datavorous/entrance-exam-dataset huggingface dataset:
Which of the following statement are true for a stationary waves?

Options:
A
Every particle has a fixed amplitude which is different from the amplitude of its nearest particle

B
All the particles cross their mean position at the same time

C
All the particles are oscillating with same amplitude

D
There is no net transfer of energy across any plane

The correct answers are:
Every particle has a fixed amplitude which is different from the amplitude of its nearest particle
,
All the particles cross their mean position at the same time
,
There is no net transfer of energy across any plane

Solution:
As we know that, the equation of stationary wave $y=a \sin (k x) \cos \omega t$
(a) It clear that every particle at $x$ will have amplitude $(a \sin k x)$ will remain constant but varies with wavelength $(\lambda)$.
(b) Particles between two nodes are in same phase i.e. motion of particles between two nodes will be either upward or downward and crosses the mean position at sometime. For mean position $y=0$
So, $\cos \omega t=0$
and $\omega t=(2 n-1) \frac{\pi}{2}$
Hence, for a fixed value of $n$, all particles are having same value of time
$$
t=2(n-1) \frac{\pi}{2 \omega} \quad[\because \omega=\text { constant }]
$$
(c) amplitude of all the particles are $a \sin (k x)$ which is different for different particles at different values of $x$.
(d) the energy is a stationary wave is confined between two nodes. The amplitude of particles at nodes has amplitude zero, so energy does not transfer - across any plane. Hence verify option (d).

Topic: Physics, Waves and Sound
Which of the following statement is a tautology?

Options:
A ~q∧p∧q
B ~q∧p∧p∧~p
C ~q∧p∨p∨~p
D p∧q∧~p∧q

The correct answer is:
~q∧p∨p∨~p

Solution:
We know that p∨~p is a tautology and r∨t≡t

So,~q∧p∨p∨~p will be a tautology.

Topic: Mathematics, Mathematical Reasoning, JEE Main, JEE Main 2022 (27 Jun Shift 2)
Which of the following statement is a tautology?

Options:
A p∨~q→p∧q
B ~p∧~q→p∨q
C ~pâ¨~qâpâ§q
D ~pâ¨~qâpâ¨q

The correct answer is:
~p∨~q→p∨q

Solution:
From De Morgan's Law,

~p∨q=~p∧~q

p→q=~p∧~q

~p∧q→p∨q

=~~p∧q∧~p∧~q

=~~p∧f

=~f=t, where f is contradiction and t is tautology.

Topic: Mathematics, Mathematical Reasoning, JEE Main, JEE Main 2020 (08 Jan Shift 2)
Which of the following statement is/ are correct/incorrect?

I. A-bands of the muscle are dark and contain myosin.
II. I-bands are the light bands and contain actin.
III. During muscle contraction, the A-band contracts.
IV. The part between the two Z-lines is called a sarcomere.
V. The central gap of the thick filament, not overlapped by myosin filament is called H-zone.

Options:
A I,II, and III are correct, while IV and V are incorrect
B I,III,V are correct, while II,IV are incorrect
C I, II and IV are correct, while III and V are incorrect
D I,II,III and V are correct, while IV is incorrect

The correct answer is:
I, II and IV are correct, while III and V are incorrect

Solution:
During muscle contraction, the length of A-band remains constant, I-band shortens. H-zone is the area of A-band without thin filaments. This zone contains only thick filaments excluding the thin filaments on either side. So, H-zone in the skeletal muscle fiber is considered as an area due to the central gap between the actin filaments extending through myosin filaments in the A-band.

Topic: Biology, Locomotion and Movement, NEET
Which of the following statement is converse of the statement “If it rains then we will party”?

Options:
A We will party or it rains
B It rains or we will party
C We will not party or it rains
D We will not party or it does not rain

The correct answer is:
We will not party or it rains

Solution:
Converse of p→q is q→p≡∼q∨p

Topic: Mathematics, Mathematical Reasoning, JEE Main
Which of the following statement is correct?

