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A massless string connects two pulley of masses ' $2 \mathrm{~kg}$ ' and ' $1 \mathrm{~kg}$ ' respectively as shown in the figure.

The heavier pulley is fixed and free to rotate about its central axis while the other is free to rotate as well as translate. Find the acceleration of the lower pulley if the system was released from the rest. [Given, $g=10 \mathrm{~m} / \mathrm{s}^2$ ]
Option: 1
$\frac{4}{3} \mathrm{~gm} / \mathrm{s}^2$

Option: 2
$\frac{3}{2} \mathrm{~gm} / \mathrm{s}^2$

Option: 3
$\frac{3}{4} \mathrm{~gm} / \mathrm{s}^2$

Option: 4
$\frac{2}{3} \mathrm{~gm} / \mathrm{s}^2$

Not understanding sir

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Posted by

Raju vittal nandi

Calculate the acceleration of block $m_1$ of the following diagram. Assume all surfaces are frictionless . Here m₁ = 100kg and m₂ = 50kg

Option: 1
0.33m/s²

Option: 2
0.66m/s²

Option: 3
1m/s²

Option: 4
1.32m/s²

1.32

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Posted by

DHFM DVP

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When cell has stalled DNA replication fork, which checkpoint should be predominantly activated?

Option: 1
G₁/S

Option: 2
G₂/M

Option: 3
M

Option: 4
Both G₂M and M

G₂/M should be activated as the cell has stalled DNA replication fork.

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Posted by

Ajit Kumar Dubey

If $p\rightarrow \left ( p\: \wedge \sim q \right )$ is false, then the truth values of p and q are respectively :
Option: 1 F, T
Option: 2 T, F
Option: 3 F, F
Option: 4 T, T

Relation Between Set Notation and Truth Table -

Sets can be used to identify basic logical structures of statements. Statements have two fundamental roles either it is true or false.

Let us understand with an example of two sets p{1,2} and q{2,3}.

$\begin{array}{|c|c|c|}\hline\quad p\vee q\quad & \quad p\cup q\quad&\quad 1,2,3\quad \\ \hline p\wedge q& p\cap q&2 \\ \hline p^c& \sim p & 3,4 \\ \hline q^c& \sim q&1,4 \\ \hline\end{array}$

Using this relation we get

$\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|}\hline \text{Element } & \mathrm{\;\;\;\;\;}p\mathrm{\;\;\;\;\;}&\mathrm{\;\;\;}q\mathrm{\;\;\;}&\mathrm{\;\;\;\;\;}\sim p\mathrm{\;\;\;\;\;}&\mathrm{\;\;\;}\sim q\mathrm{\;\;\;} &\mathrm{\;\;\;}p\wedge q\mathrm{\;\;}&\mathrm{\;\;}p\vee q\mathrm{\;\;}&\sim\left (p\wedge q \right )\mathrm{\;\;}&\sim p\wedge\sim q\mathrm{\;\;} \\ \hline \hline 1& \mathrm{T}&\mathrm{F} & \mathrm{F} &\mathrm{T}&\mathrm{F}&\mathrm{T}&\mathrm{T}&\mathrm{F} \\ \hline2& \mathrm{T}&\mathrm{T} & \mathrm{F} &\mathrm{F}&\mathrm{T}&\mathrm{T}&\mathrm{F}&\mathrm{T} \\ \hline 3& \mathrm{F}&\mathrm{T} & \mathrm{T} &\mathrm{F}&\mathrm{F}&\mathrm{T}&\mathrm{T}&\mathrm{F} \\ \hline4& \mathrm{F}&\mathrm{F} & \mathrm{T} &\mathrm{T}&\mathrm{F}&\mathrm{F}&\mathrm{T}&\mathrm{F} \\ \hline\end{array}$

Practise Session - 2 -

Q1. Write the truth table for the following statement pattern:
$\\ \mathrm{1.\;\;\;\sim(p \vee((\sim q \Rightarrow q) \wedge q))}\\\mathrm{2.\;\;\;(p\wedge q)\vee(\sim r)}\\$

$\begin{array}{c|c|c}{\mathbf{p}} & {\mathbf{q}} & {(\mathbf{p} \rightarrow(\mathbf{p} \mathbf{\Lambda}-\mathbf{q}))} \\ \hline F & {F} & {\mathbf{T}} \\ \hline F & {T} & {\mathbf{T}} \\ \hline \mathbf{T} & {F} & {\mathbf{T}} \\ \hline \mathbf{T} & {T} & {F}\end{array}$

