Pratham-1 MPT-1 (24-25) Physics Past Paper PDF

4/8/24, 11:24 AM Best Educational ERP/LMS Solution Competishun 52/6, Opposite Metro Mas Hospital, Shipra Path, Mansarovar Date: 08/04/2024 Time...

4/8/24, 11:24 AM Best Educational ERP/LMS Solution Competishun 52/6, Opposite Metro Mas Hospital, Shipra Path, Mansarovar Date: 08/04/2024 Time: 3 hours Max. Marks: 300 PRATHAM-1 (24-25)_MPT-1 Physics Single Choice Question Q1 If y = sin(x) + ℓn(x) + e2x then dy will be : dx a) cos x + 1 + e 2x b) cos x + 1 + 2e2x c) –cos(x) + 2 + e2x x x x 2 d) – cosx – 2 +e 2x 2 x Q2 If , then the value of is : a) b) c) d) Q3 Convert 18 degree in to radians. a) b) c) d) rad rad rad Q4 Value of sin (37°) cos (53°) is - a) b) c) d) Q5 sin (90º + θ) is - a) sinθ b) cosθ c) – cosθ d) – sin θ Q6 Value of tan 3150 is a) 1 b) –1 c) 1.732 d) –1.732 Q7 The displacement of a particle is given by the equation s = t3 – 6t2 + 9t where t is measured in seconds and s in meters. What is the velocity after 1 sec (velocity is rate of change of displacement with respect to time): a) 1 m/sec. b) 0m/sec c) 2 m/sec. d) 3 m/sec For More Material Join: @JEEAdvanced_2026 https://lms.tutorlog.in/export-test-paper/660a81aa0c1158299b9424e4 1/10  4/8/24, 11:24 AM Best Educational ERP/LMS Solution Q8 If f(x) = sin2x – cos2x then is : a) sin 2x b) cos 2x c) 2 sin (2x) d) –2sin(2x) Q9 Find value of (cos 45º) a) 1 b) 0 c) d) –sin 45º Q10 In the shown triangle two sides and one angle is given. The third side is : a) 49 b) 7 c) (49)1/4 d) Q11 The displacement of a body at any time 't' after starting is given by x =. The velocity of the body is zero at t : (velocity is rate of change of displacement with respect to time) a) 3 sec. b) 4 sec. c) 2 sec. d) zero Q12 The radius 'r' of a cylinder increases with time at a constant rate of 2m/sec and its height decreases with time at constant rate of 3 m/sec. The rate of change of volume of cylinder at a time when radius and height of cylinder are 3m and 2m respectively will be : a) 3 πm 3 /sec. b) –3 πm 3 /sec. c) 5 πm 3 /sec. d) –10 πm 3 /sec. Q13 y = x2logx, then will be : a) x + 2x log(x) b) x logx + 2x c) 2x d) x – 2 log x Q14 Equation of this straight line is : a) 3x + 4y = 40 b) 3x – 4y = 40 c) 4x – 3y = 40 d) 4x + 3y = 40 Q15 Differentiate with respect to x a) b) c) d) Q16 cos2θ = a) 2cos 2 θ –1 b) 1–2sin2θ c) cos2θ – sin2θ d) All of the above For More Material Join: @JEEAdvanced_2026 https://lms.tutorlog.in/export-test-paper/660a81aa0c1158299b9424e4 2/10  4/8/24, 11:24 AM Best Educational ERP/LMS Solution Q17 Value of sin15º ⋅ cos15º is : a) 1 b) c) d) Q18 If sin θ= , then cosθ will be - a) b) c) d) Q19 If y = then is : a) b) c) d) Q20 If sides of a rectangle with given perimeter are a &b , then find the relation between a & b for which area of the given rectangle is maximum - a) a + b = 0 b) a = b c) a. b = 1 d) a = 4 b Numerical Q21 Find two positive numbers x & y such that x + y = 10 and xy is maximum – Q22 Value of tan 585º is : Q23 The maximum value of xy subject to x + y = 8, is: Q24 Slope of graph y = tanx drawn between y and x, at x = is : Q25 If f(x) = x + 2, then f [f (3)] is : Q26 Find value of sin2 15º + sin2 645º : Q27 If sin θ= , then cosθ will be. Find the value of x Q28 Value of sin (37°) cos (53°) is. Then find the value of x. Q29 Maximum value of f(x) = sinx+ cosx is.Then find the value of x. Q30 If y = 3t2 – 4t; then minima of y will be at t is equal to x/3. Then find the