Practice Questions

Q76.The domain of the function f(x) = 1 is √|x|−x (1) (0, ∞) (2) (−∞, 0) (3) (−∞, ∞) −{0} (4) (−∞, ∞)

Q77. x x < 0 ⎧ sin(p+1)x+sinx The value of p and q for which the function f(x) = is continuous for all x in R, is ⎨ q , x = 0 √x+x2−√x , x > 0 ⎩ x3/2 (1) p = 52 , q = 12 (2) p = −32 , q = 12 (3) p = 21 , q = 32 (4) p = 12 , q = −32

Q78. d2x equals dy2 (1) d2y −1 dy −3 (2) d2y dy −2 −( dx2 ) ( dx ) ( dx2 )( dx ) (3) −( dx2d2y )( dxdy ) −3 (4) ( dx2d2y ) −1

Q79.The shortest distance between line y −x = 1 and curve x = y2 is (1) 3√2 (2) 8 8 3√2 (3) 4 (4) √3 √3 4 dx is

Q80.The value of ∫10 8 log(1+x)1+x2 (1) π 8 log 2 (2) π2 log 2 (3) log 2 (4) π log 2 tdt. Then f has

Q81.For x ∈(0, 5π2 ), define f(x) = ∫x0 √t sin (1) local minimum at π and 2π (2) local minimum at π and local maximum at 2π (3) local maximum at π and local minimum at 2π (4) local maximum at π and 2π

Q82.The area of the region enclosed by the curves y = x, x = e, y = x1 and the positive x-axis is JEE Main 2011 JEE Main Previous Year Paper (1) 1 square units (2) 3 square units 2 (3) 5 square units (4) 1 square units 2 2

Q83.If dy = y + 3 > 0 and y(0) = 2, then y(ln 2) is equal to dx (1) 5 (2) 13 (3) -2 (4) 7

Q84.Let I be the purchase value of an equipment and V(t) be the value after it has been used for t years. The value V(t) depreciates at a rate given by differential equation dV(t)dt = −k(T −t), where k > 0 is a constant and T is the total life in years of the equipment. Then the scrap value V(T) of the equipment is (1) I −kT2 (2) 1 −k(T−t)22 (3) e−kT (4) T2 −1k → → → → 1 1 is

Q85.If →a = (3^i + ^k) and b = 7 (2^i + 3^j −6^k), then the value of (2→a− b) ⋅[(→a× b) × (→a+ 2 b)] √10 (1) −3 (2) 5 (3) 3 (4) −5

Q86.The vector →a and →b are not perpendicular and →c and →d are two vectors satisfying: →b × →c = →b × →d and →a ⋅→d = 0 . Then the vector →d is equal to →a⋅→c →b⋅→c (1) →c + (2) →b + ( →a⋅→b )→b ( →a⋅→b )→c →a⋅→c →b⋅→c (3) →c (4) →b −( →a⋅→b )→b −( →a⋅→b )→c z−3 , then λ equals and the plane x + 2y + 3z = 4 is cos−1 λ

Q87.If the angle between the line x = y−12 = 14 (√5 ) (1) 3 (2) 2 2 5 (3) 5 (4) 2 3 3

Q88.This question has Statement −1 and Statement −2. Of the four choices given after the statements, choose the one that best describes the two statements. Statement-1 : The point A(1, 0, 7) is the mirror image of the point B(1, 6, 3) in the line x1 = y−12 = z−23 . Statement-2 : The line: x1 = y−12 = z−23 bisects the line segment joining A(1, 0, 7) and B(1, 6, 3). (1) Statement −1 is true, Statement-2 is true; (2) Statement −1 is true, Statement −2 is false. Statement −2 is not a correct explanation for Statement −1 (3) Statement −1 is false, Statement −2 is true. (4) Statement −1 is true, Statement −2 is true; Statement −2 is a correct explanation for Statement −1

Q89.Consider 5 independent Bernoulli's trials each with probability of success p . If the probability of at least one failure is greater than or equal to 31 , then p lies in the interval 32 (1) ( 34 , 1112 ] (2) [0, 12 ] (3) ( 1112 , 1] (4) ( 12 , 34 ]

