Practice Questions

Q88.If the lines x−2 1 = y−31 = z−4−k and x−1k = y−42 = z−51 are coplanar, then k can have JEE Main 2013 (07 Apr) JEE Main Previous Year Paper (1) exactly two values. (2) exactly three values. (3) any value. (4) exactly one value.

Q88.If →a and →b are non-collinear vectors, then the value of α for which the vectors →u = (α −2)→a + →b and →v = (2 + 3α)→a −3→b are collinear is : (1) 3 (2) 2 2 3 (3) −32 (4) −23

Q88.If ^a,^b and ^c are unit vectors satisfying ^a −√3^b + ^c = 0, then the angle between the vectors ^a and ^c is : (1) π (2) π 4 3 (3) π (4) π 6 2

Q88.Let ABC be a triangle with vertices at points A (2, 3, 5), B (−1, 3, 2) and C(λ, 5, μ) in three dimensional space. If the median through A is equally inclined with the axes, then (λ, μ) is equal to: (1) (10, 7) (2) (7, 5) (3) (7, 10) (4) (5, 7)

Q89.If the lines x+1 2 = y−11 = z+13 and x+22 = y−k3 = 4z are coplanar, then the value of k is : (1) 11 2 (2) −112 (3) 2 9 (4) −92

Q89.Distance between two parallel planes 2x + y + 2z = 8 and 4x + 2y + 4z + 5 = 0 is (1) 7 (2) 9 2 2 (3) 3 (4) 5 2 2

Q89.The equation of a plane through the line of intersection of the planes x + 2y = 3, y −2z + 1 = 0 , and perpendicular to the first plane is : (1) 2x −y −10z = 9 (2) 2x −y + 7z = 11 (3) 2x −y + 10z = 11 (4) 2x −y −9z = 10

Q89.If the projections of a line segment on the x, y and z-axes in 3-dimensional space are 2, 3 and 6 respectively, then the length of the line segment is : (1) 12 (2) 7 (3) 9 (4) 6

Q89.Let Q be the foot of perpendicular from the origin to the plane 4x −3y + z + 13 = 0 and R be a point (−1, −6) on the plane. Then length QR is : (1) √14 (2) √192 (3) 3√72 (4) √23

Q90. A, B, C try to hit a target simultaneously but independently. Their respective probabilities of hitting the targets are 3 4 , 12 , 85 . The probability that the target is hit by A or B but not by C is : (1) 21/64 (2) 7/8 (3) 7/32 (4) 9/64 JEE Main 2013 (23 Apr Online) JEE Main Previous Year Paper

Q90.The probability of a man hitting a target is 2 . He fires at the target k times (k, a given number). Then the 5 minimum k, so that the probability of hitting the target at least once is more than 7 , is : 10 (1) 3 (2) 5 (3) 2 (4) 4 JEE Main 2013 (09 Apr Online) JEE Main Previous Year Paper

Q90.Given two independent events, if the probability that exactly one of them occurs is 26 and the probability that 49 none of them occurs is 15 , then the probability of more probable of the two events is : 49 (1) 4/7 (2) 6/7 (3) 3/7 (4) 5/7 JEE Main 2013 (22 Apr Online) JEE Main Previous Year Paper

Q90.If the events A and B are mutually exclusive events such that P(A) = 3x+13 and P(B) = 1−x4 , then the set of possible values of x lies in the interval : (1) [0, 1] (2) [ 13 , 23 ] (3) [−13 , 59 ] (4) [−79 , 49 ] JEE Main 2013 (25 Apr Online) JEE Main Previous Year Paper

Q90.A multiple choice examination has 5 questions. Each question has three alternative answers out of which exactly one is correct. The probability that a student will get 4 or more correct answers just by guessing is : (1) 11 (2) 10 35 35 (3) 17 (4) 13 35 35 JEE Main 2013 (07 Apr) JEE Main Previous Year Paper

Q1. A student measured the diameter of a wire using a screw gauge with the least count 0.001 cm and listed the measurements. The measured value should be recorded as (1) 5.3200 cm (2) 5.3 cm (3) 5.32 cm (4) 5.320 cm

Q1. Given that K = energy, V = velocity, T = time. If they are chosen as the fundamental units, then what is dimensional formula for surface tension? (1) [KV −2 T−2] (2) [K 2V 2T −2] (3) [K 2V −2T −2] (4) [KV 2T 2]

Q1. Resistance of a given wire is obtained by measuring the current flowing in it and the voltage difference applied across it. If the percentage errors in the measurement of the current and the voltage difference are 3% each, then error in the value of resistance of the wire is (1) 6% (2) zero (3) 1% (4) 3%

Q1. The amount of heat produced in an electric circuit depends upon the current (I), resistance (R) and time (t). If the error made in the measurements of the above quantities are 2%, 1% and 1% respectively then the maximum possible error in the total heat produced will be (1) 1% (2) 2% (3) 6% (4) 3%

Q1. The electrical resistance R of a conductor of length l and area of cross section a is given by R = ρla where ' ρ ' is the electrical resistivity. What is the dimensional formula for electrical conductivity ' σ ' which is reciprocal of resistivity? (1) [M −1L−3T 3A2] (2) [ML−3T −3A2] (3) [ML3T −3A−2] (4) [M −2L3T 2A−1]

Q2. A ball is dropped vertically downwards from a height h above the ground. It hits the ground inelastically and bounces up vertically. Neglecting subsequent motion and air resistance, which of the following graph represents variation between speed (v) and height (h) correctly? (1) (2) (3) (4)

Q2. The graph of an object's motion (along the x− axis) is shown in the figure. The instantaneous velocity of the object at points A and B are vA and vB respectively. Then (1) vA = vB = 0.5 m/s (2) vA = 0.5 m/s < vB (3) vA = 0.5 m/s > vB (4) vA = vB = 2 m/s

Q2. A boy can throw a stone up to a maximum height of 10 m. The maximum horizontal distance that the boy can throw the same stone up to will be (1) 20√2 m (2) 10 m (3) 10√2 m (4) 20 m

Q2. The distance travelled by a body moving along a line in time t is proportional to t3 . The acceleration-time (a, t) graph for the motion of the body will be (1) (2) (3) (4)

Q2. A goods train accelerating uniformly on a straight railway track, approaches an electric pole standing on the side of track. Its engine passes the pole with velocity u and the guard's room passes with velocity v. The middle wagon of the train passes the pole with a velocity. (1) u+v (2) 1 √u2 + v2 2 2 2 ) (3) √uv (4) √( u2+v2

Q3. A satellite moving with velocity v in a force free space collects stationary interplanetary dust at a rate of dM dt = αv where M is the mass (of satellite + dust) at that instant. The instantaneous acceleration of the satellite is (1) −αv22M (2) −αv2M (3) −αv2 (4) −2αv2M