JEE Main 2023-24 Full Test-1 (Physics, Chemistry, Mathematics) PDF

JEE MAIN-2023-24 (FULL TEST-1) 1 (Physics, Chemistry and Mathematics) FULL TEST...

JEE MAIN-2023-24 (FULL TEST-1) 1 (Physics, Chemistry and Mathematics) FULL TEST CLASS-XI Date :-................ Time :- 3:00 Hrs. Marks :- 300 Important Instructions : 1. The test duration is of 3 hours. 2. The Test Booklet consists of 90 questions. The maximum marks are 300. 3. There are three parts in the question paper consisting of Physics, Chemistry and Mathematics having 30 questions in each part of equal weightage. Each part (subject) has two sections. (i) Section-A: This section contains 20 multiple choice questions which have only one correct answer. Each question carries 4 marks for correct answer and –1 mark for wrong answer. (ii) Section-B: This section contains 10 questions. In Section-B, attempt any five questions out of 10. The answer to each of the questions is a numerical value. Each question carries 4 marks for correct answer and –1 mark for wrong answer. For Section-B, the answer should be rounded off to the nearest integer. Student’s Name :-............................................................................................................................ School Name :-................................................................................................................................. Student’s Signature :-......................... Invigilator’s Signature :-............................  CAMPUS EDUCATION A SANJAY BAGDE GROUP OF INSTITUTE Head Office: E101, World of Mother Behind Jay Ganesh Vision Akurdi Pune - 411035. Mobile: 9822312073 E-mail: [email protected] PHYSICS (SECTION-A) 1. A sinusoidal travelling wave in a string has a 6. The displacement of two identical particles velocity of propogation 300 m/sec. The time executing SHM are represented by equations period of oscillations of the particles of the string is 0.04 sec. Then the phase difference   between the oscillations of two points at x1 = 4 sin 10t   and x2 = 5 cos t  6 distances 10 m and 16 m respectively from source of oscillation is : For what value of  energy of both the (A) /2 (B) 2 (C) /4 (D)  particles is same ? (A) 16 unit (B) 6 unit 2. A rod of mass m (uniformly distributed) and (C) 4 unit (D) 8 unit length  is in equilibrium between two vertical walls as shown in figure. 7. A particle covers a distance in a straight line with uniform acceleration. Find maximum possible speed at midpoint of path, if particle’s average speed is u for the motion.  S (A) 2 u (B) 2u (C) u (D) none of these d PU One wall has a small pulley. All surfaces are smooth. Distance between wall is d. Find cos . 8. A ball of mass 3kg is suspended from a bar of same mass with a light in extensible cord. 1 1 Initially system is held at rest as shown.  d 3  2d  3 (A)   (B)   m     3 3 M  d  2d  (C)   (D)       450 m 3. A cubical block of wood weighs 13kg and has Find the tension in string just after system is a relative density 0.6. It is to be in water with A released. Wedge is fixed and there is no 0.9 of its volume immersed. What mass of a metal is needed to be attached to bottom of friction between any surface. (g = 10 m/s2) wood. (Relative density of metal = 14) mg 2mg (A) 6kg (B) 6.5kg (A) (B) C 3 3 (C) 5kg (D) 7kg mg (C) (D) mg 4. A horizontal spring–block system of mass 2kg 2 executes S.H.M. When the block is passing through its equilibrium position, an object of 9. A variable force F = 5t (t is sec) is acting on a mass 1kg is put gently on it and the two move uniform solid sphere of mass 1kg, which is together. The new amplitude of vibration is (A placed at a rough horizontal surface ( = 0.6). being its initial amplitude) : F is acting horizontally in the line of centre of 2 3 (A) A (B) A sphere. 