Practice Questions

Q86.If the differential equation representing the family of all circles touching x-axis at the origin is (x2 −y2) dxdy = g(x)y, then g(x) equals (1) 1 x2 (2) 2x 2 (3) 1 x (4) 2x2 2 → → →

Q86.Let the population of rabbits surviving at a time t be governed by the differential equation dp(t) . If p(0) = 100, then p(t) equals dt = 12 {p(t) −400} (1) 600 − 500 e 2t (2) 400 −300 e −t2 (3) 400 − 300 et/2 (4) 300 −200 e −t2 2 → → → → a b then λ is equal to

Q87.If |→c|2 = 60 and →c × (^i + 2^j + 5^k) = 0, then a value of →c ⋅(−7^i + 2^j + 3^k) is: (1) 4√2 (2) 12 (3) 24 (4) 12√2 y−2

Q87.If ^x, ^y and ^z are three unit vectors in threedimensional space, then the minimum value of |^x + ^y|2 + |^y + ^z|2 + |^z + ^x|2 (1) 3 (2) 3 2 (3) 3√3 (4) 6

Q87.If →a = 2, b = 3 and 2→a− b = 5, then 2→a+ b equals : (1) 5 (2) 7 (3) 17 (4) 1 y−2

Q87.If ×→b →b ×→c c = λ [→a ×→a] [ c] (1) 0 (2) 1 (3) 2 (4) 3 y−3

Q87.If x = 3ˆi −6ˆj −ˆk , y = ˆi + 4ˆj −3ˆk and →z= 3ˆi −4ˆj −12ˆk, then the magnitude of the projection of x ×→y on →zis (1) 14 (2) 12 (3) 15 (4) 10

Q88.The plane containing the line x−1 1 = 2 = z−33 and parallel to the line x1 = y1 = 4z passes through the point: (1) (1, −2, 5) (2) (1, 0, 5) (3) (0, 3, −5) (4) (−1, −3, 0)

Q88.A symmetrical form of the line of intersection of the planes x = ay + b and z = cy + d is (1) x−b a = y−11 = z−dc (2) x−b−aa = y−11 = z−d−cc (3) x−a b = y−01 = z−cd (4) x−b−ab = y−10 = z−d−cd

Q88.The image of the line x−1 3 = 1 = z−4−5 in the plane 2x −y + z +3=0 is the line (1) x−3 3 = y+51 = z−2−5 (2) x−3−3 = y+5−1 = z−25 (3) x+3 3 = y−51 = z−2−5 (4) x+3−3 = y−5−1 = z+25

Q88.Equation of the plane which passes through the point of intersection of lines x−1 3 = 1 = z−32 and x−3 1 = y−12 = z−23 and has the largest distance from the origin is: JEE Main 2014 (09 Apr Online) JEE Main Previous Year Paper (1) 4x + 3y + 5z = 50 (2) 3x + 4y + 5z = 49 (3) 5x + 4y + 3z = 57 (4) 7x + 2y + 4z = 54

Q88.If the angle between the line 2(x + 1) = y = z + 4 and the plane 2x −y + √λz + 4 = 0 is π6 , then the value of λ is (1) 45 (2) 135 7 11 (3) 135 (4) 45 7 11 y

Q89.The angle between the lines whose direction cosines satisfy the equations l + m + n = 0 and l2 = m2 + n2 is (1) π (2) π 6 2 (3) π (4) π 3 4 = 14 , where A stands for¯¯¯

Q89.Equation of the line of the shortest distance between the lines x 1 = −1 = 1z and x−10 = y+1−2 = 1z is JEE Main 2014 (19 Apr Online) JEE Main Previous Year Paper (1) −2 x = 1y = 2z (2) x1 = −1y = −2z y+1 (3) x−1 1 = −1 = −2z (4) x−11 = y+1−1 = 1z

Q89.A set S contains 7 elements. A non-empty subset A of S and an element x of S are chosen at random. Then the probability that x ∈A is: (1) 1 (2) 64 2 127 (3) 63 (4) 31 128 128

Q89.If the distance between planes, 4x −2y −4z + 1 = 0 and 4x −2y −4z + d = 0 is 7 , then d is: (1) 41 or −42 (2) 42 or −43 (3) −41 or 43 (4) −42 or 44

Q89.A line in the 3 -dimensional space makes an angle θ(0 < θ ≤π2 ) with both the X and Y −axes. Then, the set of all values of θ is in the interval : (1) ( π3 , π2 ] (2) (0, π4 ] (3) [ π4 , π2 ] (4) [ π6 , π3 ]

Q90.If A and B are two events such that P(A ∪B) = P(A ∩B), then the incorrect statement amongst the following statements is : (1) P(A) + P(B) = 1 (2) P(A ∩B′) = 0 (3) A & B are equally likely (4) P(A′ ∩B) = 0 JEE Main 2014 (09 Apr Online) JEE Main Previous Year Paper

Q90.Let A and E be any two events with positive probabilities Statement I: P(E/A) ≥P(A/E)P(E). Statement II: P(A/E) ≥P(A ∩E). (1) Both the statements are false (2) Both the statements are true (3) Statement - I is false, Statement - II is true (4) Statement - I is true, Statement - II is false JEE Main 2014 (19 Apr Online) JEE Main Previous Year Paper

Q90.A number x is chosen at random from the set {1, 2, 3, 4, … . , 100}. Define the event: A = the chosen number x satisfies (x−10)(x−50) ≥0 Then P(A) is: (x−30) (1) 0.71 (2) 0.70 (3) 0.51 (4) 0.20 JEE Main 2014 (12 Apr Online) JEE Main Previous Year Paper

Q90.If X has a binomial distribution, B(n, p) with parameters n and p such that P(X = 2) = P(X = 3), then E(X), the mean of variable X, is (1) 2 −p (2) 3 −p (3) p (4) p 2 3 JEE Main 2014 (11 Apr Online) JEE Main Previous Year Paper

Q90.Let A and B be two events such that P(A ∪B) = 16 , P(A ∩B) = 41 and P(A) the complement of the event A . Then the events A and B are (1) Independent but not equally likely. (2) Independent and equally likely. (3) Mutually exclusive and independent. (4) Equally likely but not independent. JEE Main 2014 (06 Apr) JEE Main Previous Year Paper

Q1. If the time period t of the oscillation of a drop of liquid of density d, radius r, vibrating under surface tension s . The is given by the formula t = √r2bscda/2 . It is observed that the time period is directly proportional to √ds value of b should therefore be : (1) 3 (2) √3 4 (3) 3 (4) 2 2 3

Q1. A block is placed on a rough horizontal plane. A time dependent horizontal force F = kt acts on the block, where k is a positive constant. The acceleration - time graph of the block is : (1) (2) (3) (4)

Q1. Let [∈0] denote the dimensional formula of the permittivity of vacuum. If M = mass, L = length, T = time and A = electric current, then : (1) [∈0] = [M−1 L2 T−1 A−2] (2) [∈0] = [M−1 L2 T−1 A] (3) [∈0] = [M−1 L−3 T2 A] (4) [∈0] = [M−1 L−3 T4 A2] + m s−1 , where ˆi is along the ground and ˆj is along the vertical