Practice Test 02 _ Test Paper __ Arjuna JEE 2025.pdf

Arjuna JEE (2025) PRACTICE TEST - 02 DURATION ::180 DURATION Minutes 90 Minutes DATE : 09/06/2024 M.MARKS : 300...

Arjuna JEE (2025) PRACTICE TEST - 02 DURATION ::180 DURATION Minutes 90 Minutes DATE : 09/06/2024 M.MARKS : 300 Topics Covered Physics: Units and Measurements (Complete Chapter), Mathematical Tools (Complete Chapter) Chemistry: Structure of Atom (Full Chapter) Mathematics: Sets (Complete Chapter), Relation Function (Complete Chapter) General Instructions: 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 the question paper, Section I, II & III consisting of Section-I (Physics), Section-II (Chemistry), Section-III (Mathematics) and having 30 questions in each part in which first 20 questions are compulsory and are of Objective Type and Last 10 questions are integers type in which you have to attempt 5 questions only. 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 MCQ 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. 9. Do not fold or make any stray mark on the Answer Sheet (OMR). OMR Instructions: 1. Use blue/black dark ballpoint pens. 2. Darken the bubbles completely. Don't put a tick mark or a cross mark where it is specified that you fill the bubbles completely. Half-filled or over-filled bubbles will not be read by the software. 3. Never use pencils to mark your answers. 4. Never use whiteners to rectify filling errors as they may disrupt the scanning and evaluation process. 5. Writing on the OMR Sheet is permitted on the specified area only and even small marks other than the specified area may create problems during the evaluation. 6. Multiple markings will be treated as invalid responses. 7. Do not fold or make any stray mark on the Answer Sheet (OMR). Name of the Student (In CAPITALS) : _______________________________________________________________ Roll Number : _____________________________________________________________________________________________ OMR Bar Code Number : ________________________________________________________________________________ Candidate’s Signature : _______________________________ Invigilator’s Signature _____________________  Section-I (PHYSICS) Single Correct Type Questions (1)  MLT 2  (2)  ML3T 3  1. Turpentine oil is flowing through a tube of length     l and radius r. The pressure difference between (3)  ML2T 3  (4)  ML1T 1  the two ends of the tube is p. The viscosity of oil is given by    p r 2  x2  , where v is velocity 7. Which of the following physical quantities has 4vl same unit in all the three system of units? of oil at a distance x from the axis of the tube. The (1) Mass dimensional formula of viscosity is (2) Length (3) Time (1)  M 0 L0T 0  (2)  M 1 L1T 1  (4) None of these (3)  ML2T 1  (4)  M 1 L1T 1     t2 8. The dimensions of in the equation F .  v 2 2. Young's modulus of steel is 1.9 1011 Nm2. When where F is the force, v is velocity and t is time, is expressed in cgs units of dyne cm2 , it will be (1)  MLT 1  (2)  ML1T 2  equal to (1) 1.9 1010 (2) 1.9 1011 (3)  ML3T 4  (4)  ML2T 4  (3) 1.9 1012 (4) 1.9 1013 3. If the speed of light (c), acceleration due to gravity 9. If the value of force is 100 N and value of (g) and pressure (p) are taken as fundamental units, acceleration is 0.001 ms–2, what is the value of the dimensions of gravitational constant (G) are - mass in this system of units? (1) 103 kg (2) 104 kg (1) c 0 gp 3 (2) c 2 g 3 p 2 5 (3) 10 kg (4) 106 kg (3) c 0 g 2 p 1 (4) c 2 g 2 p 2 10. Taking into account the significant figures, what is 4. A physical quantity P is given by the the value of (9.99 m – 0.0099 m)? relation. P  P0e  t  2 If t denotes the time, the (1) 9.98 m (2) 9.980 m dimensions of constant  are (3) 9.9 m (1) [T] (2) [T2] (4) 9.9801 m (3) [T–1] (4) [T–2] 11. At x  0 , value of slope is 5. Statement I: Number of significant figures in 0.005 is one and that in 0.500 is three. Statement II: Zeros are not significant. Choose the correct option from the following. (1) Both statement I and statement II are true and statement II is the correct explanation of statement I. (1) 0 (2) 1 (2) Both statement I and statement II are true but (3) –1 (4) Infinite statement II is not the correct explanation of statement I. Find the value of 1  x  1/2 12. if x  1 (3) Statement I is true but statement II is false. (4) Both statement I and statement II are false.  x (1) 1   (2) 1  x   2 1 6. A force is represented by F  ax 2  bt 2 where x =  x  x (3) 1   (4) 1   distance and t = time. The dimensions of b2 / a  2  3 are: 13. P-V graph for ideal gas at constant temperature is 18. Determine the position where potential energy will n {ideal gas eq PV = nRT} be minimum if U(x) = 100 – 50x + 1000x2 J. (1) 0.25 102 (2) 2.5 102 (3) 2.5 101 (4) 250 102 (1) 19. Derivative of given function w.r.t. the independent 2x  1 variable is z  2 x 1 2 x 2  2 x  2 (1)  x2  1 2 (2) 2 x 2  2 x  2 (2)  x2  1 2 (3) 2 x 2  2 x  2 (3)  x  12 2 x 2  2 x  2  x2  1 (4) (4) 20. Use a definite integral to find the area of the region 14. The slope of v  t is zero at point between the given curve and the x -axis on the interval [0, b] y = 2x (1) A (2) B (3) C (4) D 15. Convert angle from radian to degree (1) b 2 (2) b3 4 rad : b3 3 (3) 2b 2 (4) 3 (1) 120 (2) 240 (3) 150 (4) 0 Integer Type Questions 21. Energy of a particle is 5J. If unit of length and time 16. Number of fundamental units in SI system is are doubled and unit of mass is halved then (1) 2 (2) 3 numerical value of the energy in this new system (3) 4 (4) 7 will be 5n. Value of n is. 17. First derivative and second derivative of given 22. The speed of light (C), gravitational constant (G) functions w.r.t. Corresponding independent and planks constant (h) are taken as fundamental variable is: y  sin x  cos x unit in system. The dimension of time in this new (1) cos x  cos x, sin x  sin x system is G a hbC c , the magnitude of value of (2) sin x  sin x, sin x  cos x a  b  c is x find x. (3) cos x  sin x, sin x  cos x 10 (4) sin x  cos x, cos x  cos x 23. Number of significant figures in 0.007m2 is___.  tan 28. Find angle (in degrees) subtended by a circular arc 24. If y  , then find the value of y , if   10  of radius 6 cm and length  cm at its centre. dy 25. Find at  0,3 for given equation dv dx 29. Find at t = 2, if v = 2t2 + 4t dt y 2 e2 x  3 y  x 2 30. According to Joule's law of heating, heat produced 26. Find the value of cos105  cos 75. H = I2Rt, where I is current, R is resistance and t is time. If the errors in the measurement of I, R and t are 3%, 4% and 6% respectively then error (in %) 27. Evaluate the following integral in the measurement of H is  /3 0 sec x tan xdx Section-II (CHEMISTRY) Single Correct Type Questions 36. The order of filling of electrons in the orbitals of 31. Statement I: Bohr model is applicable only for an atom will be single electron species. (1) 3d, 4s, 4p, 4d, 5s Statement II: Bohr model could not explain (2) 4s, 3d, 4p, 5s, 4d Zeeman effect. (3) 5s, 4p, 3d, 4d, 5s (1) Statement I is true but statement II is false (4) 3d, 4p, 4s, 4d, 5s (2) Statement II is true but statement I is false (3) Statement I and statement II both are false 37. The orbital angular momentum of an electron in (4) Statement I and statement II both are true 2s orbital is 1 h 14 and 14 (1) . (2) 0 32. 6 C 7 N are the examples of 2 2 (1) isobars (2) isotopes h h (3) isotones (4) None of these (3) (4) 2 2 2 33. Photon of which light has maximum energy: 38. The following graph is plotted for ns-orbital. (1) Red (2) Blue (3) Violet (4) Green 34. Which of the following is/are drawbacks of Thomson's model of atom? (1) Thomson consider mass to be evenly spread across the atom. (2) It does not reflect the movement of electrons. The value of n will be: (1) 1 (2) 2 (3) It could not explain the stability of an (3) 3 (4) 4 atom... (4) All of these 39. If the radius of the 3rd orbit of Li 2 ion is x, then find the radius of the 1st orbit of He in 35. Which of the following conclusions could not be terms of x. derived from Rutherfords  -particle scattering x x experiment? (1) (2) 8 6 (1) Most of the space in the atom is empty. 