JEE Mains Jan 27, 2024 Shift 1 Questions with solutions

Question 1

Which of the following has highly acidic hydrogen?

Options:

A)

JEE Main 2024 (Online) 27th January Morning Shift Chemistry - Basics of Organic Chemistry Question 20 English Option 1

B)

JEE Main 2024 (Online) 27th January Morning Shift Chemistry - Basics of Organic Chemistry Question 20 English Option 2

C)

JEE Main 2024 (Online) 27th January Morning Shift Chemistry - Basics of Organic Chemistry Question 20 English Option 3

D)

Question 2

Consider the following complex ions

$\begin{aligned} & \mathrm{P}=\left[\mathrm{FeF}_6\right]^{3-} \\ & \mathrm{Q}=\left[\mathrm{V}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]^{2+} \\ & \mathrm{R}=\left[\mathrm{Fe}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]^{2+} \end{aligned}$

The correct order of the complex ions, according to their spin only magnetic moment values (in B.M.) is :

Options:

A)

R < Q < P

B)

R < P < Q

C)

Q < R < P

D)

Q < P < R

Question 3

The ascending order of acidity of $-\mathrm{OH}$ group in the following compounds is :

JEE Main 2024 (Online) 27th January Morning Shift Chemistry - Alcohols, Phenols and Ethers Question 9 English 1

Choose the correct answer from the options given below:

Options:

A)

(A) < (D) < (C) < (B) < (E)

B)

(C) < (A) < (D) < (B) < (E)

C)

(C) < (D) < (B) < (A) < (E)

D)

(A) < (C) < (D) < (B) < (E)

Question 4

The correct statement regarding nucleophilic substitution reaction in a chiral alkyl halide is ;

Options:

A)

Retention occurs in

S_N 1

reaction and inversion occurs in

\mathrm{S}_{\mathrm{N}} 2

reaction.

B)

Racemisation occurs in

\mathrm{S}_{\mathrm{N}} 1

reaction and retention occurs in

\mathrm{S}_{\mathrm{N}} 2

reaction.

C)

Racemisation occurs in both

\mathrm{S}_{\mathrm{N}} 1

and

\mathrm{S}_{\mathrm{N}} 2

reactions.

D)

Racemisation occurs in

S_N 1

reaction and inversion occurs in

\mathrm{S}_{\mathrm{N}} 2

reaction.

Numerical TypeQuestion 5

The mass of silver (Molar mass of $\mathrm{Ag}: 108 \mathrm{~gmol}^{-1}$ ) displaced by a quantity of electricity which displaces $5600 \mathrm{~mL}$ of $\mathrm{O}_2$ at S.T.P. will be ______ g.

Numerical TypeQuestion 6

If three moles of an ideal gas at $300 \mathrm{~K}$ expand isotherrnally from $30 \mathrm{~dm}^3$ to $45 \mathrm{~dm}^3$ against a constant opposing pressure of $80 \mathrm{~kPa}$ , then the amount of heat transferred is _______ J.

Question 7

If

\int\limits_0^1 \frac{1}{\sqrt{3+x}+\sqrt{1+x}} \mathrm{~d} x=\mathrm{a}+\mathrm{b} \sqrt{2}+\mathrm{c} \sqrt{3}

, where

\mathrm{a}, \mathrm{b}, \mathrm{c}

are rational numbers, then

2 \mathrm{a}+3 \mathrm{~b}-4 \mathrm{c}

is equal to :

Options:

A)

10

B)

7

C)

4

D)

8

Question 8

Let

S=\{1,2,3, \ldots, 10\}

. Suppose

M

is the set of all the subsets of

S

, then the relation

\mathrm{R}=\{(\mathrm{A}, \mathrm{B}): \mathrm{A} \cap \mathrm{B} \neq \phi ; \mathrm{A}, \mathrm{B} \in \mathrm{M}\}

is :

Options:

A)

symmetric only

B)

reflexive only

C)

symmetric and reflexive only

D)

symmetric and transitive only

Question 9

If the shortest distance of the parabola

y^2=4 x

from the centre of the circle

x^2+y^2-4 x-16 y+64=0

is

\mathrm{d}

, then

\mathrm{d}^2

is equal to :

Options:

A)

16

B)

24

C)

20

D)

36

Question 10

Consider the function.

