FIITJEE - JEE (Main) SAMPLE TEST - Time Allotted: Hours Maximum 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 maximum marks are 60. 5. There are three sections in the question paper I, II, III consisting of ysics, 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 textual material, printed or written, bits of papers, pager, mobile phone, any electronic device, etc. except the Admit Card inside the examination hall / room. 0. n completion of the test, the candidate must hand over the Answer Sheet to the Invigilator on duty in the oom / 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 Examination : FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -006, 4606000, 656949, Fax 6594
JEE-MAIN -SAMPLE TEST --PCM- Useful Data Chemistry: Gas Constant = 8.4 J K mol = 0.08 Lit atm K mol =.987 Cal K mol Avogadro's Number N a = 6.0 0 Planck s Constant h = 6.66 0 4 Js = 6.5 x 0-7 erg.s Faraday = 96500 Coulomb calorie = 4. Joule amu =.66 x 0-7 kg ev =.6 x 0-9 J Atomic No : H=, D=, Li=, Na=, K=9, b=7, Cs=55, F=9, Ca=0, He=, =8, Au=79. Atomic Masses: He=4, Mg=4, C=, =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 ysics: Acceleration due to gravity g = 0 m / s FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -006, 4606000, 656949, Fax 6594
JEE-MAIN -SAMPLE TEST --PCM- Section I (ysics). A particle is projected vertically upwards with a velocity of 0 m/sec. Find the time at which the distance travelled is twice the displacement + 4 / sec. sec. + / 4 sec. A For AB s v u g B s/ s 0 00 0. C 0 0 40 S s 0 Now, s ut gt A 40 0t 0t n solving t 4. Two men who can swim with a speed v in still water start from the middle of a river of width d and move in opposite directions always swimming at an angle with the banks. What is the distance between them along the river when they reach the opposite banks, if the velocity of the river is v dv dv cot cos dv v tan d dv v v v v sin. D d / t v sin d Distance = v v cos v v cos v sin vd v sin. A uniform chain of mass m hangs from a light pulley, with unequal lengths of the chain hanging from the two sides of pulley the force exerted by moving chain on the pulley is = mg > mg < mg either b or c depending upon acceleration of chain. C Force is less than mg as it is accelerated FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -006, 4606000, 656949, Fax 6594
JEE-MAIN -SAMPLE TEST --PCM-4 4. In the figure ball A is released from rest, when the spring is at its natural length. For the block B of mass M to leave contact with the ground at some stage, the minimum mass of A must be M M M/ a function of M and force constant of spring. A 4. C For B Just to loose contact Mg Mg Kx x K Applying WET WD WD KE g Kx mgx m M s 0 Mg Kx N B M 5. A system is shown in figure pulleys and strings are ideal system is released from rest a acceleration of kg, a = acceleration of kg (i) a = a (ii) a = a (iii) a = a = 0 s = / (iv) Tension T in the string = 5 N (v) frictional force between kg & incline = 5N (vi) frictional force between kg & incline = 5N (ii), (iv) & (vi) are correct (iii), (v) are correct (iii), (iv) & (v) are correct (i), (iv) & (vi) are correct 5. D Using constraint a 0 T a a a a.() Applying Newton s law and N solving T f 5N g sin f g cos kg 0 0 g kg T a 6. A bullet of mass 0 gm is fired from a rifle with a velocity of 800 m/s. After passing through a mud wall 80 cm thick, the velocity drops to 00 m/s. The average resistance of the wall is 750 N 50 N 750 N 50 N 6. C Using Kinematics find time taken by bullet P Then, F 750 N t 7. A body is gently dropped on a conveyor belt moving m/s. If = 0.5 how far will the body move relative to the belt before coming to rest? (g = 0m/s ) 0. m 0.6 m 0.9 m 0.8 m 7. C FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -006, 4606000, 656949, Fax 6594
