Lakshya JEE (2026) Practice Test 01 PDF

Lakshya JEE (2026) PRACTICE TEST - 01 DURATION ::180 DURATION Minutes 90 Minutes DATE : 11/05/2025 M.MARKS : 300...

Lakshya JEE (2026) PRACTICE TEST - 01 DURATION ::180 DURATION Minutes 90 Minutes DATE : 11/05/2025 M.MARKS : 300 Topics Covered Physics: Electric Charges and Fields, Introduction: Charge, Coulomb's Law, Electric Field, Conductors and Insulators, Electric Field of a Continuous Charge Distribution, Motion of a Charged Particle in Uniform Electric Field, Electric Field Lines, Electric Flux Chemistry: Solutions (Complete Chapter) Mathematics: Determinants (Complete Chapter), Except integration and differentiation of determinants 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 75 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 25 questions in each Section in which first 20 questions are Objective Type and last 5 questions are integer type with answers ranging from ‘0’ to ‘999’ where answer needs to be rounded off to the nearest integer and all 25 questions are compulsory. 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. 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 (3) 1  2 1. A charge q is placed at the mid point of the line (4) The tension in A is greater than tension in joining two equal charges Q. The system of the B. three charges will be in equilibrium if q is equal 5. An electron falls through a small distance in a to : uniform electric field of magnitude 2×104 NC–1 Q Q The direction of the field is reversed keeping the (1)  (2)  2 4 magnitude unchanged and a proton falls through Q Q the same distance. The time of fall will be (3)  (4)  (1) Same in both cases 4 2 (2) More in the case of an electron (3) More in the case of proton 2. ABC is an equilateral triangle. Three charges q (4) Independent of charge each are placed at each corner as shown in fig. The 6. In a region of space the electric field is given by electric field intensity at centre O will be E  8ıˆ  4 ˆj  3kˆ. The electric flux through a surface of area of 100 units in the x-y plane is : (1) 800 units (2) 300 units (3) 400 units (4) 1500 units 7. The figure shows the electric lines of force emerging from a charged body. If the electric fields at A and B are E A and EB respectively and if the distance between A and B is r , then 1 3q 1 q (1) (2) 40 r2 4 o r 2 1 3q (3) (4) zero 4 o r2 3. A charge particle q1 is at position  2, 1,3. The electrostatic force on another charged particle q2 (1) E A  EB (2) E A  EB at  0,0,0  is : EB EB (3) E A  (4) E A  (1) q1q2 560  2iˆ  ˆj  3kˆ  r r2 (2) 1 q1q2  2iˆ  ˆj  3kˆ  8. The charge per unit length of the four quadrants of   40 14 3 the ring is 2λ, 2λ,λ and λ , respectively. What  j  2i  3kˆ  q1q2 ˆ ˆ is the electric field at the centre? (3) 560 (4) q1q2 56 140  2iˆ  ˆj  3kˆ  4. Two identical simple pendulums, A and B , are suspended from the same point. The bobs are given positive charges, with A having more charge than B. They diverge and reach equilibrium with A and B making angles 1 and  2 with the vertical, respectively. Which of the  ˆ  (1) i (2) ĵ 20 R 20 R following is correct? (1) 1  2 2 ˆ (3) i (4) None of these (2) 1  2 4 0 R 9. Which one of the followed pattern of electric lines 13. Six charges are kept at the vertices of a regular of force cannot be possible for the field produced hexagon as shown in the figure. by a static charge- (1) (2) The magnitude of force applied by Q charge (3) (4) on +q charge is F. If the net electric force on Q charge is nF then find the value of n. (1) 4 (2) 5 (3) 7 (4) 9 10. Statement-I: A positive point charge initially at rest in a uniform electric field starts moving along 14. The intensity of the electric field required to keep a electric lines of forces. (Neglect all other forces water drop of radius 10–5 cm just suspended in air except electric forces.) when charged with one electron is approximately Statement-II: A point charge released from rest in an electric field always moves along the lines of  g  10 N / kg , e  1.6 1019 C ) force. (1) 260 V / cm (2) 260 N / C (1) Statement-I is True, Statement-II is True; (3) 130 V / cm (4) 130 N / C Statement-II is a correct explanation for Statement-I. 15. An infinite number of charges, each of (2) Statement-I is True, Statement-II is True; charge 1C, are placed on the x-axis with Statement-II is NOT a correct explanation for coordinates x  1,2,4,8, , where x is in metres. Statement-I. If a charge of 1 C is kept at the origin, then what (3) Statement-I is True, Statement-II is False. is the net force acting on 1 C charge? (4) Statement-I is False, Statement-II is True. (1) 9000 N (2) 12000 N (3) 24000 N (4) 36000 N 11. Two charge q and –3q are placed fixed on x-axis 16. Two spherical conductor B and C having equal separated by a distance 'd '. Where should a third radii and carrying equal charges in them repel each charge 2q be placed such that it will not experience other with a force F when kept apart at some any force? distance. A third spherical conductor having same radius as that of B but uncharged brought in (1) d 2   1  3 to the left of q contact with B , then brought in contact with C and finally removed away from both. The new (2) d 2   1  3 to the right of q force of repulsion, between B and C is (1) F / 4 (2) 3F / 4 (3) d 2   1  5 to the left of q (3) F / 8 (4) 3F / 8 17. Four charges are placed at the circumference of a (4) d 2   1  5 to the right of q dial clock as shown in the figure. If the clock has only hour hand and a charge q0 is placed at the centre, then the hour hand points in the direction 12. Two particles of equal mass m and charge q are which shows the time as placed at a distance of 16 cm. They do not q experience any force. The value of is m 0 (1) 1 (2) G G (3) (4) 4  0 G 40 (1) 1 : 30 PM (2) 7 : 30 PM (3) 4 : 30 PM (4) 1 0: 30 PM 18. A particle of mass m and charge –q moves Integer Type Questions diametrically through a uniformly charged sphere 21. Electric field is given in a region of radius R with total charge Q. The angular frequency of the particle’s simple harmonic   E  6iˆ  5 ˆj  3kˆ N/C. Find flux linkage (in SI motion, if its amplitude < R, is given by units) through a surface area 30 m2 that is in YZ plane? 1 qQ 1 qQ (1) (2) 40 mR 40 mR 2 22. A force of 2.25 N acts on a charge of 15 × 10–3 C. 1 qQ 1 m Calculate the intensity of electric field at that point (3) (4) 40 mR3 40 qQ (in N/C) 19. Three charges, each equal to q, are placed at the 23. In a certain region of space, there exists a uniform three corners of a square of side a, Find the electric electric field of 2  103 kˆ Vm–1. A rectangular coil field at fourth corner. of dimension 10 cm × 20 cm is placed in x – y (1)  2 1  q 80 a 2 plane. The electric flux through the coil in Vm is  (2) 2 2  1  q 80 a 2 24. A particle having a charge of q = 8.85 C is placed on the axis of a circular