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JEE Mains 2025 (22 Jan, 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 symmetric thin biconvex lens is cut into four equal parts by two planes AB and CD as shown in figure. If the power of original lens is 4D then the power of a part of the divided lens is

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  2. 2
    A small rigid spherical ball of mass MM is dropped in a long vertical tube containing glycerine. The velocity of the ball becomes constant after some time. If the density of glycerine is half of the density of the ball, then the viscous force acting on the ball will be (consider g as acceleration due to gravity)

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  3. 3
    The maximum percentage error in the measurement of density of a wire is [Given, mass of wire =(0.60±0.003)g= (0.60 \pm 0.003)g, radius of wire =(0.50±0.01)cm= (0.50 \pm 0.01)cm, length of wire =(10.00±0.05)cm= (10.00 \pm 0.05)cm]

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  4. 4
    A series LCR circuit is connected to an alternating source of emf EE. The current amplitude at resonant frequency is I0I_{0}. If the value of resistance RR becomes twice of its initial value then amplitude of current at resonance will be

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  5. 5
    For a short dipole placed at origin O , the dipole moment PP is along xx-axis, as shown in the figure. If the electric potential and electric field at A are V0V_{0} and E0E_{0}, respectively, then the correct combination of the electric potential and electric field, respectively, at point BB on the yy-axis is given by

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  6. 6
    Which one of the following is the correct dimensional formula for the capacitance in F? M, L,TL,T and C stand for unit of mass, length, time and charge,

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  7. 7
    An electron projected perpendicular to a uniform magnetic field B moves in a circle. If Bohr's quantization is applicable, then the radius of the electronic orbit in the first excited state is :

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  8. 8
    For a diatomic gas, if γ1=(CpCv)\gamma_{1}=\left( \frac{Cp}{Cv} \right) for rigid molecules and γ2=(CpCv)\gamma_{2}=\left( \frac{Cp}{Cv} \right) for another diatomic molecules, but also having vibrational modes. Then, which one of the following options is correct ? (Cp and Cv are specific heats of the gas at constant pressure and volume)

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  9. 9
    A rectangular metallic loop is moving out of a uniform magnetic field region to a field free region with a constant speed. When the loop is partially inside the magnate field, the plot of magnitude of induced emf(ε)emf(\varepsilon) with time (t)(t) is given by

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  10. 10
    A light source of wavelength λ\lambda illuminates a metal surface and electrons are ejected with maximum kinetic energy of 2 eV . If the same surface is illuminated by a light source of wavelength λ2\frac{\lambda}{2}, then the maximum kinetic energy of ejected electrons will be (The work function of metal is 1 eV )

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  11. 11
    Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : A simple pendulum is taken to a planet of mass and radius, 4 times and 2 times, respectively, than, the Earth. The time period of the pendulum remains same on earth and the planet. Reason (R) : The mass of the pendulum remains unchanged at Earth and the other planet. In the light of the above statements, choose the correct answer from the options given below :

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  12. 12
    The torque due to the force (2i^+j^+2k^)(2\widehat{i}+\widehat{j}+ 2\widehat{k}) about the origin, acting on a particle whose position vector is (i^+j^+k^)(\widehat{i}+\widehat{j}+\widehat{k}), would be

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  13. 13
    ABY
    001
    010
    100
    111
    To obtain the given truth table, following logic gate should be placed at GG :

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  14. 14
    A force F→=2i^+bj^+k^\overrightarrow{F}= 2\widehat{i}+ b\widehat{j}+\widehat{k} is applied on a particle and it undergoes a displacement i^−2j^−k^\widehat{i}- 2\widehat{j}-\widehat{k}. What will be the value of bb, if work done on the particle is zero.

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  15. 15
    Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : In Young's double slit experiment, the fringes produced by red light are closer as compared to those produced by blue light. Reason (R) : The fringe width is directly proportional to the wavelength of light. In the light of above statements, choose the correct answer from the options given below :

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  16. 16
    A ball of mass 100 g is projected with velocity 20 m/s20\text{ }m/s at 60∘60^{\circ} with horizontal. The decrease in kinetic energy of the ball during the motion from point of projection to highest point is :

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  17. 17
    A transparent film of refractive index, 2.0 is coated on a glass slab of refractive index, 1.45. What is the minimum thickness of transparent film to be coated for the maximum transmission of Green light of wavelength 550 nm . [Assume that the light is incident nearly perpendicular to the glass surface.]

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  18. 18
    The tube of length L is shown in the figure. The radius of cross section at the point (1) is 2 cm and at the point (2) is 1 cm , respectively. If the velocity of water entering at point (1) is 2 m/s2\text{ }m/s, then velocity of water leaving the point (2) will be :

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  19. 19
    Given are statements for certain thermodynamic variables, (A) Internal energy, volume (V) and mass (M) are extensive variables. (B) Pressure (P), temperature (T) and density ( ρ\rho ) are intensive variables. (C) Volume (V), temperature (T) and density ( ρ\rho ) are intensive variables. (D) Mass (M), temperature (T) and internal energy are extensive variables. Choose the correct answer from the points given below :

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  20. 20
    A body of mass 100 g is moving in circular path of radius 2 m on vertical plane as shown in figure. The velocity of the body at point A is 10 m/s10\text{ }m/s. The ratio of its kinetic energies at point B and C is : (Take acceleration due to gravity as 10 m/s210\text{ }m/s^{2} )

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  21. 21
    A proton is moving undeflected in a region of crossed electric and magnetic fields at a constant speed of 2×105 ms−12 \times10^{5}{\text{ }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/Cx \times10^{4}\text{ }N/C. the value of x is ______\_\_\_\_\_\_ Take the mass of the proton =1.6×10−27 kg= 1.6 \times10^{- 27}\text{ }kg.
  22. 22
    Two long parallel wires X and Y , separated by a distance of 6 cm , carry currents of 5 A and 4 A , respectively, in opposite directions as shown in the figure. Magnitude of the resultant magnetic field at point PP at a distance of 4 cm from wire Y is x×10−5 Tx \times10^{- 5}\text{ }T. The value of xx is ______\_\_\_\_\_\_ . Take permeability of free space as μ0=4π×10−7\mu_{0}= 4\pi \times10^{- 7} SI units.
  23. 23
    A parallel plate capacitor of area A=16 cm2A = 16{\text{ }cm}^{2} and separation between the plates 10 cm , is charged by a DC current. Consider a hypothetical plane surface of area A0=3.2 cm2A_{0}= 3.2{\text{ }cm}^{2} inside the capacitor and parallel to the plates. At an instant, the current through the circuit is 6 A . At the same instant the displacement current through A0A_{0} is ______\_\_\_\_\_\_ mA .
  24. 24
    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 FαM\sqrt{\frac{F}{\alpha M}} in SI unit. The value of α\alpha is_____
  25. 25
    The net current flowing in the given circuit is ______\_\_\_\_\_\_ A.

Chemistry

25 questions

  1. 26
    Arrange the following compounds in increasing order of their dipole moment : HBr,H2 S,NF3HBr,H_{2}\text{ }S,NF_{3} and CHCl3CHCl_{3}

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  2. 27
    Identify the number of structure/s from the following which can be correlated to D-glyceraldehyde.

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  3. 28
    The maximum covalency of a non-metallic group 15 element ' E ' with weakest E−EE - E bond is :

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  4. 29
    Consider the given figure and choose the correct option :

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  5. 30
    When sec-butylcyclohexane reacts with bromine in the presence of sunlight, the major product is :

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  6. 31
    The species which does not undergo disproportionation reaction is :

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  7. 32
    Match the Compounds (List-I) with the appropriate Catalyst/Reagents (List-II) for their reduction into corresponding amines.
    List-I (Compound)List-II (Catalyst/Reagents)
    (A)R−CONH2R-CONH_{2}(I)NaOHNaOH (aqueous)
    (B)Nitrobenzene, C6H5NO2C_{6}H_{5}NO_{2}(II)H2/NiH_{2}/Ni
    (C)R−C≡NR-C \equiv N(III)LiAlH4LiAlH_{4}, H2OH_{2}O
    (D)N-Alkylphthalimide(IV)Sn,HClSn, HCl
    Choose the correct answer from the options given below :

