Practice Questions

Q85.The area bounded by the curve y = ln(x) and the lines y = 0, y = ln(3) and x = 0 is equal to: (1) 3 (2) 3 ln(3) −2 (3) 3 ln(3) + 2 (4) 2

Q85.The integral ∫7π/37π/4 √tan2 (1) log 2√2 (2) log 2 (3) 2 log 2 (4) log √2

Q85.The equation of the curve passing through the origin and satisfying the differential equation (1 + x2) dxdy + 2xy = 4x2 is (1) (1 + x2)y = x3 (2) 3 (1 + x2)y = 2x3 (3) (1 + x2)y = 3x3 (4) 3 (1 + x2)y = 4x3

Q85.The area (in square units) bounded by the curves y=√x, 2y −x + 3 = 0 , X -axis and lying in the first quadrant is (1) 18 sq. units (2) 274 sq. units (3) 9 sq. units (4) 36 sq. units

Q86.Let →a = 2^i −^j + ^k,→b = ^i + 2^j −^k and →c = ^i + ^j −2^k be three vectors. A vector of the type →b + λ→c for some scalar λ, whose projection on →a is of magnitude is : √23 (1) 2^i + ^j + 5^k (2) 2^i + 3^j −3^k (3) 2^i −^j + 5^k (4) 2^i + 3^j + 3^k

Q86.The value of ∫π/2−π/2 sin21+2xx (1) π (2) π 2 (3) 4π (4) π4

Q86.The area of the region (in sq. units), in the first quadrant bounded by the parabola y = 9x2 and the lines x = 0, y = 1 and y = 4 , is : (1) 7/9 (2) 14/3 (3) 7/3 (4) 14/9

Q86.At present, a firm is manufacturing 2000 items. It is estimated that the rate of change of production P w.r.t. additional number of workers x is given by dP dx = 100 −12√x. If the firm employs 25 more workers, then the new level of production of items is (1) 3500 (2) 4500 (3) 2500 (4) 3000 −−

Q87.If the vectors AB→ = 3ˆi + 4ˆk and AC→ = 5ˆi −2ˆj + 4ˆk are the sides of a triangle ABC, then the length of the median through A is: (1) √33 (2) √45 (3) √18 (4) √72

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

Q87.The vector (^i × →a ⋅→b)^i + (^j × →a→b)^j + (^k × →a ⋅→b)^k is equal to: (1) →b × →a (2) →a (3) →a × →b (4) →b JEE Main 2013 (09 Apr Online) JEE Main Previous Year Paper

Q87.The area under the curve y = | cos x −sin x|, 0 ≤x ≤π2 , and above x-axis is : (1) 2√2 (2) 2√2 −2 (3) 2√2 + 2 (4) 0

Q87.Consider the differential equation : dy y3 = dx 2 (xy2 −x2) JEE Main 2013 (22 Apr Online) JEE Main Previous Year Paper Statement-1: The substitution z = y2 transforms the above equation into a first order homogenous differential equation. Statement-2: The solution of this differential equation is y2e−y2/x = C . (1) Both statements are false. (2) Statement-1 is true and statement- 2 is false. (3) Statement-1 is false and statement-2 is true. (4) Both statements are true. →

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.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.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.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 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

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. 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

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]

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. 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)