Practice Questions

Q87.Let ABCD be a parallelogram such that AB→ =→q, AD→ = →p and ∠BAD be an acute angle. If →r is the vector that coincides with the altitude directed from the vertex B to the side AD, then →r is given by (1) →r = 3→q −3(→p⋅→q) →p (2) →r = −→q+ (→p⋅→p) ( →p⋅→p→p⋅→q )→p →p⋅→q 3(→p⋅→q) (3) →r = →q (4) →r = −3→q + →p −( →p⋅→p )→p (→p⋅→p)

Q87.If the three planes x = 5, 2x −5ay + 3z −2 = 0 and 3bx + y −3z = 0 contain a common line, then (a, b) is equal to (1) ( 158 , −15 ) (2) ( 15 , −815 ) (3) (−815 , 51 ) (4) (−15 , 158 )

Q88.A unit vector which is perpendicular to the vector 2^i −^j + 2^k and is coplanar with the vectors ^i + ^j −^k and 2^i + 2^j −^k is (1) 2^j+^k (2) 3^i+2^j−2^k √5 √17 (3) 3^i+2^j+2^k (4) 2^i+2^j−^k √17 3

Q13.Three perfect gases at absolute temperatures T1, T2 and T3 are mixed. The masses of molecules are m1 , m2 and m3 and the number of molecules are n1, n2 and n3 respectively. Assuming no loss of energy, the final temperature of the mixture is : 2 2 +n3T 32 (1) n1T1+n2T2+n3T3 (2) n1T1+n2T n1+n2+n3 n1T1+n2T2+n3T3 1 (3) n21T 2 +n22T 22 +n23T 32 (4) (T1+T2+T3) n1T1+n2T2+n3T3 3

Q16.The transverse displacement y(x, t) of a wave on a string is given by y(x, t) = e−(ax2+bt2+2√abxt) . This represents a (1) (2) standing wave of frequency √b wave moving in −x direction with speed √ba (3) standing wave of frequency 1 (4) wave moving in +x direction with √ab √b JEE Main 2011 JEE Main Previous Year Paper

Q20.A current I flows in an infinitely long wire with cross section in the form of a semicircular ring of radius R. The magnitude of the magnetic induction along its axis is (1) μ0I (2) μ0I 2π2R 2πR (3) μ0I (4) μ0l 4π2R π2R

Q39.The entropy change involved in the isothermal reversible expansion of 2 moles of an ideal gas from a volume of 10dm3 to a volume of 100dm3 at 27∘C is : (1) 35.8 J mol−1 K−1 (2) 32.3 J mol−1 K−1 (3) 42.3 J mol−1 K−1 (4) 38.3 J mol−1 K−1

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

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

Q15.Let there be a spherically symmetric charge distribution with charge density varying as ρ(r) = ρ0 ( 54 −rR ) upto r = R, and ρ(r) = 0 for r > R, where r is the distance from the origin. The electric field at a distance r(r < R) from the origin is given by (1) 4πρ0r 3ε0 ( 53 −rR ) (2) 4ε0ρ0r ( 53 −rR ) (3) 4ρ0r 3ε0 ( 54 −rR ) (4) 3ε0ρ0r ( 54 −rR ) JEE Main 2010 JEE Main Previous Year Paper

Q23.An initially parallel cylindrical beam travels in a medium of refractive index μ(I) = μ0 + μ2I , where μ0 and μ2 are positive constants and I is the intensity of the light beam. The intensity of the beam is decreasing with increasing radius. As the beam enters the medium, it will (1) diverge (2) converge (3) diverge near the axis and converge near the (4) travel as a cylindrical beam periphery

Q28.A nucleus of mass M + Δm is at rest and decays into two daughter nuclei of equal mass M2 each. Speed of light is C. The speed of daughter nuclei is (1) c Δm (2) M+Δm c√2ΔmM (3) c√ΔmM (4) c√ M+ΔmΔm