f(x)=\left\{\begin{array}{cc} \frac{\mathrm{a}\left(7 x-12-x^2\right)}{\mathrm{b}\left|x^2-7 x+12\right|} & , x<3 \\\\ 2^{\frac{\sin (x-3)}{x-[x]}} & , x>3 \\\\ \mathrm{~b} & , x=3, \end{array}\right.

where

[x]

denotes the greatest integer less than or equal to

x

. If

\mathrm{S}

denotes the set of all ordered pairs (a, b) such that

f(x)

is continuous at

x=3

, then the number of elements in

\mathrm{S}

is :

Options:

A)

Infinitely many

B)

4

C)

2

D)

1

Question 11

Let

\mathrm{a}_1, \mathrm{a}_2, \ldots \mathrm{a}_{10}

be 10 observations such that

\sum\limits_{\mathrm{k}=1}^{10} \mathrm{a}_{\mathrm{k}}=50

and

\sum\limits_{\forall \mathrm{k} < \mathrm{j}} \mathrm{a}_{\mathrm{k}} \cdot \mathrm{a}_{\mathrm{j}}=1100

. Then the standard deviation of

\mathrm{a}_1, \mathrm{a}_2, \ldots, \mathrm{a}_{10}

is equal to :

Options:

A)

5

B)

\sqrt{115}

C)

10

D)

\sqrt{5}

Question 12

The function

f: \mathbf{N}-\{1\} \rightarrow \mathbf{N}

; defined by

f(\mathrm{n})=

the highest prime factor of

\mathrm{n}

, is :

Options:

A)

one-one only

B)

neither one-one nor onto

C)

onto only

D)

both one-one and onto

Numerical TypeQuestion 13

A fair die is tossed repeatedly until a six is obtained. Let

X

denote the number of tosses required and let

a=P(X=3), b=P(X \geqslant 3)

and

c=P(X \geqslant 6 \mid X>3)

. Then

\frac{b+c}{a}

is equal to __________.

Question 14

A proton moving with a constant velocity passes through a region of space without any change in its velocity. If $\overrightarrow{\mathrm{E}}$ and $\overrightarrow{\mathrm{B}}$ represent the electric and magnetic fields respectively, then the region of space may have :

(A) $\mathrm{E}=0, \mathrm{~B}=0$

(B) $\mathrm{E}=0, \mathrm{~B} \neq 0$

(C) $\mathrm{E} \neq 0, \mathrm{~B}=0$

(D) $\mathrm{E} \neq 0, \mathrm{~B} \neq 0$

Choose the most appropriate answer from the options given below :

Options:

A)

(A), (B) and (C) only

B)

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

C)

(A), (B) and (D) only

D)

(B), (C) and (D) only

Question 15

The radius of third stationary orbit of electron for Bohr's atom is R. The radius of fourth stationary orbit will be:

Options:

A)

\frac{4}{3} \mathrm{R}

B)

\frac{16}{9} R

C)

\frac{3}{4} R

D)

\frac{9}{16} \mathrm{R}

Question 16

A rectangular loop of length $2.5 \mathrm{~m}$ and width $2 \mathrm{~m}$ is placed at $60^{\circ}$ to a magnetic field of $4 \mathrm{~T}$ . The loop is removed from the field in $10 \mathrm{~sec}$ . The average emf induced in the loop during this time is

Options:

A)

-2 \mathrm{~V}

B)

+2 \mathrm{~V}

C)

+1 \mathrm{~V}

D)

-1 \mathrm{~V}

Question 17

A wire of resistance $\mathrm{R}$ and length $\mathrm{L}$ is cut into 5 equal parts. If these parts are joined parallely, then resultant resistance will be :

Options:

A)

\frac{1}{25} \mathrm{R}

B)

\frac{1}{5} R

C)

25 R

D)

5 R

Numerical TypeQuestion 18

A particle starts from origin at $t=0$ with a velocity $5 \hat{i} \mathrm{~m} / \mathrm{s}$ and moves in $x-y$ plane under action of a force which produces a constant acceleration of $(3 \hat{i}+2 \hat{j}) \mathrm{m} / \mathrm{s}^2$ . If the $x$ -coordinate of the particle at that instant is $84 \mathrm{~m}$ , then the speed of the particle at this time is $\sqrt{\alpha} \mathrm{~m} / \mathrm{s}$ . The value of $\alpha$ is _________.

