Practice Questions

Q98.The solution of the differential equation dx dy = x+yx satisfying the condition y(1) = 1 is (1) y = ln x + x (2) y = x ln x + x2 (3) y = xe(x−1) (4) y = x ln x + x

Q99.The differential equation of the family of circles with fixed radius 5 units and centre on the line y = 2 is (1) (x −2)y′2 = 25 −(y −2)2 (2) (y −2)y′2 = 25 −(y −2)2 (3) (y −2)2y′2 = 25 −(y −2)2 (4) (x −2)2y′2 = 25 −(y −2)2 Q100.The non-zero verctors →a,→b and →c are related by →a = 8→b and →c = −7→b. Then the angle between →a and→cis (1) 0 (2) π/4 (3) π/2 (4) π Q101.The vector →a = α^i + 2^j + β^k lies in the plane of the vectors →b = ^i + ^j and →c = ^j + ^k and bisects the angle between →b and →c. Then which one of the following gives possible values of α and β ? (1) α = 2, β = 2 (2) α = 1, β = 2 (3) α = 2, β = 1 (4) α = 1, β = 1 Q102.The line passing through the points (5, 1, a) and (3, b, 1) crosses the yz− plane at the point (0, 172 , −132 ). Then JEE Main 2008 JEE Main Previous Year Paper (1) a = 2, b = 8 (2) a = 4, b = 6 (3) a = 6, b = 4 (4) a = 8, b = 2 Q103.If the straight lines x−1 k = y−22 = z−33 and x−23 = y−3k = z−12 intersect at a point, then the integer k is equal to (1) −5 (2) 5 (3) 2 (4) −2 Q104.It is given that the events A and B are such that P(A) = 41 , P ( BA ) = 12 and P ( BA ) = 32 . Then P(B) is (1) 1 (2) 1 6 3 (3) 2 (4) 1 3 2 Q105.A die is thrown. Let A be the event that the number obtained is greater than 3 . Let B be the event that the number obtained is less than 5 . Then P(A ∪B) is (1) 3 (2) 0 5 (3) 1 (4) 2 5 JEE Main 2008 JEE Main Previous Year Paper

Q3. A particle just clears a wall of height b at distance a and strikes the ground at a distance c from the point of projection. The angle of projection is (1) tan−1 acb (2) 45∘ (3) tan−1 a(c−a)bc (4) tan−1 bca

Q4. A block of mass ' m ' is connected to another block of mass ' M ' by a spring (massless) of spring constant ' k '. The blocks are kept on a smooth horizontal plane. Initially the blocks are at rest and the spring is unstretched. Then a constant force ' F' starts acting on the block of mass ' M' to pull it. Find the force on the block of mass ' m' (1) mF (2) (M+m)F M m (3) mF (4) MF (m+M) (m+M)

Q5. A 2 kg block slides on a horizontal floor with a speed of 4 m/s. It strikes a uncompressed spring, and compresses it till the block is motionless. The kinetic friction force is 15 N and spring constant is 10, 000. N/m. The spring compresses by (1) 5.5 cm (2) 2.5 cm (3) 11.0 cm (4) 8.5 cm

Q6. A body weighing 13 kg is suspended by two strings 5 m and 12 m long, their other ends being fastened to the extremities of a rod 13 m long. If the rod be so held that the body hangs immediately below the middle point. The tensions in the strings are (1) 12 kg and 13 kg (2) 5 kg and 5 kg (3) 5 kg and 12 kg (4) 5 kg and 13 kg

Q7. A circular disc of radius R is removed from a bigger circular disc of radius 2R such that the circumferences of the discs coincide. The centre of mass of the new disc is α/R from the centre of the bigger disc. The value of α is (1) 1/3 (2) 1/2 (3) 1/6 (4) 1/4 JEE Main 2007 JEE Main Previous Year Paper

Q9. A round uniform body of radius R, mass M and moment of inertia ' I', rolls down (without slipping) an inclined plane making an angle θ with the horizontal. Then its acceleration is θ g sin g sin (1) θ (2) I MR2 1+ 1+ MR2 I (3) g sinI θ (4) g sin θ 1− MR2 1−MR2I

Q11.One end of a thermally insulated rod is kept at a temperature T1 and the other at T2 . The rod is composed of two sections of lengths ℓ1 and ℓ2 and thermal conductivities k1 and k2 respectively. The temperature at the interface of the two sections is (1) (k2ℓ2T1 + k1ℓ1T2)/ (k1ℓ1 + k2ℓ2) (2) (k2ℓ1T1 + k1ℓ1T2)/ (k2ℓ1 + k1ℓ2) (3) (k1ℓ2T1 + k2ℓ1T2)/ (k1ℓ2 + k2ℓ1) (4) (k1ℓ1T1 + k2ℓ2T2)/ (k1ℓ1 + k2ℓ2)

