Milestone Test - 01 Test Paper PDF

Class 12th JEE MKJM/12 Milestone Test-01 Phase-1 DURATION: 180 Minutes DATE: 26/05/2024...

Class 12th JEE MKJM/12 Milestone Test-01 Phase-1 DURATION: 180 Minutes DATE: 26/05/2024 M.MARKS: 300 Topic Covered Physics : Electric Charges and Fields Chemistry : Solutions, Organic 11th - Revision (GOC) Mathematics : Determinants, Matrices, Basic Mathematics GENERAL INSTRUCTION 1. Immediately fill in the particulars on this page of the test booklet. 2. The test is of 3 hours duration. 3. The test booklet consists of 90 questions. The maximum marks are 300. 4. There are three sections in this question paper. Sections I, II and III, are of Physics, Chemistry and Mathematics, respectively. Each section consists of 30 questions, of which the first 20 are mandatory and are of Multiple Option type and the last 10 are of integer answer type. You need to attempt any 5 integer type questions (out of 10) in each of the three sections. 5. There is only one correct response for each question. 6. Each correct answer will give 4 marks while 1 Mark will be deducted for a wrong response. 7. No student is allowed to carry any textual material, printed or written, bits of papers, pager, mobile phone, any electronic device, etc. inside the examination room/hall. 8. 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.  SECTION-I (PHYSICS)  Single Correct Type Questions (1-20) field E = E0 xkˆ is applied on the square. The flux 1. A charge particle q1 is at position (2, –1, 3). The passing through the square is electrostatic force on another charged particle q2 at E0 a 3 (1) E0a3 (2) (0, 0, 0) is: (Assume uniformity of units) 2 q1 q2 3 E0 a 2 (1) (2 iˆ − ˆj + 3 kˆ) (3) E0 a (4) 56 π ∈0 3 2 q1 q2 (2) (2 iˆ − ˆj + 3 kˆ) 7. Two equal and like charges when placed 5 cm 56 14 π ∈0 apart experience a repulsive force of 0.144 newton. q1 q2 ˆ (3) ( j − 2 iˆ − 3 kˆ) The magnitude of the charge in microcoulomb will 56 π ∈0 be : q1 q2 (1) 0.2 (2) 2 (4) ( ˆj − 2 iˆ − 3 kˆ) (3) 20 (4) 12 56 14 π ∈0 8. Two spherical shells A and B respectively of radii 2. Three charge 4q, Q and q are placed in a straight 2 cm and 4 cm are charged equally, then the ratio line of length  at points distance 0, /2 and  of charge density on the surfaces of the two shells respectively. First and second charge are fixed at respectively will be - (1) 1 : 2 (2) 4 : 1 their location what should be the value of Q in (3) 8 : 1 (4) 1 : 4 order to make the net force on charge q to be zero? (1) –q (2) –2q 9. A charged water drop of radius 0.1 µm is under (3) –q/2 (4) 4q equilibrium in some electric field. The charge on the drop is equivalent to electronic charge. The 3. The electric field intensity due to a uniformly intensity of electric field is approximated charged sphere is zero: (g = 10 m/s2)- (1) at the centre of sphere only (1) 1.61 NC–1 (2) 26.2 NC–1 (2) at infinity only (3) 262 NC–1 (4) 1610 NC–1 (3) at the centre and at infinite distance  10. An electric dipole of dipole moment p , is placed (4) on the surface of sphere  in an electric field E and is in stable equilibrium. 4. Two large sized charged plates made of dielectric The torque required to maintain this dipole at a material have a charge density of +σ and -σ. The position at angle θ from its initial position will be- resultant force on the proton (charge e) located (1) pE cos θ (2) pE sin θ midway between them will be - (3) pE tan θ (4) –pE cosθ (1) σe/ε0 (2) σe/2ε0 11. Eight point charges (can be assumed as small (3) 2σe/ε0 (4) zero spheres uniformly charged and their centres at the corner of the cube) having values q each are fixed 5. The maximum electric field intensity on the axis of at vertices of a cube. The electric flux through a uniformly charged ring of charge q and radius R square surface ABCD of the cube is will be: 1 q 1 2q (1) (2) 4πε 0 3 3R 2 