FULL TEST : ID - 005Page 1 SPACE FOR ROUGH WORK PCM : TEST PAPER XII – JEE MAINS MATHEMATICS SECTION - A 1. If a b 2c b c a 2c [a b c], then λ is equal to (1) 1 (2) 1 (3) 2 (4) 3 1 1 x2 2. The integral 1 2x 2 e x x dx, is equal to [Note : C denotes constant of integration] 1 1 1 1 x2 x2 x2 x2 (1) (2x 1)e x C (2) (2x 1)e x C (3) xe x C (4) xe x C 3. Let f (x) (a2 a 2)x2 (a 4)x 7, x R. If unity lies between the roots of equation f(x) = 0 then number of integral values of a is (1) 5 (2) 4 (3) 3 (4) 2 4. A circle x2 y2 6x 16 0 cuts the x-axis at A and B and positive y-axis at the point D (0, d). The value of d equals (1) 2 (2) 4 (3) 9 (4) 16 5. Let Sn n2015 (1 22014 32014 32014 ..... n2014 ), then LimSn is n 1 1 2014 (1) 1 (2) (3) (4) 2014 2015 2015 x 2 y2 6. The common tangent of parabola y2 4x and hyperbola 1 touches them at P and Q 4 3 respectively, then Q can be (1) (4, 3) (2) (3, 4) (3) (4, 3) (4) (4, 3) 7. For x (1,1), the number of solutions of the equation tan1 (x x2 x3 x4 ....) cot 1 (6 6x 6x 2 ....) is 2 (1) 0 (2) 1 (3) 2 (4) 4 Page 1 SPACE FOR ROUGH WORK JEE-MAINS TEST PAPER 8. If the smallest radius of a circle passing through the intersection of x2 y2 2x 0 and x y 0 , is r then the value of (10 r 2 ) is equal to (1) 2 (2) 4 (3) 5 (4) 10 9. Three positive numbers form an increasing G.P. If the first term is doubled and second term is trebled, the new numbers are in A.P. Then the common ratio of the G.P. is - (1) 3 7 (2) 3 7 (3) 2 (4) 7 dy 1 y2 10. The solution of the differential equation, xy (1 x x2 ) given that when x = 1, y = 0 is dx 1 x2 1 y2 (1) ln 1 y2 ln(x) tan 1 (x) (2) ln 2 2tan1(x) 2 x 2 1 y2 1 y2 (3) ln 2 2tan1 x (4) ln 2 tan1 (x) x 4 x 4 11. The plane x + y + z = 5 is rotated by 90 along the line of intersection with the plane x – y – z = 2. If the equation of plane in new position is ax + by + cz + d = 0 where a, b, c, d I, then least value of | a b c d | is (1) 10 (2) 9 (3) 4 (4) 11 12. The sum of all value(s) of λ for which the lines 2x + y + 1 = 0 ; 3x + 2λy + 4 = 0 ; x + y – 3λ = 0 are concurrent, is 1 1 7 7 (1) (2) (3) (4) 4 2 2 12 13. A line L in R passing through (1, 1) intersect lines L1 :12x 5y 13 and L2 :12x 5y 65 at A and B respectively. If AB = 5, then line L can be - (1) 16x – 33y + 17 = 0 (2) 8x + 9y – 17 = 0 (3) 16x + 63y – 79 = 0 (4) 56x + 23y – 33 = 0 14. Let p and q be two statements. Then, (~ p q) (~ p ~ q) is a (1) tautology (2) contradiction (3) neither tautology nor contradiction (4) either tautology or contradiction Page 2 SPACE FOR ROUGH WORK JEE-MAINS TEST PAPER x2 15. If the circle x2 y2 2x 4y k 0 and director circle of ellipse y2 1 intersects orthogonally then 4 k equals (1) 0 (2) 5 (3) -5 (4) 2 16. Length fo the normal chord of the parabola, y2 4x, which makes an angle of with the axis of x is 4 (1) 8 (2) 8 2 (3) 4 (4) 4 2 17. Let ABC be a variable triangle such that A is (1, 2), B and C lie on the line y = x + λ (where λ is a variable). The locus of the orthocentre of triangle ABC is a straight line whose y-intercept is equal to (1) 2 (2) 3 (3) 4 (4) 5 18. STATEMENT 1 : Consider two curves C1 : zz iz iz b 0 and C2 : zz (1 i)z (1 i)z 4 0 where (b R, z x iy and i 1) If C1 and C2 intersects orthogonally then b = - 2. STATEMENT 2 : If two curves intersects orthogonally then the angle between the tangents at all their points of intersection is . 