JEE Mains Feb 1, 2024 Shift 2 Questions with solutions

Question 1

In the given reactions identify

A

and

B

JEE Main 2024 (Online) 1st February Evening Shift Chemistry - Hydrocarbons Question 10 English

Options:

A)

A : n-Pentane B : Cis - 2 - butene

B)

A : 2-Pentyne B : Cis-2-butene

C)

A : n-Pentane B : trans-2-butene

D)

A : 2-Pentyne B : trans-2-butene

Question 2

Solubility of calcium phosphate (molecular mass, M) in water is

\mathrm{W_{g}}

per

100 \mathrm{~mL}

at

25^{\circ} \mathrm{C}

. Its solubility product at

25^{\circ} \mathrm{C}

will be approximately.

Options:

A)

10^7\left(\frac{W}{M}\right)^3

B)

10^3\left(\frac{\mathrm{W}}{\mathrm{M}}\right)^5

C)

10^7\left(\frac{W}{M}\right)^5

D)

10^5\left(\frac{\mathrm{W}}{\mathrm{M}}\right)^5

Question 3

\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_6\right]^{3+}

and

\left[\mathrm{CoF}_6\right]^{3-}

are respectively known as :

Options:

A)

Inner orbital Complex, Spin paired Complex

B)

Spin paired Complex, Spin free Complex

C)

Spin free Complex, Spin paired Complex

D)

Outer orbital Complex, Inner orbital Complex

Question 4

Match List - I with List - II.

List I (Reactants)	List II (Product)
(A) Phenol, Zn/Δ	(I) Salicylaldehyde
(B) Phenol, CHCl₃, NaOH, HCl	(II) Salicylic acid
(C) Phenol, CO₂, NaOH, HCl	(III) Benzene
(D) Phenol, Conc. HNO₃	(IV) Picric acid

Choose the correct answer from the options given below :

Options:

A)

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

B)

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

C)

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

D)

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

Question 5

The strongest reducing agent among the following is :

Options:

A)

\mathrm{SbH}_3

B)

\mathrm{NH}_3

C)

\mathrm{BiH}_3

D)

\mathrm{PH}_3

Question 6

The functional group that shows negative resonance effect is :

Options:

A)

-\mathrm{OH}

B)

-\mathrm{OR}

C)

-\mathrm{COOH}

D)

-\mathrm{NH}_2

Question 7

The number of radial node/s for

3 p

orbital is :

Options:

A)

3

B)

2

C)

1

D)

4

Numerical TypeQuestion 8

The number of tripeptides formed by three different amino acids using each amino acid once is ______.

Question 9

If

z

is a complex number such that

|z| \leqslant 1

, then the minimum value of

\left|z+\frac{1}{2}(3+4 i)\right|

is :

Options:

A)

2

B)

\frac{5}{2}

C)

\frac{3}{2}

D)

3

Question 10

Consider a

\triangle A B C

where

A(1,3,2), B(-2,8,0)

and

C(3,6,7)

. If the angle bisector of

\angle B A C

meets the line

B C

at

D

, then the length of the projection of the vector

\overrightarrow{A D}

on the vector

\overrightarrow{A C}

is :

Options:

A)

\frac{37}{2 \sqrt{38}}

B)

\sqrt{19}

C)

\frac{39}{2 \sqrt{38}}

D)

\frac{\sqrt{38}}{2}

Question 11

Consider the relations

R_1

and

R_2

defined as

a R_1 b \Leftrightarrow a^2+b^2=1

for all

a, b \in \mathbf{R}

and

(a, b) R_2(c, d) \Leftrightarrow

a+d=b+c

for all

(a, b),(c, d) \in \mathbf{N} \times \mathbf{N}

. Then :

Options:

A)

R_1

and

R_2

both are equivalence relations

B)

Only

R_1

is an equivalence relation

C)

Only

R_2

is an equivalence relation

D)

Neither

R_1

nor

R_2

is an equivalence relation

Question 12

Let the system of equations

x+2 y+3 z=5,2 x+3 y+z=9,4 x+3 y+\lambda z=\mu

have infinite number of solutions. Then

\lambda+2 \mu

is equal to :

Options:

A)

22

B)

17

C)

15

D)

28

Question 13

Let Ajay will not appear in JEE exam with probability

\mathrm{p}=\frac{2}{7}

, while both Ajay and Vijay will appear in the exam with probability

\mathrm{q}=\frac{1}{5}

. Then the probability, that Ajay will appear in the exam and Vijay will not appear is :

Options:

A)

\frac{9}{35}

B)

\frac{3}{35}

C)

\frac{24}{35}

D)

