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JEE Mains 2025 (3 Apr, Shift 2), Paper 1 (B.E./B.Tech) question paper

75 questions · 300 marks · 180 minutes · +4 per correct answer, -1 per wrong one

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Physics

25 questions

  1. 1
    A magnetic dipole experiences a torque of 803 N m80\sqrt{3}\text{ }N\text{ }m when placed in uniform magnetic field in such a way that dipole moment makes angle of 60∘60^{\circ} with magnetic field. The potential energy of the dipole is :

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  2. 2
    In the resonance experiment, two air columns (closed at one end) of 100 cm and 120 cm long, give 15 beats per second when each one is sounding in the respective fundamental modes. The velocity of sound in the air column is :

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  3. 3
    Two cylindrical vessels of equal cross sectional area of 2 m22{\text{ }m}^{2} contain water upto height 10 m and 6 m , respectively. If the vessels are connected at their bottom then the work done by the force of gravity is : (Density of water is 103 kg/m310^{3}\text{ }kg/m^{3} and g=10 m/s2g = 10\text{ }m/s^{2} )

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  4. 4
    Width of one of the two slits in a Young's double slit interference experiment is half of the other slit. The ratio of the maximum to the minimum intensity in the interference pattern is:

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  5. 5
    An ideal gas exists in a state with pressure P0P_{0}, volume V0V_{0}. It is isothermally expanded to 4 times of its initial volume (V0)\left( V_{0} \right), then isobarically compressed to its original volume. Finally the system is heated isochorically to bring it to its initial state. The amount of heat exchanged in this process is

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  6. 6
    Two monochromatic light beams have intensities in the ratio 1:91:9. An interference pattern is obtained by these beams. The ratio of the intensities of maximum to minimum is.

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  7. 7
    Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A : The Bohr model is applicable to hydrogen and hydrogen-like atoms only. Reason R : The formulation of Bohr model does not include repulsive force between electrons. In the light of the above statements, choose the correct answer from the options given below

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  8. 8
    Using a battery, a 100 pF capacitor is charged to 60 V and then the battery is removed. After that, a second uncharged capacitor is connected to the first capacitor in parallel. If the final voltage across the second capacitor is 20 V , its capacitance is : (in pF)

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  9. 9
    A monochromatic light of frequency 5×1014 Hz5 \times10^{14}\text{ }Hz travelling through air, is incident on a medium of refractive index ' 2 '. Wavelength of the refracted light will be :

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  10. 10
    Consider two blocks A and B of masses m1=10 kgm_{1}= 10\text{ }kg and m2=5 kgm_{2}= 5\text{ }kg that are placed on a frictionless table. The block A moves with a constant speed v=3 m/sv= 3\text{ }m/s towards the block B kept at rest. A spring with spring constant k=3000 N/mk = 3000\text{ }N/m is attached with the block B as shown in the figure. After the collision, suppose that the blocks A and B, along with the spring in constant compression state, move together, then the compression in the spring is, (Neglect the mass of the spring)

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  11. 11
    A particle is projected with velocity uu so that its horizontal range is three times the maximum height attained by it. The horizontal range of the projectile is given as nu225g\frac{nu^{2}}{25g}, where value of nn is : (Given ' gg ' is the acceleration due to gravity).

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  12. 12
    A solid steel ball of diameter 3.6 mm acquired terminal velocity 2.45×10−2 m/s2.45 \times10^{- 2}\text{ }m/s while falling under gravity through an oil of density 925 kg m−3925\text{ }kg{\text{ }m}^{- 3}. Take density of steel as 7825 kg m−37825\text{ }kg{\text{ }m}^{- 3} and g as 9.8 m/s2m/s^{2}. The viscosity of the oil in SI unit is.

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  13. 13
    The truth table corresponding to the circuit given below is.

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  14. 14
    A particle moves along the xx-axis and has its displacement xx varying with time tt according to the equation
    x=c0(t2−2)+c(t−2)2x =c_{0}\left( t^{2}- 2 \right)+ c(t - 2)^{2}
    where c0c_{0} and cc are constants of appropriate dimensions. Then, which of the following statements is correct?