JEE-MAIN -SAMPLE TEST --PCM-5 With respect to belt v u as 0 g s s 9m 8. Consider the disc kept on a rough horizontal surface as shown in the diagram. If a horizontal force F has to be applied such that the disc starts pure rolling, what should be the value of h? h F / / Body can t start pure rolling for any value of h 8. C For Pure rolling a h CM F. F h m m n solving, h 9. Moment of inertia of a half shell of mass M about an axis tangential to it, as shown, would be 9. B M Applying parallel axis theorem I M M M none of these 0. Consider bodies namely a disc A, a sphere B and a hollow cylinder all with same mass and radius being released from top of fixed inclined plane. If t A, t B & t c be the time they take to reach the bottom, find the correct alternative for each of given situations. In absence of any friction t C > t A > t B t C < t A < t B t C = t A = t B none of these 0. C In absence of friction only mg is acting through CM. So, this case of sliding in all cases and time taken will be same as a CM is same. FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -006, 4606000, 656949, Fax 6594
JEE-MAIN -SAMPLE TEST --PCM-6. A small ball starts rolling on an inclined track which becomes loop if radius in vertical plane. h= speed of the ball at highest point is zero but and highest point is above the ground. speed of the ball at highest point is non zero but highest point is above the ground speed of the ball is along horizontal at highest point and highest point is less than the above the ground. speed of the ball is along horizontal at highest point but height of highest point above the ground can not be calculated.. C In Pure rolling, energy is conserved PE T. KE. KE. A double star consists of two stars having mass M and M. The distance between their centre is equal to r. They revolve under their mutual gravitational interaction. Then which of the following statements is/are correct. heavier star revolves in orbit of radius r/ kinetic energy of heavier star is twice of that of the other star. lighter star revolves in orbit of radius r 5 all above are correct.. A Taking M as origin applying CM M 0 m r xcm r M r So, from heavier black. Three small identical bodies each of mass m are moving in circular orbit around a fixed point with same angular velocity under their gravitational interaction. If the separation between any two bodies is, the total energy possessed by the system is given by GM GM GM GM 4 cos0. A Total potential energy = Total K.E. = GM So, total energy = GM GM KE P. E 4. A man of mass M stands at one end of a plank of length L which lies at rest on a frictionless surface. The man walks to the other end of the plank. If the mass of the plank is M/, the distance that the man moves relative to the ground is L 4L L L 4 5 4 4. C FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -006, 4606000, 656949, Fax 6594
JEE-MAIN -SAMPLE TEST --PCM-7 Let the distance moved by plank be x. Now, there is no external force so CM Will not move mn mn xcm m m M M L x x 0 4M Mx ML Mx 44 ML Mx. x L 4 So, distance moved by person wrt. 4 L 5. The centre of mass of a half disc shown is at C while is the centre. Thus C is / / 4 none of the above C 5. C CM of sector = Here 4 r 4 sin 6. If the tension in a stretched string fixed at both ends in changed by 0%, the fundamental frequency is found to change by 5 Hz. Then the original frequency is 50 Hz velocity of propagation of the transverse wave along the string changes by 5 % velocity of propagation of the transverse wave along the string change by 0 % fundamental wavelength on the string does not change. 6. B ' T.T v T 7. Beats are produced by two progressive waves. Maximum loudness at the waxing is x times the loudness of each wave. The value of x is 4 7. D At maximum net amplitude = A Loudness A FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -006, 4606000, 656949, Fax 6594