value of x For More Material Join: @JEEAdvanced_2026 https://lms.tutorlog.in/export-test-paper/660a81aa0c1158299b9424e4 3/10  4/8/24, 11:24 AM Best Educational ERP/LMS Solution Chemistry Single Choice Question Q31 Consider various unit system for PV = nRT, select incorrect option : a) dyne Physical quantity → P; SI or MKS → N 2 orP a ; CGS → ; Other Unit m cm2 system (atm-L) → atm b) Physical quantity → V; SI or MKS → dm3; CGS → mL; Other Unit system (atm-L) → L c) Physical quantity → n; SI or MKS → mol; CGS → mol; Other Unit system (atm- L) → mol d) Physical quantity → T; SI or MKS → K; CGS → K; Other Unit system (atm-L) → K Q32 Calculate total number of atoms in 115 g of sodium. a) 5 b) 3 c) 5 N A d) 7 NA Q33 Determine total numbers of moles of acetone (C3H6O) in a sample having58 g of acetone C3H6O+ 6.02 × 1023 C3H6O molecules + 11.2 L acetone vapour at STP +2 mol acetone. [Take molar volume of gas = 22.4 lit/mol] a) 1.5 mol b) 4.5 mol c) 2.5 mol d) None of these Q34 Calculate average molar mass (in g/mol) of a gaseous mixture which contains 2 mol of O2, 3 mol of CO2& 5 Mol of SO2. a) 44 b) 48 c) 51.6 d) 75.6 Q35 If an atom of an element B contain equal no. of protons and neutrons. Its atomic number (Z) and mass number (A) are related as 2A + 3Z = 140 then the total number of nucleons present in one atom of element is : a) 60 b) 80 c) 40 d) 50 Q36 Which of the following is not correctly matched? a) mega (M) = 10 6 b) zeta (Z) = 10 21 c) hecto (h) = 10 2 d) pico (p) = 10–10 Q37 Three different containers contain three different gases with following parameter. Container 1 of 67.2 L containing gas X at 00C and 1.01325 bar Container 2 of 44.8 L containing gas Y at 546 K & 760 mm of Hg Container 3 of 89.6 L containing Z gas at 101325 N/m2& 00C. Now they are mixed in single container. If gram molecular mass of X, Y & Z are 20 g, 40 g and 80 g respectively. Then which of the following statements are correct. [Take molar volume of gas = 22.4 lit/mol] (I) Mole percent of gas Z in final mixture is 50% (II) Average molecular mass of final mixture is 26.25 amu. (III) Mole ratio of gas X and gas Z is 3 : 4 (IV) Number of molecules present in final mixture is equal to number of atoms in 300 g Ca. a) I, II, III b) I, II, III, IV c) II, III, IV d) I, III For More Material Join: @JEEAdvanced_2026 https://lms.tutorlog.in/export-test-paper/660a81aa0c1158299b9424e4 4/10  4/8/24, 11:24 AM Best Educational ERP/LMS Solution Q38 Which of the following gas molecule has atomicity 3 ? a) Sulphur dioxide b) Ozone c) Both (A) and (B) d) None of these Q39 A gas sample is having 2280 mm of Hg pressure, determine corresponding pressure in atm. a) 6 atm b) 2 atm c) 3 atm d) 4 atm Q40 8 g of O2– ion has amount of charge equal to : (NA = 6.02 × 1023) a) 5 N A e b) 2 N A e c) N A e d) 1 NA e 2 Q41 The volume occupied by 1.5 g of ethane (C2H6) gas at 2.46 atm pressure and 27ºC temperature is: a) 200 cm 3 b) 500 mL c) 0.2 dm 3 d) 0.5 m 3 Q42 A graph is plotted for different samples of an element, by taking its weight (in gram) on X-axis and number of atoms present on Y-axis. Determine the atomic weight of element (in u). (NA = 6.0 ×1023) a) 20 u b) 40 u c) 60 u d) 80 u Q43 Which of the following sample must have average molar mass greater than that of a mixture of N2 andCO2? a) Mixture of H 2 and SO 3 b) Mixture of CH 4 & SO 3 c) Mixture of SO 2 and SO 3 d) None of these Q44 In molecule, the hybridization of carbon 1, 