JEE Mains Apr 15, 2023 Shift 1 Questions with solutions

Question 1

Which is not true for arginine?

Options:

A)

It has a fairly high melting point.

B)

It is associated with more than one

\mathrm{pK}_{\mathrm{a}}

values.

C)

It has high solubility in benzene.

D)

It is a crystalline solid.

Question 2

Decreasing order of reactivity towards electrophilic substitution for the following compounds is :

JEE Main 2023 (Online) 15th April Morning Shift Chemistry - Compounds Containing Nitrogen Question 27 English

Options:

A)

\mathrm{a}>\mathrm{d}>\mathrm{e}>\mathrm{b}>\mathrm{c}

B)

\mathrm{d}>\mathrm{a}>\mathrm{e}>\mathrm{c}>

b

C)

\mathrm{c}>\mathrm{b}>\mathrm{a}>\mathrm{d}>\mathrm{e}

D)

\mathrm{e}>\mathrm{d}>\mathrm{a}>\mathrm{b}>\mathrm{c}

Numerical TypeQuestion 3

For a reversible reaction

\mathrm{A} \rightleftharpoons \mathrm{B}

, the

\Delta \mathrm{H}_{\text{forward reaction}} = 20 \mathrm{~kJ} \mathrm{~mol}^{-1}

. The activation energy of the uncatalysed forward reaction is

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

. When the reaction is catalysed keeping the reactant concentration same, the rate of the catalysed forward reaction at

27^{\circ} \mathrm{C}

is found to be same as that of the uncatalysed reaction at

327^{\circ} \mathrm{C}

.

The activation energy of the catalysed backward reaction is ___________

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

.

Question 4

If

\int\limits_{0}^{1} \frac{1}{\left(5+2 x-2 x^{2}\right)\left(1+e^{(2-4 x)}\right)} d x=\frac{1}{\alpha} \log _{e}\left(\frac{\alpha+1}{\beta}\right), \alpha, \beta>0

, then

\alpha^{4}-\beta^{4}

is equal to :

Options:

A)

-21

B)

21

C)

19

D)

0

Question 5

The number of real roots of the equation

x|x|-5|x+2|+6=0

, is :

Options:

A)

4

B)

3

C)

5

D)

6

Question 6

If

(\alpha, \beta)

is the orthocenter of the triangle

\mathrm{ABC}

with vertices

A(3,-7), B(-1,2)

and

C(4,5)

, then

9 \alpha-6 \beta+60

is equal to :

Options:

A)

30

B)

40

C)

25

D)

35

Question 7

Let

\mathrm{S}

be the set of all values of

\lambda

, for which the shortest distance between

the lines

\frac{x-\lambda}{0}=\frac{y-3}{4}=\frac{z+6}{1}

and

\frac{x+\lambda}{3}=\frac{y}{-4}=\frac{z-6}{0}

is 13. Then

8\left|\sum\limits_{\lambda \in S} \lambda\right|

is equal to :

Options:

A)

306

B)

304

C)

308

D)

302

Numerical TypeQuestion 8

Consider the triangles with vertices

A(2,1), B(0,0)

and

C(t, 4), t \in[0,4]

.

If the maximum and the minimum perimeters of such triangles are obtained at

t=\alpha

and

t=\beta

respectively, then

6 \alpha+21 \beta

is equal to ___________.

Numerical TypeQuestion 9

Let

A=\{1,2,3,4\}

and

\mathrm{R}

be a relation on the set

A \times A

defined by

R=\{((a, b),(c, d)): 2 a+3 b=4 c+5 d\}

. Then the number of elements in

\mathrm{R}

is ____________.

Question 10

A single slit of width

a

is illuminated by a monochromatic light of wavelength

600 \mathrm{~nm}

. The value of '

a

' for which first minimum appears at

\theta=30^{\circ}

on the screen will be :

Options:

A)

{3} \mu \mathrm{m}

B)

0.6 \mu \mathrm{m}

C)

1.8 \mu \mathrm{m}

D)

1.2 \mu \mathrm{m}

Question 11

For designing a voltmeter of range

50 \mathrm{~V}

and an ammeter of range

10 \mathrm{~mA}

using a galvanometer which has a coil of resistance

54 \Omega

showing a full scale deflection for

1 \mathrm{~mA}

as in figure.

