datavorous/entrance-exam-dataset huggingface dataset:
Which of the following is the correct prediction about observed \( \mathrm{B}-\mathrm{F} \) bond length in \( \mathrm{BF}_{3} \) molecule?

Options:
A \( \mathrm{B}-\mathrm{F} \) bond length in \( \mathrm{BF}_{3} \) is found to be less than theoretical value because the electronegativity values of \( \mathrm{B}(2.04) \) and 4.0) suggest the bond length to be ionic and hence, the attraction between oppositely charged ions must decrease the nd length.
B \( \mathrm{BF}_{3} \) and \( \left[\mathrm{BF}_{4}\right]^{-} \)have equal \( \mathrm{B}-\mathrm{F} \) bond length.
C The decrease in the \( \mathrm{B}-\mathrm{F} \) bond length in \( \mathrm{BF}_{3} \) is due to delocalised \( \mathrm{p} \pi-\mathrm{p} \pi \) bonding between vacant \( 2 \mathrm{p} \) orbital of \( \mathrm{B} \) filled 2p orbital of \( \mathrm{F} \)
D The correct \( \mathrm{B}-\mathrm{X} \) bond length order is \( \mathrm{B}-\mathrm{F}>\mathrm{B}-\mathrm{Cl}>\mathrm{B}-\mathrm{Br}>\mathrm{B}-\mathrm{I} \)

The correct answer is:
The decrease in the \( \mathrm{B}-\mathrm{F} \) bond length in \( \mathrm{BF}_{3} \) is due to delocalised \( \mathrm{p} \pi-\mathrm{p} \pi \) bonding between vacant \( 2 \mathrm{p} \) orbital of \( \mathrm{B} \) filled 2p orbital of \( \mathrm{F} \)

Solution:
It has partial double character in BâF bond due to p Ï - p Ï back bonding.

Topic: Chemistry, Chemical Bonding and Molecular Structure, JEE Main
Which of the following is the correct sequence of the noble gases in their group in the periodic table

Options:
A $\mathrm{He}, \mathrm{Ar}, \mathrm{Ne}, \mathrm{Kr}, \mathrm{Xe}, \mathrm{Rn}$
B $\mathrm{Ar}, \mathrm{He}, \mathrm{Kr}, \mathrm{Ne}, \mathrm{Rn}, \mathrm{Xe}$
C $\mathrm{He}, \mathrm{Ne}, \mathrm{Kr}, \mathrm{Ar}, \mathrm{Xe}, \mathrm{Rn}$
D $\mathrm{He}, \mathrm{Ne}, \mathrm{Ar}, \mathrm{Kr}, \mathrm{Xe}, \mathrm{Rn}$

The correct answer is:
$\mathrm{He}, \mathrm{Ne}, \mathrm{Ar}, \mathrm{Kr}, \mathrm{Xe}, \mathrm{Rn}$

Solution:
Sequence of the noble gases is in increasing order of atomic number
$\mathrm{He}=2, \mathrm{Ne}=10, \mathrm{Ar}=18, \mathrm{Kr}=36, \mathrm{Xe}=54, \mathrm{Rn}=86$

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

Options:
A
B
C
D

The correct answer is:

Solution:
Adenosine is a nucleoside which is obtained by combination of adenine with ribose sugar.

Above is the structure of adenosine.

Topic: Chemistry, Biomolecules, JEE Main, JEE Main 2018 (15 Apr)
Which of the following is the correct structure of adenosine ?

Options:
A

B

C

D

The correct answer is:

Solution:
No Solution Available

Topic: Chemistry, Biomolecules, JEE Main, JEE Main 2018 (15 Apr Shift 1 Online)
Which of the following is the dimension, of Magnetic flux?

Options:
A ML2T2I-1
B ML-2T-2I-2
C $\mathrm{ML}^{2} \mathrm{T}^{-2} \mathrm{I}^{-1}$
D ML2T-2I-2

The correct answer is:
$\mathrm{ML}^{2} \mathrm{T}^{-2} \mathrm{I}^{-1}$

Solution:
∵ emf=magnetic fluxTime
WorkCharge Time=Magnetic flux
Magnetic flux=M1L2T-2T1I T
=M1L2T-2I-1

Topic: Physics, Units and Dimensions, JEE Main
Which of the following is the dimensional formula for electric polarisation?