Q90.If C and D are two events such that C ⊂D and P(D) ≠0 , then the correct statement among the following is JEE Main 2011 JEE Main Previous Year Paper (1) P(C ∣D) ≥P(C) (2) P(C ∣D) < P(C) (3) P(C ∣D) = P(D)P(C) (4) P(C ∣D) = P(C) JEE Main 2011 JEE Main Previous Year Paper

Q1. The respective number of significant figures for the numbers 23.023, 0.0003 and 2.1 × 10−3 are (1) 5, 1, 2 (2) 5, 1, 5 (3) 5, 5, 2 (4) 4, 4, 2

Q2. A particle is moving with velocity →v = K(y^i + x^j), where K is a constant. The general equation for its path is (1) y = x2+ constant (2) y2 = x+ constant (3) xy = constant (4) y2 = x2+ constant

Q3. A small particle of mass m is projected at an angle θ with the x-axis with an initial velocity v0 in the x −y plane as shown in the figure. At a time t < v0 sing θ , the angular momentum of the particle is where ^i,^j and ^k are unit vectors along x, y and z-axis respectively. (1) −mgv0 t2 cos θ^j (2) mgv0 t cos θ^k (3) −12 mgv0t2 cos θ^k (4) 21 mgv0t2 cos θ^i

Q4. Two fixed frictionless inclined plane making an angle 30∘ and 60∘ with the vertical are shown in the figure. Two block A and B are placed on the two planes. What is the relative vertical acceleration of A with respect to B ? (1) 4.9 ms−2 in horizontal direction (2) 9.8 ms−2 in vertical direction (3) zero (4) 4.9 ms−2 in vertical direction

Q5. The potential energy function for the force between two atoms in a diatomic molecule is approximately given by U(x) = a − b , where a and b are constants and x is the distance between the atoms. If the dissociation x12 x6 energy of the molecule is D = [U(x = ∞) −Uat equilbrium ], D is (1) b2 (2) b2 2a 12a (3) b2 (4) b2 4a 6a

Q6. Statement-1 : Two particles moving in the same direction do not lose all their energy in a completely inelastic collision. Statement-2 : Principle of conservation of momentum holds true for all kinds of collisions. Of the four choices given after the statements, choose the one that best describes the two statements. Of the four choices given after the statements, choose the one that best describes the two statements. JEE Main 2010 JEE Main Previous Year Paper (1) Statement-1 is true, Statement-2 is true; (2) Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation of Statement-2 is not the correct explanation of Statement-1. Statement1 (3) Statement-1 is false, Statement-2 is true. (4) Statement-1 is true, Statement-2 is false.

Q7. The figure shows the position - time (x −t) graph of one-dimensional motion of a body of mass 0.4 kg. The magnitude of each impulse is (1) 0.4Ns (2) 0.8Ns (3) 1.6Ns (4) 0.2Ns

Q8. A point P moves in counter-clockwise direction on a circular path as shown in the figure. The movement of ' P ' is such that it sweeps out a length s = t3 + 5 , where s is in metres and t is in seconds. The radius of the path is 20 m. The acceleration of ' P ' when t = 2 s is nearly (1) 13 m/s2 (2) 12 m/s2 (3) 7.2 m/s2 (4) 14 m/s2

Q9. For a particle in uniform circular motion the acceleration →a at a point P(R, θ) on the circle of radius R is (here θ is measured from the x-axis) (1) −v2R cos θ^i + v2R sin θ^j (2) −v2R sin θ^i + v2R cos θ^j (3) −v2R cos θ^i −v2R sin θ^j (4) v2R ^i + v2R ^j

Q10.A ball is made of a material of density ρ where ρoil < ρ < ρwater with ρoil and ρwater representing the densities of oil and water, respectively. The oil and water are immiscible. If the above ball is in equilibrium in a mixture of this oil and water, which of the following pictures represents its equilibrium position? JEE Main 2010 JEE Main Previous Year Paper (1) (2) (3) (4)