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  8. 33
    RBr⟶(i) Mg, dry ether(ii) H2O2-methylbutaneRBr \underset{\text{(ii) }H_{2}O}{\overset{\text{(i) }Mg,\ \text{dry ether}}{\longrightarrow}} \text{2-methylbutane} The maximum number of RBr producing 2-methylbutane by above sequence of reactions is ________\_\_\_\_\_\_\_\_ (Consider the structural isomers only)

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  9. 34
    Match List-I with List-II.
    List-I (Partial Derivatives)List-II (Thermodynamic Quantity)
    (A)
    (∂G∂T)P\left( \frac{\partial G}{\partial T} \right)_{P}
    		(I)
    CPC_{P}
    (B)
    (∂H∂T)P\left( \frac{\partial H}{\partial T} \right)_{P}
    		(II)-S
    (C)
    (∂G∂P)T\left( \frac{\partial G}{\partial P} \right)_{T}
    		(III)
    CVC_{V}
    (D)
    (∂U∂T)V\left( \frac{\partial U}{\partial T} \right)_{V}
    		(IV)V
    Choose the correct answer from the options given below :

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  10. 35
    The correct order of the following complexes in terms of their crystal field stabilization energies is :

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  11. 36
    Density of 3 M NaCl solution is 1.25 g/mL1.25\text{ }g/mL. The molality of the solution is :

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  12. 37
    The molar solubility(s) of zirconium phosphate with molecular formula (Zr4+)3(PO43−)4\left( Zr^{4 +} \right)_{3}\left( PO_{4}^{3 -} \right)_{4} is given by relation :

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  13. 38
    The most stable carbocation from the following is :

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  14. 39
    Given below are two statements : Statement (I) : An element in the extreme left of the periodic table forms acidic oxides. Statement (II) : Acid is formed during the reaction between water and oxide of a reactive element present in the extreme right of the periodic table. 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) : A spectral line will be observed for a 2px→2py2p_{x}\rightarrow 2p_{y} transition. Statement (II) : 2px2p_{x} and 2py2p_{y} are degenerate orbitals. 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 statement : Statement (I) : Nitrogen, sulphur, halogen and phosphorus present in an organic compound are detected by Lassaigne's Test. Statement (II) : The elements present in the compound are converted from covalent form into ionic form by fusing the compound with Magnesium in Lassaigne's test. In the light of the above statements, choose the correct answer from the options given below :

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  17. 42
    Identify the homoleptic complex(es) that is/are low spin. (A) [Fe(CN)5NO]2−\left\lbrack Fe(CN)_{5}NO \right\rbrack^{2 -} (B) [CoF6]3−\left\lbrack CoF_{6} \right\rbrack^{3 -} (C) [Fe(CN)6]4−\left\lbrack Fe(CN)_{6} \right\rbrack^{4 -} (D) [Co(NH3)6]3+\left\lbrack Co\left( NH_{3} \right)_{6} \right\rbrack^{3 +} (E) [Cr(H2O)6]2+\left\lbrack Cr\left( H_{2}O \right)_{6} \right\rbrack^{2 +} Choose the correct answer from the options given below :

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  18. 43
    →(i)CrO2Cl2 CS2(ii)H3O+(iii)NaHSO3\underset{\begin{array}{r} \left( ii \right)H_{3}O^{+} \\ \left( iii \right)NaHSO_{3} \end{array}}{\overset{\left( i \right)CrO_{2}Cl_{2\ }CS_{2}}{\rightarrow}} Filter → Residue (A) (Toluene excess) Residue (A) +HCl (dil.) →\rightarrow Compound (B) Structure of residue (A) and compound (B) Formed respectively is : [A] [B]

