datavorous/entrance-exam-dataset huggingface dataset:
Which of the following conditions of path difference represent destructive interference?

Options:
A \( 37 \lambda \)
B \( 12.5 \lambda \)
C \( 26 \lambda \)
D \( 19 \lambda \)

The correct answer is:
\( 12.5 \lambda \)

Solution:
According to Young's double-slit experiment, the condition for destructive fringe (minimum intensity) is given as, ∆x=2n+1λ2.

Here, n is integer and λ is wavelength.

Checking all the given options now,

i 37λ=∆x

2n+1λ2=37λ⇒n=36.5

ii12.5λ=∆x

2n+1λ2=12.5λ⇒n=12

iii 26λ=∆x

2n+1λ2=26λ⇒n=25.5

iv 19λ=∆x

2n+1λ2=19λ⇒n=18.5

So, from the above analysis, it is clear that for path difference 12.5λ, we have destructive interference.

Topic: Physics, Wave Optics, JEE Main
Which of the following conditions represents an equilibrium

Options:
A Freezing of ice in a open vessel, temperature of ice is constant
B Few drops of water is present along with air in a balloon, temperature of balloon is constant
C Water is boiling in an open vessel over stove, temperature of water is constant
D All the statements (a), (b) and (c) are correct for the equilibrium

The correct answer is:
Few drops of water is present along with air in a balloon, temperature of balloon is constant

Solution:
The correct option is B Few drops of water is present along with air inside a balloon, temperature of balloon is constant Equilibrium can only be achieved in closed vessel. System (b) is closed so an equilibrium will be established between water (liquid) and water (vapour) phase.
In (a) and (c), equilibrium will not be established.

Topic: Chemistry, Chemical Equilibrium, JEE Main
Which of the following conformations will be the most stable?

Options:
A
B
C
D

The correct answer is:

Solution:
Staggered conformation has the lowest van der Waal and torsional strain. Hydrogen atoms are equally placed and there is minimum repulsion between them. Hence, it must be most stable.

Topic: Chemistry, General Organic Chemistry, JEE Main, JEE Main 2023 (25 Jan Shift 1)
Which of the following conformers for ethylene glycol is most stable?

Options:
A

B

C

D

The correct answer is:

Solution:
This conformation is most stable due to intramolecular H-bonding.

Topic: Chemistry, General Organic Chemistry, NEET, NEET 2010 (Mains)
Which of the following connotations are not true about the special creation theory of the origin of life?

Options:
A All living organisms that we see today were created as such.
B The earth is about 4000 years old.
C There has been gradual evolution of life form.
D Diversity was always the same since creation and will remain same in future also.

The correct answer is:
There has been gradual evolution of life form.

Solution:
Special creation theory stated that:
(i) All living organisms that we see today were created as such.
(ii) The earth is about 4000 years old.
(iii) Diversity was always the same since creation and will remain same in future also.

Topic: Biology, Evolution, NEET
Which of the following connotations are not true about the special creation theory of the origin of life?

Options:
A All living organisms that we see today were created as such.
B The earth is about 4000 years old.
C There has been gradual evolution of life form.
D Diversity was always the same since creation and will remain same in future also.

The correct answer is:
There has been gradual evolution of life form.

Solution:
Special creation theory stated that: (i) All living organisms that we see today were created as such. (ii) The earth is about 4000 years old. (iii) Diversity was always the same since creation and will remain same in future also.

Topic: Biology, Evolution, NEET
Which of the following contains a coordinate covalent bond

Options:
A $\mathrm{N}_2 \mathrm{O}_5$
B $\mathrm{BaCl}_2$
C $\mathrm{HCl}$
D $\mathrm{H}_2 \mathrm{O}$

The correct answer is:
$\mathrm{N}_2 \mathrm{O}_5$

Solution:
Structure of \(\mathrm{N}_2 \mathrm{O}_5\) is \(O=\underset{| \atop \stackrel{ \atop }{\huge O}}{N}-O-\underset{| \atop \stackrel{ \atop }{\huge O}}{N}=0\)

Topic: Chemistry, Chemical Bonding and Molecular Structure, JEE Main
Which of the following contains asymmetric centre