JEE-MAIN -SAMPLE TEST --PCM-8 8. A thermodynamic system undergoes a cyclic process as shown in the figure. The cycle consists of two closed loops. ver one complete cycle, the system performs positive work negative work zero work nothing can be predicted 8. B Area under PV graph is greater is anticlockwise direction. So, net W.D. is negative P V 9. A half ring of radius is charged with a linear charged density. The field at the centre is 0 k/ k/ k/ 9. C dl d dq. K. dq de / dq K E K. cos / d 0. The maximum electric field strength E due to a uniformly charged ring of radius r, happens at a distance x, where value of x is (x is measured from the centre of the ring) x = x = / x = x = 0. C E KQx x / de For maximum 0 dx So, x. Two charges +q and q are placed fixed on the corner of a massless rigid rod of length L.Calculate the potential energy of the dipole thus formed.. B PE = 4 o q 4L KqV q r 4 L 0 4 o q L o q L +q q L None of these. FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -006, 4606000, 656949, Fax 6594
JEE-MAIN -SAMPLE TEST --PCM-9. If the above discussed dipole is placed in a uniform electric field E as shown, calculate the proper potential energy of the dipole. q q 4qLE 4 o L 4 o L q qle 4 o L. D Net PE = PE due to EF + PE of system q 4qLE 4 L 0 4qLE q 4 L o +q L E. In the shown network current through 0 resistor equals 0 V 0 V A 9 A A A 0. A Applying KVL I A 0 4. Equivalent resistance between the points A and B is 4 A B 4. D Using node removal method h eq 5. The two rails of a railway track; insulated from each other and the ground, are connected to millivoltmeter. What is the reading of the millivoltmeter when a train passes at a speed of 80 km/hr along the track, given that the horizontal component of earth s magnetic field is 0. 0-4 wb/m and rails are separated by metre 0 - V 0 mv V mv 5. D dl. B v mv 6. In an -L-C circuit v = 0 sin (4 t + 5/6) and i = 0 sin (4 t + /) The power factor of the circuit is 0.5 0.966 0.866 6. C Conceptual based 7. A circular current carrying coil has a radius a. The distance from the centre of coil, on its axis, where the magnetic induction will be /8 th of its value at centre of coil is a + a a a / 7. C FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -006, 4606000, 656949, Fax 6594
JEE-MAIN -SAMPLE TEST --PCM-0 B I 0 0 / x x a I B 8. In photoelectric effect, the photo current increases with increase of frequency of incident photon decreases with increase of frequency of incident photon does not depend on the frequency of the photon but depends only on intensity of incident light. depends both on intensity and frequency of photon. 8. C Conceptual based 9. If refractive index of water is 4/ and glass is 5/ then critical angle so that light travelling form glass to water is completely reflected is sin - (4/5) sin - (5/4) sin - (/5) sin - (5/) 9. A Applying sin i sin r 4 sin 5 0. When a ray of light enters a glass slab from air its wavelength decreases its frequency increases 0. A v f f req remains constant Here volume increases, so decreases its wavelength increases neither wavelength nor frequency changes space for rough work FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -006, 4606000, 656949, Fax 6594
