Practice Questions

Q62.Let Sa denote the sum of first n terms an arithmetic progression. If S20 = 790 and S10 = 145, then S15−S5 is : JEE Main 2024 (30 Jan Shift 1) JEE Main Previous Year Paper (1) 395 (2) 390 (3) 405 (4) 410

Q63.The number of ways in which 21 identical apples can be distributed among three children such that each child gets at least 2 apples, is (1) 406 (2) 130 (3) 142 (4) 136

Q63.The 20th term from the end of the progression 20, 191 181 173 … , - 1291 is :- 4, 2, 4, 4 (1) -118 (2) -110 (3) -115 (4) -100

Q63.If A denotes the sum of all the coefficients in the expansion of (1 −3x + 10x2) and B denotes the sum of all the coefficients in the expansion of (1 + x2)n , then : (1) A = B3 (2) 3 A = B (3) B = A3 (4) A = 3 B

Q64.If sin x = −35 , where π < x < 3π2 , then 80 (tan2 x −cos x) is equal to (1) 108 (2) 109 (3) 18 (4) 19 JEE Main 2024 (08 Apr Shift 1) JEE Main Previous Year Paper

Q64.A line passing through the point A(9, 0) makes an angle of 30° with the positive direction of x-axis. If this line is rotated about A through an angle of 15° in the clockwise direction, then its equation in the new position is (1) y + x = 9 (2) x + y = 9 √3−2 √3−2 (3) x + y = 9 (4) y + x = 9 √3+2 √3+2

Q67. lim 𝑒2sin𝑥- 2sin𝑥- 1 𝑥→0 𝑥2 (1) is equal to -1 (2) does not exist (3) is equal to 1 (4) is equal to 2

Q67.If the length of the minor axis of ellipse is equal to half of the distance between the foci, then the eccentricity of the ellipse is : (1) √5 (2) √3 3 2 (3) 1 (4) 2 √3 √5 π 1 x ∫x0 f(t)dt lim = α, then 8α2 is equal

Q69.Let M denote the median of the following frequency distribution. Class 0 −4 4 −8 8 −12 12 −16 16 −20 Frequency 3 9 10 8 6 Then 20M is equal to : (1) 416 (2) 104 (3) 52 (4) 208 Q70. 2 cos4 x 2 sin4 x 3 + sin2 2x If f(x) = 3 + 2 cos4 x 2 sin4 x sin2 2x then 15 f ′(0) is equal to ________. 2 cos4 x 3 + 2 sin4 x sin2 2x JEE Main 2024 (30 Jan Shift 1) JEE Main Previous Year Paper (1) 0 (2) 1 (3) 2 (4) 6

Q70.Considering only the principal values of inverse trigonometric functions, the number of positive real values of 𝑥 satisfying tan-1 (x) + tan-1 (2x) = π is : 4 (1) More than 2 (2) 1 (3) 2 (4) 0

Q73.Let 𝑓𝑥= 2𝑥2 + 5𝑥- 3, 𝑥∈𝑅. If 𝑚 and 𝑛 denote the number of points where 𝑓 is not continuous and not differentiable respectively, then 𝑚+ 𝑛 is equal to: (1) 5 (2) 2 (3) 0 (4) 3

Q78.Let →𝑎 and →𝑏 be two vectors such that | →𝑏| = 1 and | →𝑏× →𝑎| = 2 Then |( →𝑏× →𝑎) - →𝑏| (1) 3 (2) 5 (3) 1 (4) 4

Q79.Let P(3, 2, 3), Q(4, 6, 2) and R(7, 3, 2) be the vertices of Δ PQR. Then, the angle ∠QPR is (1) π 6 (2) cos−1( 187 ) (3) cos−1( 181 ) (4) π3

Q79.Two marbles are drawn in succession from a box containing 10 red, 30 white, 20 blue and 15 orange marbles, with replacement being made after each drawing. Then the probability, that first drawn marble is red and second drawn marble is white, is 2 4 (1) (2) 25 25 (3) 2 (4) 4 3 75

Q80.Let Ajay will not appear in JEE exam with probability 𝑝= 2 while both Ajay and Vijay will appear in the 7, exam with probability 𝑞= 15. Then the probability, that Ajay will appear in the exam and Vijay will not appear is: 9 18 (1) (2) 35 35 (3) 24 (4) 3 35 35

Q80.A coin is biased so that a head is twice as likely to occur as a tail. If the coin is tossed 3 times, then the probability of getting two tails and one head is- 2 1 (1) (2) 9 9 (3) 2 (4) 1 27 27

Q83.Remainder when 643232 is divided by 9 is equal to _____.

Q85.Let A = {2, 3, 6, 7} and B = {4, 5, 6, 8}. Let R be a relation defined on A × B by (a1, b1)R (a2, b2) if and only if a1 + a2 = b1 + b2 . Then the number of elements in R is _________

Q86.Let the inverse trigonometric functions take principal values. The number of real solutions of the equation 2 sin−1 x + 3 cos−1 x = 2π5 , is _______

Q87.Let f(x) = 2x −x2, x ∈R. If m and n are respectively the number of points at which the curves y = f(x) and y = f ′(x) intersects the x−axis, then the value of m + n is

Q89.The least positive integral value of α, for which the angle between the vectors αˆi −2ˆj + 2ˆk and αˆi + 2αˆj −2ˆk is acute, is _____.

Q1. Match List I with List II List I List II A Torque I kg m–1 s–2 B Energy density II kg m s–1 C Pressure gradient III kg m–2 s–2 D Impulse IV kg m2 s–2 Choose the correct answer from the options given below : (1) A-IV, B-III, C-I, D-II (2) A-I, B-IV, C-III, D-II (3) A-IV, B-I, C-II, D-III (4) A-IV, B-I, C-III, D-II

Q1. Electric field in a certain region is given by →𝐸= 𝐴 ^i + 𝐵 ^j. The SI unit of 𝐴 and 𝐵 are : 𝑥2 𝑦3 (1) N m3 C-1; N m2 C-1 (2) N m2 C-1; N m3 C-1 (3) N m3 C; N m2 C (4) N m2 C; N m3 C

Q1. If 𝑅, 𝑋𝐿 and 𝑋𝐶 represent resistance, inductive reactance and capacitive reactance. Then which of the following is dimensionless: 𝑅 (1) 𝑅 𝑋𝐿 𝑋𝐶 (2) √𝑋𝐿𝑋𝑐 𝑅 𝑋𝐿 (3) (4) 𝑅 𝑋𝐿𝑋𝑐 𝑋𝑐

Q1. Match List I with List II : List-I (Physical Quantity) List-II (Dimensional Formula) A Pressure gradient I [M0L2T−2] B Energy density II [M1L−1T−2] C Electric Field III [M1L−2T−2] D Latent heat IV [M1L1T−3A−1] Choose the correct answer from the options given below: (1) A-III, B-II, C-I, D-IV (2) A-II, B-III, C-IV, D-I (3) A-III, B-II, C-IV, D-I (4) A-II, B-III, C-I, D-IV