JEE Main 2023 (Online) 15th April Morning Shift Physics - Current Electricity Question 48 English

(A) for voltmeter

R \approx 50 \mathrm{k} \Omega

(B) for ammeter

\mathrm{r} \approx 0.2 \Omega

(C) for ammeter

\mathrm{r}=6 \Omega

(D) for voltmeter

R \approx 5 \mathrm{k} \Omega

(E) for voltmeter

R \approx 500 \Omega

Choose the correct answer from the options given below:

Options:

A)

(\mathrm{A})

and

(\mathrm{C})

B)

(A) and (B)

C)

(C) and (E)

D)

(C) and (D)

Question 12

A thermodynamic system is taken through cyclic process. The total work done in the process is :

JEE Main 2023 (Online) 15th April Morning Shift Physics - Heat and Thermodynamics Question 48 English

JEE Main 2023 (Online) 15th April Morning Shift Physics - Heat and Thermodynamics Question 48 English

Options:

A)

100 \mathrm{~J}

B)

Zero

C)

300 \mathrm{~J}

D)

200 \mathrm{~J}

Question 13

Given below are two statements:

Statement I : The equivalent resistance of resistors in a series combination is smaller than least resistance used in the combination.

Statement II : The resistivity of the material is independent of temperature.

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

Options:

A)

Statement I is true but Statement II is false

B)

Both Statement I and Statement II are true

C)

Both Statement I and Statement II are false

D)

Statement I is false but Statement II is true

Numerical TypeQuestion 14

In the given figure the total charge stored in the combination of capacitors is

100~ \mu \mathrm{C}

. The value of '

x

' is _________.

JEE Main 2023 (Online) 15th April Morning Shift Physics - Capacitor Question 20 English

Numerical TypeQuestion 15

As per given figure

A, B

and

C

are the first, second and third excited energy levels of hydrogen atom respectively. If the ratio of the two wavelengths

\left(\right.

i.e.

\left.\frac{\lambda_{1}}{\lambda_{2}}\right)

is

\frac{7}{4 n}

, then the value of

n

will be __________.

JEE Main 2023 (Online) 15th April Morning Shift Physics - Atoms and Nuclei Question 42 English

Numerical TypeQuestion 16

The refractive index of a transparent liquid filled in an equilateral hollow prism is

\sqrt{2}

. The angle of minimum deviation for the liquid will be ___________

^\circ

.

Question 17

During water-gas shift reaction

Options:

A)

water is evaporated in presence of catalyst.

B)

carbon monoxide is oxidized to carbon dioxide.

C)

carbon is oxidized to carbon monoxide.

D)

carbon dioxide is reduced to carbon monoxide.

Question 18

The complex with highest magnitude of crystal field splitting energy

\left(\Delta_{0}\right)

is :

Options:

A)

\left[\mathrm{Fe}\left(\mathrm{OH}_{2}\right)_{6}\right]^{3+}

B)

\left[\mathrm{Mn}\left(\mathrm{OH}_{2}\right)_{6}\right]^{3+}

C)

\left[\mathrm{Cr}\left(\mathrm{OH}_{2}\right)_{6}\right]^{3+}

D)

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

Question 19

The major product formed in the Friedel-Craft acylation of chlorobenzene is

Options:

A)

JEE Main 2023 (Online) 15th April Morning Shift Chemistry - Haloalkanes and Haloarenes Question 24 English Option 1

B)

JEE Main 2023 (Online) 15th April Morning Shift Chemistry - Haloalkanes and Haloarenes Question 24 English Option 2

C)

JEE Main 2023 (Online) 15th April Morning Shift Chemistry - Haloalkanes and Haloarenes Question 24 English Option 3

D)

JEE Main 2023 (Online) 15th April Morning Shift Chemistry - Haloalkanes and Haloarenes Question 24 English Option 4

Question 20

Which of the following statement is correct for paper chromatography?

Options:

A)

Water present in the mobile phase gets absorbed by the paper which then forms the stationary phase.

B)

Water present in the pores of the paper forms the stationary phase.

C)

Paper sheet forms the stationary phase.

D)

Paper and water present in its pores together form the stationary phase.