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  19. 44
    Given below are two statements : Statement (I) : Corrosion is an electrochemical phenomenon in which pure metal acts as an anode and impure metal as a cathode. Statement (II) : The rate of corrosion is more in alkaline medium than in acidic medium. In the light of the above statements, choose the correct answer from the options given below :

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  20. 45
    The alkane from below having two secondary hydrogens is :

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  21. 46
    The compound with molecular formula C6H6C_{6}H_{6}, which gives only one monobromo derivative and takes up four moles of hydrogen per mole for complete hydrogenation has ________\_\_\_\_\_\_\_\_ π\pi electrons.
  22. 47
    Niobium ( Nb ) and ruthenium ( Ru ) have " x " and " yy " number of electrons in their respective 4d4d orbitals. The value of x+yx + y is ______\_\_\_\_\_\_
  23. 48
    The complex of Ni2+Ni^{2 +} ion and dimethyl glyoxime contains____ number of Hydrogen (H)(H) atoms.
  24. 49
    Consider the following cases of standard enthalpy of reaction (ΔHr∘\left( \Delta H_{r}^{\circ} \right. in  kJmol−1)\left. \ kJmol^{- 1} \right)
    C2H6( g)+72O2( g)→2CO2( g)+3H2O(l)ΔH1∘=−1550C( graphite )+O2( g)→CO2( g)ΔH2∘=−393.5H2( g)+12O2( g)→H2O(l)ΔH3∘=−286\begin{matrix} & C_{2}H_{6}(\text{ }g) +\frac{7}{2}O_{2}(\text{ }g) \rightarrow 2CO_{2}(\text{ }g) + 3H_{2}O(l)\quad \Delta H_{1}^{\circ}= - 1550 \\ & C(\text{~graphite~}) +O_{2}(\text{ }g) \rightarrow CO_{2}(\text{ }g)\quad \Delta H_{2}^{\circ}= - 393.5 \\ & H_{2}(\text{ }g) +\frac{1}{2}O_{2}(\text{ }g) \rightarrow H_{2}O(l)\quad \Delta H_{3}^{\circ}= - 286 \end{matrix}
    The magnitude of ΔfH∘\Delta_{f}H^{\circ} of C2H6(g)C_{2}H_{6}(g) is ______\_\_\_\_\_\_ kJmol−1kJmol^{- 1} (Nearest integer).
  25. 50
    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\times10^{- 2}M. (Nearest integer).

Mathematics

25 questions

  1. 51
    Let α,β,γ\alpha,\beta,\gamma and δ\delta be the coefficients of x7,x5,x3x^{7},x^{5},x^{3} and xx respectively in the expansion of (x+x3−1)5+(x−x3−1)5,x>1\left( x +\sqrt{x^{3}- 1} \right)^{5}+\left( x -\sqrt{x^{3}- 1} \right)^{5},x > 1. If uu and vv satisfy the equations
    αu+βv=18,γu+δv=20,\begin{matrix} & \alpha u + \beta v = 18, \\ & \gamma u + \delta v = 20, \end{matrix}
    then u+vu + v equals :

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  2. 52
    In a group of 3 girls and 4 boys, there are two boys B1B_{1} and B2B_{2}. The number of ways, in which these girls and boys can stand in a queue such that all the girls stand together, all the boys stand together, but B1B_{1} and B2B_{2} are not adjacent to each other, is :

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  3. 53
    Let P(4,43)P(4,4\sqrt{3}) be a point on the parabola y2=4axy^{2}= 4ax and PQPQ be a focal chord of the parabola. If MM and N are the foot of perpendiculars drawn from P and QQ respectively on the directrix of the parabola, then the area of the quadrilateral PQMN is equal to:

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  4. 54
    For a 3×33 \times 3 matrix M , let trace (M)(M) denote the sum of all the diagonal elements of M . Let A be a 3×33 \times 3 matrix such that ∣A∣=12|A| =\frac{1}{2} and trace (A)=3(A) = 3. If B=adj(adj(2A))B = adj(adj(2A)), then the value of ∣B∣+trace(B)|B| + trace(B) equals:

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  5. 55
    Suppose that the number of terms in an A.P. is 2 k , k∈Nk \in N. If the sum of all odd terms of the A.P. is 40 , the sum of all even terms is 55 and the last term of the A.P. exceeds the first term by 27 , then k is equal to

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  6. 56
    Let a line pass through two distinct points P(−2,−1,3)P( - 2, - 1,3) and Q , and be parallel to the vector 3i^+2j^+2k3\widehat{i}+ 2\widehat{j}+ 2k. If the distance of the point QQ from the point R(1,3,3)R(1,3,3) is 5 , then the square of the area of △PQR\bigtriangleup PQR is equal to:

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  7. 57
    If lim⁡x→∞((e1−e)(1e−x1+x))x=α\lim_{x \rightarrow \infty} \left( \left( \frac{e}{1 - e} \right)\left( \frac{1}{e}-\frac{x}{1 + x} \right) \right)^{x}= \alpha, then the value of log⁡eα1+log⁡eα\frac{\log_{e}\alpha}{1 +\log_{e}\alpha} equals :

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  8. 58
    Let f(x)=∫0x2t2−8t+15etdt,x∈Rf(x) =\int_{0}^{x^{2}} \frac{t^{2}- 8t + 15}{e^{t}}dt,x \in R. Then the numbers of local maximum and local minimum points of ff, respectively, are :

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  9. 59
    The perpendicular distance, of the line x−12=y+2−1=z+32\frac{x - 1}{2}=\frac{y + 2}{- 1}=\frac{z + 3}{2} from the point P(2,−10,1)P(2, - 10,1), is:

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  10. 60
    If x=f(y)x = f(y) is the solution of the differential equation
    (1+y2)+(x−2etan⁡−1y)dydx=0,y∈(−π2,π2)\left( 1 +y^{2} \right)+\left( x - 2e^{\tan^{- 1}y} \right)\frac{dy}{dx}= 0,y \in\left( -\frac{\pi}{2},\frac{\pi}{2} \right)
    with f(0)=1f(0) = 1, then f(13)f\left( \frac{1}{\sqrt{3}} \right) is equal to :

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  11. 61
    If ∫ex(xsin⁡−1x1−x2+sin⁡−1x(1−x2)3/2+x1−x2)dx=g(x)+C\int e^{x}\left(\frac{x\sin^{-1}x}{\sqrt{1-x^{2}}}+\frac{\sin^{-1}x}{\left(1-x^{2}\right)^{3/2}}+\frac{x}{1-x^{2}}\right)dx = g(x)+C, where CC is the constant of integration, then g(12)g\left(\frac{1}{2}\right) equals:

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  12. 62
    Let αθ\alpha_{\theta} and βθ\beta_{\theta} be the distinct roots of 2x2+(cos⁡θ)x−1=0,θ∈(0,2π)2x^{2}+ (\cos\theta)x - 1 = 0,\theta \in (0,2\pi). If mm and MM are the minimum and the maximum values of αθ4+βθ4\alpha_{\theta}^{4}+\beta_{\theta}^{4}, then 16(M+m)16(M + m) equals :

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  13. 63
    Let A={1,2,3,4}\mathbf{A = \{ 1,2,3,4\}} and B={1,4,9,16}\mathbf{B = \{ 1,4,9,16\}}. Then the number of many-one functions f:A→Bf:A \rightarrow B such that 1∈f(A)1 \in f(A) is equal to :

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  14. 64
    If the system of linear equations :
    x+y+2z=62x+3y+az=a+1 −x−3y+bz=2b\begin{matrix} & x + y + 2z = 6 \\ & 2x + 3y + az = a + 1 \\ & \ - x - 3y + bz = 2b \end{matrix}
    where a,b∈Ra,b \in R, has infinitely many solutions, then 7a+3b7a + 3b is equal to :

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  15. 65
    Let a→\overrightarrow{a} and b→\overrightarrow{b} be two - unit vectors such that the angle between them is π3\frac{\pi}{3}. If λa→+2b→\lambda\overrightarrow{a}+ 2\overrightarrow{b} and 3a→−λb→3\overrightarrow{a}- \lambda\overrightarrow{b} are perpendicular to each other, then the number of values of λ\lambda in [−1,3]\lbrack - 1,3\rbrack is :