Correct Option (4)

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Posted by

avinash.dongre

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In a fluorescent lamp choke ( a small transformer) 100 V of reverse voltage is produced when the choke current changes uniformly from 0.25 A to 0 in a duration of 0.025 ms. The self-inductance of the choke (in mH) is estimated to be _____.
Option: 1 10
Option: 2 20
Option: 3 30
Option: 4 40

$V = L\frac{\text d i}{\text d t}\Rightarrow 100 = L\frac{0.25}{0.025} \\ \Rightarrow L = 10 \ \text{mH}$

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Posted by

avinash.dongre

At 300 K and 1 atm, 15 mL of a gaseous hydrocarbon requires 375 mL air containing 20% O₂ by volume for complete combustion. After combustion, the gases occupy 330 mL. Assuming that the water formed is in liquid form and the volumes were measured at the same temperature and pressure, the formula of the hydrocarbon is :
Option: 1 C₄H₈
Option: 2 C₄H₁₀
Option: 3 C₃H₆
Option: 4 C₃H₈

Volume of N₂ in air = 375 × 0.8 = 300 ml

Volume of O₂ in air = 375 × 0.2 = 75 ml

$C_{x}H_{y} +\left ( x +\frac{y}{4} \right )O_{2} \; \rightarrow \; xCO_{2}(g) + \frac{y}{2} H_{2}O(l)$

15ml $15\left ( x +\frac{y}{4} \right )$

0 0 15x -

After combustion total volume

$330 =V_{N_{2}} + V_{CO_{2}}$

330 = 300 + 15x

x = 2

Volume of O₂used

$15\left ( x +\frac{y}{4} \right ) = 75$

$\left ( x +\frac{y}{4} \right ) = 5$

y = 12

So hydrocarbon is = C₂H₁₂

None of the options matches it therefore it is a BONUS.

----------------------------------------------------------------------

Alternatively Solution

$C_{x}H_{y} +\left ( x +\frac{y}{4} \right )O_{2} \; \rightarrow \; xCO_{2}(g) + \frac{y}{2} H_{2}O(l)$

15ml $15\left ( x +\frac{y}{4} \right )$

0 0 15x -

Volume of O₂ used

$15\left ( x +\frac{y}{4} \right ) = 75$

$\left ( x +\frac{y}{4} \right ) = 5$

If further information (i.e., 330 ml) is neglected, option (C₃H₈ ) only satisfy the above equation.

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Posted by

Ritika Jonwal

NEET 2024 Most scoring concepts

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An ideal gas undergoes a quasi static, reversible process in which its molar heat capacity C remains constant. If during this process the relation of pressure P and volume V is given by PVⁿ=constant, then n is given by (Here C_P and C_V are molar specific heat at constant pressure and constant volume, respectively)
Option: 1   $n=\frac{C_{p}}{C_{v}}$

Option: 2   $n=\frac{C-C_{p}}{C-C_{v}}$

Option: 3 $n=\frac{C_{p}-C}{C-C_{v}}$

Option: 4   $n=\frac{C-C_{v}}{C-C_{p}}$

For a polytropic preocess

$c=c_{v}+\frac{R}{1-n} \: or \: \frac{R}{1-n} = c-c_{v}$

$\Rightarrow 1-n=\frac{R}{c-c_{v}} \: or\: n=1-\frac{R}{c-c_{v}}$

$\Rightarrow n=\frac{c-\left ( c_{v}+R \right )}{c-c_{v}} = \frac{c-c_{p}}{c-c_{v}}$

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Posted by

Ritika Jonwal

A point particle of mass m, moves along the uniformly rough track PQR as shown in the figure. The coefficient of friction, between the particle and the rough track equals µ. The particle is released, from rest, from the point P and it comes to rest at a point R. The energies, lost by the ball, over the parts, PQ and QR, of the track, are equal to each other, and no energy is lost when particle changes direction from PQ to QR. The values of the coefficient of friction µ and the distance x(=QR), are, respectively close to :
Option: 1 0.2 and 6.5 m
Option: 3 0.2 and 3.5 m
Option: 4 0.29 and 6.5 m