Question 21

Consider the following sequence of reactions:

JEE Main 2023 (Online) 15th April Morning Shift Chemistry - Compounds Containing Nitrogen Question 28 English

JEE Main 2023 (Online) 15th April Morning Shift Chemistry - Compounds Containing Nitrogen Question 28 English

The product '

\mathrm{B}

' is

Options:

A)

JEE Main 2023 (Online) 15th April Morning Shift Chemistry - Compounds Containing Nitrogen Question 28 English Option 1

B)

JEE Main 2023 (Online) 15th April Morning Shift Chemistry - Compounds Containing Nitrogen Question 28 English Option 2

C)

JEE Main 2023 (Online) 15th April Morning Shift Chemistry - Compounds Containing Nitrogen Question 28 English Option 3

D)

JEE Main 2023 (Online) 15th April Morning Shift Chemistry - Compounds Containing Nitrogen Question 28 English Option 4

Question 22

Consider the following statements:

(A) NF₃ molecule has a trigonal planar structure.

(B) Bond length of

\mathrm{N}_{2}

is shorter than

\mathrm{O}_{2}

.

(C) Isoelectronic molecules or ions have identical bond order.

(D) Dipole moment of

\mathrm{H}_{2}\mathrm{S}

is higher than that of water molecule.

Choose the correct answer from the options given below:

Options:

A)

(C) and (D) are correct

B)

(A) and (B) are correct

C)

(B) and (C) are correct

D)

(A) and (D) are correct

Question 23

JEE Main 2023 (Online) 15th April Morning Shift Chemistry - Alcohols, Phenols and Ethers Question 27 English

'A' formed in the above reaction is

Options:

A)

JEE Main 2023 (Online) 15th April Morning Shift Chemistry - Alcohols, Phenols and Ethers Question 27 English Option 1

B)

JEE Main 2023 (Online) 15th April Morning Shift Chemistry - Alcohols, Phenols and Ethers Question 27 English Option 2

C)

JEE Main 2023 (Online) 15th April Morning Shift Chemistry - Alcohols, Phenols and Ethers Question 27 English Option 3

D)

JEE Main 2023 (Online) 15th April Morning Shift Chemistry - Alcohols, Phenols and Ethers Question 27 English Option 4

Numerical TypeQuestion 24

The number of correct statements from the following is _______.

(A) Conductivity always decreases with decrease in concentration for both strong and weak electrolytes.

(B) The number of ions per unit volume that carry current in a solution increases on dilution.

(C) Molar conductivity increases with decrease in concentration

(D) The variation in molar conductivity is different for strong and weak electrolytes

(E) For weak electrolytes, the change in molar conductivity with dilution is due to decrease in degree of dissociation.

Numerical TypeQuestion 25

In Chromyl chloride, the oxidation state of chromium is

(+)

_______________.

Numerical TypeQuestion 26

30.4 \mathrm{~kJ}

of heat is required to melt one mole of sodium chloride and the entropy change at the melting point is

28.4 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}

at 1 atm. The melting point of sodium chloride is _______________ K (Nearest Integer)

Numerical TypeQuestion 27

The homoleptic and octahedral complex of

\mathrm{Co}^{2+}

and

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

has ___________ unpaired electron(s) in the

t_{2\mathrm{g}}

set of orbitals.

Question 28

Let

[x]

denote the greatest integer function and

f(x)=\max \{1+x+[x], 2+x, x+2[x]\}, 0 \leq x \leq 2

. Let

m

be the number of

points in

[0,2]

, where

f

is not continuous and

n

be the number of points in

(0,2)

, where

f

is not differentiable. Then

(m+n)^{2}+2

is equal to :

Options:

A)

3

B)

6

C)

2

D)

11

Question 29

A bag contains 6 white and 4 black balls. A die is rolled once and the number of balls equal to the number obtained on the die are drawn from the bag at random. The probability that all the balls drawn are white is :

Options:

A)

\frac{1}{4}

B)

\frac{9}{50}

C)

\frac{1}{5}

D)

\frac{11}{50}

Question 30

If the set

\left\{\operatorname{Re}\left(\frac{z-\bar{z}+z \bar{z}}{2-3 z+5 \bar{z}}\right): z \in \mathbb{C}, \operatorname{Re}(z)=3\right\}

is equal to

the interval

(\alpha, \beta]

, then

24(\beta-\alpha)

is equal to :

Options:

A)

36

B)

27

C)

42

D)

30

Numerical TypeQuestion 31

Let

f(x)=\int \frac{d x}{\left(3+4 x^{2}\right) \sqrt{4-3 x^{2}}},|x|<\frac{2}{\sqrt{3}}

. If

f(0)=0

and

f(1)=\frac{1}{\alpha \beta} \tan ^{-1}\left(\frac{\alpha}{\beta}\right)

,

\alpha, \beta>0

, then

\alpha^{2}+\beta^{2}

is equal to ____________.

