Practice Questions

Q70.Statement-1: ∼(p ↔∼q) is equivalent to p ↔q . Statement-2 : ∼(p ↔∼q) is a tautology. (1) Statement-1 is true, Statement-2 is true; (2) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-2 is not a correct explanation for Statement-1 Statement-1 (3) Statement-1 is true, Statement-2 is false (4) Statement-1 is false, Statement-2 is true

Q71.If the mean deviation of number 1, 1 + d, 1 + 2d, … . , 1 + 100d from their mean is 255 , then the d is equal to (1) 10.0 (2) 20.0 (3) 10.1 (4) 20.2

Q72.Statement-1 : The variance of first n even natural numbers is n2−14 Statement-2 : The sum of first n natural numbers is n(n+1) 2 and the sum of squares of first n natural numbers is n(n+1)(2n+1)6 (1) Statement-1 is true, Statement-2 is true; (2) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-2 is not a correct explanation for Statement-1 Statement-1 (3) Statement-1 is true, Statement-2 is false (4) Statement-1 is false, Statement-2 is true

Q76.Let A and B denote the statements A: cos α + cos β + cos γ = 0 B: sin α + sin β + sin γ = 0 If cos(β −γ) + cos(γ −α) + cos(α −β) = −32 , then (1) A is true and B is false (2) A is false and B is true (3) both A and B are true (4) both A and B are false

Q78.Let f(x) = (x + 1)2 −1, x ≥−1 Statement-1: The set {x : f(x) = f −1(x)} = {0, −1} Statement-2 : f is a bijection. (1) Statement-1 is true, Statement-2 is true; (2) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-2 is not a correct explanation for Statement-1 Statement-1 (3) Statement-1 is true, Statement-2 is false (4) Statement-1 is false, Statement-2 is true

Q80.Let y be an implicit function of x defined by x2x −2xx cot y −1 = 0 . Then y′(1) equals (1) −1 (2) 1 (3) log 2 (4) −log 2

Q81.Given P(x) = x4 + ax3 + bx2 + cx + d such that x = 0 is the only real root of P ′(x) = 0 . If P(−1) < P(1), then in the interval [−1, 1] (1) P(−1) is the minimum and P(1) is the (2) P(−1) is not minimum but P(1) is the maximum maximum of P of P (3) P(−1) is the minimum and P(1) is not the (4) neither P(−1) is the minimum nor P(1) is the maximum of P maximum of P

Q82.The shortest distance between the line y −x = 1 and the curve x = y2 is (1) 3√2 (2) 2√3 8 8 (3) 3√2 (4) √3 5 4 Q83. ∫π0 [cot x]dx, [∙] denotes the greatest integer function, is equal to (1) π (2) 1 2 (3) −1 (4) −π2

Q84.The area of the region bounded by the parabola (y −2)2 = x −1, the tangent to the parabola at the point (2, 3) and the x-axis is (1) 3 (2) 6 (3) 9 (4) 12 JEE Main 2009 JEE Main Previous Year Paper

Q86.If →u, →v, ¯w are non-coplanar vectors and p, q are real numbers, then the equality [ 3→u p→v p→w ] −[ p→v →w q→u ] −[ 2→w q→v q→u ] = 0 holds for (1) exactly one value of (p, q) (2) exactly two values of (p, q) (3) more than two but not all values of (p, q) (4) all values of (p, q)

Q87.Let the line x−2 3 = y−1−5 = z+22 lies in the plane x + 3y −αz + β = 0. Then (α, β) equals (1) (6, −17) (2) (−6, 7) (3) (5, −15) (4) (−5, 15)

Q88.The projections of a vector on the three coordinate axis are 6, −3, 2 respectively. The direction cosines of the vector are (1) 6, −3, 2 (2) 65 , −35 , 25 (3) 7 6 , −37 , 27 (4) −67 , −37 , 27

Q90.One ticket is selected at random from 50 tickets numbered 00, 01, 02, … , 49. Then the probability that the sum of the digits on the selected ticket is 8 , given that the product of these digits is zero, equals (1) 1 (2) 1 14 7 (3) 5 (4) 1 14 50 JEE Main 2009 JEE Main Previous Year Paper

Q2. A body is at rest at x = 0. At t = 0 , it starts moving in the positive x-direction with a constant acceleration. At the same instant another body passes through x = 0 moving in the positive x direction with a constant speed. The position of the first body is given by x1(t) after time ' t ' and that of the second body by x2(t) after the same time interval. Which of the following graphs correctly describes (x1 −x2) as a function of time ' t '? (1) (2) (3) (4)

