Practice Questions

Q89.The equation of the plane containing the line of intersection of 2x −5y + z = 3; x + y + 4z = 5, and parallel to the plane, x + 3y + 6z = 1, is (1) 2x + 6y + 12z = −13 (2) 2x + 6y + 12z = 13 (3) x + 3y + 6z = −7 (4) x + 3y + 6z = 7

Q90.Let X be a set containing 10 elements and P(X) be its power set. If A and B are picked up at random from P(X), with replacement, then the probability that A and B have equal number of elements is: (1) (210−1) (2) 20C10 220 220 (3) 20C10 (4) (210−1) 210 210 JEE Main 2015 (10 Apr Online) JEE Main Previous Year Paper

Q90.If 12 identical balls are to be placed in 3 identical boxes, then the probability that one of the boxes contains exactly 3 balls is (1) 22( 13 )11 (2) 195 (3) 55( 32 )10 (4) 220( 31 )12 JEE Main 2015 (04 Apr) JEE Main Previous Year Paper

Q90.If the lengths of the sides of a triangle are decided by the three throws of a single fair die, then the probability that the triangle is of maximum area given that it is an isosceles triangle, is: (1) 1 (2) 1 69 26 (3) 1 (4) 1 21 15 JEE Main 2015 (11 Apr Online) JEE Main Previous Year Paper

Q1. From the following combinations of physical constants (expressed through their usual symbols) the only combination, that would have the same value in different systems of units, is: (1) ch (2) e2 2πε2o 2πεoGm2e (3) μoεo G (4) 2π√μoεo h c2 he2 ce2 G

Q1. The current voltage relation of diode is given by I = (e1000 V/T - 1) mA, where the applied voltage V is in volts and the temperature T is in degree Kelvin. If a student makes an error measuring ±0.01 V while measuring the current of 5 mA at 300 K, what will be the error in the value of current in mA ? (1) 0.2 mA (2) 0.02 mA (3) 0.5 mA (4) 0.05 mA

Q1. In terms of resistance R and time T , the dimensions of ratio με of the permeability μ and permittivity ε is: (1) [RT−2] (2) [R2 T−1] (3) [R2] (4) [R2 T2]

Q1. An experiment is performed to obtain the value of acceleration due to gravity g by using a simple pendulum of length L. In this experiment time for 100 oscillations is measured by using a watch of 1 second least count and the value is 90.0 seconds. The length L is measured by using a meter scale of least count 1 mm and the value is 20.0 cm. The error in the determination of g would be : (1) 4.4% (2) 2.27% (3) 1.7% (4) 2.7%

Q1. A bullet loses ( n1 ) th such planks that are required to stop the bullet can be: (1) Infinite (2) n (3) n2 (4) 2n2 (2n−1) (n−1)

Q2. The position of a projectile launched from the origin at t = 0 is given by→r= (40 ˆi + 50 ˆj)m at t = 2s. If the projectile was launched at an angle θ from the horizontal, then θ is (take g = 10 ms-2). (1) tan−1 23 (2) tan−1 32 (3) tan−1 74 (4) tan−1 45

Q2. A person climbs up a stalled escalator in 60 s. If standing on the same but escalator running with constant velocity he takes 40 s. How much time is taken by the person to walk up the moving escalator? (1) 37 s (2) 27 s (3) 24 s (4) 45 s

Q2. A heavy box is to be dragged along a rough horizontal floor. To do so, the person A pushes it at an angle 30° from the horizontal and requires a minimum force FA , while the person B pulls the box at an angle 60° from the horizontal and needs minimum force FB . If the coefficient of friction between the box and the floor is √35 , the ratio FA is FB (1) √32 (2) √32 (3) √3 (4) 5 √3

Q2. The initial speed of a bullet fired from a rifle is 630 m/s. The rifle is fired at the centre of a target 700 m away at the same level as the target. How far above the centre of the target ? (1) 1.0 m (2) 4.2 m (3) 6.1 m (4) 9.8 m

