SR IIT STAR MODEL-A&APEX JEE MAIN 2025 Mock Test

APEX & STAR MODEL-A MOCK TEST-18 Time:3HRS Max. Marks: 300M PHYSICS MAX.MARKS: 100 SECTION – I...

APEX & STAR MODEL-A MOCK TEST-18 Time:3HRS Max. Marks: 300M PHYSICS MAX.MARKS: 100 SECTION – I (SINGLE CORRECT ANSWER TYPE) This section contains 20 multiple choice questions. Each question has 4 options A), B), C) and D) for its answer, out of which ONLY ONE option can be correct. Marking scheme: +4 for correct answer, 0 if not attempted and -1 if not correct. 1. The potential difference between A and B in the circuit shown is 3V 2V B 2 3 10V A 10 A) 10 V B) 5 V C) 15 V D) Zero 2. 12 cells, each of emf 1V and internal resistances of each is 1  , are connected in series such that 2 cells are wrongly connected. The current sent by this battery in a resistance of 4  A) 1 A B) 0.5 A C) 1.5 A D) 3 A 3. The current through 2  will be 2V 1 3V 1 2 A) 1 A B) 2 A C) 1.5 A D) 1.7 A 4. In the circuit shown, the current drawn by the cell is 3 4 10 V 1 5 2 3 A) 1.2 A B) 2.5 A C) 0.6 A D) 3.8 A 5. The given circuit is the part of a certain circuit. The current through resistors are shown. The potential difference VP  VQ is Page 1 of 16  A) 2 V B) 19 V C) 22 V D) 19 V 6. In the circuit shown, the charge on the 3 F capacitor at steady state will be 2 A) 6C B) 4C C) mC D) 3C 3 7. In the circuit shown, C1  1  F , C2  3 F in steady state, the energy stored in these capacitors are respectively A) 6 J , 18 J B) 18 J , 6  J C) 6 J , 6 J D) 18 J , 18 J 8. An ammeter and a milliammeter are converted from identical galvanometers. Which one has smaller resistance? A) Ammeter B) Milliammeter C) Both have equal resistances D) The resistance of ammeter may be more than or equal to that of millimeter depending upon its range 9. In the figure shown, What is the current (in Ampere) drawn from the batter? Your are given: R1  15 , R2  10, R3  20, R4  5, R5  25, R6  30, E  15V Page 2 of 16  13 9 20 7 A) B) C) D) 24 32 3 18 10. Determine the charge on the capacitor in the following circuit. A) 200  C B) 60 C C) 10  C D) 2 C 11. In the figure shown, the current in the 10 V battery is close to A) 0.36 A from negative to positive terminal B) 0.42 A from positive to negative terminal C) 0.71A from positive to negative terminal D) 0.21A from positive to negative terminal 12. A metal wire of resistance 3  is elongated to make a uniform wire of double its previous length. This new wire is now bent and the ends joined to make a circle. If two points on this circle make an angle 60 at the centre, the equivalent resistance between these two points will be 5 5 7 12 A)  B)  C)  D)  3 2 2 5 13. The resistance of a galvanometer is 50  and the maximum current which can be passed through it is 0.002 A. What resistance must be connected to it in order to convert it into an ammeter of range 0  0.5 A ? A) 0.2  B) 0.002  C) 0.5  D) 0.02  14. In a conductor, if the number of conduction electrons per unit volume is 8.5  1028 m3 and mean free time is 25 fs (femto second), its approximate resistivity is m e  9.1  1031 kg  A) 105 m B) 106 m C) 107 m D) 108 m Page 3 of 16 15. Model a torch batter of length l to be made up of a thin cylindrical bar of radius ‘ a ’ and a concentric thin cylindrical shell of radius ‘ b ’ filled in between with an electrolyte of resistivity  (see figure). If the battery is connected to a resistance of value R, the maximum Joule heating in R will take place for  b 2  b   b  b A) R  ln   B) R  ln C) R  ln   D) R  l  a   l  a  2 l  a    2 l  a  16. During an experiment with a metre bridge, the galvanometer shows a null point when the jockey is pressed at 40.0 cm using a standard resistance of 90 , as shown in the figure. The least count of the scale used in the metre bridge is 1 mm. The