\frac{18}{35}

Question 14

Let

f(x)=\left|2 x^2+5\right| x|-3|, x \in \mathbf{R}

. If

\mathrm{m}

and

\mathrm{n}

denote the number of points where

f

is not continuous and not differentiable respectively, then

\mathrm{m}+\mathrm{n}

is equal to :

Options:

A)

5

B)

3

C)

2

D)

0

Numerical TypeQuestion 15

Let

f:(0, \infty) \rightarrow \mathbf{R}

and

\mathrm{F}(x)=\int\limits_0^x \mathrm{t} f(\mathrm{t}) \mathrm{dt}

. If

\mathrm{F}\left(x^2\right)=x^4+x^5

, then

\sum\limits_{\mathrm{r}=1}^{12} f\left(\mathrm{r}^2\right)

is equal to ____________.

Numerical TypeQuestion 16

Let

A B C

be an isosceles triangle in which

A

is at

(-1,0), \angle A=\frac{2 \pi}{3}, A B=A C

and

B

is on the positve

x

-axis. If

\mathrm{BC}=4 \sqrt{3}

and the line

\mathrm{BC}

intersects the line

y=x+3

at

(\alpha, \beta)

, then

\frac{\beta^4}{\alpha^2}

is __________.

Question 17

From the statements given below :

(A) The angular momentum of an electron in

n^{\text {th }}

orbit is an integral multiple of

\hbar

.

(B) Nuclear forces do not obey inverse square law.

(C) Nuclear forces are spin dependent.

(D) Nuclear forces are central and charge independent.

(E) Stability of nucleus is inversely proportional to the value of packing fraction.

Choose the correct answer from the options given below :

Options:

A)

(B), (C), (D), (E) only

B)

(A), (C), (D), (E) only

C)

(A), (B), (C), (E) only

D)

(A), (B), (C), (D) only

Question 18

Monochromatic light of frequency

6 \times 10^{14} \mathrm{~Hz}

is produced by a laser. The power emitted is

2 \times 10^{-3} \mathrm{~W}

.

How many photons per second on an average, are emitted by the source ?

(Given

\mathrm{h}=6.63 \times 10^{-34} \mathrm{Js}

)

Options:

A)

5 \times 10^{15}

B)

7 \times 10^{16}

C)

6 \times 10^{15}

D)

9 \times 10^{18}

Question 19

C_1

and

C_2

are two hollow concentric cubes enclosing charges

2 Q

and

3 Q

respectively as shown in figure. The ratio of electric flux passing through

C_1

and

C_2

is :

JEE Main 2024 (Online) 1st February Evening Shift Physics - Electrostatics Question 17 English

Options:

A)

3: 2

B)

5: 2

C)

2: 5

D)

2: 3

Question 20

Given below are two statements :

Statement (I) :

\mathrm{SiO}_2

and

\mathrm{GeO}_2

are acidic while

\mathrm{SnO}

and

\mathrm{PbO}

are amphoteric in nature.

Statement (II) : Allotropic forms of carbon are due to property of catenation and

\mathrm{p} \pi-\mathrm{d} \pi

bond formation.

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

Options:

A)

Statement I is false but Statement II is true

B)

Both Statement I and Statement II are false

C)

Both Statement I and Statement II are true

D)

Statement I is true but Statement II is false

Question 21

The set of meta directing functional groups from the following sets is :

Options:

A)

-\mathrm{CN},-\mathrm{NH}_2,-\mathrm{NHR},-\mathrm{OCH}_3

B)

-\mathrm{CN},-\mathrm{CHO},-\mathrm{NHCOCH}_3,-\mathrm{COOR}

C)

-\mathrm{NO}_2,-\mathrm{NH}_2,-\mathrm{COOH},-\mathrm{COOR}

D)

-\mathrm{NO}_2,-\mathrm{CHO},-\mathrm{SO}_3 \mathrm{H},-\mathrm{COR}

Question 22

Given below are two statements :

Statement (I) : A

\pi

bonding MO has lower electron density above and below the inter-nuclear axis.

Statement (II) : The

\pi^*

antibonding MO has a node between the nuclei.

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

Options:

A)

Both Statement I and Statement II are true

B)

Both Statement I and Statement II are false

C)

Statement I is true but Statement II is false

D)

Statement I is false but Statement II is true

Question 23

Given below are two statements :

Statement (I) : Both metals and non-metals exist in p and d-block elements.

Statement (II) : Non-metals have higher ionisation enthalpy and higher electronegativity than the metals.

In the 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 true

C)

Statement I is false but Statement II is true

D)

Statement I is true but Statement II is false

Question 24

Which of the following compounds show colour due to d-d transition?

