Practice Questions

Q82.Let p(x) be a function defined on R such that p′(x) = p′(1 −x), for all x ∈[0, 1], p(0) = 1 and p(1) = 41 . Then ∫10 p(x)dx equals (1) 21 (2) 41 (3) 42 (4) √41

Q83.The area bounded by the curves y = cos x and y = sin x between the ordinates x = 0 and x = 3π2 is (1) 4√2 + 2 (2) 4√2 −1 (3) 4√2 + 1 (4) 4√2 −2

Q84.Solution of the differential equation cos xdy = y(sin x −y)dx, 0 < x < π2 is (1) y sec x = tan x + c (2) y tan x = sec x + c (3) tan x = (sec x + c)y (4) sec x = (tan x + c)y

Q85.Let →a = ^j −^k and →c = ^i −^j −^k. Then vector →b satisfying →a × →b + →c =→0 and →a ⋅→b = 3 is (1) 2^i −^j + 2^k (2) ^i −^j −2^k (3) ^i + ^j −2^k (4) −^i + ^j −2^k →

Q87.Statement-1: The point A(3, 1, 6) is the mirror image of the point B(1, 3, 4) in the plane x −y + z = 5. Statement-2: The plane x −y + z = 5 bisects the line segment joining A(3, 1, 6) and B(1, 3, 4). (1) Statement-1 is true, Statement-2 is true; (2) Statement-1 is true, Statement-2 is false Statement-2 is not the 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 the correct explanation for Statement-1 JEE Main 2010 JEE Main Previous Year Paper

Q90.An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colour is (1) 2 (2) 1 7 21 (3) 2 (4) 1 23 3 JEE Main 2010 JEE Main Previous Year Paper

Q2. Consider a rubber ball freely falling from a height h = 4.9 m onto a horizontal elastic plate. Assume that the duration of collision is negligible and the collision with the plate is totally elastic. Then the velocity as a function of time the height as function of time will be (1) (2) (3) (4)

Q3. A thin uniform rod of length ℓ and mass m is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is ω. Its centre of mass rises to a maximum height of (1) 1 ℓ2ω2 (2) 1 ℓω 3 g 6 g (3) 1 ℓ2ω2 (4) 1 ℓ2ω2 2 g 6 g

Q5. Two wires are made of the same material and have the same volume. However wire 1 has crosssectional area A and wire-2 has cross-sectional area 3A. If the length of wire 1 increases by Δx on applying force F , how much force is needed to stretch wire 2 by the same amount? (1) F (2) 4 F (3) 6 F (4) 9 F

Q7. Assuming the gas to be ideal the work done on the gas in taking it from A to B is (1) 200R (2) 300R (3) 400R (4) 500R

Q8. The work done on the gas in taking it from D to A is (1) −414R (2) +414R (3) −690R (4) +690R

Q9. The net work done on the gas in the cycle ABCDA is (1) Zero (2) 276R (3) 1076R (4) 1904R

Q10.One kg of a diatomic gas is at a pressure of 8 × 104 N/m2 . The density of the gas is 4 kg/m−3 . What is the energy of the gas due to its thermal motion? (1) 3 × 104 J (2) 5 × 104 J (3) 6 × 104 J (4) 7 × 104 J

Q12.A motor cycle starts from rest and accelerates along a straight path at 2 m/s2 . At the starting point of the motor cycle there is a stationary electric sire. How far has the motor cycle gone when the driver hears the frequency of the siren at 94% of its value when the motor cycle was at rest? (speed of sound = 330 ms−1) (1) 49 m (2) 98 m (3) 147 m (4) 196 m

Q14.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 - 1: For a charged particle moving from point P to point Q, the net work done by an electrostatic field on the particle is independent of the path connecting point P to point Q. Statement-2: The net work done by a conservative force on an object moving along a closed loop is zero (1) Statement-1 is true, Statement-2 is false (2) Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation of Statement-1. (3) Statement-1 is true, Statement-2 is true; (4) Statement-1 is false, Statement-2 is true Statement-2 is not the correct explanation of Statement-1.