Question 32

A wire of length '

L

' and radius '

r

' is clamped rigidly at one end. When the other end of the wire is pulled by a force

f

, its length increases by '

l

'. Another wire of same material of length '

2 \mathrm{~L}

' and radius '

2 r

' is pulled by a force '

2 f

'. Then the increase in its length will be :

Options:

A)

2 l

B)

4 l

C)

l

D)

l / 2

Question 33

A body is released from a height equal to the radius

(\mathrm{R})

of the earth. The velocity of the body when it strikes the surface of the earth will be

(Given

g=

acceleration due to gravity on the earth.)

Options:

A)

\sqrt{\frac{g R}{2}}

B)

\sqrt{4 g R}

C)

\sqrt{2 g R}

D)

\sqrt{g R}

Question 34

A vector in

x-y

plane makes an angle of

30^{\circ}

with

y

-axis. The magnitude of

\mathrm{y}

-component of vector is

2 \sqrt{3}

. The magnitude of

x

-component of the vector will be :

Options:

A)

\sqrt{3}

B)

2

C)

6

D)

\frac{1}{\sqrt{3}}

Question 35

The speed of a wave produced in water is given by

v=\lambda^{a} g^{b} \rho^{c}

. Where

\lambda, g

and

\rho

are wavelength of wave, acceleration due to gravity and density of water respectively. The values of

a, b

and

c

respectively, are :

Options:

A)

\frac{1}{2}, 0, \frac{1}{2}

B)

1,1,0

C)

1,-1,0

D)

\frac{1}{2}, \frac{1}{2}, 0

Numerical TypeQuestion 36

An electron in a hydrogen atom revolves around its nucleus with a speed of

6.76 \times 10^6 \mathrm{~ms}^{-1}

in an orbit of radius

0.52 \mathrm{~A}^{\circ}

. The magnetic field produced at the nucleus of the hydrogen atom is _________ T.

Numerical TypeQuestion 37

The fundamental frequency of vibration of a string stretched between two rigid support is

50 \mathrm{~Hz}

. The mass of the string is

18 \mathrm{~g}

and its linear mass density is

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

. The speed of the transverse waves so produced in the string is ___________

\mathrm{ms}^{-1}

Numerical TypeQuestion 38

A

20 \mathrm{~cm}

long metallic rod is rotated with

210~ \mathrm{rpm}

about an axis normal to the rod passing through its one end. The other end of the rod is in contact with a circular metallic ring. A constant and uniform magnetic field

0.2 \mathrm{~T}

parallel to the axis exists everywhere. The emf developed between the centre and the ring is ____________

\mathrm{mV}

.

Take

\pi=\frac{22}{7}

Numerical TypeQuestion 39

There is an air bubble of radius

1.0 \mathrm{~mm}

in a liquid of surface tension

0.075~ \mathrm{Nm}^{-1}

and density

1000 \mathrm{~kg} \mathrm{~m}^{-3}

at a depth of

10 \mathrm{~cm}

below the free surface. The amount by which the pressure inside the bubble is greater than the atmospheric pressure is _________

\mathrm{Pa}\left(\mathrm{g}=10 \mathrm{~ms}^{-2}\right)

Numerical TypeQuestion 40

A solid sphere and a solid cylinder of same mass and radius are rolling on a horizontal surface without slipping. The ratio of their radius of gyrations respectively

\left(k_{\text {sph }}: k_{\text {cyl }}\right)

is

2: \sqrt{x}

. The value of

x

is ____________ .

Question 41

Given below are two statements:

Statement I : According to Bohr's model of hydrogen atom, the angular momentum of an electron in a given stationary state is quantised.

Statement II : The concept of electron in Bohr's orbit, violates the Heisenberg uncertainty principle.

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 incorrect

B)

Statement I is correct but Statement II is incorrect

C)

Both Statement I and Statement II are correct

D)

Statement I is incorrect but Statement II is correct

Question 42

Which of the following statement(s) is/are correct?

(A) The

\mathrm{pH}

of

1 \times 10^{-8}~ \mathrm{M} ~\mathrm{HCl}

solution is 8 .

(B) The conjugate base of

\mathrm{H}_{2} \mathrm{PO}_{4}^{-}

is

\mathrm{HPO}_{4}^{2-}

.