JEE-MAIN -SAMPLE TEST --PCM-. For the equations C diamond H g CH g ; H ; Section II (Chemistry) 4 C graphite H g CH g H 4 Predict whether H H H H H H H H H vap H diss H. B This is because diamond is more stable than graphite and has more energy content.. Which of the following can behave as both electrophile and nucleophile? CH C N CHH CH CH CH CHNH. A CHCN can behave as both electrophile and nucleophile.. Steam reacts with iron at high temperature as follows: Fe s 4H g Fe s 4H g 4 The correct expression for the equilibrium constant (K P ) is: p p H H p p H H. B Molar concentration or partial pressure of solid =. 4 4 4 p H Fe 4 4 ph Fe Fe Fe 4 4. In which of the following solvents, AgBr has the maximum solubility? 0 - M NaBr 0 - M NH 4 H Pure water 4. B AgBr reacts with NH 4 H to form a soluble complex. AgBr NH 4H Ag NH Br H. 0 M HBr 5. The electrode potential of a copper wire dipped in 0. M CuS 4 solution at 5 0 C (the standard reduction potential of copper is 0.4V): 0.4V 0.V 0.49 V 0.8 V 5. B The electrode reaction written as reduction reaction is Cu e Cu n 0 0.059 Applying Nernst equation, E = E log Cu s Cu 0.059 0.4 log 0. 0.4 0.095 0.05V 6. The strongest reducing agent among the following is F - Cl - Br - I - 6. D I - can losses electrons easily (undergoes oxidation easily). So strong reducing agent FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -006, 4606000, 656949, Fax 6594
JEE-MAIN -SAMPLE TEST --PCM- 7. Diazonium salt decomposes as: C H N Cl C H Cl N 6 5 6 5 0 At 0 C, the evolution of N becomes two times faster when the initial concentration of the salt is doubled., Therefore, it is a first order reaction a second order reaction independent of the initial concentration of the salt a zero order reaction. 7. A Because rate conc 8. If 8. B.680 mole of a solution containing an ion the oxidation of n A to n A requires.6 0 mole of Mn 4 for A in an acidic medium, then what is the value of n? 5 4 mole A Mn A Mn n 4.680.6 0.68 0 5 n.60 5 5 n n 9. The equivalent weight of MnS 4 is half its molecular weight when it is converted to Mn Mn Mn 4 Mn 9. B 4 Mn Mn e nf M. wt E. wt 0. The largest number of molecules is in 6 g of H 8 g of C 46 g of CH CH H 54 g of N 5 (Use atomic weight: = 6, C =, N = 4, H = ) 0. A 6 N H N AV N AV 8 8 NC N AV N AV 8 46 NC H5H N AV N AV 46 N 54 N 5 8 80 0.5 N N AV AV. Consider a titration of 7 FeS4. NH 4 S 4.6H using diphenylamine as indicator. The number of moles of Mohr s salt required per mole of dichromate is H 7 Fe Cr Fe Cr K Cr with acidified Mohr s salt solution 4 5 6 FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -006, 4606000, 656949, Fax 6594 4
JEE-MAIN -SAMPLE TEST --PCM-. D neq Mohr salt = neq Cr 7 n 6 n 6. The normality of 0. M phosphorus acid HP is 0. 0.9 0. 0.6. D H P H H nf N 0. 0.6. The energy of hydrogen atom in the ground state is.6 ev. Its energy corresponding to the quantum number n = 5 is 0.54eV 5.40 ev 0.85eV.7eV ]. A.6 E n n 4. If r is the radius of first orbit of hydrogen atom, then the radii of second, third and fourth orbit in terms of r are 8 r, 7 r,64r r,6 r,8r 4 r,9 r,6r r, r,r 4. C r r n n 5. If kinetic energy of an electron is increased nine times, the de-broglie wavelength associated with it would become times 9 times times 9 times 5. C KE 6. Which electronic level allows the hydrogen atom to absorb a photon but not emit a photon? s p s d 6. C s is the lowest energy level CH 7. NaMe CH H reaction Br E Product. Product of the reaction is: CH FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -006, 4606000, 656949, Fax 6594
