JEE Mains Jan 31, 2023 Shift 2 Questions with solutions

Question 1

When a hydrocarbon A undergoes complete combustion it requires 11 equivalents of oxygen and produces 4 equivalents of water. What is the molecular formula of

A

?

Options:

A)

\mathrm{C}_{9} \mathrm{H}_{8}

B)

\mathrm{C}_{5} \mathrm{H}_{8}

C)

\mathrm{C}_{11} \mathrm{H}_{4}

D)

\mathrm{C}_{11} \mathrm{H}_{8}

Question 2

Cyclohexylamine when treated with nitrous acid yields

(\mathrm{P})

. On treating

(\mathrm{P})

with

\mathrm{PCC}

results in (Q). When

(\mathrm{Q})

is heated with dil.

\mathrm{NaOH}

we get

(\mathrm{R})

The final product (R) is :

Options:

A)

JEE Main 2023 (Online) 31st January Evening Shift Chemistry - Aldehydes, Ketones and Carboxylic Acids Question 44 English Option 1

B)

JEE Main 2023 (Online) 31st January Evening Shift Chemistry - Aldehydes, Ketones and Carboxylic Acids Question 44 English Option 2

C)

JEE Main 2023 (Online) 31st January Evening Shift Chemistry - Aldehydes, Ketones and Carboxylic Acids Question 44 English Option 3

D)

JEE Main 2023 (Online) 31st January Evening Shift Chemistry - Aldehydes, Ketones and Carboxylic Acids Question 44 English Option 4

Question 3

Compound

\mathrm{A}, \mathrm{C}_{5} \mathrm{H}_{10} \mathrm{O}_{5}

, given a tetraacetate with

\mathrm{Ac}_{2} \mathrm{O}

and oxidation of

\mathrm{A}

with

\mathrm{Br}_{2}-\mathrm{H}_{2} \mathrm{O}

gives an acid,

\mathrm{C}_{5} \mathrm{H}_{10} \mathrm{O}_{6}

. Reduction of

\mathrm{A}

with

\mathrm{HI}

gives isopentane. The possible structure of

\mathrm{A}

is

Options:

A)

JEE Main 2023 (Online) 31st January Evening Shift Chemistry - Alcohols, Phenols and Ethers Question 41 English Option 1

B)

JEE Main 2023 (Online) 31st January Evening Shift Chemistry - Alcohols, Phenols and Ethers Question 41 English Option 2

C)

JEE Main 2023 (Online) 31st January Evening Shift Chemistry - Alcohols, Phenols and Ethers Question 41 English Option 3

D)

Question 4

An organic compound

[\mathrm{A}]\left(\mathrm{C}_{4} \mathrm{H}_{11} \mathrm{~N}\right)

, shows optical activity and gives

\mathrm{N}_{2}

gas on treatment with

\mathrm{HNO}_{2}

. The compound

[\mathrm{A}]

reacts with

\mathrm{PhSO}_{2} \mathrm{Cl}

producing a compound which is soluble in

\mathrm{KOH}

. The structure of

\mathrm{A}

is :

Options:

A)

JEE Main 2023 (Online) 31st January Evening Shift Chemistry - Compounds Containing Nitrogen Question 44 English Option 1

B)

JEE Main 2023 (Online) 31st January Evening Shift Chemistry - Compounds Containing Nitrogen Question 44 English Option 2

C)

JEE Main 2023 (Online) 31st January Evening Shift Chemistry - Compounds Containing Nitrogen Question 44 English Option 3

D)

JEE Main 2023 (Online) 31st January Evening Shift Chemistry - Compounds Containing Nitrogen Question 44 English Option 4

Question 5

Which of the following elements have half-filled f-orbitals in their ground state?

(Given : atomic number

\mathrm{Sm}=62 ; \mathrm{Eu}=63 ; \mathrm{Tb}=65 ; \mathrm{Gd}=64, \mathrm{Pm}=61

)

A.

\mathrm{Sm}

B. Eu

C.

\mathrm{Tb}

D. Gd

E.

\mathrm{Pm}

Choose the correct answer from the options given below :

Options:

A)

B and D only

B)

A and

B

only

C)

C

and

\mathrm{D}

only

D)

A and E only

Question 6

Evaluate the following statements for their correctness.

A. The elevation in boiling point temperature of water will be same for

0.1 \mathrm{M} \, \mathrm{NaCl}

and

0.1 \mathrm{M}

urea.