ring of radius R =  (3) 2 2  1  q 40 a 2 30 cm. Distance of the particle from centre of the ring is a = 40 cm. Calculate the electric flux (4) 0 passing through the ring [in 105 N/C] 20. Two free point charges +q and +4q are placed at x distance apart. A third charge is so placed that 25. Three point charges of magnitude 5C , 0.16C , all the three charges are in equilibrium. Then and 0.3C are located at the vertices A, B, C of a 4 q right angled triangle whose sides are (1) unknown charge is 9 AB  3cm, BC  3 2cm and CA  3cm and 9 q (2) unknown charge is point A is the right angle corner. Charge at point 4 x A experiences__________ N of electrostatic (3) it should be at   from smaller charge force due to the other two charges. 6 between them  2x  (4) it should be placed at   from smaller  3  charge between them Section-II (CHEMISTRY) Single Correct Type Questions 28. What will be the molality of a solution having 18 26. Which of the following is not a colligative g of glucose (mol. mass = 180) dissolved in 500 property? g of water? (1) Vapour pressure (1) 1 m (2) 0.5 m (2) Depression in freezing point (3) 0.2 m (4) 2 m (3) Elevation in boiling point (4) Osmotic pressure 29. At 100°C the vapour pressure of a solution of 6.5 g of a solute in 100 g water is 732 mm of Hg. If 27. A solution of acetone in ethanol: Kb = 0.52 K/m, the boiling point of this solution (1) Shows a positive deviation from Raoult's will be: law (1) 100°C (2) Behaves like a near ideal solution (2) 102°C (3) Obeys Raoult’s law (3) 103°C (4) Shows a negative deviation from Raoult’s (4) 101°C law 30. Calculate the molar mass of a substance whose 35. The van't Hoff factor for 0.1M Ba  NO3 2 7.0% by mass solution in water freezes at solution is 2.74. The degree of dissociation is: –0.93°C. The cryoscopic constant of water is (1) 91.3% (2) 87% 1.86°C kg mol–1. (3) 100% (4) 74% (1) 140 g mol–1 (2) 150.5 g mol–1 (3) 160 g mol–1 (4) 155 g mol–1 36. A membrane which allows the movement of only solvent particles through it is called: 31. Which one of the following statement is false? (1) Animal membrane (1) Raoult’s law states that the vapour pressure (2) Plant membrane of a component over a solution is (3) Semipermeable membrane proportional to its mole fraction. (4) Permeable membrane (2) Two sucrose solutions of the same molality prepared in different solvents will have the 37. The value of Henry's law constant: same freezing point depression. (1) Increases with increase in temperature. (3) The correct order of osmotic pressure for (2) Decreases with increase in temperature 0.01 M aqueous solution of each compound is BaCl2 > KCl > CH3COOH > Sucrose. (3) Increases with decrease in temperature. (4) The osmotic pressure () = MRT, where M (4) Independent of temperature and depend only is the molarity of the solution. on pressure. 32. The unit of cryoscopic constant is: 38. A solution is prepared by adding 4 moles of (1) K.g/mol (2) Kg/mol K substance A to 300 g of water. Calculate molality (3) K Kg/mol (4) mol/Kg K of the solution. 