Options:
A 2-butene
B 2, 2-dimethylpropane
C 2-hexyne
D Lactic acid

The correct answer is:
Lactic acid

Solution:

Topic: Chemistry, General Organic Chemistry, JEE Main
Which of the following contains three pairs of electrons

Options:
A Carbocation
B Carbanion
C Free radical
D None of these

The correct answer is:
Carbocation

Solution:
The correct option is (1) Carbocation
The explanation for the correct answer:
(1) Carbocation
- A carbocation is a carbon atom having a positive charge and three bonds.
- It is also known as carbonium ion.
- Carbocation is an even-electron cation that has a positive charge on the carbon atom.
- Carbocations have six electrons in their valence shell making them electron deficient.
- They are unstable electrophiles and react very with nucleophiles.
- Therefore, carbocation has three pairs of electrons and it is the correct answer.

Topic: Chemistry, General Organic Chemistry, JEE Main
Which of the following contains three pairs of electrons

Options:
A Carbocation
B Carbanion
C Free radical
D None of these

The correct answer is:
Carbocation

Solution:

Topic: Chemistry, General Organic Chemistry, JEE Main
Which of the following contraceptive methods do involve a role of hormone?

Options:
A Lactational amenorrhea, Pills, Emergency contraceptives
B Barrier method, Lactational amenorrhea, Pills
C CuT, Pills, Emergency contraceptives
D Pills, Emergency contraceptives, Barrier methods

The correct answer is:
Lactational amenorrhea, Pills, Emergency contraceptives

Solution:
(i) Lactational amenorrhea: Breastfeeding delays the resumption of normal ovarian cycles by disrupting the pattern of pulsatile release of GnRH from the hypothalamus due to production of prolactin and hence FSH and LH from the pituitary.
(ii) Progestin-only emergency contraceptive pills (morning after pills) are pills that contain levonorgestrel, a type of the hormone progestin researchers have found prevents pregnancy when taken in the few days after sex.
(iii) There are two main kinds of birth control pills — combination birth control pills, which contain estrogen and progestin.

Topic: Biology, Reproductive Health, NEET, NEET 2019 (All India)
Which of the following conversions involves change in both shape and hybridisation?

Options:
A H2OÂ âÂ H3O+Â
B BF3 âBF4-
C CH4Â âÂ C2H6
D NH3Â âÂ NH4+

The correct answer is:
BF3 âBF4-

Solution:
Hybridization in Chemistry is defined as the concept of mixing two atomic orbitals to give rise to a new type of hybridized orbitals. This intermixing usually results in the formation of hybrid orbitals having entirely different energies, shapes, etc. The atomic orbitals of the same energy level mainly take part in hybridization. However, both fully filled and half-filled orbitals can also take part in this process, provided they have equal energy.

Here, BF3 has sp2 hybridisation while BF4- has sp3 hybridisation.

Topic: Chemistry, Chemical Bonding and Molecular Structure, JEE Main, JEE Main 2018 (16 Apr Online)
Which of the following coordination compounds has maximum number of isomers ?

Options:
A Pt NH 3 4 Cl 2 2+
B Pt gly 3 2−
C Pt en 3 4+
D Pt NH 3 2 Cl 2

The correct answer is:
Pt gly 3 2−

Solution:
Pt NH 3 4 Cl 2 2+ has 2 geometrical isomers.
Pt gly 3 2− will have 2 geometrical isomers, both of which will be optical active, giving a total of 4 isomers.
Pt en 3 4+ will have no geometrical isomers, but the compound will be optically active, hence total two isomers.
Pt NH 3 2 Cl 2 will have two geometrical isomers.

Topic: Chemistry, Coordination Compounds, JEE Main
Which of the following coordination compounds would exhibit optical isomerism ?

Options:
A Pentaamminenitrocobalt (III) iodide
B Diamminedichloroplatinum (II)
C Trans-dicyanobis (ethylenediamine) chromium (III) chloride
D Tris-(ethylenediamine) cobalt (III) bromide

The correct answer is:
Tris-(ethylenediamine) cobalt (III) bromide

Solution:
Ma5b+nâ no orbital activity
Ma2b2+nâ plane of symmetry
trans-MAA2b2+nâ plane of symmetry

Enantiomers exist in M AA 3 + n

Topic: Chemistry, Coordination Compounds, JEE Main
Which of the following correctly depicts the aestivation of petals in the flower of cotton?

