#mht-cet pcm
- The spin-only magnetic moment of Fe2+ ion (Z of Fe = 26) is Answer: A. 4.90 BM Fe²⁺ is 3d⁶ with 4 unpaired electrons: μ=√(4×6)=√(24)≈4.90 BM. 1
- The total number of stereoisomers of [Co(en)2Cl2]+ is Answer: D. 3 Trans form is optically inactive (1); cis form is chiral and exists as a pair of enantiomers (2). Total =3 . 1
- Which of the following undergoes SN1 reaction fastest? Answer: D. (CH3)3CBr S_N1 rate depends on carbocation stability; the tertiary carbocation is the most stable. 1
- Capacitors of 3 μF and 6 μF are connected in series across a 90 V supply. The potential difference across the 3 μF capacitor is Answer: A. 60 V C_s=2 μF, Q=180 μC, V₃=180/3=60 V. 1
- In a metre bridge, a 2 Ω resistance is in the left gap and an unknown resistance \(X\) in the right gap. The null point is at 40 cm from the left end. Then \(X\) is Answer: D. 3 Ω 2/X=40/60⇒ X=3\ Ω . 1
- A potentiometer wire 4 m long of resistance 8 Ω is connected in series with a 12 Ω resistor and a 2 V cell of negligible internal resistance. The balancing length for a cell of emf 0.5 V is Answer: C. 2.5 m I=2/20=0.1 A; potential gradient =0.1×8/4=0.2 V/m; l=0.5/0.2=2.5 m. 1
- A galvanometer of resistance 50 Ω gives full-scale deflection for 5 mA. The shunt needed to convert it into an ammeter of range 0–5 A is approximately Answer: D. 0.05 Ω S=I_gG/I-I_g=0.005×50/4.995≈0.05\ Ω . 1
- A circular coil of 100 turns and radius 10 cm carries a current of 5 A. The magnetic field at its centre is (\(\mu_0=4\pi\times10^{-7}\) T m/A) Answer: D. π×10⁻³ T B=μ₀NI/2R=frac4π×10⁻⁷×100×50.2=π×10⁻³ T. 1
- Chlorobenzene reacts with methyl chloride and sodium in dry ether. The main product is Answer: C. toluene Wurtz–Fittig reaction: C₆H₅Cl+CH₃Cl+2Na→ C₆H₅CH₃+2NaCl . 1
- Phenol reacts with bromine water to give Answer: B. 2,4,6-tribromophenol In polar water, phenol is strongly activated and is brominated at all o- and p-positions, giving a white pre... 1
- Anisole on heating with HI gives Answer: A. phenol and methyl iodide The O–C(aryl) bond has partial double-bond character and is not cleaved. I⁻ attacks the methyl group (S_... 1
- Which of the following undergoes the Cannizzaro reaction? Answer: D. Benzaldehyde The Cannizzaro reaction needs an aldehyde with no α-hydrogen; benzaldehyde has none. 1
- A proton and an α-particle having the same kinetic energy enter a uniform magnetic field perpendicular to it. The ratio of the radii of their circular paths \(r_p:r_\alpha\) is Answer: A. 1 : 1 r=√(2mK)/qB . For α: mass 4m , charge 2e gives √(8mK)/2eB=√(2mK)/eB , same as proton. 1
- A rectangular coil of 50 turns and area 0.02 m2 carries 2 A in a uniform field of 0.5 T. The torque on it when its plane is parallel to the field is Answer: B. 1 N m Plane parallel to field means the normal is perpendicular to B : τ=NIAB=50×2×0.02×0.5=1 N m. 1
- The magnetic susceptibility of a paramagnetic salt is \(\chi\) at 300 K. Its susceptibility at 200 K will be Answer: D. 1.5chi Curie's law: chi∝1/T⇒chi'=chi×300/200=1.5chi . 1
- A conducting rod of length 1 m moves at 5 m/s perpendicular to a uniform magnetic field of 0.4 T on frictionless rails connected through a 4 Ω resistor (other resistances negligible). The external force needed to keep it moving at constant speed is Answer: D. 0.2 N e=Blv=2 V, I=0.5 A, F=BIl=0.4×0.5×1=0.2 N. 1
- When the current in a coil falls uniformly from 2 A to zero in 0.05 s, an emf of 8 V is induced in it. The self-inductance of the coil is Answer: A. 0.2 H L=e/dI/dt=8/2/0.05=0.2 H. 1
- The strongest acid among the following is Answer: C. Cl3CCOOH Three −I chlorine atoms stabilise the carboxylate ion the most. 1
- Acetophenone on Clemmensen reduction (Zn–Hg / conc. HCl) gives Answer: D. ethylbenzene Clemmensen reduction converts >C=O to >CH₂: C₆H₅COCH₃ → C₆H₅CH₂CH₃. 1
- Acetamide on treatment with Br2 and aqueous NaOH gives Answer: D. methanamine Hofmann bromamide degradation gives a primary amine with one carbon fewer: CH₃CONH₂ → CH₃NH₂. 1
- Light of wavelength 310 nm falls on a metal of work function 2.5 eV. The stopping potential is (take \(hc=1240\) eV nm) Answer: C. 1.5 V E=1240/310=4 eV; eV₀=4-2.5=1.5 eV, so V₀=1.5 V. 1
- The de Broglie wavelength of an electron accelerated from rest through a potential difference of 100 V is about Answer: B. 1.227 Å λ=12.27/sqrt V Å =12.27/10=1.227 Å. 1
- The ratio of the wavelength of the first line of the Balmer series to that of the first line of the Lyman series in hydrogen is Answer: D. 27/5 frac1λ_B∝1/4-1/9=5/36 , frac1λ_L∝1-1/4=3/4 . λ_B/λ_L=3/4/5/36=27/5 . 1
- \({}^{238}_{92}\mathrm{U}\) decays to \({}^{206}_{82}\mathrm{Pb}\). The numbers of α and β− particles emitted are Answer: D. 8 α and 6 β α count =238-206/4=8 , lowering Z by 16 to 76. To reach 82, 6 β⁻ are needed. 1