FULL TEST : ID - 004Page 1 SPACE FOR ROUGH WORK PCM : TEST PAPER XII – JEE MAINS MATHEMATICS SECTION - A x2 n(1 4t) 1. The value of Limcosec x x0 4 0 t 2 1 dt is (1) 1 (2) 2 (3) 3 (4) 4 3 2 2. Consider the matrix A . Then all possible values of λ such that the determinant of B A I is 4 1 1 0 0, where I and i 1, is 0 1 (1) 1 2i (2) 2 3i (3) 3 4i (4) 5 6i 1 1 2 2 4 4 3. The equation x2 x 0 has both the roots equal, then p q q r r p 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 (1) 2 (2) (3) (4) r p p q q r p q r p p q r p q r 4. If n (e 1)exy x 2 x 2 y2 , then dy dx at (1, 0) is equal to [Note : e denotes Napier’s constant] (1) 0 (2) 1 (3) 2 (4) 3 5. Let A [aij ]33 , B [bij ]33 where bi j 3i j ai j and C [ci j ]33 , where ci j 4i j bi j be any three matrices. If det. A = 2, then det. B + det. C is equal to (1) 4 (2) 3 (3) 2 (4) 1 6. For two data sets, each of size 5, the variances are given to be 4 and 5 and the corresponding means are given to be 2 and 4, respectively. The variance of the combined data set is 11 13 5 (1) (2) 6 (3) (4) 2 2 2 Page 1 SPACE FOR ROUGH WORK JEE-MAINS TEST PAPER 7. The locus of the foot of the perpendiculars drawn from the vertex on a variable tangent to the parabola y2 4ax is (1) x(x2 y2 ) ay2 0 (2) y(x2 y2 ) ax2 0 (3) x(x2 y2 ) ay2 0 (4) x2 y2 ay2 0 8. Number of distinct real solutions of the equation x7 14x5 16x3 30x 420 0 is equal to (1) 0 (2) 1 (3) 2 (4) 3 9. Let a = 8 and b = 39 and we define a sequence {u n } as follows 1 u ; if unis multiple of 3 u1 b, un1 3 n un a; otherwise then u500 u300 u 400 is equal to (1) 1 (2) 3 (3) 5 (4) 7 10. Let f : (1,1) R be a differentiable function with f (0) 1 and f '(0) 1. Let g(x) f (2f (x) 2) , then g'(0) equals 2 (1) -4 (2) 0 (3) -2 (4) 4 11. The maximum number of positive solutions of equation cos sin2x 3,x 0, , lies in 3 3 2 (1) 0, (2) , (3) , (4) , 6 9 6 9 3 3 2 12. The equation to the locus of the middle point of the portion of the tangent to the ellipse x2 y2 1 included between the co-ordinate axes is the curve 16 9 (1) 9x2 16y2 4x2 y2 (2) 16x2 9y2 4x2 y2 (3) 3x2 4y2 4x2 y2 (4) 9x2 16y2 x2 y2 13. Let P(a,b,c) be any point on the plane 3x 2y z 7 then the least value of (a2 b2 c2 ), is 7 (1) 7 (2) 14 (3) (4) 4 2 Page 2 SPACE FOR ROUGH WORK JEE-MAINS TEST PAPER 14. Given p and q are respectively the maximum and minimum value of f (x) 5sin(x) 12cos(x) 1. If (p, q) is the centre of the circle touching the x-axis then radius of the circle is (1) 14 (2) 12 (3) 13 (4) 11 3 2sin3 x 15. The value of the definite integral cos5 x dx, is equal to 4 (1) 1 (2) 2 (3) 3 (4) 4 16. TP and TQ are tangents to the parabola y2 4ax at P and Q. If the chord PQ passes through the fixed point (a,b) then the locus of T is (1) ay 2b(x b) (2) bx 2a(y a) (3) by 2a(x a) (4) ab 2b(y b) 17. Tangents are drawn to the circle x2 y2 32 from a point A lying on the x-axis. The tangents cut the y-axis at point B and C, then the possible coordinates of A such that the area of ABC is minimum, are (1) (8 2,0) (2) (12,0) (3) (8,0) (4) (8 2,0) 18. If the ellipse 4x2 9y2 36 and the hyperbola 2 x2 y2 4 intersects orthogonally, then the value of can be (1) 5 (2) 4 (3) 3 (4) 2 3 3 19. The upper th portion of a vertical pole subtends an angle tan1 at a point in the horizontal