Numerical TypeQuestion 19

In a nuclear fission process, a high mass nuclide $(A \approx 236)$ with binding energy $7.6 \mathrm{~MeV} /$ Nucleon dissociated into middle mass nuclides $(\mathrm{A} \approx 118)$ , having binding energy of $8.6 \mathrm{~MeV} / \mathrm{Nucleon}$ . The energy released in the process would be ______ $\mathrm{MeV}$ .

Question 20

Given below are two statements :

Statement (I) : The $4 \mathrm{f}$ and $5 \mathrm{f}$ - series of elements are placed separately in the Periodic table to preserve the principle of classification.

Statement (II) : S-block elements can be found in pure form in nature.

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 21

Cyclohexene

JEE Main 2024 (Online) 27th January Morning Shift Chemistry - Basics of Organic Chemistry Question 26 English

is ________ type of an organic compound.

Options:

A)

Benzenoid aromatic

B)

Benzenoid non-aromatic

C)

Acyclic

D)

Alicyclic

Question 22

Yellow compound of lead chromate gets dissolved on treatment with hot $\mathrm{NaOH}$ solution. The product of lead formed is a :

Options:

A)

Tetraanionic complex with coordination number six

B)

Neutral complex with coordination number four

C)

Dianionic complex with coordination number six

D)

Dianionic complex with coordination number four

Numerical TypeQuestion 23

Among the given organic compounds, the total number of aromatic compounds is

JEE Main 2024 (Online) 27th January Morning Shift Chemistry - Basics of Organic Chemistry Question 22 English

Numerical TypeQuestion 24

From the given list, the number of compounds with +4 oxidation state of Sulphur ________.

$\mathrm{SO}_3, \mathrm{H}_2 \mathrm{SO}_3, \mathrm{SOCl}_2, \mathrm{SF}_4, \mathrm{BaSO}_4, \mathrm{H}_2 \mathrm{S}_2 \mathrm{O}_7$

Question 25

If

(a, b)

be the orthocentre of the triangle whose vertices are

(1,2),(2,3)

and

(3,1)

, and

\mathrm{I}_1=\int\limits_{\mathrm{a}}^{\mathrm{b}} x \sin \left(4 x-x^2\right) \mathrm{d} x, \mathrm{I}_2=\int\limits_{\mathrm{a}}^{\mathrm{b}} \sin \left(4 x-x^2\right) \mathrm{d} x

, then

36 \frac{\mathrm{I}_1}{\mathrm{I}_2}

is equal to :

Options:

A)

80

B)

72

C)

66

D)

88

Question 26

Let

x=x(\mathrm{t})

and

y=y(\mathrm{t})

be solutions of the differential equations

\frac{\mathrm{d} x}{\mathrm{dt}}+\mathrm{a} x=0

and

\frac{\mathrm{d} y}{\mathrm{dt}}+\mathrm{by}=0

respectively,

\mathrm{a}, \mathrm{b} \in \mathbf{R}

. Given that

x(0)=2 ; y(0)=1

and

3 y(1)=2 x(1)

, the value of

\mathrm{t}

, for which

x(\mathrm{t})=y(\mathrm{t})

, is :

Options:

A)

\log _{\frac{2}{3}} 2

B)

\log _{\frac{4}{3}} 2

C)

\log _4 3

D)

\log _3 4

Question 27

The distance, of the point

(7,-2,11)

from the line

\frac{x-6}{1}=\frac{y-4}{0}=\frac{z-8}{3}

along the line

\frac{x-5}{2}=\frac{y-1}{-3}=\frac{z-5}{6}

, is :

Options:

A)

12

B)

18

C)

21

D)

14

Question 28

Consider the matrix

f(x)=\left[\begin{array}{ccc}\cos x & -\sin x & 0 \\ \sin x & \cos x & 0 \\ 0 & 0 & 1\end{array}\right]

.

Given below are two statements :

Statement I :

f(-x)

is the inverse of the matrix

f(x)

.

Statement II :

f(x) f(y)=f(x+y)

.