3 2 A m = 1 kg (C) 2A (D) 2 F = 5t 5. What is the Young's modulus of elasticity for a  = 0.6 perfectly rigid body ? (A) infinity (B) zero What will the possible a vs t graph ? (a is (C) 1 (D) – 1 acceleration of centre sphere) PG #1  CAMPUS EDUCATION A SANJAY BAGDE GROUP OF INSTITUTE Head Office: E101, World of Mother Behind Jay Ganesh Vision Akurdi Pune - 411035. Mobile: 9822312073 E-mail: [email protected] a 13. An ideal gas whose internal energy U is at absolute zero temperature is equal to zero undergoes a reversible adiabatic compression. (A) If U, P, V, T represents the internal energy, pressure, volume and absolute temperature t a  CP  respectively for ideal gas then       CV  (B) (A) UV = constant (B) UP = constant t (C) TU = constant a 1  1 (D) VU = constant (C) 14. A soap bubble is blown slowly at end of a tube by a pump supplying air at a constant rate. t Which one of the graph represents the correct a variation of the excess pressure inside bubble S with time. (D) P 10. t PU If  represents the co-efficient of viscosity (A) t and S surface tension, then the dimension of P S is same as that of  (B) M (A) speed (B) time t (C) length (D) length × speed P 11. A rectangular plate has length (4 ± 0.04) cm A and width (2 ± 0.02) cm. The maximum (C) percentage error in the measurement of its area is – t (A) 2% (B) 6% P C (C) 3% (D) 4% (D) 12. A particle is projected from point 'A' with t velocity u 2 at an angle of 45º with the horizontal as shown in the figure. It strikes the 15. P – V diagram of ideal monoatomic gas is as inclined plane BC at right angle. The velocity shown. Find net heat given to the gas in the of the particle just before the collision with the process ABC. inclined is : P B 3P0 P0 C A V V0 3V0 3 u u 2u (A) 2P0V0 (B) 5P0V0 (A) (B) (C) (D) u 2 2 3 (C) 6P0V0 (D) 7P0V0 PG #2  CAMPUS EDUCATION A SANJAY BAGDE GROUP OF INSTITUTE Head Office: E101, World of Mother Behind Jay Ganesh Vision Akurdi Pune - 411035. Mobile: 9822312073 E-mail: [email protected] 16. Two forks A and B when sounded together 20. Two beads A and B move along a semicircular produce 4 beats/s. The fork A is in unison with wire frame as shown in figure. The beads are 30cm length of a sonometer wire and B is in connected by an inelastic string which always unison with 25cm length of the same wire at the same tension. What can be frequency of remains tight. At an instant the speed of A is u, forks. BAC = 45° and BOC = 75°, where O is the (A) fA = 20 HZ, fB = 24 HZ centre of the semicircular arc. The speed of (B) fA = 24 HZ, fB = 20 HZ (C) fA can be 20 HZ or 24 HZ bead B at that instant is : (D) fA = 16 HZ, fB = 20 HZ 17. A block of mass m is given a velocity towards another block of mass M kept at rest on a smooth horizontal surface at same distance from a wall. All collisions are elastic. To occur only one collision between blocks. Which of the following correct ? (A) 2 u (B) u u 2 (C) (D) u S 2 2 3 (SECTION-B) →u m M PU (A) u has to be less than a given value 21. A particle is projected towards north with speed 20m/s at an angle 45º with horizontal. (B) M ≤ 3m Ball get horizontal acceleration of 7.5 m/s2 (C) M ≥ 3m towards east due to wind. Range of ball (in (D) u has to be greater than a given value meter) minus 42 m will be – M 