unknown resistance is A) 60  0.15 B) 135  0.56 C) 60  0.25 D) 135  0.23 17. A part of a circuit is shown in the figure in steady state. The energy stored in the capacitor is A) 1.2 mJ B) 0.4 mJ C) 2 mJ D) 0.8 mJ 18. Find resistance of following carbon resistor A) 26  102  10% B) 62  106  10% C) 26  102  5% D) 62  106  5% Page 4 of 16 19. The current in a wire varies with time according to equation. i  2  2t , where t is in second. The amount of charge which passes through a cross-section of wire during t  0 s to t  2 s is A) 8C B) 4C C) 6C D) 3C th 1 20. A wire is uniformly stretched to make its area of cross-section times  n  0 . n What will be its new resistance? 1 1 A) 2 times B) n2 times C) times D) n times n n SECTION – II (Numerical Value Answer Type) This section contains 5 questions. The answer to each question is a Numerical value. If the Answer in the decimals, Round off to the nearest Integer only. Have to answer any 5 only out of 5 questions and question will be evaluated according to the following marking scheme. Marking scheme: +4 for correct answer, 0 if not attempted and -1 if not correct. 21. In the circuit shown, initially there is no charge on capacitors and keys S1 and S 2 are open. The values of the capacitors are C1  10  F , C2  30  F and C3  C4  80  F. If key S1 is kept closed for long time such that capacitors are fully charged, the voltage across the capacitor C will be 22. Equivalent resistance (in  ) between points A and B is ________. (Given r  10 ) 23. In the following figure, the current in arm AB is _________ Page 5 of 16  10 V 10 V B 2 2 2 2 10 2 A 2 24. In the circuit shown, the value of R in  for which no current flows through the 5 V battery, is _______ 2 10 V R 3 5V 25. AT t  0, capacitor is uncharged. If current through capacitor as function of time is  2t 2V NRC e then find N 3R CHEMISTRY MAX.MARKS: 100 SECTION – I (SINGLE CORRECT ANSWER TYPE) This section contains 20 multiple choice questions. Each question has 4 options A), B), C) and D) for its answer, out of which ONLY ONE option can be correct. Marking scheme: +4 for correct answer, 0 if not attempted and -1 if not correct. 26. Boron compounds behave as Lewis acid because of their A) octet configuration B) covalent nature C) electron deficiency D) ionization property 27. Which statement regarding H 3 BO3 is not correct? A) It is a weak tribasic acid B) It is prepared by acidifying an aqueous solution of borax C) It has a layer structure in which planar BO3 units are joined by H-bonds D) It does not act as proton donor but acts as Lewis acid by accepting OH  ions 28. Which of the following can undergo incomplete hydrolysis A) BI3 B) AlCl3 C) BF3 D) BCl3 Page 6 of 16 29. AlCl3 exists as dimer because A) Al has greater ionization potential B) Al has larger radius C) high charge on the nucleus D) incomplete p-orbital 30. The stability of +1 oxidation state increases in the sequence A) Ga  In  Al  Tl B) Al  Ga  In  Tl C) Tl  In  Ga  Al D) In  Tl  Ga  Al 31. Which of the following oxides is acidic in nature A) B2O3 B) Al2O3 C) Ga2O3 D) In2O3 32. The order of acidic strength of boron trihalides A) BF3  BCl3  BBr3  BI 3 B) BI 3  BBr3  BCl3  BF3 C) BCl3  BBr3  BI 3  BF3 D) BBr3  BCl3  BF3  BI 3 33. Which of the following cation cannot exist in aqueous solution A) Al3+ B) B3+ C) Ga3+ D) In3+ 34. Which of the following is a correct statement about the compounds I and II? CH3 H3C H5C2 C2 H5 H H H C2 H5 H H5 C2 H3C CH3 Liquid - I Liquid - II A) I and II have are optically inactive and identical. B) I and II are optically active and identical. C) I and II are optically active and their mixture cannot be separated by fractional distillation. D) I and II are optically active and their mixture can be separated by fractional distillation. 