datavorous/entrance-exam-dataset huggingface dataset:
What is the radius of curvature of the parabola traced out by the projectile in the previous problem at a point where the particle velocity makes an angle $\frac{\theta}{2}$ with the horizontal?

Options:
A $r=\frac{v^2 \cos ^2 \theta}{g \cos ^2 \frac{\theta}{2}}$
B $r=\frac{2 v \sin \theta}{g \tan \theta}$
C $r=\frac{v \cos \theta}{g \sin ^2 \frac{\theta}{2}}$
D $r=\frac{3 v \cos \theta}{g \cot \theta}$

The correct answer is:
$r=\frac{v^2 \cos ^2 \theta}{g \cos ^2 \frac{\theta}{2}}$

Solution:
Let $v$ be the velocity at the point where it makes an angle $\frac{\theta}{2}$ with the horizontal.
The horizontal component remains unchanged.So,
$v_m \cos \left(\frac{\theta}{2}\right)=u \cos \theta$
$\Rightarrow \quad v=\frac{u \cos \theta}{\cos \left(\frac{\theta}{2}\right)}$ $\ldots$(i)
From figure, $m g \cos \left(\frac{\theta}{2}\right)=\frac{m v^2}{r}$
$r=\frac{v^2}{g \cos \frac{\theta}{2}}$
Putting the value of $v$ from Eq. (i), we get
$r=\frac{v^2 \cos ^2 \theta}{g \cos ^2 \frac{\theta}{2}}$

Topic: Physics, Motion In Two Dimensions, JIPMER, JIPMER 2015
What is the radius of the imaginary concentric sphere that divides the electrostatic field of a metal sphere of a radius 20 cm and charge of 8ââÎ¼C in two regions of identical energy?

Options:
A 30Â cm
B 40 cm
C 60Â cm
D 80Â cm

The correct answer is:
40 cm

Solution:
Energy between shell 1 &â2â= energy outside shell 2.
energy between

shell 1 & 2 =â«r=ar=b12Îµ0KQr22Ã4Ïr2dr
=Îµ0K2Q22Ã4Ïâââ-1rab=Îµ0K2Q22ââ1a-1b
Energy beyond shell 2=â«r=br=â12Îµ0KQr22Ã4Ïr2âdr
=12Îµ0K2Q2Ã4Ï1b
â´ââââââââââââââââââââââââ12Îµ0K2Q2Ã4Ï 1a-1b
=12Îµ0K2Q2Ã4Ï1b
1a=2b
â b = 2a
a= 20 cm
b= 40 cm

Topic: Physics, Electrostatics, JEE Main
What is the rate at which a trapped bubble of $2 \mathrm{~mm}$ diameter rises slightly through a solution of density $13.6 \times 10^3 \mathrm{~kg} / \mathrm{m}^3$ and coefficient of viscosity 1.5 centipoise? Assume, the density of air is negligible and $g=10 \mathrm{~m} / \mathrm{s}^2$.

Options:
A $20 \mathrm{~m} / \mathrm{s}$
B $2 \mathrm{~m} / \mathrm{s}$
C $0.2 \mathrm{~m} / \mathrm{s}$
D $0.02 \mathrm{~m} / \mathrm{s}$

The correct answer is:
$20 \mathrm{~m} / \mathrm{s}$

Solution:
Emperical formula for velocity of small bubbles rising through a fluid is
$$
v_{\text {terminal }}=1.15\left(\frac{g d\left(\rho_f-\rho_g\right)}{\eta_f}\right) \times 10^{-2}
$$
where, $d=$ mean diameter, $\rho_f=$ density of fluid, $\rho_g=$ density of gas of bubble and $\eta_f=$ viscosity index of fluid.
$$
\begin{aligned}
v & =\frac{1.15 \times 10 \times 2 \times 10^{-3} \times 1.3 \times 10^3 \times 10^{-2}}{1.5 \times 10^{-2}} \\
& =19.99 \mathrm{~ms}^{-1}=20 \mathrm{~ms}^{-1} .
\end{aligned}
$$

Topic: Physics, Mechanical Properties of Fluids, JEE Main
What is the ratio between the total acceleration of the electron in singly ionized helium atom and a hydrogen atom, when both are in ground state?