18. A uniform rod of length  is applied upon by 22. A movable conducting piston is inserted in a two horizontal forces at both ends end as cylinder closed on both ends. One end of the cylinder contains m grams of a certain gas and shown, on a smooth horizontal surface. Which the other 2m grams of the same gas. Find the A of the following option is correct. ratio of volume occupied by 2m grams of the gas to the volume occupied by m grams of the F→ →F gas. C (A) uniform stress will developed at each cross 23. A transverse sinusoidal wave move along a section string in the positive x-direction at a speed (B) length of rod will increase 5cm/s. The wavelength of the wave 0.2m and (C) centre of mass of rod will shift towards its amplitude is 5cm. At given instant velocity right on rod (D) centre of mass of rod will shift towards left of P is v (cm/s) and acceleration is a (cm/s2) on rod   when its displacement is 2.5cm. If  v. a  is 19. Rain is falling with speed a 10m/s at an angle   of 45º with vertical. A bird moving up with a given by x 3 3 cm2/s3, find the value of 100 constant speed at some angle with horizontal x. observes rain is falling vertically. Another bird y moving vertically with 5m/s, find first bird moving horizontally. Find speed of first bird. All motion are in same vertical plane. (A) 5m/s (B) 5 3 m/s x (C) 5 2 m/s   (D) 5 2  1 m/s P PG #3  CAMPUS EDUCATION A SANJAY BAGDE GROUP OF INSTITUTE Head Office: E101, World of Mother Behind Jay Ganesh Vision Akurdi Pune - 411035. Mobile: 9822312073 E-mail: [email protected] 24. A particle hanging from a string of length  is 2m 1m A B projected with speed g horizontally at 4m bottom most point. Find radial acceleration of particle in m/s2, when tension in the string equals weight of the particle. [g = 10m/s2] P 25. A particle is moved along the path. AB-BO- 28. A sphere of mass m = 0.5 kg carrying positive OA, in the presence of force   charge q = 110 µC is connected with a light,   F    2 y i  3x j  N. Find the work done flexible and inextensible spring of length r =   60cm and whirled in a vertical circle. If a (in J) by force F on particle. vertically upwards electric field of strength y (in m) E = 105 N/C exists in the space then the (0,3) A B minimum velocity of sphere in m/s required at highest point so that it may just complete the x(in m) O (2,0) circle is (g = 10 m/s2) S 26. A diatomic molecule can be modelled as two PU 29. A satellite is revolving round the earth in a rigid ball connected with spring such that the circular orbit of radius ‘a’ with velocity v0. A ball can vibrate with respect to centre of mass particle is projected from satellite in a forward of the system (spring + balls). Consider a direction with relative velocity diatomic gas contain such diatomic molecule.  5  If gas performs 20 Joule work under isobaric v =  – 1 v. Then it is found that the  4  0 condition, then heat given to the gas (in Joule)   is. maximum distance of particle from earth's M na centre is. Then the value of n is 27. Two small sound sources A and B emit pure 3 sinusoidal waves in phase. If the speed of sound is 350 m/s, for what minimum 30. A ball of mass m moving with K.E. 3J frequency does destructive interference occur undergoes head on collision with another A at point P. Answer is in the form of n × 102 Hz. stationary ball of mass 2m. During impact What is n ? maximum potential energy of system can be – C PG #4  CAMPUS EDUCATION A SANJAY BAGDE GROUP OF INSTITUTE Head Office: E101, World of Mother Behind Jay Ganesh