Options:
A Gluconic acid is a dicarboxylic acid
B Gluconic acid is a partial oxidation product of glucose
C Gluconic acid can form cyclic (acetal/hemiacetal) structure
D Gluconic acid is obtained by oxidation of glucose with HNO3

The correct answer is:
Gluconic acid is a partial oxidation product of glucose

Solution:
Here only B is correct and rest are incorrect. As Gluconic acid is a monocarboxylic acid which is formed by the partial oxidation of glucose.
As Gluconic acid can not form cyclic (acetal/hemiacetal) structure and oxidation of glucose with HNO3 gives Saccharic acid.

Topic: Chemistry, Biomolecules, JEE Main
Which of the following statement is correct ?

Options:
A H3 PO3 is tribasic and reducing

B H3 PO3 is tribasic and non- reducing
C H3 PO3 is diabasic and non-reducing
D H3 PO3 is diabasic and reducing

The correct answer is:
H3 PO3 is diabasic and reducing

Solution:
The structure of H3 PO3 is
Since it contains two -OH groups, it is diabasic. Also it contains H atom directly attached to P, hence, it is reducing.

Topic: Chemistry, p Block Elements (Group 15, 16, 17 & 18), JEE Main
Which of the following statement is correct?

Options:
A formation of diamond is exothermic
B formation of graphite is endothermic
C graphite is more stable than diamond
D diamond is more stable than graphite

The correct answer is:
graphite is more stable than diamond

Solution:
In graphite and diamond, carbon is present in its standard state. Thus, the enthalpy of the graphite and diamond must be zero, but the enthalpy of the diamond is non-zero. So, the diamond is less stable than the graphite.

Topic: Chemistry, Thermodynamics (C), JEE Main
Which of the following statement is correct?

Options:
A Light waves are transverse but sound waves and waves on strings are longitudinal
B Sound waves and waves on a string are transverse but light waves are longitudinal
C Light waves and waves on a string are transverse but sound waves are longitudinal
D Light waves and sound waves are transverse but waves on string are longitudinal

The correct answer is:
Light waves and waves on a string are transverse but sound waves are longitudinal

Solution:
Light and waves on the string transverse but sound waves in air are longitudinal

Topic: Physics, Waves and Sound, JEE Main
Which of the following statement is correct?

Options:
A In primary rainbow, observer sees red colour on the top and violet on the bottom
B In primary rainbow, observer sees violet colour on the top and red on the bottom
C In primary rainbow, light wave suffers total internal reflection twice before coming out of water drops
D Primary rainbow is less bright than secondary rainbow.

The correct answer is:
In primary rainbow, observer sees red colour on the top and violet on the bottom

Solution:
In primary rainbow, red colour is at top and violet is at bottom. The colours are in the order of violet, indigo, blue, green, yellow, orange and red (VIBGYOR). Since violet colour has the smallest wavelength, in the primary rainbow, it suffers maximum refraction. That is why it appears on the innermost position.

Intensity of secondary rainbow is less in comparison to primary rainbow.

Topic: Physics, Ray Optics, JEE Main, JEE Main 2022 (25 Jul Shift 1)
Which of the following statement is correct about heart failure?

Options:
A a condition in which heart stops beating.
B when the heart muscle is suddenly damaged by an adequate blood supply.
C congestion of the lungs is one of the main symptoms of this disease.
D chest pain appears when no enough oxygen is reaching to the heart muscles

The correct answer is:
congestion of the lungs is one of the main symptoms of this disease.

Solution:
Heart failure means the state of heart when it is not pumping blood effectively enough to meet the needs of the body. It is sometimes called congestive heart failure because congestion of the lungs is one of the main symptoms of this disease.

Topic: Biology, Body Fluids and Circulation, NEET
Which of the following statement is correct about reproduction in bacteria?