JEE-MAIN -SAMPLE TEST --PCM-4 Me No reaction 7. D Since there is no H present anti to Br, hence E doesn t occur. CH 8. Cl NaEt Major product of the reaction is: CH CH CH CH 8. B CH CH The product obtained are: and (major) (minor) 9. Which of the given options best describes the product of the following reaction? CH K tbu Product CD E Br Absolute configuration has been inverted Absolute configuration has been retained acemisation (loss of absolute configuration) Loss of chirality has occurred (the product is achiral) 9. D CH CH Br CD K t Bu E CD FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -006, 4606000, 656949, Fax 6594
JEE-MAIN -SAMPLE TEST --PCM-5 0. Which one of the following undergoes nucleophlic aromatic substitution at the fastest rate? Cl Cl Cl Cl N Cl CH Me 0. A The electron withdrawing groups make nucleophilic aromatic substitution proceed at the fastest rate. Br. N H A Product of the following reaction is: Br Br N H N H Br N Br N H H Br Br. B The electron-withdrawing groups at ortho or para position to the leaving group help nucleophilic aromatic substitution proceed at a faster rate.. H H HS4 P 99% yield The product (P) is: C H C. A H H H H H H. An organic compound B is formed by the reaction of ethyl magnesium iodide CH CH MgI with a substance A, followed by treatment with dil. aqueous acid. Compound B doesnot react with PCC. Identify A? FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -006, 4606000, 656949, Fax 6594
JEE-MAIN -SAMPLE TEST --PCM-6 CH. B C H C H CH CH C CH (MgI) CH CH H CH CH C CH EtMgI CH CH C CH dil aq CH CH C CH acid A Et Et B PCC No reaction 4. C H 8 H H C H X H. Identify X X C 8 X C 8 X C X C CH CH CH CH (Esterification) (Esterification) (Saponification) (Hydrolysis) 4. B H C H 8 H C H H C 8 CH C H 8 CH H H H 8 C X CH 5. SCl pyridine / Zn H CH CH CH CH CH H A B C H Cl 4 7 Compound is FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -006, 4606000, 656949, Fax 6594
JEE-MAIN -SAMPLE TEST --PCM-7 C H C CH CH CH HC CH CH CH CH Cl HC CH CH CH Cl HC CH CH CH Cl 5. C / Zn CH CH CH CH CH Cl HCH CH CH H CH CH Cl A B 6. Equimolar solutions of two non electrolytes in the same solvent have same b.pt but different f.pt same f.pt but different b.pt same b.pt and same f.pt different b.pt and different f.pt 6. C Tf and Tb are constant for a solvent. 7. The degree of dissociation of weak electrolyte Ax B y is related to van t Hoff s factor (i) by the expression: i x y 7. A A B y xa yb x y i x y i x y x x y i x y i x y 8. When 0 gm of naphthoic acid 8 FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -006, 4606000, 656949, Fax 6594 x y i x y i C H is dissolved in 50 gm of benzene f.7 freezing point depression of k is observed. The van t Hoff factor (i) is 0.5 8. A Tf K f molality i 0 000.7 i 7 50 i 0.5 k, a
JEE-MAIN -SAMPLE TEST --PCM-8 9. A 0.004 M solution of NaS 4 is isotonic with a 0.0 M solution of glucose at same temperature. 9. C The apparent degree of dissociation of NaS 4 is 5% 50% 75% 85% NaS4 Glu cose CT CT 0.004 0.0 0.75 75% 0. If equal volumes of BaCl and NaF solutions are mixed, which of these combination will not 7 give a precipitate. K sp of BaF.7 0 0 M BaCl and.5 0 M BaCl and 0. C For precipitation Qsp Ksp 0 M NaF 0 M NaF 0 M BaCl 0 M BaCl and and.5 0 M NaF 0 M NaF pace for rough work FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -006, 4606000, 656949, Fax 6594