Options:
A M0L-2T1I1
B M-1L-2T1I-1
C M0L-1T1I1
D M1L-2T1I1

The correct answer is:
M0L-2T1I1

Solution:
Electric polarisation (P) is given by
P=ε0χE
where, E is electrical field and χ is electric susceptibility and it is dimensionless quantity, Dimension formula of P = Dimension formula of ε0× Dimension formula of E
=M-1L-3T4I2=M0L-2T1

Topic: Physics, Units and Dimensions, JEE Main
Which of the following is the electron deficient molecule

Options:
A $B_2 H_6$
B $\mathrm{C}_2 \mathrm{H}_6$
C $\mathrm{PH}_3$
D $\mathrm{SiH}_4$

The correct answer is:
$B_2 H_6$

Solution:
$\mathrm{B}_2 \mathrm{H}_6$ is electron deficient because $16$ electrons are required to form 8 normal covalent bonds but only $12$ electrons are available from the $2 \mathrm{~B}$ and $6 \mathrm{H}$ atoms.

Topic: Chemistry, p Block Elements (Group 13 & 14), JEE Main
Which of the following is the energy of a possible excited state of hydrogen?

Options:
A + 6.8 eV
B + 13.6 eV
C - 6.8 eV
D - 3.4 eV

The correct answer is:
- 3.4 eV

Solution:
E n =−13.6× Z 2 n 2 eV Z=1   for  H.
E n = - 13.6 n 2 eV
Where n = 2 ⇒ E 2 = - 3.40 eV

Topic: Chemistry, Structure of Atom, JEE Main, JEE Main 2015 (04 Apr)
Which of the following is the example of $S N^2$ reaction

Options:
A $\mathrm{CH}_3 \mathrm{Br}+\mathrm{OH}^{-} \quad \mathrm{CH}_3 \mathrm{OH}+\mathrm{Br}^{-}$
B

C $\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{OH} \xrightarrow{-\mathrm{H}_2 \mathrm{O}} \mathrm{CH}_2=\mathrm{CH}_2$
D

The correct answer is:
$\mathrm{CH}_3 \mathrm{Br}+\mathrm{OH}^{-} \quad \mathrm{CH}_3 \mathrm{OH}+\mathrm{Br}^{-}$

Solution:
Only $1^{\circ}$ alkyl halides, i.e. $\mathrm{CH}_3 \mathrm{Br}$ undergoes $S_N 2$ reaction.

Topic: Chemistry, Haloalkanes and Haloarenes, JEE Main
Which of the following is the graph of the curve $\sqrt{|y|}=x$ is?

Options:
A

B

C

D

The correct answer is:

Solution:
$\begin{gathered}\sqrt{|y|}=x \quad(\because x\gt0) \\ \Rightarrow \quad|y| \quad=x^2 \\ \Rightarrow \quad y \quad=x^2 \quad y \geq 0 \\ \quad y=-x^2 \quad y \lt 0\end{gathered}$

Topic: Mathematics, Functions, JEE Main
Which of the following is the largest gland in an adult man ?

Options:
A Thymus
B Liver
C Thyroid
D Pancreas

The correct answer is:
Liver

Solution:
Liver is endodermal in origin and is the largest gland in human body. It is the busiest and largest chemical factory in the body.Liver cells secrete bile directly into bile capillaries, which is used in the emulsification and absorption of fats. Besides, it also functions in manufacture of anticoagulant heparin, plasma protein like albumin, fibrinogen and prothrombin and in deamination of proteins.Thyroid gland (measures 3-7 cm in length and 25 gm in weight in adults) a median endocrine gland located below larynx is the largest endocrine gland in the body. Thyroxine $\left(\mathrm{T}_4\right)$, produced by thyroid gland, function mainly in controlling metabolism, ie, basal metabolic rate of the body.Pancreas is a mixed gland (heterocrine gland) with both exocrine and endocrine portions. The average length of pancreas is $12-15 \mathrm{~cm}$ and weight is $50-70 \mathrm{gm}$. Insulin, glucagon, somatostatin are the hormones secreted by different cells of endocrine portion of pancreas.Thymus gland (at birth weights 10-12 gm, at puberty $20-30 \mathrm{gm}$ and at old age it weighs 3-6 gm ) is mainly concerned with immunological functions but becomes inconspicuous after puberty.