2, 3 and 4 respectively are : a) sp3, sp, sp3, sp3 b) sp2, sp2, sp2, sp3 c) sp2, sp, sp2, sp3 d) sp2, sp3, sp2, sp3 Q45 An organic compound has molecular formula C9H18. Its all carbon atoms are sp3hybridised and its all hydrogen atoms are identical. Its structure can be : a) b) c) d) Q46 All the members of a homologous series have same - a) Molecular mass b) Molecular formula c) Physical properties d) General molecular formula Q47 and are : a) Identical b) Homologous c) Alkane d) Saturated hydrocarbon For More Material Join: @JEEAdvanced_2026 https://lms.tutorlog.in/export-test-paper/660a81aa0c1158299b9424e4 5/10  4/8/24, 11:24 AM Best Educational ERP/LMS Solution Q48 Which of the following is unsaturated hydrocarbon ? a) b) c) d) Q49 A primary amine has amino(–NH2) group attached to : a) A primary carbon atom only b) A secondary carbon atom only c) A tertiary carbon atom only d) Primary, secondary, tertiary carbon atoms Q50 Which of the following is molecular formula of ? a) C7H14 b) C7H12 c) C7H10 d) C7H8 Numerical Q51 The no. of molecules present in a drop of water with volume 0.06 cm3 having density 1 gm/cm3 is approximately x × 1021. Value of x is : Q52 How many NA electron is present in 5.1 g NH3 ? Q53 The total cationic charge in coulomb present in 51gm of Al2O3 is x Faraday. x is : Q54 Number of hydrogen atoms in the given compound is : Q55 Number of primary hydrogen is the given compound are Q56 An element is found in nature in two isotopic forms with mass numbers (A – 1) and (A + 3). If the average atomic mass of the element is found to be A, then the relative abundance (in %) of the heavier isotope in the nature will be : Q57 Calculate mass of carbon in 0.01 mole of K4[Fe(CN)6]. Report your answer after dividing by 0.08. Q58 What is the number of gram atoms of oxygen in 6.023 ×1024 CO-molecule. Q59 A gaseous mixture contains SO3(g) and CH4(g) in 25 : 1 ratio by mass. What is ratio of total number of atoms present in SO3(g) to total number of atoms present in CH4(g) in the mixture. Q60 A gaseous mixture is composed of equal number of moles of CH4, C2H6 and C2H2. Determine the average molecular mass of mixture (in amu). For More Material Join: @JEEAdvanced_2026 https://lms.tutorlog.in/export-test-paper/660a81aa0c1158299b9424e4 6/10  4/8/24, 11:24 AM Best Educational ERP/LMS Solution Mathematics Single Choice Question Q61 An investigator interviewed 100 students to determine their preferences for the three drinks; milk (M), coffee (C) and Tea (T). He reported the following : 10 students had all the three drinks M.C.T. 20 had M and C; 30 had C and T, 25 has M and T; 12 had M only, 5 had C only and 8 had T only. Number of students did not take any of the three drinks a) 0 b) 20 c) 40 d) 80 Q62 If A ⊆ B, then B’ – A’ is equal to a) A’ b) B’ c) A d) ϕ Q63 Which of the following is true? a) {2, 3} ∈ {1, 2, 3, 4} b) {1,2, 3} ⊆ {{1, 2, 3}, 4,5,6} c) {{1}} ∈ {{1}, 2, 3, 4} d) {{1, 2}} ⊆ {{1, 2}, 3, 4} Q64 If A and B are two sets, then A ∩ (A∪ B)' is equal to a) A b) B c) ϕ d) None of these Q65 In a school there are 20 teachers who teach mathematics or physics. Of these, 12 teach mathematics and 4 teach both physics and mathematics, the number of teachers who teach physics are- a) 12 b) 16 c) 8 d) 4 Q66 For any two sets A and B which of the following is pair wise disjoint family of sets a) A ∩ B, A – B, A ∪ B b) A ∩ B, B – A, A ∪ B c) A – B, A ∩ B, B – A d) None of these Q67 Number of