JEE MainFULL TEST : ID - 001 Page 1 SPACE FOR ROUGH WORK PCM : TEST PAPER XII – JEE MAINS MATHEMATICS SECTION - A 1 2 n(1 2x) 1. The value of definite integral 0 1 4x2 dx, equal n2 n2 n2 n2 (1) (2) (3) (4) 8 4 32 16 2sin x, x 2 a cos(x) b, x 0 2 2. If f (x) is continuous in [, ] ,then number of points at which f(x) is not 2 cosx,0 x 2 csin x, x 2 differentiable is /are (1) 0 (2) 1 (3) 2 (4) 3 x 2 y2 3 3. Tangent to the ellipse 1 having slope meet the coordinate axes in A and B the area of 32 18 4 AOB (O is origin) equals (1) 12 (2) 8 (3) 24 (4) 32 4. In which one of the following of the functions, Rolle’s theorem is applicable? (1) f (x) x ,in 2 x 2 (2) f (x) tan x,in0 x 2 (3) f (x) 1 x 2 3 ,in1 x 3 (4) f (x) x (x-2 )2 in 0 x 2 5. A house of height 100m subtends a right angle at the window of an opposite house. If the height of the window is 64m,then the distance between the two house is (1) 48m (2) 36m (3) 54m (4) 72m Page 1 SPACE FOR ROUGH WORK JEE-MAINS TEST PAPER 6. The area of the triangle inscribed in an ellipse bears the ratio 5 :3 to the area of the triangle formed by joining the points on the auxiliary circle corresponding to the vertices of the first triangle, then the eccentricity of the ellipse is 2 3 5 3 (1) (2) (3) (4) 3 4 3 5 7. The distance between the origin and the normal to the curve y e2x x2at x 0,is 1 2 2 1 (1) (2) (3) (4) 5 5 3 2 1 x2 1 dy 8. If y cos1 , then is equal to 2 1 x 2 dx 1 1 1 1 (1) (2) (3) (4) 1 x2 1 x2 2(1 x2 ) 2(1 x2 ) 9. Let p be the statement ‘7 is not greater then 4’and q be the statement ‘paris is in France’ then (p q) is the statement (1) 7 is greater than 4 or Paris is not in France (2) 7 is not greater than 4 or Paris is not in France. (3) 7 is greater than 4 or Paris is in France (4) 7 is greater than 4 or Paris is not in France 10. Let f (t) t 2for0 t 1 and g (t) t3for0 t 1the value of c with 0 c 1and at which f (1) f (0) f '(c) , is g(1) g(0) g'(c) 2 1 1 1 (1) (2) (3) (4) 3 3 2 6 1 1 1 11. Let A and B be two events such that p (A B) P(A B) , and P (A) , where A stands for 6, 4 4 complement of event A. then, events A and B are (1) Mutually exclusive and independent. (2) independent but not equally likely. (3) equally likely but not independent. (4) equally likely and mutually exclusive. Page 2 SPACE FOR ROUGH WORK JEE-MAINS TEST PAPER 12. A chord is drawn through the focus of parabola y2 6x such that its distance from the vertex of this 5 parbola is ,then its slope can be 2 5 3 2 2 (1) (2) (3) (4) 2 2 5 3 1 dx 13. If I , then 0 1 x 2 (1) loge 2 I (2) loge 2 I (3) I (4) I loge 2 4 4 dx 1 14. If sin1 (ksin x) c,then K2 (1 k2 )(1 k4 )(1 k2 k12 ) is equal to [note :c constant of 1 tan2 x k integration] (1) 2010 (2) 2012 (3) 2013 (4) 2014 18 18 15. If x1 ,x 2 ,...x18 are observations such that (x j 8) 9and(xJ 8)2 45, then the standard deviation of j I j I observations is 18 3 (1) (2) 5 (3) 5 (4) 34 2 10 16. The sum (r rl 2 1) (r!) is equal to (1) 101 x (10!) (2) (11)! (3) 10 x (11)! (4) 11 x (11!) k3 17. If x x (0,3)andy (0,4), then maximum value of (3 - x) (4 - y) (3x + 4y) is ,where K is equal to 12 25 25 25 25 (1) (2) (3) (4) 3 6 2 12 18. The set S {x R : cos(2x) 2cos2 (x) 2}, is equal to (1) 2n : n I (2) n : n I (3) n : n I (4) 2n : n I 3 6 3 3 Page 3 SPACE FOR ROUGH WORK JEE-MAINS TEST PAPER z2 19. The locus of P(z) where z = x + iy and satisfying Re 0 is z 1 (1) { x,y R2 | x2 y2 —3y 2 0} (2) { x,y R 2 | x2 y2 3x 2 