Practice Questions

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 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.

Q47. In the given circuit the sliding contact is pulled outwards such that electric current in the circuit changes at the rate of 8 A/s. At an instant when R is 12Ω, the value of the current in the circuit will be ______ A.

Q48.The position vectors of two 1 kg particles, (A) and (B), are given by→rA = (α1t2^i + α2t^j + α3t^k)m , respectively; →rB = (β1t^i + β2t2^j + β3t^k)m (α1 = 1 m/s2, α2 = 3nm/s, α3 = 2 m/s, β1 = 2 m/s, β2 = −1 m/s2, β3 = 4pm/s), where t is time, n and p −→ are constants. At t = 1 s, VA = →VB and velocities →VA and →VB of the particles are orthogonal to each other. At t = 1 s, the magnitude of angular momentum of particle (A) with respect to the position of particle (B) is √Lkgm2 s−1 . The value of L is _______ .

Q48.Two light beams fall on a transparent material block at point 1 and 2 with angle θ1 and θ2′ respectively, as shown in figure. After refraction, the beams intersect at point 3 which is exactly on the interface at other end of the block. Given : the distance between 1 and 2, d = 4√3 cm and θ1 = θ2 = cos−1 ( 2n1n2 ), where refractive index of the block n2 > refractive index of the outside medium n1 , then the thickness of the block is ________ cm.

Q49. A conducting bar moves on two conducting rails as shown in the figure. A constant magnetic field B exists into the page. The bar starts to move from the vertex at time t = 0 with a constant velocity. If the induced EMF is E ∝tn , then value of n is _.

Q49.A tube of length 1 m is filled completely with an ideal liquid of mass 2 M , and closed at both ends. The tube is rotated uniformly in horizontal plane about one of its ends. If the force exerted by the liquid at the other end is F then angular velocity of the tube is in SI unit. The value of α is __________. √FαM

Q50.A force f = x2y^i + y2^j acts on a particle in a plane x + y = 10. The work done by this force during a displacement from (0, 0) to (4 m, 2 m) is Joule (round off to the nearest integer)

Q54.The element that does not belong to the same period of the remaining elements (modern periodic table) is: 2025 (23 Jan Shift 1) JEE Main Previous Year Paper (1) Iridium (2) Platinum (3) Osmium (4) Palladium

Q71.The compound with molecular formula C6H6 , which gives only one monobromo derivative and takes up four moles of hydrogen per mole for complete hydrogenation has ________ = electrons. 2025 (22 Jan Shift 2) JEE Main Previous Year Paper Q72.20 mL of 2 M NaOH solution is added to 400 mL of 0.5 M NaOH solution. The final concentration of the solution is _______ ×10−2M. (Nearest integer)

Q71.Electrolysis of 600 mL aqueous solution of NaCl for 5 min changes the pH of the solution to 12 . The current in Amperes used for the given electrolysis is ____. (Nearest integer).

Q72.Isomeric hydrocarbons → negative Baeyer's test (Molecular formula C9H12 ) The total number of isomers from above with four different non-aliphatic substitution sites is -

Q72. A → B The molecule A changes into its isomeric form B by following a first order kinetics at a temperature of 1000 K . If the energy barrier with respect to reactant energy for such isomeric transformation is 191.48 kJ mol−1 and the frequency factor is 1020 , the time required for 50% molecules of A to become B is _________ picoseconds (nearest integer). [R = 8.314 J K−1 mol−1]

Q73.Total number of molecules/species from following which will be paramagnetic is ______ O2, O+2 , O−2 , NO, NO2, CO, K2 [NiCl4], [Co(NH3)6]Cl3, K2 [Ni(CN)4]

Q73.Consider the following sequence of reactions: 11.25 mg of chlorobenzene will produce __________ ×10−1mg of product B . (Consider the reactions result in complete conversion.) [Given molar mass of C, H, O, N and Cl as 12, 1, 16, 14 and 35.5 g mol−1 respectively]

Q73.Consider the following low-spin complexes K3 [Co(NO2)6], K4 [Fe(CN)6], K3 [Fe(CN)6], Cuu2 [Fe(CN)6] and Zn2 [Fe(CN)6] The sum of the spin-only magnetic moment values of complexes having yellow colour is. _____ B.M. (answer in nearest integer)

Q73.The sum of sigma (σ) and pi (π) bonds in Hex-1,3-dien-5-yne is _______. Q74. 0.1 mole of compound ' S ' will weigh _______ g. (Given molar mass in gmol−1C : 12, H : 1, O : 16)

Q73.Consider a complex reaction taking place in three steps with rate constants k1, k2 and k3 respectively. The overall rate constant k is given by the expression k = . If the activation energies of the three steps are √k1k3k2 60,30 and 10 kJ mol−1 respectively, then the overall energy of activation in kJmol−1 is … … . (Nearest integer)

Q74.In the Claisen-Schmidt reaction to prepare, dibenzalacetone from 5.3 g of benzaldehyde, a total of 3.51 g of product was obtained. The percentage yield in this reaction was ______ %.

Q74.Some CO2 gas was kept in a sealed container at a pressure of 1 atm and at 273 K . This entire amount of CO2 gas was later passed through an aqueous solution of Ca(OH)2 . The excess unreacted Ca(OH)2 was later neutralized with 0.1 M of 40 mL HCl . If the volume of the sealed container of CO2 was x, then x is ________ cm3 (nearest integer). [Given : The entire amount of CO2( g) reacted with exactly half the initial amount of Ca(OH)2 present in the aqueous solution.] 2025 (22 Jan Shift 1) JEE Main Previous Year Paper

Q74.The bond dissociation enthalpy of X2ΔHbond calculated from the given data is kJmol−1 . (Nearest M+X−(s) →M+(g) + X−(g)ΔH∗lattice = 800 kJ mol−1 integer) M( s) →M( g)ΔH∘sub = 100 kJ mol−1 M( g) →M+(g) + e−(g)ΔHi = 500 kJ mol−1 X( g) + e−(g) →X−(g)ΔH∗eg = −300 kJ mol−1 M( s) + 12 X2( g) →M+X−(s)ΔH∘f = −400 kJ mol−1 [Given : M+X− is a pure ionic compound and X forms a diatomic molecule X2 in gaseous state] 2025 (23 Jan Shift 2) JEE Main Previous Year Paper

Q21.A particle is moving in a circle of radius 50 cm in such a way that at any instant the normal and tangential components of its acceleration are equal. If its speed at t = 0 is 4 m s−1 , the time taken to complete the first revolution will be 1 [1 −e−2π] s, where α =______. α

Q21.A body starts falling freely from height 𝐻 hits an inclined plane in its path at height ℎ. As a result of this perfectly elastic impact, the direction of the velocity of the body becomes horizontal. The value of 𝐻 for which ℎ the body will take the maximum time to reach the ground is _____.

Q22.A circular table is rotating with an angular velocity of ωrad/s about its axis (see figure). There is a smooth groove along a radial direction on the table. A steel ball is gently placed at a distance of 1 m on the groove. All the surfaces are smooth. If the radius of the table is 3 m , the radial velocity of the ball w.r.t. the table at the time ball leaves the table is x√2ωm/s, where the value of x is _____.