Practice Questions

Q38.A gun fires a lead bullet of temperature 300 K into a wooden block. The bullet having melting temperature of 600 K penetrates into the block and melts down. If the total heat required for the process is 625 J , then the mass of the bullet is grams. (Latent heat of fusion of lead = 2.5 × 104JKg−1 and specific heat capacity of lead = 125JKg−1 K−1) (1) 10 (2) 20 (3) 5 (4) 15

Q40.A cup of coffee cools from 90∘C to 80∘C in t minutes when the room temperature is 20∘C. The time taken by the similar cup of coffee to cool from 80∘C to 60∘C at the same room temperature is : (1) 13 10 t (2) 1013 t (3) 13 5 t (4) 135 t

Q41.A light hollow cube of side length 10 cm and mass 10 g , is floating in water. It is pushed down and released to execute simple harmonic oscillations. The time period of oscillations is yπ × 10−2 s, where the value of y is (Acceleration due to gravity, g = 10 m/s2 , density of water = 103 kg/m3 ) 2025 (23 Jan Shift 1) JEE Main Previous Year Paper (1) 6 (2) 2 (3) 4 (4) 1

Q41.If a satellite orbiting the Earth is 9 times closer to the Earth than the Moon, what is the time period of rotation of the satellite? Given rotational time period of Moon = 27 days and gravitational attraction between the satellite and the moon is neglected. (1) 27 days (2) 1 day (3) 81 days (4) 3 days

Q43.The motion of an airplane is represented by velocity-time graph as shown below. The distance covered by airplane in the first 30.5 second is _______ km . (1) 12 (2) 3 (3) 6 (4) 9

Q45.A solid sphere of mass ' m ' and radius ' r ' is allowed to roll without slipping from the highest point of an inclined plane of length ' L ' and makes an angle 30∘ with the horizontal. The speed of the particle at the bottom of the plane is v1 . If the angle of inclination is increased to 45∘ while keeping L constant. Then the new speed of the sphere at the bottom of the plane is v2 . The ratio v21 : v22 is (1) 1 : √2 (2) 1 : √3 (3) 1 : 3 (4) 1 : 2 2025 (23 Jan Shift 1) JEE Main Previous Year Paper

Q46.A double slit interference experiment performed with a light of wavelength 600 nm forms an interference fringe pattern on a screen with 10 th bright fringe having its centre at a distance of 10 mm from the central maximum. Distance of the centre of the same 10th bright fringe from the central maximum when the source of light is replaced by another source of wavelength 660 nm would be _________ mm .

Q46.In a hydraulic lift, the surface area of the input piston is 6 cm2 and that of the output piston is 1500 cm2 . If 100 N force is applied to the input piston to raise the output piston by 20 cm, then the work done is _______ kJ. 2025 (29 Jan Shift 1) JEE Main Previous Year Paper

Q46.A current of 5A exists in a square loop of side 1 m . Then the magnitude of the magnetic field B at the centre √2 of the square loop will be p × 10−6 T. where, value of p is _____ . [ Take μ0 = 4π × 10−7TmA−1].

Q46.The magnetic field inside a 200 turns solenoid of radius 10 cm is 2.9 × 10−4Tesla. If the solenoid carries a current of 0.29 A , then the length of the solenoid is ________ πcm .

Q46.A thin transparent film with refractive index 1.4 , is held on circular ring of radius 1.8 cm . The fluid in the film evaporates such that transmission through the film at wavelength 560 nm goes to a minimum every 12 seconds. Assuming that the film is flat on its two sides, the rate of evaporation is ____ π × 10−13 m3/s. 2025 (28 Jan Shift 2) JEE Main Previous Year Paper

Q46.A positive ion A and a negative ion B has charges 6.67 × 10−19C and 9.6 × 10−10C, and masses 19.2 × 10−27 kg and 9 × 10−27 kg respectively. At an instant, the ions are separated by a certain distance r. At that instant the ratio of the magnitudes of electrostatic force to gravitational force is P × 1045 , where the value of 10 P is (Take 1 = 9 × 109Nm2C−1 and universal gravitational constant as 6.67 × 10−11Nm2 kg−2 4πε0 ) Assume that charge may not be an integral multiple of electrons.

Q46.The driver sitting inside a parked car is watching vehicles approaching from behind with the help of his side view mirror, which is a convex mirror with radius of curvature R = 2 m . Another car approaches him from behind with a uniform speed of 90 km/hr. When the car is at a distance of 24 m from him, the magnitude of the acceleration of the image of the car in the side view mirror is ' a '. The value of 100 a is _______ m/s2 .

Q46.A proton is moving undeflected in a region of crossed electric and magnetic fields at a constant speed of 2 × 105 ms−1 . When the electric field is switched off, the proton moves along a circular path of radius 2 cm . The magnitude of electric field is x × 104 N/C. The value of x is _______ Take the mass of the proton = 1.6 × 10−27 kg.

Q46.The ratio of the power of a light source S1 to that the light source S2 is 2. S1 is emitting 2 × 1015 photons per second at 600 nm . If the wavelength of the source S2 is 300 nm , then the number of photons per second emitted by S2 is … … ×1014 . 2025 (24 Jan Shift 2) JEE Main Previous Year Paper

Q46.A time varying potential difference is applied between the plates of a parallel plate capacitor of capacitance 2.5μ F. The dielectric constant of the medium between the capacitor plates is 1 . It produces an instantaneous displacement current of 0.25 mA in the intervening space between the capacitor plates, the magnitude of the rate of change of the potential difference will be _____ Vs−1 .

Q47.A square loop of sides a = 1 m is held normally in front of a point charge q = 1C. The flux of the electric 1 Nm2 field through the shaded region is , where the value of p is _____. 5 × p C ε0

Q47. A string of length L is fixed at one end and carries a mass of M at the other end. The mass makes ( π3 ) rotations per second about the vertical axis passing through end of the string as shown. The tension in the string is … … ML.

Q47.In a measurement, it is asked to find modulus of elasticity per unit torque applied on the system. The measured quantity has dimension of [M aLbT c]. If b = −3, the value of c is ________

Q47.The value of current I in the electrical circuit as given below, when potential at A is equal to the potential at B, will be ____ A.

Q47.Two soap bubbles of radius 2 cm and 4 cm , respectively, are in contact with each other. The radius of curvature of the common surface, in cm , is ______ . and

Q47.The net current flowing in the given circuit is_______ A.

Q47.The coordinates of a particle with respect to origin in a given reference frame is (1, 1, 1) meters. If a force of → F = ^i −^j + ^k acts on the particle, then the magnitude of torque (with respect to origin) in z-direction is ______.

Q47.In a series LCR circuit, a resistor of 300Ω, a capacitor of 25 nF and an inductor of 100 mH are used. For maximum current in the circuit, the angular frequency of the ac source is _____ ×104 radians s−1 .

Q47.A parallel plate capacitor consisting of two circular plates of radius 10 cm is being charged by a constant current of 0.15 A . If the rate of change of potential difference between the plates is 7 × 108 V/s then the integer value of the distance between the parallel plates is ( Take, ϵ0 = 9 × 10−12 mF , π = 227 ) ________ μm . 2025 (29 Jan Shift 2) JEE Main Previous Year Paper