Q12.A Carnot engine, having an efficiency of η = 1/10 as heat engine, is used as a refrigerator. If the work done on the system is 10 J, the amount of energy absorbed from the reservoir at lower temperature is (1) 99 J (2) 90 J (3) 1 J (4) 100 J

Q15.The displacement of an object attached to a spring and executing simple harmonic motion is given by x = 2 × 10−2 cos πt metres. The time at which the maximum speed first occurs is (1) 0.5 s (2) 0.75 s (3) 0.125 s (4) 0.25 s

Q17.Two springs, of force constants k1 and k2 , are connected to a mass m as shown. The frequency of oscillation of the mass is f . If both k1 and k2 are made four times their original values, the frequency of oscillation becomes (1) f/2 (2) f/4 (3) 4f (4) 2f

Q18.A particle of mass m executes simple harmonic motion with amplitude ' a ' and frequency ' v '. The average kinetic energy during its motion from the position of equilibrium to the end is (1) π2ma2v2 (2) 41 π2ma2v2 (3) 4π2ma2v2 (4) 2π2ma2v2

Q20.An electric charge 10−3μC is placed at the origin (0, 0) of X −Y co-ordinate system. Two points A and B are situated at (√2, √2) and (2, 0) respectively. The potential difference between the points A and B will be (1) 9 volt (2) zero (3) 2 volt (4) 4.5 volt

Q21.Charges are placed on the vertices of a square as shown. Let E be the electric field and V the potential at the centre. If the charges on A and B are interchanged with those on D and C respectively, then JEE Main 2007 JEE Main Previous Year Paper (1) →E remains unchanged, V changes (2) Both →E and V change (3) →E and V remains unchanged (4) →E changes, V remains unchanged

Q24.A battery is used to charge a parallel plate capacitor till the potential difference between the plates becomes equal to the electromotive force of the battery. The ratio of the energy stored in the capacitor and the work done by the battery will be (1) 1 (2) 2 (3) 1 (4) 1 4 2

Q26.The resistance of a wire is 5 ohm at 50∘C and 6 ohm at 100∘C. The resistance of the wire at 0∘C will be (1) 2 ohm (2) 1 ohm (3) 4 ohm (4) 3 ohm

Q27.A long straight wire of radius ' a ' caries a steady current i. The current is uniformly distributed across its cross section. The ratio of the magnetic field at a and 2a is 2 (1) 1 (2) 4 4 (3) 1 (4) 12

Q29.A charged particle with charge q enters a region of constant, uniform and mutually orthogonal fields →E and →B with a velocity →v perpendicular to both →E and →B, and comes out without any change in magnitude or direction of →v. Then (1) →v = →E × →B/B2 (2) →v = →B × →E/B2 → → (3) →v = →E × →B/E2 (4) →v = B × E/E2

Q31.Two identical conducting wires AOB and COD are placed at right angles to each other. The wire AOB carries an electric current I1 and COD carries a current I2 . The magnetic field on a point lying at a distance ' d ' from O, in a direction perpendicular to the plane of the wires AOB and COD, will be given by (1) μ0 I1+I2 1/2 (2) μ0 2πd (I21 + I22)1/2 2π ( d ) (3) 2πd μ0 (I1 + I2) (4) 2πdμ0 (I21 + I22)

Q32.An ideal coil of 10H is connected in series with a resistance of 5Ω and a battery of 5 V . 2 second after the connection is made the current flowing in amperes in the circuit is (1) (1 −e) (2) e (3) e−1 (4) (1 −e−1)

Q35.In a Young's double slit experiment the intensity at a point where the path difference is λ ( λ being the 6 wavelength of the light used) is I. If I0 denotes the maximum intensity, I0I is equal to (1) 1 (2) √3 √2 2 (3) 1/2 (4) 3/4

Q38.If Mo is the mass of an oxygen isotope 8O17, Mp and MN are the masses of a proton and a neutron respectively, the nuclear binding energy of the isotope is (1) (Mo −8Mp)C2 (2) (Mo −8Mp −9MN)C2 (3) MoC2 (4) (Mo −17MN)C2

Q40.The half-life period of a radio-active element X is same as the mean life time of another radioactive element Y . Initially they have the same number of atoms. Then (1) X will decay faster than Y (2) Y will decay faster than X (3) X and Y have same decay rate initially (4) X and Y decay at same rate always.

Q41. If in a p −n junction diode, a square input signal of 10 V is applied as shown Then the output signal across RL will be (1) (2) (3) (4)