Practice Questions

Q79.If 2x = y 15 + y−15 and (x2 −1) dx2d2y + λx dxdy + ky = 0 (1) 26 (2) −24 (3) −23 (4) −26

Q79.If for 𝑥∈0, 4, the derivative of tan-1⁡1 - 9𝑥3 is √𝑥 ⋅𝑔𝑥 , then 𝑔𝑥 equals: JEE Main 2017 (02 Apr) JEE Main Previous Year Paper 9 3𝑥√𝑥 (1) (2) 1 + 9𝑥3 1 - 9𝑥3 3𝑥 3 (3) (4) 1 - 9𝑥3 1 + 9𝑥3

Q79.Let f(x) = 210x + 1 and g(x) = 310x −1. If (fog)(x) = x, then x is equal to: JEE Main 2017 (08 Apr Online) JEE Main Previous Year Paper (1) 210−1 (2) 1−2−10 210−3−10 310−2−10 (3) 310−1 (4) 1−3−10 310−2−10 210−3−10 15 15 dy is equal to + + x dx , then (x2 −1) dx2d2y

Q80.If y = [x + √x2 −1] [x −√x2 −1] (1) 224 y2 (2) 125 y (3) 225 y (4) 225 y2

Q80.Twenty meters of wire is available for fencing off a flower-bed in the form of a circular sector. Then the maximum area (in sq. m) of the flower-bed, is: (1) 12 . 5 (2) 10 (3) 25 (4) 30

Q80.The function f defined by f(x) = x3 −3x2 + 5x + 7 is: (1) Decreasing in R (2) Increasing in R (3) Increasing in (0, ∞) and decreasing in (−∞, 0) (4) Decreasing in (0, ∞) and increasing in (−∞, 0)

Q81.The normal to the curve 𝑦𝑥- 2 𝑥- 3 = 𝑥+ 6 at the point where the curve intersects the 𝑦-axis passes through the point: (1) -1 - 1 (2) 1 1 2, 2 2, 2 (3) 1 - 1 (4) 1 1 2, 3 2, 3

Q81.If f( 3x−43x+4 ) = x + 2, x ≠−43 , and ∫f(x)dx = A log|1 −x| + Bx + C , then the ordered pair (A, B) is equal to (1) (−83 , −23 ) (2) (−83 , 32 ) (3) ( 83 , 32 ) (4) ( 38 , −23 ) 2 dx k , then k is equal to

Q81.The tangent at the point (2, −2) to the curve, x2y2 −2x = 4(1 −y) does not pass through the point: (1) (−2, −7) (2) (8, 5) (3) (−4, −9) (4) (4, 13 )

Q82.The integral ∫√1 + 2 cot x(cosec x + cot x)dx, (0 < x < π2 ) is equal to (1) 2 log sin x2 + c (2) 4 log sin x2 + c (3) 4 log cos x2 + c (4) 2 log cos x2 + c Q83. π4 The integral ∫ 8 cos 2x dx equals π (tan x+cot x)3 12 (1) 13 (2) 15 256 64 (3) 13 (4) 15 32 128

Q82.Let, 𝐼𝑛= ∫tan𝑛𝑥𝑑𝑥𝑛> 1 . If 𝐼4 + 𝐼6 = 𝑎tan5𝑥+ 𝑏𝑥5 + 𝑐, then the ordered pair 𝑎, 𝑏, is equal to 1 1 (1) - 5, 1 (2) 5, 0 (3) 1 - 1 (4) -1 0 5, 5, Q83. 3𝜋4 The integral ∫ 𝑑𝑥 is equal to 𝜋 1 + cos𝑥 4 (1) -2 (2) 2 (3) 4 (4) -1

Q82.If ∫ 3 = k+5 1 (x2−2x+4) 2 (1) 4 (2) 2 (3) 3 (4) 1 lim = 601 for some positive real number a, then a is equal to 1a+2a+…+na ) (n+1)a−1[(na+1)+(na+2)+…+(na+n)]

Q83.If n→∞( (1) 17 (2) 15 2 2 (3) 7 (4) 8

Q84.Let f be a polynomial function such that f(3x) = f ′(x). f ′′(x), for all x ∈R. Then : (1) f(2) + f ′(2) = 28 (2) f ′′(2) −f ′(2) = 0 (3) f(2) −f ′(2) + f ′′(2) = 10 (4) f ′′(2) −f(2) = 4