35. Which of the following structure is the most stable? ++ O H3C A) N B) O H3C C C) N D) Page 7 of 16 36. Which one of the following has no stereo genic center? OH OH A) H B) H C) H D) O 37. What is the IUPAC name for the following compound? H CH2OH CH3 H A) cis – 1 – hydroxy methyl – 3 – methyl cyclohexane B) trans – 1 – hydroxy methyl – 3 – methyl cyclohexane C) trans – 3 – hydroxy methyl – 1 – methyl cyclohexane D) (3-methylcyclohexyl) methanol 38. The correct statement about Cyanic acid (H O C N) and isocyanic acid (H N C O) are: A) They are chain isomers B) They have same conjugate base. C) They differ in the positions of their electrons and represent resonance structures. D) The total number of lone pairs of electrons is different in both. 39. The number of resonance structures is least for + NH2 NH3 OH A) B) C) D) 40. The IUPAC name of the following compound is: H3C CH2 CH3 (H3 CO) 2HC H3C A) (3R)-3-(dimethoxymethyl)-3,4-dimethylpent-1-ene B) (3S)-3-(dimethoxymethyl)-3,4-dimethylpent-1-ene C) (3S)-3-(dimethoxymethyl)-3,4,4-trimethylbut-1-ene D) (3R)-3-(dimethoxymethyl)-3,4,4-trimethylbut-1-ene Page 8 of 16 41. Br2 Br2 CH2 A CH2Br2 CH2 B CH2Br2 singlet triplet In the above reactions the intermediate products A and B are (consider intermediate products containing carbon only): A) A = B = a carbon free radical B) A = B = a carbanion C) A = a carbon free radical, B = a carbanion D) A = a carbanion, B = a carbon free radical 42. The following compound exhibits enantiomerism, but cannot be resolved at normal temperatures. A) Cis – 1,2 – dimethyl cyclohexane B) Trans – 1,4 – dimethyl cyclohexane C) Cis – 1,4 – dimethyl cylcohexane D) Trans – 1,2 – dimethyl cyclopentane 43. Which of the following is not a permissible contributing resonance structure? + - H2C H2C H2C H2C - + - + N O N O N O N O A) H3C B) H3C C) H3C D) H3C 44. In which of the following, forward reaction is favourable? O O CH2 + CH3CH2COOH CH2 + CH3CH2COO- - O OH (pKa = 4.87) Ka (p = 4.3) A) - - - O OH O O O O O + + + + O N N - N N - O O O O + + Me3N O -  Me3 N OH + + - N - N O O O O Ka (p = 1.8) (pKa = 0.7) B) O O - + F 3C O - + F3C OH H3C OH H3C O (pKa = 4.76) (pKa = 12.4) C) Page 9 of 16  O CF3 CF3 O +F C O2N OH + - O2N - OH F 3C O 3 O (pKa = 9.3) (pKa = 1.76) D) 45. What is the correct relation among I, II and III? - O O OH + + HN NH HN NH N N - + - O N O O N O I) H II) HO N OH III) H A) III is a resonance structure of I B) III is conjugate acid of II C) III is a resonance structure of II D) III is conjugate base of II SECTION – II (Numerical Value Answer Type) This section contains 5 questions. The answer to each question is a Numerical value. If the Answer in the decimals, Round off to the nearest Integer only. Have to answer any 5 only out of 5 questions and question will be evaluated according to the following marking scheme. Marking scheme: +4 for correct answer, 0 if not attempted and -1 if not correct. 46. One of the drugs used to treat acquired immune deficiency syndrome (AIDS) is commonly known as AZT and it has the following structure. AZT stands for 3’– azido–3’–deoxythymidine. The number of sigma and pi bonds present in the X Y compound respectively are X and Y. Find the value of 4 47. (i) The number of compounds correctly named from the following is ‘X’. a) (CH 3)2CHCH2CH2CH 2CHO (5-methyl-1-hexanal) b) (CH3)2CHCH2C  C–COOH (5-methyl-2-hexynoic acid) c) CH 3CH2CH 2CH 2CH(CH 3)COOH (2-methylhexanoic acid) d) CH3CH2CH = CH – COCH 3 (3-hexen-5-one) (ii) The correct orders in the following as indicated is ‘Y’. Find the value of X + Y? Page 10 of 16  a) CH3-CH2-NH2 < CH3-CH=NH < CH3-CN (Basic strength) b) CH3-CH3 < CH2=CH2 < CHCH < C2H5-OH (Acidic strength) c) NH3 < (CH3)3N < CH 3-NH2 < (CH 3)2NH (Basic strength) d) PhOH  H2CO3  PhCOOH  HCOOH (Acidic strength) 48. TlI 3 is ionic compound and ionizes completely in aqueous solutions. Find the number of moles of ions furnished by 1.5 moles of the salt in a dilute solution? 