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

Q48.Two particles are located at equal distance from origin. The position vectors of those are represented by ¯A = 2^i + 3n^j + 2^k and ¯B = 2^i −2^j + 4p^k, respectively. If both the vectors are at right angle to each other, the value of n−1 is _____ .

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.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.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.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

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

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