datavorous/entrance-exam-dataset huggingface dataset:
Best method of preparing alkyl chloride is

Options:
A $\mathrm{ROH}+\mathrm{SOCl}_2 \longrightarrow$
B $\mathrm{ROH}+\mathrm{PCl}_5 \longrightarrow$
C $\mathrm{ROH}+\mathrm{PCl}_3 \longrightarrow$
D $\mathrm{ROH}+\mathrm{HCl} \xrightarrow{\text { anhy. } \mathrm{ZnCl}_2}$

The correct answer is:
$\mathrm{ROH}+\mathrm{SOCl}_2 \longrightarrow$

Solution:
The chlorination of alcohol by $\mathrm{SOCl}_2$ (thionyl chloride) is the best method for the preparation of alkyl halides as in this method all the other product are gaseous and thus halides are obtained on quite pure state $\mathrm{R}-\mathrm{OH}+\mathrm{SOCl}_2 \xrightarrow{\Delta} \mathrm{R}-\mathrm{Cl}+\mathrm{HCl} \uparrow+\mathrm{SO}_2 \uparrow$

Topic: Chemistry, Haloalkanes and Haloarenes, JEE Main
Best reagent for nuclear iodination of aromatic compounds is

Options:
A $\mathrm{KI} / \mathrm{CH}_{3} \mathrm{COCH}_{3}$
B $I_{2} / C H_{3} C N$
C $\mathrm{KI} / \mathrm{CH}_{3} \mathrm{COOH}$
D $\mathrm{I}_{2} / \mathrm{HNO}_{3}$

The correct answer is:
$\mathrm{I}_{2} / \mathrm{HNO}_{3}$

Solution:
Best reagent for nuclear iodination of aromatic compounds is $\mathrm{I}_{2} / \mathrm{HNO}_{3}$

Topic: Chemistry, Hydrocarbons, JEE Main
Between the following two statements:
Statement I : Let $\vec{a}=\hat{i}+2 \hat{j}-3 \hat{k}$ and $\vec{b}=2 \hat{i}+\hat{j}-\hat{k}$. Then the vector $\vec{r}$ satisfying $\vec{a} \times \vec{r}=\vec{a} \times \vec{b}$ and $\vec{a} \cdot \vec{r}=0$ is of magnitude $\sqrt{10}$.
Statement II : In a triangle $A B C, \cos 2 A+\cos 2 B+\cos 2 C \geq-\frac{3}{2}$.

Options:
A Statement I is incorrect but Statement II is correct.
B Both Statement I and Statement II are correct.
C Statement I is correct but Statement II is incorrect.
D Both Statement I and Statement II are incorrect.

The correct answer is:
Statement I is incorrect but Statement II is correct.

Solution:
$\begin{aligned} & \bar{a}=\hat{i}+2 \hat{j}-3 \hat{k} \\ & \bar{a}=2 \hat{i}+\hat{j}-\hat{k} \\ & \bar{a} \times \bar{r}=\bar{a} \times \bar{b} ; \bar{a} \cdot \bar{r}=0 \\ & \Rightarrow \bar{a} \times(\bar{r}-\bar{b})=\overline{0} \\ & \Rightarrow \bar{a}=\lambda(\bar{r}-\bar{b}) \\ & \bar{a} \cdot \bar{a}=\lambda(\bar{a} \cdot \bar{r}-\bar{a} \cdot \bar{b}) \\ & 14=-7 \lambda \Rightarrow \lambda=-2 \\ & \frac{-\bar{a}}{2}=\bar{r}-\bar{b} \Rightarrow \bar{r}=\bar{b}-\frac{\bar{a}}{2} \\ & =\frac{2 \bar{b}-\bar{a}}{2}=\frac{3 \hat{i}+\hat{k}}{2}\end{aligned}$
Statement (I) is incorrect
$\begin{aligned}
& \cos 2 \mathrm{~A}+\cos 2 \mathrm{~B}+\cos 2 \mathrm{c} \geq-\frac{3}{2} \\
& 2 \mathrm{~A}+2 \mathrm{~B}+2 \mathrm{C}=2 \pi \\
& \cos 2 \mathrm{~A}+\cos 2 \mathrm{~B}+\cos 2 \mathrm{C} \\
& =-1-4 \cos \mathrm{A} \cdot \cos \mathrm{B} \cdot \cos \mathrm{C} \\
& \geq-1-4 \times \frac{1}{2} \times \frac{1}{2} \times \frac{1}{2} \\
& =-\frac{3}{2}
\end{aligned}$
Statement (II) is correct.