49. How many of the following statements are correct with regard to boron? i) Crystalline boron is chemically inert in nature ii) Amorphous boron is chemically active iii) Boron is a good conductor of heat and electricity iv) Boron dissolves in fused alkalies, liberating hydrogen v) Boron is used as a deoxidizer in the casting of copper vi) Boron carbide rods are used to control the nuclear reactions vii) Boron is used as a food preservative viii) Orthoboric acid is used in the preparation of antiseptic lotions 50. How many statements are true for the following pair of compounds? (i) Dipolemoment of trans isomer is zero (ii) Boiling point of cis isomer is more than trans isomer (iii) Cis isomer is more stable than trans isomer (iv) These are also called configurational diastereomers (v) These are readily interconvertible under normal conditions (vi) Melting point of trans isomer is more than cis isomer (vii) Trans isomer is more soluble than cis isomer in polar solvents Page 11 of 16 MATHS MAX.MARKS: 100 SECTION – I (SINGLE CORRECT ANSWER TYPE) This section contains 20 multiple choice questions. Each question has 4 options A), B), C) and D) for its answer, out of which ONLY ONE option can be correct. Marking scheme: +4 for correct answer, 0 if not attempted and -1 if not correct. 51. If a circle passes through the point  a, b  and cuts the circle x 2  y 2  4 orthogonally, then the locus of its centre is A) 2ax  2by   a 2  b2  4   0 B) 2ax  2by   a 2  b2  4   0 C) 2ax  2by   a 2  b 2  4   0 D) 2ax  2by   a 2  b 2  4   0 52. The lengths of the tangent drawn from any point on the circle 15 x 2  15 y 2  48 x  64 y  0 to the two circles 5x 2  5 y 2  24 x  32 y  75  0 and 5x 2  5 y 2  48x  64 y  300  0 are in the ratio of A) 1: 2 B) 2 : 3 C) 3 : 4 D) None of these 53. AB is a focal chord of x 2  2 x  y  2  0 whose focus is S. If AS  l1.Then BS is equal to 4l1 l1 2l1 A) l1 B) C) D) 4l1  1 4l1  1 4l1  1 54. The point  P  1 ,  P ( where  x is the greatest integer less than or equal to x) , lying inside the region bounded by the circle x 2  y 2  2 x  15  0 and x 2  y 2  2 x  7  0 , then A) P   1, 0  [0,1)  [1, 2) B) P  [1, 2)  0,1 C) P   1,2  D) None of these 55. The condition that the parabolas y 2  4ax and y 2  4c  x  b  have a common normal other than x  axis (a, b, c being distinct positive real numbers) is b b b b A) 2 B) 2 C) 1 D) 1 a c ac a c a c 56. The locus of a point divides a chord of slope 2 of the parabola y 2  4 x internally in the ratio 1: 2 is a parabola. Find the vertex of this parabola 4 2 2 2 8 2 2 8 A)  ,  B)  ,  C)  ,  D)  ,  9 9   9 9   9 9   9 9   Page 12 of 16 57. The line through P perpendicular to the chord of contact of tangent drawn from the point P to the parabola y 2  16 x touches the parabola x 2  12 y. The locus of P is 2ax  3 y  4a 2  0, then a is A)2 B) 3 C) 2 D) 4 58. If P and Q are the points of intersection of the circles x 2  y 2  3x  7 y  2 p  5  0 and x 2  y 2  2 x  2 y  p 2  0 then there is a circle passing through P, Q and 1,1 for: A) all except one value of p B) all except two values of p C) exactly one value of p D) all values of p 59. The equation of the common tangent touching the circle  x  32  y 2  9 and the parabola y 2  4 x above the x -axis is A) 3 y  3 x  1 B) 3 y   x  3 C) 3 y  x  3 D) 3 y  3x 1 60. The distance of the point 6, 2 2  from the common tangent y  mx  c, m  0 ,of the curves x  2 y 2 and x  1 y 2 is 1 14 A) B) 5 C) D) 5 3 3 3  3 61. If the point on the curve y 2  6 x, nearest to the point 3,  is ,   , then 2   is  2 equal to 15 A) 9 B) 6 C) 3 