plane 4 5 through its foot and at a distance 40m. from the foot. The height of vertical pole is (1) 20m (2) 40m (3) 60 m (4) 80 m 20. Let 3x y 8 0 be the equation of tangent to a parabola at the point (7, 13). If the focus of the parabola is at (1, 1), its directrix is (1) x 8y 19 0 (2) 8x y 19 0 (3) 8x y 19 0 (4) x 8y 19 0 21. Consider the following statements P : Suman is brilliant Q : Suman is rich R : Suman is honest The negation of the statement ‘Suman is brilliant and dishonest if and only if Suman is rich’ can be expressed as (1) ~ Q (P ~ R) (2) ~ Q ~ P R (3) ~ (P ~ R) Q (4) ~ P (Q ~ R) Page 3 SPACE FOR ROUGH WORK JEE-MAINS TEST PAPER 22. The area (in sq. units) of the region consisting of points (x, y) on xy plane which satisfy | x | 1 | y | and | y | 1 is (1) 4 (2) 6 (3) 8 (4) 12 ax2 bx c 23. If Lim 2, then which of the following relation is correct? x1 (x 1)2 (1) a2 b2 c2 12 (2) a c b (3) a 2 c2 2b (4) b2 2(a2 c2 ) 24. If the circle x2 y2 4x 22y c 0 bisects the circumference of the circle x2 y2 2x 8y d 0 then (c d) equals (1) 50 (2) 52 (3) 54 (4) 56 x2 y2 25. Let P be a variable point on the ellipse 1 with foci at S1 and S2 . If A is the area of triangle 25 16 PS1 S2 , then the maximum value of A is (1) 12 (2) 24 (3) 36 (4) 48 1 26. Let g(x) be a differentiable function on R and x g(x)dx (1 sin t), where t 0, 2 . Then the value sin t 2 1 of g equals 2 1 1 (1) (2) (3) 2 (4) 1 2 2 x2 2 t 1 27. Let f (x) e 1dt. If a is the point of local maxima and b and c (b > c) are the points of the local 0 t minima, then (1) a b c 1 (2) a b c (3) a c b (4) b c a Page 4 SPACE FOR ROUGH WORK JEE-MAINS TEST PAPER 28. Let a i 2j 3k; b i j 4k; c 4i 3j 6k; d 3i 6j 5k then the value of a b c d is equal to (1) 214 (2) 342 (3) 392 (4) 476 x 7 y 7 z 3 x 1 y 1 z 1 29. Consider two lines L1 : and L2 : . 3 2 1 2 4 3 If a line L whose direction ratios are 2,2,1 intersect the lines L1 and L2 at A and B then distance AB is (1) 18 (2) 24 (3) 36 (4) 50 30. If α and β are different complex numbers with 1, then is equal to 1 1 (1) 0 (2) (3) 1 (4) 2 2 Page 5 SPACE FOR ROUGH WORK JEE-MAINS TEST PAPER PHYSICS SECTION - B 31. If mass of an element is 5.74 gm and its volume is 1.2 cm3. Its density will be : (1) 4.783 g/cm3 (2) 4.78 g/cm3 (3) 4.7 g/cm3 (4) 4.8 g/cm3 32. The resistance and inductance of a coil are 1 ohm and 2 Henry respectively. A capacitor of 2F capacitor is discharged through the above coil. The frequency (n) and quality factor (Q) of L-C circuit will be : (1) 59.5Hz,103 (2) 69.5Hz,103 (3) 79.5Hz,103 (4) 35.5Hz,102 33. If v Ax BeCt where v is velocity, x is distance, t is time then dimensions of A, B and C are : (1) LT1, L, T (2) T1 ,LT1 ,T1 (3) L, LT1,T (4) T, T, T 34. A neutral metallic sphere is present infront of a uniformly charged very large conducting plane force between sphere and plane is F and torque on sphere is ' ' then (1) F 0, 0 (2) F 0, 0 (3) F 0, 0 (4) F 0, 0 35. A particle changes its velocity from 6 ms-1 towards east to 6 ms-1 towards north in 3 second. Then magnitude of its average acceleration will be : (1) 0 (2) 2 ms1 (3) 2 2 ms2 (4) 6 2 ms2 36. A rod is projected vertically up, such that it is rotating about its c.m. during its flight. Its angular velocity: (1) during ascent decreases (2) during