) and (, y ) are always Vertices of a rhombus Vertices of a square Con-cyclic Collinear 8. A closet has 5 pair of shoes. The number of ways in which 4 shoes can be drawn such that there will be no complete pair is Solution of the differential equation dy y d y is k ( + y ) = k ( y ) + = 0 k ( y ) = k ( + y ) + = 0 0. The comple number z = + i is rotated through an angle / in anticlockwise direction about the origin and stretched by additional unit, then the new comple number is i i i None of these FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -006, Ph , , Fa 6594

11 JEE-MAIN -SAMPLE TEST --PCM-. If z 4, then iz 4i is less than If 4a + b + c = 0, then the equation a + b + c = 0 has at least one real root lying between 0 and and 0 and none of these. / 4 / sec cos ec d is equal to tan / cot / tan / cot / The value of 5. If f d (where {} is the fractional part of ) is None of these cos e ( ) sin sec tan then the value of / / f ( ) d is equal to 0 None of these 6. The lines p(p +) y + q = 0 and (p + ) + (p + ) y + q = 0 are perpendicular to a common line for No value of p Eactly one value of p Eactly two values of p More than two values of p 7. Tangents to the circle + y = a cut the circle + y = a at P and Q. The tangents at P and Q to the circle + y = a intersect at angle, then is equal to The length of the latus rectum of parabola 4y + 0y + 7 = 0 is 6 ½ 0 9. S and T are the foci of an ellipse and B is an end of the minor ais. If STB is an equilateral triangle, then the eccentricity of the ellipse is. /4 / / / 0. The tangent at any point P on the hyperbola FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -006, Ph , , Fa 6594 a y b meets the straight lines b ay = 0 and b + ay = 0 in the points Q and R respectively. If C is the centre of the hyperbola, then CQ.CR is a b a + b ab a b y 4 z 5. The number of points common to the line and the plane 4 y z = is 0 infinite none of these. If 4a 5b 9c 0, then ( ab) bcca A vector perpendicular to plane of, a b and c A scalar quantity 0 is equal to

12 JEE-MAIN -SAMPLE TEST --PCM- None of these. A unit vector in y-plane which makes an angle of 45 0 with the vector i j and an angle of 60 0 with the vector i 4 j is i j i j i None of these 4. If + y = a + b, + y = a + b, then n + y n = a n + b n is true for n N n 4 n None of these 5. If + sin sin... 4,0, /, sin then, 6 5, The value of tan r0 r r is equal to / / The centre and radius of the circle zz ( i) z ( i) z 7 0 is - i, + i, i, 4 + i, 4 8. If and y, then the sum to infinity of the series ( + y) + ( + y + y ) + ( + y + y + y ) + to is ( y y) ( y y) ( y y) ( ) ( y) ( ) ( y) ( ) ( y) infinite 9. If the roots of the equation b + c + a = 0 be imaginary, then for all real values of, the epression b + 6bc + c is Greater than 4ab Less than 4ab Greater than 4ab Less than 4ab 0. The coefficient of 98 in the epansion of if - 0 space for rough work FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -006, Ph , , Fa 6594