Q51.Consider the reaction : Cl2(aq) + H2 S(aq) →S(s) + 2H+(aq) + 2Cl−(aq) The rate equation for this reaction is rate = k [Cl2] [H2 S] Which of these mechanisms is/are consistent with this rate equation? (A) Cl2 + H2 →H+ + Cl−+ Cl+ + HS− (slow) Cl+ + HS−→H+ + Cl−+ S (fast) (B) H2 S ⇔H+ + HS− (fast equilibrium) Cl2 + HS−→2Cl−+ H+ + S (slow) (1) B only (2) Both A and B (3) Neither A nor B (4) A only

Q70.Let f : R →R be a positive increasing function with limx→∞ f(3x)f(x) = 1. Then limx→∞ f(2x)f(x) (1) 2 (2) 3 3 2 (3) 3 (4) 1

Q75.The number of 3 × 3 non-singular matrices, with four entries as 1 and all other entries as 0 , is (1) 5 (2) 6 (3) at least 7 (4) less than 4

Q11.If x, v and a denote the displacement, the velocity and the acceleration of a particle executing simple harmonic motion of time period T, then, which of the following does not change with time? (1) a2T 2 + 4π2v2 (2) aTx (3) aT + 2πv (4) aTv

Q15.Let P(r) = Q r be the charge density distribution for a solid sphere of radius R and total charge Q. for a πR4 point ' p ' inside the sphere at distance r1 from the centre of the sphere, the magnitude of electric field is JEE Main 2009 JEE Main Previous Year Paper (1) 0 (2) Q 4πε0r21 (3) Qr21 (4) Q21 4πε0R4 3πε0R4

Q38.The bond dissociation energy of B −F in BF3 is 646 kJ mol −1 whereas that of C −F in CF4 is 515 kJ mol −1 . The correct reason for higher B-F bond dissociation energy as compared to that of C - F is : (1) smaller size of B-atom as compared to that of C- (2) stronger σ bond between B and F in BF3 as atom compared to that between C and F in CF4 (3) significant pπ −pπ interaction between B and F (4) lower degree of pπ −pπ interaction between B in BF3 whereas there is no possibility of such and F in BF3 than that between C and F in CF4 . interaction between C and F in CF4 . –––

Q50.Which one of the following reactions of Xenon compounds is not feasible ? (1) XeO3 + 6HF →Xe6 + 3H2O (2) 3Xe4 + 6H2O →2Xe + XeO3 + 12HF + 1.5O2 (3) 2XeF2 + 2H2O →2Xe + 4HF + O2 (4) XeF6 + RbF →Rb (XeF7]

Q68.If P and Q are the points of intersection of the circles x2 + y2 + 3x + 7y + 2p −5 = 0 and x2 + y2 + 2x + 2y −p2 = 0, then there is a circle passing through P, Q and (1, 1) for (1) all values of p (2) all except one value of p (3) all except two values of p (4) exactly one value of p

Q85.The differential equation which represents the family of curves y = c1ec2x , where c1 and c2 are arbitrary constants is (1) y′ = y2 (2) y′′ = y′y (3) yy′′ = y′ (4) yy′′ = (y′)2

Q75.How many different words can be formed by jumbling the letters in the word MISSISSIPPI in which no two S are adjacent? (1) 8 ⋅6C4 ⋅7C4 (2) 6.8 ⋅7C4 (3) 6 ⋅7 ⋅8C4 (4) 7 ⋅6C4 ⋅8C4

Q96.Let I = ∫10 sin√xx dx and J = ∫10 cos√xx (1) I > 32 and J > 2 (2) I < 23 and J < 2 (3) I < 32 and J > 2 (4) I > 23 and J < 2

Q8. For the given uniform square lamina ABCD, whose centre is O, (1) √2IAC = IEF (2) IAD = 3IEF (3) IAC = IEF (4) IAC = √2IEF