5x 7x (3) (4) (2) The radius of the atom is about 1010 m 8 8 while that of nucleus is 1015 m. 40. The first emission line in the atomic spectrum of (3) Electrons move in a circular path of fixed hydrogen in the Balmer Series appears at energy called orbits 9R H 7R H (4) Electrons and the nucleus are held together (1) cm 1 (2) cm 1 400 144 by electrostatic forces of attraction 3R H 5R H (3) cm 1 (4) cm 1 4 36 41. According to the Aufbau principle: 48. The orbitals identified by quantum number n (1) electrons enter the lowest available energy and l, (i) n = 4, l = 1 (ii) n = 4, l = 0 (iii) n = 3, l = level. 2 (iv) n = 3, l = 1 can be placed in the order of (2) only two electrons can occupy an orbital. increasing energy as: (3) orbitals are regions where one is likely to (1) (i) < (ii) < (iii) < (iv) find an electron. (2) (iv) < (iii) < (ii) < (i) (4) electrons tend to remain unpaired. (3) (iv) < (ii) < (iii) < (i) (4) (iv) < (i) < (ii) < (iii) 42. Which of the following orbitals have the equal numbers of radial and angular nodes? 49. The uncertainty in position and velocity of a (1) 4p (2) 3p particle are 1011 m and 5.27 × 1024 ms1 , (3) 4f (4) 6f respectively. The minimum mass of the particle (in kg) is: 43. The principal quantum number describes: (1) 2 (2) 1 (1) Energy and size of the orbital (3) 3 (4) 0.1 (2) The shape of the orbital (3) Spatial orientation of the orbital 50. For a given value of azimuthal quantum (4) The spin of the electron number l, the total number of values of the magnetic quantum number m are given by: 44. The ratio of energies of first excited state of He (1) l + 1 (2) 2l + 1 ion and ground state of H-atom is: (3) 2l – 1 (4) l + 2 (1) 1 : 1 (2) 4 : 1 (3) 1 : 4 (4) 16 : 1 Integer Type Questions 51. An atom has d8 configuration. The maximum 45. Which of the following is not permissible? number of electrons in the same spin is: (1) n = 4, l = 3, m = 0 (2) n = 3, l = 2, m = 1 52. The work function (  ) of some metals is listed (3) n = 4, l = 4, m = 1 below. The number of metals which will show (4) n = 3, l = 0, m = 0 photoelectric effect when light of 300 nm wavelength falls on the metals is 46. Match the Column-I with Column-II. 53. In Bohr's model, the atomic radius of the first orbit of hydrogen atom is y, the radius of the 3rd orbit of hydrogen atom is ny. What is the value of n. (1) (I)(R), (II)(S), (III)(P), (IV)(Q) (2) (I)(Q), (II)(P), (III)(S), (IV)(R) 54. What will be the number of angular nodes for 4f (3) (I)(S), (II)(R), (III)(P), (IV)(Q) atomic orbital? (4) (I)(P), (II)(Q), (III)(S), (IV)(R) 55. An atom of aluminium has an atomic number of 47. The momentum of a particle which has a de 13 and a mass number of 27. How many neutrons Broglie wavelength of 0.1 nm is: (h = 6.6 × does it have? 1034 Js) 56. When the excited electrons of a H atom from n = (1) 3.2 10–24 kg ms1 5 drops the ground state, the maximum number (2) 4.3 10–22 kg ms1 of emission lines observed are _____. (3) 5.3 10–22 kg ms1 57. The number of electrons present in all the (4) 6.6 10–24 kg ms1 completely filled subshells having n = 4 and s = +1/2 is _____. (where n = principal quantum number and s = spin quantum number) 58. The energy of one mole of photons of radiation 59. How many electrons are present in the orbitals of frequency 2 × 1012 Hz in J mol1 is ______ with l = 2 in Cr? (Nearest integer) (Given: h = 6.626 × 1034 60. A moving particle is associated with wavelength Js, N A = 6.022 × 1023 mol1 ) 5 × 108 m. If its momentum is reduced to half of its value, compoute the new wavelength. If answer is 10 x then find x. Section-III (MATHEMATICS) Single Correct Type Questions (1) , 61. If A = {1, 2, 4}, B = {2, 4, 5}, C = {2, 5}, then (A – B) × (B – C) is (2) , , (1) {(1, 2), (1, 5), (2, 5)} (2) {(1, 4)} (3) ,,,, (3) (1, 4) (4)  (4) none of these 68. If A = {1, 3, 4} and 62. Which of the following is a null set? (1) {x :| x | 1, x  N}  B  x : x  R and x 2  7 x  12  0 ,  (2) {x :| x | 5, x  N} then which of the following is true ? (1) A  B (2) A  B (3) x : x2  2 x  1  0, x  R (3) B  A (4) A is equivalent to B (4) None of the above 69. Domain of the function ƒ given by 63. If R is a relation on the set A = {1, 2, 3, 4, 5, 6, 7, 8, ƒ(x) = 2 – |x –5| is 9} given by xRy ⇔ y = 3x, then R = (1) R+ (2) R – {5} (1) {(3, 1), (6, 2), (8, 2), (9, 3)} (3) R – {–5} (4) R (2) {(3, 1), (6, 2), (9, 3)} (3) {(3, 1), (2, 6), (3, 9)} 70. Consider the following relations: (4) none of these (i) A  B  A  ( A  B) (ii) A  ( A  B)  ( A  B) 64. If A = {x : x is a letter in word BELOW}, (iii) A  ( B  C )  ( A  B)  ( A  C ) B = {x : x is a letter in word WOOL} and Which of these is/are correct? C = A – B, then the number of subsets of C is (1) (i) and (ii) (1) 1 (2) 2 (2) (i) and (iii) (3) 3 (4) None of the above (3) (ii) only (4) (ii) and (iii) 65. If A = {1, 2, 3}, B = {1, 4, 6, 9} and R is a relation from A to B defined by x is greater than y. The 71. Range of sgn (|x|) is range of R is (1) {–1, 0} (2) {–1, 1} (1) {1, 4, 6, 9} (2) {4, 6, 9} (3) {–1} (4) {1, 0} (3) {1} (4) none of these. 72. Given 66. If f ( x)  ax  b , where a and b are integers, n  A  11, n  B   13, n  C   16, n  A  B   3 , f (1)  5 and f (3)  3 , then a and b are respectively n  B  C   6, n  A  C   5 and n  A  B  C   2 (1) a = – 3, b = –1 (2) a = 2, b = 3. If n  A   B  C    p and n  C   A  B   q , (3) a = 2, b = – 3 then value of p  q is (4) a = 0, b = 2 (1) 6 (2) 8 67. If A  , , then P(A) is (3) 10 (4) 12 73. Let A = {1, 2, 3, ….., 45} and R be the relation 'is square of element' on A. Which of the following is 80. If R   x, y  : x, y  Z , x2  y 2  4 is a relation on false? Z, then domain of R is (1) R = {(1, 1), (4, 2), (9, 3), (16, 4), (25, 5), (36, 6)} (1) {0, 1, 2} (2) {0, –1, –2} (2) Domain of R = {1, 4, 9, 16, 25, 36} (3) {–2, –1, 0, 1, 2} (4) none of these (3) Range of R = {1, 2, 3, 4, 5, 6} (4) None of these Integer Type Questions 81. If n  A  B   9, n  A  B   10 and 74. In a city, 20 per cent of the population travels by n  A  B   24 , then n  A  B   car, 50 per cent travels by bus and 10 per cent travels by both car and bus. Then persons travelling by car or bus is: 82. If n(U )  50, n( A)  20, n(( A  B)')  18 then (1) 80% (2) 40% n(B – A) is (3) 60% (4) 70% 83. Two finite sets have m and n elements. The number 75. If A   x : 2 x  1  13, x  R , of subsets of the first set is 240 more than that of m B   x : 4  3 x  2, x  R and C   2,4  5,10  the second set. The value of is equal to n then which of following false? (1) A  B   2,6  84. There are 280 members in a club, each have at least (2) A  C   , 2   4,5  one beverage, 100 of them drink tea and 75 drink tea but not coffee. Then the numbers of members (3) Number of integers in A  B  C is 5 drinking coffee is (4) Number of integers in A  B  C is 4 85. If n(A) = 3, n(B) = 4, then n(A × A × B) is 76. If R is a relation from a finite set A having m elements to a finite set B having n elements, then 86. In a class of 60 students, 30 students like the number of relations from A to B is Mathematics, 25 like Science and 15 like both. (1) 2mn (2) 2mn – 1 Then, the number of students who like either (3) 2mn (4) mn Mathematics or Science is 77. A survey shows that 61% of Indian like cheese 87. If A = {2, 3, 7, 9} and n(A × B) = 12, then the whereas 72% like mangoes. If  % of the Indian number of elements in set B is like both cheese and mangoes then the minimum value of  is (1) 37 (2) 33 88. If A = {1, 2, 3, 4, 5, 7, 8, 9} and B = {2, 4, 6, 7, 9} (3) 61 (4) 38 then find the number of proper subsets of A  B ? 78. Let R be the relation defined on the set W of whole 89. Let A be the sets of the letters in the word numbers by the rule xRy iff 4x + 5y = 20, then “RAIGARH" and B be the sets of the letters in the domain of R is word “PRATAPGARH" then n( A  B) represents (1) {4, 5} (2) {0, 5} (3) {0, 4} (4) {0, 2} 90. In a class 140 students numbered 1 to 140, all even 1 numbered students opted Mathematics course, 79. If 5 x  x   x  and  x    x  , (where {x} and those whose number is divisible by 3 opted Physics 2 [x] are fractional and integral part of x) then x is course and those whose number is divisible 5 opted (1) 1/2 (2) 3/2 Chemistry course. Then the number of student who (3) 5/2 (4) 7/2 did not opt for any of the three courses is PW Web/App - https://smart.link/7wwosivoicgd4 Library- https://smart.link/sdfez8ejd80if