Options:
A
B
C
D

The correct answer is:

Solution:
The mode of arrangement of sepals or petals in the floral bud with respect to the other members of the same whorl is known as aestivation. The main types of aestivation are valvate, twisted, imbricate, and vexillary.
In pea and bean flowers, there are five petals, the largest (standard) overlaps the two lateral petals (wings) which in turn overlap the two smallest anterior petals (keel); this type of aestivation is known as vexillary or papilionaceous (Figure A). When sepals or petals in a whorl just touch one another at the margin, without overlapping, as in Calotropis, it is said to be valvate (Figure B). If the margins of sepals or petals overlap one another but not in any particular direction as in Cassia and Gulmohar, the aestivation is called imbricate (Figure C). If one margin of the appendage overlaps that of the next one and so on as in china rose, lady's finger and cotton, it is called twisted (Figure D).

Topic: Biology, Morphology of Flowering Plants, NEET
Which of the following correctly describes probiotics?

Options:
A Cancer-inducing microbes
B New kind of food allergens
C Live microbial food supplement
D Safe antibiotics

The correct answer is:
Live microbial food supplement

Solution:
Probiotics are living organisms claimed to provide health benefits on consumption. These generally help by improving the gut flora and the digestive system. These have been know to maintain the natural balance of microbes in the gut if at all disrupted by any illness or treatment.
Probiotics are generally sold as food than medicines, thus, they do not undergo the stringent process of regulations and development of medicines.
As such, it is difficult to know is the given probiotic has the product actually contains the bacteria stated on the food label or the product contains enough bacteria to have an effect or the bacteria are able to survive long enough to reach your gut.

Topic: Biology, Microbes in Human Welfare, NEET
Which of the following correctly describes the functions of FSH in females?

Options:
A It stimulates growth and development of the ovarian follicles.
B It induces ovulation of fully mature follicles and maintains the corpus luteum.
C It stimulates the synthesis and secretion of hormones called androgens from testis.
D It regulates spermatogenesis.

The correct answer is:
It stimulates growth and development of the ovarian follicles.

Solution:
Functions of FSH:
(i) In males: Regulation of Spermatogenesis by FSH and androgens.
(ii) In females: FSH stimulates growth and development of the ovarian follicles in females.

Topic: Biology, Chemical Coordination and Integration, NEET
Which of the following correctly represents Nernst equation?
[ $P=$ products, $R=$ reactants $]$

Options:
A $\Delta G=\Delta G^{\circ}+2.303 R T \log \frac{[R]}{[P]}$
B $\Delta G=\Delta G^{\circ}-2.303 R T \log \frac{[P]}{[R]}$
C $\Delta G^{\circ}=\Delta G+2.303 R T \log \frac{[R]}{[P]}$
D $\Delta G^{\circ}=\Delta G-2.303 R T \log \frac{[R]}{[P]}$

The correct answer is:
$\Delta G=\Delta G^{\circ}+2.303 R T \log \frac{[R]}{[P]}$

Solution:
Nernst equation is
$$
\begin{gathered}
E_{\text {cell }}=E_{\text {cell }}^{\circ}-\frac{2.303 R T}{n F} \log \frac{[P]}{[R]} \\
\Delta G=-n F E_{\text {cell }}, \Delta G^{\circ}=-n F E_{\text {cell }}^{\circ} \\
\Delta G=\Delta G^{\circ}+2.303 R T \log \frac{[P]}{[R]} \\
\Delta G^{\circ}=\Delta G+2303 R T \log \frac{[R]}{[P]}
\end{gathered}
$$

Topic: Chemistry, Electrochemistry, JEE Main
Which of the following correctly represents the variation of electric potential (V) of a charged spherical conductor of radius (R) with radial distance (r) from the centre?

Options:
A
B
C
D

The correct answer is:

Solution:
As electric field inside the charged conducting sphere is zero, therefore potential will be constant for the inside part.

For outside part, electric potential decreases as V=kqr and the conducting sphere behaves like a point charge concentrated at the centre.

Topic: Physics, Electrostatics, JEE Main, JEE Main 2023 (31 Jan Shift 1)
Which of the following could act as apropellant for rockets?