its flight decreases (3) during ascent increases (4) remain same 37. At what temperature does the rms speed of gas molecules will be double the rms speed at NTP (Pressure is assumed constant) : (1) 546 K (2) 273C (3) 819C (4) 1092C 38. If F yi x j is acting on particle during its displacement from (0, 0) to (2, 3) then find work done by the force (1) 6 J (2) 4 J (3) 5 J (4) data insufficient Page 6 SPACE FOR ROUGH WORK JEE-MAINS TEST PAPER 39. If three tuning forks of frequencies 500, 501 and 502 Hz are sounded together then the number of beats produced per second will be : (1) 2 (2) 3 (3) 1 (4) 0 40. Two bodies of mass ‘m’ and 9m are placed at distance r. The gravitational potential at a point on the line joining them where the gravitational field is zero is : 16Gm 16Gm 3Gm (1) zero (2) (3) (4) r 3r 16r 41. A hydrogen atom and Li ion are both in the second excited state. If LH and LLi are their respective electronic angular momenta, and EH and ELi their respective energies, then : (1) LH LLi and EH ELi (2) LH LLi and EH ELi (3) LH LLi and EH ELi (4) LH LLi and EH ELi 42. A particle of mass 2 kg has potential energy U 8x2 4x4 . Then its angular frequency for small oscillation about its equilibrium position will be : (1) 2 2 rad / sec (2) 2 rad/sec (3) 1 rad/sec (4) 4 rad/sec 43. One thousand small water drops of equal radii combine to form a big drop. The ratio of final surface energy to the total initial surface energy. (1) 1000 : 1 (2) 1 : 1000 (3) 10 : 1 (4) 1 : 10 44. If three consecutive frequency produced by an organ pipe is 200 Hz, 250 Hz and 300 Hz then the organ pipe. (1) must be open pipe (2) must be closed organ pipe (3) may be closed organ pipe (4) none 45. If the experiment of Newton’s law of cooling, the graph drawn between logarithm of excess of temperature with the surroundings and the time is obtained as : (1) a straight line passing through origin of positive gradient (2) a straight line of positive gradient, not passing through origin (3) a straight line of negative gradient, not passing through origin (4) none of the above Page 7 SPACE FOR ROUGH WORK JEE-MAINS TEST PAPER 46. At any instant, before its maximum height, power during ascent of a projectile on parabolic path must be (1) positive (2) negative (3) zero (4) data insufficient 47. An object is moving with a velocity of 5 cm/s at an angle of 60 with respect to the optic axis of a concave mirror of focal length 100 cm. The object is at a distance of 50 cm form the mirror. Find the velocity of image at the given instant. (1) (10i 5 3 j) cm / s (2) (10i 5 3 j) cm / s (3) (10i 5 3 j) cm / s (4) (10i 5 3 j) cm / s 48. A carnot engine takes 840 J heat from the source. If its efficiency is 20%. How much heat will be rejected to sink. (1) 200 cal (2) 180 cal (3) 42 cal (4) 160 cal 49. A charged particle having some mass is resting in equilibrium at a height H above the centre of a uniformly charged nonconducting horizontal ring of radius R. The force of gravity acts downwards. The nature of equilibrium of the particle will be stable (1) for all values of H (2) only if H R / 2 (3) Only if H R / 2 (4) H R / 2 50. The work function of a metallic surface is 5.01 eV. Photoelectrons are emitted when light of wavelength 2000 Å falls on it. The