Practice Questions

Q89.The distance of the point (1, −2, 4) from the plane passing through the point (1, 2, 2) and perpendicular to the planes x −y + 2z = 3 and 2x −2y + z + 12 = 0, is : (1) 2 (2) √2 (3) 2√2 (4) 1 √2

Q90.An experiment succeeds twice as often as it fails. The probability of at least 5 successes in the six trials of this experiment is (1) 496 (2) 192 729 729 (3) 240 (4) 256 729 729 JEE Main 2016 (10 Apr Online) JEE Main Previous Year Paper

Q90.If A and B are any two events such that P(A) = 25 and P(A ∩B) = 203 , then the conditional probability, P(A|(A′ ∪B′)), where A′ denotes the complement of A , is equal to : (1) 11 (2) 5 20 17 (3) 8 (4) 1 17 4 JEE Main 2016 (09 Apr Online) JEE Main Previous Year Paper

Q90.Let two fair six-faced dice A and B be thrown simultaneously. If E1 is the event that die A shows up four, E2 is the event that die B shows up two and E3 is the event that the sum of numbers on both dice is odd, then which of the following statements is not true? (1) E1 and E3 are independent (2) E1, E2 and E3 are independent (3) E1 and E2 are independent (4) E2 and E3 are independent JEE Main 2016 (03 Apr) JEE Main Previous Year Paper

Q1. If the capacitance of a nanocapacitor is measured in terms of a unit u, made by combining the electronic charge e, Bohr radius a0, Planck's constant h and speed of light c then hc u = (1) u = e2a0hc (2) e2a0 (3) u = e2c (4) u = e2h ha0 ca0

Q1. The period of oscillation of a simple pendulum is T = 2π√lg 1 mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using a wristwatch of 1 s resolution. The accuracy in the determination of g is (1) 5% (2) 4% (3) 3% (4) 1%

Q1. A vector A is rotated by a small angle Δθ radians (Δθ ≪1) to get a new vector B . In that case B − A is : (1) → (2) 0 A [1 −(Δθ)22 ] → → → (3) (4) A Δ θ B Δ θ − A

Q2. Two stones are thrown up simultaneously from the edge of a cliff 240 m high with an initial speed of 10 m s−1 and 40 m s−1 respectively. Which of the following graph best represents the time variation of the relative position of the second stone with respect to the first? (Assume stones do not rebound after hitting the ground and neglect air resistance, take g = 10 ms−2 )(the figure are schematic and not drawn to scale) (1) (2) (3) (4)

Q3. A block of mass m = 0.1 kg is connected to a spring of unknown spring constant k. It is compressed to a distance x from its equilibrium position and released from rest. After approaching half the distance ( x2 ) from the equilibrium position, it hits another block and comes to rest momentarily, while the other block moves with velocity 3 m s−1 . The total initial energy of the spring is: (1) 0 .6 J (2) 0 .8 J (3) 1 .5 J (4) 0 .3 J

Q3. Given in the figure are two blocks A and B of weight 20 N and 100 N , respectively. These are being pressed against a wall by a force F and kept in equilibrium as shown. If the coefficient of friction between the blocks is 0. 1 and between block B and the wall is 0. 15 , the frictional force applied by the wall on block B is: (1) 150 N (2) 100 N (3) 80 N (4) 120 N

Q5. A particle of mass m moving in the x direction with speed 2v is hit by another particle of mass 2m moving in the y direction with speed v. If the collision is perfectly inelastic, the percentage loss in the energy during the collision is close to: (1) 62% (2) 44% (3) 50% (4) 56%

Q5. A large number (n) of identical beads, each of mass m and radius r are strung on a thin smooth rigid horizontal rod of length L(L ≫r) and are at rest at random positions. The rod is mounted between two rigid supports (see figure). If one of the beads is now given a speed v, the average force experienced by each support after a long time is (assume all collisions are elastic): (1) mv2 (2) mv2 L−nr L−2nr (3) mv2 (4) Zero 2(L−nr)

Q5. Consider a thin uniform square sheet made of a rigid material. If its side is a, mass m and moment of inertia I about one of its diagonals, then: ma2 I < (1) I = ma224 (2) ma224 < 12 ma2 I = (3) I > ma212 (4) 12