4πε 0 3R 2 1 2q 1 3q (3) (4) 4πε 0 3 3R 2 4πε 0 2 3R 2 q q (1) (2) 6. A square of side 'a' is lying in xy plane such that 24 ∈0 12 ∈0 two of its sides are lying on the axis. If an electric q q (3) (4) 6 ∈0 8 ∈0 12. Two infinite linear charges are placed parallel at 0.1m calculate the time period of oscillation when the apart. If each has charge density of 5µ C/m, then the bob is slightly displace from its mean position is : force per unit length on one of linear charges in N/m is: (1) 2.5 (2) 3.25 (3) 4.5 (4) 7.5 13. Total charge on a uniformly charged sphere of radius 10 cm is 1 µC. The maximum electric field due to the sphere in N/C will be - (1) 9 × 10–5 (2) 9 × 103  (1) 2π (3) 9 × 105 (4) 9 × 1015 g 14. A charged particle of charge q and mass m is    (2) 2π   released from rest in an uniform electric field E.  qE  Neglecting the effect of gravity, the kinetic energy  g + m  of the charged particle after time ‘t’ seconds is    (3) 2π   Eqm E 2 q 2t 2  qE  (1) (2)  g − t 2m m  2E 2t 2 Eq 2 m  (3) (4) (4) 2π mq 2t 2 2  qE  g2 +     m  15. An electric dipole of moment p is placed at the origin along the positive x-axis. If the angle made 18. The force on a charge situated on the axis of a by electric field produced by the dipole with dipole is F. If the charge is shifted to double the positive x-axis at a point Q, whose position vector distance, the acting force will be - makes an angle θ with positive x-axis, is (α + θ) (1) 4F (2) F/2 then (3) F/4 (4) F/8 θ (1) tanα = tanθ (2) α = 2 19. A charged wire is bent in the from of a semi- tan θ circular arc of radius a. If charge per unit length is (3) tan α = (4) α = θ 2 λ coulomb/metre, the electric field at the centre O is : 16. The intensity of an electric field at some point λ λ (1) (2) distant r from the axis of infinite long line charge 2 π 2 aε 0 4π2 ε 0 a distribution having charge per unit length as q will λ be : (3) (4) zero 2πε 0 a (1) proportional to r2 (2) proportional to r3 20. Statement I: Electrostatic field lines originate from (3) inversely proportional to r. positive charges and terminate on negative charges. (4) inversely proportional to r2. Statement II: Electrostatic field lines at a point represent the direction of the force experienced by a 17. A simple pendulum has a length , mass of bob m. positive test charge placed in the field. The bob is given a charge q coulomb. The (1) Statement I is true and Statement II is true pendulum is suspended in a uniform horizontal (2) Statement I is true and Statement II is false electric field of strength E as shown in figure, then (3) Statement I is false and Statement II is true (4) Statement I is false and Statement II is false Integer Type Questions (21 to 30) string of length 10 10 m. Find tension in the 21. Eight point charges, 1µC, –7µC, –4µC, 10µC, string (in N). (Ignore gravitational interaction) 2µC, –5µC, –3µC and 6µC are situated at the eight corners of a cube of side 20 cm. A spherical 26. Four charges equal to –Q each are placed at the surface of radius 80 cm encloses this cube. The four corners of a square and a charge q is at its centre of the sphere coincides with the centre of centre. If the system is in equilibrium, the value of ( ) the cube. Then the total outgoing flux from the Q q is 1 + x. Value of x is equal to _______. spherical surface (in Nm2/C) is- 4 22. A closed cylinder of radius R and length L is 27. Two charges of charge Q each are placed at two placed in a uniform electric field E which is of the opposite corners of a square. A charge q parallel to the axis of the cylinder. Then the net is placed at each of the other two corners. If the electric flux through the cylinder must be equal to net electrical force on Q is zero, then xπR2E. Value of x is ____. Q magnitude of is equal to n. Value of n is q 23. A solid non-conducting sphere of radius R, having _____. R a spherical cavity of radius , such that centre of 2 28. Two identical charged spheres are suspended in R cavity is at distance from centre of original the vertical plane by strings of equal lengths. The 2 strings make an angle of 30º with each other from sphere carries a uniformly distributed net charge suspended point. When suspended in a liquid of equal to q. The electric field at the centre of the density 0.8 g cm–3, the angle remains the same. If cavity is E. If there were no cavity and charge density of the material of the sphere is 1.6 g cm–3, remains same (q), the field at the same point will the dielectric constant of the liquid is _______. x be E. Value of x + y is equal to _____. x and y y 29. Two point charges placed at a distance r in air are co-prime numbers. exert a force F on each other. The value of distance R at which they experience force 4F when 24. Electric field in a region is given by placed in a medium of dielectric constant K = 16 is  E=− 4 xiˆ + 6 y ˆj. Then the charge enclosed in r equal to. Value of n is equal to ______. the cube of side 1m oriented as shown in the n diagram is equal to xε0. Value of x is ______. (Assume all quantities in SI units) 30. The diagram shows two charges q1 and q2 with an electrostatic field line originating at q1 and terminating at q2 as shown in the figure. The ratio q1 of magnitudes of charges that is is equal to q2 _________. 25. Two charge particles having charges 2mC and 3mC respectively are kept on smooth horizontal surface and both are connected with the help of  SECTION-II (CHEMISTRY) Single Correct Type Questions (31-50) 36. Statement 1: Ice melts at 0° C, 1 atm if NaCl is 1 1 poured on it. 31. The plots of (on y-axis) vs. (on x-axis) XA YA Statement 2: The freezing point of water is where X A and YA are the mole fraction of liquid lowered on addition of NaCl. A in liquid and vapour phase respectively is (1) Statement 1 is True, Statement 2 is True; linear with slope and intercepts respectively: Statement 2 is correct explanation for (PA0 - PB0 ) Statement 1 (1) PA0 / PB0    and (2) Statement 1 is True, Statement 2 is True; PB0 Statement 2 is not correct explanation for (PB0 - PA0 ) (2) PA0 / PB0    and Statement 1 PB0 (3) Statement 1 is True, Statement 2 is False (PA0 - PB0 ) (4) Statement 1 is False, Statement 2 is True (3) PB0 / PA0    and PB0 37. Match the following Column-I and Column-II (PB0 - PA0 ) (4) PB0 / PA0    and Column-I Column-II PB0 A Raoult’s law p Effect of pressure on 32. Which of the following liquid pair shows a the solubility of gas in positive deviation from Raoult’s law? liquid (1) Water-nitric acid B Henry’s law q=PT X A Pº A + X B Pº B (2) Acetone-chloroform (3) Water-hydrochloric acid C HNO3 + Water r Positive deviation from (4) Benzene-methanol raoults law D Bromo Benzene + s Negative deviation 33. Consider the following carbanions Chloro benzene from raoults law (I) CH 3O CH 2 A B C D (1) p q r s (II) O2 N CH2 (2) r s p q (3) q p s q (III) CH2 (4) s r q p Correct order of stability is 38. In the following carbocations, the stability order (1) I > II > III (2) III > II > I is: (3) II > III > I (4) I > III > II CH3 + 34. The stability of 2,3-dimethyl but-2-ene is more (I) RCH 2 C H 2 (II) C+ than 2-butene. This can be explained in terms of : CH3 (1) Resonance (2) Hyperconjugation (3) Electromeric effect + (4) Inductive effect only (III) C + (IV) CH2 35. As a result of osmosis, the volume of the concentrated solution: (1) Gradually decreases (1) III > II > IV > I (2) Gradually increases (2) IV > I > II > III (3) Suddenly increases (3) IV > III > II > I (4) None of these (4) III > IV > II > I [ 5] 39. Heterolysis of carbon-chlorine bond produces: 44. The stability of the free radicals allyl, benzyl, (1) Two free radicals (5αH)3°, (3αH)2°, (2αH)1° and CH 3 is in the (2) Two carbonium ions order (3) Two carbanions (1) Benzyl > allyl > 3° > 2° > 1° > CH 3 (4) One cation and one anion (2) Allyl > 3° > benzyl > 2° > 1° > CH 3 40. The most unlikely representation of resonance (3) 3° > 2° > 1° > CH 3 >allyl > benzyl structure of p -nitrophenoxide ion is : – (4) 3º > 2º > 1º > CH 3 > allyl = benzyl O – O O O + + 45. The correct order of increasing basicity of the N N given conjugate bases (R= CH 3 ) is (1) (2) (1) RCOO < HC ≡ C < R < NH 2 (2) R < HC ≡ C < RCOO < NH 2 O O – – (3) RCOO < NH 2 < HC ≡ C < R O O O O + + (4) RCOO < HC ≡ C < NH 2 < R N N 46. Which of the following orders is not correct (3) (4) regarding the – 𝐼𝐼 effect of the substitutents? O– (1) − I > −Cl > −Br > −F O – + + (2) − N R 3 < – O R 2 41. The vapour pressure of CCl4 at 25°C is 143 mm (3) − NR 2 < –OR < − F of Hg if 0.5g of a non-volatile solute (mol. wt = 65) is + dissolved in 100 mL CCl4. Find the vapour (4) −SR < −OR < − O R 2 pressure of the solution. 47. Which of the following species is paramagnetic? (Density of CCl4 = 1.58 g / cm3 ) (1) A carbocation (1) 94.39 mm of Hg (2) A free radical (2) 141.93 mm of Hg (3) A carbanion ion (3) 134.44 mm of Hg (4) All of these (4) 199.34 mm of Hg 48. Electrophiles are : 42. 1.0 g of a non-electrolyte solute (molar mass (1) Electron loving species 250 g mol−1 ) was dissolved in 51.2 g of benzene. (2) Electron hating species If the freezing point depression constant of (3) Nucleus loving reagents benzene is 5.12 K kg mol−1 , the lowering in (4) Electron rich species freezing point will be : (1) 0.5 K (2) 0.2 K 49. The stabilization due to resonance is maximum in: (3) 0.4 K (4) 0.3 K (1) Cyclohexane (2) Cyclohexene 43. The reaction which is not the example of (3) 1,3-cyclohexadiene nucleophilic substitution among the following is (4) 1,3,5-cyclohexatriene (1) CH3 − Br + CH3OH → CH3 − OCH3 + HBr 50. Electromeric effect is (2) CH 3 − Cl + aq.KOH → CH 3 − OH + KCl (1) Permanent effect (3) Cl (2) Temporary effect + alc. KOH + KCl + H 2O (3) Resonance effect (4) Br + aq. KOH OH + KBr (4) Inductive effect Integer Type Questions (51-60) 56. The total number of isomeric carbocations 51. What is the total number of moles of H 2SO 4 possible for the formula C4 H 9+ is : needed to prepare 5.0 L of a 2.0 M solution of H 2SO 4 ? 57. The total number of α-hydrogen (involving –C–H bonds) for the following carbocation is H 3C + CH CH 52. How many gram of NaOH will be required to 2 3 w prepare 500 g solution containing 10% NaOH w solution? 53. The vapour pressure of benzene at 90 °C is 1020 58. Find the percentage degree of dissociation of 0.1 M torr. A solution of 5 g of a solute in 58.5 g Ba(NO3)2 solution having van’t Hoff factor 2.54. benzene has vapour pressure 990 torr. The molecular weight of the solute is : (in gm/mol) 59. 95 g of NaCl is dissolved in 1 kg water, if k f for water is 1.86 K kg mol−1. Find the depression in 54. How many of the following statements are correct? freezing point of the solution. (Nearest integer) I. Hexa-1, 5-diene is a conjugated diene II. Propa-1, 2-diene is conjugated diene 60. At 88º C , benzene has a vapour pressure of 900 III. Hexa-1, 3-diene is a conjugated diene torr and toluene has a vapour pressure of 360 torr. IV. Buta-1, 3-diene is an isolated diene What is the mole percent of benzene in the V. Propa-1, 2-diene is a cumulative diene mixture with toluene that will boil at 88ºC at 1 atm pressure, benzene-toluene form an ideal 55. The number of 𝜋𝜋-electrons involved in resonance solution? (Nearest Integer) in benzene molecule is : SECTION-III (MATHEMATICS ) Single Correct Type Questions (61-80) 2 1 1 −2 1   cos 2θ – sin 2θ  63. If A =   and B =  3 2  , then ( AB )T 61. Inverse of the matrix   is  2 1 3  1 1   sin 2θ cos 2θ  cos 2θ – sin 2θ  is equal to (1)    sin 2θ cos 2θ   −3 −2   −3 10  (1)   (2)    cos 2θ sin 2θ  10 7   −2 7  (2)   sin 2θ − cos 