Vision Akurdi Pune - 411035. Mobile: 9822312073 E-mail: [email protected] CHEMISTRY SECTION-A 31. Which concentration term is temperature 39. What is the correct IUPAC name of the following independent? compound (A) Molarity (B) % w/v Cl (C) % v/v (D) Oleum labelling 32. Which of the following molecule does not exist? (A) (2E, 4Z, 6Z)-4-chloro octa-2, 4, 6-triene (A) PF5 (B) NOF3 (B) (2Z, 4E, 6E-5-chloro octa-2, 4, 6-triene (C) FCl3 (D) NO2Cl (C) (2E, 4E, 6Z)-4-chloro octa-2, 4, 6-triene (D) (2Z, 4Z, 6E-5-chloro octa-2, 4, 6-triene 33. Select the correct statement regarding B2H6. (A) It has only 2C – 2e– bond 40. The hybridisation of orbitals of N atom in NO3¯, (B) It is planar NO2+ and NH4+ are respectively? (C) It does not react with NH3. (A) sp, sp2 and sp3 (B) sp2, sp and sp3 3 (C) sp, sp and sp 2 (D) sp2, sp3 and sp (D) Hybridisation of boron is sp3 34. Give the correct order of initials T (true) or F (false) 41. The most acidic oxide is : (A) SO3 (B) P2O5 (C) Cl2O7 (D) P2O3 for following statements. S (i) The ratio of the radii of the first three Bohr orbit 42. In a collection of 'H' atoms all electrons jumps from of hydrogen atom is 1 : 8 : 27 n = 5 to finally ground level (directly or indirectly) (ii) The ratio of magnitude of Total Energy : Kinetic then its wavelength is 500 nm PU Energy : Potential Energy for any orbit is 1 : 1 : 2 (iii) The frequency of a green light is 6 × 1014 Hz, without emitting any line in Paschen series the number of possible different radiations are (A) 7 (B) 8 (C) 6 (D) 5 (iv) The ratio of de-broglie wavelength of a 'H' atom, CH 3  CH 2  CH 2  CH  COOH 'He' atom and CH4 molecule moving with equal | kinetic energy is 4 : 2 : 1 CH 2 | (A) FFTT (B) FTFT (C) TFTF (D) FTTT M 43. CO | 35. The correct order of bond angle is : OH Number of carbon in selected principal carbon chain (A) ClO 2  ClO 2  ClO 2 for IUPAC nomenclature will be (B) ClO 2  ClO 2  ClO 2 (A) 3 (B) 4 (C) 5 (D) 6 A (C) ClO 2  ClO 2  ClO 2 44. What combination of diene and dienophile would (D) ClO 2  ClO 2  ClO 2 you choose in order to prepare the following compound? C 36. Which of the following would produce cyclic silicone on hydrolysis? (A) (CH3)3SiCl (B) SiCl4 (C) (CH3)2SiCl2 (D) All of these 37. The equivalent mass of HCl as per the following (A) redox reaction (in terms of its molecular mass 'M') is given by : HCl + KMnO4 — MnCl2 + H2O + Cl2 + KCl (B) M M 16M 10M (A) (B) (C) (D) 1 10 10 16 38. The incorrect statement among the following is (C) (A) The first I.P. of Al is less than the 1st I.P. of Mg (B) The 2nd I.P. of Mg is less than the 2nd I.P. of Na (C) The |E.A.| of oxygen is greater than that of chlorine. (D) (D) the b.p. of H2O2 is greater than H2O. PG #5  CAMPUS EDUCATION A SANJAY BAGDE GROUP OF INSTITUTE Head Office: E101, World of Mother Behind Jay Ganesh Vision Akurdi Pune - 411035. Mobile: 9822312073 E-mail: [email protected] 45. If reaction quotient (Q) < 1 then which of the (SECTION-B) following statements is correct : 51. Calculate the molarity of H+ ions obtained by mixing (A) G > G° (B) G = G° 200 ml of 0.5 M H 2 SO 4 solution (C) G° > G (D) Can't comment (dsolution = x gm/ml), 100 ml of 0.7 M HNO3 solution (dsolution = 1.2 x gm/ml) and 100 ml of 0.3 M HCl 46. Pressure of CO2(g) (in bar) over a sample of solution (dsolution = 1.3 x gm/ml) such that density CaCO3(s) at 2727°C if G° = –57.575 kJ/mol for of final solution is 1.5 x gm/ml. 25 reaction : [Given : R = J/mol-K] 52. Equilibrium constant for the reaction : 3 CaCO3(s) CaO(s) + CO2(g) 1 1 l 2 I2(g) + Br2(g) IBr(g) 2 l (A) 10–2 (B) 101 (C) 10 (D) 102 Can be represented by 47. Which halogen in its reference state will have  170.2  log K°P =   0.1  greatest absolute entropy per mole  T  (A) Fluorine (B) Chlorine Find |rG°| for the reaction. (in kJ/mol) (C) Bromine (D) Iodine [Take : R = 8.3 J/mol-K, ln10 = 2.3] [Round off your answer to nearest integer] 48. Which of the following structure is least stable? 