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IIT JEE Exam 2026 : Advanced

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Arjuna JEE (2026) Advanced Practice Test 02 DURATION ::180 Minutes DURATION 90 Minutes DATE : 10/08/2025 Adv. Paper-2 M. MARKS : 180 Topics Covered Physics: Motion in a Plane (Complete Chapter), Laws of Motion (Complete Chapter). Chemistry: Classification of Elements and Periodicity in Properties (Complete Chapter), Chemical Bonding and Molecular Structure (Complete Chapter). Trigonometric functions (complete chapter), Trigonometric equation (complete chapter). Mathematics: 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 51 questions. The maximum marks are 180. SECTION-1 (Maximum Marks: 12) This section contains FOUR (04) questions. Each question has FOUR options (A), (B), (C) and (D). ONLY ONE of these four options is the correct answer. For each question, choose the option corresponding to the correct answer. Answer to each question will be evaluated according to the following marking scheme: Full Marks : +3 If ONLY the correct option is chosen; Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered); Negative Marks : 1 In all other cases. SECTION-2 (Maximum Marks: 12) This section contains THREE (03) questions. Each question has FOUR options (A), (B), (C) and (D). ONE OR MORE THAN ONE of these four option(s) is(are) correct answer(s). For each question, choose the option(s) corresponding to (all) the correct answer(s). Answer to each question will be evaluated according to the following marking scheme: Full Marks : +4 ONLY if (all) the correct option(s) is(are) chosen; Partial Marks : +3 If all the four options are correct but ONLY three options are chosen; Partial Marks : +2 If three or more options are correct but ONLY two options are chosen, both of which are correct; Partial Marks : +1 If two or more options are correct but ONLY one option is chosen and it is a correct option; Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered); Negative Marks : 2 In all other cases. For example, in a question, if (A), (B) and (D) are the ONLY three options corresponding to correct answers, then choosing ONLY (A), (B) and (D) will get +4 marks; [1] choosing ONLY (A) and (B) will get +2 marks; choosing ONLY (A) and (D) will get +2 marks; choosing ONLY (B) and (D) will get +2 marks; choosing ONLY (A) will get +1 mark; choosing ONLY (B) will get +1 mark; choosing ONLY (D) will get +1 mark; choosing no option (i.e. the question is unanswered) will get 0 marks; and choosing any other combination of options will get 2 marks. SECTION-3 (Maximum Marks: 24) This section contains SIX (06) questions. The answer to each question is a NON-NEGATIVE INTEGER. For each question, enter the correct integer corresponding to the answer using the mouse and the onscreen virtual numeric keypad in the place designated to enter the answer. Answer to each question will be evaluated according to the following marking scheme: Full Marks : +4 If ONLY the correct integer is entered; Zero Marks : 0 In all other cases. SECTION-4 (Maximum Marks: 12) This section contains TWO (02) paragraphs. Based on each paragraph, there are TWO (02) questions. The answer to each question is a NUMERICAL VALUE. For each question, enter the correct numerical value of the answer using the mouse and the onscreen virtual numeric keypad in the place designated to enter the answer. If the numerical value has more than two decimal places, truncate/round-off the value to TWO decimal places. Answer to each question will be evaluated according to the following marking scheme: Full Marks : +3 If ONLY the correct numerical value is entered in the designated place; Zero Marks : 0 In all other cases. 