Q84.The area (in sq. units) of the smaller portion enclosed between the curves, x2 + y2 = 4 and y2 = 3x, is: (1) √3 1 + 4π3 (2) √31 + 2π3 (3) 2√3 1 + π3 (4) 2√31 + 2π3

Q84.The area (in sq. units) of the region 𝑥, 𝑦: 𝑥≥0, 𝑥+ 𝑦≤3, 𝑥2 ≤4𝑦 and 𝑦≤1 + √𝑥 is 59 3 (1) sq . units (2) sq . units 12 2 (3) 7 sq . units (4) 5 sq . units 3 2

Q85.If 2 + sin𝑥 𝑑𝑦 𝑦+ 1cos𝑥= 0 and 𝑦0 = 1, then 𝑦 𝜋 is equal to 𝑑𝑥+ 2 (1) 1 (2) -2 3 3 1 4 (3) - (4) 3 3 → →

Q85.The curve satisfying the differential equation, ydx −(x + 3y2)dy = 0 and passing through the point (1, 1) also passes through the point (1) ( 41 , −12 ) (2) (−13 , 13 ) (3) ( 41 , 12 ) (4) ( 13 , −13 )

Q86.If the vector b = 3ˆj + 4ˆk is written as the sum of a vector b1 , parallel to →a = ˆi + ˆj and a vector b2, → → perpendicular to →a, then b1 × b2 is equal to : JEE Main 2017 (09 Apr Online) JEE Main Previous Year Paper (1) 6ˆi −6ˆj + 29 ˆk (2) −3ˆi + 3ˆj −9ˆk (3) −6ˆi + 6ˆj −92 ˆk (4) 3ˆi −3ˆj + 9ˆk

Q86.The area (in sq. units) of the parallelogram whose diagonals are along the vectors 8ˆi −6ˆj and 3ˆi + 4ˆj −12ˆk, is: (1) 20 (2) 65 (3) 52 (4) 26

Q86.Given, →𝑎= 2 ^𝑖+ ^𝑗- 2 ^𝑘 and 𝑏= ^𝑖+ ^𝑗. Let →𝑐 be a vector such that →𝑐- →𝑎= 3, →𝑎× 𝑏× →𝑐= 3 and the angle between →𝑐 and →𝑎× →𝑏 be 30° . Then →𝑎⋅ →𝑐 is equal to: 25 (1) (2) 2 8 (3) 5 (4) 1 8

Q87.If the image of the point 𝑃1, - 2, 3 in the plane, 2𝑥+ 3𝑦- 4𝑧+ 22 = 0 measured parallel to the line, 𝑥 𝑦 𝑧 = = is 𝑄, then 𝑃𝑄 is equal to: 1 4 5 (1) 3√5 (2) 2√42 (3) √42 (4) 6√5

Q87.The coordinates of the foot of the perpendicular from the point (1, −2, 1) on the plane containing the lines x+1 6 = y−17 = z−38 and x−13 = y−25 = z−37 , is: (1) (2, −4, 2) (2) (1, 1, 1) (3) (0, 0, 0) (4) (−1, 2, −1) = 2, is,

Q88.The line of intersection of the planes →r ⋅(3ˆi −ˆj + ˆk) = 1 and →r ⋅(ˆi + 4ˆj −2ˆk) (1) x−613 y−513 z (2) x−47 y z+ 57 2 = 7 = −13 2 = −7 = 13 y z−57 (3) x−613 y−513 z (4) x−47 2 = −7 = −13 −2 = 7 = 13

Q88.The distance of the point 1, 3, - 7 from the plane passing through the point 1, - 1, - 1 , having normal 𝑥- 1 𝑦+ 2 𝑧- 4 𝑥- 2 𝑦+ 1 𝑧+ 7 perpendicular to both the lines = = and = = , is: 1 -2 3 2 -1 -1 (1) 20 (2) 10 √74 √83 (3) 5 (4) 10 √83 √74 JEE Main 2017 (02 Apr) JEE Main Previous Year Paper