Topic: Mathematics, Vector Algebra, JEE Main, JEE Main 2024 (09 Apr Shift 2)
Bidentate ligand is

Options:
A $\mathrm{CN}^{-}$
B Ethylene diammine (en)
C $\mathrm{SCN}^{-}$
D EDTA

The correct answer is:
Ethylene diammine (en)

Solution:
Ethylene diammine (en)

Topic: Chemistry, Coordination Compounds, JEE Main
Binding energy of a certain nucleus is $18 \times 10^8 \mathrm{~J}$. How much is the difference between total mass of all the nucleons and nuclear mass of the given nucleus:

Options:
A $10 \mu \mathrm{g}$
B $20 \mu \mathrm{g}$
C $0.2 \mu \mathrm{g}$
D $2 \mu \mathrm{g}$

The correct answer is:
$20 \mu \mathrm{g}$

Solution:
$\begin{aligned} & \Delta \mathrm{mc}^2=18 \times 10^8 \\ & \Delta \mathrm{m} \times 9 \times 10^{16}=18 \times 10^8 \\ & \Delta \mathrm{m}=2 \times 10^{-8} \mathrm{~kg}=20 \mu \mathrm{g}\end{aligned}$

Topic: Physics, Nuclear Physics, JEE Main, JEE Main 2024 (08 Apr Shift 1)
Binding energy per nucleon verses mass number curve for nuclei is shown in the figure. \( W, X, Y \) and \( Z \) are four nuclei indicated on the curve. The process that would release the energy is,

Options:
A \( Y \rightarrow 2 Z \)
B \( W \rightarrow X+Z \)
C \( W \rightarrow 2 Y \)
D \( X \rightarrow Y+Z \)

The correct answer is:
\( W \rightarrow 2 Y \)

Solution:
Energy is released in a process where the binding energy of the products is greater than the binding energy of the reactants.

Binding energy is given by = BE per nucleon×number of nucleons

For, Y →2Z

Total binding energy of the reactants =8.5×60 MeV

=510 MeV

Total binding energy of the products =2×5×30 MeV

=300 MeV

Binding energy of the product is lesser than that of the reactants.

For, W→X+Y

Total binding energy of the reactants =120×7.5 MeV

=900 MeV

Total binding energy of the products =90×8 + 30×5 MeV

=870 MeV

Here, also the binding energy of the product is lesser than that of the reactants.

For, W→2Y

Total binding energy of the reactants =120×7.5 MeV

=900 MeV

Total binding energy of the products =2×(60×8.5) MeV

=1020 MeV

Here, energy is released as the binding energy of the product is greater than that of the reactants.

For, X→Y+Z

Total binding energy of reactants =90×8 MeV

=720 MeV

Total binding energy of products =60×8.5 +30×5 MeV

=660 MeV

Here, also binding energy of the product is lesser than that of the reactants.

So, energy is released in W→2Y

Topic: Physics, Nuclear Physics, JEE Main
Biochemical Oxygen Demand BOD is the amount of oxygen required (in ppm ):

Options:
A for sustaining life in a water body.
B by bacteria to break-down organic waste in a certain volume of a water sample.
C for the photochemical breakdown of waste present in 1m3 volume of a water body
D by anaerobic bacteria to breakdown. inorganic waste present in a water body.