Options:

The correct answer is:
8

Solution:
a=V2r

∵V∝Z,

∵r∝1Z

⇒a∝Z21/Z⇒a∝Z3

aHe+aH=ZHe+ZH3=23=8

Topic: Physics, Atomic Physics, JEE Main
What is the ratio of number of nodal planes present in π 2p * and σ 1s * molecular orbitals ?

Options:
A 0
B ∞
C 2
D 1

The correct answer is:
2

Solution:
No. of Nodal planes in π 2p *  = 2
σ 1s *  = 1

Topic: Chemistry, Chemical Bonding and Molecular Structure, JEE Main
What is the ratio of packing density in fcc, bcc and cubic structure repectively?

Options:
A \( 1: 0.92: 0.70 \)
B \( 0.70: 0.92: 1 \)
C \( 1: 0.70: 0.92 \)
D \( 0.92: 0.70: 1 \)

The correct answer is:
\( 1: 0.92: 0.70 \)

Solution:
Packing density in fcc, bcc and cubic sturture are 0.74, 0.68 and 0.52 respectively.
0.74 0.74 : 0.68 0.74 : 0.52 0.74
1 : 0.92 : 0.70

Topic: Chemistry, Solid State, JEE Main
What is the ratio of radioactive to non-radioactive molecules in the solution when equilibrium is attained?

Options:
A It decreases with time.
B It remains constant.
C It increases with time.
D It fluctuates.

The correct answer is:
It remains constant.

Solution:
In a dynamic equilibrium, the ratio of radioactive to non-radioactive molecules in the solution increases until it attains a constant value.

Topic: Chemistry, Chemical Equilibrium, NEET
What is the ratio of the coordination number of cation and anion in the fluorite structure?

Options:
A \( 1: 4 \)
B \( 4: 8 \)
C \( 8: 4 \)
D \( 2: 3 \)

The correct answer is:
\( 8: 4 \)

Solution:
Fluorite is CaF2

Topic: Chemistry, Solid State, JEE Main
What is the reaction of acetaldehyde with concentrated sulphuric acid?

Options:
A No reaction
B Decomposition
C Charred to black residue
D Polymerisation

The correct answer is:
Decomposition

Solution:

Topic: Chemistry, Aldehydes and Ketones, JEE Main
What is the reason behind the secondary structure of proteins?

Options:
A Peptide bond
B Hydrogen bond
C Covalent bond
D Co-ordinate bond

The correct answer is:
Hydrogen bond

Solution:
Secondary structure is formally defined by the pattern of hydrogen bonds between the amino hydrogen and carboxyl oxygen atoms in the peptide backbone

Topic: Chemistry, Biomolecules, JEE Main
What is the reduction electrode potential (in volts) of copper electrode when $\left[\mathrm{Cu}^{2+}\right]=0.01 \mathrm{M}$ is in a solution at $25^{\circ} \mathrm{C}$ ?
$\left(E^{\circ}\right.$ of $\mathrm{Cu}^{2+} / \mathrm{Cu}$ electrode is $\left.+0.34 \mathrm{~V}\right)$

Options:
A $0.3991$
B $0.2809$
C $0.3105$
D $0.3695$

The correct answer is:
$0.2809$

Solution:
$\begin{aligned} E_{\text {cell }} & =E_{\text {cell }}^{\circ}+\frac{0.0591}{n} \log \left[M^{+}\right] \\ & =0.34+\frac{0.0591}{2} \log [0.01] \\ & =0.34-\frac{0.0591}{2} \times 2 \\ & =0.2809 \text { volt }\end{aligned}$

Topic: Chemistry, Electrochemistry, JEE Main
What is the relationship between bond enthalpy and bond formation?

Options:
A Bond enthalpy decreases during bond formation.
B Bond enthalpy remains constant during bond formation.
C Bond enthalpy increases during bond formation.
D Cannot be determined.

The correct answer is:
Bond enthalpy increases during bond formation.

Solution:
The energy gets released when the bond is formed between two hydrogen atoms, indicating that bond enthalpy increases during bond formation.

