datavorous/entrance-exam-dataset huggingface dataset:
Which of the following does not given yellow soild on treatment with sodium hypoiodite?

Options:
A Acetophenone
B Pentan – 3 – one
C Pentan – 2 –one
D Ethanal

The correct answer is:
Pentan – 3 – one

Solution:
Pentan – 3 – one does not give yellow solid on treatment with sodium hypoiodite because this reaction is given by only methyl ketones. Ketones that have at least one methyl group linked to the carbonyl carbon atom are oxidised by sodium hypoiodite to sodium salts of corresponding carboxylic acids. This reaction is called iodoform reaction.

Topic: Chemistry, Aldehydes and Ketones, JEE Main
Which of the following does not have a metal carbon bond?

Options:
A $\mathrm{Al}\left(\mathrm{OC}_2 \mathrm{H}_5\right)_3$
B $\mathrm{C}_2 \mathrm{H}_5 \mathrm{MgBr}$
C $\mathrm{K}\left[\mathrm{Pt}\left(\mathrm{C}_2 \mathrm{H}_4\right) \mathrm{Cl}_3\right]$
D $\mathrm{Ni}(\mathrm{CO})_4$

The correct answer is:
$\mathrm{Al}\left(\mathrm{OC}_2 \mathrm{H}_5\right)_3$

Solution:
$\mathrm{Al}\left(\mathrm{OC}_2 \mathrm{H}_5\right)_3$ contains bonding through $\mathrm{O}$ and thus it does not have metal-carbon bond.

Topic: Chemistry, Coordination Compounds, JEE Main
Which of the following does not have coordinate bond?

Options:
A $\mathrm{SO}_2$
B $\mathrm{HNO}_3$
C $\mathrm{H}_2 \mathrm{SO}_3$
D $\mathrm{HNO}_2$

The correct answer is:
$\mathrm{HNO}_2$

Solution:
A. $\mathrm{SO}_2$ (Sulfur Dioxide)
1. Sulfur has 6 valence electrons and each oxygen has 6 valence electrons.
2. In $\mathrm{SO}_2$, sulfur forms two double bonds with two oxygen atoms.
3. One of the oxygen atoms can donate a lone pair to sulfur, forming a coordinate bond.
4. Therefore, $\mathrm{SO}_2$ has a coordinate bond.
B. $\mathrm{HNO}_3$ (Nitric Acid)
1. Nitrogen has 5 valence electrons, each oxygen has 6, and hydrogen has 1.
2. In $\mathrm{HNO}_3$, nitrogen forms one double bond with one oxygen and single bonds with the other oxygen and hydrogen.
3. The nitrogen can use a lone pair to form a coordinate bond with one of the oxygens.
4. Therefore, $\mathrm{HNO}_3$ has a coordinate bond.
C. $\mathrm{H}_2 \mathrm{SO}_3$ (Sulfurous Acid)
1. Sulfur has 6 valence electrons, each oxygen has 6, and hydrogen has 1.
2. In $\mathrm{H}_2 \mathrm{SO}_3$, sulfur forms two single bonds with two hydroxyl groups \((\mathrm{OH})\) and one double bond with an oxygen atom.
3. The sulfur can donate a lone pair to form a coordinate bond with the remaining oxygen.
4. Therefore, $\mathrm{H}_2 \mathrm{SO}_3$ has a coordinate bond.
D. $\mathrm{HNO}_2$ (Nitrous Acid)
1. Nitrogen has 5 valence electrons, each oxygen has 6, and hydrogen has 1.
2. In HNO 2, nitrogen forms one double bond with one oxygen and a single bond with the hydroxyl group (OH).
3. The nitrogen does not have a lone pair available to donate to form a coordinate bond.
4. Therefore, $\mathrm{HNO}_2$ does not have a coordinate bond.
Conclusion
The compound that does not have a coordinate bond is $\mathrm{HNO}_2$.

Topic: Chemistry, Chemical Bonding and Molecular Structure, JIPMER, JIPMER 2009
Which of the following does not have valence electron in $3 d$ -subshell?