Options:
A
Liquid oxygen $+$ liquid argon

B
Liquid hydrogen + liquid oxygen

C
Liquid nitrogen $+$ liquid oxygen

D
Liquid hydrogen $+$ liquid nitrogen

The correct answer is:
Liquid hydrogen + liquid oxygen

Solution:
Liquid hydrogen and liquid oxygen are used as excellent fuel for rockets. $\mathrm{H}_2(l)$ has low mass and high enthalpy of combustion whereas oxygen is a strong supporter of combustion

Topic: Chemistry, Solutions, JEE Main, JEE Main 2003
Which of the following could not produce a virtual image

Options:
A Plane mirror
B Convex mirror
C Concave mirror
D All the above can produce a virtual image

The correct answer is:
All the above can produce a virtual image

Solution:
All of the above can produce a virtual image

Topic: Physics, Ray Optics, JEE Main
Which of the following countries has the highest biodiversity?

Options:
A
(a) Brazil

B
South Africa

C
Russia

D
India

The correct answer is:
(a) Brazil

Solution:
The climate of Brazil remains relatively undisturbed, constant and predictable giving tune for diversification, that favours rich biodiversity.

Topic: Biology, Biodiversity and its Conservation
Which of the following cranial nerve controls the movement of tongue?

Options:
A V cranial nerve
B X cranial nerve
C XII cranial nerve
D VIII cranial nerve

The correct answer is:
XII cranial nerve

Solution:
Cranial nerves are sensory, motor and mixed. Out of 12 pairs, 1st, 2nd and 8th are sensory in origin and 3rd , 4th, 6th, 11th and 12th are pure motor nerves and remaining are mixed nerves. 12th cranial nerve is a hypoglossal nerve (hypo is below and glossia is tongue). This nerve innervates almost all muscles of tongue and thus controls the movement of tongue. This nerve arises from medulla oblongata which is a part of hind brain.

Topic: Biology, Neural Control and Coordination, NEET
Which of the following curve is correct for a given amount of an ideal gas at constant pressure?

Options:
A
B
C
D

The correct answer is:

Solution:
VαT
V=KT
VT=KT2
VT=αT2=yαx

Topic: Chemistry, States of Matter, JEE Main
Which of the following curve is correct for blackbody radiation?
(Given: T1< T2< T3< T4 )

Options:
A
B
C
D

The correct answer is:

Solution:
The spectral distribution of the thermal energy radiated by a blackbody (i.e. the pattern of the intensity of the radiation over a range of wavelengths or frequencies) depends only on its temperature. As the temperature increases wavelength of peak emission decreases.
And the graph follows as:

Topic: Chemistry, Structure of Atom, JEE Main
Which of the following curve will represent the variation of conductance C during titration of CH3COOH by gradual addition of NaOH solution (V)

Options:
A
B
C
D

The correct answer is:

Solution:
CH3COOH is weak acid, NaOH is strong base neutralisation produces strong electrolyte CH3COONa . Thus, conductance C is low in the beginning, increases gradually and slowly till equivalence point and thereafter increases rapidly.

Topic: Chemistry, Electrochemistry, JEE Main
Which of the following cylindrical rods will conduct maximum heat, when their ends are maintained at the same temperature difference?

Options:
A l=1 m, r=0.2 m
B l=1 m, r=0.1 m
C l=10 m, r=0.1 m
D l=0.1 m, r=0.3 m

The correct answer is:
l=0.1 m, r=0.3 m

Solution:
ÎQÎt=KAÎTÎx= KÏr2âTlâr2l
As r2l is maximum for (d), so it is the correct choice.

Topic: Physics, Thermal Properties of Matter, JEE Main
Which of the following describes the function of the skin bag which encloses the testis?

Options:
A It synthesises and secretes testicular hormones called androgens.
B It provides nutrition to the germ cells.
C It maintains the low temperature of the testes necessary for spermatogenesis.
D It is made up of a special tissue that helps in erection of the penis to facilitate insemination.

The correct answer is:
It maintains the low temperature of the testes necessary for spermatogenesis.

Solution:
The male gonads, the testes, lie outside the abdomen within the scrotum, which is a sacâlike structure derived from the skin and fascia of the abdominal wall. The scrotum helps in maintaining the low temperature of the testes (2â2.5Â°C lower than the normal internal body temperature) necessary for spermatogenesis.

