Practice Questions

Q1. If the first term of an A.P. is 3 and the sum of its first four terms is equal to one-fifth of the sum of the next four terms, then the sum of the first 20 terms is equal to (1) −1080 (2) −1020 (3) −1200 (4) −120

Q3. The number of solutions of the equation ( x9 9 + 2) ( x2 7 + 3) (1) 2 (2) 3 (3) 1 (4) 4

Q7. (2x2−3x+5)(3x−1) 2 limx→∞ is equal to : (3x2+5x+4)√(3x+2)x (1) 2 (2) 2e √3e √3 (3) 2 (4) 2e 3√e 3

Q10.Let →a and →b be two unit vectors such that the angle between them is . If λ→a + 2→b and 3→a −λ→b are 3 perpendicular to each other, then the number of values of λ in [−1, 3] is : (1) 2 (2) 1 (3) 0 (4) 3 e 1 x x loge α

Q15. In an arithmetic progression, if S40 = 1030 and S12 = 57, then S30 −S10 is equal to : (1) 525 (2) 510 (3) 515 (4) 505

Q18.The value of (sin 70∘) (cot 10∘cot 70∘−1) is (1) 2/3 (2) 1 (3) 0 (4) 3/2 dx 1 1 1 , then 3( b + c) is equal to

Q20.The relation R = {(x, y) : x, y ∈Z and x + y is even } is: (1) reflexive and symmetric but not transitive (2) an equivalence relation (3) symmetric and transitive but not reflexive (4) reflexive and transitive but not symmetric Q21. ⎧3x, x < 0 Let f(x) = min{1 + x + [x], x + 2[x]}, 0 ≤x ≤2 where [.] denotes greatest integer function. If α and β ⎨ ⎩5, x > 2, are the number of points, where f is not continuous and is not differentiable, respectively, then α + β equals __________

Q23.If limt→0 (∫10 5)tdx)

Q24.Number of functions f : {1, 2, … , 100} →{0, 1}, that assign 1 to exactly one of the positive integers less than or equal to 98 , is equal to ________. y2 + = 1 be two hyperbolas having length of latus rectums 15√2 and = 1 and H2 : −x2

Q26.Which of the following figure represents the relation between Celsius and Fahrenheit temperatures ? (1) (2) (3) (4) ∣∣ 2025 (24 Jan Shift 2) JEE Main Previous Year Paper

Q26. A B Y 0 0 1 0 1 1 1 0 0 1 1 1 To obtain the given truth table, following logic gate should be placed at G: 2025 (22 Jan Shift 2) JEE Main Previous Year Paper (1) OR Gate (2) AND Gate (3) NOR Gate (4) NAND Gate

Q26.A galvanometer having a coil of resistance 30Ω need 20 mA of current for full-scale deflection. If a maximum current of 3 A is to be measured using this galvanometer, the resistance of the shunt to be added to the galvanometer should be 30 X Ω, where X is Options (1) 596 (2) 149 (3) 298 (4) 447

Q27.A ball having kinetic energy KE, is projected at an angle of 60∘ from the horizontal. What will be the kinetic energy of ball at the highest point of its flight ? (1) (KE) (2) (KE) 8 2 (3) (KE) (4) (KE) 16 4

Q28.Two charges 7μc and −4μc are placed at (−7 cm, 0, 0) and (7 cm, 0, 0) respectively. Given, ϵ0 = 8.85 × 10−12C2 N−1 m−2 , the electrostatic potential energy of the charge configuration is : (1) -1.8 J (2) -2.0 J (3) -1.5 J (4) -1.2 J

Q28.Two bodies A and B of equal mass are suspended from two massless springs of spring constant k1 and k2 , respectively. If the bodies oscillate vertically such that their amplitudes are equal, the ratio of the maximum velocity of A to the maximum velocity of B is (1) k1 (2) k2 √k1k2 (3) (4) k2 k1 √k2k1

Q28.The output of the circuit is low (zero) for : (A) X = 0, Y = 0 (B) X = 0, Y = 1 (C) X = 1, Y = 0 (D) X = 1, Y = 1 Choose the correct answer from the options given below : (1) (B), (C) and (D) only (2) (A), (B) and (C) only (3) (A), (C) and (D) only (4) (A), (B) and (D) only

Q28.The torque due to the force (2^i + ^j + 2^k) about the origin, acting on a particle whose position vector is (^i + ^j + ^k), would be (1) ^i −^k (2) ^i + ^k (3) ^j + ^k (4) ^i −^j + ^k

Q28.The velocity-time graph of an object moving along a straight line is shown in figure. What is the distance covered by the object between t = 0 to t = 4 s ? (1) 30 m (2) 11 m (3) 10 m (4) 13 m

Q28.The position of a particle moving on x-axis is given by x(t) = A sin t + B cos2 t + Ct2 + D , where t is time. The dimension of ABC is D (1) L2T −2 (2) L2 (3) L (4) L3 T−2

Q30. The truth table for the circuit given below is : (1) (2) (3) (4)

Q30.Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Electromagnetic waves carry energy but not momentum. Reason ( R): Mass of a photon is zero. In the light of the above statements, choose the most appropriate answer from the options given below : (1) Both (A) and (R) are true and (R) is the correct (2) Both (A) and (R) are true but (R) is not the explanation of (A) correct explanation of (A) (3) (A) is false but (R) is true (4) (A) is true but ( R) is false

Q30.A massless spring gets elongated by amount x1 under a tension of 5 N . Its elongation is x2 under the tension of 7 N . For the elongation of (5x1 −2x2), the tension in the spring will be, (1) 39 N (2) 15 N (3) 11 N (4) 20 N

Q31.Two projectiles are fired with same initial speed from same point on ground at angles of (45∘−α) and (45∘+ α), respectively, with the horizontal direction. The ratio of their maximum heights attained is : (1) 1−tan α (2) 1−sin 2α 1+tan α 1+sin 2α (3) 1+sin 2α (4) 1+sin α 1−sin 2α 1−sin α

Q31.Given below are two statements: Statement I: The hot water flows faster than cold water Statement II: Soap water has higher surface tension as compared to fresh water. In the light above statements, choose the correct answer from the options given below (1) Statement I is true but Statement II is false (2) Statement I is false but Statement II is true (3) Both Statement I and Statement II are false (4) Both Statement I and Statement II are true

Q32.If λ and K are de Broglie wavelength and kinetic energy, respectively, of a particle with constant mass. The correct graphical representation for the particle will be 2025 (29 Jan Shift 1) JEE Main Previous Year Paper (1) (2) (3) (4)