integral value of x satisfying a) 1 b) 3 c) 2 d) 4 Q68 The solution of the inequality (x2 – 3x + 2) (x3 – 3x2) (4 – x2) ≥ 0 is a) b) c) d) Q69 The largest integral value of x which satisfies the inequality is: a) 1 b) 3 c) 4 d) 2 Q70 If x is an integer satisfying x2 – 6x + 5 ≤ 0 and x2 – 2x > 0 then the number of possible values of x is a) 3 b) 4 c) 2 d) infinite For More Material Join: @JEEAdvanced_2026 https://lms.tutorlog.in/export-test-paper/660a81aa0c1158299b9424e4 7/10  4/8/24, 11:24 AM Best Educational ERP/LMS Solution Q71 Least natural number satisfying the inequation is a) 1 b) 2 c) 3 d) 4 Q72 Solution set of the inequation is a) b) c) d) Q73 Which of the following sets satisfy, ? a) [0, 2) b) (4, 7] c) [5, 6) d) [2, 4) Q74 The complete solution set of the inequality is a) b) c) d) Q75 If then the value(s) of x is/are ….. (x> 0) a) 5, –4 b) 4 c) 5 d) 4, –5 – Q76 , then x3 + is equal to 1 If x = 3 – √8 3 x – a) 6 b) 198 c) 6√ 2 d) 102 Q77 Which of the following number is irrational a) b) c) d) Q78 The value of 4 is equal to 1/3 1/3 9 – 3 +1 a) 31/3 + 1 b) 31/3 – 1 c) 31/3 + 2 d) 31/3 – 2 Q79 The expression is simplified to a) a16 b) a12 c) a8 d) a4 Q80 Which of the following sets is empty set? a) A = {x : x ∈ N, 3 < x ≤ 4} b) B = {x : x is prime, 90 < x < 96} c) C = {x : x is an even prime} d) D = {x : x ∈ Rational numbers & 1 < x < 2} Numerical Q81 If in a class there are 200 students in which 120 take Mathematics, 90 take Physics, 60 take Chemistry, 50 take Mathematics & Physics, 50 take Mathematics & Chemistry, 43 take Physics & Chemistry and 38 take Mathematics, Physics & Chemistry, then the number of students who have taken exactly one subject is For More Material Join: @JEEAdvanced_2026 https://lms.tutorlog.in/export-test-paper/660a81aa0c1158299b9424e4 8/10  4/8/24, 11:24 AM Best Educational ERP/LMS Solution Q82 Two finite sets have m and n elements. The total number of subsets of the first set is 56 more than the total number of subsets of the second set. Find the values of m + n. Q83 Given the sets A = {1, 2, 3}, B = {3, 4}, C = {4, 5, 6}, then number of element in A ∪ (B ∩ C) is. Q84 Find the sum of all the solutions of inequality. Q85 If , then complete solution set is (a, –1) ∪ (b, c). Find a – 3b – 12c. Q86 If n, m N and , then find the value of m. ∈ Q87 The number of positive integral solution of, is Q88 If n(A) = 12, n(B) = 15, If x and y are minimum and maximum of n(A' ∩ B) then x + y= Q89 The number of subsets of the power set of set A = {10, 11} is Q90 Let n(U) = 700, n(A) = 200, n(B) = 300 and n(A∩ B) = 100. Find the value of ′ ′ n(A ∩B ) 10 = For More Material Join: @JEEAdvanced_2026 https://lms.tutorlog.in/export-test-paper/660a81aa0c1158299b9424e4 9/10  4/8/24, 11:24 AM Best Educational ERP/LMS Solution Answer Key Que. 1 2 3 4 5 6 7 8 9 10 Ans. B A A A B B B C B D Que. 11 12 13 14 15 16 17 18 19 20 Ans. C B A A B D C C C B Que. 21 22 23 24 25 26 27 28 29 30 Ans. 25 1 16 2 7 1 2 9 2 2 Que. 31 32 33 34 35 36 37 38 39 40 Ans. B C B C C D D C C C Que. 41 42 43 44 45 46 47 48 49 50 Ans. B B C C B D B D D C Que. 51 52 53 54 55 56 57 58 59 60 Ans. 2 3 3 12 18 25 9 10 4 24 Que. 61 62 63 64 65 66 67 68 69 70 Ans. B D D A A C D C D A Que. 71 72 73 74 75 76 77 78 79 80 Ans. C B C D C B C A D B Que. 81 82 83 84 85 86 87 88 89 90 Ans. 98 9 4 2 6 29 3 18 16 30 For More Material Join: @JEEAdvanced_2026 https://lms.tutorlog.in/export-test-paper/660a81aa0c1158299b9424e4 10/10