Topic: Chemistry, Chemical Bonding and Molecular Structure, NEET
What is the relationship between kinetic energy and the striking of gas particles on the container walls?

Options:
A Kinetic energy decreases with increased striking
B There is no relationship
C Kinetic energy increases with increased striking
D Kinetic energy remains constant

The correct answer is:
Kinetic energy increases with increased striking

Solution:
When a gas is heated, the kinetic energy of the particles increases, and as a result, they strike the walls of the container more frequently, thus exerting more pressure.

Topic: Chemistry, States of Matter, NEET
What is the relationship between meromyosins and the thick filament in a myofibril?

Options:
A Meromyosins are the main component of the thick filament
B Meromyosins run close to the thick filament
C Meromyosins are distributed at regular intervals on the thick filament
D Meromyosins have no relationship with the thick filament

The correct answer is:
Meromyosins are the main component of the thick filament

Solution:
Myosin makes up the thick filament and is a polymerised protein. It is made up of meromyosin, a monomeric protein. Meromyosin has 2 parts: a globular head with short arm, called heavy meromyosin, and the tail, called light meromyosin.

Topic: Biology, Locomotion and Movement, NEET
What is the relationship between natural selection and heritability?

Options:
A Natural selection is not related to heritability
B Heritability is the main factor that drives natural selection
C Natural selection is based on heritable variations
D Heritability is the result of natural selection

The correct answer is:
Natural selection is based on heritable variations

Solution:
Natural selection is based on the observation that variations, which are heritable and which make resource utilization better for few (adapted to habitat better) will enable only those to reproduce and leave more progeny.

Topic: Biology, Evolution, NEET
What is the relationship between species richness and area for different taxa, according to Alexander von Humboldt's observations?

Options:
A Species richness decreases with increasing area
B Species richness remains constant with increasing area
C Species richness increases with increasing area, but only up to a limit
D Species richness decreases logarithmically with increasing area

The correct answer is:
Species richness increases with increasing area, but only up to a limit

Solution:
During his explorations in the wilderness of South American jungles, Alexander von Humboldt observed that within a region, species richness increases with increasing explored area, but only up to a limit. The relationship between species richness and area for a wide variety of taxa turns out to be a rectangular hyperbola.

Topic: Biology, Biodiversity and its Conservation, NEET
What is the relationship between standard electrode potential (Eo) and reducing power for alkali metals?

Options:
A Higher Eo indicates higher reducing power.
B Higher Eo indicates lower reducing power.
C Eo and reducing power are not related.
D Eo remains constant for all alkali metals.

The correct answer is:
Higher Eo indicates lower reducing power.

Solution:
In the context of alkali metals, a more negative standard electrode potential (Eo) indicates higher reducing power. So, higher Eo values correspond to lower reducing power.

Topic: Chemistry, s Block Elements, NEET
What is the relationship between the given structures (look at the arrows)?

Options:
A Enantiomers
B Anomers
C Diastereomers
D Metamers

The correct answer is:
Anomers

Solution:
The isomers which differ in position at C-1 carbon are known as anomers.

Topic: Chemistry, Biomolecules, JEE Main
What is the relationship between the structures below ?

Options:
A Structural isomers
B Diastereomers
C Enantiomers
D Same compound

The correct answer is:
Enantiomers

Solution:
Convert them into Fischer projection form and compare, they are enantiomers.
decide priority according to CIP rule.

Topic: Chemistry, General Organic Chemistry, JEE Main
What is the relationship between the volume of the 1 M NaOH solution and its concentration after dilution?

Options:
A The volume increases, and the concentration decreases
B The volume decreases, and the concentration increases
C The volume and concentration remain the same
D There is no relationship between them

The correct answer is:
The volume increases, and the concentration decreases

Solution:
When the 1 M NaOH solution is diluted to make a 0.2 M solution, the volume increases while the concentration decreases.

Topic: Chemistry, Some Basic Concepts of Chemistry, NEET
What is the relative speed between the two balls as a function of time when one ball is dropped from a building of height 45 m and another ball is thrown up with a speed of 40 m/s?