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 _____________________ [2] IMPORTANT CONSTANTS Speed of light in free space, : 3.00 108 ms 1 Permeability of free space, : 4 10 7 Hm 1 Permittivity of free space, : 8.85 10 12 Fm 1 The Planck constant, : 6.63 10 34 Js Rest mass of electron, : 9.1 10 31 kg Rest mass of proton, : 1.67 10 27 kg Molar gas constant, : 8.31 JK 1 mol 1 The Avogadro constant, : 6.02 1023 mol 1 The Boltzmann constant, : 1.38 10 23 JK 1 Gravitational constant, : 6.67 10 11 N m2kg 2 Acceleration of free fall : 9.8 ms 2 Rydberg Constant : 1.097 107 m 1 Atomic mass unit : 1.67 10 27 kg Charge on proton : 1.6 10 19 C IMPORTANT VALUES 2 = 1.414 ln 10 = 2.303 3 = 1.732 log102 = 0.3010 5 = 2.236 log103= 0.4770 = 3.142 log107 = 0.845 e (Euler s constant) = 2.718 * Use above values unless otherwise specified in a question. [3] PART-I (PHYSICS) SECTION-1 Single Correct Type Questions 1. A particle moves in XY plane such that its position, velocity and acceleration are given by r = xi + yj ; v = vx i + v y j; a = a xi + a y j which of the following condition is correct if the particle is speeding down? (A) xvx + yvy < 0 (B) xvx + yvy > 0 (C) axvx + ayvy < 0 (D) axvx + ayvy > 0 2. SECTION-2 One or More Than One Correct Type Questions 5. Throughout a time interval, while the speed of a particle increases as it moves along the x-axis, its velocity and acceleration might be (A) positive and positive respectively (B) positive and negative respectively (C) negative and negative respectively (D) negative and positive respectively 6. The force exerted by the floor of an elevator on the foot of a person standing there is more than the weight of the person if the elevator is (A) going up and slowing down (B) going up and speeding up (C) going down and slowing down (D) going down and speeding up 7. A body is acted upon by balanced forces (A) If it is in rest only (B) If it is moving with constant speed (C) If even number of forces are acting on it (D) If it is not accelerating A ball is projected as shown in figure. The ball will return to: (A) point O (B) left to point O (C) right to point O (D) none of these 3. Two weights W1 & W2 in equilibrium and at rest, are suspended as shown in figure. Then the ratio W1 : W2 SECTION-3 Non-Negative Integer Type Questions 8. Airplanes A and B are flying with constant velocity in the same vertical plane at angles 30 and 60 with respect to the horizontal respectively as shown in the figure. The speed of (A) 5/4 (C) 8/5 4. A is 100 3 ms 1 . At time t = 0s, an observer in A finds B at a distance of 500 m. This observer sees B moving with a constant velocity perpendicular to the line of motion of A . If at t = t0 , A just escapes being hit by B, t0 in seconds (B) 4/5 (D) None of these is A uniform sphere of weight w and radius 3 m is being held by a string of length 2 m attached to a frictionless wall as shown in the figure. The tension in the string will be: 9. (A) 5 w/4 (C) 15 w/16 (B) 15 w/4 (D) None of these Between two stations a train starting from rest first accelerates uniformly, then moves with constant velocity and finally retards uniformly to come to rest. If the ratio of the time taken be 1 : 8 : 1 and the maximum speed attained be 60 km/h, then the average speed over the whole journey is _____ km/h [4] 10. A drunkard is walking along a straight road. He takes 5 steps forward and 3 steps backward and so on. Each step is 1 m long and takes 1 s. There is a pit on the road 11 m away from the starting point. The drunkard will fall into the pit after ____sec. 11. A body of mass 2 kg moves under a force of ( SECTION-4 Paragraph Type Questions Paragraph for question nos. (14-15) A particle is moving with a constant acceleration in xy-plane from x = 4m, y = 3m and has velocity v = 2i 9 j m / s . The acceleration of ( ( ) the particle is given by vector a = 4i + 3 j m / s 2 ) 2i + 3 j + 5k N . It starts from rest and was at the origin initially. After 4s, its new coordinates are (8, b,20) . The value of b is: (Round off to the ) 14. The magnitude of velocity vector at t = 2s is _____ m/s 15. The magnitude of position vector at t = 4 s is ____m Nearest Integer). 