Practice Questions

Q86.Let →a = 2^i + ^j −2^k,→b = ^i + ^j. If →c is a vector such that →a ∙→c = |→c|, |→c −→a| = 2√2 and the angle between →a × →b and →c is 30∘ , then |(→a × →b) × →c| equals: (1) 1 (2) 3√3 2 2 (3) 3 (4) 23

Q3. A satellite moving with velocity v in a force free space collects stationary interplanetary dust at a rate of dM dt = αv where M is the mass (of satellite + dust) at that instant. The instantaneous acceleration of the satellite is (1) −αv22M (2) −αv2M (3) −αv2 (4) −2αv2M

Q6. A circular hole of diameter R is cut from a disc of mass M and radius R; the circumference of the cut passes through the centre of the disc. The moment of inertia of the remaining portion of the disc about an axis perpendicular to the disc and passing through its centre is (1) ( 1532 )MR2 (2) ( 18 )MR2 (3) ( 83 )MR2 (4) ( 1332 )MR2

Q8. A large number of droplets, each of radius, r coalesce to form a bigger drop of radius, R. An engineer designs a machine so that the energy released in this process is converted into the kinetic energy of the drop. Velocity of the drop is ( T = surface tension, ρ = density) JEE Main 2012 (19 May Online) JEE Main Previous Year Paper (1) T 1 1/2 (2) 6T 1 1/2 [ ρ ( r −1R )] [ ρ ( r −1R )] (3) 3T 1 1/2 (4) 2T 1 1/2 [ ρ ( r −1R )] [ ρ ( r −1R )]

Q8. A wooden wheel of radius R is made of two semicircular parts (see figure); The two parts are held together by a ring made of a metal strip of cross sectional area S and length L. L is slightly less than 2πR. To fit the ring on the wheel, it is heated so that its temperature rises by ΔT and it just steps over the wheel. As it cools down to surrounding temperature, it presses the semicircular parts together. If the coefficient of linear expansion of the metal is α, and its Youngs' modulus is Y , the force that one part of the wheel applies on the other part is : (1) 2πSYαΔT (2) SYαΔT (3) πSYαΔT (4) 2SYαΔT

Q10.Helium gas goes through a cycle ABCDA (consisting of two isochoric and two isobaric lines) as shown in figure. Efficiency of this cycle is nearly: (Assume the gas to be close to ideal gas) (1) 15.4% (2) 9.1% (3) 10.5% (4) 12.5%

Q14.A uniform tube of length 60.5 cm is held vertically with its lower end dipped in water. A sound source of frequency 500 Hz sends sound waves into the tube. When the length of tube above water is 16 cm and again when it is 50 cm, the tube resonates with the source of sound. Two lowest frequencies (in Hz ), to which tube will resonate when it is taken out of water, are (approximately). (1) 281,562 (2) 281,843 (3) 276,552 (4) 272,544

Q18.Two circuits (a) and (b) have charged capacitors of capacitance C, 2C and 3C with open switches. Charges on each of the capacitor are as shown in the figures. On closing the switches Circuit (a) Circuit (b) (1) No charge flows in (a) but charge flows from R (2) Charges flow from L to R in both (a) and (b) to L in (b) (3) Charges flow from R to L in (a) and from L to R (4) No charge flows in (a) but charge flows from L in (b) to R in (b)

Q26.A diatomic molecule is made of two masses m1 and m2 which are separated by a distance r. If we calculate its rotational energy by applying Bohr's rule of angular momentum quantization, its energy will be given by ( n is an integer) (1) (m1+m2)2n2h2 (2) n2h2 2m21m22r2 2(m1+m2)r2 (3) 2n2h2 (4) (m1+m2)n2h2 (m1+m2)r2 2m1m2r2 JEE Main 2012 (Offline) JEE Main Previous Year Paper

Q28.A sample originally contained 1020 radioactive atoms, which emit α-particles. The ratio of α particles emitted in the third year to that emitted during the second year is 0.3. How many α particles were emitted in the first year? JEE Main 2012 (07 May Online) JEE Main Previous Year Paper (1) 3 × 1018 (2) 3 × 1019 (3) 5 × 1018 (4) 7 × 1019

Q34.In which of the following arrangements, the sequence is not strictly according to the property written against it? (1) CO2 < SiO2 < SnO2 < PbO2 : increasing (2) NH3 < PH3 < AsH3 < SbH3 : increasing basic oxidising power strength (3) HF < HCl < HBr < HI : increasing acid (4) B < C < O < N : increasing first ionisation strength enthalpy.