33. Given below are two statements: one is labelled (1) 0.1333 m (2) 1.333 m as Assertion A and the other is labelled as (3) 0.0133 m (4) 13.33 m Reason R: Assertion A: Boiling point of 1 m Al2(SO4)3 is 39. At 298 K, the vapour pressure of pure liquid A greater than that of 1 m NaCl. (molecular weight = 40) is 100 torr, while that of Reason R: Van't Hoff factor of Al2(SO4)3 is pure liquid B is 40 torr, (molecular weight = 80). lower than that of NaCl. In the light of the above The vapour pressure at 298 K of a solution statements, choose the correct answer from the options given below: containing 20 g of each A and B, is: (1) A is true but R is false. (1) 59.8 torr (2) 80 torr (2) A is false but R is true. (3) 48 torr (4) 68 torr (3) Both A and R are true and R is the correct explanation of A. 40. Colligative properties have many practical uses, (4) Both A and R are true but R is NOT the some of them may be: correct explanation of A. I: Melting of snow by salt II: Desalination of sea water 34. Match the laws given in column I with III: Determination of molar mass expression given in column II. IV: Determination of melting point and boiling Column-I Column-II point of solvent (A) Roult’s law (P) Tf  K f m Actual practical uses are: (1) I, II (2) III, IV (B) Henry’s law (Q)  = CRT (3) I, II, III (4) II, III, IV Elevation in (C) (R) p 1 p1o  2po2 boiling point 41. A solution containing 1.8g of a compound Depression in (D) (S) Tb  K b m (empirical formula CH2O) in 40g of water is freezing point observed to freeze at 0.465 C. The molecular Osmotic (E) (T) P  K H  formula of the compound is (Kf of water = 1.86 pressure kg K mol–1, atomic mass in g/mol of C = 12, H = (1) A R; B T; C S; D P; E Q 1 and O = 16) (2) A P; B B; C R; D T; E S (1) C2H 4O2 (2) C3H 6O3 (3) A Q; B R; C T; D S; E P (4) A T; B S; C P; D Q; E R (3) C4H8O4 (4) C6 H12O 6 42. Soft drinks and soda water bottles are sealed (1) 1  2  3 (2) 3  1  2 under high pressure (3) 2  1  3 (4) 2  3  1 (1) to increase their taste (2) to increase the solubility of CO 2 Integer Type Questions (3) to decrease temperature of the gas dissolved 46. How many of the following molecules or ionic (4) All of the above compound have van’t Hoff factor greater than 2. If   100% Glucose, Urea, C2H5OH, Phenol, 43. Of the following measurements, the one most CaCl2, K4[Fe(CN)6], HCl and Na3PO4 suitable for the determination of the molecular mass of oxyhaemoglobin, a molecule with a 47. 10 g of a non-volatile solute when dissolved in molecular mass of many thousands, is 100 g benzene raises its boiling point by 1°C. (1) the elevation of the boiling point Molar mass of the solute is: (2) the depression of the freezing point (Kb for benzene = 2.53 K kg/mol) (3) the osmotic pressure (4) any of the previous three, as they are all 48. The osmotic pressure of a dilute solution is 7 × equally good 105 Pa at 273 K. Osmotic pressure of the same solution at 283 K is ______ × 104 Nm–2. (Nearest 44. Elevation in boiling point was 0.52 C when 6g integer) of a compound X was dissolved in 100g of water. 49. Calculate the mass percent of a solution obtained Molar mass of X is: by mixing 100g of 10% urea solution with 150g  K b  0.52 K kg mol1  of 15% urea solution. (1) 120 (2) 60 (3) 600 (4) 180 50. If the concentration of glucose  C6H12O6  in blood is 0.72 gL–1, the molarity of glucose in 45. The relationship between osmotic pressures blood is_______ ×10–3M. (Nearest Integer)  1, 2 and 3  at a definite temperature when (Given: Atomic mass of C = 12u, H = 1u, 1g glucose, 1g urea and 1g sucrose are dissolved O = 16u) in 1 litre of water is: (assume i  1 for all) Section-III (MATHEMATICS) Single Correct Type Questions 2 3 2 x 2 6 2 54. If x x x  3  0 , then the value of x is 51. If  , then x is equal to 18 x 18 6 4 9 1 (1) 6 only (2) ±6 (1) 3 (2) 0 (3) –6 