2 (1) Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1. (2) Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1. (3) Statement-1 is true, statement-2 is false (4) Statement-1 is false, statement-2 is true 19. Let A be a square matrix of order 3. If det. A = 2 then the value of det. (adj. A3) is equal to (1) 23 (2) 26 (3) 29 (4) 212 2 20. sin(4x)cot(x)dx is equal to 0 (1) (2) 0 (3) (4) 2 2 Page 3 SPACE FOR ROUGH WORK JEE-MAINS TEST PAPER 21. A circle S = 0 passes through points of intersection of circles x2 y2 2x 4y 1 and x2 y2 4x 2y 5 0 and cuts the circle x2 y2 4 0 orthogonally. Then the length of tangent from origin on circle S = 0, is (1) 3 (2) 2 (3) 1 (4) 4 x2 sin xdx 22. Let f (x) 0 , x 0 x3 k, x 0 If f(x) is continuous at x = 0 then k equals 1 2 4 (1) (2) (3) (4) does not exist 3 3 3 23. The equation of common tangent to the curves y2 8x and xy 1, is (1) 3y 9x 2 (2) y 2x 1 (3) y x 2 (4) 2y x 8 dy 24. Let y = y(x) satisfy the differential equation, x y x2 . If y(1) = 0 then the area bounded by the curve dx and the x-axis is 1 1 1 1 (1) (2) (3) (4) 2 3 4 6 25. A function f is continuous and differentiable on R0 and satisfies the condition x f '(x) f (x) 1 throughout its domain, with f (1) 2. Then the range of the function is (1) (, ) (2) (,1) (1, ) (3) (0, ) (4) (1, ) x2 1 26. Let g :[2,2] R where g(x) x2015 sgn(x) be an odd function for all x [2,2] then the p smallest integral value of p is equal to [Note : [k] denote the greatest integer less than or equal to k.] (1) 6 (2) 5 (3) 3 (4) 2 Page 4 SPACE FOR ROUGH WORK JEE-MAINS TEST PAPER 27. A function f is defined by f (x) cost cos(x t)dt, 0 x 2 then the minimum value of f(x) is 0 (1) (2) (3) (4) 4 2 2 4 28. If f (x) x3 3x2 2x a, a R , then the real values of x satisfying f (x2 1) f (2x2 2x 3) will be (1) (, ) (2) (0, ) (3) (,0) (4) 29. From the point (4, 6), a pair of tangent lines are drawn to the parabola y2 8x. The area of the triangle formed by these pair of tangent lines and the chord of contact of the point (4, 6) is (1) 8 (2) 4 (3) 2 (4) 6 30. Let A and B are two square matrices of order 3 such that det.(A) = 3 and det.(B) = 2, then the value of det adj. B1A1 is equal to 1 [Note : adj M denotes the adjoint of a square matrix M.] (1) 6 (2) 9 (3) 18 (4) 36 Page 5 SPACE FOR ROUGH WORK JEE-MAINS TEST PAPER PHYSICS SECTION - B 31. The edge of a square is l = 1.5 102 m then its area will be : (1) 2.25 104 m2 (2) 2.3104 m2 (3) 2.2 104 m2 (4) 2.0 104 m2 32. 0.04 kg of nitrogen is enclosed in a vessel at a temperature of 27C . How much heat has to be transferred to the gas to double the rms speed of its molecules [R = 2 cal/mol K] (1) 2250 cal (2) 2250 J (3) 4500 J (4) 6428 cal 33. Choose correct statement : (1) Dimensionally correct equation must be correct (2) Dimensionally correct equation may be correct (3) Dimensionless quantity must not have SI units (4) The quantity which has SI units must not be dimensionless 34. If the terminal speed of a sphere of gold (density = 19.5 kg/m2) is 0.2 m/s in a viscous liquid (density = 1.5 kg/m2), find the terminal speed of a sphere of sliver (density = 10.5 kg/m 3) of the same size in the same liquid: (1) 0.4 m/s (2) 0.133 m/s (3) 0.1 m/s (4) 0.2 m/s 35. A particle is projected vertically up with 20 ms-1 then find average velocity in initial 3sec : (g 10 ms2 ) (1) 15 ms1 (2) 25/ 3 ms1 (3) 5 ms1 (4) 15 ms1 36. 