Practice Questions

Q89.For three events, 𝐴, 𝐵 and 𝐶, 𝑃(Exactly one of 𝐴 or 𝐵 occurs) = 𝑃(Exactly one of 𝐵 or 𝐶 occurs) 1 1 = 𝑃(Exactly one of 𝐶 or 𝐴 occurs) = and 𝑃(All the three events occur simultaneously) = . 4 16 Then the probability that at least one of the events occurs, is: (1) 7 (2) 7 32 16 7 3 (3) (4) 64 16

Q89. From a group of 10 men and 5 women, four member committees are to be formed each of which must contain at least one women. Then the probability for these committees to have more women than men, is : (1) 3 (2) 2 11 23 (3) 1 (4) 21 11 220

Q2. A point particle of mass m, moves along the uniformly rough track PQR as shown in the figure. The coefficient of friction, between the particle and the rough track equals μ . The particle is released, from rest, from the point P and it comes to rest at a point R. The energies, lost by the ball, over the parts, PQ and QR, of the track, are equal to each other, and no energy is lost when particle changes direction from PQ to QR. The values of the coefficient of friction μ and the distance x = (QR) , are respectively close to: (1) 0.29 and 3.5 m (2) 0.29 and 6.5 m (3) 0.2 and 6.5 m (4) 0.2 and 3.5 m

Q4. A particle of mass m is moving along the side of a square of side 'a', with a uniform speed υ in the x-y plane as shown in the figure: → Which of the following statements is false for the angular momentum L about the origin? JEE Main 2016 (03 Apr) JEE Main Previous Year Paper → → mυ (1) R (2) L = + L = Rˆk a]ˆk mυ[ √2 √2 when the particle is moving from B to C. when the particle is moving from D to A. → → R (3) (4) L = −mυ + a]ˆk √2 Rˆk L = mυ[ √2 when the particle is moving from A to B. when the particle is moving from C to D.

Q5. A roller is made by joining together two cones at their vertices O. It is kept on two rails AB and CD which are placed asymmetrically (see figure), with its axis perpendicular to CD and its centre O at the centre of line joining AB and CD (see figure). It is given a light push so that it starts rolling with its centre O moving parallel to CD in the direction shown. As it moves, the roller will tend to: (1) go straight. (2) turn left and right alternately. (3) turn left. (4) turn right.

Q7. A uniformly tapering conical wire is made from a material of Young's modulus Y and has a normal, unextended length L. The radii, at the upper and lower ends of this conical wire, have values R and 3R, respectively. The upper end of the wire is fixed to a rigid support and a mass M is suspended from its lower end. The equilibrium extended length, of this wire, would equal: (1) L(1 + 29 πYR2Mg ) (2) L(1 + 19 πYR2Mg ) (3) L(1 + 13 πYR2Mg ) (4) L(1 + 23 πYR2Mg )

Q7. A pendulum clock loses 12 s a day if the temperature is 40o C and gains 4s a day if the temperature is 20o C. The temperature at which the clock will show correct time, and the co-efficient of linear expansion (α) of the metal of the pendulum shaft are respectively: (1) 30oC; α = 1.85 × 10−3 / oC (2) 55oC; α = 1.85 × 10−2 / oC (3) 25oC; α = 1.85 × 10−5 / oC (4) 60oC; α = 1.85 × 10−4 / oC

Q8. Consider a water jar of radius R that has water filled up to height H and is kept on a stand of height h (see JEE Main 2016 (09 Apr Online) JEE Main Previous Year Paper figure). Through a hole of radius r (r << R) at its bottom, the water leaks out and the stream of water coming down towards the ground has a shape like a funnel as shown in the figure. If the radius of the cross-section of water stream when it hits the ground is x. Then: (1) 1 (2) x = r( H+hH ) x = r( H+hH ) 4 1 H ) 2 (3) x = r( H+hH ) 2 (4) x = r( H+h

Q9. A bottle has an opening of radius a and length b . A cork of length b and radius (a + Δa) where (Δa ≪a), is compressed to fit into the opening completely (see figure). If the bulk modulus of cork is B and the coefficient of friction between the bottle and cork is μ , then the force needed to push the cork into the bottle is (1) (πμBb)a (2) (2πμBb) Δ a (3) (πμBb) Δ a (4) (4πμBb) Δ a

Q9. An ideal gas undergoes a quasi-static, reversible process in which its molar heat capacity C remains constant. If during this process the relation of pressure P and volume V is given by PVn = constant, then n is given by (Here CP and CV are molar specific heat at constant pressure and constant volume, respectively) : (1) n = CP−C (2) n = C−CV C−CV C−CP (3) n = CP (4) n = C−CP CV C−CV

Q12.A uniform string of length 20 m is suspended from a rigid support. A short wave pulse is introduced at its lowest end. It starts moving up the string. The time taken to reach the support is (Take, g = 10 m s−2 ) (1) 2√2 s (2) √2 s (3) 2π√2 s (4) 2 s

