Practice Questions

Q1. From the following, the quantity (constructed from the basic constants of nature), that has the dimensions, as well as correct order of magnitude, vis-a-vis typical atomic size, is: (1) e2 (2) 4πε0e2 4πε0mc2 me2 (3) me2 (4) 4πε0mc2 4πε0b2 e2

Q2. The maximum range of a bullet fired from a toy pistol mounted on a car at rest is R0 = 40 m. What will be the acute angle of inclination of the pistol for maximum range when the car is moving in the direction of firing with uniform velocity v = 20 m/s on a horizontal surface? (g = 10 m/s2) (1) 30∘ (2) 60∘ (3) 75∘ (4) 45∘

Q4. A projectile of mass M is fired so that the horizontal range is 4 km . At the highest point the projectile explodes in two parts of masses M/4 and 3M/4 respectively and the heavier part starts falling down vertically with zero initial speed. The horizontal range (distance from point of firing) of the lighter part is : (1) 16 km (2) 1 km (3) 10 km (4) 2 km

Q5. The gravitational field, due to the 'left over part' of a uniform sphere (from which a part as shown, has been 'removed out'), at a very far off point, P, located as shown, would be (nearly) : JEE Main 2013 (09 Apr Online) JEE Main Previous Year Paper (1) 5 GM (2) 8 GM 6 x2 9 x2 (3) 7 GM (4) 6 GM 8 x2 7 x2

Q9. A thin tube sealed at both ends is 100 cm long. It lies horizontally, the middle 20 cm containing mercury and two equal ends containing air at standard atmospheric pressure. If the tube is now turned to a vertical position, by what amount will the mercury be displaced ? (Given : cross-section of the tube can be assumed to be uniform) (1) 2.95 cm (2) 5.18 cm (3) 8.65 cm (4) 0.0 cm

Q11.An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass M . The piston and the cylinder have equal cross-sectional area A . When the piston is in equilibrium, the volume of the gas is V0 and its pressure is M0 . The piston is slightly displaced from the equilibrium position and released. Assuming that the system is completely isolated from its surrounding, the piston executes a simple harmonic motion with frequency [Assume the system is in space.] 0 1 (1) (2) . 0 . 2π 1 √MVAγP 0 2π √A2γPMV 0 (3) 1 AγP 0 (4) 1 V 0MP 0 . 2π V 0M 2π A2γ

Q17.A letter ′A′ is constructed of a uniform wire with resistance 1.0Ω per cm, The sides of the letter are 20 cm and the cross piece in the middle is 10 cm long. The apex angle is 60 . The resistance between the ends of the legs is close to: (1) 50.0Ω (2) 10Ω (3) 36.7Ω (4) 26.7Ω

Q20.A circular loop of radius 0. 3 cm lies parallel to a much bigger circular loop of radius 20 cm. The centre of the small loop is on the axis of the bigger loop. The distance between their centres is 15 cm. If a current of 2. 0 A flows through the smaller loop, then the flux linked with a bigger loop is: (1) 3 .3 ×10−11 weber (2) 6 .6 ×10−9 weber (3) 9 .1 ×10−11 weber (4) 6 × 10−11 weber

Q27.In the Bohr's model of hydrogen-like atom the force between the nucleus and the electron is modified as e2 1 F = + β , where β is a constant. For this atom, the radius of the nth orbit in terms of the Bohr 4πε0 ( r2 r3 ) ε0h2 radius = is : (a0 mπe2 ) (1) rn = a0n −β (2) rn = a0n2 + β (3) rn = a0n2 −β (4) rn = a0n + β JEE Main 2013 (23 Apr Online) JEE Main Previous Year Paper

Q28.Orbits of a particle moving in a circle are such that the perimeter of the orbit equals an integer number of de- Broglie wavelengths of the particle. For a charged particle moving in a plane perpendicular to a magnetic field, the radius of the nth orbital will therefore be proportional to : JEE Main 2013 (22 Apr Online) JEE Main Previous Year Paper (1) n2 (2) n (3) n1/2 (4) n1/4

Q30.Which of the following modulated signal has the best noise-tolerance ? (1) Long-wave (2) Short-wave (3) Medium-wave (4) Amplitude-modulated Q31. 6 litres of an alkene require 27 litres of oxygen at constant temperature and pressure for complete combustion. The alkene is : (1) Ethene (2) Propene (3) 1−Butene (4) 2−Butene