Options:
A In bacteria reproduction occurs mainly by binary fission.
B Spores are formed under unfavorable condition in some bacteria only.
C Sexual reproduction occurs by a primitive type of transfer of DNA from one bacterium to another
D All of these

The correct answer is:
All of these

Solution:
Bacteria is a prokaryotic cell which lacks cytoskeleton, thus mitosis and meiosis are absent. It reproduces mainly by binary fission and sexual reproduction occurs by primitive type of gene transfer, by transformation, transduction and conjugation.

Topic: Biology, Biological Classification, NEET
Which of the following statement is correct for paper chromatography?

Options:
A Water present in the pores of the paper forms the stationary phase.
B Paper sheet forms the stationary phase.
C Water present in the mobile phase gets absorbed by the paper which then forms the stationary phase.
D Paper and water present in its pores together form the stationary phase.

The correct answer is:
Water present in the pores of the paper forms the stationary phase.

Solution:
The principle of paper chromatography is partition. In paper chromatography there are two phases one is the stationary phase and the other is the mobile phase. Here, water trapped in the paper acts as the stationary phase and solvent acts as the mobile phase.

Topic: Chemistry, General Organic Chemistry, JEE Main, JEE Main 2023 (15 Apr Shift 1)
Which of the following statement is correct for the function g(α) for α∈R such that gα=∫π6π3sinαxcosαx+sinαxdx

Options:
A g(α) is a strictly increasing function
B g(α) has an inflection point at α=-12
C g(α) is a strictly decreasing function
D g(α) is an even function

The correct answer is:
g(α) is an even function

Solution:
gα=∫π6π3sinαxsinαx+cosαxdx …i

gα=∫π6π3cosαxsinαx+cosαxdx …ii

Adding 1+2

2gα=π3-π6=π6

⇒gα=π12

Which is constant and an even function.

Topic: Mathematics, Definite Integration, JEE Main, JEE Main 2021 (17 Mar Shift 1)
Which of the following statement is correct for the reactivity in SN2 reaction?

Options:
A is more reactive than
B is more reactive than
C is more reactive than
D is more reactive than

The correct answer is:
is more reactive than

Solution:
The electronegativity order of hybridized carbons is sp>sp2>sp3 . So in an allylic halide, such as CH2=CH-CH2-I , the alpha carbon is much more partially positive than the alpha carbon in CH3-CH2-CH2I . Therefore, the attacking nucleophile will be attracted to the alpha carbon more in the allylic halide compound than in the primary halide. Hence, allylic halides tend to follow S N 2 pathways more than primary halides.

Topic: Chemistry, Haloalkanes and Haloarenes, JEE Main
Which of the following statement is correct regarding Rutherford's nuclear model of an atom?
1. The size of the nucleus is very large as compared to the size of the atom.
2. There is a positively charged centre in an atom called the nucleus.

Options:
A Only $1$
B Only $2$
C Both $1$ and $2$
D Neither $1$ nor $2$

The correct answer is:
Only $2$

Solution:
The Nucleus being positively charged is the correct statement about Rutherford's model of atoms.
Explanation: Alpha particles are positively charged. These particles are deflected by the nucleus.

Topic: Physics, Atomic Physics, JEE Main
Which of the following statement is correct when a mixture of \( \mathrm{NaCl} \) and \( \mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7} \) is gently warmed with conc. \( \mathrm{H}_{2} \mathrm{SO}_{4} \) ?
1. A deep red vapour is evolved
2. The vapour when passed into \( \mathrm{NaOH} \) solution gives a yellow solution of \( \mathrm{Na}_{2} \mathrm{CrO}_{4} \)
3. Chlorine gas is evolved
4. Chromyl chloride is formed

Options:
A \( 1,2,4 \)
B \( 1,2,3 \)
C \( 2,3,4 \)
D all are correct

The correct answer is:
\( 1,2,4 \)