25 cm long closed organ pipe is in resonance with 330 Hz tuning fork in fundamental mode, find the minimum length of an open organ pipe which is also in resonance with same tuning fork (neglect end correction) (1) 50 cm (2) 75 cm (3) 100 cm (4) 150 cm 37. A uniform ring is released form rest and start rolling on an inclined plane having inclination 30. Find out the time taken by it to travel 5 m along the greatest slope of the inclined plane. (g = 10 -2) (1) 2sec (2) 6sec (3) 3sec (4) 1 sec Page 6 SPACE FOR ROUGH WORK JEE-MAINS TEST PAPER 38. If amplitude of a damped harmonic oscillator becomes half in initial one minute and it will become 1/x of initial amplitude after three minutes then the x is : (1) 2 (2) 4 (3) 8 (4) 16 39. A 2kg block is thrown on a rough (coefficient of friction is 0.2 horizontal surface with 4 ms-1. Then work done by kinetic friction on the horizontal surface and on the block with respect to an observer moving with constant velocity 4m/sec parallel to the velocity of the block respectively will be: (1) 0 J, 16 J (2) 16 J, - 16 J (3) 0 J, - 16 J (4) - 16 J, 8 J 40. The amount of work required for increasing the length of a given wire of length l by l will be : (A = Area, Y = Young’s modulus of material of the wire) (1) YAl/2 (2) Yl/2A (3) Yl2/2A (4) None 41. Ratio of gravitational acceleration due to the earth at height R to the acceleration at the depth R/2 will be : (R is radius of the earth) 8 (1) (2) 2 (3) 1/2 (4) 1 9 42. The length of a needle floating the surface of water is 2.5 cm. The minimum force needed to lift the needle above the surface of water will be : (T = 7.2 N/cm) (1) 3.6 N (2) 1.8 N (3) 72 N (4) 18 N 43. Two particles are executing SHM of the same amplitude A about same equilibrium position and having same frequency ω along the x-axis. Initially one particle is at x = 0 and moving towards positive extreme and another at x = A. Find their phase difference : (1) (2) (3) (4) 2 3 4 44. A gas undergoes cyclic process as shown in the figure, 5-1 and 3-4 are adiabatic process, 1-2 and 4-5 are isochoric process, 2-3 is isobaric process. Find efficiency of the cycle. (1) 15% (2) 30% (3) 45% (4) 60% Page 7 SPACE FOR ROUGH WORK JEE-MAINS TEST PAPER 45. When three progressive wave : Y1 4sin(2x 6t), y2 6 sin(2x 6t ) and Y3 12 sin(2x 6t ) are 2 superimposed then find amplitude of resultant wave (1) 6 (2) 2 (3) 10 (4) 8 46. In Carnot engine the work done by working substance is equivalent to : (1) Heat taken by source (2) Heat given to sink (3) Difference between above two (4) Ratio of heat taken and heat given 47. If acceleration and velocity of a particle are 5ms-2 j and 3i 4j ms1 respectively then centripetal acceleration and radius of curvature are at that point of the path where particle is present will be : 25 4 1 (1) 3ms2 , m (2) 4ms2 , m (3) 5ms2 , m (4) None 3 25 25 48. When photons of energy 4.25 eV strike the surface of a metal A, the ejected photoelectrons have maximum kinetic energy, TA expressed in eV and de-Broglie wavelength A . The maximum kinetic energy of photoelectrons liberated from another metal B by photons of energy 4.70 eV is TB (TA 1.50 eV). If the de-Broglie wavelength of these photoelectrons is B 2A , then (1) the work function of A is 2.25 eV (2) the work function of B is 2.25 eV (3) TA 2.75 eV (4) TB 1.25 eV 49. The diameter of the outer conductor of a cylindrical capacitor is D2. What should be the diameter of the core (inner cylinder) D1 of this capacitor be, so that for given potential difference between the outer conductor and the core, the electric field strength at the core is minimum. 