JEE Main 2025 (22 Jan Shift 2)

65 Questions • 75 Minutes • 2025

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The species which does not undergo disproportionation reaction is :

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The molar solubility(s) of zirconium phosphate with molecular formula $(\mathrm{Zr^{4+}})_3(\mathrm{PO_4^{3-}})_4$ is given by relation :

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Identify the homoleptic complex(es) that is/are low spin. (A) [Fe(CN)₅NO]²⁻ (B) [CoF₆]³⁻ (C) [Fe(CN)₆]⁴⁻ (D) [Co(NH₃)₆]³⁺ (E) [Cr(H₂O)₆]²⁺ Choose the correct answer from the options given below :

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Match List - I with List - II. [table] List - I (Partial Derivatives) | List - II (Thermodynamic Quantity) ; (A) $\left(\frac{\partial G}{\partial T}\right)_P$ | (I) $C_p$ ; (B) $\left(\frac{\partial H}{\partial T}\right)_P$ | (II) $-S$ ; (C) $\left(\frac{\partial G}{\partial P}\right)_T$ | (III) $C_v$ ; (D) $\left(\frac{\partial U}{\partial T}\right)_V$ | (IV) $V$ [/table] Choose the correct answer from the options given below :

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Given below are two statements : Statement (I) : A spectral line will be observed for a $2p_x\to2p_y$ transition. Statement (II) : $2P_x$ and $2p_y$ are degenerate orbitals. In the light of the above statements, choose the correct answer from the options given below :

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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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The alkane from below having two secondary hydrogens is :

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

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The most stable carbocation from the following is :

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Match the Compounds (List - I) with the appropriate Catalyst/Reagents (List - II) for their reduction into corresponding amines. [table] List - I (Compounds) | List - II (Catalyst/Reagents) ; (A) R–CO–NH₂ (amide) | (I) NaOH (aqueous) ; (B) nitrobenzene (C₆H₅–NO₂) | (II) H₂/Ni ; (C) R–C≡N (nitrile) | (III) LiAlH₄, H₂O ; (D) N-alkylphthalimide (phthalimide–N–R) | (IV) Sn, HCl [/table] Choose the correct answer from the options given below :

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Arrange the following compounds in increasing order of their dipole moment : $\mathrm{HBr},\ \mathrm{H_2S},\ \mathrm{NF_3}$ and $\mathrm{CHCl_3}$

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The maximum covalency of a non-metallic group 15 element 'E' with weakest E – E bond is :

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If $\sum_{r=1}^{30}\frac{r^2\left({}^{30}C_r\right)^2}{{}^{30}C_{r-1}}=\alpha\times2^{29}$, then $\alpha$ is equal to _______

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Let $A=\{1,2,3\}$. The number of relations on $A$, containing $(1,2)$ and $(2,3)$, which are reflexive and transitive but not symmetric, is _______ -

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Let $A(6,8)$, $B(10\cos\alpha,-10\sin\alpha)$ and $C(-10\sin\alpha,10\cos\alpha)$, be the vertices of a triangle. If $L(a,9)$ and $G(h,k)$ be its orthocenter and centroid respectively, then $(5a-3h+6k+100\sin2\alpha)$ is equal to _______ -.

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Let $y=f(x)$ be the solution of the differential equation $\frac{dy}{dx}+\frac{xy}{x^2-1}=\frac{x^6+4x}{\sqrt{1-x^2}}$, $-1<x<1$ such that $f(0)=0$. If $6\int_{-1/2}^{1/2}f(x)\,dx=2\pi-\alpha$ then $\alpha^2$ is equal to _______ .

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Let the distance between two parallel lines be 5 units and a point $P$ 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 $R$ lies on the other. Then $(QR)^2$ is equal to _______ -.

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A proton is moving undeflected in a region of crossed electric and magnetic fields at a constant speed of $2\times10^5\ \mathrm{m\,s^{-1}}$. When the electric field is switched off, the proton moves along a circular path of radius 2 cm. The magnitude of electric field is $x\times10^4$ N/C. The value of $x$ is _______ Take the mass of the proton $=1.6\times10^{-27}$ kg.

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A parallel plate capacitor of area $A=16\ \mathrm{cm^2}$ and separation between the plates 10 cm, is charged by a DC current. Consider a hypothetical plane surface of area $A_0=3.2\ \mathrm{cm^2}$ inside the capacitor and parallel to the plates. At an instant, the current through the circuit is 6A. At the same instant the displacement current through $A_0$ is _______ mA.

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A tube of length 1 m is filled completely with an ideal liquid of mass 2M, 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 $\sqrt{\frac F{\alpha M}}$ in SI unit. The value of $\alpha$ is __________.

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Paper Info

Exam: JEE
Year: 2025
Questions: 65
Duration: 75 mins

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