Practice Questions

Q86.If a curve y = f(x) passes through the point (1, −1) and satisfies the differential equation, y (1 + xy)dx = x dy, then f(−12 ) is equal to (1) 2 (2) 4 5 5 (3) −25 (4) −45 → → → → If b is not parallel to →c, then the b × b + = √32

Q87.The number of distinct real values of λ , for which the lines x−1 1 = = z−12 , are 2 = z+3λ2 and x−31 = y−2λ2 coplanar is (1) 2 (2) 4 (3) 3 (4) 1 JEE Main 2016 (10 Apr Online) JEE Main Previous Year Paper

Q87.In a triangle ABC , right angle at vertex A , if the position vectors of A, B and C are respectively 3ˆi + ˆj − ˆk, −ˆi + 3ˆj + pˆk and 5ˆi + qˆj −4ˆk , then the point (p, q) lies on a line: (1) Making an obtuse angle with the positive (2) Parallel to x −axis direction of x −axis (3) Parallel to y −axis (4) Making an acute angle with the positive direction of x −axis

Q87.Let →a, b and →cbe three unit vectors such that →a × ( →c) ( →c). → angle between →a and b is (1) 2π (2) 5π 3 6 (3) 3π (4) π 4 2

Q88.If the line, x−3 2 = y+2−1 = z+43 lies in the plane lx + my −z = 9, then l2 + m2 is equal to (1) 5 (2) 2 (3) 26 (4) 18

Q88. ABC is a triangle in a plane with vertices A(2, 3, 5), B(−1, 3, 2) and C(λ, 5, μ) . If the median through A is equally inclined to the coordinate axes, then the value of (λ3 + μ3 + 5) is (1) 1130 (2) 1348 (3) 1077 (4) 676 → →a+→b+→c

Q88.The shortest distance between the lines x 2 = 2y = 1z and x+2−1 = y−48 = z−54 , lies in the interval: (1) (3, 4] (2) (2, 3] (3) [1, 2) (4) [0, 1)

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

Q89.The distance of the point (1, −5, 9) from the plane x −y + z = 5 measured along the line x = y = z is (1) 10 (2) 20 √3 3 (3) 3√10 (4) 10√3

Q89.Let ABC be a triangle whose circumcentre is at P . If the position vectors A, B, C and P are →a, b,→cand 4 respectively, then the position vector of the orthocentre of this triangle, is : → → (1) →a + b + →c (2) →a + b + →c 2 −( ) (3) (→a +→b+ →c) (4) →0 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.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

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

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

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

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)

Q2. A block of mass m = 10 kg rests on a horizontal table. The coefficient of friction between the block and the table is 0. 05. When hit by a bullet of mass 50 g moving with speed v, that gets embedded in it, the block moves and comes to stop after moving a distance of 2 m on the table. If a freely falling object were to acquire speed 10v after being dropped from height H , then neglecting energy losses and taking g = 10 m s−2 , the value of H is close to (1) 0. 2 km . (2) 0. 5 km . (3) 0. 4 km . (4) None of these.

Q2. A beaker contains a fluid of density ρ kg , specific heat S kgoCJ and viscosity η . The beaker is filled up to height m3 ˙Q h. To estimate the rate of heat transfer per unit area ( A ) by convection when beaker is put on a hot plate, a Δθ ( inoC ) is the difference in the student proposes that it should depend on η , ( SΔθh ) and ( ρg1 ) when ˙Q temperature between the bottom and top of the fluid. In that situation the correct option for ( A ) is: (1) ( SΔθh )η (2) η( SΔθh )( ρ1g ) ηh (3) ( SΔθηh )( ρg1 ) (4) SΔθ

Q3. If electronic charge e, electron mass m, speed of light in vacuum c and Planck's constant h are taken as fundamental quantities, the permeability of vacuum μ0 can be expressed in units of: (1) ( mc2he2 ) (2) ( me2h ) (3) ( me2hc ) (4) ( ce2h )

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

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

Q4. Distance of the centre of mass of a solid uniform cone from its vertex is z0 . If the radius of its base is R and its height is h then z0 is equal to: JEE Main 2015 (04 Apr) JEE Main Previous Year Paper (1) 3h2 (2) h2 8R 4R (3) 3h (4) 5h 4 8

Q4. If a body moving in a circular path maintains constant speed of 10 m s−1 , then which of the following correctly describes the relation between acceleration and radius? (1) (2) (3) (4)

Q4. From the top of a 64 metres high tower, a stone is thrown upwards vertically with the velocity of 48 m/s. The greatest height (in metres) attained by the stone, assuming the value of the gravitational acceleration g = 32 m/s2 , is: (1) 112 (2) 88 (3) 128 (4) 100