In the light of the above statements, choose the correct 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 29

Four distinct points

(2 k, 3 k),(1,0),(0,1)

and

(0,0)

lie on a circle for

k

equal to :

Options:

A)

\frac{3}{13}

B)

\frac{2}{13}

C)

\frac{5}{13}

D)

\frac{1}{13}

Question 30

If the shortest distance between the lines

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

and

\frac{x-\lambda}{2}=\frac{y+1}{4}=\frac{z-2}{-5}

is

\frac{6}{\sqrt{5}}

, then the sum of all possible values of

\lambda

is :

Options:

A)

10

B)

5

C)

7

D)

8

Question 31

{ }^{n-1} C_r=\left(k^2-8\right){ }^n C_{r+1}

if and only if :

Options:

A)

2 \sqrt{2}<\mathrm{k}<2 \sqrt{3}

B)

2 \sqrt{2}<\mathrm{k} \leq 3

C)

2 \sqrt{3}<\mathrm{k}<3 \sqrt{3}

D)

2 \sqrt{3}<\mathrm{k} \leq 3 \sqrt{2}

Question 32

Let

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

\overrightarrow{\mathrm{b}}=3(\hat{i}-\hat{j}+\hat{k})

.
Let

\overrightarrow{\mathrm{c}}

be the vector such that

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

and

\vec{a} \cdot \vec{c}=3

.
Then

\vec{a} \cdot((\vec{c} \times \vec{b})-\vec{b}-\vec{c})

is equal to :

Options:

A)

32

B)

36

C)

24

D)

20

Numerical TypeQuestion 33

If

8=3+\frac{1}{4}(3+p)+\frac{1}{4^2}(3+2 p)+\frac{1}{4^3}(3+3 p)+\cdots \cdots \infty

, then the value of

p

is ____________.

Numerical TypeQuestion 34

Let the area of the region

\left\{(x, y): x-2 y+4 \geqslant 0, x+2 y^2 \geqslant 0, x+4 y^2 \leq 8, y \geqslant 0\right\}

be

\frac{\mathrm{m}}{\mathrm{n}}

, where

\mathrm{m}

and

\mathrm{n}

are coprime numbers. Then

\mathrm{m}+\mathrm{n}

is equal to _____________.

Question 35

Position of an ant ( $\mathrm{S}$ in metres) moving in $\mathrm{Y}$ - $\mathrm{Z}$ plane is given by $S=2 t^2 \hat{j}+5 \hat{k}$ (where $t$ is in second). The magnitude and direction of velocity of the ant at $\mathrm{t}=1 \mathrm{~s}$ will be :

Options:

A)

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

in

y

-direction

B)

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

in

x

-direction

C)

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

in

\mathrm{z}

-direction

D)

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

in

y

-direction

Question 36

Given below are two statements :

Statement (I) :Viscosity of gases is greater than that of liquids.

Statement (II) : Surface tension of a liquid decreases due to the presence of insoluble impurities.

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

Options:

A)

Statement I is correct but statement II is incorrect

B)

Statement I is incorrect but Statement II is correct

C)

Both Statement I and Statement II are incorrect

D)

Both Statement I and Statement II are correct

Question 37

Identify the physical quantity that cannot be measured using spherometer :

Options:

A)

Radius of curvature of concave surface

B)

Specific rotation of liquids

C)

Thickness of thin plates

D)

Radius of curvature of convex surface

Question 38

An electric charge $10^{-6} \mu \mathrm{C}$ is placed at origin $(0,0)$ $\mathrm{m}$ of $\mathrm{X}-\mathrm{Y}$ co-ordinate system. Two points $\mathrm{P}$ and $\mathrm{Q}$ are situated at $(\sqrt{3}, \sqrt{3}) \mathrm{m}$ and $(\sqrt{6}, 0) \mathrm{m}$ respectively. The potential difference between the points \mathrm{P}$ and $\mathrm{Q} will be :

Options:

A)

\sqrt{3} \mathrm{~V}

B)

\sqrt{6} \mathrm{~V}

C)

0 \mathrm{~V}

D)

3 \mathrm{~V}

Question 39

A convex lens of focal length $40 \mathrm{~cm}$ forms an image of an extended source of light on a photoelectric cell. A current I is produced. The lens is replaced by another convex lens having the same diameter but focal length $20 \mathrm{~cm}$ . The photoelectric current now is :

Options:

A)

\mathrm{\frac{I}{2}}

B)

4 I

C)

2 I

D)

I

Question 40

A body of mass $1000 \mathrm{~kg}$ is moving horizontally with a velocity $6 \mathrm{~m} / \mathrm{s}$ . If $200 \mathrm{~kg}$ extra mass is added, the final velocity (in $\mathrm{m} / \mathrm{s}$ ) is:

Options:

A)