Options:

A)

\mathrm{K}_2 \mathrm{Cr}_2 \mathrm{O}_7

B)

\mathrm{CuSO}_4 \cdot 5 \mathrm{H}_2 \mathrm{O}

C)

\mathrm{KMnO}_4

D)

\mathrm{K}_2 \mathrm{CrO}_4

Question 25

Select the compound from the following that will show intramolecular hydrogen bonding.

Options:

A)

JEE Main 2024 (Online) 1st February Evening Shift Chemistry - Chemical Bonding & Molecular Structure Question 23 English Option 1

B)

\mathrm{H}_2 \mathrm{O}

C)

\mathrm{C}_2 \mathrm{H}_5 \mathrm{OH}

D)

\mathrm{NH}_3

Numerical TypeQuestion 26

Mass of ethylene glycol (antifreeze) to be added to

18.6 \mathrm{~kg}

of water to protect the freezing point at

-24^{\circ} \mathrm{C}

is ________

\mathrm{kg}

(Molar mass in

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

for ethylene glycol

62, \mathrm{~K}_f

of water

=1.86 \mathrm{~K}

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

)

Numerical TypeQuestion 27

For a certain reaction at

300 \mathrm{~K}, \mathrm{~K}=10

, then

\Delta \mathrm{G}^{\circ}

for the same reaction is - ____________

\times 10^{-1} \mathrm{~kJ} \mathrm{~mol}^{-1}

.

(Given

\mathrm{R}=8.314 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}

)

Numerical TypeQuestion 28

Following Kjeldahl's method,

1 \mathrm{~g}

of organic compound released ammonia, that neutralised

10 \mathrm{~mL}

of

2 \mathrm{M} ~\mathrm{H}_2 \mathrm{SO}_4

. The percentage of nitrogen in the compound is ___________

\%

.

Numerical TypeQuestion 29

Consider the following redox reaction :

\mathrm{MnO}_4^{-}+\mathrm{H}^{+}+\mathrm{H}_2 \mathrm{C}_2 \mathrm{O}_4 \rightleftharpoons \mathrm{Mn}^{2+}+\mathrm{H}_2 \mathrm{O}+\mathrm{CO}_2

The standard reduction potentials are given as below

\left(\mathrm{E}_{\text {red }}^0\right)

:

\begin{aligned} & \mathrm{E}_{\mathrm{MnO}_4^{-} / \mathrm{Mn}^{2+}}^{\circ}=+1.51 \mathrm{~V} \\\\ & \mathrm{E}_{\mathrm{CO}_2 / \mathrm{H}_2 \mathrm{C}_2 \mathrm{O}_4}^{\circ}=-0.49 \mathrm{~V} \end{aligned}

If the equilibrium constant of the above reaction is given as

\mathrm{K}_{\mathrm{eq}}=10^x

, then the value of

x=

__________ (nearest integer)

Numerical TypeQuestion 30

Number of compounds which give reaction with Hinsberg's reagent is _________.

JEE Main 2024 (Online) 1st February Evening Shift Chemistry - Compounds Containing Nitrogen Question 12 English

JEE Main 2024 (Online) 1st February Evening Shift Chemistry - Compounds Containing Nitrogen Question 12 English

Question 31

If the domain of the function

f(x)=\frac{\sqrt{x^2-25}}{\left(4-x^2\right)}+\log _{10}\left(x^2+2 x-15\right)

is

(-\infty, \alpha) \cup[\beta, \infty)

, then

\alpha^2+\beta^3

is equal to :

Options:

A)

140

B)

175

C)

125

D)

150

Question 32

If

\int\limits_0^{\frac{\pi}{3}} \cos ^4 x \mathrm{~d} x=\mathrm{a} \pi+\mathrm{b} \sqrt{3}

, where

\mathrm{a}

and

\mathrm{b}

are rational numbers, then

9 \mathrm{a}+8 \mathrm{b}

is equal to :

Options:

A)

2

B)

1

C)

3

D)

\frac{3}{2}

Question 33

Let

\mathrm{P}

and

\mathrm{Q}

be the points on the line

\frac{x+3}{8}=\frac{y-4}{2}=\frac{z+1}{2}

which are at a distance of 6 units from the point

\mathrm{R}(1,2,3)

. If the centroid of the triangle PQR is

(\alpha, \beta, \gamma)

, then

\alpha^2+\beta^2+\gamma^2

is :

Options:

A)

18

B)

24

C)

26

D)

36

Question 34

Let

f(x)=\left\{\begin{array}{l}x-1, x \text { is even, } \\ 2 x, \quad x \text { is odd, }\end{array} x \in \mathbf{N}\right.

.

