Practice Questions

Q54.The major product of the following reaction is: JEE Main 2018 (16 Apr Online) JEE Main Previous Year Paper (1) (2) (3) (4)

Q55.The total number of possible isomers for squareplanar [Pt(Cl) (NO2) (NO3)(SCN)]2− is: (1) 16 (2) 12 (3) 8 (4) 24

Q57.The reagent(s) required for the following conversion are: (1) (i) NaBH4 , (ii) Raney Ni/H2 , (iii) H3O+ (2) (i) LiAlH4 , (ii) H3O+ (3) (i) B2H6 , (ii) DIBAL −H, (iii) H3O+ (4) (i) B2H6 , (ii) SnCl2/HCl, (iii) H3O+

Q63.The set of all α ∈R, for which w = 1+(1−8α)z1−z is a purely imaginary number, for all and Re(z) ≠1 , is : (1) {0} (2) {0, 14 , −14 } (3) equal to R (4) an empty set

Q66.If n is the degree of the polynomial, 1 8 1 8 + [ √5x3 + 1 −√5x3 −1 ] [ √5x3 + 1 + √5x3 −1 ] and m is the coefficient of xn in it, then the ordered pair (n, m) is equal to (1) (12, (20)4) (2) (8, 5(10)4) (3) (24, (10)8) (4) (12, 8(10)4) JEE Main 2018 (15 Apr Shift 1 Online) JEE Main Previous Year Paper

Q67.If n is the degree of the polynomial, 8 8 m is the coefficient of xn + [ √5x3+1−√5x3−12 ] [ √5x3+1+√5x3−12 ] and in it, then the ordered pair (n, m) is equal to (1) (8, 5(10)4) (2) (12, 8(10)4) (3) (12, (20)4) (4) (24, (10)8)

Q69.The sides of a rhombus ABCD are parallel to the lines, x −y + 2 = 0 and 7x −y + 3 = 0. If the diagonals of the rhombus intersect at P(1, 2) and the vertex A (different from the origin) is on the y axis, then the ordinate of A is (1) 2 (2) 7 4 (3) 7 (4) 5 2 2

Q69.Two parabolas with a common vertex and with axes along the x-axis and y-axis respectively, intersect each other in the first quadrant. If the length of the latus rectum of each parabola is 3 , then the equation of the common tangent to the two parabolas is : (1) 3(x + y) + 4 = 0 (2) 8(2x + y) + 3 = 0 (3) x + 2y + 3 = 0 (4) 4(x + y) + 3 = 0 JEE Main 2018 (15 Apr) JEE Main Previous Year Paper cos θ, √3 sin

Q70.Tangent and normal are drawn at P(16, 16) on the parabola y2 = 16x, which intersect the axis of the parabola at A & B, respectively. If C is the center of the circle through the points P, A & B and ∠CPB = θ, then a value of tan θ is: (1) 4 (2) 1 3 2 (3) 2 (4) 3

Q70.Let P be a point on the parabola x2 = 4y. If the distance of P from the center of the circle x2 + y2 + 6x + 8 = 0 is minimum, then the equation of the tangent to the parabola at P is (1) x + y + 1 = 0 (2) x + 4y −2 = 0 (3) x + 2y = 0 (4) x −y + 3 = 0

Q70.If β is one of the angles between the normals to the ellipse x2 + 3y2 = 9 at the points (3 θ) and θ ∈(0, π2 ); then 2sincot2θβ is equal to : (−3 sin θ, √3 cos θ); (1) 1 (2) √3 √3 4 (3) 2 (4) √2 √3

Q72.If the tangents drawn to the hyperbola 4y2 = x2+ 1 intersect the co-ordinate axes at the distinct points A and B, then the locus of the mid point of AB is (1) x2 −4y2 + 16x2y2 = 0 (2) 4x2 −y2 + 16x2y2 = 0 (3) 4x2 −y2 −16x2y2 = 0 (4) x2 −4y2 −16x2y2 = 0