Topic: Biology, Digestion and Absorption, JIPMER, JIPMER 2009
Which of the following is the main application of Zener diode?

Options:
A Amplifier
B Multivibrator
C Voltage regulator
D Rectifier

The correct answer is:
Voltage regulator

Solution:
- A Zener diode is used as a voltage regulator in reverse biased mode.
- The breakdown voltage in the Zener diode when connected in the reverse-biased is called Zener voltage. This Zener voltage so steady and constant it has huge applications circuits, most importantly, voltage regulation.

Topic: Physics, Semiconductors, JEE Main
Which of the following is the main commercial method for the production of dinitrogen?

Options:
A The liquefaction and fractional distillation of air
B The treatment of an aqueous solution of ammonium chloride with sodium nitrite
C The thermal decomposition of ammonium dichromate
D The thermal decomposition of sodium or barium azide

The correct answer is:
The liquefaction and fractional distillation of air

Solution:
The paragraph states that dinitrogen is produced commercially by the liquefaction and fractional distillation of air. Liquid dinitrogen (b.p. 77.2 K) distils out first leaving behind liquid oxygen (b.p. 90 K).

Topic: Chemistry, p Block Elements (Group 15, 16, 17 & 18), NEET
Which of the following is the most basic oxide?

Options:
A $\mathrm{SO}_3$
B $\mathrm{SeO}_3$
C $\mathrm{POO}$
D $\mathrm{TeO}$

The correct answer is:
$\mathrm{POO}$

Solution:
Dxygen is common in all oxides of group 16, and electronegativity decreases as we down the group thus basic nature of oxide increase. Herse PoO is the most basic oxide.

Topic: Chemistry, Classification of Elements and Periodicity in Properties, JEE Main
Which of the following is the most basic oxide?

Options:
A $\mathrm{SeO}_2$
B $\mathrm{Al}_2 \mathrm{O}_3$
C $\mathrm{Sb}_2 \mathrm{O}_3$
D $\mathrm{Bi}_2 \mathrm{O}_3$

The correct answer is:
$\mathrm{Bi}_2 \mathrm{O}_3$

Solution:
$\mathrm{Bi}_2 \mathrm{O}_3$ is the most basic oxide because of higher reactivity with acid.
$$
\mathrm{Bi}_2 \mathrm{O}_3+6 \mathrm{HCl} \rightarrow 2 \mathrm{BiCl}_3+3 \mathrm{H}_2 \mathrm{O}
$$
$\mathrm{Al}_2 \mathrm{O}_3$ and $\mathrm{Sb}_2 \mathrm{O}_3$ are amphoteric and $\mathrm{SeO}_2$ is acidic.

Topic: Chemistry, p Block Elements (Group 13 & 14), JEE Main
Which of the following is the most precise device for measuring length?
(a) a Vernier callipers with 20 divisions on the sliding scale coinciding with 19 main scale division
(b) a screw gauge of pitch $1 \mathrm{~mm}$ and 100 divisions on the circular scale
(c) an optical instrument that can measure length within a wavelength of light ?

Options:

None

Solution:
(a) Least count of Vernier callipers
$$
\begin{aligned}
&=1 \mathrm{SD}-1 \mathrm{VD} \\
&=1 \mathrm{SD}-\frac{19}{20} \mathrm{SD}=\frac{1}{20} \mathrm{SD} \\
&=\frac{1}{20} \mathrm{~mm}=0.005 \mathrm{~cm}
\end{aligned}
$$
(b) Least count of screw gauge
$$
\begin{aligned}
&=\frac{\text { pitch }}{\text { no. of division on circu }} \\
&=\frac{1}{100} \mathrm{~mm}=0.001 \mathrm{~cm}
\end{aligned}
$$
(c) Wavelength of light, $\lambda=10^{-5} \mathrm{~cm}$ $=0,00001 \mathrm{~cm}$
Since most precise device should have minimum least count, optical instrument is the most precise one.