potential difference required to stop the fastest photoelectrons is : (h 4.14 1015 eVs) (1) 1.2 V (2) 2.4 V (3) 3.6 V (4) 4.8 V 51. A person slides small ball with speed u along the smooth floor from point A. The ball returns to A after sliding on the circular smooth surface in the vertical plane from B to C and becoming a projectile at C. What is the minimum value of x for which the game could be planed if contact must be maintained at point C. neglect friction. (1) 2R (2) 3R (3) 4R (4) R Page 8 SPACE FOR ROUGH WORK JEE-MAINS TEST PAPER 52. In X-ray tube, when the accelerating voltage V is halved, the difference between the wavelengths of K line and minimum wavelength of continuous X-ray spectrum. (1) remains constant (2) becomes more than two times (3) becomes half (4) becomes less than two times 53. In the circuit diagram shown in figure, the capacitor of capacitance C is uncharged when the key k is open. The key is closed for time during which the capacitor becomes charged to a voltage V. Determine the amount of heat Q2 liberated during this time in the resistor of resistance R2 if the emf of the source is E, and its internal resistance can be neglected. 2R1CV 2R1CV (1) (E V) (2) (E V) (R1 R2 ) 2(R1 R2 ) R1CV R1CV (3) (E V) (4) (2E V) 2(R1 R2 ) 2(R1 R2 ) 54. A bar of diamagnetic substance is placed in a magnetic field with its length making angle 30 with the direction of the magnetic field. How will the bar behave? (1) It will align itself parallel to the magnetic field (2) It will align itself perpendicular to the magnetic field (3) It will remain as before (4) Its behavior cannot be predicted 55. The current through 10 resistor in the circuit given below is (the diodes are ideal) (1) zero (2) 80 mA (3) 30 mA (4) 20 mA 56. The magnetic field inside a current carrying toroidal solenoid is B. If its radius is doubled and the current through it is also doubled keeping the total number of turns same, the magnetic field inside the solenoid will be : (1) B/2 (2) B (3) 2 B (4) 4B Page 9 SPACE FOR ROUGH WORK JEE-MAINS TEST PAPER 57. Two small balls having the same mass and charge are located on the same vertical line at height h 1 and h2. They are thrown simultaneously with the same velocity in the same direction along the horizontal. The first ball hits the ground at a distance l from the initial vertical line. At what height will the second ball be at this instant (h1 h2 ) 2 2 2 l l l (1) h1 h2 g (2) h1 h2 g (3) h1 h2 g (4) None of these v v v 58. If a carrier wave of 1000 kHz is used to carry the signal, the length of transmitting antenna will be equal to : (1) 3 m (2) 30 m (3) 75 m (4) 3000 m 59. You are given a parabolic mirror whose inner surface is silvered. The equation of the curve formed by its x2 intersection with x-y plane is given by y . A ray travelling in x – y plane along line y = x + 3 it’s the 4 mirror in second quadrant and gets reflected. Find the unit vector in the direction of reflected ray. (1) 1 2 (i j) (2) 1 2 (i j) (3) 1 2 i j (4) None of these 60. As shown in figure, a convergent lens is placed inside a cell filled with liquid. The lens has focal length + 20 cm when in air and its material has refractive index 1.50. If the liquid has refractive index 1.60, the focal length of the