Options:
A Fe(III)
B $\mathrm{Mn}(\mathrm{II})$
C $\mathrm{Cr}(\mathrm{I})$
D $\mathrm{P}(0)$

The correct answer is:
$\mathrm{P}(0)$

Solution:
$\mathrm{P}$ (At no. 15 ) has electronic configuration $1 s^{2}, 2 s^{2} p^{6}, 3 s^{2} p^{3},$ hence no electron in $d$ -subshell.

Topic: Chemistry, Classification of Elements and Periodicity in Properties, JEE Main
Which of the following does not illustrate the anomalous properties of lithium

Options:
A The melting point and boiling point of $L i$ are comparatively high
B $L i$ is much softer than the other group I metals
C $\mathrm{Li}$ forms a nitride $L i_3 N$ unlike group I metals
D The ion of $\mathrm{Li}$ and its compounds are more heavily hydrated than those of the rest of the group

The correct answer is:
$L i$ is much softer than the other group I metals

Solution:
Actually Li is harder then other alkali metals

Topic: Chemistry, s Block Elements, JEE Main
Which of the following does not illustrate the anomalous properties of lithium?

Options:
A Li is much softer than the other group first metals
B The melting point and boiling point of Li are comparatively high
C Li forms a nitride Li3N unlike group first metals
D The ions of Li and its compounds are more heavily hydrated than those of the rest of the group first elements

The correct answer is:
Li is much softer than the other group first metals

Solution:
Li is much softer than the other group first metals. Actually, Li is harder than other alkali metals.

Topic: Chemistry, s Block Elements, JEE Main
Which of the following does not obey the octet rule

Options:
A $\mathrm{Co}$
B $\mathrm{NH}_3$
C $\mathrm{H}_2 \mathrm{O}$
D $\mathrm{PCl}_5$

The correct answer is:
$\mathrm{PCl}_5$

Solution:
Correct option is 4. $P C l_5$
Co has only 6 electrons while $\mathrm{PCl}_5$ has 10 electrons after sharing so both don't follow octet rule.

Topic: Chemistry, Chemical Bonding and Molecular Structure, JEE Main
Which of the following does not show geometrical isomerism?

Options:
A
1, 2-dichloro - 1- pentene

B
1, 3 - dichloro - 2- pentene

C
1, 1- dichloro - 1- pentene

D
1, 4 - dichloro - 2- pentene

The correct answer is:
1, 1- dichloro - 1- pentene

Solution:
No Solution Available

Topic: Chemistry, General Organic Chemistry, JEE Main, JEE Main 2002
Which of the following does not show optical isomerism -
(en = Ethylenediamine)

Options:
A $\left[\mathrm{Co}(\mathrm{en})_3\right]^{3+}$
B $\left[\mathrm{Co}(\mathrm{en})_2 \mathrm{Cl}_2\right]^{+}$
C $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_3 \mathrm{Cl}_3\right]^{-}$
D $\left[\mathrm{Co}(\mathrm{en}) \mathrm{Cl}_2\left(\mathrm{NH}_3\right)_2\right]^{+}$

The correct answer is:
$\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_3 \mathrm{Cl}_3\right]^{-}$

Solution:
As complexes of the type $\left[\mathrm{MA}_3 \mathrm{~B}_3\right]$ can show geometrical isomerism knows as facmer isomerism and not optical isomerism. So here $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_3 \mathrm{Cl}_3\right]^0$ can not show optical isomerism.

Topic: Chemistry, Coordination Compounds, NEET, NEET 2009 (Mains)
Which of the following does not undergo aldol condensation reaction?

Options:
A $\mathrm{CH}_{3}-\mathrm{CHO}$
B $\mathrm{ClCH}_{2}-\mathrm{CHO}$
C $\mathrm{C}_{6} \mathrm{H}_{5}-\mathrm{CHO}$
D $\mathrm{CHCl}_{2}-\mathrm{CHO}$

The correct answer is:
$\mathrm{C}_{6} \mathrm{H}_{5}-\mathrm{CHO}$

Solution:
Aldol condensation is a characteristic reaction of aldehyde having $\alpha$-hydrogen atom :
Benzaldehyde do not contain any $\alpha$-hydrogen atom.
$\therefore$ It do not undergoes aldol condensation reaction.