Topic: Biology, Human Reproduction, NEET
Which of the following describes the hypothetical scenario if the dimensions of the solar system were scaled proportionally to those of an atom in Rutherford's nuclear model, where the radius of the electron's orbit is 105 times larger than the nucleus's radius?

Options:
A The Earth would be closer to the Sun than its actual distance.
B The Earth would be at the same distance from the Sun as its actual distance.
C The Earth would be farther away from the Sun than its actual distance.
D The Earth's position relative to the Sun would remain unchanged.

The correct answer is:
The Earth would be farther away from the Sun than its actual distance.

Solution:
Correct Option is : (C)
The Earth would be farther away from the Sun than its actual distance.

Topic: Chemistry, Atomic Physics, NEET
Which of the following describes the nature of parathormone?

Options:
A Hypercalcemic
B Hypocalcemic
C Hyperkalemic
D Hypokalemic

The correct answer is:
Hypercalcemic

Solution:
Parathormone (PTH) maintains the total calcium concentration in blood by acting on bone, increasing absorption of calcium in the small intestine and in the kidney. It is a hypercalcemia hormone, meaning it increases the calcium levels in the blood.

Topic: Biology, Chemical Coordination and Integration, NEET
Which of the following describes the process of epoxidation?

Options:
A Addition of water to an alkene
B Addition of hydrogen to an alkene
C Formation of an epoxide by the addition of an oxygen atom to an alkene
D Cleavage of an alkene into two carbonyl compounds

The correct answer is:
Formation of an epoxide by the addition of an oxygen atom to an alkene

Solution:
Formation of an epoxide by the addition of an oxygen atom to an alkene
Explanation: Epoxidation involves the addition of an oxygen atom to the carbon-carbon double bond of an alkene, forming an epoxide (oxirane).

Topic: Chemistry, Alcohols Phenols and Ethers, JEE Main
Which of the following diagrams, shows correctly the dispersion of white light by a prism

Options:
A

B

C

D

The correct answer is:

Solution:
Correct option is 2.
Because in dispersion of white light, the rays of different colours are not parallel to each other. Also deviation takes place in same direction. hence option $\mathrm{2}$ is correct.

Topic: Physics, Ray Optics, JEE Main
Which of the following differential equations has the same order and degree

Options:
A $\frac{d^4 y}{d x^4}+8\left(\frac{d y}{d x}\right)^6+5 y=e^x$
B $5\left(\frac{d^3 y}{d x^3}\right)^4+8\left(1+\frac{d y}{d x}\right)^2+5 y=x^8$
C $\left[1+\left(\frac{d y}{d x}\right)^3\right]^{2 / 3}=4 \frac{d^3 y}{d x^3}$
D $y=x^2 \frac{d y}{d x}+\sqrt{1+\left(\frac{d y}{d x}\right)^2}$

The correct answer is:
$\left[1+\left(\frac{d y}{d x}\right)^3\right]^{2 / 3}=4 \frac{d^3 y}{d x^3}$

Solution:
Option (a) has order $=4$, degree $=1$
Option (b) has order $=3$, degree $=4$
Option (c) has order $=3$, degree $=3$ (taking cube)
Option (d) has order $=1$, degree $=2$ (squaring).

Topic: Mathematics, Differential Equations, JEE Main
Which of the following diode exhibits negative resistance in its I-V characteristics?

Options:
A Schottky diode
B PIN diode
C Voltage variable capacitor diode
D Tunnel diode

The correct answer is:
Tunnel diode

Solution:
- It is a highly doped PN Junction diode, used for low-voltage high-frequency switching applications.
- It works on the tunneling principle.
- When compared to a normal p-n junction diode, a tunnel diode has a narrow depletion width.
- In normal forward-biased operation, it exhibits the "Negative resistance region" as shown:
- The negative differential resistance in their operation, allows them to be used as oscillators, amplifiers, and switching circuits.
- Their low capacitance allows them to function at microwave frequencies.
- Tunnel diodes are not good rectifiers.

Topic: Physics, Semiconductors, JEE Main
Which of the following diodes is used in forward biased condition?

