#mht-cet pcm
- The solubility of Ag2CrO4 in water is \(1\times10^{-4}\) mol L-1. Its solubility product is Answer: A. 4×10⁻¹² K_sp=(2s)²s=4s³=4×10⁻¹² . 1
- A buffer contains 0.02 M acetic acid and 0.2 M sodium acetate. If p\(K_a\) of acetic acid is 4.74, the pH of the buffer is Answer: B. 5.74 pH =pK_a+log[salt]/[acid]=4.74+log10=5.74 . 1
- For the reaction \(\mathrm{N_2(g)+3H_2(g)\rightarrow2NH_3(g)}\) at 298 K, \(\Delta H-\Delta U\) is approximately Answer: A. -4.96 kJ Δ n_g=2-4=-2 ; Δ H-Δ U=Δ n_gRT=-2×8.314×298≈-4955 J. 1
- For a reaction \(\Delta H=+30\) kJ mol-1 and \(\Delta S=+100\) J K-1 mol-1. The reaction becomes spontaneous above Answer: B. 300 K Δ G<0 when T>Δ H/Δ S=30000/100=300 K. 1
- Given: \(\mathrm{C(s)+O_2(g)\rightarrow CO_2(g)}\), \(\Delta H=-393.5\) kJ; \(\mathrm{CO(g)+\frac12O_2(g)\rightarrow CO_2(g)}\), \(\Delta H=-283.0\) kJ. The standard enthalpy of formation of CO(g) is Answer: D. -110.5 kJ mol-1 Subtract the second equation from the first: Δ_fH(CO)=-393.5-(-283.0)=-110.5 kJ mol⁻¹. 1
- If \(A=\begin{bmatrix}1&2\\3&4\end{bmatrix}\) satisfies \(A^2-5A-2I=O\), then \(A^{-1}\) equals Answer: A. 1/2(A-5I) A(A-5I)=2I⇒ A⁻¹=1/2(A-5I) . 1
- If \(A\) is a square matrix of order 3 with \(|A|=4\), then \(|\operatorname{adj}(2A)|\) is Answer: B. 1024 |2A|=2³·4=32 ; |adjB|=|B|² for order 3, so 32²=1024 . 1
- The system \(x+y+z=1,\ x+2y+3z=2,\ x+3y+kz=3\) has infinitely many solutions when \(k=\) Answer: B. 5 Δ=k-5=0⇒ k=5 . Then E₂-E₁ and E₃-E₂ both give y+2z=1 , so the system is consistent. 1
- For the Daniell cell \(\mathrm{Zn|Zn^{2+}(1M)||Cu^{2+}(1M)|Cu}\), \(E^\circ_{\mathrm{Zn}}=-0.76\) V and \(E^\circ_{\mathrm{Cu}}=+0.34\) V. The standard Gibbs energy change is Answer: C. -212.3 kJ E^°_cell=0.34-(-0.76)=1.10 V; Δ G^°=-nFE^°=-2×96500×1.10=-212.3 kJ. 1
- A current of 2 A is passed through CuSO4 solution for 965 s. The mass of copper deposited is (Cu = 63.5, F = 96500 C) Answer: A. 0.635 g Q=1930 C =0.02 F; Cu²⁺ needs 2F/mol, so 0.01 mol =0.635 g. 1
- The electrode potential of a hydrogen electrode (\(P_{H_2}\) = 1 bar) dipped in a solution of pH 3 at 298 K is Answer: D. -0.177 V E=-0.0592 pH=-0.0592×3≈-0.177 V. 1
- The conductivity of a 0.1 M solution of an electrolyte is 0.0129 S cm-1. Its molar conductivity is Answer: A. 129 S cm2 mol-1 Lambda_m=1000kappa/C=1000×0.0129/0.1=129 S cm² mol⁻¹. 1
- The rate constant of a first-order reaction is \(6.93\times10^{-3}\) s-1. The time required for 75% completion is Answer: A. 200 s t_(1/2)=0.693/k=100 s; 75% completion takes two half-lives, i.e. 200 s. 1
- The value of \(\tan^{-1}2+\tan^{-1}3\) is Answer: D. 3π/4 Since 2·3>1 and both are positive, the sum =π+tan⁻¹2+3/1-6=π-fracπ4=3π/4 . 1
- In \(\triangle ABC\), \(a=3,\ b=5,\ c=7\). Then angle \(C\) is Answer: A. 2π/3 cos C=9+25-49/2·3·5=-1/2⇒ C=2π/3 . 1
- The acute angle between the lines represented by \(x^2-4xy+y^2=0\) is Answer: B. 60° tanθ=|2√(h²-ab)/a+b|=2√(4-1)/2=sqrt3⇒θ=60^° . 1
- If the lines represented by \(kx^2+6xy-7y^2=0\) are perpendicular, then \(k=\) Answer: A. 7 Perpendicular when a+b=0 : k-7=0⇒ k=7 . 1
- The rate of a reaction doubles when temperature is raised from 300 K to 310 K. The activation energy is approximately (R = 8.314 J K-1 mol-1, log 2 = 0.301) Answer: C. 53.6 kJ mol-1 log2=E_a/2.303R·T₂-T₁/T₁T₂⇒ E_a=2.303×8.314×0.301×300×310/10≈53.6 kJ mol⁻¹. 1
- The oxidation state of sulphur in peroxodisulphuric acid (H2S2O8) is Answer: A. +6 There is one peroxide O–O link (each O −1) and six oxygens at −2: 2+2x-2-12=0⇒ x=+6 . 1
- In acidic medium, the number of moles of KMnO4 required to oxidise 1 mole of Fe2+ to Fe3+ is Answer: A. 0.2 mathrmMnO₄^-+5Fe²⁺+8H^+→ Mn²⁺+5Fe³⁺+4H₂O ; 1 mol Fe²⁺ needs 1/5 mol MnO₄⁻. 1
- The IUPAC name of [Co(NH3)5Cl]Cl2 is Answer: C. pentaamminechloridocobalt(III) chloride Cation complex: x+0-1=+2⇒ Co(III). Ligands are named alphabetically (ammine before chlori... 1
- [Ni(CN)4]2− is diamagnetic. Its hybridisation and geometry are Answer: D. dsp2, square planar Ni²⁺ is 3d⁸. Strong-field CN⁻ pairs the electrons, leaving one 3d orbital free for dsp² (square planar, diama... 1
- The distance of the point \((2,1,-1)\) from the plane \(x-2y+4z=9\) is Answer: C. 13/√(21) d=|2-2-4-9|/√(1+4+16)=13/√(21) . 1
- The maximum value of \(z=3x+2y\) subject to \(x+y\le4,\ x+3y\le6,\ x\ge0,\ y\ge0\) is Answer: C. 12 Corner points: (0,0)→0, (4,0)→12, (3,1)→11, (0,2)→4. Maximum =12 . 1