Topic: Chemistry, Aldehydes and Ketones, JEE Main
Which of the following doesn't give a ppt. with silver nitrate solution.

Options:
A Ethyl bromide
B Sodium bromide
C Calcium chloride
D Sodium chloride

The correct answer is:
Ethyl bromide

Solution:
Ethyl bromide doesn't give a ppt. with silver nitrate solution because it does not provide free ions to react with.

Topic: Chemistry, Practical Chemistry, JEE Main
Which of the following doesn't secrete saliva?

Options:
A Parotid glands
B Supra-maxillary glands
C Sub-mandibular glands
D Sub-lingual glands

The correct answer is:
Supra-maxillary glands

Solution:
Saliva is mainly produced by three pairs of salivary glands, the parotids (cheek), the submaxillary/ sub-mandibular (lower jaw) and the sub-linguals (below the tongue). These glands situated just outside the buccal cavity secrete salivary juice into the buccal cavity.

Topic: Biology, Digestion and Absorption, NEET
Which of the following drugs is not classified in the criteria based on the pharmacological effect?

Options:
A Antihistamines
B Antiseptics
C Analgesics
D Antipyretics

The correct answer is:
Antihistamines

Solution:
Pharmacological effects of drugs provides a wide range of drugs that have a same effect on a specific type of problem. Analgesics have pain killing effect, antiseptics prevent the growth of microbes and antipyretics help in lowering body temperature during fever.

Topic: Chemistry, Chemistry in Everyday Life, JEE Main
Which of the following electrolytes will have maximum coagulating value for AgIAg+ sol?

Options:
A Na2S
B Na3PO4
C Na2SO4
D NaCl

The correct answer is:
NaCl

Solution:
Coagulating power ∝1coagulating value∝charge
As AgIAg+ is a positive sol so negative ion will cause the coagulation.
Ions of the given electrolytes are, S2-,PO43-,SO42- and Cl- .
As Cl- has minimum charge thus has maximum coagulating value.

Topic: Chemistry, Surface Chemistry, JEE Main
Which of the following electronic configuration is not possible according to Hund's rule

Options:
A $1 s^2 2 s^2$
B $1 s^2 2 s^1$
C $1 s^2 2 s^2 2 p_x^1 2 p_y^1 2 p_x^1$
D $1 s^2 2 s^2 2 p_x^2$

The correct answer is:
$1 s^2 2 s^2 2 p_x^2$

Solution:
According to Hund's rule electron first fill in unpaired form in vacant orbital then fill in paired form to stabilized the molecule by which $1 s^2, 2 s^2, 2 p_x^2$ is not possible. According to Hund's rule. Because $2 p_x, p_y, p_z$ have the same energy level so electron first fill in unpaired form not in paired form so it should be $1 s^2, 2 s^2, 2 p_x^1, 2 p_y^1$.

Topic: Chemistry, Structure of Atom, JEE Main
Which of the following electronic configuration is that of a transitional element

Options:
A $1 s^2, 2 s^2 p^6, 3 s^2 p^6 d^{10}, 4 s^2 p^6$
B $1 s^2, 2 s^2 p^6, 3 s^2 p^6 d^{10}, 4 s^2 p^1$
C $1 s^2, 2 s^2 p^6, 3 s^2 p^6 d^2, 4 s^2$
D $1 s^2, 2 s^2 p^6, 3 s^2 p^6, 4 s^2$

The correct answer is:
$1 s^2, 2 s^2 p^6, 3 s^2 p^6 d^2, 4 s^2$

Solution:
$1 s^2, 2 s^2 p^6, 3 s^2 p^6 d^2, 4 s^2$ is the electronic configuration of a transitional element as last electron enters into \(\mathrm{d}\) subshell.

Topic: Chemistry, d and f Block Elements, JEE Main
Which of the following electronic configuration would be associated with the highest magnetic moment ?