Solution:
4NaCl+K2Cr2O7+6H2SO4conc.→2KHSO4+4NaHSO4+2CrO2Cl2orange redChromyl chloride+3H2O
Chromyl chloride vapours when passed through NaOH solution gives a yellow solution of Na2CrO4 .
CrO2Cl2+4NaOH→Na2CrO4+2NaCl+2H2O

Topic: Chemistry, d and f Block Elements, JEE Main
Which of the following statement is correct when a mixture of NaCl and K2Cr2O7 is gently warmed with conc. H2SO4 ?
1 . a deep red vapour is evolved
2. The vapour when passed into NaOH solution gives a yellow solution of Na2CrO4
3. chlorine gas is evolved
4. chromyl chloride is formed

Options:
A 1, 2, 4
B 1, 2 ,3
C 2, 3, 4
D all are correct

The correct answer is:
1, 2, 4

Solution:
4NaCl+K2Cr2O7+6H2SO4conc.→2KHSO4+4NaHSO4+2CrO2Cl2orange redChromyl chloride+3H2O
Chromyl chloride vapours when passed through NaOH solution gives a yellow solution of Na2CrO4 .
CrO2Cl2+4NaOH→Na2CrO4+2NaCl+2H2O

Topic: Chemistry, d and f Block Elements, JEE Main
Which of the following statement is correct with refrence to RSÎ and ROÎ . ?

Options:
A RSΘ is less basic and less nucleophilic than ROΘ
B RSΘ is less basic but more nucleophilic than ROΘ
C RSΘ is less basic and more nucleophilic than ROΘ
D RSΘ is more basic but less nucleophilic than ROΘ

The correct answer is:
RSΘ is less basic but more nucleophilic than ROΘ

Solution:
Nucleophilic strength increases down a column of the Periodic Table (in solvents
that can have hydrogen bonds, such as water, alcohols, thio alcohols).
Nucleophilic strength ROΘ<RSΘ . Base strength ROΘ>RSΘ . Thus, RSΘ is more nucleophilic but less basic than ROΘ

Topic: Chemistry, General Organic Chemistry, JEE Main
Which of the following statement is correct with respect to the property of elements in the carbon family with an increase in atomic number, their

Options:
A Atomic size decreases
B Ionization energy increases
C Metallic character decreases
D Stability of +2 oxidation state increases

The correct answer is:
Stability of +2 oxidation state increases

Solution:
In carbon family stability +2 oxidation state increases on moving down the group in the periodic table with an increase in atomic number due to screening effect.

Topic: Chemistry, p Block Elements (Group 13 & 14), JEE Main
Which of the following statement is equivalent to the statement "If 2+2=4 then India is a country"?

Options:
A 2+2=4 or India is a country
B 2+2=4 and India is a country
C 2+2≠4 or India is a country
D 2+2=4 or India is not a country

The correct answer is:
2+2≠4 or India is a country

Solution:
Let p: 2+2=4
q: India is a country
p→q≡~p∨q

Topic: Mathematics, Mathematical Reasoning, JEE Main
Which of the following statement is false?

Options:
A Permanent magnetic moment of [CuNH3)42+ is 1.732 B.M.
B Equilibrium constant is the ratio of rate constants of forward and backward reactions
C [NiCO)4 is tetrahedral
D For forming NCl5 'N' adopts sp3d hybrid state

The correct answer is:
For forming NCl5 'N' adopts sp3d hybrid state

Solution:
As vacant d-orbitals are not available in nitrogen hence it can not exhibit a valency of 5 i.e. NCl5 is not possible. Rest other statements are correct here.
Keq=KfKb
[NiCO)4 is tetrahedral as Ni is having sp3 hybridisation.
Permanent magnetic moment of [CuNH3)42+ is 1.732 B.M as in it Cu2+ has 1 unpaired electron so μ=nn+2=11+2=1.73 BM

Topic: Chemistry, Coordination Compounds, JEE Main
Which of the following statement is false?