53. What volume of 0.02 M Ba(OH)2 should be mixed S (A) with 40 ml of 0.02 M NaOH & 20 ml of 0.01 M HNO3 to get solution that contain pH = 12.3 (B) PU [Use : log 2 = 0.3] 54. How many alkene an catalytic hydrogenation give (C) iso-pentane as a product. 55. In 50 ml of 0.2 M - H2A solution, 10 ml of 0.5 M - (D) NaOH solution is added at 25°C. The pH of resulting M solution is (for H2A, K a1 = 10–6; K a 2 = 10–12) 49. Which alcohol when heated with H2SO4, will undergo dehydration more rapidly. 56. How many stereoisomer may have this natural occuring compound. A (A) 57. 1 gm of an iron ore containing 50% ferrous (Fe2+) and ferric ion (Fe3+) and rest 50% impurities was dissolved in concentrated hydrochloric acid and the filtered solution was raised to 100 ml in flask. 50 C (B) ml of the solution were treated with M/10 K2Cr2O7, (C) Ph–CH2–CH2–OH which give titre value of 5 ml. Find the percentage of ferric ion in the ore. OH | 58. An aqueous solution which is 20% (w/w) and 30% CH  CH 3 (w/v) in NaOH. What will be mass fraction of water (D) in 30 ml of such solution. 50. One mole of an ideal gas is subjected to adiabatic 59. Ionisation energy and electron affinity of fluorine expansion from initial state of (10 atm, 300K) to final are respectively 17.42 eV and 3.45 eV, then pressure of 1 atm against constant external pressure. electronegativity of F atom on Pauling scale will be Which of the following options contain correct (nearest integer) change in thermodynamics parameters for the above process. 60. The given molecule is 4 CF2 = C = C = C = C = CH2 (Given :  of gas = ) Find the maximum number of nodal plane of -bonds 3 (A) U = 270 R (B) S = R ln 10 those are lying in the plane perpendicular to the (C) H = 230 R (D) w = – 202.5 R molecular plane. PG #6  CAMPUS EDUCATION A SANJAY BAGDE GROUP OF INSTITUTE Head Office: E101, World of Mother Behind Jay Ganesh Vision Akurdi Pune - 411035. Mobile: 9822312073 E-mail: [email protected] MATHEMATICS (SECTION-A) 61. The area of the region bounded by the ellipse 69. Equation of latus rectum of hyperbola  2 x  y = 1 and the ordinates x = ±ae where (10 x  5)  (10 y  2)  9(3x  4 y  7) 2 2 2 2 a b2 is b2 = a2 (1 – e2) and e < 1, is given by - 1 3 1 (A) y    x   (A) 2ab (e 1 e 2 + sin–1 e) sq. units 5 4 2 (B) 2ab (e 1 e 2 – sin–1 e) sq. units 1 3 1 (B) y   x  2 –1 5 4 2 (C) ab (e 1 e – sin e) sq. units (D) None of these 1 3 1 (C) y    x  62. Let E = (2n + 1) (2n + 3) (2n + 5)…(4n – 3) (4n – 5 4 2 1) where n > 1. then 2n Eis divisible by 1 3 1 (A) 2nCn (B) 4nC2n (D) y   x  2n (C) Cn/2 (D) 4nCn/2 5 4 2  n n 70. Out of the two roots of 1 4 x  1   4 x  1   S   63. If  1  1 4x  1   2    2     2 x  (1  2 ) x      2  0  2  one root is greater than 3 and the other root is less = a0 + a1x +..... + a5x5, then n equals – (A) 11 (C) 10 (B) 9 PU (D) None of these then 3, then the limits of (A)  2  are (B) 2    5 5 9c (C)  5 (D)   64. If a + b + c > and quadratic equation ax2 + 2 4 2bx – 5c = 0 has non-real roots, then - If the line ax  by  1 passes through point of M 71. (A) a > 0, c > 0 (B) a > 0, c < 0 (C) a < 0, c < 0 (D) a < 0, c > 0 intersection of y  x tan   p sec  , y sin  30     x cos  30     p and 65. Coefficient of x25 in expansion of expression 50 is inclined at 30 with y  tan  x , then the  50 Cr (2x – 3)r(2 – x)50 – r is : A r 0 2 2 value of a  b can be- (A) 50C25 (B) – 50C30 (C) 50C30 (D) – 50C25 1 2 (A) (B) p2 p2 C 66. The number of ways in which a mixed doubles 3 3 tennis game be arranged between 10 players (C) (D) consisting of 6 men and 4 women? 