0} (3) { x,y R 2 | x2 y2 3x 2 0} (4) none of above 20. Hat W contains two white balls and one black ball. Hat B contains two black balls and one white ball. At random, one of the following strategies is selected: Two different balls are drawn from hat W. Two different balls are drawn from hat B One ball is drawn from each hat. The probability of getting at least one white ball, is 1 1 22 21 (1) (2) (3) (4) 2 4 27 27 dy 21. Let y f (x) satisfies the differential equation (1 x2 ) 2xy 2xandf (0) 2 then the number of dx integers in the range of f (x) is (1) 1 (2) 2 (3) 3 (4) 4 22. On the set N of all natural numbers, define the relation R by aRb if and only if the greatest common divisor of a and b is 2, then R is (1) reflexive but not symmetric (2) symmetric only (3) reflexive and transitive (4) equivalence 23. Let a, b, c be non zero real numbers if the system of equations y z a 2x , x z b 2y , c x y c 2z is consistent and b = 4a + , then the absolute value of sum of roots of the equation 4 ax2 bx c 0 , is equal to (1) 1 (2) 2 (3) 3 (4) 4 9 1 24. Let the term independent of x in the expansion of x2 has the value p and q be the sum of the x coefficients of its middle terms then (p-q) equals 9 9 (1) 0 (2) 2.9 C4 (3) C5 (4) C3 Page 4 SPACE FOR ROUGH WORK JEE-MAINS TEST PAPER 25. Consider the ten numbers ar,ar 2 ,ar 3 ,.......ar10 if their sum is 18 and the sum of their reciprocals is 6 then the product of these ten number, is (1) 324 (2) 343 (3) 243 (4) 729 4 0 0 If A is a square matrix such that A (adj. A) = 0 4 0 , then adj(adj.A) 26. is equal to adj.A 0 0 4 (1) 256 (2) 64 (3) 32 (4) 16 1 27. For x R,x 0,x 1, let f0 (x) and fn 1 (x) f0 (fn (x)),n 0,1,2..... then the value of 1 x 2 3 f100 (3) f1 f2 is equal to 3 2 8 5 1 4 (1) (2) (3) (4) 3 3 3 3 28. If the parabola y2 2ax(a 0) meets the rectangular hyperbola xy 4 2 orthogonally then the value of ‘a’ is (1) 2 (2) 2 (3) 2 2 (4) 4 4 1 29. Let B = , then which of the following will not be an element of B100? 9 2 (1) 300 (2) 301 (3) -299 (4) 100 30. Number of ways in which three distinct numbers can be selected between 1 and 20 both inclusive whose sum is even is (1) 120 (2) 450 (3) 570 (4) 620 Page 5 SPACE FOR ROUGH WORK JEE-MAINS TEST PAPER PHYSICS SECTION - B 31. If time period measured are 8.01sec and 8.41 sec using a stop watch having least count 0.01 sec then find best reported time in second. (1) 8.2 0.2 (2) 8.41 0.01 (3) 8.01 0.01 (4) 8.2 0.01 32. Five identical capacitor plates, each of area A are arranged such that adjacent plates are at a distance d apart, the plates are connected to a source of emf V as shown. The charge on plate 4 is 20AV 20AV 0 AV 0AV (1) (2) (3) (4) d d d d 33. Choose correct statement regarding straight line motion while symbols have their usual meaning: (1) if a =- 3ms-2 then the motion must be retarded motion (2) If a particle is project vertically up towards positive y-axis than acceleration will be negative at the time of ascent and positive at the time of its decent. (3) When velocity is zero acceleration must be zero. (4) motion is said to be retarded motion when a and v have opposite sign. 34. A rectangular loop carrying a current I is situated near a long straight wire, such that the wire is parallel to one of the sides of the loop and is in the plane of the loop. If steady current I is established in the wire as shown in the figure, the loop will: (1) rotate about an axis parallel to wire (2) Move away from the wire (3) Move towards the wire (4) remain stationary Page 6 SPACE FOR ROUGH WORK JEE-MAINS TEST PAPER 35. Find the value of ‘R’ for which current in 6 resistor will be zero 16 15 14 13 (1) (2) (3) (4) 5 4 3 3 36. What is the minimum energy required to launch a satellite of mass ‘m’ and radius ‘R’ in a circular orbit at an altitude ‘3R’ GMm GMm 7GMm 8GMm (1) (2) (3) (4) 3R 4R 8R 7R 37. The amplitude of a damped oscillator decreases to half of its original length in 3 sec. then in next 4sec. it becomes times of original amplitude where will be: 1 1 1 1 (1) (2) (3) (4) 8 4 16 32 u 38. A wall is moving with velocity u and a source of sound moves with velocity in the same direction as 2 shown in the figure. Assuming that the sound travels with velocity10u. The ratio of incident sound wavelength on the wall to the reflected sound wavelength by the wall, is equal to: (1) 9:11 (2) 11:9 (3) 4:5 (4) 5:4 39. A thin semicircular conducting ring of radius R is falling with its plane vertical in a horizontal magnetic induction B At the position MNQ the speed of the of the ring is v and the potential difference developed across the ring is : (1) zero (2) BvR2 / 2 and M is at higher potential (3) BRv and Q is at higher potential (4) 2RBv and Q is at higher potential Page 7 SPACE FOR ROUGH WORK JEE-MAINS TEST PAPER 40. A block of ice at 10o C is slowly heated and converted to steam at 100o C which of the following curves represent the phenomena qualitatively [T=temperature, H =Heat applied] (1) (2) (3) (4) 41. The magnitude of potential energy per unit mass of the object at the surface of the earth is E and the escape velocity of the object is Ve find the correct graph (1) (2) (3) (4) 42. A bullet of mass m and charge q is fired towards a fixed solid uniformly charged sphere of radius R and total charge + q. If it strikes the surface of sphere with speed u. Find the minimum speed u so that it can penetrate through the sphere,(neglect all resistance or friction acting on bullet except electrostatic force) q q 3q 3q (1) (2) (3) (4) 20 mR 40 mR 20 mR 40mR 43. In a region of space magnetic field exists in a cylindrical region having axis of the cylinder parallel to the z axis, of radius a centered at origin. the field is given by: B B0 tk the force experienced by a stationary charge q placed at (r,0,0) where r > a is: qB0a 2 q,B0 r (1) qB0 (2) (3) (4) zero 2r 2 Page 8 SPACE FOR ROUGH WORK JEE-MAINS TEST PAPER 44. A metallic rod of length ( ) is tied to a string of length (3 ) and made to rotate with constant angular velocity () on horizontal table with one end of the string is fixed. There is a vertical magnetic field B in the region, the emf induced across the ends of the rod is: B 2 7B 2 5B 2 (1) B V (2) (3) (4) 2 2 2 45. In the circuit shown, the current through: (1) the 3 resistor is 0.50A (2) the 3 resistor is 0.25A (3) the 4 resistor is 0.50A (4) the 4 resistor is 0.25A 46. An unpolarised beam of light of intensity I is incident on a set of four polarising plates such that each plate makes an angle of / 3 with preceding sheet. The intensity of light transmitted through the combination is: 1 1 1 1 (1) (2) (3) (4) 64 128 32 256 47. In figure s is a monochromatic source emitting light of wavelength 500 nm and a thin lens of focal length 0.10 m is cut into identical halves. The two halves are placed symmetrically about the central axis So with a gap of d =0.5 