Topic: Physics, Units and Dimensions
Which of the following is the most stable alkene

Options:
A $R_2 C=C R_2$
B $\mathrm{RCH}=\mathrm{CHR}$
C $\mathrm{RCH}_2=\mathrm{CH}_2 \mathrm{R}$
D $\mathrm{CH}_2=\mathrm{CH}_2$

The correct answer is:
$R_2 C=C R_2$

Solution:
We know that greater the number of alkyl groups attached to double bonded carbon atoms, more stable is the alkene. Therefore most stable is $R_2 C=C R_2$

Topic: Chemistry, Hydrocarbons, JEE Main
Which of the following is the most stable compound

Options:
A $\mathrm{Ph}_3 \stackrel{+}{\mathrm{C}}$
B $\mathrm{Ph}_2 \stackrel{+}{\mathrm{C}} \mathrm{H}$
C $\mathrm{Ph}_3 \stackrel{+}{\mathrm{C}} \mathrm{H}_2$
D $\stackrel{+}{\mathrm{Ph}} \mathrm{H}_2$

The correct answer is:
$\mathrm{Ph}_3 \stackrel{+}{\mathrm{C}}$

Solution:
Triphenyl methyl cation has three benzene resonating ring so it is most stable compound.

Topic: Chemistry, General Organic Chemistry, JEE Main
Which of the following is the negation of the statement "for all M>0, there exists x∈S such that x≥M''?

Options:
A there exists M>0, such that x<M for all x∈S
B there exists M>0, there exists x∈S such that x≥M
C there exists M>0, there exists x∈S such that x<M
D there exists M>0 such that x≥M for all x∈S

The correct answer is:
there exists M>0, such that x<M for all x∈S

Solution:
P: for all M>0, there exists x∈S such that x≥M

~P: there exists M>0, for all x∈S such that x<m

Negation of 'there exsits' is 'for all'.

Topic: Mathematics, Mathematical Reasoning, JEE Main, JEE Main 2021 (27 Jul Shift 2)
Which of the following is the one common feature found in all types of connective tissues despite their variation in different aspects?

Options:
A Tough collagenous fibres
B Elasticity and strength
C Abundant matrix
D Vascularity

The correct answer is:
Abundant matrix

Solution:
There are four types of animal tissues: Epithelial tissue, Connective tissue, Muscular tissue and Nervous tissue. Connective tissue is the most abundant animal tissue. It is further divided into Lose Connective tissue, Dense Connective tissue and Specialised Tissue. All these types are very different in structure and function but have certain common features. The main feature common to all connective tissue is presence of Matrix. This is seen only in this tissue. It consists of cells and sometimes fibres too.

Topic: Biology, Structural Organisation in Animals, NEET
Which of the following is the product of aldol condensation?

Options:
A

B

C

D

The correct answer is:

Solution:

Topic: Chemistry, Alcohols Phenols and Ethers, JEE Main, JEE Main 2013 (23 Apr Online)
Which of the following is the property of Rydberg constant?

Options:
A It is universal constant
B It is same for all hydrogen like atom
C It depends on the atomic number of the atom
D It depends on the mass number of the atom

The correct answer is:
It is same for all hydrogen like atom

Solution:
We know that, Rydberg constant,
$R=\frac{e^4 m}{8 \varepsilon_0^2 h^3 c}=1.09 \times 10^7 \mathrm{~m}^{-1}$
It remains constant for a atom, like hydrogen or hydrogen like atom.

Topic: Physics, Atomic Physics, AP EAMCET, AP EAMCET 2021 (24 Aug Shift 2)
Which of the following is the strongest acid?