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  16. 66
    Let E:x2a2+y2 b2=1,a>bE:\frac{x^{2}}{a^{2}}+\frac{y^{2}}{{\text{ }b}^{2}}= 1,a > b and H:x2 A2−y2 B2=1H:\frac{x^{2}}{{\text{ }A}^{2}}-\frac{y^{2}}{{\text{ }B}^{2}}= 1. Let the distance between the foci of EE and the foci of HH be 232\sqrt{3}. If a−A=2a - A = 2, and the ratio of the eccentricities of EE and HH is 13\frac{1}{3}, then the sum of the lengths of their latus rectums is equal to :

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  17. 67
    If AA and BB are two events such that P(A∩B)=0.1P(A \cap B) = 0.1, and P(A∣B)P(A \mid B) and P(B∣A)P(B \mid A) are the roots of the equation 12x2−7x+1=012x^{2}- 7x + 1 = 0, then the value of P(A‾∪B‾)P(A‾∩B‾)\frac{P(\overline{A}\cup\overline{B})}{P(\overline{A}\cap\overline{B})} is:

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  18. 68
    The sum of all values of θ∈[0,2π]\theta \in \lbrack 0,2\pi\rbrack satisfying 2sin⁡2θ=cos⁡2θ2\sin^{2}\theta = \cos2\theta and 2cos⁡2θ=3sin⁡θ2\cos^{2}\theta = 3\sin\theta is

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  19. 69
    Let the curve z(1+i)+zˉ(1−i)=4,z∈Cz(1 + i) +\bar{z}(1 - i) = 4,z \in C, divide the region ∣z−3∣≤1|z - 3| \leq 1 into two parts of areas α\alpha and β\beta. Then ∣α−β∣|\alpha - \beta| equals :

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  20. 70
    The area of the region enclosed by the curves y=x2−4x+4y =x^{2}- 4x + 4 and y2=16−8xy^{2}= 16 - 8x is :

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  21. 71
    Let y=f(x)y=f(x) be the solution of the differential equation dydx+xyx2−1=x6+4x1−x2, −1<x<1\frac{dy}{dx}+\frac{xy}{x^{2}-1}=\frac{x^{6}+4x}{\sqrt{1-x^{2}}},\ -1<x<1, such that f(0)=0f(0)=0. If 6∫−1/21/2f(x)dx=2π−α6\int_{-1/2}^{1/2} f(x)dx = 2\pi-\alpha, then α2\alpha^{2} is equal to
  22. 72
    Let A(6,8),B(10cos⁡α,−10sin⁡α)A(6,8),B(10\cos\alpha, - 10\sin\alpha) and C (−10sin⁡α,10cos⁡α)( - 10\sin\alpha,10\cos\alpha), be the vertices of a triangle. If L(a,9)L(a,9) and G(h,k)G(h,k) be its orthocenter and centroid respectively, then (5a−3h+6k+100sin⁡2α)(5a - 3h + 6k + 100\sin2\alpha) is equal to ______\_\_\_\_\_\_
  23. 73
    Let the distance between two parallel lines be 5 units and a point PP lie between the lines at a unit distance from one of them. An equilateral triangle PQR is formed such that Q lies on one of the parallel lines, while RR lies on the other. Then (QR)2(QR)^{2} is equal to ____\_\_\_\_
  24. 74
    If ∑r=130r2( 30Cr)2 30Cr−1=α×229\sum_{r = 1}^{30} \frac{r^{2}\left( \ ^{30}C_{r} \right)^{2}}{\ ^{30}C_{r - 1}} = \alpha \times 2^{29}, then α\alpha is equal to
  25. 75
    Let A={1,2,3}\mathbf{A = \{ 1,2,3\}}. The number of relations on A , containing (1,2)(1,2) and (2,3)(2,3), which are reflexive and transitive but not symmetric, is  ____\ \_\_\_\_

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