Work done by friction at QR = μmgx

In triangle, sin 30° = 1/2 = 2/PQ

PQ = 4 m

Work done by friction at PQ = μmg × cos 30° × 4 = μmg × √3/2 × 4 = 2√3μmg

Since work done by friction on parts PQ and QR are equal,

μmgx = 2√3μmg

x = 2√3 ≅ 3.5 m

Applying work energy theorem from P to R

decrease in P.E.=P.E.= loss of energy due to friction in PQPQ and QR

$\\ m g h=(\mu m g \cos \theta) P Q+\mu m g \times Q R\\ h=\mu \cos \theta \times P Q+\mu m g \times Q R\\ h=\mu \cos \theta \times P Q+\mu \times Q R =\mu \cos 30^{\circ} \times 4+\mu \times 2 \sqrt{3} =\mu\left(4 \times \frac{\sqrt{3}}{2}+2 \sqrt{3}\right)\\ h=\mu \times 4 \sqrt{3}\\ \mu=\frac{2}{4 \sqrt{3}}=\frac{1}{2 \sqrt{3}}=0.29$ where h=2(given)

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Ritika Jonwal

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In the following structure, the double bonds are marked as I, II, III and IV Geometrical isomerism is not possible at site (s) :
Option: 1 III
Option: 2 I
Option: 3 I and II
Option: 4 III and IV

Geometrical isomerism is not possible at Site I as two identical methyl groups are attached to the same carbon bearing the double bond.

Hence, the answer is Option (2)

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Posted by

vishal kumar

Which one of the following is an oxide ?
Option: 1 KO₂
Option: 2 BaO₂
Option: 3 SiO₂
Option: 4 CsO₂

SiO₂ - oxide

KO_???2? , CsO_????2 - superoxides

BaO_????2 - peroxide

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Posted by

vishal kumar

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Posted by

Raju vittal nandi

Calculate the acceleration of block of the following diagram. Assume all surfaces are frictionless . Here m1 = 100kg and m2 = 50kg Option: 1 0.33m/s2Option: 2 0.66m/s2Option: 3 1m/s2Option: 4 1.32m/s2

Posted by

DHFM DVP

Crack CUET with india's "Best Teachers"

When cell has stalled DNA replication fork, which checkpoint should be predominantly activated? Option: 1 G1/S Option: 2 G2/M Option: 3 M Option: 4 Both G2 M and M

Posted by

Ajit Kumar Dubey

If is false, then the truth values of p and q are respectively : Option: 1 F, TOption: 2 T, F Option: 3 F, F Option: 4 T, T

Posted by

avinash.dongre

JEE Main high-scoring chapters and topics

In a fluorescent lamp choke ( a small transformer) 100 V of reverse voltage is produced when the choke current changes uniformly from 0.25 A to 0 in a duration of 0.025 ms. The self-inductance of the choke (in mH) is estimated to be _____. Option: 1 10 Option: 2 20 Option: 3 30 Option: 4 40

Posted by

Calculate the acceleration of block $m_1$ of the following diagram. Assume all surfaces are frictionless . Here m₁ = 100kg and m₂ = 50kg

Option: 1
0.33m/s²

Option: 2
0.66m/s²

Option: 3
1m/s²

Option: 4
1.32m/s²

When cell has stalled DNA replication fork, which checkpoint should be predominantly activated?

Option: 1
G₁/S

Option: 2
G₂/M

Option: 3
M

Option: 4
Both G₂M and M

If $p\rightarrow \left ( p\: \wedge \sim q \right )$ is false, then the truth values of p and q are respectively :
Option: 1 F, T
Option: 2 T, F
Option: 3 F, F
Option: 4 T, T

In a fluorescent lamp choke ( a small transformer) 100 V of reverse voltage is produced when the choke current changes uniformly from 0.25 A to 0 in a duration of 0.025 ms. The self-inductance of the choke (in mH) is estimated to be _____.
Option: 1 10
Option: 2 20
Option: 3 30
Option: 4 40

In the following structure, the double bonds are marked as I, II, III and IV Geometrical isomerism is not possible at site (s) :
Option: 1 III
Option: 2 I
Option: 3 I and II
Option: 4 III and IV

Which one of the following is an oxide ?
Option: 1 KO₂
Option: 2 BaO₂
Option: 3 SiO₂
Option: 4 CsO₂