12. A system to 10 balls each of mass 2kg are connected via massless and unstretchable string. The system is allowed to slip over the edge of a smooth table as shown in figure. Tension on the string between the 7 th and 8th ball is ______ N when 6th ball just leaves the table. 13. A cricket ball of mass 0.15 kg is thrown vertically up by a bowling machine so that it rises to a maximum height of 20m after leaving the machine. If the part pushing the ball applies a constant force F on the ball and moves horizontal a distance of 0.2 m while launching the ball, the value of F (in N) is 50x. Find the value of x. Paragraph for question nos. (16-17) The velocity-time graph of a particle in straight line motion is shown in figure. The particle starts its motion from origin. 16. The displacement of the particle from the origin after 8 s in metres is 17. Find the average retardation from 2s to 6s (in m/s2) PART-II (CHEMISTRY) SECTION-1 Single Correct Type Questions 18. In the Lother-Mayer graph, A, B, C, D & E element are; (A) (B) (C) (D) Halogens Alkaline earth metals Alkali metals Transition metals 19. The correct order of covalent character in the bond is: (A) MgCl2 < CaCl2 < SrCl2 (B) SrCl2 < CaCl2 < MgCl2 (C) MgCl2 < SrCl2 < CaCl2 (D) CaCl2 < SrCl2 < MgCl2 20. Which among the following statements are correct? A. s block, p block and d block elements are together known as Representative elements. B. The elements after uranium are called Transuranium elements. C. f block elements are known as Inner transition elements. Choose the most appropriate answer from the options given below. (A) Only A and B (B) Only A and C (C) Only B and C (D) A, B and C [5] 21. Which of the following molecule(s) obey the octet rule? (i) [BF4] (ii) [AlCl4] (iii) CO2 (iv) Cl2 (A) (i), (ii), (iii), (iv) (B) Only (ii), (iii), (iv) (C) Only (i), (iii), (iv) (D) Only (i), (ii), (iii) SECTION-2 One or More Than One Correct Type Questions 22. The first ionization energy of first atom is greater than that of second atom, whereas reverse order is true for their second ionization energy. Which set of elements is in accordance to above statement? (A) C > B (B) P > S (C) Be > B (D) Mg > Na 23. In which of the following option(s) the dipole moment of the left side molecule is greater than that of the right side molecule? (A) NH3, NF3 (B) SCl2, BeCl2 (C) SF4, CF4 (D) PF5, IF5 24. Which of the following statement(s) is/are correct regarding Mendeleev's periodic table? (A) It is based on atomic number (B) Only 63 elements were known (C) He left the gap under aluminimum and a gap under silicon (D) Positon of isotopes were not fixed SECTION-3 Non-Negative Integer Type Questions 25. How many of the following radii order(s) is/are incorrect? (i) N3 > P3 (ii) O2 > F 2+ 2+ (iii) Ca > Sr (iv) S2 > S (v) Cl > S2 26. The formal charge on the central O-atom in the O3 molecule is +x, the value of x is 27. How many of the following orders for electron affinity is/are correct? (a) S > Se (b) Cl > F (c) S > O (d) O > S (e) P > N 28. If x and y are the total number of 90 bond angles present in SF6 and IF7 respectively, then the value of |x y| is ________. 29. How many of the following species have radius greater than O2 ? O , S2 , Cl , Na+, N3 , O 30. Among the following species: N 2 , N 2+ , N 2 ,O 2 ,O 2+ ,O 2 The number of species showing paramagnetism is/are ______. SECTION-4 Paragraph Type Questions Paragraph for question nos. (31-32) In the modern periodic table, elements are arranged in order of increasing atomic numbers which is related to the electronic configuration. Depending upon the type of orbitals receiving the last electron, the elements in the periodic table have been divided into four blocks, viz. s, p, d and f. The modern periodic table consists of 7 periods and 18 groups. Each period begins with the filling of a new energy shell. In accordance with the Aufbau principle, the seven periods (1 to 7) have 2, 8, 8, 18, 18, 32 and 32 elements respectively. The seventh period is still incomplete. To avoid the periodic table being too long, the two series of f-block elements, called lanthanoids and actinoids are placed at the bottom of the main body of the periodic table. 