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  15. 15
    An electric bulb rated as 100 W−220 V100\text{ }W - 220\text{ }V is connected to an ac source of rms voltage 220 V . The peak value of current through the bulb is :

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  16. 16
    Match the LIST-I with LIST-II
    LIST-ILIST-II
    A. Boltzmann constantI. [ML2T−1]\left[ML^{2}T^{-1}\right]
    B. Coefficient of viscosityII. [MLT−3K−1]\left[MLT^{-3}K^{-1}\right]
    C. Planck's constantIII. [ML2T−2K−1]\left[ML^{2}T^{-2}K^{-1}\right]
    D. Thermal conductivityIV. [ML−1T−1]\left[ML^{-1}T^{-1}\right]
    Choose the correct answer from the options given below:

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  17. 17
    Pressure of an ideal gas, contained in a closed vessel, is increased by 0.4%0.4\% when heated by 1∘C1^{\circ}C. Its initial temperature must be :

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  18. 18
    A motor operating on 100 V draws a current of 1 A . If the efficiency of the motor is 91.6%91.6\%, then the loss of power in units of cal/scal/s is.

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  19. 19
    A block of mass 1 kg , moving along xx with speed vi=10 m/sv_{i}= 10\text{ }m/s enters a rough region ranging from x=0.1 mx = 0.1\text{ }m to x=1.9 mx = 1.9\text{ }m. The retarding force acting on the block in this range is Fr=−kxNF_{r}= - kxN, with k=10 N/mk = 10\text{ }N/m. Then the final speed of the block as it crosses rough region is.

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  20. 20
    Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A : If oxygen ion (O−2)\left( O^{- 2} \right) and Hydrogen ion (H+)\left( H^{+} \right)enter normal to the magnetic field with equal momentum, then the path of O−2O^{- 2} ion has a smaller curvature than that of H+H^{+}. Reason R : A proton with same linear momentum as an electron will form a path of smaller radius of curvature on entering a uniform magnetic field perpendicularly. In the light of the above statement, choose the correct answer from the options given below

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  21. 21
    Light from a point source in air falls on a spherical glass surface (refractive index, μ=1.5\mu = 1.5 and radius of curvature =50 cm= 50\text{ }cm ). The image is formed at a distance of 200 cm from the glass surface inside the glass. The magnitude of distance of the light source from the glass surface is ____\_\_\_\_ m.
  22. 22
    The excess pressure inside a soap bubble AA in air is half the excess pressure inside another soap bubble B in air. If the volume of the bubble A is nn times the volume of the bubble B , then, the value of nn is ____\_\_\_\_.
  23. 23
    Two cells of emf 1 V and 2 V and internal resistance 2Ω2\Omega and 1Ω1\Omega, respectively, are connected in series with an external resistance of 6Ω6\Omega. The total current in the circuit is I1I_{1}. Now the same two cells in parallel configuration are connected to same external resistance. In this case, the total current drawn is I2I_{2}. The value of (I1I2)\left( \frac{I_{1}}{I_{2}} \right) is x3\frac{x}{3}. The value of xx is .
  24. 24
    An electron in the hydrogen atom initially in the fourth excited state makes a transition to nth n^{\text{th~}} energy state by emitting a photon of energy 2.86 eV . The integer value of n will be .
  25. 25
    A physical quantity C is related to four other quantities p,q,rp,q,r and s as follows C=pq2r3 sC = \frac{{pq}^{2}}{r^{3}\sqrt{\text{ }s}}.The percentage errors in the measurement of p, q, r and ss are 1%,2%,3%1\%, 2\%, 3\% and 2%2\% respectively. The percentage error in the measurement of CC will be ____ %\_\_\_\_\ \%.

Chemistry

25 questions

  1. 26
    40 mL of a mixture of CH3COOHCH_{3}COOH and HCl (aqueous solution) is titrated against 0.1 M NaOH solution conductometric ally. Which of the following statement is correct?