2D2 D2 D2 (1) (2) (3) (4) None of these e e e2 Page 8 SPACE FOR ROUGH WORK JEE-MAINS TEST PAPER 50. A hydrogen like atom (atomic number Z) is in a higher excited state a quantum number n. This excited atom can make a transition to the first excited state by successively emitting two photons of energies 10.2 eV and 16.8 eV respectively. Alternatively, the atom from the same excited state can make a transition to the second excited 4.25 eV and 5.95 eV respectively. The values of n and Z are respectively (Ground state energy of hydrogen atom is 13.6 eV) (1) 6 and 6 (2) 3 and 3 (3) 6 and 3 (4) 3 and 6 51. Two small identical balls lying on a horizontal plane are connected by a massless spring. One ball is fixed and the other is free. The balls are charged identically as a result of which the spring length increases two fold. Determine the factor by which frequency of small harmonic vibrations of the system will change. Assume that force constant of spring is constant. It does not change with length of spring. (1) 3 (2) 2 2 (3) 3 2 (4) 2 52. For a carrier frequency of 100 kHz and a modulating frequency of 5 kHz, what is the band width of AM transmission? (1) 5 kHz (2) 10 kHz (3) 20 kHz (4) 200 kHz 53. A conducting disc of radius R is rotating with an angular velocity ω. Allowing for the fact that electrons are the current carries in a conductor, determine the potential difference between the centre of the disc and the edge. Mass of the electron is m and charge is e. m2R 2 2m2 R 2 m2R 2 (1) (2) (3) (4) None of these e e 2e 54. If the voltage between the terminals A and B is 17 V and Zener breakdown voltage is 9V, then the potential voltage across R is : (1) 6 V (2) 8 V (3) 9 V (4) 17 V Page 9 SPACE FOR ROUGH WORK JEE-MAINS TEST PAPER 55. A concave mirror and a glass slab (μ = 1.5) are arranged as shown in the figure. A converging bundle of paraxial rays is incident on the slab as shown. Find the position of the final image. (1) 21.3 cm from the mirror (towards right) (2) 20 cm from the mirror (towards right) (3) 3.21 cm from the mirror (towards right) (4) none of these 56. Light ray is incident on a prism of refracting angle 4 degree and refractive index of its material is 1.5. Find the minimum angle of deviation. (1) 1 degree (2) 2 degree (3) 3 degree (4) 4 degree 57. A magnet of length 14 cm and magnetic moment M is broken into two parts of length 6 cm and 8 cm. They are put at right angles to each other with the opposite poles together. The magnetic dipole moment of the combination is M (1) (2) M (3) 1.4 M (4) 2.8 M 1.4 58. An induction coil has an impedance of 10 when an AC signal of frequency 1000 Hz is applied to the coil and the voltage leads the current by 45. Then the inductance of the coil is : 1 1 1 1 (1) (2) (3) (4) 2 2 200 2 20 200 59. A particle of specific charge α (charge per unit mass) is released at time t = 0 from origin with an initial velocity of v v0 i in a uniform magnetic field B B0 k. Find the velocity of particle at any time t. (1) v0 cos(B0 t)i v0 sin(B0 t)j (2) v0 cos(B0 t)i v0 sin(B0 t)j (3) v0 cos(B0 t)i v0 sin(B0 t)j (4) None of these 60. An AC voltage is given by V V0 V1 cos t. What is its rms value for one cycle ? V12 V12 V12 V12 (1) V02 (2) V02 (3) V02 (4) V02 2 2 