Options:
A Ca2+ ions are not important in maintaining the regular beating of the heart.
B Mg2+ ions are important in the green parts of the plants.
C Mg2+ ions form a complex with ATP.
D Ca2+ ions are important in blood clotting.

The correct answer is:
Ca2+ ions are not important in maintaining the regular beating of the heart.

Solution:
Ca2+ ions are important in maintaining the regular beating of the heart. Ca2+ ions are also important in blood clotting and are required to trigger the contraction of muscle.

Topic: Chemistry, s Block Elements, NEET
Which of the following statement is FALSE?

Options:
A TMV has a double stranded RNA molecule.
B Most plant viruses are RNA viruses.
C Bacteriophage has a double stranded DNA molecule.
D Most animal viruses are DNA viruses.

The correct answer is:
TMV has a double stranded RNA molecule.

Solution:
Tobacco mosaic virus (TMV) is a virus of the tobacco plant and infects a wide range of plants mainly members from the family Solanaceae. This virus has single stranded RNA as the genetic material.
Bacteriophages are viruses that infect bacteria and their genetic material is double stranded DNA. Also, majority of the animal viruses are DNA viruses. Although, the viruses infecting plants are mainly RNA viruses.

Topic: Biology, Biological Classification, NEET
Which of the following statement is false

Options:
A Every solid substance can be brought into colloidal state
B Colloidal particles carry electrical charges
C Every solid substance can be made to behave like a lyophilic colliod
D Addition of electrolytes causes flocculation of colloidal particles

The correct answer is:
Every solid substance can be made to behave like a lyophilic colliod

Solution:
Correct option is 3. Every solid substance can be made to behave like a lyophilic colloid
Every solid substance is not a lyophilic colloid.

Topic: Chemistry, Surface Chemistry, JEE Main
Which of the following statement is false for the properties of electromagnetic waves?

Options:
A Both electric and magnetic field vectors attain the maxima and minima at the same place and same time
B The energy in electromagnetic wave is divided equally between electric and magnetic vectors
C Both electric and magnetic field vectors are parallel to each other and perpendicular to the direction of propagation of wave
D These waves do not require any material medium for propagation

The correct answer is:
Both electric and magnetic field vectors are parallel to each other and perpendicular to the direction of propagation of wave

Solution:
The time varying electric and magnetic fields are mutually perpendicular to each other and also perpendicular to the direction of propagation of the wave.

Topic: Physics, Electromagnetic Waves, JEE Main
Which of the following statement is false for trisilylamine ?

Options:
A Three $\mathrm{sp}^2$ orbitals are used for $\sigma$ bonding, giving a plane triangular structure.
B The lone pair of electrons occupy a p-orbital at right angles to the plane triangle and this overlaps
C The $\mathrm{N}-\mathrm{Si}$ bond length is shorter than the expected $\mathrm{N}-\mathrm{Si}$ bond length.
D It is a weaker Lewis base than trimethyl amine.

The correct answer is:
The lone pair of electrons occupy a p-orbital at right angles to the plane triangle and this overlaps

Solution:
There is $p \pi-d \pi$ delocalization of lone pair of electron on nitrogen atom and empty d-orbital of silicon but not $\mathrm{p} \pi-\mathrm{p} \pi$, one of the $2 \mathrm{~s}$-orbital electrons jumps to the last $\mathrm{P}_{\mathrm{Z}}$ orbital and does not participate in $\mathrm{sp}^2$ hybridisation.

Topic: Chemistry, Chemical Bonding and Molecular Structure, JEE Main
Which of the following statement is incorrect?

Options:
A Different substances move independently along their concentration gradient in mass flow.
B Active absorption of ions from the soil by the root is mainly affected by respiratory activity of root.
C The translocation of organic solutes in sieve tube members is supported by mass flow.
D Root pressure develops due to active absorption.

The correct answer is:
Different substances move independently along their concentration gradient in mass flow.