If for some

\mathrm{a} \in \mathbf{N}, f(f(f(\mathrm{a})))=21

, then

\lim\limits_{x \rightarrow \mathrm{a}^{-}}\left\{\frac{|x|^3}{\mathrm{a}}-\left[\frac{x}{\mathrm{a}}\right]\right\}

, where

[t]

denotes the greatest integer less than or equal to

t

, is equal to :

Options:

A)

169

B)

121

C)

225

D)

144

Question 35

A body of mass

4 \mathrm{~kg}

experiences two forces

\vec{F}_1=5 \hat{i}+8 \hat{j}+7 \hat{k}

and

\overrightarrow{\mathrm{F}}_2=3 \hat{i}-4 \hat{j}-3 \hat{k}

. The acceleration acting on the body is :

Options:

A)

2 \hat{i}+\hat{j}+\hat{k}

B)

4 \hat{i}+2 \hat{j}+2 \hat{k}

C)

-2 \hat{i}-\hat{j}-\hat{k}

D)

2 \hat{i}+3 \hat{j}+3 \hat{k}

Question 36

The transition metal having highest

3^{\text {rd }}

ionisation enthalpy is :

Options:

A)

\mathrm{Mn}

B)

\mathrm{Fe}

C)

\mathrm{Cr}

D)

V

Question 37

Given below are two statements :

Statement (I) : Dimethyl glyoxime forms a six-membered covalent chelate when treated with

\mathrm{NiCl}_2

solution in presence of

\mathrm{NH}_4 \mathrm{OH}

.

Statement (II) : Prussian blue precipitate contains iron both in

(+2)

and

(+3)

oxidation states.

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

Options:

A)

Statement I is false but Statement II is true

B)

Both Statement I and Statement II are true

C)

Statement I is true but Statement II is false

D)

Both Statement I and Statement II are false

Question 38

Lassaigne's test is used for detection of :

Options:

A)

Phosphorous and halogens only

B)

Nitrogen, Sulphur and Phosphorous only

C)

Nitrogen, Sulphur, phosphorous and halogens

D)

Nitrogen and Sulphur only

Numerical TypeQuestion 39

Total number of isomeric compounds (including stereoisomers) formed by monochlorination of 2-methylbutane is _______ .

Numerical TypeQuestion 40

The following data were obtained during the first order thermal decomposition of a gas A at constant volume :

\mathrm{A}(\mathrm{g}) \rightarrow 2 \mathrm{~B}(\mathrm{~g})+\mathrm{C}(\mathrm{g})

S.No.	Time /s	Total pressure /(atm)
1.	0	0.1
2.	115	0.28

The rate constant of the reaction is ________

\times 10^{-2} \mathrm{~s}^{-1}

(nearest integer)

Numerical TypeQuestion 41

The amount of electricity in Coulomb required for the oxidation of

1 \mathrm{~mol}

of

\mathrm{H}_2 \mathrm{O}

to

\mathrm{O}_2

is __________

\times 10^5 \mathrm{C}

.

Numerical TypeQuestion 42

10 \mathrm{~mL}

of gaseous hydrocarbon on combustion gives

40 \mathrm{~mL}

of

\mathrm{CO}_2(\mathrm{~g})

and

50 \mathrm{~mL}

of water vapour. Total number of carbon and hydrogen atoms in the hydrocarbon is _________ .

Question 43

Let

\alpha

and

\beta

be the roots of the equation

p x^2+q x-r=0

, where

p \neq 0

. If

p, q

and

r

be the consecutive terms of a non constant G.P. and

\frac{1}{\alpha}+\frac{1}{\beta}=\frac{3}{4}

, then the value of

(\alpha-\beta)^2

is :

Options:

A)

8

B)

9

C)

\frac{20}{3}

D)

\frac{80}{9}

Question 44

Let

\mathrm{P}

be a point on the ellipse

\frac{x^2}{9}+\frac{y^2}{4}=1

. Let the line passing through

\mathrm{P}

and parallel to

y

-axis meet the circle

x^2+y^2=9

at point

\mathrm{Q}

such that

\mathrm{P}

and

\mathrm{Q}

are on the same side of the

x

-axis. Then, the eccentricity of the locus of the point

R

on

P Q

such that

P R: R Q=4: 3

as

P

moves on the ellipse, is :

Options:

A)

\frac{13}{21}

B)

\frac{\sqrt{139}}{23}

C)

\frac{\sqrt{13}}{7}

D)

\frac{11}{19}

Question 45

Consider 10 observations

x_1, x_2, \ldots, x_{10}

such that

\sum\limits_{i=1}^{10}\left(x_i-\alpha\right)=2

and

\sum\limits_{i=1}^{10}\left(x_i-\beta\right)^2=40

, where

\alpha, \beta

are positive integers. Let the mean and the variance of the observations be

\frac{6}{5}

and

\frac{84}{25}

respectively. Then

\frac{\beta}{\alpha}

is equal to :

Options:

A)

2

B)

1

C)

\frac{5}{2}

D)

\frac{3}{2}

Question 46

The number of solutions of the equation

4 \sin ^2 x-4 \cos ^3 x+9-4 \cos x=0 ; x \in[-2 \pi, 2 \pi]

is :

Options:

A)

0

B)

3

C)

1

D)

2

Question 47

Let the locus of the midpoints of the chords of the circle

x^2+(y-1)^2=1

drawn from the origin intersect the line

x+y=1

at

\mathrm{P}

and

\mathrm{Q}

. Then, the length of

\mathrm{PQ}

is :

Options:

A)

\frac{1}{2}

B)

1

C)

\frac{1}{\sqrt{2}}

D)

\sqrt{2}

Question 48

The value of

\int\limits_0^1\left(2 x^3-3 x^2-x+1\right)^{\frac{1}{3}} \mathrm{~d} x

is equal to :

Options:

A)

-1

B)

2

C)

0

D)

1

Numerical TypeQuestion 49

If

y=\frac{(\sqrt{x}+1)\left(x^2-\sqrt{x}\right)}{x \sqrt{x}+x+\sqrt{x}}+\frac{1}{15}\left(3 \cos ^2 x-5\right) \cos ^3 x

, then

96 y^{\prime}\left(\frac{\pi}{6}\right)

is equal to :

Numerical TypeQuestion 50

Let

\overrightarrow{\mathrm{a}}=\hat{i}+\hat{j}+\hat{k}, \overrightarrow{\mathrm{b}}=-\hat{i}-8 \hat{j}+2 \hat{k}

and

\overrightarrow{\mathrm{c}}=4 \hat{i}+\mathrm{c}_2 \hat{j}+\mathrm{c}_3 \hat{k}

be three vectors such that

\overrightarrow{\mathrm{b}} \times \overrightarrow{\mathrm{a}}=\overrightarrow{\mathrm{c}} \times \overrightarrow{\mathrm{a}}

. If the angle between the vector

\overrightarrow{\mathrm{c}}

and the vector

3 \hat{i}+4 \hat{j}+\hat{k}

is

\theta

, then the greatest integer less than or equal to

\tan ^2 \theta

is _______________.

Numerical TypeQuestion 51

The lines

\mathrm{L}_1, \mathrm{~L}_2, \ldots, \mathrm{L}_{20}

are distinct. For

\mathrm{n}=1,2,3, \ldots, 10

all the lines

\mathrm{L}_{2 \mathrm{n}-1}

are parallel to each other and all the lines

L_{2 n}

pass through a given point

P

. The maximum number of points of intersection of pairs of lines from the set

\left\{\mathrm{L}_1, \mathrm{~L}_2, \ldots, \mathrm{L}_{20}\right\}

is equal to ___________.

Question 52

Match List - I with List - II.

List I (Compound)	List II (Use)
(A) Carbon tetrachloride	(I) Paint remover
(B) Methylene chloride	(II) Refrigerators and air conditioners
(C) DDT	(III) Fire extinguisher
(D) Freons	(IV) Non Biodegradable insecticide

Choose the correct answer from the options given below :

Options:

A)

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

B)

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

C)

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

D)

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

Question 53

JEE Main 2024 (Online) 1st February Evening Shift Chemistry - Hydrocarbons Question 9 English

Acid D formed in above reaction is :

Options:

A)

Malonic acid

B)

Oxalic acid

C)

Succinic acid

D)

Gluconic acid

Question 54

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

Assertion (A) : In aqueous solutions

\mathrm{Cr}^{2+}

is reducing while

\mathrm{Mn}^{3+}

is oxidising in nature.

Reason (R) : Extra stability to half filled electronic configuration is observed than incompletely filled electronic configuration.

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

Options:

A)

(A) is true but (R) is false

B)

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

C)

Both (A) and (R) are true but (R) is not the correct explanation of (A)

D)

(A) is false but (R) is true

Question 55

Which among the followng has highest boiling point?

Options:

A)

\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{CH}_2 \mathrm{CH}_2-\mathrm{OH}

B)

\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{CH}_2 \mathrm{CH}_3

C)

\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{CH}_2 \mathrm{CHO}

D)

\mathrm{H}_5 \mathrm{C}_2-\mathrm{O}-\mathrm{C}_2 \mathrm{H}_5

Question 56

Let

\alpha

be a non-zero real number. Suppose

f: \mathbf{R} \rightarrow \mathbf{R}

is a differentiable function such that

f(0)=2

and

\lim\limits_{x \rightarrow-\infty} f(x)=1

. If

f^{\prime}(x)=\alpha f(x)+3

, for all

x \in \mathbf{R}

, then

f\left(-\log _{\mathrm{e}} 2\right)

is equal to :