The correct answer is:
by bacteria to break-down organic waste in a certain volume of a water sample.

Solution:
The amount of oxygen required by bacteria to break down the organic matter present in a certain volume of a sample of water, is called Biochemical oxygen Demand (BOD).

Topic: Chemistry, Environmental Chemistry, JEE Main, JEE Main 2020 (09 Jan Shift 2)
Biochemical Oxygen Demand (BOD) in a river water

Options:
A remains unchanged when algal bloom occurs
B has no relationship with concentration of oxygen in the water
C gives a measure of Salmonetla in the water
D increases when sewage gets mixed with river water

The correct answer is:
increases when sewage gets mixed with river water

Solution:
Biochemical Oxygen Demand (BOD) is the amount of oxygen used for biochemical oxidation by micro-organisms in a unit volume of water. Polluted water has high BOD. Thus, when sewage gets mixed with river water, BOD will increase.

Topic: Biology, Microbes in Human Welfare, NEET, NEET 2009 (Screening)
Biochemical Oxygen Demand (BOD) in a river water :

Options:
A Increases when sewage gets mixed with river water
B Remains unchanged when algal bloom occurs
C has no relationship with concentration of oxygen in the water
D Gives a measure of Salmonella in the water

The correct answer is:
Increases when sewage gets mixed with river water

Solution:
No Solution Available

Topic: Biology, Environmental Issues, NEET, NEET 2009 (Mains)
Biochemical oxygen demand(BOD) value can be a measure of water pollution caused by the organic matter. Which of the following statements is correct?

Options:
A
Polluted water has BOD value higher than $10 \mathrm{ppm}$

B
Aerobic bacteria decreases the BOD value

C
Anaerobic bacteria increases the BOD value

D
Clean water has BOD value higher than 10 ppm

The correct answer is:
Polluted water has BOD value higher than $10 \mathrm{ppm}$

Solution:
Clean water has BOD value less than $5 \mathrm{ppm}$. Polluted water has BOD value higher than 10 ppm.

Topic: Chemistry, Environmental Chemistry, JEE Main, JEE Main 2018 (15 Apr Shift 2 Online)
Biodegradable detergents contains:

Options:
A n-alkyl chain
B polyester group
C phenyl side chain
D cyclohexyl side chain

The correct answer is:
n-alkyl chain

Solution:
Main problem that appears in the use of detergents is that if their hydrocarbon chain is highly branched, then bacteria cannot degrade this easily. Slow degradation of detergents leads to their accumulation.

These days the branching of the hydrocarbon chain is controlled and kept to the minimum. Unbranched chains, i.e., n-alkyl chains can be biodegraded more easily and hence pollution is prevented.

Topic: Chemistry, Chemistry in Everyday Life, NEET
Biodiversity of a geographical region represents

Options:
A endangered species found in the region
B the diversity in the organism living in the region
C genetic diversity present in the dominant species of the region
D species endemic to the region

The correct answer is:
the diversity in the organism living in the region

Solution:
Biodiversity is the term popularised by the sociobiologist Edward Wilson to describe the combined diversity at all the levels of biological organisation. The most important of them are genetic diversity, species diversity and ecological diversity.

Topic: Biology, Biodiversity and its Conservation, NEET, NEET 2011 (Mains)
Biofertilizers include

Options:
A Rhizobium, Azotobacter, Azospirilium and blue green algae (BGA).
B Glomus, Anabaena, Nostoc, Frankia.
C Rhodospirullum, Rhodopseudomonas, Clostridium, Bacillus, Beijerinkia.
D All of these