JEE-MAIN -SAMPLE TEST --PCM-9. n (n ) n. B n n C n r C r r r n equals to Section III (Mathematics) n n n C r = r n n n n Cr r = n r n n n ( Cr C r ) = r n n n Cr Cr n n n ( n ) n n.. Statement -: If a, b, c are distinct and x, y, z are not all zero, then ax by cz 0 bx cy az 0 cx ay bz 0 Gives a + b + c 0 Statement : a b c ab bc ca if a, b, c are distinct. Statement- is true, Statement- is true, but Statement- is a correct explanation for Statement-. Statement- is true, Statement- is true, but Statement- is not a correct explanation for Statement-. Statement- is true, Statement- is false. Statement- is false, Statement- is true.. D Let D = a b c b c a c a b = a b c abc a b ca b c ab bc ca Now a b c ab bc ca 0 the given system of equations can have non-zero solution (x, y, z are not all zero) If D = 0, i. e. If a b c 0 Statement - is false. Again a b c ab bc ca a b c ab bc ca 0 a b b c c a a, b, c are all different Statement- is true. D holds. a b c ab bc ca. If f x is an odd periodic function with period, then f 4 equals 0 4-4 FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -006, 4606000, 656949, Fax 6594
JEE-MAIN -SAMPLE TEST --PCM-0. A f 4 f f 0 0 dy 4. The solution of the differential equation x y dx represents straight lines circle parabola ellipse 4. C dy y dx x x I. F. x y c x 5. If [x] denotes the greatest integer less than or equal to x, then the value of 5. B 4 8 5 x dx x dx 0 x dx 5 x dx is 6. A tower AB leans towards west making an angle with the vertical. The angular elevation of B, the top most point of the tower, is, as observed from a point C due east of A at a distance d from A. If the angular elevation of B from a point due east of C is at a distance d from C is, then tan cot cot tan cot cot tan cot cot None of these 6. B West h B 90 A C x d d East Let h be height of tower then h tan 90... x h tan... x d h tan... d x Solve (), () and () tan cot cot f x x ax bx 5sin x be an increasing function in the set of real number. Then 7. Let 7. C a b 5 0 a b 5 0 a b 5 0 a 0 and b 0 FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -006, 4606000, 656949, Fax 6594
JEE-MAIN -SAMPLE TEST --PCM- dy x ax b 0 sin x cos x dx and discriminant < 0 8. If,,,... 8. C a a a are in H.P. and n f k ar ak, then r a a,, a,..., a n f f f f n are in A.P. G.P. H.P. None of these Let n r a r S n,,,... in A.P. a a a an Sn Sn Sn Sn,,,..., in A.P. a a a an Sn Sn Sn,,... in A.P. a a a,,... H.P. S S S n n n a a a a a a,,,... in H.P. f f f 9. A problem in mathematics is given to students whose chances of solving individually are, and. 4 The probability that the problem will be solved atleast by one is 4 4 9. D Nobody solves the problem 4 4 4 0. If a I and the equation x a x 0 0 has integral roots, then the values of a are 6, 8 8, 0 0, 8, 0. D x a x 0 so either x a and x 0 or x 0 and x a. If x 6y touches the hyperbola x y 4, then the point of contact is, 6 5, 6, 4, 6 6. D FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -006, 4606000, 656949, Fax 6594
JEE-MAIN -SAMPLE TEST --PCM- 6y Put x in equation of hyperbola y 6 x 4. Consider a circle with its centre lying on the focus of the parabola y px such that it touches the directrix of the parabola. Then a point of intersection of the circle and the parabola is p p, p or, p p p, p p p, p,. A If focal chord is diameter of the circle then it touches the directrix of the parabola x. If a, a falls inside the angle made by the linear equations y, x 0 and y x, x 0, then a belongs to, 0,,,. D Locus of point a,a y x is y x y x x y x and y (, 9) x y x 0, y x, y x, 4 x 0, a 4. The straight lines whose direction cosines satisfy al bm cn 0, fmn gnl hlm 0 are perpendicular if a b c af bg ch 0 0 f g h f g h 0 a b c 4. C bm cn Put l in the another equation, a bm cn fmn gn hm 0 a bhm mn bg ch af cgn 0 m m n n l l g / b h / c f / a 5. Domain of derivative of the function f (x) = sin (x ) is a f b g c h 0 FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -006, 4606000, 656949, Fax 6594