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  2. 27
    10 mL of 2 M NaOH solution is added to 20 mL of 1 M HCl solution kept in a beaker. Now, 10 mL of this mixture is poured into a volumetric flask of 100 mL containing 2 moles of HCl and made the volume upto the mark with distilled water. The solution in this flask is :

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  3. 28
    Fat soluble vitamins are : A. Vitamin B1B_{1} B. Vitamin C C. Vitamin E D. Vitamin B12B_{12} E. Vitamin K Choose the correct answer from the options given below:

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  4. 29
    Match the LIST-I with LIST-II.
    LIST-I (Family)LIST-II (Symbol of Element)
    A.Pnicogen (group 15)I.Ts
    B.ChalcogenII.Og
    C.HalogenIII.Lv
    D.Noble gasIV.Mc
    Choose the correct answer from the options given below:

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  5. 30
    For electron in ' 2 s ' and ' 2 p ' orbitals, the orbital angular momentum values, respectively are :

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  6. 31
    Compounds that should not be used as primary standards in titrimetric analysis are A. Na2Cr2O7{Na}_{2}{Cr}_{2}O_{7} B. Oxalic acid C. NaOH D. FeSO4⋅6H2O{FeSO}_{4} \cdot 6H_{2}O E. Sodium tetraborate Choose the most appropriate answer from the options given below:

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  7. 32
    The major product (P)(P) in the following reaction is P Major product \underset{\text{~Major product~}}{P}.

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  8. 33
    In the following series of reactions identify the major products A& BA\&\text{ }B respectively.

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  9. 34
    The standard cell potential (Ecell ⊖)\left( E_{\text{cell~}}^{\ominus} \right) of a fuel cell based on the oxidation of methanol in air that has been used to power television relay station is measured as 1.21 V . The standard half cell reduction potential for O2(EO2/H2Oo)O_{2}\left( E_{O_{2}/H_{2}O}^{o} \right) is 1.229 V . Choose the correct statement:

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  10. 35
    Identify the diamagnetic octahedral complex ions from below ; A. [Mn(CN)6]3−\left\lbrack Mn(CN)_{6} \right\rbrack^{3 -} B. [Co(NH3)6]3+\left\lbrack Co\left( {NH}_{3} \right)_{6} \right\rbrack^{3 +} C. [Fe(CN)6]4−\left\lbrack Fe(CN)_{6} \right\rbrack^{4 -} D. [Co(H2O)3 F3]\left\lbrack Co\left( H_{2}O \right)_{3}{\text{ }F}_{3} \right\rbrack Choose the correct answer from the options given below :

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  11. 36
    In Dumas' method for estimation of nitrogen 0.4 g of an organic compound gave 60 mL of nitrogen collected at 300 K temperature and 715 mm Hg pressure. The percentage composition of nitrogen in the compound is (Given : Aqueous tension at 300 K=15 mmHg300\text{ }K = 15\text{ }mmHg )

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  12. 37
    Mass of magnesium required to produce 220 mL of hydrogen gas at STP on reaction with excess of dil. HCl is Given : Molar mass of Mg is 24 g mol−124\text{ }g{\text{ }mol}^{- 1}.

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  13. 38
    Given below are two statements : Statement I : Wet cotton clothes made of cellulose based carbohydrate takes comparatively longer time to get dried than wet nylon polymer based clothes. Statement II : Intermolecular hydrogen bonding with water molecule is more in nylon-based clothes than in the case of cotton clothes. In the light of above statements, choose the Correct answer from the options given below

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  14. 39
    Given below are two statements: Statement I: CrO3{CrO}_{3} is a stronger oxidizing agent than MoO3{MoO}_{3} Statement II : Cr(VI)Cr(VI) is more stable than Mo(VI)Mo(VI) In the light of the above statements, choose the correct answer from the options given below

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  15. 40
    Given below are two statements : Statement I : Hyperconjugation is not a permanent effect. Statement II : In general, greater the number of alkyl groups attached to a positively charged C -atom, greater is the hyperconjugation interaction and stabilization of the cation. In the light of the above statements, choose the correct answer from the options given below