Q13.The region between two concentric spheres of radii 'a' and 'b', respectively (see figure), has volume charge density ρ = Ar , where A is a constant and r is the distance from the centre. At the centre of the spheres is a point charge Q. The value of A such that the electric field in the region between the spheres will be constant, JEE Main 2016 (03 Apr) JEE Main Previous Year Paper is: (1) 2Q (2) 2Q π(a2−b2) πa2 (3) Q (4) Q 2πa2 2π(b2−a2)

Q14.Within a spherical charge distribution of charge density ρ(r), N equipotential surfaces of potential V0, V0 + ΔV , V0 + 2 Δ V , … V0 + N Δ V (ΔV > 0), are drawn and have increasing radii r0, r1, r2, … rN, respectively. If the difference in the radii of the surfaces is constant for all values of V0 and Δ V then : (1) ρ(r) = constant (2) ρ (r) ∝ 1 r2 (3) ρ (r) ∝ 1r (4) ρ (r) ∝ r

Q15.Three capacitors each of 4 μF are to be connected in such a way that the effective capacitance is 6 μF . This can be done by connecting them (1) all in series (2) all in parallel (3) two in parallel and one in series (4) two in series and one in parallel

Q17.The resistance of an electrical toaster has a temperature dependence given by R(T) = R0[1 + α(T −T0)] in its range of operation. At T0 = 300 K, R = 100 Ω and at T = 500 K, R = 120 Ω . The toaster is connected JEE Main 2016 (10 Apr Online) JEE Main Previous Year Paper to a voltage source at 200 V and its temperature is raised at a constant rate from 300 to 500 K in 30 s. The total work done in raising the temperature is : Note: This question was awarded as the bonus since all options were incorrect in the exam. (1) 60000 ln( 65 ) J (2) 200 ln 32 J (3) 300 J (4) 400 ln( 1.31.5 ) J

Q22.The box of a pin hole camera, of length L, has a hole of radius a. It is assumed that when the hole is illuminated by a parallel beam of light of wavelength λ the spread of the spot (obtained on the opposite wall of the camera) is the sum of its geometrical spread and the spread due to diffraction. The spot would then have its minimum size (say bmin ) when: and bmin = √4λL (1) a = √λL and bmin = √4λL (2) a = λ2L and bmin = (3) a = λ2L ( 2λ2L ) (4) a = √λL and bmin = ( 2λ2L )

Q23.A convex lens, of focal length 30 cm, a concave lens of focal length 120 cm, and a plane mirror are arranged as shown. For an object kept at a distance of 60 cm from the convex lens, the final image, formed by the combination, is a real image, at a distance of: (1) 60 cm from the convex lens (2) 60 cm form the concave lens (3) 70 cm from the convex lens (4) 70 cm from the concave lens

Q23.A hemispherical glass body of radius 10 cm and refractive index 1.5 is silvered on its curved surface. A small air bubble is 6 cm below the flat surface inside it along the axis. The position of the image of the air bubble made by the mirror is seen : (1) 14cm below flat surface (2) 20cm below flat surface (3) 16cm below flat surface (4) 30cm below flat surface

Q26.A neutron moving with a speed 'v' makes a head on collision with a stationary hydrogen atom in ground state. The minimum kinetic energy of the neutron for which perfactly inelastic collision will take place is : (1) 20.4 eV (2) 10.2 eV (3) 12.1 eV (4) 16.8 eV

Q26.An electron in a hydrogen atom makes a transition from n = 2 to n = 1 and emits a photon. This photon strikes a doubly ionized lithium atom which was already in an excited state and completely removes the orbiting electron. The least quantum number for the excited state of the lithium-ion for the process is (1) 2 (2) 4 (3) 5 (4) 3

Q34.The group of molecules having identical shape is: (1) PCl5, IF5, XeO2F2 (2) BF3, PCl3, XeO3 (3) SF4, XeF4, CCl4 (4) ClF3, XeOF2, XeF+3

Q56.The correct statement about the synthesis of erythritol (C(CH2OH)4) used in the preparation of PETN is (1) The synthesis requires three aldol condensations (2) Alpha hydrogen of ethanol and methanol are and one Cannizzaro reaction. involved in this reaction. (3) The synthesis requires two aldol condensation (4) The synthesis requires four aldol condensations and two Cannizzaro reactions. between methanol and ethanol.

Q67.If A > 0, B > 0 and A + B = π6 , then the minimum positive value of (tan A + tan B) is : (1) √3 −√2 (2) 4 −2√3 (3) 2 (4) 2 −√3 √3 be two sets. Then and Q = : sin θ −cos θ = √2 cos θ} {θ : sin θ + cos θ = √2 sin θ},

Q68.Two sides of a rhombus are along the lines, x −y + 1 = 0 and 7x −y −5 = 0 . If its diagonals intersect at (−1, −2) , then which one of the following is a vertex of this rhombus ? (1) ( 31 , −83 ) (2) (−103 , −73 ) (3) (−3, −9) (4) (−3, −8)

Q68.The number of x ∈[0, 2π] for which √2 sin4 x + 18 cos2 x − √2 cos4 x + 18 sin2 x = 1 is: (1) 2 (2) 6 (3) 4 (4) 8