The correct answer is:
All of these

Solution:
Biofertilizers are organisms that enrich the nutrient quality of the soil. The main sources of biofertilizers are bacteria, fungi and cyanobacteria. These bacteria fix atmospheric nitrogen into organic forms, which is used by the plant as nutrients. The bacteria involved in fixing atmospheric nitrogen are Rhizobium, Frankia, Beijerinkia, Rhodospirullum, Rhodopseudomonas, Azospirillum, Clostridium, Azotobacter, Anabaena, Nostoc etc. They enrich the nitrogen content of the soil. Fungi are also known to form symbiotic associations with plants (mycorrhiza). Many members of the genus Glomus form mycorrhiza. The fungal symbiont in these associations absorbs phosphorus from soil and passes it to the plant. Plants having such associations show other benefits also, such as resistance to root-borne pathogens, tolerance to salinity and drought, and an overall increase in plant growth and development.

Topic: Biology, Microbes in Human Welfare, NEET
Biofertilizers include

Options:
A Nitrogen fixing bacteria
B Nitrogen fixing cyanobacteria
C Both bacteria and cyanobacteria
D Bacteria, cyanobacteria and mycorrhizal fungi

The correct answer is:
Bacteria, cyanobacteria and mycorrhizal fungi

Solution:
Biofertilizers contain microbes, which promote the growth of plants by increasing the supply of essential nutrients to them. It is mainly made up of living organisms which include mycorrhizal fungi, blue-green algae (cyanobacteria), and bacteria.

Topic: Biology, Microbes in Human Welfare, NEET
Biogas is a composition of certain gases. Select the one that is not correct.

Options:
A 30Â âÂ 40%Â CO2
B 30-40%Â CO
C 50Â âÂ 70%Â CH4
D 1 â 5% H2

The correct answer is:
30-40% CO

Solution:
Biogas is a renewable gas formed by the action of anaerobic bacteria. Biogas is mainly composed of methane 50%-70% and carbondioxide 30%-40% and other gases in trace amount. It does not contain carbon monoxide in it.

Topic: Biology, Microbes in Human Welfare, NEET
Biolistics (gene-gun) is suitable for

Options:
A disarming pathogen vectors
B transformation of plant cells
C constructing recombinant DNA by joining with vectors
D DNA fingerprinting

The correct answer is:
constructing recombinant DNA by joining with vectors

Solution:
In biolistic or gene gun method 1-2 $\mu \mathrm{g}$ tungeston or gold particle (called microprojectile) coated with DNA to be used for transformation are accelerated to velocities which enable their entry into plant cells/nuclei. This technique has general applicability to plant species and can be used to deliver DNA into virtually all tissues.

Topic: Biology, Biotechnology - Principles and Processes, NEET, NEET 2012 (Mains)
Biological concept of species is mainly based on

Options:
A reproductive isolation
B morphological features only
C methods of reproduction only
D morphology and methods of reproduction

The correct answer is:
reproductive isolation

Solution:
A species can be defined as a group of closely related organisms which are capable of inbreeding to produce fertile offspring. Thus biological concept of species is mainly based on reproductive isolation, which preserve the integrity of the species by checking hybridization.

Topic: Biology, Evolution, JIPMER, JIPMER 2009
Biological equilibrium is maintained with the help of

Options:
A producers and consumers
B consumers and decomposers
C photosynthesis and transpiration
D photosynthesis and respiration.

The correct answer is:
photosynthesis and respiration.

Solution:
Two process in ecosystem which are necessary to maintain biological equilibrium is photosynthesis and the other is respiration. Photosynthesis is source of energy for all organism on earth and maintains oxygen balance. Respiration is important in carbon cycle.

Topic: Biology, Ecosystem, NEET
Biomass available for consumers and the rate of formation of new organic matter by consumers are respectively:

Options:
A Gross primary productivity and net primary productivity
B Net primary productivity and gross primary productivity
C Gross primary productivity and secondary productivity
D Net primary productivity and secondary productivity

The correct answer is:
Net primary productivity and secondary productivity

Solution:
Total biomass produced by producers is called gross primary productivity (GPP). In producers, some energy or biomass is utilized in respiration and other metabolic processes, so available biomass to next trophic level i.e. primary consumers are called net primary productivity (NPP). In these consumers, some amount of biomass is utilized in respiration and other metabolic processes and the remaining amount is assimilated in tissues, which is called as secondary productivity.