B. Azeotropic mixtures boil without change in their composition.

C. Osmosis always takes place from hypertonic to hypotonic solution.

D. The density of

32 \% \, \mathrm{H}_{2} \mathrm{SO}_{4}

solution having molarity

4.09 ~\mathrm{M}

is approximately

1.26 \mathrm{~g} \mathrm{~mL}^{-1}

E. A negatively charged sol is obtained when KI solution is added to silver nitrate solution.

Choose the correct answer from the options given below :

Options:

A)

A, B and D only

B)

A and C only

C)

B and D only

D)

B, D and E only

Question 7

Arrange the following orbitals in decreasing order of energy.

A.

\mathrm{n}=3, \mathrm{l}=0, \mathrm{~m}=0

B.

\mathrm{n}=4, \mathrm{l}=0, \mathrm{~m}=0

C.

\mathrm{n}=3, \mathrm{l}=1, \mathrm{~m}=0

D.

\mathrm{n}=3, \mathrm{l}=2, \mathrm{~m}=1

The correct option for the order is :

Options:

A)

\mathrm{B}>\mathrm{D}>\mathrm{C}>\mathrm{A}

B)

\mathrm{A}>\mathrm{C}>\mathrm{B}>\mathrm{D}

C)

\mathrm{D}>\mathrm{B}>\mathrm{A}>\mathrm{C}

D)

\mathrm{D}>\mathrm{B}>\mathrm{C}>\mathrm{A}

Question 8

In Dumas method for the estimation of

\mathrm{N}_{2}

, the sample is heated with copper oxide and the gas evolved is passed over :

Options:

A)

Copper oxide

B)

Copper gauze

C)

\mathrm{Pd}

D)

\mathrm{Ni}

Question 9

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R)

Assertion (A): The first ionization enthalpy of

3 \mathrm{~d}

series elements is more than that of group 2 metals

Reason (R): In 3d series of elements successive filling of d-orbitals takes place.

In the light of the above statements, choose the correct answer from the options given below :

Options:

A)

Both (A) and (R) are true and (R) is the correct explanation of (A)

B)

(A) is true but (R) is false

C)

Both (A) and (R) are true but

(\mathbf{R})

is not the correct explanation of (A)

D)

(A) is false but (R) is true

Question 10

A hydrocarbon '

\mathrm{X}

' with formula

\mathrm{C}_{6} \mathrm{H}_{8}

uses two moles of

\mathrm{H}_{2}

on catalytic hydrogenation of its one mole. On ozonolysis, '

\mathrm{X}

' yields two moles of methane dicarbaldehyde. The hydrocarbon '

\mathrm{X}

' is:

Options:

A)

hexa-1, 3, 5-triene

B)

cyclohexa-1, 4-diene

C)

cyclohexa - 1,3 - diene

D)

1-methylcyclopenta-1, 4-diene

Question 11

Given below are two statements :

Statement I: Upon heating a borax bead dipped in cupric sulphate in a luminous flame, the colour of the bead becomes green

Statement II: The green colour observed is due to the formation of copper(I) metaborate

In light of the above statements, choose the most appropriate answer from the options given below :

Options:

A)

Both Statement I and Statement II are false

B)

Both Statement I and Statement II are rue

C)

Statement I is false but Statement II is true

D)

Statement I is true but Statement II is false

Question 12

In the following halogenated organic compounds, the one with the maximum number of chlorine atoms in its structure is :

Options:

A)

Gammaxene

B)

Chloropicrin

C)

Chloral

D)

Freon-12

Question 13

The incorrect statement for the use of indicators in acid-base titration is :

Options:

A)

Phenolphthalein is a suitable indicator for a weak acid vs strong base titration.

B)

Methyl orange may be used for a weak acid vs weak base titration.

C)

Methyl orange is a suitable indicator for a strong acid vs weak base titration.

D)

Phenolphthalein may be used for a strong acid vs strong base titration.

Numerical TypeQuestion 14

Assume carbon burns according to the following equation :

2 \mathrm{C}_{(\mathrm{s})}+\mathrm{O}_{2(\mathrm{~g})} \rightarrow 2 \mathrm{CO}(\mathrm{g})

when

12 \mathrm{~g}

carbon is burnt in

48 \mathrm{~g}

of oxygen, the volume of carbon monoxide produced is ___________

\times 10^{-1} \mathrm{~L}

at STP [nearest integer]

[Given: Assume

\mathrm{CO}

as ideal gas, Mass of

\mathrm{C}

is

12 \mathrm{~g} \mathrm{~mol}^{-1}

, Mass of

\mathrm{O}

is

16 \mathrm{~g} \mathrm{~mol}^{-1}

and molar volume of an ideal gas at STP is

22.7 \mathrm{~L} \mathrm{~mol}^{-1}

]

Numerical TypeQuestion 15

The number of molecules which gives the haloform test among the following molecules is ________.

JEE Main 2023 (Online) 31st January Evening Shift Chemistry - Aldehydes, Ketones and Carboxylic Acids Question 43 English

JEE Main 2023 (Online) 31st January Evening Shift Chemistry - Aldehydes, Ketones and Carboxylic Acids Question 43 English

Numerical TypeQuestion 16

Amongst the following, the number of species having the linear shape is _________.

\mathrm{XeF}_{2}, \mathrm{I}_{3}^{+}, \mathrm{C}_{3} \mathrm{O}_{2}, \mathrm{I}_{3}^{-}, \mathrm{CO}_{2}, \mathrm{SO}_{2}, \mathrm{BeCl}_{2}

and

\mathrm{BCl}_{2}^{\ominus}

Numerical TypeQuestion 17

Enthalpies of formation of

\mathrm{CCl}_{4}(\mathrm{~g}), \mathrm{H}_{2} \mathrm{O}(\mathrm{g}), \mathrm{CO}_{2}(\mathrm{~g})

and

\mathrm{HCl}(\mathrm{g})

are

-105,-242,-394

and

-92 ~\mathrm{kJ}

\mathrm{mol}^{-1}

respectively. The magnitude of enthalpy of the reaction given below is _________

\mathrm{kJ} ~\mathrm{mol}^{-1}

. (nearest integer)

\mathrm{CCl}_{4}(\mathrm{~g})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) \rightarrow \mathrm{CO}_{2}(\mathrm{~g})+4 \mathrm{HCl}(\mathrm{g})

Numerical TypeQuestion 18

At

298 \mathrm{~K}

, the solubility of silver chloride in water is

1.434 \times 10^{-3} \mathrm{~g} \mathrm{~L}^{-1}

. The value of

-\log \mathrm{K}_{\mathrm{sp}}

for silver chloride is _________.

(Given mass of

\mathrm{Ag}

is

107.9 \mathrm{~g} \mathrm{~mol}^{-1}

and mass of

\mathrm{Cl}

is

35.5 \mathrm{~g} \mathrm{~mol}^{-1}

)

Numerical TypeQuestion 19

The resistivity of a

0.8 \mathrm{M}

solution of an electrolyte is

5 \times 10^{-3} \Omega~ \mathrm{cm}

.

Its molar conductivity is _________

\times 10^{4}~ \Omega^{-1} \mathrm{~cm}^{2} \mathrm{~mol}^{-1}

. (Nearest integer)

Numerical TypeQuestion 20

A sample of a metal oxide has formula

\mathrm{M}_{0.83} \mathrm{O}_{1.00}

. The metal

\mathrm{M}

can exist in two oxidation states

+2

and

+3

.

In the sample of

\mathrm{M}_{0.83} \mathrm{O}_{1.00}

, the percentage of metal ions existing in

+2

oxidation state is __________

\%

. (nearest integer)

Numerical TypeQuestion 21

If the CFSE of

\left[\mathrm{Ti}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}

is

-96.0 \mathrm{~kJ} / \mathrm{mol}

, this complex will absorb maximum at wavelength ___________

\mathrm{nm}

. (nearest integer)

Assume Planck's constant (h)

=6.4 \times 10^{-34} \mathrm{Js}

, Speed of light

(\mathrm{c})=3.0 \times 10^{8} \mathrm{~m} / \mathrm{s}

and Avogadro's

Constant

\left(\mathrm{N}_{\mathrm{A}}\right)=6 \times 10^{23} / \mathrm{mol}

Numerical TypeQuestion 22

The rate constant for a first order reaction is

20 \mathrm{~min}^{-1}

. The time required for the initial concentration of the reactant to reduce to its

\frac{1}{32}

level is _______

\times 10^{-2} \mathrm{~min}

. (Nearest integer)

(Given :

\ln 10=2.303

and

\log 2=0.3010 \text { )}

Question 23

Let

\vec{a}=\hat{i}+2 \hat{j}+3 \hat{k}, \vec{b}=\hat{i}-\hat{j}+2 \hat{k}

and

\vec{c}=5 \hat{i}-3 \hat{j}+3 \hat{k}

be three vectors. If

\vec{r}

is a vector such that,

\vec{r} \times \vec{b}=\vec{c} \times \vec{b}

and

\vec{r} \cdot \vec{a}=0

, then

25|\vec{r}|^{2}

is equal to :

Options:

A)

336

B)

449

C)

339

D)

560

Question 24

Let

f: \mathbb{R}-\{2,6\} \rightarrow \mathbb{R}

be real valued function

defined as

f(x)=\frac{x^2+2 x+1}{x^2-8 x+12}

.

Then range of

f

is

Options:

A)

\left(-\infty,-\frac{21}{4}\right] \cup[1, \infty)

B)

\left(-\infty,-\frac{21}{4}\right) \cup(0, \infty)

C)

\left(-\infty,-\frac{21}{4}\right] \cup[0, \infty)

D)

\left(-\infty,-\frac{21}{4}\right] \cup\left[\frac{21}{4}, \infty\right)

Question 25

The equation

\mathrm{e}^{4 x}+8 \mathrm{e}^{3 x}+13 \mathrm{e}^{2 x}-8 \mathrm{e}^{x}+1=0, x \in \mathbb{R}

has :

Options:

A)

two solutions and both are negative

B)

two solutions and only one of them is negative

C)

four solutions two of which are negative

D)

no solution

Question 26

Let (a, b)

\subset(0,2 \pi)

be the largest interval for which

\sin ^{-1}(\sin \theta)-\cos ^{-1}(\sin \theta)>0, \theta \in(0,2 \pi)

, holds.

If

\alpha x^{2}+\beta x+\sin ^{-1}\left(x^{2}-6 x+10\right)+\cos ^{-1}\left(x^{2}-6 x+10\right)=0

and

\alpha-\beta=b-a

, then

\alpha

is equal to :

Options:

A)

\frac{\pi}{16}

B)

\frac{\pi}{48}

C)

\frac{\pi}{8}

D)

\frac{\pi}{12}

Question 27

Let

\alpha>0

. If

\int\limits_0^\alpha \frac{x}{\sqrt{x+\alpha}-\sqrt{x}} \mathrm{~d} x=\frac{16+20 \sqrt{2}}{15}

, then

\alpha

is equal to :

Options:

A)

4

B)

2

C)

2 \sqrt{2}

D)

\sqrt{2}

Question 28

Let the mean and standard deviation of marks of class A of 100 students be respectively 40 and

\alpha(>

0 ), and the mean and standard deviation of marks of class

B

of

n

students be respectively 55 and 30

-\alpha

. If the mean and variance of the marks of the combined class of

100+\mathrm{n}

studants are respectively 50 and 350 , then the sum of variances of classes

A

and

B

is :

Options:

A)

450

B)

900

C)

650

D)

500

Question 29

Let

a_1, a_2, a_3, \ldots

be an A.P. If

a_7=3

, the product

a_1 a_4

is minimum and the sum of its first

n

terms is zero, then

n !-4 a_{n(n+2)}

is equal to :

Options:

A)

24

B)

\frac{381}{4}

C)

9

D)

\frac{33}{4}

Question 30

The complex number

z=\frac{i-1}{\cos \frac{\pi}{3}+i \sin \frac{\pi}{3}}

is equal to :

Options:

A)

\cos \frac{\pi}{12}-i \sin \frac{\pi}{12}

B)

\sqrt{2}\left(\cos \frac{\pi}{12}+i \sin \frac{\pi}{12}\right)

C)

\sqrt{2} i\left(\cos \frac{5 \pi}{12}-i \sin \frac{5 \pi}{12}\right)

D)

\sqrt{2}\left(\cos \frac{5 \pi}{12}+i \sin \frac{5 \pi}{12}\right)

Question 31

Among the relations

\mathrm{S}=\left\{(\mathrm{a}, \mathrm{b}): \mathrm{a}, \mathrm{b} \in \mathbb{R}-\{0\}, 2+\frac{\mathrm{a}}{\mathrm{b}}>0\right\}

and

\mathrm{T}=\left\{(\mathrm{a}, \mathrm{b}): \mathrm{a}, \mathrm{b} \in \mathbb{R}, \mathrm{a}^{2}-\mathrm{b}^{2} \in \mathbb{Z}\right\}

,

Options:

A)

\mathrm{S}

is transitive but

\mathrm{T}

is not

B)

both

\mathrm{S}

and

\mathrm{T}

are symmetric

C)

neither

S

nor

T

is transitive

D)

T

is symmetric but

S

is not

Question 32

The absolute minimum value, of the function

f(x)=\left|x^{2}-x+1\right|+\left[x^{2}-x+1\right]

,

where

[t]

denotes the greatest integer function, in the interval

[-1,2]

, is :

Options:

A)

\frac{3}{4}

B)

\frac{3}{2}

C)

\frac{1}{4}

D)

\frac{5}{4}

Question 33

If

\phi(x)=\frac{1}{\sqrt{x}} \int\limits_{\frac{\pi}{4}}^x\left(4 \sqrt{2} \sin t-3 \phi^{\prime}(t)\right) d t, x>0

,

then

\emptyset^{\prime}\left(\frac{\pi}{4}\right)

is equal to :

Options:

A)

\frac{4}{6+\sqrt{\pi}}

B)

\frac{4}{6-\sqrt{\pi}}

C)

\frac{8}{\sqrt{\pi}}

D)

\frac{8}{6+\sqrt{\pi}}

Question 34

Let

\mathrm{H}

be the hyperbola, whose foci are

(1 \pm \sqrt{2}, 0)

and eccentricity is

\sqrt{2}

. Then the length of its latus rectum is :

Options:

A)

\frac{5}{2}

B)

3

C)

2

D)

\frac{3}{2}

Question 35

\lim\limits_{x \rightarrow \infty} \frac{(\sqrt{3 x+1}+\sqrt{3 x-1})^6+(\sqrt{3 x+1}-\sqrt{3 x-1})^6}{\left(x+\sqrt{x^2-1}\right)^6+\left(x-\sqrt{x^2-1}\right)^6} x^3

Options:

A)

is equal to 9

B)

is equal to

\frac{27}{2}

C)

does not exist

D)

is equal to 27

Question 36

Let

y=y(x)

be the solution of the differential equation

\left(3 y^{2}-5 x^{2}\right) y \mathrm{~d} x+2 x\left(x^{2}-y^{2}\right) \mathrm{d} y=0

such that

y(1)=1

. Then

\left|(y(2))^{3}-12 y(2)\right|

is equal to :

Options:

A)

64

B)

16 \sqrt{2}

C)

32

D)

32 \sqrt{2}

Question 37

The set of all values of

a^{2}

for which the line

x+y=0

bisects two distinct chords drawn from a point

\mathrm{P}\left(\frac{1+a}{2}, \frac{1-a}{2}\right)

on the circle

2 x^{2}+2 y^{2}-(1+a) x-(1-a) y=0

, is equal to :

Options:

A)

(0,4]

B)

(4, \infty)

C)

(2,12]

D)

(8, \infty)

Numerical TypeQuestion 38

Let the area of the region

\left\{(x, y):|2 x-1| \leq y \leq\left|x^{2}-x\right|, 0 \leq x \leq 1\right\}

be

\mathrm{A}

.

Then

(6 \mathrm{~A}+11)^{2}

is equal to

Numerical TypeQuestion 39

The coefficient of

x^{-6}

, in the

expansion of

\left(\frac{4 x}{5}+\frac{5}{2 x^{2}}\right)^{9}

, is

Numerical TypeQuestion 40

Let

\mathrm{A}=\left[\mathrm{a}_{i j}\right], \mathrm{a}_{i j} \in \mathbb{Z} \cap[0,4], 1 \leq i, j \leq 2

.

The number of matrices A such that the sum of all entries is a prime number

\mathrm{p} \in(2,13)

is __________.

Numerical TypeQuestion 41

If

{ }^{2 n+1} \mathrm{P}_{n-1}:{ }^{2 n-1} \mathrm{P}_{n}=11: 21

,

then

n^{2}+n+15

is equal to :

Numerical TypeQuestion 42

Let

\vec{a}, \vec{b}, \vec{c}

be three vectors such that

|\vec{a}|=\sqrt{31}, 4|\vec{b}|=|\vec{c}|=2

and

2(\vec{a} \times \vec{b})=3(\vec{c} \times \vec{a})

.

If the angle between

\vec{b}

and

\vec{c}

is

\frac{2 \pi}{3}

, then

\left(\frac{\vec{a} \times \vec{c}}{\vec{a} \cdot \vec{b}}\right)^{2}

is equal to __________.

Numerical TypeQuestion 43

Let A be the event that the absolute difference between two randomly choosen real numbers in the sample space

[0,60]

is less than or equal to a . If

\mathrm{P}(\mathrm{A})=\frac{11}{36}

, then

\mathrm{a}

is equal to _______.

Numerical TypeQuestion 44

If the constant term in the binomial expansion of

\left(\frac{x^{\frac{5}{2}}}{2}-\frac{4}{x^{l}}\right)^{9}

is

-84

and the coefficient of

x^{-3 l}

is

2^{\alpha} \beta

, where

\beta<0

is an odd number, then

|\alpha l-\beta|

is equal to ________.

Question 45

For a solid rod, the Young's modulus of elasticity is

3.2 \times 10^{11} \mathrm{Nm}^{-2}

and density is

8 \times 10^3 \mathrm{~kg} \mathrm{~m}^{-3}

. The velocity of longitudinal wave in the rod will be.

Options:

A)

3.65 \times 10^3 \mathrm{~ms}^{-1}

B)

6.32 \times 10^3 \mathrm{~ms}^{-1}

C)

18.96 \times 10^3 \mathrm{~ms}^{-1}

D)

145.75 \times 10^3 \mathrm{~ms}^{-1}

Question 46

Heat energy of

735 \mathrm{~J}

is given to a diatomic gas allowing the gas to expand at constant pressure. Each gas molecule rotates around an internal axis but do not oscillate. The increase in the internal energy of the gas will be :

Options:

A)

572 \mathrm{~J}

B)

441 \mathrm{~J}

C)

525 \mathrm{~J}

D)

735 \mathrm{~J}

Question 47

The radius of electron's second stationary orbit in Bohr's atom is R. The radius of 3rd orbit will be

Options:

A)

2.25R

B)

3 \mathrm{R}

C)

\frac{\mathrm{R}}{3}

D)

9 \mathrm{R}

Question 48

If the two metals

\mathrm{A}

and

\mathrm{B}

are exposed to radiation of wavelength

350 \mathrm{~nm}

. The work functions of metals

\mathrm{A}

and

\mathrm{B}

are

4.8 \mathrm{eV}

and

2.2 \mathrm{eV}

. Then choose the correct option.

Options:

A)

Metal B will not emit photo-electrons

B)

Both metals

\mathrm{A}

and

\mathrm{B}

will not emit photo-electrons

C)

Metal A will not emit photo-electrons

D)

Both metals A and B will emit photo-electrons

Question 49

The number of turns of the coil of a moving coil galvanometer is increased in order to increase current sensitivity by

50 \%

. The percentage change in voltage sensitivity of the galvanometer will be :

Options:

A)

0 \%

B)

75 \%

C)

100 \%

D)

50 \%

Question 50

Match List I with List II

LIST I		LIST II
A.	Microwaves	I.	Physiotherapy
B.	UV rays	II.	Treatment of cancer
C.	Infra-red light	III.	Lasik eye surgery
D.	X-ray	IV.	Aircraft navigation

Choose the correct answer from the options given below:

Options:

A)

A - IV, B - III, C - I, D - II

B)

A - II, B - IV, C - III, D - I

C)

A - III, B - II, C - I, D - IV

D)

A - IV, B - I, C - II, D - III

Question 51

The

\mathrm{H}

amount of thermal energy is developed by a resistor in

10 \mathrm{~s}

when a current of

4 \mathrm{~A}

is passed through it. If the current is increased to

16 \mathrm{~A}

, the thermal energy developed by the resistor in

10 \mathrm{~s}

will be :

Options:

A)

\frac{\mathrm{H}}{4}

B)

16 \mathrm{H}

C)

H

D)

4 \mathrm{H}

Question 52

A body weight

\mathrm{W}

, is projected vertically upwards from earth's surface to reach a height above the earth which is equal to nine times the radius of earth. The weight of the body at that height will be :

Options:

A)

\frac{W}{91}

B)

\frac{\mathrm{W}}{3}

C)

\frac{\mathrm{W}}{100}

D)

\frac{\mathrm{W}}{9}

Question 53

Considering a group of positive charges, which of the following statements is correct ?

Options:

A)

Net potential of the system cannot be zero at a point but net electric field can be zero at that point

B)

Net potential of the system at a point can be zero but net electric field can't be zero at that point.

C)

Both the net potential and the net electric field cannot be zero at a point.

D)

Both the net potential and the net field can be zero at a point.

Question 54

A body of mass

10 \mathrm{~kg}

is moving with an initial speed of

20 \mathrm{~m} / \mathrm{s}

. The body stops after

5 \mathrm{~s}

due to friction between body and the floor. The value of the coefficient of friction is:

(Take acceleration due to gravity

g=10 \mathrm{~ms}^{-2}

)

Options:

A)

0.3

B)

0.2

C)

0.5

D)

0.4

Question 55

A hypothetical gas expands adiabatically such that its volume changes from 08 litres to 27 litres. If the ratio of final pressure of the gas to initial pressure of the gas is

\frac{16}{81}

. Then the ratio of

\frac{\mathrm{Cp}}{\mathrm{Cv}}

will be.

Options:

A)

\frac{3}{1}

B)

\frac{4}{3}

C)

\frac{1}{2}

D)

\frac{3}{2}

Question 56

A long conducting wire having a current I flowing through it, is bent into a circular coil of

\mathrm{N}

turns. Then it is bent into a circular coil of

\mathrm{n}

turns. The magnetic field is calculated at the centre of coils in both the cases. The ratio of the magnetic field in first case to that of second case is :

Options:

A)

N^{2}: n^{2}

B)

\mathrm{N}: \mathrm{n}

C)

\mathrm{n}: \mathrm{N}

D)

n^{2}: N^{2}

Question 57

A microscope is focused on an object at the bottom of a bucket. If liquid with refractive index

\frac{5}{3}

is poured inside the bucket, then the microscope has to be raised by

30 \mathrm{~cm}

to focus the object again. The height of the liquid in the bucket is :

Options:

A)

50 \mathrm{~cm}

B)

18 \mathrm{~cm}

C)

75 \mathrm{~cm}

D)

12 \mathrm{~cm}

Question 58

Match List I with List II

LIST I		LIST II
A.	Angular momentum	I.	$\left[\mathrm{ML}^{2} \mathrm{~T}^{-2}\right]$
B.	Torque	II.	$\left[\mathrm{ML}^{-2} \mathrm{~T}^{-2}\right]$
C.	Stress	III	$\left[\mathrm{ML}^{2} \mathrm{~T}^{-1}\right]$
D.	Pressure gradient	IV.	$\left[\mathrm{ML}^{-1} \mathrm{~T}^{-2}\right]$

Choose the correct answer from the options given below:

Options:

A)

A - I, B - IV, C - III, D - II

B)

A - III, B - I, C - IV, D - II

C)

A - IV, B - II, C - I, D - III

D)

A - II, B - III, C - IV, D - I

Question 59

Under the same load, wire A having length

5.0 \mathrm{~m}

and cross section

2.5 \times 10^{-5} \mathrm{~m}^{2}

stretches uniformly by the same amount as another wire B of length

6.0 \mathrm{~m}

and a cross section of

3.0 \times 10^{-5}

\mathrm{m}^{2}

stretches. The ratio of the Young's modulus of wire A to that of wire

B

will be :

Options:

A)

1: 2

B)

1: 4

C)

1: 1

D)

1: 10

Question 60

An alternating voltage source

\mathrm{V}=260 \sin (628 \mathrm{t}

) is connected across a pure inductor of

5 \mathrm{mH}

Inductive reactance in the circuit is :

Options:

A)

6.28 \Omega

B)

0.318 \Omega

C)

0.5 \Omega

D)

3.14 \Omega

Question 61

A stone of mass

1 \mathrm{~kg}

is tied to end of a massless string of length

1 \mathrm{~m}

. If the breaking tension of the string is

400 \mathrm{~N}

, then maximum linear velocity, the stone can have without breaking the string, while rotating in horizontal plane, is :

Options:

A)

20 \mathrm{~ms}^{-1}

B)

40 \mathrm{~ms}^{-1}

C)

400 \mathrm{~ms}^{-1}

D)

10 \mathrm{~ms}^{-1}

Question 62

A body is moving with constant speed, in a circle of radius

10 \mathrm{~m}

. The body completes one revolution in

4 \mathrm{~s}

. At the end of 3rd second, the displacement of body (in

\mathrm{m}

) from its starting point is :

Options:

A)

15 \pi

B)

30

C)

10 \sqrt{2}

D)

5 \pi

Numerical TypeQuestion 63

A water heater of power

2000 \mathrm{~W}

is used to heat water. The specific heat capacity of water is

4200 \mathrm{~J}

\mathrm{kg}^{-1} \mathrm{~K}^{-1}

. The efficiency of heater is

70 \%

. Time required to heat

2 \mathrm{~kg}

of water from

10^{\circ} \mathrm{C}

to

60^{\circ} \mathrm{C}

is _________ s.

(Assume that the specific heat capacity of water remains constant over the temperature range of the water).

Numerical TypeQuestion 64

A series

\mathrm{LCR}

circuit consists of

\mathrm{R}=80 \Omega, \mathrm{X}_{\mathrm{L}}=100 \Omega

, and

\mathrm{X}_{\mathrm{C}}=40 \Omega

. The input

voltage is 2500

\cos (100 \pi \mathrm{t}) \mathrm{V}

. The amplitude of current, in the circuit, is _________ A.

Numerical TypeQuestion 65

Two light waves of wavelengths 800 and

600 \mathrm{~nm}

are used in Young's double slit experiment to obtain interference fringes on a screen placed

7 \mathrm{~m}

away from plane of slits. If the two slits are separated by

0.35 \mathrm{~mm}

, then shortest distance from the central bright maximum to the point where the bright fringes of the two wavelength coincide will be ______

\mathrm{mm}

.

Numerical TypeQuestion 66

Two bodies are projected from ground with same speeds

40 \mathrm{~ms}^{-1}

at two different angles with respect to horizontal. The bodies were found to have same range. If one of the body was projected at an angle of

60^{\circ}

, with horizontal then sum of the maximum heights, attained by the two projectiles, is

\mathrm{m}

. (Given

\mathrm{g}=10 \mathrm{~ms}^{-2}

)

Numerical TypeQuestion 67

The displacement equations of two interfering waves are given by

y_{1}=10 \sin \left(\omega t+\frac{\pi}{3}\right) \mathrm{cm}, y_{2}=5[\sin \omega t+\sqrt{3} \cos \omega t] \mathrm{cm}

respectively.

The amplitude of the resultant wave is _______

\mathrm{cm}

.

Numerical TypeQuestion 68

For the given circuit, in the steady state,

\left|\mathrm{V}_{\mathrm{B}}-\mathrm{V}_{\mathrm{D}}\right|=

________ V.

JEE Main 2023 (Online) 31st January Evening Shift Physics - Capacitor Question 26 English

Numerical TypeQuestion 69

Two discs of same mass and different radii are made of different materials such that their thicknesses are

1 \mathrm{~cm}

and

0.5 \mathrm{~cm}

respectively. The densities of materials are in the ratio

3: 5

. The moment of inertia of these discs respectively about their diameters will be in the ratio of

\frac{x}{6}

. The value of

x

is ________.

Numerical TypeQuestion 70

A ball is dropped from a height of

20 \mathrm{~m}

. If the coefficient of restitution for the collision between ball and floor is

0.5

, after hitting the floor, the ball rebounds to a height of ________

\mathrm{m}

.

Numerical TypeQuestion 71

If the binding energy of ground state electron in a hydrogen atom is

13.6\, \mathrm{eV}

, then, the energy required to remove the electron from the second excited state of

\mathrm{Li}^{2+}

will be :

x \times 10^{-1} \mathrm{eV}

. The value of

x

is ________.

Numerical TypeQuestion 72

Two parallel plate capacitors

C_{1}

and

C_{2}

each having capacitance of

10 \mu \mathrm{F}

are individually charged by a 100 V D.C. source. Capacitor

C_{1}

is kept connected to the source and a dielectric slab is inserted between it plates. Capacitor

\mathrm{C}_{2}

is disconnected from the source and then a dielectric slab is inserted in it. Afterwards the capacitor

C_{1}

is also disconnected from the source and the two capacitors are finally connected in parallel combination. The common potential of the combination will be ________ V.

(Assuming Dielectric constant

=10

)