Practice Questions

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.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

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

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.A tangent to the curve, y = f(x) at P(x, y) meets x -axis at A and y -axis at B . If AP : BP = 1 : 3 and f(1) = 1, then the curve also passes through the point (1) ( 13 , 24) (2) ( 21 , 4) (3) (2, 18 ) (4) (3, 281 ) → → →

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.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

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

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.If the line, x−3 1 = y+2−1 = z+λ−2 lies in the plane, 2x −4y + 3z = 2 , then the shortest distance between this line and the line, x−1 12 = 9y = 4z is (1) 1 (2) 2 (3) 3 (4) 0

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.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

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

Q89.An unbiased coin is tossed eight times. The probability of obtaining at least one head and at least one tail is: JEE Main 2017 (08 Apr Online) JEE Main Previous Year Paper (1) 127 (2) 63 128 64 (3) 255 (4) 1 256 2

Q89.For three events, 𝐴, 𝐵 and 𝐶, 𝑃(Exactly one of 𝐴 or 𝐵 occurs) = 𝑃(Exactly one of 𝐵 or 𝐶 occurs) 1 1 = 𝑃(Exactly one of 𝐶 or 𝐴 occurs) = and 𝑃(All the three events occur simultaneously) = . 4 16 Then the probability that at least one of the events occurs, is: (1) 7 (2) 7 32 16 7 3 (3) (4) 64 16

Q89. From a group of 10 men and 5 women, four member committees are to be formed each of which must contain at least one women. Then the probability for these committees to have more women than men, is : (1) 3 (2) 2 11 23 (3) 1 (4) 21 11 220

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.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

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

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