Options:
A Increases with time
B Decreases with time
C Remains constant at 40 m/s
D Depends on the mass of the balls

The correct answer is:
Remains constant at 40 m/s

Solution:
Correct Option is : (C)
Remains constant at 40 m/s

Topic: Chemistry, Motion In One Dimension, NEET
What is the remainder of \(2 x^3-5 x^2+7\) when divided with \((x-2)\) ?

Options:
A -3
B -2
C 3
D 2

The correct answer is:
3

Solution:
Using remainder theorem, remainder is \(P(x=2)\).
So, remainder is,
\(\begin{aligned}
P(x=2) & =2 \times 2^3-5 \times 2^2+7 \\
& =16-20+7 \\
& =3
\end{aligned}\)

Topic: Mathematics, Binomial Theorem, AP EAMCET, AP EAMCET 2020 (17 Sep Shift 2)
What is the remarkable property of Plaster of Paris when mixed with water?

Options:
A It becomes liquid
B It becomes a gas
C It forms a plastic mass that hardens
D It remains unchanged

The correct answer is:
It forms a plastic mass that hardens

Solution:
Plaster of Paris forms a plastic mass that gets into a hard solid when mixed with water.

Topic: Chemistry, s Block Elements, NEET
What is the required condition, if the light incident on one face of a prism, does not emerge from the other face?

Options:
A n<cosecA2
B n<sec⁡A2
C n>sec⁡A
D n>cosecA2

The correct answer is:
n>cosecA2

Solution:
Consider the situation shown in figure.
Light rays PQ is incident on the face AB. It goes along QR and then along RS.
Here,
i= angle of incidence at the face AB
r1= angle of refraction through AB
r2= angle of incidence at AC
n= refractive index of the material of the prims.
For the prism, we have
r1+r2=A .....(i)
Now for light not to emerge from the face AC,
r2>C
Similarly for no emergence from the face AB,
r1>C
â r1+r2>2C
Here, C is critical angle.
â A>2C âµ r1+r2=A
â A2>C
â sinâ¡A2>sinâ¡C
âsinâ¡A2>1n
â n>1sinâ¡A2
â n>cosecA2

Topic: Physics, Ray Optics, JEE Main
What is the result of the antibiotic revolution in terms of life expectancy?

Options:
A Life expectancy has decreased
B Life expectancy has remained the same
C Life expectancy has almost doubled
D Life expectancy has slightly increased

The correct answer is:
Life expectancy has almost doubled

Solution:
The antibiotic revolution has almost doubled life expectancy.

Topic: Chemistry, Chemistry in Everyday Life, NEET
What is the result of the first meiotic division?

Options:
A Chromosome number is increased
B Chromosome number is reduced to one fourth
C Chromosome number is reduced to half
D Chromosome number remains the same

The correct answer is:
Chromosome number is reduced to half

Solution:
In the first meiotic division, homologous chromosomes pair to form bivalents and undergo crossing over. During anaphase I, homologous chromosomes move to the opposite poles with both their chromatids. Each pole receives half the chromosome number of the parent cell.

Topic: Biology, Cell Cycle and Cell Division, NEET
What is the role of a catalyst in a reversible reactions?

Options:
A Increase the rate of forward reaction
B Decrease the rate of backward reaction
C Alter the equilibrium constant of the reaction
D Allow the equilibrium to be achieved quickly

The correct answer is:
Allow the equilibrium to be achieved quickly

Solution:
An increase in rate of reaction in forward direction by a catalyst for a reaction in equilibrium brings in an increase in concentration of products and thus rate of backward reaction also increase to same magnitude and so allow the equilibrium to be achieved quickly.

Topic: Chemistry, Chemical Equilibrium, JEE Main
What is the role of aldosterone in our body?

Options:
A Maintains the electrolytes, body fluid volume, osmotic pressure and blood pressure
B Stimulates the RBC production
C Stimulates gluconeogenesis and lipolysis
D Promotes production of antibodies

The correct answer is:
Maintains the electrolytes, body fluid volume, osmotic pressure and blood pressure

Solution:
Aldosterone acts mainly at the renal tubules and stimulates the reabsorption of Na+ and water and excretion of K+ and phosphate ions. Thus, aldosterone helps in the maintenance of electrolytes, body fluid volume, osmotic pressure and blood pressure.