6

B)

2

C)

3

D)

5

Question 41

A plane electromagnetic wave propagating in $\mathrm{x}$ -direction is described by

$E_y=\left(200 \mathrm{Vm}^{-1}\right) \sin \left[1.5 \times 10^7 t-0.05 x\right] \text {; }$

The intensity of the wave is :

(Use $\epsilon_0=8.85 \times 10^{-12} \mathrm{C}^2 \mathrm{~N}^{-1} \mathrm{~m}^{-2}$ )

Options:

A)

35.4 \mathrm{~Wm}^{-2}

B)

53.1 \mathrm{~Wm}^{-2}

C)

26.6 \mathrm{~Wm}^{-2}

D)

106.2 \mathrm{~Wm}^{-2}

Question 42

A wire of length $10 \mathrm{~cm}$ and radius $\sqrt{7} \times 10^{-4} \mathrm{~m}$ connected across the right gap of a meter bridge. When a resistance of $4.5 \Omega$ is connected on the left gap by using a resistance box, the balance length is found to be at $60 \mathrm{~cm}$ from the left end. If the resistivity of the wire is $\mathrm{R} \times 10^{-7} \Omega \mathrm{m}$ , then value of $\mathrm{R}$ is :

Options:

A)

63

B)

70

C)

66

D)

35

Numerical TypeQuestion 43

Two coils have mutual inductance $0.002 \mathrm{~H}$ . The current changes in the first coil according to the relation $\mathrm{i}=\mathrm{i}_0 \sin \omega \mathrm{t}$ , where $\mathrm{i}_0=5 \mathrm{~A}$ and $\omega=50 \pi$ rad/s. The maximum value of emf in the second coil is $\frac{\pi}{\alpha} \mathrm{~V}$ . The value of $\alpha$ is _______.

Numerical TypeQuestion 44

Four particles each of mass $1 \mathrm{~kg}$ are placed at four corners of a square of side $2 \mathrm{~m}$ . Moment of inertia of system about an axis perpendicular to its plane and passing through one of its vertex is _____ $\mathrm{kgm}^2$ .

JEE Main 2024 (Online) 27th January Morning Shift Physics - Rotational Motion Question 10 English

Numerical TypeQuestion 45

The charge accumulated on the capacitor connected in the following circuit is _______ $\mu \mathrm{C}$ (Given $\mathrm{C}=150 \mu \mathrm{F})$

JEE Main 2024 (Online) 27th January Morning Shift Physics - Capacitor Question 5 English

Numerical TypeQuestion 46

If average depth of an ocean is $4000 \mathrm{~m}$ and the bulk modulus of water is $2 \times 10^9 \mathrm{~Nm}^{-2}$ , then fractional compression $\frac{\Delta V}{V}$ of water at the bottom of ocean is $\alpha \times 10^{-2}$ . The value of $\alpha$ is _______ (Given, $\mathrm{g}=10 \mathrm{~ms}^{-2}, \rho=1000 \mathrm{~kg} \mathrm{~m}^{-3}$ )

Question 47

Two nucleotides are joined together by a linkage known as :

Options:

A)

Phosphodiester linkage

B)

Glycosidic linkage

C)

Disulphide linkage

D)

Peptide linkage

Question 48

Highest enol content will be shown by:

Options:

A)

JEE Main 2024 (Online) 27th January Morning Shift Chemistry - Aldehydes, Ketones and Carboxylic Acids Question 13 English Option 1

B)

JEE Main 2024 (Online) 27th January Morning Shift Chemistry - Aldehydes, Ketones and Carboxylic Acids Question 13 English Option 2

C)

JEE Main 2024 (Online) 27th January Morning Shift Chemistry - Aldehydes, Ketones and Carboxylic Acids Question 13 English Option 3

D)

JEE Main 2024 (Online) 27th January Morning Shift Chemistry - Aldehydes, Ketones and Carboxylic Acids Question 13 English Option 4

Question 49

Which of the following is strongest Bronsted base?