Q72.A normal to the hyperbola, 4x2 −9y2 = 36 meets the co-ordinate axes x and y at A and B, respectively. If the parallelogram OABP(O being the origin) is formed, then the locus of P is (1) 4x2 −9y2 = 121 (2) 4x2 + 9y2 = 121 (3) 9x2 −4y2 = 169 (4) 9x2 + 4y2 = 169

Q75.In a triangle ABC , coordinates of A are (1, 2) and the equations of the medians through B and C are respectively, x + y = 5 and x = 4 . Then area of ΔABC (in sq. units) is : (1) 12 (2) 4 (3) 9 (4) 5

Q77.Let A be a matrix such that A . [10 23 ] (1) [40 −3236 ] (2) [−324 360 ] (3) [−3236 04] (4) [360 −324 ]

Q80.Let S = {(λ, μ) ∈R × R : f(t) = (|λ |e|t| −μ) sin(2|t|), t ∈R is a differential function}. Then, S is a subset of : (1) (−∞, 0) × R (2) R × [0 , ∞) (3) [0 , ∞) × R (4) R × (−∞, 0)

Q82.If ∫ 1+tantanx+tan2x x dx = x − √AK tan−1( K tan√Ax+1 ) (K, A) is equal to (1) (2, 1) (2) (2, 3) (3) (−2, 1) (4) (−2, 3) x −sin t)dt, then

Q82.If a right circularcone having maximum volume, is inscribed in a sphere of radius 3 cm, then the curved surface area (in cm2 ) of this cone is (1) 8√3π (2) 6√2π (3) 6√3π (4) 8√2π

Q82.Let f(x) be a polynomial of degree 4 having extreme values at x = 1 and x = 2. If limx→0 f(x)x2 + = 3 ( 1) then f(−1) is equal to (1) 1 (2) 3 2 2 (3) 5 (4) 9 2 2

Q85.The differential equation representing the family of ellipses having foci either on the x-axis or on the y-axis, center at the origin and passing through the point (0, 3) is (1) xyy′ −y2 + 9 = 0 (2) xyy′′ + x(y′)2 −yy′ = 0 (3) xyy′ + y2 −9 = 0 (4) x + yy′′ = 0 → → → →

Q88.If L1 is the line of intersection of the planes 2x −2y + 3z −2 = 0, x −y + z + 1 = 0 and L2 is the line of intersection of the planes x + 2y −z −3 = 0, 3x −y + 2z −1 = 0, then the distance of the origin from the plane, containing the lines L1 and L2 is (1) 1 (2) 1 √2 4√2 (3) 1 (4) 1 3√2 2√2

Q88.An angle between the lines whose direction cosines are given by the equations, l + 3m + 5n = 0 and 5lm −2mn + 6nl = 0, is (1) cos−1 ( 81 ) (2) cos−1 ( 61 ) (3) cos−1 ( 31 ) (4) cos−1 ( 41 )

Q89.An angle between the plane, x + y + z = 5 and the line of intersection of the planes, 3x + 4y + z −1 = 0 and 5x + 8y + 2z + 14 = 0 , is (1) cos−1 3 (2) cos−1 17 ( √17 ) (√3 ) 3 (4) (3) sin−1 sin−1 17 ( √17 ) (√3 )

Q90.A player X has a biased coin whose probability of showing heads is p and a player Y has a fair coin. They start playing a game with their own coins and play alternately. The player who throws a head first is a winner. If X starts the game, and the probability of winning the game by both the players is equal, then the value of ' p ' is (1) 1 (2) 1 3 5 (3) 1 (4) 2 4 5 JEE Main 2018 (15 Apr Shift 2 Online) JEE Main Previous Year Paper

Q4. The machine as shown has 2 rods of length 1 m connected by a pivot at the top. The end of one rod is connected to the floor by a stationary pivot and the end of the other rod has roller that rolls along the floor in a slot. As the roller goes back and forth, a 2 kg weight moves up and down. If the roller is moving towards right at a constant speed, the weight moves up with a : (1) Speed which is 3 4 th of that of the roller when the (2) Constant speed weight is 0. 4 m above the ground (3) Decreasing speed (4) Increasing speed