2θ   −3 7  1 0  (3)   (4)   sin 2θ – cos 2θ  10 2  0 1  (3)    cos 2θ sin 2θ  64. If log10 2 = 0.3010, then log5 64 =  cos 2θ sin 2θ  (4)    − sin 2θ cos 2θ  602 233 (1) (2) 233 602 202 633 62. The solution set of the equation (3) (4) ( ) 633 202 log1/3 x 2 + x + 1 + 1 =0, is (1) (0, 1) 1 1 If A =   and n ∈ N , then A is equal to 5 65. (2) [−1, 2] 1 1 (3) {−2, 1} (1) 25A (2) 24A (4) (−∞, ∞) (3) 5A (4) 52A  66. Statement I : For any square matrix B, B –BT is (1) Det ( A ) = 0 skew- symmetric matrix (2) Det ( A ) ∈ ( −∞,0 ) Statement II : For any square matrix A, A + AT is symmetric matrix. (3) Det ( A ) ∈ [ 2, 4] (1) Statement I is correct and Statement II is (4) Det ( A ) ∈ [ −2, ∞ ) incorrect (2) Statement I is incorrect and Statement II is 3 9 27 correct (3) Statement I is correct and Statement II is 71. The value of 2 6 39 is correct 5 15 42 (4) Statement I is incorrect and Statement II is (1) 0 (2) 239 incorrect (3) –35 (4) 134 67. If D diag [ d1 , d 2 , d3 ,…, d n ] , where = 72. If A3×3 = 3 then, match the column −1 di ≠ 0 ∀ i= 1, 2,…, n then D is equal to Column-I Column-II (1) D 2A = 9 I P (2) I n 2 AAT = 18 (3) diag  d1−1 , d 2−1 , d3−1 ,…, d n−1  II Q   (4) diag [ – d1 , – d 2 , – d3 ,…, – d n ] III 2adj A = R 24 IV 3A−1 = S 72 1 − 2   and f ( t ) = t − 3t + 7, then 2 68. If A=  I II III IV  4    5  (1) P Q R S  3        6  f ( A) +   is equal to (2) Q S R P  −12 −9  (3) R S S P 1  0   0  0  (4) Q S P R (1)   (2)   0 1 0   0  x a b + c  0 1 1 1   (3)   (4)   73. Matrix A =  x b c + a  , is non invertible if 1   0  0  0   x c a + b  (1) x = a (2) x = b b2c 2 bc b+c (3) x = c (4) x has any value 69. c2a2 ca c + a is equal to a 2b 2 ab a + b  2 1   −3 2  1 0 74. If   A = 1  , then the matrix 1  3 2   5 −3 0 (1) ( ab + bc + ca ) A equals abc (2) ab + bc + ca 1 1  1 1 (1)   0 1 (2) (3) 0 1 0   (4) a + b + c 1 0  0 1 (3)   (4)  1 1  1 1  1 sin θ 1  Let A =−  sin θ  , where 70.  sin θ 1 75. The solution set of x – 1 < 1 − x , for x ∈ R is  −1 − sin θ 1  (1) ( −∞, ∞ ) (2) ( 0,∞ ) 0 ≤ θ < 2 π. Then, which of the following is correct? (3) ( −1, ∞ ) (4) φ 76. The set of values of x for which the inequalities 1   2   3   −1   − 2  =   A = [ Pij ]  2   3   4   −2    0     −4 − 5 − 6  , x − 3 x − 10 < 0 and 10 x − x − 16 > 0 hold 2 2    0       0     1  simultaneously, is  3   4   5   0   − 4  (1) (–2, 5) (2) (2, 8) then P22 is equal to (3) (–2, 8) (4) (2, 5)  a    b  83. The value of 2 log3 7 − 7log3 2 is 77. If A =   is such that | A | = 0 and  c   d  1 0 0  A − ( a + d ) A + kI = 2 O, then k is equal to 84. If A = 0 α 2  and A3 = 125, then positive   (1) b +c (2) a + d 0 2 α  + cd (3) ab    (4) Zero value of α is 78. The set of all real x satisfying the inequality 85. If ( x + x + 4)(3 − x) 2 3 1 2 ( x − 1) 3 ( x − 1)( x − 2 ) >0 ( x + 1)(4 − x) 4 f ( x ) =− x 1 ( x − 1)( x − 2 ) ( x − 1)( x − 2 )( x − 3) x ( x − 1) x ( x − 1)( x − 2 ) (1) ( −∞, 3) ∪ ( 4, ∞ ) (2) ( −∞, −4 ) ∪ ( 4, ∞ ) x Then, the value of f (49) is (3) ( −∞, −3) ∪ ( 4, ∞ ) (4) ( −∞, −3) ∪ ( 3, ∞ ) 86. The value of determinant α 0  1 0  If A =  and B =   , then value of α 79.  0 d 2d 1 1 5 1  3d 4d 5d where d ≠ 0, is equal to for which A2 = B is 6d 7d 8d (1) 1 (2) −1 (3) 4 (4) No real value 1 2 3 3 7 10 The value of λ such that x + 3 y + λz =0, ∆′ 80. 87. If ∆ = 2 5 7 and ∆′ = 2 5 7 , then = ∆ 2x + 4 y − = z 0, x + 5 y − 2= z 0 has a non-zero 3 9 13 3 9 13 solution is (1) 1 (2) −1 log x logy log z 88. If = = , then x a −b. y b −c.z c − a = 3 a+b b+c c+a (3) 0 (4) 2 89. If A and B are square matrices of order 3 such Integer Type Questions (81-90) that A = −1, B =3, then 3 AB + 100 equals 81. The number of real solutions of 2| x −1| = 3| x −1| is 90. The number of solutions of 3x = –x is 82. If matrix Kindly Share Your Feedback For this Paper  PW Web/App - https://smart.link/7wwosivoicgd4 Library- https://smart.link/sdfez8ejd80if