Practice Questions

Q21.A vector has magnitude same as that of 𝐴= 3 ^j + 4 ^j and is parallel to 𝐵= 4 ^i + 3 ^j. The 𝑥 and 𝑦 components of this vector in first quadrant are 𝑥 and 3 respectively where x = ____.

Q21.A bus moving along a straight highway with speed of 72 km/h is brought to halt within 4s after applying the brakes. The distance travelled by the bus during this time (Assume the retardation is uniform) is _____m.

Q21.For three vectors →A = (−x^i −6^j −2^k), →B = (−^i + 4^j + 3^k) and →C = (−8^i −^j + 3^k), if →A ⋅(→B × →C) = 0, then value of x is _________

Q21.The maximum height reached by a projectile is 64 m. If the initial velocity is halved, the new maximum height of the projectile is _____ m . JEE Main 2024 (05 Apr Shift 2) JEE Main Previous Year Paper

Q22.A force (3x2 + 2x −5)N displaces a body from x = 2 m to x = 4 m . Work done by this force is ________ J .

Q23.If average depth of an ocean is 4000 m and the bulk modulus of water is 2 × 109 N m−2 , then fractional compression ΔV of water at the bottom of ocean is α × 10−2 . The value of α is _______, (Given, V g = 10 m s−2, ρ = 1000 kg m−3 )

Q24.At room temperature (27∘C), the resistance of a heating element is 50Ω. The temperature coefficient of the material is 2.4 × 10−4∘C−1 . The temperature of the element, when its resistance is 62Ω, is _____ ∘C.

Q24.A simple harmonic oscillator has an amplitude A and time period 6π second. Assuming the oscillation starts from its mean position, the time required by it to travel from x = A to x = √32 A will be πx s, where x = _______.

Q24.A particle is doing simple harmonic motion of amplitude 0.06 m and time period 3.14 s. The maximum velocity of the particle is _______ cm/s.

Q24.The displacement of a particle executing SHM is given by x = 10 sin (wt + π3 )m. The time period of motion is 3.14 s. The velocity of the particle at t = 0 is ______ m/s.

Q24.A sonometer wire of resonating length 90 cm has a fundamental frequency of 400 Hz when kept under some tension. The resonating length of the wire with fundamental frequency of 600 Hz under same tension _____ cm .

Q24.When the displacement of a simple harmonic oscillator is one third of its amplitude, the ratio of total energy to the kinetic energy is x , where x =_________. 8

Q24.A mass 𝑚 is suspended from a spring of negligible mass and the system oscillates with a frequency 𝑓1 . The frequency of oscillations if a mass 9𝑚 is suspended from the same spring is 𝑓2 . The value of 𝑓1 is _____ . 𝑓2

Q25.An electric field, E = √6 passes through the surface of 4 m2 area having unit vector ^n = ( √6 ) electric flux for that surface is ______ Vm .

Q25.A point source is emitting sound waves of intensity 16 × 10-8 W m-2 at the origin. The difference in intensity (magnitude only) at two points located at a distances of 2 m and 4 m from the origin respectively will be ________ × 10-8 W m-2.

Q25.The electric potential at the surface of an atomic nucleus ( 𝑍= 50 ) of radius 9 × 10-13 cm is 𝛼× 106 V. What is the value of 𝛼? (Charge of proton 1 . 6 × 10-19 C)

Q26.A charge of 4. 0 μC is moving with a velocity of 4. 0 × 106 m s−1 along the positive y-axis under a magnetic field B of strength T. The force acting on the charge is xˆi N. The value of x is ______. (2ˆk)

Q26.The current in a conductor is expressed as 𝐼= 3𝑡2 + 4𝑡3, where 𝐼 is in Ampere and 𝑡 is in second. The amount of electric charge that flows through a section of the conductor during 𝑡= 1 s to 𝑡= 2 s is ____________ C .

Q26.In the following circuit, the battery has an emf of 2 V and an internal resistance of 𝛺. The power 3 consumption in the entire circuit is ______ W.

Q27.To determine the resistance (R) of a wire, a circuit is designed below. The V −I characteristic curve for this circuit is plotted for the voltmeter and the ammeter readings as shown in figure. The value of R is ______ Ω.

Q27.A horizontal straight wire 5 m long extending from east to west falling freely at right angle to horizontal component of earth's magnetic field 0. 60 × 10−4 Wb m−2 . The instantaneous value of emf induced in the wire when its velocity is 10 m s−1 is _______ ×10−3 V . JEE Main 2024 (29 Jan Shift 2) JEE Main Previous Year Paper

Q27.Two long, straight wires carry equal currents in opposite directions as shown in figure. The separation between the wires is 5. 0 cm. The magnitude of the magnetic field at a point P midway between the wires is _____ μT . (Given: μ0 = 4π × 10−7 T m A−1 )

Q28.The current in an inductor is given by I = (3t + 8) where t is in second. The magnitude of induced emf produced in the inductor is 12mV . The self-inductance of the inductor _____ mH .

Q28.A rod of length 60 cm rotates with a uniform angular velocity 20rads−1 about its perpendicular bisector, in a uniform magnetic filed 0.5T . The direction of magnetic field is parallel to the axis of rotation. The potential difference between the two ends of the rod is _____V.

Q28.The magnetic flux 𝜙 (in weber) linked with a closed circuit of resistance 8 𝛺 varies with time (in seconds) as 𝜙= 5𝑡2 −36𝑡+ 1. The induced current in the circuit at 𝑡 = 2 s is _______ A.