Q17.A charge Q is placed at each of the opposite corners of a square. A charge q is placed at each of the other two corners. If the net electrical force on Q is zero, then the Q/q equals (1) −2√2 (2) −1 (3) 1 (4) −1 √2

Q18.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-1: The temperature dependence of resistance is usually given as R = R0(1 + αΔt). The resistance of a wire changes from 100Ω to 150Ω when its temperature is increased from 27∘C to 227∘C. This implies that α = 2.5 × 10−3/∘C. Statement 2: R = Ri(1 + αΔT) is valid only when the change in the temperature ΔT is small and ΔR = (R −R0) ≪R0 . (1) Statement-1 is true, Statement-2 is false (2) Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation of Statement-1. (3) Statement-1 is true, Statement-2 is true; (4) Statement-1 is false, Statement-2 is true Statement-2 is not the correct explanation of Statement-1.

Q19.The magnitude of the magnetic field (B) due to loop ABCD at the origin (O) is (1) zero (2) μ0(b−a) 24ab (3) μ0I 4π [ b−aab ] (4) μo∣4π [2(b −a) + π3 (a + b)]

Q20.Due to the presence of the current l1 at the origin (1) The forces on AB and DC are zero (2) The forces on AD and BC are zero (3) The magnitude of the net force on the loop is (4) The magnitude of the net force on the loop is given by μ0I1 4π [2(b −a) + π3 (a + b)] given by μ0∥124ab (b −a)

Q21.An inductor of inductance L = 400mH and resistors of resistances R1 = 2Ω and R2 = 2Ω are connected to a battery of emf 12 V as shown in the figure. The internal resistance of the battery is negligible. The switch S is closed at t = 0. The potential drop across L as a function of time is (1) 6e−5tV (2) 12t e−3tV (3) 6 (1 −e−t/0.2)V (4) 12e−5tV JEE Main 2009 JEE Main Previous Year Paper

Q22.In an optics experiment, with the position of the object fixed, a student varies the position of a convex lens and for each position, the screen is adjusted to get a clear image of the object. A graph between the object distance u and the image distance v, from the lens, is plotted using the same scale for the two axes. A straight line passing through the origin and making an angle of 45∘ with the x-axis meets the experimental curve at P . The coordinates of P will be (1) (2f, 2f) (2) ( f2 , f2 ) (3) (f, f) (4) (4f, 4f)

Q23.A transparent solid cylindrical rod has a refractive index of 2 . It is surrounded by air. A light ray is incident √3 at the mid point of one end of the rod as shown in the figure. The incident angle θ for which the light ray grazes along the wall of the rod is (1) sin−1 ( 21 ) (2) sin−1 ( √32 ) (3) sin−1 ( √32 ) (4) sin−1 ( √31 )

Q24.A mixture of light, consisting of wavelength 590 nm and an unknown wavelength, illuminates Young's double slit and gives rise to two overlapping interference patterns on the screen. The central maximum of both lights coincide. Further, it is observed that the third bright fringe of known light coincides with the 4th bright fringe of the unknown light. From this data, the wavelength of the unknown light is (1) 393.4 nm (2) 885.0 nm (3) 442.5 nm (4) 776.8 nm

Q26.The transition from the state n = 4 to n = 3 in a hydrogen like atom results in ultraviolet radiation. Infrared radiation will be obtained in the transition from (1) 2 →1 (2) 3 →2 (3) 4 →2 (4) 5 →4

Q27.The above is a plot of binding energy per nucleon Eb , against the nuclear mass M; A, B, C, D, E, F correspond to different nuclei. Consider four reactions: (i) A + B →C + ε (ii) C →A + B + ε (iii) D + E →F + ε and (iv) F →D + E + ε where ε is the energy released? In which reactions is ε positive? (1) (i) and (iv) (2) (i) and (iii) (3) (ii) and (iv) (4) (ii) and (iii) JEE Main 2009 JEE Main Previous Year Paper