(C)

\mathrm{K}_{\mathrm{w}}

increases with increase in temperature.

(D) When a solution of a weak monoprotic acid is titrated against a strong base at half neutralisation point,

\mathrm{pH}=\frac{1}{2} \mathrm{pK}_{\mathrm{a}}

Choose the correct answer from the options given below:

Options:

A)

(\mathrm{A}),(\mathrm{B}),(\mathrm{C})

B)

(B), (C)

C)

(B), (C), (D)

D)

(A), (D)

Numerical TypeQuestion 43

The volume (in

\mathrm{mL}

) of

0.1 \mathrm{M} ~\mathrm{AgNO}_{3}

required for complete precipitation of chloride ions present in

20 \mathrm{~mL}

of

0.01 \mathrm{M}

solution of

\left[\mathrm{Cr}\left(\mathrm{H}_{2} \mathrm{O}\right)_{5} \mathrm{Cl}\right] \mathrm{Cl}_{2}

as silver chloride is __________.

Numerical TypeQuestion 44

The vapour pressure of

30 \%(\mathrm{w} / \mathrm{v})

aqueous solution of glucose is __________

\mathrm{mm} ~\mathrm{Hg}

at

25^{\circ} \mathrm{C}

.

[Given : The density of

30 \%

(w/v), aqueous solution of glucose is

1.2 \mathrm{~g} \mathrm{~cm}^{-3}

and vapour pressure of pure water is

24 \mathrm{~mm}~ \mathrm{Hg}

.]

(Molar mass of glucose is

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

.)

Numerical TypeQuestion 45

The total change in the oxidation state of manganese involved in the reaction of

\mathrm{KMnO}_{4}

and potassium iodide in the acidic medium is ____________.

Question 46

Let

x=x(y)

be the solution of the differential equation

2(y+2) \log _{e}(y+2) d x+\left(x+4-2 \log _{e}(y+2)\right) d y=0, y>-1

with

x\left(e^{4}-2\right)=1

. Then

x\left(e^{9}-2\right)

is equal to :

Options:

A)

\frac{4}{9}

B)

\frac{32}{9}

C)

\frac{10}{3}

D)

3

Question 47

The mean and standard deviation of 10 observations are 20 and 8 respectively. Later on, it was observed that one observation was recorded as 50 instead of 40. Then the correct variance is :

Options:

A)

11

B)

12

C)

13

D)

14

Question 48

Let

A_{1}

and

A_{2}

be two arithmetic means and

G_{1}, G_{2}, G_{3}

be three geometric

means of two distinct positive numbers. Then

G_{1}^{4}+G_{2}^{4}+G_{3}^{4}+G_{1}^{2} G_{3}^{2}

is equal to :

Options:

A)

\left(A_{1}+A_{2}\right)^{2} G_{1} G_{3}

B)

\left(A_{1}+A_{2}\right) G_{1}^{2} G_{3}^{2}

C)

2\left(A_{1}+A_{2}\right) G_{1}^{2} G_{3}^{2}

D)

2\left(A_{1}+A_{2}\right) G_{1} G_{3}

Numerical TypeQuestion 49

The number of elements in the set

\left\{n \in \mathbb{N}: 10 \leq n \leq 100\right.

and

3^{n}-3

is a multiple of 7

\}

is ___________.

Question 50

The electric field due to a short electric dipole at a large distance

(r)

from center of dipole on the equatorial plane varies with distance as :

Options:

A)

\frac{1}{r^{2}}

B)

\frac{1}{r}

C)

r

D)

\frac{1}{r^{3}}

Question 51

The de Broglie wavelength of an electron having kinetic energy

\mathrm{E}

is

\lambda

. If the kinetic energy of electron becomes

\frac{E}{4}

, then its de-Broglie wavelength will be :

Options:

A)

\sqrt{2} \lambda

B)

2 \lambda

C)

\frac{\lambda}{2}

D)

\frac{\lambda}{\sqrt{2}}

Question 52

In a linear Simple Harmonic Motion (SHM)

(A) Restoring force is directly proportional to the displacement.

(B) The acceleration and displacement are opposite in direction.

(C) The velocity is maximum at mean position.

(D) The acceleration is minimum at extreme points.

