Practice Questions

Q76.The number of real values of λ for which the system of linear equations, 2x + 4y −λz = 0 , 4x + λy + 2z = 0 and λx + 2y + 2z = 0 , has infinitely many solutions, is: (1) 3 (2) 1 (3) 2 (4) 0 Q77. ⎧ 0 cos x −sin x ⎫ π If S = x ∈[0, 2π] : sin x 0 cos x = 0 , then ∑x ∈S tan( 3 + x) is equal to: ⎨ ⎬ ⎩ cos x sin x 0 ⎭ (1) 4 + 2√3 (2) −4 -2 √3 (3) −2 + √3 (4) -2 −√3 |x| < 12 , x ≠0, is equal to:

Q77.The function f : N →I defined by f(x) = x −5[ x5 ] , where N is the set of natural numbers and [x] denotes the greatest integer less than or equal to x, is: (1) one-one but not onto (2) one-one and onto (3) neither one-one nor onto (4) onto but not one-one Q78. 4 tantan 5x4x π 5 ) , 0 < x < 2 π The value of k which the function f(x) = is continuous at x = 2 , is 2 π {( k + 5 , x = 2 (1) 2 5 (2) −25 (3) 17 (4) 3 20 5 , then λ + k is equal to

Q77.The function 𝑓 : 𝑅→-1 1 defined as 𝑓𝑥= 𝑥 is: 2, 2 1 + 𝑥2, (1) Invertible (2) Injective but not surjective (3) Surjective but not injective (4) Neither injective nor surjective

Q78.The value of tan−1[ √1+x2−√1+x2+ √1−x2√1−x2 ], (1) π 4 + 21 cos−1x2 (2) π4 −cos−1x2 (3) π 4 −12 cos−1x2 (4) π4 + cos−1x2

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

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

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 )

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

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.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

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

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 )

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 → →

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

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

Q88.If a variable plane, at a distance of 3 units from the origin, intersects the coordinate axes at A, B & C , then the locus of the centroid of ΔABC is (1) 1 + 1 + 1 = 1 (2) x2 y2 z2 x2 1 + y21 + z21 = 3 (3) 1 + 1 + 1 = 9 (4) 1 + 1 + 1 = 91 x2 y2 z2 x2 y2 z2

Q90.Three persons P, Q and R independently try to hit a target. If the probabilities of their hitting the target are 4 3 , 12 and 58 respectively, then the probability that the target is hit by P or Q but not by R is: (1) 3964 (2) 2164 (3) 9 (4) 15 64 64 JEE Main 2017 (08 Apr Online) JEE Main Previous Year Paper

Q90.If two different numbers are taken from the set 0, 1, 2, 3, . . . . . , 10; then the probability that their sum as well as absolute difference are both multiple of 4, is: (1) 6 (2) 12 55 55 (3) 14 (4) 7 45 55 JEE Main 2017 (02 Apr) JEE Main Previous Year Paper

Q90.Let E & F be two independent events. The probability that E & F happen is 121 and the probability that neither E nor F happens is 1 , then a value of P(E) is: 2 P(F) (1) 4 (2) 1 3 3 (3) 3 (4) 5 2 12 JEE Main 2017 (09 Apr Online) JEE Main Previous Year Paper

Q1. A student measures the time period of 100 oscillations of a simple pendulum four times. The data set is 90 s, 91 s, 95 s and 92 s. If the minimum division in the measuring clock is 1 s, then the reported mean time should be: (1) 92 ± 1.8 s (2) 92 ± 3 s (3) 92 ± 2 s (4) 92 ± 5.0 s

Q1. In the following I refers to current and other symbols have their usual meaning. Choose the option that corresponds to the dimensions of electrical conductivity: (1) M−1L−3T3I (2) M−1L−3T3I2 (3) M−1L3T3I (4) ML−3T−3I2