Q6. A uniform solid cylindrical roller of mass m is being pulled on a horizontal surface with force F parallel to the surface and applied at its centre. If the acceleration of the cylinder is a and it is rolling without slipping then the value of F is: (1) 3 ma (2) 2 ma 2 (3) 5 ma (4) ma 3 JEE Main 2015 (10 Apr Online) JEE Main Previous Year Paper

Q6. A particle is moving in a circle of radius r under the action of a force F = αr2 which is directed towards centre of the circle. Total mechanical energy (kinetic energy + potential energy) of the particle is (take potential energy = 0 for r = 0): JEE Main 2015 (11 Apr Online) JEE Main Previous Year Paper (1) 5 6 αr3 (2) αr3 (3) 2 1 αr3 (4) 43 αr3

Q7. A uniform thin rod AB of length L has linear mass density μ(x) = a + bxL , where x is measured from A. If the CM of the rod lies at a distance of ( 127 L) from A, then a and b are related as: (1) 2a = b (2) a = 2b (3) a = b (4) 3a = 2b

Q7. A very long (length L) cylindrical galaxy is made of uniformly distributed mass and has radius R (R << L). A star outside the galaxy is orbiting the galaxy in a plane perpendicular to the galaxy and passing through its centre. If the time period of the star is T and its distance from the galaxy's axis is r, then (1) T ∝ √r (2) T ∝r (3) T ∝r2 (4) T 2 ∝r3

Q8. If two glass plates have water between them and are separated by very small distance (see figure), it is very difficult to pull them apart. It is because the water in between forms cylindrical surface on the side that gives rise to lower pressure in the water in comparison to atmosphere. If the radius of the cylindrical surface is R and surface tension of water is T then the pressure in water between the plates is lower by: (1) RT (2) 4RT (3) 4TR (4) 2TR

Q8. A particle of mass 2 kg is on a smooth horizontal table and moves in a circular path of radius 0. 6 m. The height of the table from the ground is 0. 8 m. If the angular speed of the particle is 12 rad s−1 , the magnitude of its angular momentum about a point on the ground right under the center of the circle is: (1) 14 .4 kg m2 s−1 (2) 11.52 kg m2 s−1 (3) 20.16 kg m2 s−1 (4) 8.64 kg m2 s−1

Q9. Which of the following most closely depicts the correct variation of the gravitation potential, V (r) with distance r due to a large planet of radius R and uniform mass density? (figures are not drawn to scale) (1) (2) (3) (4)

Q9. If it takes 5 minutes to fill a 15 litre bucket from a water tap of diameter 2 cm then the Reynolds number for √π the flow is (density of water = 103 kg/m3 and viscosity of water = 10−3 Pa. s ) close to: (1) 5500 (2) 550 (3) 1100 (4) 11,000

Q10.An ideal gas goes through a reversible cycle a →b →c →d has the V - T diagram shown below. Process d →a and b →c are adiabatic. The corresponding P - V diagram for the process is (all figures are schematic and not drawn to scale) : JEE Main 2015 (10 Apr Online) JEE Main Previous Year Paper (1) (2) (3) (4)

Q11.A solid body of constant heat capacity 1 J (℃)−1 is being heated by keeping it in contact with reservoirs in two ways: (i) Sequentially keeping in contact with 2 reservoirs such that each reservoir supplies the same amount of heat. (ii) Sequentially keeping in contact with 8 reservoirs such that each reservoir supplies the same amount of heat. In both, cases the body is brought from initial temperature 100 K to final temperature 200 K . Entropy change of the body in the two cases respectively is: Note: This question was awarded as a bonus since temperatures were given in centigrade instead of in Kelvin. Proper corrections are made in the question to avoid it. (1) 2 ln 2, 8 ln 2 (2) ln 2, 4 ln 2 (3) ln 2, ln 2 (4) ln 2, 2 ln 2

Q11.In an ideal gas at temperature T, the average force that a molecule applies on the walls of a closed container depends on T as T q . A good estimate for q is: (1) 2 (2) 12 (3) 1 (4) 14

Q11.Using equipartition of energy, the specific heat (in J kg−1 K−1 ) of Aluminium at high temperature can be estimated to be (atomic weight of Aluminium = 27) (1) 25 (2) 1850 (3) 410 (4) 925