Options:
A CIO3(OH)
B CIO2(OH)
C SO(OH)2
D SO2(OH)2

The correct answer is:
CIO3(OH)

Solution:
As you go from left to right in the periodic table, the acidic strength goes on increasing. Also, as you increases the oxidation state of the central atom, the acidic strength increases.
The more the electronegativity and oxidation number of the central atom (Cl), more is the acidic character.

Topic: Chemistry, Classification of Elements and Periodicity in Properties, JEE Main
Which of the following is the strongest base?

Options:
A
< smiles>Nc1ccccc1 < /smiles>
B
< smiles>NCc1ccccc1 < /smiles>
C
< smiles>Cc1ccccc1N < /smiles>
D
< smiles>CNc1ccccc1 < /smiles>

The correct answer is:
< smiles>NCc1ccccc1 < /smiles>

Solution:
No Solution Available

Topic: Chemistry, Amines, JEE Main, JEE Main 2004
Which of the following is the strongest base :-

Options:
A

B

C

D

The correct answer is:

Solution:
Order acidic strength :

Thus the order of basic strength of conjugate base will be opposite.
Hence, the strongest conjugate base is

Basic strength â1/ + Hyperconjugation

Topic: Chemistry, General Organic Chemistry, JEE Main
Which of the following is the strongest oxidising agent

Options:
A $\mathrm{BrO}_3^{-} / \mathrm{Br}^{2+}, E^{\circ}=+1.50$
B $\mathrm{Fe}^{3+} / \mathrm{Fe}^{2+}, E^{\circ}=+0.76$
C $\mathrm{MnO}_4^{-} / \mathrm{Mn}^{2+}, E^{\circ}=+1.52$
D $\mathrm{Cr}_2 \mathrm{O}_7^{2-} / \mathrm{Cr}^{3+}, E^{\circ}=+1.33$

The correct answer is:
$\mathrm{MnO}_4^{-} / \mathrm{Mn}^{2+}, E^{\circ}=+1.52$

Solution:
Higher is the reduction potential stronger is the oxidising agent. Hence in the given options.
$\mathrm{MnO} \mathrm{O}_4$ is, strongest oxidising agent.

Topic: Chemistry, Redox Reactions, JEE Main
Which of the following is the strongest reducing agent in aqueous solution?

Options:
A Na
B Li
C K
D Cs .

The correct answer is:
Li

Solution:
Li+ has very high hydration energy. Therefore, it is the strongest reducing agent in aqueous solution.

Topic: Chemistry, Classification of Elements and Periodicity in Properties, JEE Main
Which of the following is the sweetest sugar?

Options:
A Glucose
B Fructose
C Lactose
D Sucrose

The correct answer is:
Fructose

Solution:
Sugar : frucotse Lactose Glucose Sucrose Relative sweetness 1 6 7 4 1 0 0

Topic: Chemistry, Biomolecules, JEE Main
Which of the following is the unit of mobility of a electron in a conductor?

Options:
A $\mathrm{kg}^{-1} \mathrm{~s}^2 \mathrm{~A}^{-1}$
B $\mathrm{kg}^{-1} \mathrm{~s}^2 \mathrm{~A}$
C $\mathrm{kg}^{-1} \mathrm{~ms}^2 \mathrm{~A}^{-1}$
D $\mathrm{kg} \mathrm{ms}^{-1} \mathrm{~A}^{-1}$

The correct answer is:
$\mathrm{kg}^{-1} \mathrm{~s}^2 \mathrm{~A}$

Solution:
Mobility is given as $\mu=\frac{e \tau}{\mathrm{m}}$
So, unit of $\mu$ is $\frac{\text { coulomb }-\mathrm{sec}}{\mathrm{kg}}$ i.e. $\mathrm{kg}^{-1} \mathrm{~s}^2 \mathrm{~A}$

Topic: Physics, Units and Dimensions, JEE Main
Which of the following is the weakest base?

Options:
A Ethyl amine
B Ammonia
C Dimethyl amine
D Methyl amine

The correct answer is:
Ammonia

Solution:
Alkyl group (an electron releasing $(+I)$ group) increases electron density at N-atom, hence, basic nature is increased.
In ammonia, no alkyl group is present, so it is least basic.