Choose the correct answer from the options given below:

Options:

A)

{\text {(A), (B) and (D) only }}

B)

(C) and (D) only

C)

(A), (B) and (C) Only

D)

(A), (C) and (D) only

Question 53

Two identical particles each of mass '

m

' go round a circle of radius

a

under the action of their mutual gravitational attraction. The angular speed of each particle will be :

Options:

A)

\sqrt{\frac{G m}{2 a^{3}}}

B)

\sqrt{\frac{G m}{a^{3}}}

C)

\sqrt{\frac{G m}{8 a^{3}}}

D)

\sqrt{\frac{G m}{4 a^{3}}}

Question 54

Match List I with List II of Electromagnetic waves with corresponding wavelength range :

List I	List II
(A) Microwave	(I) $400 \mathrm{~nm}$ to $1 \mathrm{~nm}$
(B) Ultraviolet	(II) $1 \mathrm{~nm}$ to $10^{-3} \mathrm{~nm}$
(C) X-Ray	(III) $1 \mathrm{~mm}$ to $700 \mathrm{~nm}$
(D) Infra-red	(IV) $0.1 \mathrm{~m}$ to $1 \mathrm{~mm}$

Choose the correct answer from the options given below:

Options:

A)

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

B)

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

C)

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

D)

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

Question 55

12 \mathrm{~V}

battery connected to a coil of resistance

6 \Omega

through a switch, drives a constant current in the circuit. The switch is opened in

1 \mathrm{~ms}

. The emf induced across the coil is

20 \mathrm{~V}

. The inductance of the coil is :

Options:

A)

5 ~ \mathrm{mH}

B)

8 ~\mathrm{mH}

C)

10~ \mathrm{mH}

D)

12 ~\mathrm{mH}

Question 56

The number of

\mathrm{P}-\mathrm{O}-\mathrm{P}

bonds in

\mathrm{H}_{4} \mathrm{P}_{2} \mathrm{O}_{7},\left(\mathrm{HPO}_{3}\right)_{3}

and

\mathrm{P}_{4} \mathrm{O}_{10}

are respectively :

Options:

A)

1,3,6

B)

1,2,4

C)

0,3,4

D)

0,3,6

Question 57

JEE Main 2023 (Online) 15th April Morning Shift Chemistry - Aldehydes, Ketones and Carboxylic Acids Question 29 English

In the above conversion the correct sequence of reagents to be added is

Options:

A)

(i)

\mathrm{KMnO}_{4}

, (ii)

\mathrm{Br}_{2} / \mathrm{Fe}

, (iii)

\mathrm{Fe} / \mathrm{H}^{+}

, (iv)

\mathrm{Cl}_{2}

B)

(i)

\mathrm{Fe} / \mathrm{H}^{+}

, (ii)

\mathrm{HONO}

, (iii)

\mathrm{CuCl}

, (iv)

\mathrm{KMnO}_4

, (v)

\mathrm{Br}_2

C)

(i)

\mathrm{Br}_{2} / \mathrm{Fe}

, (ii)

\mathrm{Fe} / \mathrm{H}^{+}

, (iii)

\mathrm{HONO}

, (iv)

\mathrm{CuCl}

, (v)

\mathrm{KMnO}_{4}

D)

(i)

\mathrm{Br}_{2} / \mathrm{Fe}

, (ii)

\mathrm{Fe} / \mathrm{H}^{+}

, (iii)

\mathrm{KMnO}_{4}

, (iv)

\mathrm{Cl}_{2}

Question 58

The product formed in the following multistep reaction is :

JEE Main 2023 (Online) 15th April Morning Shift Chemistry - Hydrocarbons Question 21 English

JEE Main 2023 (Online) 15th April Morning Shift Chemistry - Hydrocarbons Question 21 English

Options:

A)

JEE Main 2023 (Online) 15th April Morning Shift Chemistry - Hydrocarbons Question 21 English Option 1

B)

JEE Main 2023 (Online) 15th April Morning Shift Chemistry - Hydrocarbons Question 21 English Option 2

C)

\mathrm{CH}_{3}-\mathrm{CH}_{2}-\mathrm{CH}_{2}-\mathrm{CH}_{2}-\mathrm{OH}

D)

JEE Main 2023 (Online) 15th April Morning Shift Chemistry - Hydrocarbons Question 21 English Option 4

Numerical TypeQuestion 59

The total number of isoelectronic species from the given set is ___________.

