Practice Questions

Q70.A ray of light is incident along a line which meets another line 7x −y + 1 = 0 at the point (0, 1). The ray is then reflected from this point along the line y + 2x = 1 . Then the equation of the line of incidence of the ray of light is : (1) 41x −25y + 25 = 0 (2) 41x + 25y −25 = 0 (3) 41x −38y + 38 = 0 (4) 41x + 38y −38 = 0

Q73. (n+1) (n+2)….3n n1 is equal to lim n2n ) n→∞( (1) 9 (2) 3 log 3 −2 e2 (3) 18 (4) 27 e4 e2 1 2x

Q73.A hyperbola whose transverse axis is along the major axis of the conic x2 3 + 4 = 4 and has vertices at the foci of the conic. If the eccentricity of the hyperbola is 3 , then which of the following points does not lie on 2 the hyperbola ? (1) (√5, 2√2) (2) (0, 2) (3) (5, 2√3) (4) (√10, 2√3) is

Q74.If f(x) is a differentiable function in the interval (0, ∞) such that f(1) = 1 and lim t−x = 1,for each t→x x > 0, then f( 23 ) is equal to JEE Main 2016 (09 Apr Online) JEE Main Previous Year Paper (1) 23 (2) 13 18 6 (3) 25 (4) 31 9 18 a − 4 ) 2x = e3 , then a is equal to x x2

Q80.Let a, b ∈R, (a ≠0). If the function f , defined as , 0 ≤x < 1 ⎧ 2x2a f(x) = a, 1 ≤x < √2 ,is continuous in the interval [0, ∞), then an ordered pair (a, b) can be ⎨ 2b2−4b ⎩ x3 , √2 ≤x < 8 1 −1 + −√3) (2) (√2, √3) (1) (−√2, 1 1 + −√3) (4) (−√2, √3) (3) (√2,

Q83.If the tangent at a point P, with parameter t, on the curve x = 4t2 + 3, y = 8t3 −1, t ∈R, meets the curve again at a point Q, then the coordinates of Q are : (1) (16t2 + 3, −64t3 −1) (2) (4t2 + 3, −8t3 −1) (3) (t2 + 3, t3 −1) (4) (t2 + 3, −t3 −1)

Q84.For x ∈R, x ≠0, if y(x) is a differentiable function such that x ∫x y(t)dt = (x + 1) ∫x ty(t)dt, then y(x) 1 1 equals (where C is a constant) (1) Cx3 e x1 (2) C e−1x x2 (3) C x (4) C e−1x x e−1 x3 dx, where [x] denotes the greatest integer less than or equal to x, is

Q85.The area (in sq. units) of the region {(x, y) : y2 ≥2x and x2 + y2 ≤4x, x ≥0, y ≥0} is (1) π −4√23 (2) π2 −2√23 (3) π −43 (4) π −83 JEE Main 2016 (03 Apr) JEE Main Previous Year Paper

Q86.The area (in sq. units) of the region described by A = {(x, y) y ≥x2 −5x + 4, x + y ≥1, y ≤0} is (1) 19 (2) 17 6 6 (3) 7 (4) 13 2 6

Q2. A beaker contains a fluid of density ρ kg , specific heat S kgoCJ and viscosity η . The beaker is filled up to height m3 ˙Q h. To estimate the rate of heat transfer per unit area ( A ) by convection when beaker is put on a hot plate, a Δθ ( inoC ) is the difference in the student proposes that it should depend on η , ( SΔθh ) and ( ρg1 ) when ˙Q temperature between the bottom and top of the fluid. In that situation the correct option for ( A ) is: (1) ( SΔθh )η (2) η( SΔθh )( ρ1g ) ηh (3) ( SΔθηh )( ρg1 ) (4) SΔθ

Q3. If electronic charge e, electron mass m, speed of light in vacuum c and Planck's constant h are taken as fundamental quantities, the permeability of vacuum μ0 can be expressed in units of: (1) ( mc2he2 ) (2) ( me2h ) (3) ( me2hc ) (4) ( ce2h )

Q6. From a solid sphere of mass M and radius R, a cube of the maximum possible volume is cut. Moment of inertia of cube about an axis passing through its centre and perpendicular to one of its faces is: (1) 4MR2 (2) MR2 3√3π 32√2π (3) MR2 (4) 4MR2 16√2π 9√3π

Q7. From a solid sphere of mass M and radius R, a spherical portion of radius ( R2 ) is removed as shown in the figure. Taking gravitational potential V = 0 at r = ∞, the potential at the centre of the cavity thus formed is ( G =gravitational constant) (1) −2GM (2) −GM R 2R (3) −GM (4) −2GM R 3R

Q8. A pendulum made of a uniform wire of cross sectional area A has time period T. When an additional mass M is added to its bob, the time period changes to TM . If the Young's modulus of the material of the wire is Y , then 1 is equal to: Y ( g =gravitational acceleration) (1) T 2 A (2) T M 2 A −( TM ) Mg T ) Mg [1 ] [( −1] (3) T M 2 Mg (4) TM 2 A T ) A −( T ) Mg [( −1] [1 ]

