Soluble in aqueous NaOH

If \[ (2\alpha+1,\; \alpha^2-3\alpha,\; \frac{\alpha-1}{2}) \] is the image of the point \[ (\alpha,\; 2\alpha,\; 1) \] in the line \[ \frac{x-2}{3}=\frac{y-1}{2}=\frac{z}{1}, \] then find the possible values of \(\alpha\).

JEE Main - 2026
3D Geometry

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For a given reversible reaction at \(300\,K\): \[ 2\text{N}_2\text{O}_5(g) \rightleftharpoons 4\text{NO}_2(g) + \text{O}_2(g) \] If \( \text{N}_2\text{O}_5 \) is 50% dissociated at 5 bar and 300 K at equilibrium, then find \( \Delta G^\circ \) for the reaction? [Given: \( \log 2 = 0.3,\ \log 7 = 0.84 \)]

JEE Main - 2026
Physical Chemistry

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For the reaction: \[ R \rightarrow P \] The variation of concentration of reactant \([R]\) with time is shown below. Statements: I. Curve 1 will be observed when order of reaction is 1. II. If curve 2 & curve 3 are observed for \(1^{st}\) order then rate constant for \(3^{rd}\) curve will be greater than rate constant for \(2^{nd}\) curve. III. Decomposition of HI on gold surface represent curve (1). Select the option representing correct set of statements: