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Locus of the midpoint of any focal chord of $\mathrm{y}^2=4 \mathrm{ax}$ is

Option: 1
$\mathrm{y}^2=\mathrm{a}(\mathrm{x}-2 \mathrm{a})$

Option: 2
$\mathrm{y}^2=2 \mathrm{a}(\mathrm{x}-2 \mathrm{a})$

Option: 3
$\mathrm{y}^2=2 \mathrm{a}(\mathrm{x}-\mathrm{a})$

Option: 4
$\text{None of these}$

Let the midpoint be $\mathrm{P}(\mathrm{h}, \mathrm{k})$ . Equation of this chord is $\mathrm{\mathrm{T}=\mathrm{S}_1}$ . i.e., $\mathrm{\mathrm{yk}-2 \mathrm{a}(\mathrm{x}+\mathrm{h})=\mathrm{k}^2-4 \mathrm{ah}}$ . It must pass through $(\mathrm{a}, 0)$

$\mathrm{\Rightarrow 2 \mathrm{a}(\mathrm{a}+\mathrm{h})=\mathrm{k}^2-4 \mathrm{ah}}$ . Thus required locus is $\mathrm{\mathrm{y}^2=2 \mathrm{ax}-2 \mathrm{a}^2.}$

Hence option 2 is correct.

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Posted by

SANGALDEEP SINGH

No. of transition state in given figure

Option: 1
1

Option: 2
2

Option: 3
3

Option: 4
4

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Posted by

Mura

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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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Ritika Jonwal

Which of the following is an anionic detergent?
Option: 1 Sodium stearate
Option: 2 Sodium lauryl sulphate
Option: 3 Cetyltrimethyl ammonium bromide
Option: 4 Glyceryl oleate

As we have learned

Phenol formation from Benzenesulphonic acid -

Acidification of sodium salt gives phenol.

- wherein

$C_{6}H_{5}SO_{3}Na+NaOH\xrightarrow[HCl]{fuse}C_{6}H_{5}-OH+Na_{2}SO_{3}$

Sodium lauryl sulphate has anionic charge

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Ritika Jonwal

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

The absolute configuration of is :
Option: 1 (2R, 3S)
Option: 2 (2S, 3R)
Option: 3 (2S, 3S)
Option: 4 (2R, 3R)

As we learnt ,

Chiral Carbon -

Those carbon on which four different groups are present.

- wherein

For C2 $\rightarrow$

$\Rightarrow$ This rotation suggests R but the least prior group is at horizontal position so the configuration is R.

For C3 $\rightarrow$

$\Rightarrow$ This rotation suggests S but the least prior group is at horizontal position so the configuration is S.

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Ritika Jonwal

The equilibrium constant at 298 K for a reaction A+BC+D is 100. If the initial concentration of all the four species were 1 M each, then equilibrium concentration of D (in mol L⁻¹) will be :
Option: 1 0.182
Option: 2 0.818
Option: 3 0.818
Option: 4 1.182

As we dicussed in the concept

Law of Chemical equilibrium -

At a given temperature, the product of concentration of the reaction products raised to the respective stoichiometric coefficient in the balanced chemical equation divided by the product of concentration of the reactants raised to their individual stoichiometric coefficients has a constant value.

- wherein

$aA+bB\rightleftharpoons cC+dD$

$K_{c}=\frac{[C]^{c\:[D]^{d}}}{[A]^{a}\:[B]^{b}}$

$[A],\:[B],\:[C]\:[D]$

are equilibrium concentration

For reaction $A+B\rightleftharpoons C+D$

Initial concentration IM IM IM IM

At equilibarium if degree of dissociation is $A+B\rightleftharpoons C+D\alpha$ then

$A+B\rightleftharpoons C+D$

1- $\alpha$ 1- $\alpha$ H $\alpha$ 1+ $\alpha$

$K_{c}=\frac{(1+\alpha)^{2}}{(1-\alpha)^{2}}=100$

$10=\frac{1+\alpha}{1-\alpha }$

$10-10\alpha =1+\alpha$

9= $11\alpha$

$\alpha =\frac{9}{11}$

Concentration of D is 1+ $\alpha$ =I+ $\frac{9}{11}$

=1.818

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Ritika Jonwal

NEET 2024 Most scoring concepts

Just Study 32% of the NEET syllabus and Score up to 100% marks

The heats of combustion of carbon and carbon monoxide are −393.5 and −283.5 kJ mol⁻¹, respectively. The heat of formation (in kJ) of carbon monoxide per mole is:
Option: 1 110.5
Option: 2 676.5
Option: 3 -676.5
Option: 4 -110

$\mathrm{C_s+O_2_g \rightarrow CO_2_g \: \: \: \: \Delta H= -393.5 KJmol^{-1}}$

$CO_{\left ( g \right )}+\frac{1}{2}O_{2} \: _{\left ( g \right )}\rightarrow CO_{2} \:_{(g)} \: \: \: \: \: \Delta H=-283.5 kJmol^{-1}$

$C_{\left ( s \right )}+\frac{1}{2}O_{2} \:_{\left ( g \right )}\rightarrow CO_{\left ( g \right )}$

$\therefore \Delta H= -393.5+283.5$

$= -110.0\ kJmol^{-1}$

Therefore, Option(4) is correct

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Ritika Jonwal

The concentration of fluoride, lead, nitrate, and iron in a water sample from an underground lake was found to be 1 ppm, 40 ppm, 100 ppm and 0.2 ppm, respectively. This water is unsuitable for drinking due to high concentration of :
Option: 1 Fluoride
Option: 10 Lead
Option: 19 Nitrate
Option: 36 Iron

As we learned in concept

Hard Water -

It contains calcium and Magnesium salt in the form of hydrogen carbonate , chloride and sulphate

- wherein

Hard water does not give Lathers with soap.

Maximum permissible concentration of constituents

lead : 50 ppm

nitrate : 50 ppm

Iron : 0.2 ppm

fluoride: 1 ppm

Therefore, option (3) is correct.

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Ritika Jonwal

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Which one of the following statements about water is FALSE?
Option: 1 Water is oxidized to oxygen during photosynthesis..
Option: 2 Water can act both as an acid and as a base
Option: 3 There is extensive intramolecular hydrogen bonding in the condensed phase
Option: 4 Ice formed by heavy water sinks in normal water.

There is intermolecular hydrogen bounding in condensed phase of water and not intramolecular hydrogen bonding.

During Photosynthesis, Water is oxidised to Oxygen according to the reaction

$6CO_2 + 6 H_2O \quad \longrightarrow \quad C_6H_{12}O_6 + 6O_2$

Water can react with both acid as well as base

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Posted by

Ritika Jonwal

The correct sequence of reagents for the following conversion will be :
Option: 1 $CH_{3}MgBr, \; \left [ Ag\left ( NH_{3} \right )_{2} \right ]^{+}OH^{-} , H^{+}/CH_{3}OH$

Option: 3 $\left [ Ag\left ( NH_{3} \right )_{2} \right ]^{+}OH^{-},$ $CH_{3}MgBr,$ $H^{+}/CH_{3}OH$

Option: 5 $\left [ Ag\left ( NH_{3} \right )_{2} \right ]^{+}OH^{-},$ $H^{+}/CH_{3}OH$ , $CH_{3}MgBr,$

Option: 7 $CH_{3}MgBr,$ $H^{+}/CH_{3}OH$ , $\left [ Ag\left ( NH_{3} \right )_{2} \right ]^{+}OH^{-},$

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Get Answers to all your Questions

All Questions

Locus of the midpoint of any focal chord of is Option: 1 Option: 2 Option: 3 Option: 4

Posted by

SANGALDEEP SINGH

No. of transition state in given figure Option: 1 1Option: 2 2Option: 3 3Option: 4 4

Posted by

Mura

Crack CUET with india's "Best Teachers"

Posted by

Ritika Jonwal

Which of the following is an anionic detergent? Option: 1 Sodium stearate Option: 2 Sodium lauryl sulphate Option: 3 Cetyltrimethyl ammonium bromide Option: 4 Glyceryl oleate

Posted by

Ritika Jonwal

JEE Main high-scoring chapters and topics

The absolute configuration of is : Option: 1 (2R, 3S) Option: 2 (2S, 3R) Option: 3 (2S, 3S) Option: 4 (2R, 3R)

Posted by

Locus of the midpoint of any focal chord of $\mathrm{y}^2=4 \mathrm{ax}$ is

Option: 1
$\mathrm{y}^2=\mathrm{a}(\mathrm{x}-2 \mathrm{a})$

Option: 2
$\mathrm{y}^2=2 \mathrm{a}(\mathrm{x}-2 \mathrm{a})$

Option: 3
$\mathrm{y}^2=2 \mathrm{a}(\mathrm{x}-\mathrm{a})$

Option: 4
$\text{None of these}$

No. of transition state in given figure

Option: 1
1

Option: 2
2

Option: 3
3

Option: 4
4

Which of the following is an anionic detergent?
Option: 1 Sodium stearate
Option: 2 Sodium lauryl sulphate
Option: 3 Cetyltrimethyl ammonium bromide
Option: 4 Glyceryl oleate

The absolute configuration of is :
Option: 1 (2R, 3S)
Option: 2 (2S, 3R)
Option: 3 (2S, 3S)
Option: 4 (2R, 3R)

The equilibrium constant at 298 K for a reaction A+BC+D is 100. If the initial concentration of all the four species were 1 M each, then equilibrium concentration of D (in mol L⁻¹) will be :
Option: 1 0.182
Option: 2 0.818
Option: 3 0.818
Option: 4 1.182

The heats of combustion of carbon and carbon monoxide are −393.5 and −283.5 kJ mol⁻¹, respectively. The heat of formation (in kJ) of carbon monoxide per mole is:
Option: 1 110.5
Option: 2 676.5
Option: 3 -676.5
Option: 4 -110