D) 2 62. Let P a, b be a point on the parabola y 2  8 x such that the tangent at P passes through the centre of the circle x 2  y 2 10 x 14 y  65  0. Let A be the product of all possible values of a and B be the product of all possible values of b. Then the value of A  B is equal to A) 0 B) 25 C) 40 D) 64 63. The length of the chord of the parabola x 2  4 y having equation x  2 y  4 2  0 is A) 3 2 B) 2 11 C) 8 2 D) 6 3 Page 13 of 16 64. The area (in sq. units) of the smaller of the two circles that touch the parabola, y 2  4 x at the point 1, 2 and the x -axis is: A) 8 2  2  B) 4  2  2  C) 4 3  2  D) 8 3  2 2  65. The locus of the centres of the circles, which touch the circle, x 2  y 2  1 externally, also touch the y  axis and lie in the first quadrant, is A) x  1 4 y , y  0 B) y  1 2 y , x  0 C) y  1  4 x , x  0 D) x  1 2 y , y  0 66. The sum of the squares of the lengths of the chords intercepted on the circle, x 2  y 2  16, by the lines, x  y  n, n  N , where N is the set of all natural numbers, is: A) 320 B) 105 C) 160 D) 210 67. If a circle of radius R passes through the origin O and intersects the coordinate axes at A and B , then the locus of the foot of perpendicular from O on AB is: A)  x 2  y 2   4 R 2 x 2 y 2 B)  x 2  y 2   4 R 2 x 2 y 2 2 3 C)  x 2  y 2   4 Rx 2 y 2 D)  x 2  y 2  x  y   R 2 xy 2 68. Two circles with equal radii are intersecting at the points 0,1 and 0, 1. The tangent at the point 0,1 to one of the circles passes through the centre of the other circle. Then the distance between the centres of these circles is: A) 1 B) 2 C) 2 2 D) 2 69. If y  mx  c is a tangent to the circle  x  32  y 2  1 and also the perpendicular to the  1 1  tangent to the circle x 2  y 2  1 at  ,  , then   2 2  A) c 2  6c  7  0 B) c 2  6c  7  0 C) c 2  6c  7  0 D) c 2  6c  7  0 70. Pair of tangent are drawn from origin to the circle x 2  y 2  8x  4 y 16  0 then square of length of chord of contact is 64 24 8 8 A) B) C) D) 5 5 5 13 Page 14 of 16  SECTION – II (Numerical Value Answer Type) This section contains 5 questions. The answer to each question is a Numerical value. If the Answer in the decimals, Round off to the nearest Integer only. Have to answer any 5 only out of 5 questions and question will be evaluated according to the following marking scheme. Marking scheme: +4 for correct answer, 0 if not attempted and -1 if not correct. 71. Consider the parabola y 2  8 x. Let 1 be the area of the triangle formed by the end 1  points of its latus rectum and the point P  , 2 on the parabola and 2 be the area of 2  the triangle formed by drawing tangents at P and at the end points of the latus. Then 1 is 2 72. An equilateral triangle ABC is inscribed in the parabola y  x 2 and one of the side of the equilateral triangle has the gradient 2. If the sum of x  coordinate s of the p vertices of the triangle is a rational in the form where p and q are coprime, then q find the value of  p  q. 73. The urns A, B and C contain 4 red, 6 black; 5 red, 5 black and  red, 4 black balls respectively. One of the urns is selected at random and a ball is drawn. If the ball drawn is red and the probability that it is drawn from urn C is 0.4 then the square of the length of the side of the largest equilateral triangle, inscribed in the parabola y 2   x with one vertex at the vertex of the parabola is 74. Let y  mx  c, m  0 be the focal chord of y 2  64 x, which is tangent to  x  10  y 2  4 Then, the value of 4 2 m  c is equal to ________ 2 75. Let the function f  x  2 x 2  log3 x, x  0 , be decreasing in 0, a and increasing in  a, 4.  1  A tangent to the parabola y 2  4ax at a point P on it passes through the point  ,0.  a  X Y If the equation of the normal at P is   1, then 2   is equal to ________   Page 15 of 16 Page 16 of 16