Practice Questions

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

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)

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.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 ]

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¯¯¯

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.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

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.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

Q1. The dimensions of angular momentum, latent heat and capacitance are, respectively. (1) ML2 T1 A2, L2 T−2, M−1 L−2 T2 (2) ML2 T−2, L2 T2, M−1 L−2 T4 A2 (3) ML2 T−1, L2 T−2, ML2TA2 (4) ML2 T−1, L2 T−2, M−1 L−2 T4 A2

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. 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. 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

Q2. Two springs of force constants 300 N/m (Spring A) and 400 N/m (Spring B) are joined together in series. The combination is compressed by 8.75 cm. The ratio of energy stored in A and B is EA . Then EA is equal to: EB EB (1) 4 (2) 16 3 9 (3) 3 (4) 9 4 16

Q2. A 70 kg man leaps vertically into the air from a crouching position. To take the leap the man pushes the ground with a constant force F to raise himself. The center of gravity rises by 0.5 m before he leaps. After the leap the c.g. rises by another 1 m . The maximum power delivered by the muscles is : (Take g = 10 ms−2 ) (1) 6.26 × 103 Watts at the start (2) 6.26 × 103 Watts at take off (3) 6.26 × 104 Watts at the start (4) 6.26 × 104 Watts at take off

Q3. A bullet of mass 10 g and speed 500 m/s is fired into a door and gets embedded exactly at the centre of the door. The door is 1.0 m wide and weighs 12 kg. It is hinged at one end and rotates about a vertical axis practically without friction. The angular speed of the door just after the bullet embeds into it will be : (1) 6.25rad/sec (2) 0.625rad/sec (3) 3.35rad/sec (4) 0.335rad/sec

Q3. A wind-powered generator converts wind energy into electrical energy. Assume that the generator converts a fixed fraction of the wind energy intercepted by its blades into electrical energy. For wind speed v, the electrical power output will be most likely proportional to (1) v4 (2) v2 (3) v (4) v3

Q3. A boy of mass 20 kg is standing on a 80 kg free to move long cart. There is negligible friction between cart and ground. Initially, the boy is standing 25 m from a wall. If he walks 10 m on the cart towards the wall, then the final distance of the boy from the wall will be (1) 15 m (2) 12.5 m (3) 15.5 m (4) 17 m

Q3. Two blocks of mass M1 = 20 kg and M2 = 12 kg are connected by a metal rod of mass 8 kg. The system is pulled vertically up by applying a force of 480 N as shown. The tension at the mid-point of the rod is: (1) 144 N (2) 96 N (3) 240 N (4) 192 N

Q3. A uniform cylinder of length L and mass M having cross-sectional area A is suspended, with its length vertical, from a fixed point by a massless spring, such that it is half submerged in a liquid of density σ at equilibrium position. The extension x0 of the spring when it is in equilibrium is : (1) Mg k (1 −LAσ2M ) (2) Mgk (1 + LAσM ) (3) Mg (4) Mg k k (1 −LAσM )

Q4. A ring of mass M and radius R is rotating about its axis with angular velocity ω. Two identical bodies each of mass m are now gently attached at the two ends of a diameter of the ring. Because of this, the kinetic energy loss will be : (1) m(M+2m) M ω2R2 (2) (M+m)Mm ω2R2 (3) Mm ω2R2 (4) (M+m)M ω2R2 (M+2m) (M+2m)

Q4. A uniform sphere of weight W and radius 5 cm is being held by a string as shown in the figure. The tension in the string will be : (1) 12 W5 (2) 5 W12 (3) 13 W5 (4) 13 W12

Q4. A body starts from rest on a long inclined plane of slope 45∘ . The coefficient of friction between the body and the plane varies as μ = 0.3x, where x is distance travelled down the plane. The body will have maximum speed (for g = 10 m/s2 ) when x = (1) 9.8 m (2) 27 m (3) 12 m (4) 3.33 m

Q4. This question has Statement - I and Statement - II of the four choices given after the Statements, choose the one that best describes the two Statements. Statement - I: A point particle of mass m moving with speed ν collides with stationary point particle of mass M . If the maximum energy loss possible is given as f( 21 mν 2) then f = ( M+mm ). Statement - II: Maximum energy loss occurs when the particles get stuck together as a result of the collision. (1) Statement- I is true, Statement- II is false. (2) Statement- I is false, Statement- II is true. (3) Statement- I is true, Statement- II is true, (4) Statement- I is true, Statement- II is true, Statement- II is a correct explanation of Statement- II is not a correct explanation of Statement- I. Statement- I.

Q5. Two blocks of masses m and M are connected by means of a metal wire of cross-sectional area A passing over a frictionless fixed pulley as shown in the figure. The system is then released. If M = 2 m, then the stress JEE Main 2013 (25 Apr Online) JEE Main Previous Year Paper produced in the wire is: (1) 2mg (2) 4mg 3 A 3 A (3) mg (4) 3mg A 4 A