mm. the distance of the lens from S is 0.15 m and that from O is 1.30 m if the third intensity maximum occurs at a point A on the screen (Perpendicular to So), find the distance OA. (1) 0.5 mm (2) 1.0 mm (3) 1.5 mm (4) 2.0mm 48. A radioactive sample P having activity 10 C ha twice the number of nuclei as another sample Q which has an activity 20 C the half lives of P and Q can be: (1) 20 years and 5 years respectively (2) 20 years and 10 years respectively (3) 10 years each (4) 5 years each Page 9 SPACE FOR ROUGH WORK JEE-MAINS TEST PAPER 49. A proton when accelerated through 24000V has wavelength associated with it An Particle in order to have the same wave length must be accelerated through: (1) 24000V (2) 9600V (3) 12000V (4) 3000V 50. In a hydrogen atom, the binding energy of electron in the ground state is E1 ,then the frequency of revolution of the electron in the nth orbit is: 2E1 2E1n3 2mE1 E1n2 (1) (2) (3) (4) n3h h n3h h 51. An X ray tube is operated at 6.6KV in the continuous spectrum of the emitted X-rays which of the following frequency will be missing. (1) 0.1018 Hz (2) 1.5 1018 Hz (3) 1.2 1018 Hz (4) 1.6 1018 Hz 52. A transistor is connected in common emitter configuration. The collector supply is 8V and the voltage drop across a resister of 800 in the collector circuit is 0.5 V if the current gain factor is 0.96,then the base currents is: (1) 20A (2) 26A (3) 30A (4) 35A 53. A light emitting diode has a voltage drop of volt across it and passes a current of 10 mA when it operates with 6 volt battery through a limiting resistor R. the value of R is (1) 40 (2) 4K (3) 200 (4) 400 54. There is a spherical cavity of radius R / 2 in uniformly charged spherical region having charge q 0 is released at point C, centre of the cavity then it will collide with the wall of the cavity with kinetic energy R 2q0 R 2q0 R 2q0 R 2q0 (1) (2) (3) (4) 30 60 40 120 55. If the TV-Telecast is cover a radius of 120km then the height of the transmitting antenna is (use radius of the earth Re = 6400km) (1) 1900 m (2) 1125 m (3) 900 m (4) 80 m Page 10 SPACE FOR ROUGH WORK JEE-MAINS TEST PAPER 56. An emf of 15 volt is applied in a circuit containing 5 Henry inductance and 10 resistance. the ratio of the current at time t = and t =1 sec. is : e1/2 e2 (1) (2) (3) 1 e1 (4) e1 e1/2 1 e2 1 57. An LCR series circuit with a resistance of 100 5 is connected to an AC-source of 200 V when the capacitor is removed from the circuit, current lags behind emf by 45o when the inductor is removed is removed from the circuit, keeping capacitor and resistor in the circuit current leads by an angle of 1 tan1 .then the current in the LCR circuit will be: 2 (1) 2A (2) 0.8A (3) 5A (4) 0.1A 58. The graph as shown represents the variation of temperature (T) of the bodies X and Y having same surface area with time (t) due to emission of radiation. Find the correct relation between emissivity and absorptivity power of the two bodies. (1) Ex Ey anda x a y (2) Ex Ey anda x a y (3) Ex Ey anda x a y (4) Ex Ey anda x a y 59. Soft iron is preferred as the core of transformers due to its: (1) high retentivity, high coercivity (2) high retentivity, low coercivity (3) low retentivity, high coercivity (4) low retentivity, low coercivity 60. EM wave can be Produced by: (1) stationary charge (2) charge moving with constant velocity (3) Oscillating charge (4) None Page 11 SPACE FOR ROUGH WORK JEE-MAINS TEST PAPER