Options:

A)

7

B)

9

C)

3

D)

5

Question 57

If the mirror image of the point

P(3,4,9)

in the line

\frac{x-1}{3}=\frac{y+1}{2}=\frac{z-2}{1}

is

(\alpha, \beta, \gamma)

, then 14

(\alpha+\beta+\gamma)

is :

Options:

A)

102

B)

138

C)

132

D)

108

Question 58

Let

S_n

denote the sum of the first

n

terms of an arithmetic progression. If

S_{10}=390

and the ratio of the tenth and the fifth terms is

15: 7

, then

\mathrm{S}_{15}-\mathrm{S}_5

is equal to :

Options:

A)

800

B)

890

C)

790

D)

690

Question 59

Let

m

and

n

be the coefficients of seventh and thirteenth terms respectively

in the expansion of

\left(\frac{1}{3} x^{\frac{1}{3}}+\frac{1}{2 x^{\frac{2}{3}}}\right)^{18}

. Then

\left(\frac{\mathrm{n}}{\mathrm{m}}\right)^{\frac{1}{3}}

is :

Options:

A)

\frac{1}{9}

B)

\frac{1}{4}

C)

\frac{4}{9}

D)

\frac{9}{4}

Numerical TypeQuestion 60

Three points

\mathrm{O}(0,0), \mathrm{P}\left(\mathrm{a}, \mathrm{a}^2\right), \mathrm{Q}\left(-\mathrm{b}, \mathrm{b}^2\right), \mathrm{a}>0, \mathrm{~b}>0

, are on the parabola

y=x^2

. Let

\mathrm{S}_1

be the area of the region bounded by the line

\mathrm{PQ}

and the parabola, and

\mathrm{S}_2

be the area of the triangle

\mathrm{OPQ}

. If the minimum value of

\frac{\mathrm{S}_1}{\mathrm{~S}_2}

is

\frac{\mathrm{m}}{\mathrm{n}}, \operatorname{gcd}(\mathrm{m}, \mathrm{n})=1

, then

\mathrm{m}+\mathrm{n}

is equal to __________.

Numerical TypeQuestion 61

The sum of squares of all possible values of

k

, for which area of the region bounded by the parabolas

2 y^2=\mathrm{k} x

and

\mathrm{ky}^2=2(y-x)

is maximum, is equal to :

Numerical TypeQuestion 62

If

\frac{\mathrm{d} x}{\mathrm{~d} y}=\frac{1+x-y^2}{y}, x(1)=1

, then

5 x(2)

is equal to __________.

Numerical TypeQuestion 63

Let

A=I_2-2 M M^T

, where

M

is a real matrix of order

2 \times 1

such that the relation

M^T M=I_1

holds. If

\lambda

is a real number such that the relation

A X=\lambda X

holds for some non-zero real matrix

X

of order

2 \times 1

, then the sum of squares of all possible values of

\lambda

is equal to __________.

Numerical TypeQuestion 64

If three successive terms of a G.P. with common ratio

\mathrm{r}(\mathrm{r}>1)

are the lengths of the sides of a triangle and

[r]

denotes the greatest integer less than or equal to

r

, then

3[r]+[-r]

is equal to _____________.

Question 65

A disc of radius

\mathrm{R}

and mass

\mathrm{M}

is rolling horizontally without slipping with speed

v

. It then moves up an inclined smooth surface as shown in figure. The maximum height that the disc can go up the incline is :

JEE Main 2024 (Online) 1st February Evening Shift Physics - Rotational Motion Question 12 English

JEE Main 2024 (Online) 1st February Evening Shift Physics - Rotational Motion Question 12 English

Options:

A)

\frac{3}{4} \frac{v^2}{\mathrm{~g}}

B)

\frac{v^2}{g}

C)

\frac{2}{3} \frac{v^2}{\mathrm{~g}}

D)

\frac{1}{2} \frac{v^2}{\mathrm{~g}}

Question 66

A galvanometer

(G)

of

2 \Omega

resistance is connected in the given circuit. The ratio of charge stored in

C_1

and

C_2

is :

JEE Main 2024 (Online) 1st February Evening Shift Physics - Capacitor Question 8 English

Options:

A)

1

B)

\frac{2}{3}

C)

\frac{3}{2}

D)

\frac{1}{2}

Question 67

A big drop is formed by coalescing 1000 small droplets of water. The surface energy will become :

Options:

A)

\frac{1}{100}

th

B)

\frac{1}{10}

th

C)

100 times

D)

10 times

Question 68

In an ammeter,

5 \%

of the main current passes through the galvanometer. If resistance of the galvanometer is

\mathrm{G}

, the resistance of ammeter will be :

Options:

A)

199 \mathrm{~G}

B)

200 \mathrm{~G}

C)

\frac{G}{20}

D)

\frac{\mathrm{G}}{199}

Numerical TypeQuestion 69

Suppose a uniformly charged wall provides a uniform electric field of

2 \times 10^4 \mathrm{~N} / \mathrm{C}

normally. A charged particle of mass

2 \mathrm{~g}

being suspended through a silk thread of length

20 \mathrm{~cm}

and remain stayed at a distance of

10 \mathrm{~cm}

from the wall.