Q9. Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion, the average time of collision between molecules increases as V q , where V is the volume of the gas. The value of q is: (γ = CPCv ) (1) γ−1 (2) 3γ+5 2 6 (3) 3γ−5 (4) γ+1 6 2 JEE Main 2015 (04 Apr) JEE Main Previous Year Paper

Q10.Consider a spherical shell of radius R at temperature T. The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume u = UV ∝T 4 and pressure p = 13 ( UV ) . If the shell now undergoes an adiabatic expansion the relation between T and R is: (1) T ∝ 1 (2) T ∝e−R R3 (3) T ∝e−3R (4) T ∝ R1

Q13.A simple harmonic oscillator of angular frequency 2 rad s−1 is acted upon by an external force F = sin t N . If the oscillator is at rest in its equilibrium position at t = 0, its position at later times is proportional to: (1) sin t + 21 cos 2t (2) cost −12 sin 2t (3) sin t −12 sin 2t (4) sin t + 12 sin 2t

Q15.A wire of length L = 20 cm is bent into a semi-circular arc and the two equal halves of the arc are uniformly charged with charges +Q and −Q as shown in the figure. The magnitude of the charge on each half is |Q| = 103ε0 , where ε0 is the permittivity of free the space. The net electric field at the centre O is (1) (25 × 103)ˆi N C−1 (2) (50 × 103)ˆi N C−1 (3) (25 × 103)ˆj N C−1 (4) (50 × 103)ˆj N C−1 → + 30 N C−1 exists in a region of space. If the potential at the origin is taken to

Q20.A wire carrying current I is tied between points P and Q and is in the shape of a circular arc of radius R due to a uniform magnetic field B (perpendicular to the plane of the paper, as shown in the figure) in the vicinity of the wire. If the wire subtends an angle 2θo at the center of the circle (of which it forms an arch) then the tension in the wire is: JEE Main 2015 (11 Apr Online) JEE Main Previous Year Paper (1) IBR (2) IBR sinθ0 (3) IBR (4) IBRθ0 2sinθ0 sinθ0

Q23.An electromagnetic wave travelling in the x− direction has frequency of 2 × 1014 H z and electric field amplitude of 27 V m–1 oscillates in Y −direction. From the options given below, which one describes the magnetic field for this wave? (1) → (2) → B(x, t) = × 10−8 B(x, t) = × sin[2π(1.5 × 10−8 x −2 × 1014 (9 T)ˆj (9 10−8T)ˆi sin[1.5 × 10−6 x −2 × 1014t] → → (3) (4) B B −2 × −2 × (x, t) = (9 × (x, t) = (3 × 10−8T)ˆj sin 2π[( 1.5×10−8x ) 1014t] 10−8T)^ksin2π[( 1.5×10−6x ) 1014t]

Q23.For the LCR circuit, shown here, the current is observed to lead the applied voltage. An additional capacitor C ′ , when joined with the capacitor C present in the circuit, makes the power factor of the circuit unity. The capacitor C ′ , must have been connected in: (1) Parallel with C and has a magnitude 1−ω2LC (2) Series with C and has a magnitude 1−ω2LC ω2L ω2L (3) Series with C and has a magnitude C (4) Parallel with C and has a magnitude C (ω2LC−1) (ω2LC−1)

Q25.Monochromatic light is incident on a glass prism of angle A. If the refractive index of the material of the prism is μ , a ray, incident at an angle θ , on the face AB would get transmitted through the face AC of the prism JEE Main 2015 (04 Apr) JEE Main Previous Year Paper provided: sin + θ > (1) θ < cos−1[μ (A sin−1( μ1 ))] (2) sin−1[μ sin(A −sin−1( μ1 ))] sin θ > + (3) θ < sin−1[μ (A −sin−1( μ1 ))] (4) cos−1[μ sin(A sin−1( μ1 ))]

Q28.If one were to apply the Bohr model to a particle of mass ′m′ and charge ′q′ moving in a plane under the influence of a magnetic field 'B', the energy of the charged particle in the nth level will be: (1) n( hqBπm ) (2) n( 4πmhqB ) (3) n( 2πmhqB ) (4) n( 8πmhqB )

Q34.At temperature T , the average kinetic energy of any particle is 32 kT. The de Broglie wavelength follows the order: (1) Visible photon >thermal electron >thermal (2) Thermal neutron >visible photon >thermal neutron. electron. (3) Thermal neutron >thermal electron >visible (4) Visible photon >thermal neutron >thermal photon. electron.

Q51.Which one of the following compounds is not a yellow colored compound ? (1) BaCrO4 (2) Zn2[Fe(CN)6] (3) K3[Co(NO2)6] (4) (NH4)3[As (Mo3O10)4]