CHEMISTRY SECTION - C 61. In an fcc crystal, which of the following shaded planes contains the following type of arrangement of atoms? (1) (2) (3) (4) 62. Calculate the e. m. f. (in V) of the Galvanic cell: Pt | H2 (g) | BOH aq || HA aq | H2 g | Pt; 0.1bar 1M 0.1M 1bar Given; K a (HA) 10 ,Kb (BOH) 10 ] 7 5 (1) 0.39V (2) 0.36V (3) 0.93V (4) 0.63V 63. A purified pepsin (Protein containing several amino acids) isolated from bovine preparation was introduced in the amino acid analysis. It was seen that 0.43 g of lysine (mol.wt = 146) was present in 100g of pepsin. Therefore minimum molecular weight of approximately is : (1) 34000 (2) 39000 (3) 40,000 (4) 46000 64. A particular state of system is arrived at starting from a given state in two different ways (1) through reversible path and (2) irreversible path. Which of the following relations would be correct if the process are isothermal? (1) Srev Sirrev (2) qrev qirrev qrev qirrev (3) Srev Sirrev (4) Sirrev Srev T T 65. The order with respect to a reaction having the following data is t (s) 0 50 100 Conc.(mol L-1) 0.68 0.34 0.17 (1) Zero (2) 1 (3) 2 (4) 3 Page 12 SPACE FOR ROUGH WORK JEE-MAINS TEST PAPER 66. A liquid mixture having composition corresponding to point Z in the figure shown is subjected to distillation at constant pressure. Which of the following statement is correct about the process? (1) the composition of distillate differs from the mixture. (2) the boiling point goes on changing (3) the mixture has highest vapour pressure than for any other composition (4) Composition of an azeotrope alters on changing the external pressure. 67. The gas A2 in the left glass bulb allowed to react with gas B2 present in right glass bulb as shown in figure: A2(g) B2(g) 2AB(g) ;Kc 4at 27o C What is the concentration of AB(g) when equilibrium is established (1) 1.33M (2) 2.66M (3) 0.66M (4) 0.33M 68. Which of the following molecules is most suitable to disperse benzene in water (1) (2) (3) (4) Page 13 SPACE FOR ROUGH WORK JEE-MAINS TEST PAPER 69. Consider the given figure showing the formation of H2 ion depending on internuclear distance versus potential energy of the system. Select the correct statement: (1) Curve 1 represents the most stable state of the system of H2 ion (2) Curve 2 represents the most stable state of the system of H2 ion (3) Curve 1 indicates that the molecular hydrogen ion is formed (4) Curve 2 represents the energy level of the antibonding region 70. Which of the following is not obtained by direct reaction of constituent elements? (1) XeF2 (2) XeF4 (3) XeO3 (4) XeF6 71. The Ellingham diagram for zinc, magnesium and carbon converting into corresponding oxides is shown below At 11000 C, which reaction is spontaneous to a maximum extent? (1) MgO C Mg CO (2) ZnO C Zn CO (3) MgO Zn Mg ZnO (4) ZnO Mg MgO Zn 72. (x) K2CO3 Air Heat (Y) CO2 (Y) Cl 2 (Z)Pink KCl which of the following is correct? (1) X black,MnO2 ,Y Blue, K2CrO4 ,Z KMnO4 (2) X green,Cr2O3 ,Y Yellow, K2CrO4 ,Z K2Cr2O7 (3) X black,MnO2 ,Y green,K2MnO4 ,Z KMnO4 (4) X black;Bi2O3 ,Y Colourless,KBiO2 ,Z KBiO3 Page 14 SPACE FOR ROUGH WORK JEE-MAINS TEST PAPER How many geometrical isomers are possible for complex Mab(AB)2 n 73. (1) 5 (2) 4 (3) 3 (4) 6 74. In which of the following transformations, the bond order has increased and the magnetic behavior has changed? (1) C2 C2 (2) NO NO (3) O2 O2 (4) N2 N2 75. X3Y2 (i 5) When reacted with A2 B3 (i 5) in