Options:
A [Ar] 3d7
B [Ar] 3d8
C [Ar] 3d3
D [Ar] 3d6

The correct answer is:
[Ar] 3d6

Solution:
A magnetic moment is a quantity that represents the magnetic strength and orientation of a magnet or any other object that produces a magnetic field. More precisely, a magnetic moment refers to a magnetic dipole moment, the component of the magnetic moment that can be represented by a magnetic dipole. The greater the number of unpaired electrons, the higher will be the magnetic moment.

Magnetic moment=nn+2

3 d73 d83 d33 d6 No. of. unpaired e-3234 Spin only Magnetic moment 15BM8BM15BM24BM

Hence, the answer is option D.

Topic: Chemistry, Structure of Atom, JEE Main, JEE Main 2024 (27 Jan Shift 1)
Which of the following element has the lowest ionization potential

Options:
A $\mathrm{Fe}$
B $\mathrm{H}$
C $Li$
D $\mathrm{He}$

The correct answer is:
$Li$

Solution:
Li belongs to $1^{\text {st }}$ group. There is $1 \mathrm{e}^{-}$in outermost shell. Thus low I.E.

Topic: Chemistry, Classification of Elements and Periodicity in Properties, JEE Main
Which of the following element shows maximum valency?

Options:
A Carbon
B Barium
C Nitrogen
D Sulphur

The correct answer is:
Sulphur

Solution:
Second period elements can not form more than four bonds due to unavailability of vacant d-orbitals.

But third period onwards elements can form more than four bonds due to availability of vacant d-orbitals.

N and C belong to the second period so they can not expand octet. Ba is metal and +2 oxidation state is more stable.

Sulphur belongs to the third period of Periodic Table hence, it has maximum valency and maximum valency of S is 6.

Topic: Chemistry, Classification of Elements and Periodicity in Properties, JEE Main
Which of the following elements have half-filled f-orbitals in their ground state ?
(Given : atomic number Sm-62;Eu=63;Tb=65;Gd=64,Pm=61)

Choose the correct answer from the options given below :

Options:
A A and B only
B C and D only
C B and D only
D A and E only

The correct answer is:
B and D only

Solution:
f-subshell contains seven orbitals in it. Hence, if seven electrons are present in these orbitals then it said to be half-filled. Electronic configuration of all the elements are:

Sm(Z=62)=4f6 s2

Eu(Z=63)=4f76S2

Tb(Z=65)=4f96s2

Gd(Z=64)=4f75d16s2

Pm(Z=61)=4f56s2

So, Eu & Gd have half-filled configuration.

Topic: Chemistry, d and f Block Elements, JEE Main, JEE Main 2023 (31 Jan Shift 2)
Which of the following elements helps in maintaining the structure of ribosomes?

Options:
A Magnesium
B Zinc
C Copper
D Molybdenum

The correct answer is:
Magnesium

Solution:
Each ribosome is made up of two subunits - a large and a small subunit. A 70S ribosome is made up of 50S, large subunit and 30S, small subunit. An 80S ribosome is made up of 60S, large subunit and 40S, small subunit. 0.001 M Mg+2 concentration is required for the association of two subunits. As a result, the intact ribosome is formed.

Topic: Biology, Mineral Nutrition, NEET, NEET 2020 (Phase 2)
Which of the following elements is most metallic ?

Options:
A Phosphorus
B Arsenic
C Antimony
D Bismuth

The correct answer is:
Bismuth

Solution:

Topic: Chemistry, p Block Elements (Group 15, 16, 17 & 18), JEE Main
Which of the following elements is not present in plant tissues in large amounts?

Options:
A C
B H
C Mo
D S

The correct answer is:
Mo

Solution:
Macronutrients are generally present in plant tissues in large amounts (in excess of 10 mmole Kg–1 of dry matter). The macronutrients include carbon, hydrogen, oxygen, nitrogen, phosphorous, sulphur, potassium, calcium and magnesium. Of these, carbon, hydrogen and oxygen are mainly obtained from CO2 and H2O, while the others are absorbed from the soil as mineral nutrition.
Micronutrients or trace elements, are needed in very small amounts (less than 10 mmole Kg –1 of dry matter). These include iron, manganese, copper, molybdenum, zinc, boron, chlorine and nickel.