31. If the number of s-block element is x and number x of p-block element is y, then what will be for y the following atomic numbers? 13, 55, 42, 76, 118, 101, 88, 20, 113, 38 32. If the total number of p-subshell electrons is x and total number of d-subshell electrons is y, x+y then what will be for atomic number 43? 2 Paragraph for question nos. (33-34) Hybridization is defined as the intermixing of atomic orbitals with the same energy levels to give the same number of a new type of hybrid orbitals. This intermixing usually results in the formation of hybrid orbitals having entirely different energies, shapes, etc. The atomic orbitals of the same energy level mainly take part in hybridization. Fully filled and half-filled orbitals, however, can both participate in this process if their energies are equivalent. The hybridization can be classified as sp3, sp2, sp, sp3d, sp3d2, and sp3d3. [6] 33. If the hybridisation of XeF5+ is spxdy, then What will be 34. x+y ? 2 In solid PBr5, maximum number of d orbitals taking part in hybridisation is x, then value of x+3 will be_____. 4 PART-III (MATHEMATICS) SECTION-1 Single Correct Type Questions 35. General solution of the equation cos x = sin x , is (A) n + ( 1) (B) 2n (C) n + n 4 4 4 40. (D) 2n + 4 36. SECTION-2 One or More Than One Correct Type Questions 39. If tan A (tan B + tan C) = 44, tan B (tan C + tan A) = 50, tan C (tan B + tan A) = 54, then which of the following statement is(are) true? (A) |tan (B + C)| < |tan (C + A)| (B) |tan (B + C)| > |tan (C + A)| (C) |tan B| + |tan C| > |tan A| (D) |tan A| + |tan B| < |tan C| ( where sin 3 cos3 cos 2tan cot = 1 , If sin cos 1 + cot 2 then (A) 0, 2 (B) , 2 3 (C) , 2 3 (D) , 2 2 The sum of all values (B) 38. 2 (D) 3 8 (B) x = y 1 y +1 ( ) ( ) If tan + cot 30o + cot 150o = ktan ( a ) , (B) a = 3 (D) a = 1 SECTION-3 Non-Negative Integer Type Questions 1 sin 2 + cos 2 42. If f ( ) = , then the value of 2cos 2 2f (11o) f (34o) is 43. Find the number of solutions of the equation (sin x 1)3 + (cos x 1)3 + (sin x)3 = (2 sin x + cos x 2)3 in [0, 2 ]. 44. If the sum of all values of x satisfying the system of equations tan x + tan y + tan x tan y = 5 and sin k (x + y) = 4 cos x cos y is , is 2 where x 0, then find the value of k. 2 If the values of x, y and z are sin130 cos80 , sin80 cos130 and 1+xy respectively then correct option is (A) x > 0, y > 0, z > 0 (B) x > 0, y < 0, 0 < z < 1 (C) x > 0, y < 0, z > 1 (D) x < 0, y < 0, 0 < z < 1 y= then (A) k = 3 (C) k = 1 of 5 4 (C) y +1 y 1 1+ x 1 x (D) xy + x y + 1 = 0 3 0, satisfying sin 2 2 + cos 4 2 = , is 4 2 (A) n ,n Z 2 (A) x = (C) 41. 37. If x = sec tan and y = cosec + cot , then [7] 45. If 9x 5y 9 xsin 5 ycos + = 56 and =0 cos sin cos 2 sin 2 3 ( 9 x )2/3 + ( 5 y )2/3 is then the value of 56 46. 47. 48. The value of p is 49. The value of q is If the equation cot4 x 2 cosec2 x + a2 4a + 6 = 0 has at least one real solution then the sum of all possible integral values of a is Paragraph for question nos. (50-51) Let a = sin 10o, b = sin 50o, c = sin 70o. With this information, answer the following questions. If sin + sin + sin = 3, , , ( 0,2 ) , 50. a + b 1 1 1 Value of 8abc + is equal to c a b c 51. Value of then cos2 + cos4 + cos6 to: SECTION-4 Paragraph Type Questions Paragraph for question nos. (48-49) If cos 4 a 4 + b4 + c4 ( ab )2 + ( bc )2 + ( ca )2 is equal to 5 3 p + cos 4 + cos 4 = 14 14 14 q (where p, q N and HCF ( p, q ) = 1 ) PW Web/App - https://smart.link/7wwosivoicgd4 Library- https://smart.link/sdfez8ejd80if [8]

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