Topic: Biology, Chemical Coordination and Integration, NEET
What is the role of charcoal in the production of high vacuum?

Options:
A It releases gases
B It adsorbs remaining traces of air
C It condenses vapors
D It increases pressure

The correct answer is:
It adsorbs remaining traces of air

Solution:
The paragraph mentions that charcoal, in a vessel evacuated by a vacuum pump, adsorbs the remaining traces of air, contributing to the production of very high vacuum.

Topic: Chemistry, Surface Chemistry, NEET
What is the role of contraceptives in reproductive health?

Options:
A Regular requirements for the maintenance of reproductive health
B Practice against a natural reproductive event
C To increase pregnancy
D To check uncontrolled growth of population

The correct answer is:
Practice against a natural reproductive event

Solution:
Contraceptives are practiced against a natural reproductive event, i.e., conception/pregnancy. One is forced to use these methods either to prevent pregnancy or to delay or space pregnancy due to personal reasons.

Topic: Biology, Reproductive Health, NEET
What is the role of cortisol in our body?

Options:
A Maintains the cardiovascular system and kidney functions
B Stimulates the RBC production
C Stimulates gluconeogenesis and lipolysis
D All of the above

The correct answer is:
All of the above

Solution:
Glucocorticoids, particularly cortisol, produces anti-inflammatory reactions and suppresses the immune response. Cortisol stimulates the RBC production and also stimulates gluconeogenesis, lipolysis and proteolysis. Cortisol is also involved in maintaining the cardiovascular system as well as the kidney functions.

Topic: Biology, Chemical Coordination and Integration, NEET
What is the role of ethylene in deep water rice plants?

Options:
A Promotes petiole elongation
B Promotes internode elongation
C Promotes root hair formation
D Promotes root growth

The correct answer is:
Promotes internode elongation

Solution:
Ethylene promotes rapid internode/petiole elongation in deep water rice plants, helping leaves and the upper parts of the shoot to remain above water.

Topic: Biology, Plant - Growth and Development, NEET
What is the role of feathers?

Options:

None

Solution:
Feathers are the epidermal out growths that form distinctive outer covering or plumage in birds.
A variety of role are played by feathers which includes:
(i) They provide life and help in flight, by creating airfoil shape for wings.
(ii) They help in maintaining body temperature.
(iii) Feathers play a vital role in mating by providing secondary sexual that characters in both the sexes the colour and markings determine the alteractiveness of mate.

Topic: Biology, Animal Kingdom
What is the role of glucagon in the body?

Options:
A It promotes the uptake of glucose from the blood into the cells
B It promotes the breakdown of glycogen in the liver to release glucose into the blood
C It promotes the digestion of fats
D It promotes the neutralization of stomach acid

The correct answer is:
It promotes the breakdown of glycogen in the liver to release glucose into the blood

Solution:
Glucagon is a hormone produced by the endocrine portion of the pancreas that promotes the breakdown of glycogen in the liver to release glucose into the blood. This helps to maintain blood glucose levels, especially when glucose uptake by cells is low.

Topic: Biology, Digestion and Absorption, NEET
What is the role of glucagons in maintaining glucose homeostasis?

Options:
A Increases blood glucose levels
B Decreases blood glucose levels
C Maintains glucose homeostasis jointly with insulin
D Does not play a role in maintaining glucose homeostasis

The correct answer is:
Maintains glucose homeostasis jointly with insulin

Solution:
The glucose homeostasis in blood is maintained jointly by insulin and glucagons.

Topic: Biology, Chemical Coordination and Integration, NEET
What is the role of hCG, hPL, and relaxin in pregnancy?

Options:
A They are produced in women only during pregnancy
B They help in the transport of substances to and from the embryo
C They support fetal growth and metabolic changes in the mother
D They maintain pregnancy and increase the levels of other hormones

The correct answer is:
They are produced in women only during pregnancy

Solution:
hCG, hPL, and relaxin are produced in women only during pregnancy.