2p2 4p2 (A) 180 (B) 90 (C) 48 (D) 12 72. If a line is drawn through a fixed point 12 18 67. The minimum value of   xy , where P( ,  ) to cut the circle x 2  y2  a 2 at x y x and y are positive real numbers, is – A and B, then find the value of PA.PB is 2 2 2 2 2 2 (A) 12 3 (B) 24 3 (A)     a (B)     a (C) 18 (D) infinity 2 (C)    2  a2 (D) None of these 2 2 68. If the circle x  y  6 x  2 y  k 0 73. If slope of lines represented by bisects the circumference of the circle 2 2 x 2  y 2  2 x  6 y  15  0 , then k ax  2hxy  by  0 are in 1: 3 ratio then (A) 23 (B) 23 h 2 : ab equals - (C) 21 (D) 21 (A) 3 / 4 (B) 1/ 4 (C) 4 / 3 (D) 1 PG #7  CAMPUS EDUCATION A SANJAY BAGDE GROUP OF INSTITUTE Head Office: E101, World of Mother Behind Jay Ganesh Vision Akurdi Pune - 411035. Mobile: 9822312073 E-mail: [email protected] 74. Angle between asymptotes of the hyperbola (SECTION-B) 2 2 81. The first two terms of a geometric progression 3x  y  3 is add up to 12. The sum of the third and the  2 (A) (B) fourth terms is 48. If the terms of the 3 3 geometric progression are alternately positive  3 and negative, then the first term is (c ) (D) 6 4 82. The sides of a right angled triangle are in 75. The point in which the join of A( 9, 4,5) arithmetic progression. If the triangle has area and B(11, 0,1) is met by the perpendicular 24, then what is the length of its smallest side ? from the origin is (A) (2, 2,1) (B) (2,1, 2)  iz  1  83. The radius of the circle Re    2 is (C) (1, 2, 2) (D) (2, 2, 2)  iz  1  76. If x and y respectively denotes the number of 84. A guard of 12 men is formed from a group of n sexagesimal and centesimal seconds in any soldiers in all possible ways. If the number of x times two particular soldiers A and B are angle then is equal to – y together on guard is thrice the number of times S 250 81 there particular soldiers C, D, E are together on (A) (B) guard, then n = 81 250 PU 71 250 85. The number of positive integer (x,y,z) of the (C) (D) 250 71 equation xyz=24 77. If the derivative of f (x) with respect to x is 86. The distance of the point ( 1, 5, 10) from 1 2 the point of intersection of the line, sin x 2 then period of f (x) is x  2 y 1 z  2   and the plane, M f ( x) 3 4 12 (A)  (B) 2 x  y  z  5 , is (C) 3  (D) 4 87. The value of 2 2 2 2 2 cos 33  cos 57 2 tan e  x  tan  e  x A 78. = lim is G.I.F. sin 21  cos 21 x0 sin 2 x 1 1 (A) (B) – 88. The number of real solutions of the equation 2 2 C 22/2  ( 2  1) x  (5  2 2)x /2 is 3 3 (C) (D) – 2 2 89. Let a1,a2,a3,.........,a11 be real numbers satisfying a1 = 15, 27 – 2a2> 0 and ak = 2ak–1 – ak–2 for k =  1  3,4,........,11. 79. lim  x  x 2  3x cos  equals x   | x |  a 2  a22 ....  a112 If 1  90 , then the value of 11 (A) 3 / 2 (B) 3 / 2 a1  a2 ...  a11 (C) 1 (D) None of these is equal to 11 80. For any three positive real numbers a, b and c, 9 (25a2 + b2) + 25 (c2 – 3ac) = 15b (3a + c). 90. Let [t] denote the greatest integer  t. If for Then. some  R – {0, 1}, (A) a, b and c are in G.P. 1 x  x (B) b, c and a are in G.P. lim  L then L is equal to (C) b, c and a are in A.P. x 0   x  x (D) a, b and c are in A.P. PG #8