Topic: Biology, Mineral Nutrition, NEET
Which of the following elements is responsible for maintaining turgor in cells?

Options:
A Potassium
B Sodium
C Magnesium
D Calcium

The correct answer is:
Potassium

Solution:
Potassium is responsible for maintaining turgor in cells. Turgor pressure increases because of a negative water potential due to an influx of potassium ions (K+). The K+ Is pumped in by active transport through channels in guard cell membranes in response to the presence of light.

Topic: Biology, Transport in Plants, NEET, NEET 2018
Which of the following elements never show positive oxidation number

Options:
A $0$
B $\mathrm{Fe}$
C $\mathrm{Ga}$
D $F$

The correct answer is:
$F$

Solution:
Fluorine is the most electronegative element in the periodic table so it never shows positive oxidation state.

Topic: Chemistry, Redox Reactions, JEE Main
Which of the following elements will form alkaline oxide?

Options:
A \( \mathrm{K} \)
B \( \mathrm{P} \)
C \( \mathrm{S} \)
D \( \mathrm{Cl} \)

The correct answer is:
\( \mathrm{K} \)

Solution:
Alkaline metal have ns1 Electronic configuration. Alkali metal are placed in group 1 Of the periodic table.

Among the given elements, potassium is the only element which is placed in group 1 of the periodic table and has 4s1 Electronic configuration . So, it is an alkali, and hence, it forms an alkaline oxide. Phosphorous is placed in group 15, sulphur is placed in group 16, and chlorine is placed in group 17 of the periodic table, and they are all non-metals. Hence, they do not form alkaline oxides.

Topic: Chemistry, s Block Elements, JEE Main
Which of the following endoparasites of humans does show viviparity?

Options:
A Ancylostoma duodenale
B Enterobius vermicularis
C Trichinella spiralis
D Ascaris lumbricoides

The correct answer is:
Trichinella spiralis

Solution:
Viviparity means development of an embryo inside the body of mother rather than laying eggs. E.g.: Trichinella spiralis is an endoparasite of human body that shows viviparity whereas the remaining endoparasites lay eggs (oviparity).

Topic: Biology, Animal Kingdom, NEET, NEET 2015 (Phase 1)
Which of the following enhances lathering property of soap?

Options:
A Sodium carbonate
B Sodium rosinate
C Sodium stearate
D Tri sodium phosphate

The correct answer is:
Sodium rosinate

Solution:
Sodium rosinate is generally added in the soapbecause it prodiuces rich lather.
Sodium rosinate is a fluid, high viscous solution of sodium soap rosin. Sodium rosinate provides highly stable emulsion over a uride range of water hardness. This is why it is used in soaps.
Sodium rosinate is used in soaps by Sapoinification Reaction.

Topic: Chemistry, Chemistry in Everyday Life, JEE Main
Which of the following enhances the lathering property of soap?

Options:
A Sodium stearate
B Sodium carbonate
C Sodium rosinate
D Trisodium phosphate

The correct answer is:
Sodium rosinate

Solution:
Shaving soaps contain glycerol to prevent rapid drying. A gum called, rosin is added while making them. It forms sodium rosinate which lathers well. Laundry soaps contain fillers like sodium rosinate, sodium silicate, borax and sodium carbonate.

Topic: Chemistry, Chemistry in Everyday Life, JEE Main, JEE Main 2022 (27 Jul Shift 2)
Which of the following enzyme converts starch into maltose?

Options:
A
Diastase

B
Maltase

C
Zymase

D
Invertase

The correct answer is:
Diastase

Solution:
Maltose is obtained by partial hydrolysis of starch by the enzyme diastase present in Malt.
$2\left(\mathrm{C}_6 \mathrm{H}_{10} \mathrm{O}_5\right)_n+n \mathrm{H}_2 \mathrm{O} \underset{n \mathrm{C}_6 \mathrm{H}_{12} \mathrm{O}_6 \text { (Maltose) }}{\stackrel{\text { Diastase }}{\longrightarrow}}$

Topic: Chemistry, Chemistry in Everyday Life, JEE Main, JEE Main 2013 (09 Apr Online)
Which of the following enzymes are used to join bits of DNA?

