Practice Questions

Q87.Let A(−3, 2) and B(−2, 1) be the vertices of a triangle ABC. If the centroid of this triangle lies on the line 3x + 4y + 2 = 0 , then the vertex C lies on the line : JEE Main 2013 (25 Apr Online) JEE Main Previous Year Paper (1) 4x + 3y + 5 = 0 (2) 3x + 4y + 3 = 0 (3) 4x + 3y + 3 = 0 (4) 3x + 4y + 5 = 0

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.A vector →n is inclined to x-axis at 45∘ , to y-axis at 60∘ and at an acute angle to z-axis. If →n is a normal to a plane passing through the point (√2, −1, 1) then the equation of the plane is : (1) 4√2x + 7y + z −2 (2) 2x + y + 2z = 2√2 + 1 (3) 3√2x −4y −3z = 7 (4) √2x −y −z = 2

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 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.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.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 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.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

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

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

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. 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.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

Q61.If a, b, c, d and p are distinct real numbers such that (a2 + b2 + c2)p2 −2p(ab + bc + cd) + (b2+ c2 + d2) ≤0, then (1) a, b, c, d are in A.P. (2) ab = cd (3) ac = bd (4) a, b, c, d are in G.P.

Q61.Let p, q, r ∈R and r > p > 0. If the quadratic equation px2 + qx + r = 0 has two complex roots α and β, then |α| + |β| is (1) equal to 1 (2) less than 2 but not equal to 1 (3) greater than 2 (4) equal to 2 x2 b

Q61.If a, b, c ∈R and 1 is a root of equation ax2 + bx +c = 0, then the curve y = 4ax2 + 3bx + 2c, a ≠0 intersect x-axis at JEE Main 2012 (26 May Online) JEE Main Previous Year Paper (1) two distinct points whose coordinates are always (2) no point rational numbers (3) exactly two distinct points (4) exactly one point Q62. |z1 + z2|2 + |z1 −z2|2 is equal to + (1) 2 (|z1| + |z2| (2) 2 (|z1|2 |z2|2) (3) |z1| |z2| (4) |z1|2 + |z2|2

Q61.If z ≠1 and z−1z2 is real, then the point represented by the complex number (1) either on the real axis or on a circle passing (2) on a circle with centre at the origin through the origin (3) either on the real axis or on a circle not passing (4) on the imaginary axis through the origin

Q61.The value of k for which the equation (K −2)x2 + 8x + K + 4 = 0 has both roots real, distinct and negative is (1) 6 (2) 3 (3) 4 (4) 1

Q62.Assuming the balls to be identical except for difference in colours, the number of ways in which one or more balls can be selected from 10 white, 9 green and 7 black balls is (1) 880 (2) 629 (3) 630 (4) 879

Q62.If the sum of the square of the roots of the equation x2 −(sin α −2)x −(1 + sin α) = 0 is least, then α is equal to (1) π (2) π 6 4 (3) π (4) π 3 2

Q63.The area of the triangle whose vertices are complex numbers z, iz, z + iz in the Argand diagram is (1) 2|z|2 (2) 1/2|z|2 (3) 4|z|2 (4) |z|2 JEE Main 2012 (12 May Online) JEE Main Previous Year Paper

Q63.Let X = {1, 2, 3, 4, 5} . The number of different ordered pairs (Y , Z) that can be formed such that Y ⊆X, Z ⊆X and Y ∩Z is empty, is (1) 52 (2) 35 (3) 25 (4) 53