Options:
A Photo diode
B LED
C Zener diode
D Varactor diode

The correct answer is:
LED

Solution:
- LED's can emit red, yellow, orange, green, and blue light that are commercially available.
- The semiconductor used for fabrication of visible LEDs must at least have a band gap of $1.8 \mathrm{eV}$
- Spectral range of visible light is from about $0.4 \mu \mathrm{m}$ to $0.7 \mu \mathrm{m}$, i.e. from about 3 eV to $1.8 \mathrm{eV}$.
- They have low power consumption; A seven-segment display requires about $140 \mu \mathrm{W}$ ( $20 \mu \mathrm{W} /$ segment).
- This is a great advantage over LEDs which require about $40 \mathrm{~mW}$ per numeral.
- They have a low cost.

Topic: Physics, Semiconductors, JEE Main
Which of the following disaccharide will not reduce Tollen's reagent?

Options:
A P
B Q
C P and Q both
D None of these

The correct answer is:
Q

Solution:
In (Q), it could be found that both the pyranose rings are attached through their reducing group, hence it will not be hydrolysed, and it can not reduce Tollen's reagent. So (Q) is not a reducing sugar, whereas in (P) one ring is hemiacetal which can be hydrolysed therefore it will be hydrolysed in solution and can reduce Tollen's reagent.

Topic: Chemistry, Biomolecules, JEE Main
Which of the following does not affect solubility of a gas in liquid?

Options:
A Nature of gas and liquid
B Pressure
C Concentration
D Temperature

The correct answer is:
Concentration

Solution:
The solubility of any gas in a particular liquid is the volume of gas that can be dissolved in unit volume of liquid. It only depend upon pressure, temperature and nature of gas and liquid.

Topic: Chemistry, Solutions, JEE Main
Which of the following does not affect the periodicity of the elements?

Options:
A Bonding behaviour
B Electronegativity
C Ionization energy
D Neutron/proton ratio

The correct answer is:
Neutron/proton ratio

Solution:
Neutron/proton ratio does not affect the periodicity of the elements as neutron/proton ratio does not affect the number of electrons in the atom so, its electronic configuration remains un-changed.

Topic: Chemistry, Classification of Elements and Periodicity in Properties, NEET
Which of the following does not contain silicon?

Options:
A Kaoline
B Agate
C Ruby
D Quartz

The correct answer is:
Ruby

Solution:
Ruby is mineral of aluminium ie, $\mathrm{Al}_{2} \mathrm{O}_{3}$. It does not contain silicon.

Topic: Chemistry, p Block Elements (Group 13 & 14), JEE Main
Which of the following does not exist in free form

Options:
A $B F_3$
B $\mathrm{BCl}_3$
C $\mathrm{BBr}_3$
D $\mathrm{BH}_3$

The correct answer is:
$\mathrm{BH}_3$

Solution:
Boron form different hydride of general formula $B_n H_{n+4}$ and $B_n H_{n+6}$ but $B H_3$ is unknown

Topic: Chemistry, p Block Elements (Group 13 & 14), JEE Main
Which of the following does not exist on the basis of molecular orbital theory

Options:
A $\mathrm{H}_2^{+}$
B $\mathrm{He}_2^{+}$
C $\mathrm{He}_2$
D $L i_2$

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

Solution:
$\mathrm{He}_2$

Topic: Chemistry, Chemical Bonding and Molecular Structure, JEE Main
Which of the following does not give white precipitate with Ammonical \(\mathrm{AgNO}_3\) solution

Options:
A $\mathrm{CH} \equiv \mathrm{CH}$
B $\mathrm{CH}_3-\mathrm{C} \equiv \mathrm{CH}$
C $\mathrm{CH}_3-\mathrm{C} \equiv \mathrm{C}-\mathrm{CH}_3$
D

The correct answer is:
$\mathrm{CH}_3-\mathrm{C} \equiv \mathrm{C}-\mathrm{CH}_3$

Solution:
$\mathrm{CH}_3-\mathrm{C} \equiv \mathrm{C}-\mathrm{CH}_3$, 2-butyne does not have acidic hydrogen. Hence, does not give white ppt. with ammonical $\mathrm{AgNO}_3$ solution.

Topic: Chemistry, Hydrocarbons, JEE Main