Topic: Biology, Organisms and Populations, NEET
Birds and mammals share one of the following characteristics as a common feature.

Options:
A
Pigmented skin

B
Pneumatic bones

C
Viviparity

D
Warm blooded body

The correct answer is:
Warm blooded body

Solution:
Warm blooded animals are capable of maintaining constant body temperature, irrespective of the surrounding environment, i.e., their body temperature is fixed. Warm blooded body is the characteristic feature in birds and mammals. This characteristic was first evolved in higher reptiles. Birds and mammals have acquired this feature from higher reptiles during evolution.
Pigmented skin is the adaptive feature seen in mammals and not present in birds. Pneumatic bones are found only in birds as their flight adaptation. These reduce body weight for flight. Viviparity is shown by mammals and not by birds as they are oviparous (lay eggs).

Topic: Biology, Animal Kingdom
Bismath has half life of 5 days. If sample originally has a mass of $800 \mathrm{mg}$. then the mass remaining after 30 days will be

Options:
A $10 \mathrm{mg} .$
B $10.5 \mathrm{mg} .$
C $12 \mathrm{mg} .$
D $12.5 \mathrm{mg} .$

The correct answer is:
$12.5 \mathrm{mg} .$

Solution:
Original mass $=800 \mathrm{mg}$.
Half life $=5$ days.
We have to calculate remaining mass after 30 days. Understand that $30 \div 5=6$.
$\begin{aligned} \therefore \text { Mass remaining } &=\left(\frac{1}{2}\right)^{6} \times 800 \\ &=\frac{800}{64}=\frac{100}{8}=12.5 \end{aligned}$

Topic: Mathematics, Differential Equations, MHT CET, MHT CET 2020 (20 Oct Shift 2)
Biuret test is not given by

Options:
A
carbohydrates

B
polypeptides

C
urea

D
proteins

The correct answer is:
carbohydrates

Solution:
It is a test characteristic of amide linkage. Urea also has amide linkage like proteins.

Topic: Chemistry, Biomolecules, JEE Main
Biuret test is not given by

Options:
A
carbohydrates

B
polypeptides

C
urea

D
proteins

The correct answer is:
carbohydrates

Solution:
It is a test characteristic of amide linkage. Urea also has amide linkage like proteins.

Topic: Chemistry, Biomolecules, JEE Main, JEE Main 2010
Black (stem) rust of wheat is caused by

Options:
A Alternaria solani
B Ustilago nuda
C Puccinia graminis
D Xanthomonas oryzae

The correct answer is:
Puccinia graminis

Solution:
Black (stem) rust of wheat is caused by Puccinia graminis tritici, a fungus belonging to Sub-class-Teliomycetidae, OrderUredinales. It is a heteroecious species which completes its life cycle on two plants, ie, barberry (Berberis) plant and wheat (Triticum aestivum .

Topic: Biology, Biotechnology and Its Applications, NEET, NEET 2010 (Mains)
Bleaching action of H2O2 is due to its:

Options:
A oxidising nature
B reducing nature
C acidic nature
D thermal instability

The correct answer is:
oxidising nature

Solution:
It acts as bleaching agent due to the release of nascent oxygen. Thus, the bleaching action of hydrogen peroxide is permanent and it is due to oxidation. It oxidizes the colouring matter to a colourless product.
H2O2→H2O+O

Topic: Chemistry, s Block Elements, JEE Main
Bleaching powder and bleach solution are produced on a large scale and used in several household products. The effectiveness of bleach solution is often measured by iodometry.