Q3. An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range (1) 200 J −500 J (2) 2 × 105 J −3 × 105 J (3) 20, 000 J −50, 000 J (4) 2, 000 J −5, 000 J

Q6. A block of mass 0.50 kg is moving with a speed of 2.00 m/s on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is (1) 0.16 J (2) 1.00 J (3) 0.67 J (4) 0.34 J

Q7. Consider a uniform square plate of side ' a ' and mass ' m '. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is (1) 5 ma2 (2) 1 ma2 6 12 (3) 7 ma2 (4) 2 ma2 12 3

Q9. This question contains Statement −1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements. Statement - I: For a mass M kept at the centre of a cube of side ' a ', the flux of gravitational field passing through its sides is 4π GM. and Statement - II If the direction of a field due to a point source is radial and its dependence on the distance ' r ' for the source is given as 1/r2 , its flux through a closed surface depends only on the strength of the source enclosed by the surface and not on the size or shape of the surface (1) Statement −1 is false, Statement −2 is true. (2) Statement −1 is true, Statement −2 is true; Statement −2 is correct explanation for Statement-1. (3) Statement −1 is true, Statement −2 is true; (4) Statement −1 is true, Statement −2 is False. Statement −2 is not a correct explanation for Statement-1.

Q10.A spherical solid ball of volume V is made of a material of density ρ1 . It is falling through a liquid of density ρ2 (ρ2 < ρ1). Assume that the liquid applies a viscous force on the ball that is proportional to the square of its speed v, i.e., Fviscous = −kv2(k > 0). The terminal speed of the ball is (1) (2) Vgρ1 k √Vg(ρ1−ρ2)k (3) gρ1 (4) Vg(ρ1−ρ2) k √V k

Q12.A capillary tube (A) is dropped in water. Another identical tube (B) is dipped in a soap water solution. Which of the following shows the relative nature of the liquid columns in the two tubes? (1) (2) (3) (4)

Q13.An insulated container of gas has two chambers separated by an insulating partition. One of the chambers has volume V1 and contains ideal gas at pressure P1 and temperature T1 . The other chamber has volume V2 and contains ideal gas at pressure P2 and temperature T2 . If the partition is removed without doing any work on the gas, the final equilibrium temperature of the gas in the container will be (1) T1T2(P1V1+P2V2) (2) P1V1T1+P2V2T2 P1V1T2+P2V2T1 P1V1+P2V2 (3) P1V1T2+P2V2T1 (4) T1T2(P1V1+P2V2) P1V1+P2V2 P1V1T1+P2V2T2

Q14.While measuring the speed of sound by performing a resonance column experiment, a student gets the first resonance condition at a column length of 18 cm during winter. Repeating the same experiment during summer, she measures the column length to be xcm for the second resonance. Then JEE Main 2008 JEE Main Previous Year Paper (1) 18 > x (2) x > 54 (3) 54 > x > 36 (4) 36 > x > 18

Q15.The speed of sound in oxygen (O2) at a certain temperature is 460 ms−1 . The speed of sound in helium (He) at the same temperature will be (assumed both gases to be ideal) (1) 460 ms−1 (2) 500 ms−1 (3) 650 ms−1 (4) None of these

Q18.A parallel plate capacitor with air between the plates has a capacitance of 9pF. The separation between its plates is ' d '. The space between the plates is now filled with two dielectrics. One of the dielectrics has dielectric constant k1 = 3 and thickness d3 while the other one has dielectric constant k2 = 6 and thickness 23d . Capacitance of the capacitor is now (1) 1.8pF (2) 45pF (3) 40.5pF (4) 20.25pF

Q20.Paragraph: Consider a block of conducting material of resistivity ' ρ ' shown in the figure. Current 'l' enters at 'A' and leaves from ' D '. We apply superposition principle to find voltage ' ΔV ' developed between ' B ' and ' C '. The calculation is done in the following steps: (i) Take current 'l' entering from 'A' and assume it to spread over a hemispherical surface in the block. (ii) Calculate field E(r) at distance ' r ' from A by using Ohm's law E = ρj, where j is the current per unit area at ' r '. (iii) From the ' r ' dependence of E(r), obtain the potential V (r) at r. (iv) Repeat (i), (ii) and (iii) for current 'l' leaving ' D ' and superpose results for ' A ' and ' D '. Question: For current entering at A , the electric field at a distance ' r ' from A is (1) ρl (2) ρl 8πr2 r2 (3) ρl (4) ρl 2πr2 4πr2