Then the charge on the particle will be

\frac{1}{\sqrt{x}} \mu \mathrm{C}

where

x=

___________ . [use

\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2

]

Numerical TypeQuestion 70

A mass

m

is suspended from a spring of negligible mass and the system oscillates with a frequency

f_1

. The frequency of oscillations if a mass

9 \mathrm{~m}

is suspended from the same spring is

f_2

. The value of

\frac{f_1}{f_2} \mathrm{i}

________.

Numerical TypeQuestion 71

A moving coil galvanometer has 100 turns and each turn has an area of

2.0 \mathrm{~cm}^2

. The magnetic field produced by the magnet is

0.01 \mathrm{~T}

and the deflection in the coil is 0.05 radian when a current of

10 \mathrm{~mA}

is passed through it. The torsional constant of the suspension wire is

x \times 10^{-5} \mathrm{~N}-\mathrm{m} / \mathrm{rad}

. The value of

x

is _______ .

Numerical TypeQuestion 72

A coil of 200 turns and area

0.20 \mathrm{~m}^2

is rotated at half a revolution per second and is placed in uniform magnetic field of

0.01 \mathrm{~T}

perpendicular to axis of rotation of the coil. The maximum voltage generated in the coil is

\frac{2 \pi}{\beta}

volt. The value of

\beta

is _______.

Numerical TypeQuestion 73

A particular hydrogen-like ion emits the radiation of frequency

3 \times 10^{15} \mathrm{~Hz}

when it makes transition from

n=2

to

n=1

. The frequency of radiation emitted in transition from

n=3

to

n=1

is

\frac{x}{9} \times 10^{15} \mathrm{~Hz}

, when

x=

________ .

Question 74

A cricket player catches a ball of mass

120 \mathrm{~g}

moving with

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

speed. If the catching process is completed in

0.1 \mathrm{~s}

then the magnitude of force exerted by the ball on the hand of player will be (in SI unit) :

Options:

A)

30

B)

24

C)

12

D)

25

Question 75

Match List - I with List - II.

List I (Number)	List II (Significant figure)
(A) 1001	(I) 3
(B) 010.1	(II) 4
(C) 100.100	(III) 5
(D) 0.0010010	(IV) 6

Choose the correct answer from the options given below :

Options:

A)

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

B)

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

C)

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

D)

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

Question 76

In a metre-bridge when a resistance in the left gap is

2 \Omega

and unknown resistance in the right gap, the balance length is found to be

40 \mathrm{~cm}

. On shunting the unknown resistance with

2 \Omega

, the balance length changes by :

Options:

A)

62.5

B)

22.5 \mathrm{~cm}

C)

20 \mathrm{~cm}

D)

65 \mathrm{~cm}

Question 77

A transformer has an efficiency of

80 \%

and works at

10 \mathrm{~V}

and

4 \mathrm{~kW}

. If the secondary voltage is

240 \mathrm{~V}

, then the current in the secondary coil is :

Options:

A)

1.33 \mathrm{~A}

B)

13.33 \mathrm{~A}

C)

1.59 \mathrm{~A}

D)

15.1 \mathrm{~A}

Numerical TypeQuestion 78

A particle initially at rest starts moving from reference point

x=0

along

x

-axis, with velocity

v

that varies as

v=4 \sqrt{x} \mathrm{~m} / \mathrm{s}

. The acceleration of the particle is __________

\mathrm{ms}^{-2}

.

Numerical TypeQuestion 79

One end of a metal wire is fixed to a ceiling and a load of

2 \mathrm{~kg}

hangs from the other end. A similar wire is attached to the bottom of the load and another load of

1 \mathrm{~kg}

hangs from this lower wire. Then the ratio of longitudinal strain of upper wire to that of the lower wire will be ________.

[Area of cross section of wire

=0.005 \mathrm{~cm}^2, \mathrm{Y}=2 \times 10^{11} \mathrm{Nm}^{-2}

and

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

]

Numerical TypeQuestion 80

In Young's double slit experiment, monochromatic light of wavelength 5000 Å is used. The slits are

1.0 \mathrm{~mm}

apart and screen is placed at

1.0 \mathrm{~m}

away from slits. The distance from the centre of the screen where intensity becomes half of the maximum intensity for the first time is _________

\times 10^{-6}

\mathrm{m}

.