JEE-MAIN -SAMPLE TEST --PCM- [, ] [, ] ~ 0, [, ] ~ {0} [, ] ~ 5. B y = sin (x ) 6. y = sin (x ) 4x sin (x ) x x x 0 and sin (x ) 0 and x x x 0, x. r tan tan equals to r 5r 7 4 6. C sin 0 cot (n ) (n ) a n = tan tan (n )(n ) (n )(n ) = tan (n + ) tan (n + ) S n = tan (n + ) tan S = tan cot sin. 0 7. If P, P, P be the lengths of perpendiculars from the vertices of the triangle ABC to the opposite sides, then P P P = abc P P P = 8 7. D a b c P P P = (where is circumradius of triangle ABC). P P P = a b c 8 P = c sin B, P = a sin C, P = b sin A a b c P P P = abc sin A sin B sin C = 8. 8. A unit vector is orthogonal to 5i ˆ j ˆ 6kˆ and is coplanar to i ˆ ˆj kˆ and ˆ i ˆ j k ˆ, then the vector is j ˆ kˆ i ˆ 5j ˆ 0 9 6i ˆ 5kˆ i ˆ j ˆ kˆ 6 8. A Let a be the unit vector FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -006, 4606000, 656949, Fax 6594
JEE-MAIN -SAMPLE TEST --PCM-4 a i ˆ ˆ j k ˆ ˆ i ˆ j k ˆ a = ( + ) + ( ) + ( + ) = 6 + 4 + = a is orthogonal to 5i ˆ j ˆ 6kˆ so, 5( + ) + ( ) + 6( + ) = 0 8 + 9 = 0 = 6 8 + = 0 = = 0 = 0 ˆj kˆ a. 0 9. If the curve y = x + bx + c touches the straight line y = x at the point (, ), then b and c are given by,,,, 9. A y = x touches y = x + bx + c = + b + c b + c = 0 () dy x b (, ) dx b b (b, c) = (, ). 0. In the sequence,,,,,, 4, 4, 4, 4..., where n consecutive terms have the value n, the 50 th term is 7 6 8 none of these 0. A,,, 4444,... 4... 67 when last time 6 will appear that will be = 6 th term so after that 7 will repeat from 7 th term to 5 th term Ans is 7 5 n. The value of, n N where {.} denotes the fractional part of x, is 4 5/4 9/4 /4 None of these. C 4 4 n z z. If z and z are two complex numbers satisfying the equation, then z z which is Positive real Negative real Zero or purely imaginary None of these. C z z is a number FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -006, 4606000, 656949, Fax 6594
JEE-MAIN -SAMPLE TEST --PCM-5 z t Let t, t t z t locus of t is line y axis. The number of ways of switching the network such that the bulb glows is 6 60 6 None of these. A C C C C 0 6 4. If sin.sec = tan -tan, then [sin.sec +sin.sec +..+sin n.sec n ] = tan n -tan tan n -ntan tan n -tan n (tan n -tan ) 4. A Using method of difference, sin sec tan tan and so on. cosc tan A 0 5. The determinate sin B 0 tan A has the value where A, B, C are angles of a triangle 0 sin B cos C 0 sina. sinb cosa cosb cosc 5. A Expand along the st row cosc tan Asin B tan Asin B cosc 6. The equation of the image of the circle x y 6x 4y 8 0 by the line mirror 4x 7 y 0 is x y x 4y 5 0 x y x 4y 5 0 x y x 4y 5 0 None of these 6. A adius will remain same, image of center (-8, ) is (-6, -) w.r.t. line 4x 7y 0 x y 7. For hyperbola cos sin abscissae of vertices eccentricity, which of the following remains constant with change in ' '? abscissae of foci directrix 7. B eccentricity = sec so foci are constant FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -006, 4606000, 656949, Fax 6594
JEE-MAIN -SAMPLE TEST --PCM-6 8. If f x 8. D sin x x x, 0 x 0, 0 Where, [x] denotes the greatest integer less than or equal to x, then lim f x x 0 equals: 0 - None of these sin x x x, 0 f x 0, x 0 lim f x 0 x0 lim x0 f x sin sin 9. For a real number y, let [y] denote the greatest integer less than or equal to y. Then the function f x tan x x is: discontinuous at some x f ' f ' x exists for all x, but the derivative f '' f '' x exists for all x continuous at all x, but the derivative 9. D It is a zero function, f x 0 0. 0. B / (sin x) / d(sin x) is equal to 4 / (sin x) / sin x sin x x does not exist for some x x does not exist for some x / sin x c / / sin x / tan c sin x / Let sin x t d sin x dt d t t Using algebraic twins, t t space for rough work tan / c sin x none of these FIITJEE Ltd., FIITJEE House, 9-A, Kalu Sarai, Sarvapriya Vihar, New Delhi -006, 4606000, 656949, Fax 6594