Q42. In the following balanced reaction, values of X, Y and Z respectively are (1) 2,5,16 (2) 8, 2, 5 (3) 5, 2, 16 (4) 5, 8, 4

Q43. The order of basicity of the compounds is (1) IV > I > III > II (2) I > III > II > IV (3) III > I > IV > II (4) II > I > III > IV JEE Main 2012 (19 May Online) JEE Main Previous Year Paper

Q48.A solution containing 0.85 g of ZnCl2 in 125.0 g of water freezes at −0.23∘C. The apparent degree of dissociation of the salt is (Kf for water = 1.86 K kg mol−1 , atomic mass: Zn = 65.3 and Cl = 35.5) (1) 1.36% (2) 73.5% (3) 7.35% (4) 2.47%

Q49.A battery is constructed of Cr and Na2Cr2O7 . The unbalanced chemical equation when such a battery discharges is following: Na2Cr2O7 + Cr + H+ →Cr3+ + H2O + Na+ If one Faraday of electricity is passed through the battery during the charging, the number of moles of Cr3+ removed from the solution is (1) 4 (2) 1 3 3 (3) 3 (4) 2 3 3

Q52.The number of S −S bonds in SO3, S2O2−3 S2O2−6 and S2O2−8 respectively are (1) 1, 0, 0, 1 (2) 1,0,1,0 (3) 0, 1, 1, 0 (4) 0, 1, 0, 1

Q54.Which branched chain isomer of the hydrocarbon with molecular mass 72 u gives only one isomer of mono substituted alky halide? (1) Tertiary butyl chloride (2) Neopentane (3) Isohexane (4) Neohexane

Q55.The complex ion [Pt (NO2)(Py) (NH3) (NH2OH)]+ will give (1) 2 isomers (Geometrical) (2) 3 isomers (Geometrical) (3) 6 isomers (Geometrical) (4) 4 isomers (Geometrical)

Q61.If a, b, c, d and p are distinct real numbers such that (a2 + b2 + c2)p2 −2p(ab + bc + cd) + (b2+ c2 + d2) ≤0, then (1) a, b, c, d are in A.P. (2) ab = cd (3) ac = bd (4) a, b, c, d are in G.P.

Q65.The sum of the series 1 + 34 + 109 + 2728 + … upto n terms is (1) 67 n + 16 − 3.2n−12 (2) 53 n −76 + 2.3n−11 (3) n + 21 − 2.3n1 (4) n −13 − 3.2n−11

Q72. limx→0 ( x−sinx x ) sin ( x1 ) (1) equals 1 (2) equals 0 (3) does not exist (4) equals −1

Q75.In a ΔPQR, if 3 sin P + 4 cos Q = 6 and 4 sin Q + 3 cos P = 1, then the angle R is equal to (1) 5π (2) π 6 6 (3) π (4) 3π 4 4 JEE Main 2012 (Offline) JEE Main Previous Year Paper Q76. ⎛1 0 0⎞ ⎛1⎞ ⎛0⎞ Let A = 2 1 0 . If u1 and u2 are column matrices such that Au1 = 0 and Au2 = 1 , then ⎝3 2 1⎠ ⎝0⎠ ⎝0⎠ u1 + u2 is equal to (1) ⎛−1⎞ (2) ⎛ −1⎞ 1 1 ⎝ 0 ⎠ ⎝ −1⎠ (3) ⎛−1⎞ (4) ⎛ 1 ⎞ −1 −1 ⎝ 0 ⎠ ⎝ −1⎠

Q77.Let P and Q be 3 × 3 matrices with P ≠Q. If P 3 = Q3 and P 2Q = Q2P , then determinant of (P 2 + Q2) is equal to (1) −2 (2) 1 (3) 0 (4) −1

Q82.If dx d G(x) = etanx x , x ∈(0, π/2), then ∫1/21/4 x2 ⋅etan(πx2)dx is equal to (1) G(π/4) −G(π/16) (2) 2[G(π/4) −G(π/16)] (3) π[G(1/2) −G(1/4)] (4) G(1/√2) −G(1/2)

Q85.The parabola y2 = x divides the circle x2 + y2 = 2 into two parts whose areas are in the ratio (1) 9π + 2 : 3π −2 (2) 9π −2 : 3π + 2 (3) 7π −2 : 2π −3 (4) 7π + 2 : 3π + 2 x dy)