Science MCQs

Calculus Problem: Differentiation & Integration Question: If y = x 5 + 3x 2 , find the derivative dy/dx and the integral ∫ y dx . Solution: Given Function: y = x 5 + 3x 2 Step 1: Differentiation Differentiating with respect to x : dy/dx = (d/dx)(x 5 ) + (d/dx)(3x 2 ) Using the power rule (d/dx)(x n ) = nx n-1 : ∴ dy/dx = 5x 5-1 + 3(2x 2-1 ) = 5x 4 + 3(2x) Answer: dy/dx = 5x 4 + 6x Step 2: Integration Now, integrating with respect to x : ∫ y dx = ∫ (x 5 + 3x 2 ) dx Separating the terms: = ∫ x 5 dx + ∫ 3x 2 dx Using the integration rule ∫ x n dx = x n+1 / (n+1) : = x 5+1 / (5+1) + 3 · x 2+1 / (2+1) = x 6 /6 + 3 · x 3 /3 + C Here, the 3 cancels out. Answer: ∫ y dx = x 6 /6 + x 3 + C *(Where C is the constant of integration)*

Vestigial organs are fascinating remnants of evolution. They are structures that once served important functions in ancestors but have become reduced, nonfunctional, or repurposed over time. Both animals and plants have vestigial organs that highlight their evolutionary history. In this article, you’ll find comprehensive tables listing well-known vestigial structures in both animals and plants. Vestigial Organs in Animals Animals show a wide variety of vestigial traits — from reduced bones to unused muscles. These structures provide some of the clearest evidence of evolutionary change. Animal Group Vestigial Organ/Structure Function in Ancestors Current Status/Use Humans Appendix Cellulose digestion Minor immune role, mostly redundant Humans Wisdom teeth (third molars) Helped chew coarse plant matter Often problematic; impacted Humans Coccyx (tailbone) Tail for balance & mobility No external tail; muscle attachment Humans Auricular muscles (ear-wigg...

Here’s a compact list of the most important basic organic chemistry reactions (just the reactions, no explanations): Combustion: C x H y + O 2 → C O 2 + H 2 O \text{C}_x\text{H}_y + O_2 \rightarrow CO_2 + H_2O Halogenation of Alkanes (Free Radical Substitution): CH 4 + C l 2 → h v CH 3 C l + H C l \text{CH}_4 + Cl_2 \xrightarrow{hv} \text{CH}_3Cl + HCl Hydrogenation of Alkenes: CH 2 = C H 2 + H 2  → N i / P t     C H 3 C H 3 \text{CH}_2=CH_2 + H_2 \xrightarrow{Ni/Pt} CH_3CH_3 Halogenation of Alkenes (Electrophilic Addition): CH 2 = C H 2 + B r 2 → B r C H 2 C H 2 B r \text{CH}_2=CH_2 + Br_2 \rightarrow BrCH_2CH_2Br Hydration of Alkenes: CH 2 = C H 2 + H 2 O → H + C H 3 C H 2 O H \text{CH}_2=CH_2 + H_2O \xrightarrow{H^+} CH_3CH_2OH Ozonolysis of Alkenes: RCH=CHR’ + O 3 → R C H O + R ′ C H O \text{RCH=CHR'} + O_3 \rightarrow RCHO + R'CHO Dehydration of Alcohols: CH 3 C H 2 O H → H 2 S O 4 , Δ           C H 2 = C H 2 + H 2...

Generated By Gemini Functional Group General Formula Suffix (as main group) Prefix (as substituent) Example from Methane Alkane R–H –ane – CH₄ → methane Alkene R–CH=CH–R –ene – CH₂=CH₂ → ethene Alkyne R–C≡C–R –yne – HC≡CH → ethyne Haloalkane R–X (X = F, Cl, Br, I) – fluoro-/chloro-/bromo-/iodo- CH₃Cl → chloromethane Alcohol R–OH –ol hydroxy- CH₃OH → methanol Ether R–O–R – alkoxy- CH₃–O–CH₃ → methoxyethane Aldehyde R–CHO –al formyl- HCHO → methanal (formaldehyde) Ketone R–CO–R –one oxo- CH₃–CO–CH₃ → propanone Carboxylic acid R–COOH –oic acid carboxy- HCOOH → methanoic acid Ester R–COOR′ –oate alkoxycarbonyl- HCOOCH₃ → methyl methanoate Acid halide R–COX –oyl halide halocarbonyl- CH₃COCl → ethanoyl chloride Amide R–CONH₂ –amide carbamoyl- CH₃CONH₂ → ethanamide Amine R–NH₂ –amine amino- CH₃NH₂ → methanamine Nitrile R–C≡N –nitrile cyano- CH₃CN → ethanenitrile Sulphonic acid R–SO₃H...