aqueous gives brown colour. These are separated by a semipermeable membrane AB as shown. Due to osmosis there is (1) brown colour formation in side X (2) brown colour formation in side Y (3) formation in both of the sides X and Y (4) no brown colour formation 76. Wave function of an orbital is plotted against the distance from nucleus. The graphical representation is for ____ orbital: (1) 1s (2) 2s (3) 3s (4) 2P 77. The percentage of ammonia obtained, if equilibrium were to be established during the Haber’s process, is plotted against the operating pressure for two temperatures, 400o C and 500o C .Which of the following graph correctly represents the process? (1) (2) Page 15 SPACE FOR ROUGH WORK JEE-MAINS TEST PAPER (3) (4) 1 78. A gas expands adiabatically at constant pressure such that T , The value of the gas is V (1) 1.30 (2) 1.50 (3) 1.70 (4) 2 79. In which of the following arrangements, the order is not correct according to the property indicated against it: (1) Increasing size: Al3 Mg2 Na F (2) Increasing I.E.1: B C N O (3) Increasing E.A.1: I Br F Cl (4) Increasing metallic radius: Li Na K Rb 80. The straight chain polymer is formed by: (1) Hydrolysis of (CH3 )SiCl2 followed by condensation polymerization. (2) Hydrolysis of (CH3 )3 SiCl followed by condensation polymerization. (3) Hydrolysis of CH3SiCl3 followed by condensation polymerization. (4) Hydrolysis of (CH3 )4 Si by addition polymerization 81. In given compound which of the following electronic effects is absent: (1) Inductive effect (2) Resonance effect (3) Hyperconjugative effect (4) Negative mesomeric effect Page 16 SPACE FOR ROUGH WORK JEE-MAINS TEST PAPER 82. Butaclamol is potent antipsychotic that has been used clinically in the treatment of schizophrenia. Although patints are given a racemic mixture of the drug, only the (+) – enantiomer has pharmacological activity. How many chiral centres does butaclamol have? (1) 1 (2) 2 (3) 3 (4) 4 83. In the Newman projection for 2,2 -Dichlorobutane Which one statement is correct? (1) If ‘X’ is H then ‘Y’ will be CH3 (2) If ‘X’ is H then ‘Y’ will be Cl (3) If ‘X’ is H then ‘Y’ will be C2 H5 (4) If ‘X’ is Cl then ‘Y’ will be CH3 84. Consider the following carbocation, If we assume that all possible rearrangements are taking place by various shifts, then which of the following rearranged carbocation cannot be formed, (1) (2) (3) (4) Page 17 SPACE FOR ROUGH WORK JEE-MAINS TEST PAPER 85. SN 2 reaction will be observes in (1) (2) (3) (4) (racemisation in reaction mixture) 86. The structure of product (P) is (1) (2) (3) (4) 87. In cannizzaro reaction given below 2PhCHO :OH PhCH2OH PhCO2 the slowest step is: (1) the transfer of hydride to the carbonyl group (2) the abstraction of proton from the carboxylic group (3) the deprotonation of PhCH2OH (4) the attack of : OH at the carboxyl group 88. The most basic ‘N’ is (1) p (2) q (3) r (4) s Page 18 SPACE FOR ROUGH WORK JEE-MAINS TEST PAPER 89. The following compound on hydrolysis will give (1) A pair of anomers (2) A pair of enantiomers (3) A pair of epimers (4) A pair of molecules having common tautomer 90. Nylon 6,10 is prepared by the condensation polymerization of : (1) adipic acid and hexamethylene diamine (2) sebacic acid and hexamethylene diamine (3) sebacic acid and hexamethylene amine (4) adipic acid and hexamethylene amine Page 19 SPACE FOR ROUGH WORK DATE :- 04 / 04 2018 JEE-MAINS ANSWER & SOLUTION Page 1