Options:
A Ligase
B Primase
C DNA polymerase
D Endonuclease

The correct answer is:
Ligase

Solution:
DNA ligase joins pieces of DNA together, mainly joins Okazaki fragments with the main DNA piece. DNA polymerase is responsible for forming new copies of DNA, in the form of nucleic acid molecules. DNA primase catalyses the synthesis of a short RNA segment called a primer complementary to a ssDNA template. Endonucleases are enzymes that cleave the phosphodiester bond within a polynucleotide chain.

Topic: Biology, Molecular Basis of Inheritance, NEET, NEET 2002
Which of the following equation depicts the oxidizing nature of H2O2?

Options:
A 2I-+H2O2+2H+→I2+2H2O
B I2+H2O2+2OH-→2I-+2H2O+O2
C Cl2+H2O2→2HCl+O2
D KIO4+H2O2→KIO3+H2O+O2

The correct answer is:
2I-+H2O2+2H+→I2+2H2O

Solution:
Oxidizing nature of H2Ã¢â¬â¹O2Ã¢â¬â¹ means it oxidizes other substance and itself gets reduced. In such reactions O2Ã¢â¬â¹ is not evolved.

2I-+H2O2+2H+→I2+2H2O

Oxygen reduces from -1 to -2

So, its reduction will takes place. Hence it will behave as oxidising agent or it shows oxidising nature. While in other option it change from (-1) to 0.

Topic: Chemistry, Hydrogen, JEE Main, JEE Main 2021 (25 Feb Shift 1)
Which of the following equation does not represent a simple harmonic motion

Options:
A $y=a \sin \omega t$
B $y=a \cos \omega t$
C $y=a \sin \omega t+b \cos \omega t$
D $y=a \tan \omega t$

The correct answer is:
$y=a \tan \omega t$

Solution:
Simple harmonic motion equation $=y=a \sin (\omega t+\varphi)$
Option (1) is representing equation with phase difference $=0$
Option (2) is representing equation with phase difference $=\pi / 2$
Option (3) is representing equation of two oscillation together (merged oscillation)
Option (4) doesn't represent any equation and does not satisfy differential equation of SHM.
$\frac{d^2 x}{d t^2}+\omega_0^2 x=0$

Topic: Physics, Oscillations, JEE Main
Which of the following equation is linear

Options:
A $\left(\frac{d^2 y}{d x^2}\right)^2+x^2\left(\frac{d y}{d x}\right)^2=0$
B $\left(\frac{d^2 y}{d x^2}\right)^2+x^2\left(\frac{d y}{d x}\right)^2=0$
C $y=\frac{d y}{d x}+\sqrt{1+\left(\frac{d y}{d x}\right)^2}$
D $\frac{d y}{d x}+\frac{y}{x}=\log x$

The correct answer is:
$\frac{d y}{d x}+\frac{y}{x}=\log x$

Solution:
$\frac{d y}{d x}+\frac{y}{x}=\log x \quad$ is a linear differential equation.

Topic: Mathematics, Differential Equations, JEE Main
Which of the following equation is non-linear

Options:
A $\frac{d y}{d x}+\frac{y}{x}-\log x$
B $y \frac{d y}{d x}+4 x=0$
C $d x+d y=0$
D $\frac{d y}{d x}=\cos x$

The correct answer is:
$y \frac{d y}{d x}+4 x=0$

Solution:
A differential equation in which the dependent variable and its differential coefficient occur only in the first degree and are not multiplied together is called a linear differential equation.
Hence $y \frac{d y}{d x}+4 x=0$ is non-linear differential equation.