Topic: Chemistry, Amines, JEE Main
Which of the following is the wrong statement?

Options:
A ONCl and ONO- are not isoelectronic
B O3 molecule is bent
C Ozone is violet-black in solid state
D Ozone is paramagnetic gas

The correct answer is:
Ozone is paramagnetic gas

Solution:
A. ONCl=8+7+17=32e- '
ONO-=8+7+8+1=24e- (correct)
B. central atom O is sp2 hybridized with 1 lone pair, so bent shape (correct)
C. Ozone is voilet-black in solid state.
D. O3 has no unpaired electrons, so diamagnetic (correct)

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

Options:
A Dacron
B Nylon
C Polythene
D All of these

The correct answer is:
Polythene

Solution:
Polythene is thermoplasitc.

Topic: Chemistry, Polymers, JEE Main
Which of the following is true?

Options:
A Umbel is a racemose inflorescence where all stalked flower aggregate on the flat receptacle.
B Raceme is a racemose inflorescence having main axis shortened \& flower born acropetally.
C Spadix is a racemose inflorescence having pendulous spike with main axis much flattened.
D Spike is a racemose inflorescence having sessile flowers.

The correct answer is:
Spike is a racemose inflorescence having sessile flowers.

Solution:
Spike is a racemose inflorescence that bears sessile flowers in an acropetal fashion, e.g., chaff flower (Achyranthes), bottle brush (Callistemon), Adathoda vasica, Amaranthus.

Topic: Biology, Morphology of Flowering Plants, AIIMS, AIIMS 2009
Which of the following is true?

Options:
A $\int_{0}^{1} e^{x} d x=e$
B $\int_{0}^{1} 2^{x} d x=\log 2$
C $\int_{0}^{1} \sqrt{x} d x=\frac{2}{3}$
D $\int_{0}^{1} x d x=\frac{1}{3}$

The correct answer is:
$\int_{0}^{1} \sqrt{x} d x=\frac{2}{3}$

Solution:
$\int_{0}^{1} e^{x} d x=\left[e^{x}\right]_{0}^{1}=e-1$
(b) $\int_{0}^{1} 2^{x} d x=\left[\frac{2^{x}}{\log _{e} 2}\right]_{0}^{1}=\frac{1}{\log 2} \cdot\left(2-2^{0}\right)=\frac{1}{\log 2}$
(c) $\int_{0}^{1} \sqrt{x} d x=\left[\frac{x^{3 / 2}}{3 / 2}\right]_{0}^{1}=\frac{2}{3}$
(d) $\int_{0}^{1} x d x=\left[\frac{x^{2}}{2}\right]_{0}^{1}=\frac{1}{2}$

Topic: Mathematics, Definite Integration, JEE Main
Which of the following is true about freons?

Options:
A These are chlorofluorocarbon compounds
B These are chemicals causing skin cancer
C These are radicals of chlorine and chlorine monoxide
D All radicals are called freons

The correct answer is:
These are chlorofluorocarbon compounds

Solution:
Freons are chlorofluorocarbon compounds that contains only carbon, chlorine, and fluorine, produced as a volatile derivative of methane, ethane and propane.

Topic: Chemistry, Environmental Chemistry, JEE Main, JEE Main 2023 (24 Jan Shift 1)
Which of the following is TRUE about ionic solids?

Options:
A In fused state, ionic solids do not conduct electricity.
B In aqueous solution, ionic solids do not conduct electricity.
C In solid state, free electrons are available in ionic solids.
D In solid state, ionic solids do not conduct electricity.

The correct answer is:
In solid state, ionic solids do not conduct electricity.

Solution:
In solid state, ionic solids do not conduct electricity. This is mainly due to the presence of strong electrostatic force in between the ions due to which they are not mobile and show no conduction in solid phase. However, when they are in solution or in fused state they show high conductance.

Topic: Chemistry, Solid State, JEE Main
Which of the following is true about the chromatids?