only (4) 0 (3) –1 (4) 1 52. The value of cofactor of a23 of matrix  1 6 1  55. If x1, x2 and y1, y2 are the roots of the equations A   5 2 5  is equal to 3x2 – 18x + 9 = 0 and y2 – 4y + 2 = 0. The value of  7 3 0  the determinant (1) 45 (2) 45 (3) 47 (4) 47 x1 x2 y1 y2 1 x1  x2 y1  y2 2 is 0 a b a c   53. The value of b  a 0 b  c is sin  x1 x2  cos  y1 y2  1 ca c b 0 2  (1) a (2) b (1) 0 (2) 1 (3) 0 (4) None of these (3) 2 (4) None of these  bc ac ab 62. Area of the triangle whose vertices are  a, b  c  , 56. The value of the determinant a b c is  b, c  a  and  c, a  b  , is 3 3 3 a b c (1) 2 sq units (1) (a + b + c) (2) 3 sq units (2) a + b + c – ab (3) 0 sq unit (3) (a2 – b2)(b2 – c2)(c2 – a2) (4) None of these (4) a2 + b2 + c2 63. If a, b, c are real then the value of 4 4 0 a2  1 ab ac 57. If a b  4 c  0 , then a + b + c is equal to determinant ab b2  1 bc  1 if a b c4 ac bc c 1 2 (1) 41 (1) a + b + c = 0 (2) a + b + c = 1 (2) 116 (3) a + b + c =  1 (4) a = b = c = 0 (3) 628 (4) –4  5 3 8 64. If A   2 0 1 , then find the value of 58. If a 2  b2  c 2  ab  bc  ca  0, a, b, c  R , 1 2 3 then value of the determinant 5 A31  3 A32  8 A33 , Aij is the cofactor of element  a  b  2 2 a 2  b2 1 aij of A 1  b  c  2 2 b2  c 2 is equal to (1) 0 (2) 1 c2  a2 1  c  a  2 2 (3) 2 (4) 3 (1) 65 (2) a2  b2  c2  31 1 x x x2  (3) 4 a 2  b 2  c 2  65. If x 1 x x2 (4) 0 x2 x 1 x =   x  1  x   2   x  3   x   4  be an 59. The system of linear equation identity in x , where  1,  2,  3,  4 are x  y  z  6, x  2 y  3z  10 & x  2 y  z   independent of x. The value of  1 ×  2 ×  3 × has infinite solutions for  4 is (1)   4,   10 (2)   5,   5 (1) –1 (2) 2 (3)   3,   10 (4)   10,   3 (3) 4 (4) 6 60. The maximum value of the function 66. If  is non-real complex cube root of unity, then 1 4cos 1 1  2 f(  ) = sin 1 4cos  2 1 is equal to 1 sin 1  2  1 (1) 14 (2) 17 (3) 17 (4) 14 (1) 0 (2) 1 (3) 3 (4) 2 61. The existence of unique solution of the system of equation, x y  z  , 67. The number of values of k for which the linear equations 5 x  y  z  10 & 4 x  ky  2 z  0, kx  4 y  z  0,2 x  2 y  z  0 2x  3 y  z  6 depends on possess a non-zero solution is : (1)  only (2)  only (1) 1 (2) zero (3)  and  both (4) neither  nor  (3) 3 (4) 2 68. The simultaneous equations 72. For a unique value of  and  , the system of kx  2 y  z  1,  k  1 y  2 z  2,  k  2  z  3 equations given by have only one solution, when x yz6 (1) k  2 (2) k  1 x  2 y  3 z  14 (3) k  0 (4) k  1 2 x  5 y  z    69. The number of values of  for which the system has infinitely many solutions, then 4 is equal of equations: to x yz x  2y  3z  1 32  k 42 32  3  k x  3y  5 z  4 73. If 42  k 52 42  4  k  0 , then find k. is inconsistent, is (1) 0 (2) 1 52  k 62 52  5  k (3) 2 (4) 3 74. If a, b, c are in A.P. then the value of the 70. If the system of equations x  2 y  5z  3,2 x  y 2y  4 5y  7 8y  a  z  1 and 11x  7 y  pz  q , has infinitely many determinant 3 y  5 6 y  8 9 y  b is solutions, then 4 y  6 7 y  9 10 y  c (1) p  q  2 (2) p  q  10 (3) pq 2 (4) pq 5 75. If pqr  0 and the system of equations (p + a)x + by + cz = 0 Integer Type Questions ax + (q + b)y + cz = 0 1  ax 1  bx 1  cx ax + by + (r + c)z = 0 71. If 1  a1 x 1  b1 x 1  c1 x has a non-trivial solution, then value of 1  a2 x 1  b2 x 1  c2 x 2  a b c     is :  A0  A1x  A2 x2  A3 x3 ,  p q r then A0 is equal to PW Web/App - https://smart.link/7wwosivoicgd4 Library- https://smart.link/sdfez8ejd80if