Solution:
Mass or bulk flow is the movement of substances in bulk from source to sink as a result of pressure differences. Mass flow is not to be confused with diffusion which depends on concentration gradients within a medium rather than pressure gradients of the medium itself.

Topic: Biology, Transport in Plants, NEET
Which of the following statement is incorrect?

Options:
A In some Pteridophytes (Selaginella, Salvinia) sporophylls may form distinct compact structures called strobili or cones.
B The Pteridophytes include Horsetails and Ferns
C In Pteridophytes, the main plant body is a sporophyte
D In Pteridophyta sexual reproduction is isogamous

The correct answer is:
In Pteridophyta sexual reproduction is isogamous

Solution:
In Pteridophyta sexual reproduction is oogamous in which multicellular and jacketed sex organs are produced. The male sex organ is antheridium which produces a flagellated male gamete and female sex organ is archegonium which produces single female gamete called egg cell.

Topic: Biology, Plant Kingdom, NEET
Which of the following statement is INCORRECT?

Options:
A Each actin filament is made of two G actin
B Each F actin is a polymer of G actin
C Troponin is a complex protein distributed at regular intervals on tropomyosin
D Tropomyosin run close to F - actin along its length

The correct answer is:
Each actin filament is made of two G actin

Solution:
Actin and Myosin are contractile proteins while Troponin and Tropomyosin are regulatory proteins involved in muscle contraction. Myosin is important protein of Dark bands while remaining three are proteins of light bands. Actin consists of two F actins which is made up of many monomeric units G actin. Troponin masks the actin filament and thus covers the myosin binding sites. Tropomyosin are trimeric structures that run close to F actin.

Topic: Biology, Locomotion and Movement, NEET
Which of the following statement is incorrect

Options:
A Silver glance mainly contains silver sulphide
B Gold is found in native state
C Zinc blende mainly contain zinc chloride
D Copper pyrites also contain Fe2S3

The correct answer is:
Zinc blende mainly contain zinc chloride

Solution:
Zinc blende is ZnS not ZnCl2
Therefore the statement that Zinc blende mainly contain zinc chloride is wrong.

Topic: Chemistry, General Principles and Processes of Isolation of Metals, NEET
Which of the following statement is incorrect?

Options:
A Low solubility of LiF in water is due to its small hydration enthalpy.
B KO2 is paramagnetic.
C Solution of sodium in liquid ammonia is conducting in nature.
D Sodium metal has higher density than potassium metal

The correct answer is:
Low solubility of LiF in water is due to its small hydration enthalpy.

Solution:
Due to the small size of Li+ ion and F-ions, the lattice energy of LiF is very high. LiF is covalent in nature. Therefore, LiF is insoluble in water.

KO2 has 1 unpaired electron in π⋆2p Molecular orbital of O2- . Therefore, it is Paramagnetic.

Lithium has lesser atomic weight than sodium. So, lithium has lesser density than sodium. But in the case of 'K' and 'Na', d-orbitals present in Potassium, which increases the volume of 'K'.

Solution of sodium in liquid ammonia is conducting in nature, due to presence of free electron.

Topic: Chemistry, s Block Elements, JEE Main, JEE Main 2022 (28 Jul Shift 1)
Which of the following statement is incorrect about electrostatic precipitators?

Options:
A ESP can remove over 99% particulate matter present in exhaust from a thermal power plant.
B Collecting plates are grounded, so it is used to attract the charged dust particle.
C Velocity of air between the plates must be low.
D Electrodes wires that are maintained at hundred volts produces corona.

The correct answer is:
Electrodes wires that are maintained at hundred volts produces corona.

Solution:
ESP can remove over 99% particulate matter present in exhaust from a thermal power plant. The electrodes wire are maintained at several thousand volts, which produces a corona of electrons. These electrons attach to dust particles giving them a net negative charge. The collecting plates are charged and attracts the charged particles, but the velocity of air between the plates must be low enough to allow the dust to fall.

Topic: Biology, Environmental Issues, NEET