Options:

A)

JEE Main 2024 (Online) 27th January Morning Shift Chemistry - Basics of Organic Chemistry Question 21 English Option 1

B)

JEE Main 2024 (Online) 27th January Morning Shift Chemistry - Basics of Organic Chemistry Question 21 English Option 2

C)

JEE Main 2024 (Online) 27th January Morning Shift Chemistry - Basics of Organic Chemistry Question 21 English Option 3

D)

JEE Main 2024 (Online) 27th January Morning Shift Chemistry - Basics of Organic Chemistry Question 21 English Option 4

Question 50

Choose the polar molecule from the following:

Options:

A)

\mathrm{CCl}_4

B)

\mathrm{CO}_2

C)

\mathrm{CH}_2=\mathrm{CH}_2

D)

\mathrm{CHCl}_3

Question 51

IUPAC name of following compound (P) is:

JEE Main 2024 (Online) 27th January Morning Shift Chemistry - Basics of Organic Chemistry Question 25 English

Options:

A)

l-Ethyl-5, 5-dimethylcyclohexane

B)

3-Ethyl-1,1-dimethylcyclohexane

C)

l-Ethyl-3, 3-dimethylcyclohexane

D)

1,1-Dimethyl-3-ethylcyclohexane

Numerical TypeQuestion 52

Mass of methane required to produce $22 \mathrm{~g}$ of $\mathrm{CO}_2$ after complete combustion is _______ g.

(Given Molar mass in g mol-1 $\mathrm{C}=12.0$ , $\mathrm{H}=1.0$ , $\mathrm{O}=16.0)$

Numerical TypeQuestion 53

3-Methylhex-2-ene on reaction with $\mathrm{HBr}$ in presence of peroxide forms an addition product (A). The number of possible stereoisomers for ' $\mathrm{A}$ ' is ________.

Numerical TypeQuestion 54

The number of electrons present in all the completely filled subshells having $\mathrm{n}=4$ and $\mathrm{s}=+\frac{1}{2}$ is _______.

(Where $\mathrm{n}=$ principal quantum number and $\mathrm{s}=$ spin quantum number)

Question 55

The length of the chord of the ellipse

\frac{x^2}{25}+\frac{y^2}{16}=1

, whose mid point is

\left(1, \frac{2}{5}\right)

, is equal to :

Options:

A)

\frac{\sqrt{1691}}{5}

B)

\frac{\sqrt{2009}}{5}

C)

\frac{\sqrt{1541}}{5}

D)

\frac{\sqrt{1741}}{5}

Question 56

If

\mathrm{a}=\lim\limits_{x \rightarrow 0} \frac{\sqrt{1+\sqrt{1+x^4}}-\sqrt{2}}{x^4}

and

\mathrm{b}=\lim\limits _{x \rightarrow 0} \frac{\sin ^2 x}{\sqrt{2}-\sqrt{1+\cos x}}

, then the value of

a b^3

is :

Options:

A)

36

B)

25

C)

32

D)

30

Question 57

If A denotes the sum of all the coefficients in the expansion of

\left(1-3 x+10 x^2\right)^{\mathrm{n}}

and B denotes the sum of all the coefficients in the expansion of

\left(1+x^2\right)^n

, then :

Options:

A)

\mathrm{B}=\mathrm{A}^3

B)

3 \mathrm{A}=\mathrm{B}

C)

A=3 B

D)

\mathrm{A}=\mathrm{B}^3

Numerical TypeQuestion 58

Let

f(x)=x^3+x^2 f^{\prime}(1)+x f^{\prime \prime}(2)+f^{\prime \prime \prime}(3), x \in \mathbf{R}

. Then

f^{\prime}(10)

is equal to ____________.

Numerical TypeQuestion 59

The least positive integral value of

\alpha

, for which the angle between the vectors

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

and

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

is acute, is ___________.

Numerical TypeQuestion 60

If

\alpha

satisfies the equation

x^2+x+1=0

and

(1+\alpha)^7=A+B \alpha+C \alpha^2, A, B, C \geqslant 0

, then

5(3 A-2 B-C)

is equal to ____________.

Question 61

If the refractive index of the material of a prism is $\cot \left(\frac{A}{2}\right)$ , where $A$ is the angle of prism then the angle of minimum deviation will be

Options:

A)

\pi-2 \mathrm{~A}

B)

\frac{\pi}{2}-2 \mathrm{~A}

C)

\pi-\mathrm{A}

D)

\frac{\pi}{2}-\mathrm{A}

Question 62

The acceleration due to gravity on the surface of earth is $\mathrm{g}$ . If the diameter of earth reduces to half of its original value and mass remains constant, then acceleration due to gravity on the surface of earth would be :

Options:

A)

g/4

B)

2g

C)

g/2

D)