2 2 Page 10 SPACE FOR ROUGH WORK JEE-MAINS TEST PAPER CHEMISTRY SECTION - C 61. If S represents then which conformation represent energy level R? (1) (2) (3) (4) 62. Consider the following compounds. Arrange these compounds in decreasing order of their basicity. (1) 1 > 2 > 3 > 4 (2) 2 > 3 > 1 > 4 (3) 4 > 1 > 3 > 2 (4) 4 > 1 > 2 > 3 Page 11 SPACE FOR ROUGH WORK JEE-MAINS TEST PAPER 63. IUPAC name of the following compound is : (1) 1,2-Dibromo-3-chlorocycloprop-1-ene (2) 1,3-Dibromo-2-chlorocycloprop-1-ene (3) 1,2 Dibromo-3-chlorocycloprop-2-ene (4) 2,3-Dibromo-1-chlorocycloprop-1-ene 64. Antiseptics and disinfectants either kill or prevent growth of microorganism. Identify which of the following statements is not true. (1) Chlorine and iodine are used strong disinfectants. (2) Dilute solutions of boric acid and hydrogen peroxide are strong antiseptics (3) Disinfectants harm the living tissues (4) A 0.2% solution of phenol is an antiseptic while 1% solution acts as a disinfectant 65. The total number of basic group in the following form of lysine. (1) 0 (2) 1 (3) 2 (4) 3 66. The reaction below is an example of an intramolecular SN 2 substitution The stereochemistry of the product is (1) meso form (2) pair of enantiomers (3) pair of diastereomers (4) only one enantiomer Page 12 SPACE FOR ROUGH WORK JEE-MAINS TEST PAPER 67. The final product Z is (1) (2) (3) (4) 68. The major product of following reaction is : (1) (2) (3) (4) 69. The most probable product of the following sequence of reactions would be : (1) (2) (3) (4) 70. What is true about the following carbohydrate : (1) It anomerizes in solution phase (2) It is a reducing sugar (3) It shows the phenomenon of inversion of sugar in acidic medium (4) It shows mutarotation Page 13 SPACE FOR ROUGH WORK JEE-MAINS TEST PAPER 71. The structure shown here represents : (1) Schottky defect (2) Frenkel defect (3) Metal excess defect (4) None of these 72. Arrange the following electrolytes in the increasing order of coagulation power for the coagulation of As2S3 sol : K2SO4 CaCl2 Na3PO4 AlCl3 (I) (II) (III) (IV) (1) I < II < III < IV (2) I = III < II < IV (3) II < IV < I < II (4) II < III < IV < I 73. According to Henry’s law, the partial pressure of gas (Pg ) is directly proportional to mole fraction of gas in liquid solution, Pgas KH Xgas , where KH is Henry’s constant. Which is of the following statement is incorrect? (1) KH us characteristic constant for a given gas-solvent system (2) Higher is the value of KH , lower is solubility of gas for a given partial pressure of gas (3) KH has temperature dependence (4) KH decreases with increase of temperature 74. A schematic plot of n Keq Vs inverse of temperature for a reaction is shown below. The reaction must be : (1) Exothermic (2) Endothermic (3) One with negligible enthalpy change (4) Highly spontaneous at ordinary temperature Page 14 SPACE FOR ROUGH WORK JEE-MAINS TEST PAPER 75. V of two same charge particle A and B are plotted against de-Broglie wavelengths. Where V is the potential on the particles. Which of the following relation is correct about the mass of particle? (1) mA mB (2) mA mB (3) mA mB (4) mA mB 76. A mixture of O2 and gas “Y” (mol. wt. 80) in the mole ratio a : b has a mean molecular weight 40. What would be mean molecular weight, if the gases are mixed in the ratio b : a under identical conditions? (gases are non-reacting) : (1) 