Numerical TypeQuestion 81

A uniform rod

A B

of mass

2 \mathrm{~kg}

and length

30 \mathrm{~cm}

at rest on a smooth horizontal surface. An impulse of force

0.2 \mathrm{~Ns}

is applied to end B. The time taken by the rod to turn through at right angles will be

\frac{\pi}{x} \mathrm{~s}

, where

x=

_______ .

Question 82

A diatomic gas

(\gamma=1.4)

does

200 \mathrm{~J}

of work when it is expanded isobarically. The heat given to the gas in the process is :

Options:

A)

800 \mathrm{~J}

B)

600 \mathrm{~J}

C)

700 \mathrm{~J}

D)

850 \mathrm{~J}

Question 83

Train A is moving along two parallel rail tracks towards north with speed $72 \mathrm{~km} / \mathrm{h}$ and train B is moving towards south with speed $108 \mathrm{~km} / \mathrm{h}$ . Velocity of train B with respect to A and velocity of ground with respect to B are (in $\mathrm{ms}^{-1}$ ):

Options:

A)

-50 and -30

B)

-50 and 30

C)

-30 and 50

D)

50 and -30

Question 84

A light planet is revolving around a massive star in a circular orbit of radius

\mathrm{R}

with a period of revolution T. If the force of attraction between planet and star is proportional to

\mathrm{R}^{-3 / 2}

then choose the correct option :

Options:

A)

\mathrm{T}^2 \propto \mathrm{R}^{7 / 2}

B)

\mathrm{T}^2 \propto \mathrm{R}^3

C)

\mathrm{T}^2 \propto \mathrm{R}^{5 / 2}

D)

\mathrm{T}^2 \propto \mathrm{R}^{3 / 2}

Question 85

A microwave of wavelength

2.0 \mathrm{~cm}

falls normally on a slit of width

4.0 \mathrm{~cm}

. The angular spread of the central maxima of the diffraction pattern obtained on a screen

1.5 \mathrm{~m}

away from the slit, will be :

Options:

A)

60^{\circ}

B)

45^{\circ}

C)

15^{\circ}

D)

30^{\circ}

Question 86

If the root mean square velocity of hydrogen molecule at a given temperature and pressure is

2 \mathrm{~km} / \mathrm{s}

, the root mean square velocity of oxygen at the same condition in

\mathrm{km} / \mathrm{s}

is :

Options:

A)

1.0

B)

1.5

C)

2.0

D)

0.5

Question 87

If frequency of electromagnetic wave is

60 \mathrm{~MHz}

and it travels in air along

z

direction then the corresponding electric and magnetic field vectors will be mutually perpendicular to each other and the wavelength of the wave (in

\mathrm{m}

) is :

Options:

A)

2.5

B)

5

C)

10

D)

2

Question 88

To measure the temperature coefficient of resistivity

\alpha

of a semiconductor, an electrical arrangement shown in the figure is prepared. The arm BC is made up of the semiconductor. The experiment is being conducted at

25^{\circ} \mathrm{C}

and resistance of the semiconductor arm is

3 \mathrm{~m} \Omega

. Arm

\mathrm{BC}

is cooled at a constant rate of

2^{\circ} \mathrm{C} / \mathrm{s}

. If the galvanometer

\mathrm{G}

shows no deflection after

10 \mathrm{~s}

, then

\alpha

is :

JEE Main 2024 (Online) 1st February Evening Shift Physics - Semiconductor Question 10 English

Options:

A)

-1 \times 10^{-2}{ }^{\circ} \mathrm{C}^{-1}

B)

-2 \times 10^{-2}{ }^{\circ} \mathrm{C}^{-1}

C)

-2.5 \times 10^{-2}{ }^{\circ} \mathrm{C}^{-1}

D)

-1.5 \times 10^{-2}{ }^{\circ} \mathrm{C}^{-1}

Question 89

Conductivity of a photodiode starts changing only if the wavelength of incident light is less than

660 \mathrm{~nm}

. The band gap of photodiode is found to be

\left(\frac{\mathrm{X}}{8}\right) \mathrm{eV}

. The value of

\mathrm{X}

is :

(Given,

\mathrm{h}=6.6 \times 10^{-34} \mathrm{Js}, \mathrm{e}=1.6 \times 10^{-19} \mathrm{C}

)

Options:

A)

11

B)

13

C)

15

D)

21

Numerical TypeQuestion 90

In an electrical circuit drawn below the amount of charge stored in the capacitor is _______

\mu

C.

JEE Main 2024 (Online) 1st February Evening Shift Physics - Capacitor Question 7 English