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  16. 41
    Given below are two statements: Statement I : When a system containing ice in equilibrium with water (liquid) is heated, heat is absorbed by the system and there is no change in the temperature of the system until whole ice gets melted. Statement II : At melting point of ice, there is absorption of heat in order to overcome intermolecular forces of attraction within the molecules of water in ice and kinetic energy of molecules is not increased at melting point. In the light of the above statements, choose the correct answer from the options given below:

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  17. 42
    The sequence from the following that would result in giving predominantly 3,4,53,4,5- Tribromo aniline is:

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  18. 43
    The correct orders among the following are Atomic radius : B<Al<Ga<In<TlB < Al < Ga < In < Tl Electronegativity: Al<Ga<In<Tl<BAl < Ga < In < Tl < B Density : Tl<In<Ga<Al<BTl < In < Ga < Al < B 1st Ionisation Energy: In<Al<Ga<Tl<BIn < Al < Ga < Tl < B Choose the correct answer from the options given below :

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  19. 44
    What is the correct IUPAC name of.

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  20. 45
    Consider the following statements related to temperature dependence of rate constants. Identify the correct statements, A. The Arrhenius equation holds true only for an elementary homogenous reaction. B. The unit of A is same as that of k in Arrhenius equation. C. At a given temperature, a low activation energy means a fast reaction. D. A and Ea as used in Arrhenius equation depend on temperature. E. When Ea >> RT. A and Ea become interdependent. Choose the correct answer from the options given below :

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  21. 46
    Xg of nitrobenzene on nitration gave 4.2 g of m -dinitrobenzene. X=X = ____ g. (nearest integer) [Given : molar mass (in gmol−1g{mol}^{- 1} ) C:12,H:1C:12,H:1, O:16, N:14]O:16,\text{ }N:14\rbrack
  22. 47
    A perfect gas (0.1 mol)(0.1\text{ }mol) having C‾v=1.50R{\overline{C}}_{v} = 1.50R (independent of temperature) undergoes the above transformation from point 1 to point 4 . If each step is reversible, the total work done (w) while going from point 1 to point 4 is (−)( - ) ____ J (nearest integer) [Given : R=0.082 L atm K−1 mol−1R = 0.082\text{ }L\text{ }atm{\text{ }K}^{- 1}{\text{ }mol}^{- 1} ].
  23. 48
    A sample of n-octane (1.14 g)(1.14\text{ }g) was completely burnt in excess of oxygen in a bomb calorimeter, whose heat capacity is 5 kJ K−15\text{ }kJ{\text{ }K}^{- 1}. As a result of combustion reaction, the temperature of the calorimeter is increased by 5 K . The magnitude of the heat of combustion of octane at constant volume is ____ kJmol−1kJ{mol}^{- 1} (nearest integer).
  24. 49
    Among, Sc,Mn,CoSc,Mn,Co and Cu , identify the element with highest enthalpy of atomisation. The spin only magnetic moment value of that element in its +2 oxidation state is ____ BM (in nearest integer).
  25. 50
    The total number of structural isomers possible for the substituted benzene derivatives with the molecular formula C9H12C_{9}H_{12} is ____ .

Mathematics

25 questions

  1. 51
    Let f:R→Rf:R\rightarrow R be a function defined by f(x)=∣∣x+2∣−2∣x∣∣f(x) = \left| |x+ 2| - 2|x| \right|. If mm is the number of points of local minima and nn is the number of points of local maxima of ff, then m+nm+n is.

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  2. 52
    Each of the angles β\beta and γ\gamma that a given line makes with the positive y−y- and zz-axes, respectively, is half of the angle that this line makes with the positive xx-axes. Then the sum of all possible values of the angle β\beta is.

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  3. 53
    If the four distinct points (4,6),(−1,5),(0,0)(4,6),( - 1,5),(0,0) and ( k,3kk,3k ) lie on a circle of radius rr, then 10k+r210k+r^{2} is equal to.