Question: Bleaching powder contains a salt of an oxoacid as one of its components. The anhydride of that oxoacid is

Options:
A $\mathrm{Cl}_{2} \mathrm{O}$
B $\mathrm{Cl}_{2} \mathrm{O}_{7}$
C $\mathrm{ClO}_{2}$
D $\mathrm{Cl}_{2} \mathrm{O}_{6}$

The correct answer is:
$\mathrm{Cl}_{2} \mathrm{O}$

Solution:
$\mathrm{Ca}(\mathrm{OCl}) \mathrm{Cl} \longrightarrow \mathrm{Ca}^{2+}+-\mathrm{OCl}+\mathrm{Cl}^{-}$

-OCl (Hypochlorite ion) is anion of the acid HOCl which on dehydration gives $\mathrm{Cl}_{2} \mathrm{O}$.

$2 \mathrm{HOCl} \longrightarrow \mathrm{H}_{2} \mathrm{O}+\mathrm{Cl}_{2} \mathrm{O}$

Topic: Chemistry, Redox Reactions, JEE Main
Bleaching powder and bleach solution are produced on a large scale and used in several household products. The effectiveness of bleach solution is often measured by iodometry.

Question: $25 \mathrm{~mL}$ of household solution was mixed with $30 \mathrm{~mL}$ of $0.50$ M KI and $10 \mathrm{~mL}$ of $4 \mathrm{~N}$ acetic acid. In the titration of the liberated iodine, $48 \mathrm{~mL}$ of $0.25 \mathrm{~N~} \mathrm{Na}_{2} \mathrm{~S}_{2} \mathrm{O}_{3}$ was used to reach the end point. The molarity of the household bleach solution is

Options:
A $0.48 \mathrm{M}$
B $0.96 \mathrm{M}$
C $0.24 \mathrm{M}$
D $0.024 \mathrm{M}$

The correct answer is:
$0.24 \mathrm{M}$

Solution:
Bleach $+2 \mathrm{KI} \longrightarrow \mathrm{I}_{2}+$ Products

$\mathrm{I}_{2}+2 \mathrm{Na}_{2} \mathrm{~S}_{2} \mathrm{O}_{3} \longrightarrow \mathrm{Na}_{2} \mathrm{~S}_{4} \mathrm{O}_{6}+2 \mathrm{NaI}$

Number of millimole of hypo $=0.25 \times 48$

$=2 \times$ millimole of $\mathrm{I}_{2}$

$\therefore$ Number of millimole of $\mathrm{I}_{2}=\frac{0.25 \times 48}{2}=6$

millimole of $\mathrm{I}_{2}=$ millimole of bleach

Molarity of bleaching solution

$=\frac{\text { Millimoles of bleach }}{\text { Vol.(in } \mathrm{mL} \text { ) of bleach }}=\frac{6}{25}=0.24$

Topic: Chemistry, Redox Reactions, JEE Main
Bleaching powder contains a salt of an oxoacid as one of its components. The anhydride of that acid is

Options:
A Cl2O
B Cl2O7
C ClO2
D Cl2O6

The correct answer is:
Cl2O

Solution:
Bleaching powder is CaCl(OCl) i.e. it contains a salt of an oxoacid which is HOCl .
and anhydride of HOCl is Cl2O .
2HOCl→P2O5,ΔCl2O

Topic: Chemistry, p Block Elements (Group 15, 16, 17 & 18), JEE Main
Bleaching powder is correctly represented as

Options:
A $\mathrm{CaOCl}_2$
B $\mathrm{CaO}$
C $\mathrm{CaO}(\mathrm{Cl})$
D $\mathrm{CaCl}(\mathrm{OCl})$

The correct answer is:
$\mathrm{CaCl}(\mathrm{OCl})$

Solution:

Topic: Chemistry, p Block Elements (Group 15, 16, 17 & 18), JEE Main
Bleaching powder produces chloroform on reaction with

Options:
A Phenol
B Nitric acid
C Amine
D Acetone

The correct answer is:
Acetone

Solution:
CaOCl2 is known as bleaching powder.

