Practice Questions

Q63.Let A = {n ∈[100, 700] ∩N : n is neither a multiple of 3 nor a multiple of 4 }. Then the number of elements in A is (1) 290 (2) 280 (3) 300 (4) 310

Q64.If the coefficients of x4, x5 and x6 in the expansion of (1 + x)n are in the arithmetic progression, then the maximum value of n is: (1) 7 (2) 21 (3) 28 (4) 14

Q64.If the term independent of x in the expansion of (√ax2 + 2x31 )10 is 105 , then a2 is equal to : (1) 2 (2) 4 (3) 6 (4) 9 JEE Main 2024 (08 Apr Shift 2) JEE Main Previous Year Paper cos 36∘+5 sin 18∘

Q64.For 𝛼, 𝛽∈0, let 3sin ( 𝛼+ 𝛽) = 2sin ( 𝛼- 𝛽) and a real number 𝑘 be such that tan𝛼= tan𝛽. Then the 2 value of 𝑘 is equal to (1) -5 (2) 5 (3) 2 (4) -2 3 3

Q64.Let |cos θ cos(60 −θ) cos(60 + θ)| ≤18 , θϵ[0, 2π]. Then, the sum of all θϵ[0, 2π], where cos 3θ attains its maximum value, is : (1) 15π (2) 18π (3) 6π (4) 9π

Q64.If 2tan2𝜃- 5sec𝜃= 1 has exactly 7 solutions in the interval 0, n𝜋 , for the least value of n ∈N then n k is 2 ∑k = 1 2k equal to : - 15 (1) 2152141 - 14 (2) 2142151 15 1 (3) 1 - (4) - 15 213 213214

Q64.Let 3, 𝑎, 𝑏, 𝑐 be in 𝐴. 𝑃. and 3, 𝑎−1, 𝑏+ 1, 𝑐+ 9 be in 𝐺. 𝑃. Then, the arithmetic mean of 𝑎, 𝑏 and 𝑐 is: (1) -4 (2) -1 (3) 13 (4) 11 1 √𝑥

Q64.Let ABC be an equilateral triangle. A new triangle is formed by joining the middle points of all sides of the triangle ABC and the same process is repeated infinitely many times. If P is the sum of perimeters and Q is be the sum of areas of all the triangles formed in this process, then : (1) P2 = 6√3Q (2) P2 = 36√3Q (3) P = 36√3Q2 (4) P2 = 72√3Q

Q64. n−1Cr = (k2 −8)nCr+1 if and only if : (1) 2√2 < k ≤3 (2) 2√3 < k ≤3√2 (3) 2√3 < k < 3√3 (4) 2√2 < k < 2√3 JEE Main 2024 (27 Jan Shift 1) JEE Main Previous Year Paper

Q64.If each term of a geometric progression a1, a2, a3, … with a1 = 18 and a2 ≠a1 , is the arithmetic mean of the next two terms and Sn = a1 + a2 + … + an , then S20 −S18 is equal to (1) 215 (2) −218 (3) 218 (4) −215

Q64.Let the first three terms 2, p and q , with q ≠2, of a G.P. be respectively the 7th , 8th and 13th terms of an A.P. If the 5th term of the G.P. is the nth term of the A.P., then n is equal to: (1) 163 (2) 151 (3) 177 (4) 169

Q64.The sum of the coefficient of x2/3 and x−2/5 in the binomial expansion of (x2/3 + 12 x−2/5) 9 (1) 21/4 (2) 63/16 (3) 19/4 (4) 69/16

Q64.If α, −π2 < α < π2 is the solution of 4 cos θ + 5 sin θ = 1, then the value of tan α is (1) 10−√10 (2) 10−√10 6 12 (3) √10−10 (4) √10−10 12 6

Q64.Let a variable line of slope m > 0 passing through the point (4, −9) intersect the coordinate axes at the points A and B. The minimum value of the sum of the distances of A and B from the origin is JEE Main 2024 (06 Apr Shift 1) JEE Main Previous Year Paper (1) 30 (2) 25 (3) 15 (4) 10

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

Q64.Let 𝛼, 𝛽, 𝛾, 𝛿∈𝑍 and let 𝐴𝛼, 𝛽, 𝐵1, 0, 𝐶𝛾, 𝛿 and 𝐷1, 2 be the vertices of a parallelogram 𝐴𝐵𝐶𝐷. If 𝐴𝐵= √10 and the points 𝐴 and 𝐶 lie on the line 3𝑦= 2𝑥+ 1, then 2𝛼+ 𝛽+ 𝛾+ 𝛿 is equal to (1) 10 (2) 5 (3) 12 (4) 8

Q64.Let two straight lines drawn from the origin O intersect the line 3x + 4y = 12 at the points P and Q such that △OPQ is an isosceles triangle and ∠POQ = 90∘ . If l = OP2 + PQ2 + QO2 , then the greatest integer less than or equal to l is : (1) 42 (2) 46 (3) 44 (4) 48

Q64.If the constant term in the expansion of 12 + , x ≠0, is α × 28 × 5√3, then 25α is equal to : ( 5√3x 2x ) 3√5 (1) 724 (2) 742 (3) 639 (4) 693

Q64.Let 𝑚 and 𝑛 be the coefficients of seventh and thirteenth terms respectively in the expansion of 3 + 2 3𝑥 2𝑥 3 1 . Then 𝑛 3 is: 𝑚 (1) 4 (2) 1 9 9 1 9 (3) (4) 4 4

Q64.Let 2nd, 8th and 44th, terms of a non-constant 𝐴. 𝑃. be respectively the 1st, 2nd and 3rd terms of 𝐺. 𝑃. If the first term of A.P. is 1 then the sum of first 20 terms is equal to- (1) 980 (2) 960 (3) 990 (4) 970

Q65.Let C be a circle with radius √10 units and centre at the origin. Let the line x + y = 2 intersects the circle C at the points P and Q. Let MN be a chord of C of length 2 unit and slope -1. Then, a distance (in units) between the chord PQ and the chord MN is (1) 3 −√2 (2) √2 + 1 (3) √2 −1 (4) 2 −√3

Q65.If 𝑥2 - 𝑦2 + 2ℎ𝑥𝑦+ 2𝑔𝑥+ 2𝑓𝑦+ 𝑐= 0 is the locus of a point, which moves such that it is always equidistant from the lines 𝑥+ 2𝑦+ 7 = 0 and 2𝑥- 𝑦+ 8 = 0, then the value of 𝑔+ 𝑐+ ℎ- 𝑓 equals (1) 14 (2) 6 (3) 8 (4) 29

Q65.A ray of light coming from the point P(1, 2) gets reflected from the point Q on the x-axis and then passes through the point R(4, 3). If the point S(h, k) is such that PQRS is a parallelogram, then hk2 is equal to : (1) 70 (2) 80 (3) 60 (4) 90

Q65.If tan𝐴= 1 tan𝐵= and tan𝐶= 𝑥−3 + 𝑥−2 + 𝑥−1 2, 0 < 𝐴, 𝐵, 𝐶< 𝜋 then 𝐴+ 𝐵 is equal √𝑥𝑥2 + 𝑥+ 1, √𝑥2 + 𝑥+ 1 2, to: (1) 𝐶 (2) 𝜋−𝐶 (3) 2𝜋−𝐶 (4) 𝜋 −𝐶 2 JEE Main 2024 (01 Feb Shift 1) JEE Main Previous Year Paper