Q38.The internuclear distances in O −O bonds for O+2 , O2, O−2 and O2−2 respectively are : (1) 1.30 Å, 1.49 Å, 1.12 Å, 1.21 Å (2) 1.49 Å, 1.21 Å, 1.12 Å, 1.30 Å (3) 1.21 Å, 1.12 Å, 1.49 Å, 1.30 Å (4) 1.12 Å, 1.21 Å, 1.30 Å, 1.49 Å

Q38.Which one of the following arrangements represents the correct order of solubilities of sparingly soluble salts Hg2Cl2, Cr2(SO4)3 , BaSO4 and CrCl3 respectively? (1) BaSO4 > Hg2Cl2 > Cr2(SO4)3 > CrCl3 (2) BaSO4 > Hg2Cl2 > CrCl3 > Cr2(SO4)3 (3) BaSO4 > CrCl3 > Hg2Cl2 > Cr2(SO4)3 (4) Hg2Cl2 > BaSO4 > CrCl3 > Cr2(SO4)3

Q42.Arrange in the correct order of stability (decreasing order) for the following molecules: (I) (II) (III) (IV) (1) (I) > (II) > (III) > (IV) (2) (IV) > (III) > (II) ≈ (I) (3) (I) > (II) ≈ (III) > (IV) (4) (III) > (I) ≈ (II) > (IV)

Q42.Given that: (i) ΔfH∘ of N2O is 82 kJ mol−1 (ii) Bond energies of N ≡N, N = N, O = O and N = O are 946, 418, 498 and 607 kJ mol−1 respectively, The resonance energy of N2O is : (1) −88 kJ (2) −66 kJ (3) −62 kJ (4) −44 kJ

Q46. Given In the above compounds correct order of reactivity in electrophilic substitution reactions will be: (1) B > A > C > D (2) D > C > B > A (3) A > B > C > D (4) B > C > A > D

Q53.Which of the following arrangements does not represent the correct order of the property stated against it? (1) Co3+ < Fe3+ < Cr3+ < Sc3+ :​ Stability in aqueous (2) Sc < Ti < Cr < Mn :​ Number of oxidation states solution (3) V2+< Cr2+ < Mn2+ < Fe2+:​ Paramagnetic (4) Ni2+ < Co2+ < Fe2+ < Mn2+ :​ Ionic size behaviour

Q57.Compound (A), C8H9 Cl, gives a white precipitate when warmed with alcoholic AgNO3 . Oxidation of (A) gives an acid (B), C8H6O4 . (B) easily forms anhydride on heating. Identify the compound (A). JEE Main 2013 (07 Apr) JEE Main Previous Year Paper (1) (2) ​ ​ (3) (4) ​ ​

Q57.An ether (A), C5H12O, when heated with excess of hot concentrated HI produced two alkyl halides which when treated with NaOH yielded compounds (B) and (C). Oxidation of (B) and (C) gave a propanone and an ethanoic acid respectively. The IUPAC name of the ether (A) is : (1) 2−ethoxypropane (2) ethoxypropane (3) methoxybutane (4) 2−methoxybutane

Q70.The x−coordinate of the incentre of the triangle that has the coordinates of midpoints of its sides as (0, 1), (1, 1) and (1, 0) is (1) 1 + √2 (2) 1 −√2 (3) 2 + √2 (4) 2 −√2

Q71.If a circle C passing through (4, 0) touches the circle x2 + y2 + 4x −6y −12 = 0 externally at a point (1, −1) , then the radius of the circle C is : (1) 5 (2) 2√5 (3) 4 (4) √57

Q73.If a and c are positive real numbers and the ellipse x2 + y2 = 1 has four distinct points ir common with the 4c2 c2 circle x2 + y2 = 9a2 , then (1) 9ac −9a2 −2c2 < 0 (2) 6ac + 9a2 −2c2 < 0 (3) 9ac −9a2 −2c2 > 0 (4) 6ac + 9a2 −2c2 > 0

Q74.If the extremities of the base of an isosceles triangle are the points (2a, 0) and (0, a) and the equation of one of the sides is x = 2a, then the area of the triangle, in square units, is : (1) 5 a2 (2) 5 a2 4 2 (3) 25a2 (4) 5a2 4

Q76.A common tangent to the conics x2 = 6y and 2x2 −4y2 = 9 is: (1) x −y = 32 (2) x + y = 1 (3) x + y = 92 (4) x −y = 1 Then the number of non-singular matrices in the set S is : : aij ∈{0, 1, 2}, a11 = a22}

Q84.If x = ∫y0 √1+t2dt , then dx2d2y (1) y (2) √1 + y2 (3) x (4) y2 √1+y2