CHCl3 is known as chloroform.

CaOCl 2 + H 2 O → Ca OH 2 + Cl 2
C CH 3 | CH 3 | = O + 3 Cl 2 → C CH 3 | CCl 3 | = O + 3 HCl
2 C CH 3 | CCl 3 | = O + Ca OH 2 → Ca CH 3 COO | CH 3 COO | + 2 CHCl 3

Topic: Chemistry, p Block Elements (Group 15, 16, 17 & 18), JEE Main
Bleeding is stopped by the application of ferric chloride. This is because

Options:
A Ferric chloride seal the blood cells.
B Blood starts flowing in the other direction
C Blood is coagulated and blood vessel is sealed
D None of these

The correct answer is:
Blood is coagulated and blood vessel is sealed

Solution:
Bleeding can be stopped by ferric chloride as ferric chloride coagulate the blood by which the blood vessel is sealed.

Topic: Chemistry, Surface Chemistry, JEE Main
Bleeding is stopped by the application of ferric chloride. This is because:

Options:
A The blood starts flowing in opposite direction
B The blood reacts and forms a solid, which seals the blood vessel
C The blood is coagulated and thus the blood vessel is sealed
D The ferric chloride seals the blood vessel

The correct answer is:
The blood is coagulated and thus the blood vessel is sealed

Solution:
Blood is a colloidal solution and FeCl 3 is a strong coagulant. Blood contains colloidal impurities and FeCl 3 neutralizes the charge on these colloidal impurities and clotting of blood begins which blocks the vessels and prevents any further flow of blood.

Topic: Chemistry, Surface Chemistry, JEE Main
Blister copper is refined by stirring molten impure metal with green logs of wood because such a wood liberates hydrocarbon gases (like CH4 ). This process X is called ________ and it is used to purify the metal that initially contain impurities of Y. Y is _______.

Options:
A X = poling, Y = CuO2
B X = cupellation, Y = CuO
C X = cupellation, Y = ZnO
D X = poling, Y = Cu2O

The correct answer is:
X = poling, Y = Cu2O

Solution:
Poling is a purification process which is used for metals which contains their own oxide as impurity.

Topic: Chemistry, General Principles and Processes of Isolation of Metals, JEE Main
Block A of mass m and block B of mass 2m are placed on a fixed triangular wedge by means of a massless, inextensible string and a frictionless pulley as shown in the figure. The wedge is inclined at 45Â° to the horizontal on both sides. The coefficient of friction between block A and the wedge is 2/3 and that between block B and the wedge is 1/3. If the blocks A and B are released from rest, find the acceleration of A.

Options:
A 0
B 1
C 2
D 3

The correct answer is:
0

Solution:
Acceleration of block A:
Maximum friction force that can be obtained at A is

(fmax)A =Î¼A(mg cos 450) = 23(mg /â2) = 2mg3

Similarly,
(fmax )B = Î¼B (2mg cos 45Â°) = 13(2mg2)=2mg3
Therefore, maximum value of friction that can be obtained on the system is 22mg3
Net pulling force on the system is

F = F1-F2 =2mg2=mg2=mg2.... (ii)

From Eqs. (i) and (ii), we can see that Net pulling force < fmax

Therefore, the system will not move or the acceleration of block A will be zero.

Topic: Physics, Laws of Motion, JEE Main
Block B starts from rest and accelerates as aB= 12t m s-2. Simultaneously another end of the string is pulled with constant acceleration a0. If at t=3 s, block A comes to rest then the value of a0 (in m s-2) is equal to

Options:

The correct answer is:
18

Solution:
12t â 2aA â a0 = 0
â aA=6t-a02
â«0vdv=â«0t6t-a02 dt
â v=3t2-a02t
â v = 0, â 3t=a02
â a0 = 6t

Topic: Physics, Laws of Motion, JEE Main