Options:
A It is a haploid chromosome
B It is a complete chromosome
C It is a duplicate chromosome
D It is one-half of the replicated chromosome

The correct answer is:
It is one-half of the replicated chromosome

Solution:
It is one-half of the replicated chromosome. DNA replication occurs during S phase of cycle cell thus DNA contents doubles. The two chromatids represents the two replicated DNA which remain attached a a point called as centromere.

Topic: Biology, Cell Cycle and Cell Division, NEET
Which of the following is true for life cycle of bryophytes?

Options:
A Dominant, diploid, multicellular sporophyte alters dominant with multicellular gametophytes.
B Dominant haploid multicellular gametophyte which alternates with diploid sporophyte.
C The plant body shows diplontic life cycle.
D The plant body shows haplontic life cycle.

The correct answer is:
Dominant haploid multicellular gametophyte which alternates with diploid sporophyte.

Solution:
In Bryophyta main plant body is haploid gametophyte which alternates with a small dependent sporophyte. Gametophyte is multicellular green and photosynthetic but the sporophyte lacks independent existence and depends on gametophyte completely or partially.

Topic: Biology, Plant Kingdom, NEET
Which of the following is true for yx that satisfies the differential equation

dydx=xy-1+x-y; y0=0

Options:
A y1=e-12-1
B y1=e12-e-12
C y1=1
D y1=e12-1

The correct answer is:
y1=e-12-1

Solution:
Given dydx=1+yx-1

⇒dy(y+1)=x-1dx

Integrate both the sides we get,

lny+1=x22-x+c

Given y0=0⇒c=0

∴ y=ex22-x-1

Topic: Mathematics, Differential Equations, JEE Main, JEE Main 2021 (17 Mar Shift 1)
Which of the following is true?
(i) If p is a statement then ~p is not a statement
(ii) If p is a statement then ~p is also a statement
(iii) Negation of "p: x is a positive real number" is, "x is a negative real number"

Options:
A Only (ii)
B Only (i)
C (i) and (iii)
D None of these

The correct answer is:
Only (ii)

Solution:
As per definition of statement,negation of a statement is also a statement
Negation of p will be x is not a positive real number.

Topic: Mathematics, Mathematical Reasoning, JEE Main
Which of the following is true regarding the Bohr model of atoms

Options:
A Assumes that the angular momentum of electrons is quantized
B Uses Faraday's laws
C Predicts continuous emission spectra for atoms
D Predicts the same emission spectra for all types of atoms

The correct answer is:
Assumes that the angular momentum of electrons is quantized

Solution:
Bohr model of atoms assumes that the angular momentum of electrons is quantized. The atom is held between the nucleus and surroundings by electrostatic forces. The other options are not valid.

Topic: Physics, Atomic Physics, JEE Main
Which of the following is true when components forming an ideal solution are mixed

Options:
A $\Delta H_m=\Delta V_m=0$
B $\Delta H_m\gt\Delta V_m$
C $\Delta H_m \lt \Delta V_m$
D $\Delta H_m=\Delta V_m=1$

The correct answer is:
$\Delta H_m=\Delta V_m=0$

Solution:
For the ideal solution $\Delta H_{\text {mix }}$ and $\Delta V_{\text {mix }}=0$.

Topic: Chemistry, Solutions, JEE Main
Which of the following is used as a stabilizer during the concentration of sulphide ores?

Options:
A Pine oils
B Fatty acids
C Xanthates
D Cresols

The correct answer is:
Cresols

Solution:
Froth flotation is a process for selectively separating hydrophobic materials from hydrophilic. The principle of froth flotation process is that sulphide ores are preferentially wetted by the pine oil, whereas the gangue particles are wetted by the water. Cresols and aniline are used as froth stabilisers.

Topic: Chemistry, General Principles and Processes of Isolation of Metals, JEE Main, JEE Main 2023 (10 Apr Shift 1)
Which of the following is used as a voltage regulator?

Options:
A Photodiode
B Solar cell
C LED
D Zener diode

The correct answer is:
Zener diode

Solution:
Zener diode was invented by Clarence Melvin Zener. It is designed to operate under reverse bias in the breakdown region and is used as a voltage regulator. It is designed to allow current to flow backward.

Topic: Physics, Semiconductors, JEE Main