system is : (1) + 80 cm (2) - 80 cm (3) - 24 cm (4) - 100 cm Page 10 SPACE FOR ROUGH WORK JEE-MAINS TEST PAPER CHEMISTRY SECTION - C 61. Select the correct statement about given square planar complex. (1) It has no geometrical isomer (2) It is optically active because it does not have plane of symmetry (3) It is optically inactive because it has symmetric carbon (4) It is optically active because it has symmetric carbon 62. In this sequence X, Y, Z are respectively : (1) Acidified H2O2 ; Alkaline H2O2 ; Acidified H2O2 (2) Alkaline H2O2 ; Acidified H2O2 ; Zn/HCl (3) Acidified H2O2 ; Heat ; Alkaline H2O2 ; (4) Alkaline H2O2 ; Acidified H2O2 ; On standing 63. Correct match of complex formed in the following methods are : (I) Mond’s process for purification of nickel (II) Removal of unreacted AgBr from photographic plate. (III) Removal of lead poisoning from the body. Page 11 SPACE FOR ROUGH WORK JEE-MAINS TEST PAPER I II III (1) Ni(CO)4 [Ag(CN)2 ] [Pb(EDTA)]2 (2) Ni(CO)4 [Ag(S2O3 )2 ]3 [Pb(EDTA)]2 (3) Ni(CO)6 [Ag(S2O3 )2 ]3 [Pb(EDTA)]4 (4) Ni(CO)6 [Ag(S2O3 )] [Pb(EDTA)]2 64. Select the incorrect statement about N2F4 and N2H4 : (I) In N2F4 , d-orbitals are contracted by electronegative fluorine atoms, but d-orbital contraction is not possible by H-atom in N2H4 . (II) The N-N bond energy in N2F4 is more N-N bond energy in N2H4 (III) The N-N bond length in N2F4 is more than that of in N2H4 (IV) The N-N bond length in N2F4 is less than that of in N2H4 (1) I, II and III (2) I and III (3) II and IV (4) II and III 65. The incorrect statement regarding above reactions is : (1) A shows amphoteric character (2) Gas ‘P’ and ‘Q’ are different (3) Both X and Y are water soluble (4) Gas Q is inflammable 66. Select the correct match : (1) Bayer’s method - Na 2CO3 (2) Matte - 98% Cu2S 2% FeS (3) van Arkel method - AgI (4) Thomas slag - Raw material for cement industry 67. In the reaction B2 H6 2KOH 2X 2Y 6H2 , X and Y are respectively. (1) H2O, KBO2 (2) HCl, KBO3 (3) H2O, KBO3 (4) H2 , H3BO3 Page 12 SPACE FOR ROUGH WORK JEE-MAINS TEST PAPER 68. A red solid is insoluble in water. However, it becomes soluble if some KI is added to water. Heating the red solid in a test results in the liberation of some violet colored fumes and droplets of a metal appear on the cooler parts of the test tube. The red solid is : (1) (NH4 )2 Cr2O7 (2) HgI2 (3) HgO (4) Pb3O4 69. The uncertainty in position for an electron is where λ is the de Broglie wavelength. The uncertainty in 4 velocity will be : v v (1) (2) v (3) 3v (4) 2 4 70. At low pressure if RT 2 a.p, (a is van der Waals’ constant), then the volume occupied by a real gas is : 2RT 2P RT 2RT (1) (2) (3) (4) P RT 2P P 71. In the following NaCl type structure : Salt Anion-anion distance Cation-anion distance MT 2.40 Å 1.70 Å MQ 1.63 Å 1.15 Å RT 2.66 Å 1.88 Å RQ 2.09 Å 1.48 Å MT is represented as : (1) (2) (3) (4) 72. Mixture of volatile components A and B total vapour pressure (in torr) p 254 119 XA where xA is mole fraction of A in mixture. Hence poA and poB are (in torr) (1) 254, 119 (2) 135, 254 (3) 119, 254 (4) 154, 119 Page 13 SPACE FOR ROUGH WORK JEE-MAINS TEST PAPER 73. Given the standard oxidation potentials, 0.4V 0.8V Fe Fe2 (aq.) Fe3 (aq.) (In acidic medium) 0.9V 0.6V Fe Fe(OH)2 Fe(OH)3 (In Alkaline medium) It is easier to oxidize Fe2 to Fe3 in : (1) Acid medium (2) Neutral medium (3) Alkaline medium (4) Both in acidic and in alkaline mediums 74. A reaction (1) forms two products : Ea2 2Ea1 If frequency factors for both the reactions are equal. Therefore, Ea1 /RT (1) k2 k1e (2) k2 k12 / A Ea1 /RT (3) k1 Ak2e (4) Both (1) and (2) are correct 75. The enthalpy of formation of H2O(l) is – 290 kJ/mol and enthalpy of neutralization of strong acid with strong alkali is – 56 kJ/equiv. What is the enthalpy of formation of OH (aq)? Given f H(H ,aq) 0 (1) 334 kJ / mol (2) 234 kJ / mol (3) 346 kJ / mol (4) 178 kJ / mol 76. A mixture of CH4 and C2H2 occupied volume at a total pressure equal to 63 torr. The same gas mixture was burnt to CO2 and H2O(l). The CO2 (g) alone was collected in the same volume and at the same temperature, the pressure was found to be 69 torr. What was the mole fraction of CH4 in the original gas mixture? 19 19 17 15 (1) (2) (3) (4) 21 20 18 16 Page 14 SPACE FOR ROUGH WORK JEE-MAINS TEST PAPER 77. Plot of log (x/m) against log P is a straight line inclined at an angle of 45. When the pressure is 0.5 atm and Freundlich parameter k is 10, the amount of solute adsorbed per gram of adsorbent will be (log 5 = 0.6990) : (1) 1 g (2) 2 g (3) 3 g (4) 5 g 78. At constant pressure, addition of helium to the reaction system : N2 (g) 3H2 (g) 2NH3 (1) Favour the formation of ammonia (2) Reduces the formation of ammonia (3) Does not effect the position of equilibrium (4) Reduces the dissociation of ammonia 79. The solubility of AgCl in water, in 0.02 M CaCl2 in 0.01 M NaCl and in 0.05M AgNO3 are S0 , S1 ,S2 and S3 respectively. Which of the following order of solubility is correct? (1) S0 S1 S2 S3 (2) S0 S2 S1 S3 (3) S0 S1 S2 S3 (4) S0 S2 S1 S1 80. In the following reaction Fe3O4 MnO4 Fe2O3 MnO2 the number of moles of OH liberated as per the balanced equation in the basic medium is (1) 1 (2) 2 (3) 3 (4) 4 81. The correct IUPAC name of following compound is (1) 4-Aminomethyl-3-hydroxycyclohex-5-ene-1-carboxylic acid (2) 2-Aminomethyl-5-carboxycyclohex-3-en-1-ol (3) 4-Aminomethyl-5-hydroxycyclohex-2-ene-1-carboxylic acid (4) 3-Hydroxy-4-aminomethylcyclohex-5-en-1-oic acid 82. In which of the following delocalization of anion is not possible ? (1) (2) (3) (4) Page 15 SPACE FOR ROUGH WORK JEE-MAINS TEST PAPER 83. (1) Enantiomers (2) Geometrical isomers (3) Position isomers (4) Conformers 84. In the given reaction, [X] as the major product among the elimination product is : (1) (2) (3) (4) 85. The major product (P) of the following reaction is : (1) (2) (3) (4) 86. Product X & Y can be : Page 16 SPACE FOR ROUGH WORK JEE-MAINS TEST PAPER (1) (2) (3) (4) 87. X, Y and Z respectively are : (1) (2) (3) (4) 88. In the following compound, the correct order of the acidity of the position X, Y and Z is : (1) X > Y > Z (2) Z > X > Y (3) X > Z > Y (4) Y > X > Z Page 17 SPACE FOR ROUGH WORK JEE-MAINS TEST PAPER 89. Which of the following is a nonreducing sugar? (1) (2) (3) (4) 90. The vitamin which is soluble neither in water nor in fat is : (1) Biotin (2) Phylloquinone (3) Thiamine (4) Ergocalciferol Page 18 SPACE FOR ROUGH WORK TEST : ID – 04 DATE :- ___-___-_____ XII # JEE-MAINS ANSWER & SOLUTION Page 1