\mathrm{O}^{2-}, \mathrm{F}^{-}, \mathrm{Al}, \mathrm{Mg}^{2+}, \mathrm{Na}^{+}, \mathrm{O}^{+}, \mathrm{Mg}, \mathrm{Al}^{3+}, \mathrm{F}

Question 60

The total number of three-digit numbers, divisible by 3, which can be formed using the digits

1,3,5,8

, if repetition of digits is allowed, is :

Options:

A)

21

B)

22

C)

18

D)

20

Question 61

Let

\mathrm{ABCD}

be a quadrilateral. If

\mathrm{E}

and

\mathrm{F}

are the mid points of the diagonals

\mathrm{AC}

and

\mathrm{BD}

respectively and

(\overrightarrow{A B}-\overrightarrow{B C})+(\overrightarrow{A D}-\overrightarrow{D C})=k \overrightarrow{F E}

, then

k

is equal to :

Options:

A)

-2

B)

4

C)

-4

D)

2

Question 62

If the domain of the function

f(x)=\log _{e}\left(4 x^{2}+11 x+6\right)+\sin ^{-1}(4 x+3)+\cos ^{-1}\left(\frac{10 x+6}{3}\right)

is

(\alpha, \beta]

, then

36|\alpha+\beta|

is equal to :

Options:

A)

72

B)

54

C)

45

D)

63

Question 63

Let

\left(a+b x+c x^{2}\right)^{10}=\sum\limits_{i=0}^{20} p_{i} x^{i}, a, b, c \in \mathbb{N}

.

If

p_{1}=20

and

p_{2}=210

, then

2(a+b+c)

is equal to :

Options:

A)

15

B)

8

C)

6

D)

12

Numerical TypeQuestion 64

A person forgets his 4-digit ATM pin code. But he remembers that in the code all the digits are different, the greatest digit is 7 and the sum of the first two digits is equal to the sum of the last two digits. Then the maximum number of trials necessary to obtain the correct code is ___________.

Numerical TypeQuestion 65

Let an ellipse with centre

(1,0)

and latus rectum of length

\frac{1}{2}

have its major axis along

\mathrm{x}

-axis. If its minor axis subtends an angle

60^{\circ}

at the foci, then the square of the sum of the lengths of its minor and major axes is equal to ____________.

Numerical TypeQuestion 66

If the area bounded by the curve

2 y^{2}=3 x

, lines

x+y=3, y=0

and outside the circle

(x-3)^{2}+y^{2}=2

is

\mathrm{A}

, then

4(\pi+4 A)

is equal to ____________.

Question 67

The position of a particle related to time is given by

x=\left(5 t^{2}-4 t+5\right) \mathrm{m}

. The magnitude of velocity of the particle at

t=2 s

will be :

Options:

A)

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

B)

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

C)

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

D)

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

Question 68

In the given circuit, the current (I) through the battery will be

JEE Main 2023 (Online) 15th April Morning Shift Physics - Semiconductor Question 24 English

JEE Main 2023 (Online) 15th April Morning Shift Physics - Semiconductor Question 24 English

Options:

A)

1A

B)

2.5 \mathrm{~A}

C)

2 \mathrm{~A}

D)

1.5 \mathrm{~A}

Question 69

The position vector of a particle related to time

t

is given by

\vec{r}=\left(10 t \hat{i}+15 t^{2} \hat{j}+7 \hat{k}\right) m

The direction of net force experienced by the particle is :

Options:

A)

Positive

x

- axis

B)

Positive

y

- axis

C)

Positive

z

- axis

D)

In

x

-

y

plane

Question 70

A flask contains Hydrogen and Argon in the ratio

2: 1

by mass. The temperature of the mixture is

30^{\circ} \mathrm{C}

. The ratio of average kinetic energy per molecule of the two gases (

\mathrm{K}

argon/K hydrogen) is :

(Given: Atomic Weight of

\mathrm{Ar}=39.9

)

Options:

A)

\frac{39.9}{2}

B)

2

C)

39.9

D)

1

Numerical TypeQuestion 71

A block of mass

10 \mathrm{~kg}

is moving along

\mathrm{x}

-axis under the action of force

F=5 x~ N

. The work done by the force in moving the block from

x=2 m

to

4 m

will be __________ J.

Numerical TypeQuestion 72

A network of four resistances is connected to

9 \mathrm{~V}

battery, as shown in figure. The magnitude of voltage difference between the points

\mathrm{A}

and

\mathrm{B}

is __________

V

.

JEE Main 2023 (Online) 15th April Morning Shift Physics - Current Electricity Question 46 English