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  4. 54
    Let the Mean and Variance of five observations x1=1,x2=3,x3=a,x4=7x_{1}= 1,x_{2}= 3,x_{3}= a,x_{4}= 7 and x5=b,a>bx_{5}=b,a>b, be 5 and 10 respectively. Then the Variance of the observations n+xn, n=1,2,…,5n +x_{n},\ n = 1,2,\ldots,5 is

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  5. 55
    Consider the lines x(3λ+1)+y(7λ+2)=17λ+5x(3\lambda+ 1) +y(7\lambda+ 2) = 17\lambda+ 5, λ\lambda being a parameter, all passing through a point P . One of these lines (say L) is farthest from the origin. If the distance of LL from the point (3,6)(3,6) is d , then the value of d2d^{2} is.

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  6. 56
    Let A={−2,−1,0,1,2,3}A=\left\{ - 2, - 1,0,1,2,3 \right\}. let RR be a relation on A defined by xRyxRy if and only if y=max{x,1}y\mathbf{= max\{}x,1\}. Let ll be the number of elements in R . Let m and n be the minimum number of elements required to be added in RR to make it reflexive and symmetric relations, respectively. Then l+m+nl+ m + n is equal to.

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  7. 57
    Let the equation x(x+2)(12−k)=2x(x+ 2)(12 -k) = 2 have equal roots. Then the distance of the point (k,k2)\left( k,\frac{k}{2} \right) from the line 3x+4y+5=03x+ 4y+ 5 = 0 is.

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  8. 58
    Line L1L_{1} of slope 2 and line L2L_{2} of slope 12\frac{1}{2} intersect at the origin O . In the first quadrant, P1,P2,….P12P_{1},P_{2},\ldots.P_{12} are 12 points on line L1L_{1} and Q1,Q2,…..Q9Q_{1},Q_{2},\ldots..Q_{9} are 9 points on line L2L_{2}. Then the total number of triangles, that can be formed having vertices at three of the 22 points O,P1,P2,…P12O,P_{1},P_{2},\ldots P_{12}, Q1,Q2,….Q9Q_{1},Q_{2},\ldots.Q_{9}, is:

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  9. 59
    The integral ∫0π8xdx4cos⁡2x+sin⁡2x\int_{0}^{\pi} \frac{8xdx}{4\cos^{2}x+\sin^{2}x} is equal to.

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  10. 60
    Let ff be a function such that f(x)+3f(24x)f(x) + 3f\left( \frac{24}{x} \right) =4x,x≠0= 4x,x\neq 0. Then f(3)+f(8)f(3) +f(8) is equal to.

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  11. 61
    The area of the region {(x,y):∣x−y∣≤y≤4x}\{(x,y):|x-y| \leq y\leq 4\sqrt{x}\} is.

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  12. 62
    If the domain of the function f(x)=log⁡7(1−log⁡4(x2−9x+18))f(x) =\log_{7}\left( 1 -\log_{4}\left( x^{2}- 9x+ 18 \right) \right) is (α,β)∪(γ,δ)(\alpha,\beta) \cup (\gamma,\delta), then α+β+γ+δ\alpha+\beta+\gamma+\delta is equal to.

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  13. 63
    If the probability that the random variable XX takes the value x is given by P(X=x)=k(x+1)3−xP(X = x) = k(x + 1)3^{- x}, x=0,1,2,3……x = 0,1,2,3\ldots\ldots, where k is a constant, then P(X≥3)P(X \geq 3) is equal to

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  14. 64
    Let y=y(x)y=y\left( x \right) be the solution of the differential equation dydx+3(tan⁡2x)y+3y=\frac{dy}{dx}+ 3\left( \tan^{2}x \right)y+ 3y= sec⁡2x\sec^{2}x, y(0)=13+e3y(0) =\frac{1}{3}+e^{3}. Then y(π4)y\left( \frac{\pi}{4} \right) is equal to.

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  15. 65
    If z1,z2,z3∈Cz_{1},z_{2},z_{3}\in C are the vertices of an equilateral triangle, whose centroid is z0z_{0}, then ∑k=13(zk−z0)2\sum_{k= 1}^{3} \left( z_{k}-z_{0} \right)^{2} is equal to.