Topic: Mathematics, Differential Equations, JEE Main
Which of the following equation is non-linear

Options:
A $\frac{d y}{d x}=\cos x$
B $\frac{d^2 y}{d x^2}+y=0$
C $d x+d y=0$
D $x \frac{d y}{d x}+\frac{3}{\frac{d y}{d x}}=y^2$

The correct answer is:
$x \frac{d y}{d x}+\frac{3}{\frac{d y}{d x}}=y^2$

Solution:
$x \frac{d y}{d x}+\frac{3}{(d y / d x)}=y^2 \Rightarrow x\left(\frac{d y}{d x}\right)^2-y^2 \frac{d y}{d x}+3=0$
Hence it is a pep-linear differential equation

Topic: Mathematics, Differential Equations, JEE Main
Which of the following equations correctly represents the standard heat of formation $\left(\Delta H_f^{\circ}\right)$ of methane

Options:
A $C$ (diamonnd) $+2 \mathrm{H}_2(g)=\mathrm{CH}_4(g)$
B $\mathrm{C}$ (graphite) $+2 \mathrm{H}_2(g)=\mathrm{CH}_4($ l)
C $\mathrm{C}$ (graphite) $+2 \mathrm{H}_2(\mathrm{~g})=\mathrm{CH}_4(\mathrm{~g})$
D $\mathrm{C}\left(\right.$ graphite) $+4 \mathrm{H}=\mathrm{CH}_4(\mathrm{~g})$

The correct answer is:
$\mathrm{C}$ (graphite) $+2 \mathrm{H}_2(\mathrm{~g})=\mathrm{CH}_4(\mathrm{~g})$

Solution:
$\mathrm{C}_{\text {(graphite) }}+2 \mathrm{H}_{2(\mathrm{~g})}=\mathrm{CH}_{4(\mathrm{~g})}$

Topic: Chemistry, Thermodynamics (C), JEE Main
Which of the following equations gives a circle?

Options:
A $r=2 \sin \theta$
B $r^2 \cos 2 \theta=1$
C $r(4 \cos \theta+5 \sin \theta)=3$
D $5=r(1+\sqrt{2} \cos \theta)$

The correct answer is:
$r=2 \sin \theta$

Solution:
Now, taking option (a)
i.e. $r=2 \sin \theta$
Let $x=r \sin \theta, y=r \cos \theta$
$\Rightarrow \quad r^2=2 r \sin \theta$
$\Rightarrow \quad x^2+y^2=2 y \quad\left[\because x^2+y^2=r^2\right]$
This equation represents a circle.

Topic: Mathematics, Circle, JEE Main
Which of the following equations is dimensionally incorrect?

Where t=time, h=height, s=surface tension, θ=angle, ρ=density ,a,r=radius, g= the acceleration due to gravity, V=volume, p=pressure, W=work done, τ=torque, ϵ=permittivity, E=electric field, J=current density, L=length.

Options:
A W=τθ
B V=πpa48ηL
C h=2scosθρrg
D J=ϵ∂E∂t

The correct answer is:
V=πpa48ηL

Solution:
Dimensions of πpa48ηL(volume flow rate) is L3 T–1.

Topic: Physics, Units and Dimensions, JEE Main, JEE Main 2021 (31 Aug Shift 1)
Which of the following equations of a line intercepts on the circle x2+y2-6x-8y=0 a chord of longest length?

Options:
A y-x=0
B x+y=0
C x+y=2
D 3x+4y-2=0

The correct answer is:
y-x=0

Solution:
The chord nearest to the centre of the circle will be the longest chord.
From options, we see that the given lines are at a distance of 12,72,52,235 respectively from the centre 3,4.

Hence, A is correct

Topic: Mathematics, Circle, JEE Main
Which of the following equations represents a travelling wave?

Options:
A y=Asin15x-2t
B y=Aexcosωt-θ
C y=Ae-x2vt+θ
D y=Asinx cosωt

The correct answer is:
y=Asin15x-2t

Solution:
The given function should be in the form of fx±vt.

So, for travelling wave y should be linear function of x and tand should be finite and continuous for all values of t.

y=Asin15x-2t→ linear function in x and t.

Topic: Physics, Waves and Sound, JEE Main, JEE Main 2021 (24 Feb Shift 2)