40 (2) 48 (3) 62 (4) 72 77. Consider the plots, given for the types of reaction nA B C These plots respectively correspond to the reaction order : (1) 0, 1, 2 (2) 1, 2, 0 (3) 1, 0, 2 (4) 0, 2, 1 78. A radioactive substance (parent) decays to it’s daughter element, the age of radioactive substance (t) is related to the daughter (d) parent (p) ratio by the equation : 1 p 1 d 1 d 1 p (1) t ln 1 (2) t ln 1 (3) t (4) t d p p d ln ln 79. The conductance of a salt solution (AB) measured by two parallel electrode of area 100 cm 2 separated by 10 cm was found to be 0.00011. If volume enclosed between two electrode contain 0.1 mole of salt, what is the molar conductivity (Scm2 mol-1) of salt at same concentration : (1) 10 (2) 0.1 (3) 1 (4) 0.01 Page 15 SPACE FOR ROUGH WORK JEE-MAINS TEST PAPER 80. Which is not correctly matched ? Factors Remarks (1) H 0, S 0 Process always spontaneous irrespective of temperature (2) H 0, S 0 Process non-spontaneous at high temperature (3) H 0, S 0 Process spontaneous at low temperature (4) H 0, S 0 Always non-spontaneous irrespective of temperature 81. Which of the following is correctly matched ? Column-I Column-II Column-III (1) [Fe(CO)5 ] Paramagnetic Octahedral, sp3d2 (2) [Fe(CO)5 ] Paramagnetic Trigonal bipyramidal, sp3d (3) [Co(CO)4 ] Diamagnetic Tetrahedral, sp3 (4) [Ni(CO)4 ] Diamagnetic Square planar, dsp2 82. Borax is converted into crystalline boron by the following steps : Borax X H3BO3 B2O3 Y B X and Y are respectively : (1) HCl, Mg (2) HCl, C (3) C, Al (4) HCl, Al 83. Match List-I with List-II and select the correct answer using the codes given below the lists : List-I (Compounds) List-II (used in) (1) BaSO4 ZnS (1) Explosive (2) NI3 (2) Oxidiser in rocket propellant (3) N2O4 (3) Space capsule (4) KO2 (4) Pigment (1) (2) (3) (4) (1) (2) (3) (4) (1) (2) (3) (4) (1) (2) (3) (4) (1) 3 1 4 2 (2) 4 1 2 3 (3) 3 4 1 2 (4) 4 3 2 1 Page 16 SPACE FOR ROUGH WORK JEE-MAINS TEST PAPER 84. When zeolite, which is hydrated sodium aluminum silicate, is teated with hard water the sodium ions are exchanged with : (1) H ions (2) Ca 2 ions (3) Mg2 ions (4) Both Ca2 and Mg2 85. 'A' H2O NaOH ; 'A' O2 400C B H2O at 25C NaOH O2 B is used for oxygenating in submarine. A and B are : (1) Na 2O2 and Na 2O (2) Na 2O and Na 2O2 (3) Na 2O2 and O2 (4) Na2O and O2 86. Lassaigne’s test for the detection of nitrogen will fail in case of : (1) NH2CONH2 (2) H2 NCONHNH2 .HCl (3) H2 N.NH2 2HCl (4) C6 H5 NHNH2 .2HCl 87. [CoCl2 (NH3 )4 ] [CoCl3 (NH3 )3 ] NH3. If in this reaction two isomers of the product are obtained, which is true for the initial (reactant) complex. (1) Compound is in cis-from (2) Compound is in trans-form (3) Compound is in both (cis and trans) form (4) Can’t be predicted 88. Which of the following substance acts as collector in froth floatation method? (1) Sodium xenate (2) Sodium pyrophosphate (3) Sodium nitroprusside (4) Sodium ethyl xanthate 89. Which of the following statements is incorrect? (1) On heating potassium dichromate, the gas evolved is oxygen (2) Compounds of La 3 are diamagnetic (3) Nd3 has greater tendency to form complex compounds than Eu3 (4) Sm2 acts as reducing agent 90. Among the following compounds, which one is not responsible for depletion of ozone layer? (1) Cl2 (2) CFCl3 (3) NO (4) CH4 Page 17 SPACE FOR ROUGH WORK TEST : ID – 05 DATE :- ___-___-_____ XII # JEE-MAINS ANSWER & SOLUTION Page 1