12th Science Maharashtra Board
In this category students supposed to ask questions which belong to std 12th maharashtra board Science
- A fair coin is tossed 6 times. The probability of getting exactly 3 heads is Answer: C. 5/16 binom63(1/2)⁶=20/64=frac516 . 1
- The mean and variance of a binomial distribution are 4 and 3 respectively. The number of trials n is Answer: D. 16 q=3/4⇒ p=1/4 ; n=4/1/4=16 . 1
- The general solution of \(\frac{dy}{dx}+\frac yx=x^2\) is Answer: B. xy=x⁴/4+C I.F. =e^(∫ dx/x)=x ; d/dx(xy)=x³⇒ xy=x⁴/4+C . 1
- A bacterial population grows at a rate proportional to its size and doubles in 2 hours. The time in which it becomes 8 times the original is Answer: B. 6 hours N=N₀e^kt , e^2k=2 . 8=2³⇒ t=3×2=6 h. 1
- A random variable \(X\) has \(P(X=x)=kx\) for \(x=1,2,3,4\). Then \(E(X)\) is Answer: C. 3 k(1+2+3+4)=1⇒ k=frac110 ; E(X)=1+4+9+16/10=3 . 1
- The p.d.f. of \(X\) is \(f(x)=kx^2\) for \(0\le x\le3\) and 0 otherwise. Then \(P(X\le1)\) is Answer: C. frac127 ∫₀³kx²dx=9k=1⇒ k=1/9 ; P(X≤1)=1/9·1/3=frac127 . 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
- Which alcohol gives turbidity immediately with Lucas reagent at room temperature? Answer: A. 2-methylpropan-2-ol Tertiary alcohols react immediately with conc. HCl/ZnCl₂ through a stable carbocation; 2-methylpropan-2-ol is... 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
- 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
- Which of the following is the strongest base in aqueous solution? Answer: C. (CH3)2NH In water, inductive effect, solvation and steric factors combine to give (CH₃)₂NH > CH₃NH₂ > (CH₃)₃N; aniline is much we... 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
- On prolonged heating with HI, glucose gives n-hexane. This shows that glucose Answer: B. has all six carbon atoms in a straight chain Complete reduction to n-hexane shows that the six carbons form an unbranched chain. 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
- For the rate law \(r=k[\mathrm A]^2[\mathrm B]\), if [A] is doubled and [B] is halved, the rate becomes Answer: C. 2 times r'=k(2[mathrm A])²[mathrm B]/2=2r . 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
- 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
- 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 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