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  16. 66
    The number of solutions of equation (4−3)sin⁡x\left( 4 -\sqrt{3} \right)\sin x −23cos⁡2x=−41+3,x∈- 2\sqrt{3}\cos^{2}x= -\frac{4}{1 +\sqrt{3}},x\in [−2π,5π2]\left\lbrack - 2\pi,\frac{5\pi}{2} \right\rbrack is.

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  17. 67
    Let C be the circle of minimum area enclosing the ellipse E:x2a2+y2b2=1E:\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}= 1 with eccentricity 12\frac{1}{2} and foci (±2,0)( \pm 2,0). Let PQR be a variable triangle, whose vertex PP is on the circle CC and the side QRQR of length 2a2a is parallel to the major axis of E and contains the point of intersection of E with the negative yy-axis. Then the maximum area of the triangle PQR is

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  18. 68
    The shortest distance between the curves y2=8xy^{2}= 8x and x2+y2+12y+35=0x^{2}+y^{2}+ 12y+ 35 = 0 is :

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  19. 69
    The distance of the point (7,10,11)(7,10,11) from the line x−41=y−40=z−23\frac{x- 4}{1}=\frac{y- 4}{0}=\frac{z- 2}{3} along the line x−92=y−133=z−176\frac{x- 9}{2}=\frac{y- 13}{3}=\frac{z- 17}{6} is.

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  20. 70
    The sum 1+1+32!+1+3+53!+1+3+5+74!+…1 +\frac{1 + 3}{2!}+\frac{1 + 3 + 5}{3!}+\frac{1 + 3 + 5 + 7}{4!}+ \ldots upto ∞\infty terms, is equal to

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  21. 71
    Let I be the identity matrix of order 3×33 \times 3 and for the matrix A=A = [λ234567−12],∣A∣=−1\begin{bmatrix} \lambda & 2 & 3 \\ 4 & 5 & 6 \\ 7 & - 1 & 2 \end{bmatrix},|A| = - 1. Let B be the inverse of the matrix adj(A adj(A2))adj\left( A\ adj\left( A^{2} \right) \right). Then ∣λB+I∣|\lambda B + I| is equal to.
  22. 72
    Let (1+x+x2)10=a0+a1x+a2x2+….+a20x20\left( 1 + x + x^{2} \right)^{10} = a_{0} + a_{1}x + a_{2}x^{2} + \ldots. + a_{20}x^{20}. If (a1+a3+a5+…+a19)−11a2=\left( a_{1} + a_{3} + a_{5} + \ldots + a_{19} \right) - 11a_{2} = 121k121k, then k is equal to .
  23. 73
    If Limx→0(tan⁡xx)1x2=p{Lim}_{x \rightarrow 0}\left( \frac{\tan x}{x} \right)^{\frac{1}{x^{2}}} = p, then 96log⁡ep96\log_{e}p is equal to.
  24. 74
    Let a→=i^+2j^+k^,b→=3i^−3j^+3k^\overrightarrow{a} = \widehat{i} + 2\widehat{j} + \widehat{k},\overrightarrow{b} = 3\widehat{i} - 3\widehat{j} + 3\widehat{k}, c→=2i^−j^+2k^\overrightarrow{c} = 2\widehat{i} - \widehat{j} + 2\widehat{k} and d→\overrightarrow{d} be a vector such that b→×d→=c→×d→\overrightarrow{b} \times \overrightarrow{d} = \overrightarrow{c} \times \overrightarrow{d} and a→⋅d→=4\overrightarrow{a} \cdot \overrightarrow{d} = 4. Then ∣(a→×d→)∣2|(\overrightarrow{a} \times \overrightarrow{d})|^{2} is equal to.
  25. 75
    If the equation of the hyperbola with foci (4,2)(4,2) and (8,2)(8,2) is 3x2−y2−αx+βy+3x^{2} - y^{2} - \alpha x + \beta y + γ=0\gamma = 0, then α+β+γ\alpha + \beta + \gamma is equal to .

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