Topic: Biology, Human Reproduction, NEET
What is the role of Henle's loop and vasa recta in the renal system?

Options:
A To transport NaCl
B To transport urea
C To maintain a concentration gradient in the medullary interstitium
D To produce a dilute urine

The correct answer is:
To maintain a concentration gradient in the medullary interstitium

Solution:
The proximity between the Henle's loop and vasa recta, as well as the counter current in them help in maintaining an increasing osmolarity towards the inner medullary interstitium, which helps in maintaining a concentration gradient in the medullary interstitium.

Topic: Biology, Excretory Products and their Elimination, NEET
What is the role of hormones in pregnancy?

Options:
A To support fetal growth and metabolic changes in the mother
B To produce several hormones like human chorionic gonadotropin (hCG) and human placental lactogen (hPL)
C To maintain pregnancy and support fetal growth
D To increase the levels of other hormones like estrogens and progestogens

The correct answer is:
To maintain pregnancy and support fetal growth

Solution:
During pregnancy, the levels of hormones like estrogens, progestogens, cortisol, prolactin, thyroxine, etC), are increased several-folds in the maternal blooD) Increased production of these hormones is essential for supporting the fetal growth, metabolic changes in the mother, and maintenance of pregnancy.

Topic: Biology, Human Reproduction, NEET
What is the role of hydroxide ions (OH–) in the anion exchange process?

Options:
A To neutralize the H+ ions released in the cation exchange process
B To increase water hardness
C To precipitate hardness ions
D To remove sodium ions

The correct answer is:
To neutralize the H+ ions released in the cation exchange process

Solution:
Hydroxide ions (OH–) in the anion exchange process neutralize the H+ ions released in the cation exchange process, maintaining the overall balance of ions in the water treatment process.

Topic: Chemistry, Hydrogen, NEET
What is the role of increased levels of hormones in pregnancy?

Options:
A To support fetal growth and metabolic changes in the mother
B To produce several hormones like human chorionic gonadotropin (hCG) and human placental lactogen (hPL)
C To maintain pregnancy and support fetal growth
D To increase the levels of other hormones like estrogens and progestogens

The correct answer is:
To maintain pregnancy and support fetal growth

Solution:
Increased production of hormones maintains the pregnancy and supports the foetal growth.

Topic: Biology, Human Reproduction, NEET
What is the role of insulin in glucose utilisation by cells?

Options:
A Inhibits glucose utilisation by cells
B Stimulates glucose utilisation by cells
C Does not play a role in glucose utilisation by cells
D Enhances glucose utilisation by cells

The correct answer is:
Enhances glucose utilisation by cells

Solution:
Insulin acts mainly on hepatocytes and adipocytes and enhances cellular glucose uptake and utilisation.

Topic: Biology, Chemical Coordination and Integration, NEET
What is the role of magnesium in photosynthesis?

Options:
A Synthesis of DNA and RNA
B Activation of enzymes of respiration
C Constituent of the ring structure of chlorophyll
D Maintenance of ribosome structure

The correct answer is:
Constituent of the ring structure of chlorophyll

Solution:
Magnesium is a constituent of the ring structure of chlorophyll and helps to maintain the ribosome structure.

Topic: Biology, Mineral Nutrition, NEET
What is the role of melatonin in the regulation of the human body?

Options:
A Maintaining sleep-wake cycle
B Regulating metabolism
C Stimulating pigmentation
D All of the above

The correct answer is:
All of the above

Solution:
Melatonin plays a very important role in the regulation of a 24-hour (diurnal) rhythm of our body. It helps in maintaining the normal rhythms of sleep-wake cycle, body temperature, influences metabolism, pigmentation, the menstrual cycle, and our defense capability.

Topic: Biology, Chemical Coordination and Integration, NEET
What is the role of nitrogen and oxygen in air pollutants?

Options:
A They are the main air pollutants
B They are pollutants
C They are harmless gases
D They are not mentioned

The correct answer is:
They are harmless gases

Solution:
Smokestacks of thermal power plants, smelters, and other industries release particulate and gaseous air pollutants together with harmless gases, such as nitrogen and oxygen.

Topic: Biology, Environmental Issues, NEET