Q2. From a tower of height H, a particle is thrown vertically upwards with a speed u. The time taken by the particle, to hit the ground, is n times that taken by it to reach the highest point of its path.The relation between H, u and n is : (1) 2 g H = n2u2 (2) g H = (n - 2)2u2 (3) 2g H = nu2(n - 2) (4) g H = (n - 2)u2

Q3. A block of mass m is placed on a surface with a vertical cross section given by y = x36 . If the coefficient of friction is 0. 5, the maximum height above the ground at which the block can be placed without slipping is (1) 1 6 m (2) 32 m (3) 3 1 m (4) 21 m

Q3. A body of mass 5 kg under the action of constant force →F = Fx^i + Fy^j has velocity at t = 0 s as →v = (6^i −2^jm/s) and at t = 10 s as →v = +6^jm/s. The force →F is: (1) (−3^i + 4^j)N (2) (−35^i + 45 ^j)N (3) (3^i −4^j)N (4) ( 5^i3 −45^j)N

Q3. A bullet of mass 4 g is fired horizontally with a speed of 300 m/s into 0.8 kg block of wood at rest on a table. If the coefficient of friction between the block and the table is 0.3, how far will the block slide approximately? (1) 0.19 m (2) 0.379 m (3) 0.569 m (4) 0.758 m

Q3. A particle is released on a vertical smooth semicircular track from point X so that, OX makes angle θ from the vertical (see figure). The normal reaction of the track on the particle vanishes at the point Y where OY makes an angle ϕ with the horizontal. Then (1) sinϕ = 23 cosθ (2) sinϕ = 34 cosθ (3) sinϕ = 12 cosθ (4) sinϕ = cosθ

Q3. Water is flowing at a speed of 1.5 m s-1 through a horizontal tube of cross-sectional area 10-2 m2 and you are trying to stop the flow by your palm. Assuming that the water stops immediately after hitting the palm, the minimum force that you must exert should be (density of water = 103 kg m-3) (1) 33.7 N (2) 45 N (3) 15 N (4) 22.5 N

Q4. A block A of mass 4 kg is placed on another block B of mass 5 kg, and the block B rests on a smooth horizontal table. If the minimum force that can be applied on A so that both the blocks move together is 12 N, the maximum force that can be applied on B for the blocks to move together will be : (1) 0 N (2) 25 N (3) 48 N (4) 27 N

Q4. A small ball of mass m starts at a point A with speed vo and moves along a frictionless track AB as shown. The track BC has coefficient of friction μ. The ball comes to stop at C after travelling a distance L which is: v20 (1) 2 o (2) μ h + 2μgv2 μ h + 2μg (3) 2μ h + μgv2o (4) 2μh + 2μgv2o

Q4. When a rubber-band is stretched by a distance x, it exerts a restoring force of magnitude F = ax + bx2 where a and b are constants. The work done in stretching the unstretched rubber-band by L is : (1) aL2 + bL3 (2) 12 (aL2 + bL3) bL3 bL3 (3) aL2 (4) + 2 + 3 2 1 ( aL22 3 )

Q4. A spring of unstretched length 1 has a mass m with one end fixed to a rigid support. Assuming spring to be made of a uniform wire, the kinetic energy possessed by it if its free end is pulled with uniform velocity v is: (1) 1 mv2 (2) mv2 2 (3) 1 3 mv2 (4) 16 mv2

Q4. Consider a cylinder of mass M resting on a rough horizontal rug that is pulled out from under it with acceleration 'a' perpendicular to the axis of the cylinder. What is Ffriction at point P ? It is assumed that the cylinder does not slip. (1) Ma (2) Ma2 (3) Ma (4) Mg 3

Q5. Three masses m, 2 m and 3 m are moving in x −y plane with speed 3u, 2u and u respectively as shown in figure. The three masses collide at the same point at P and stick together. The velocity of resulting mass will be: (1) 12 u (^i + √3^j) (2) 12u (^i −√3^j) (3) 12 u (−^i + √3^j) (4) 12u (−^i −√3^j)