4g

Question 63

Two bodies of mass $4 \mathrm{~g}$ and $25 \mathrm{~g}$ are moving with equal kinetic energies. The ratio of magnitude of their linear momentum is :

Options:

A)

3: 5

B)

5: 4

C)

2: 5

D)

4: 5

Question 64

$0.08 \mathrm{~kg}$ air is heated at constant volume through $5^{\circ} \mathrm{C}$ . The specific heat of air at constant volume is $0.17 \mathrm{~kcal} / \mathrm{kg}^{\circ} \mathrm{C}$ and $\mathrm{J}=4.18$ joule/ $\mathrm{~cal}$ . The change in its internal energy is approximately.

Options:

A)

318 J

B)

298 J

C)

284 J

D)

142 J

Question 65

The average kinetic energy of a monatomic molecule is $0.414 \mathrm{~eV}$ at temperature :

(Use $K_B=1.38 \times 10^{-23} \mathrm{~J} / \mathrm{mol}-\mathrm{K}$ )

Options:

A)

3000 K

B)

3200 K

C)

1600 K

D)

1500 K

Numerical TypeQuestion 66

A particle executes simple harmonic motion with an amplitude of $4 \mathrm{~cm}$ . At the mean position, velocity of the particle is $10 \mathrm{~cm} / \mathrm{s}$ . The distance of the particle from the mean position when its speed becomes $5 \mathrm{~cm} / \mathrm{s}$ is $\sqrt{\alpha} \mathrm{~cm}$ , where $\alpha=$ ________.

Numerical TypeQuestion 67

Two long, straight wires carry equal currents in opposite directions as shown in figure. The separation between the wires is $5.0 \mathrm{~cm}$ . The magnitude of the magnetic field at a point $\mathrm{P}$ midway between the wires is _______ $\mu \mathrm{T}$

(Given : $\mu_0=4 \pi \times 10^{-7} \mathrm{TmA}^{-1}$ )

JEE Main 2024 (Online) 27th January Morning Shift Physics - Magnetic Effect of Current Question 10 English

Question 68

Element not showing variable oxidation state is :

Options:

A)

Bromine

B)

Iodine

C)

Chlorine

D)

Fluorine

Question 69

Which of the following electronic configuration would be associated with the highest magnetic moment?

Options:

A)

[\mathrm{Ar}] 3 \mathrm{~d}^7

B)

[\mathrm{Ar}] 3 \mathrm{~d}^8

C)

[\mathrm{Ar}] 3 \mathrm{~d}^3

D)

[\mathrm{Ar}] 3 \mathrm{~d}^6

Question 70

A solution of two miscible liquids showing negative deviation from Raoult's law will have :

Options:

A)

increased vapour pressure, increased boiling point

B)

increased vapour pressure, decreased boiling point

C)

decreased vapour pressure, decreased boiling point

D)

decreased vapour pressure, increased boiling point

Question 71

Given below are two statements :

Statement (I) : p-nitrophenol is more acidic than m-nitrophenol and o-nitrophenol.

Statement (II) : Ethanol will give immediate turbidity with Lucas reagent.

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

Question 72

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

Assertion (A) : Melting point of Boron (2453 K) is unusually high in group 13 elements.

Reason (R) : Solid Boron has very strong crystalline lattice.

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

Options:

A)

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

B)

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

C)

(A) is true but (R) is false

D)

(A) is false but (R) is true

Question 73

Given below are two statements :

Statement (I) : Aqueous solution of ammonium carbonate is basic.

Statement (II) : Acidic/basic nature of salt solution of a salt of weak acid and weak base depends on $K_a$ and $K_b$ value of acid and the base forming it.

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 correct

B)

Statement I is correct but Statement II is incorrect

C)

Both Statement I and Statement II are incorrect

D)

Statement I is incorrect but Statement II is correct

Question 74

$\mathrm{NaCl}$ reacts with conc. $\mathrm{H}_2 \mathrm{SO}_4$ and $\mathrm{K}_2 \mathrm{Cr}_2 \mathrm{O}_7$ to give reddish fumes (B), which react with $\mathrm{NaOH}$ to give yellow solution (C). (B) and (C) respectively are ;

Options:

A)

\mathrm{CrO}_2 \mathrm{Cl}_2, \mathrm{Na}_2 \mathrm{CrO}_4

B)

\mathrm{Na}_2 \mathrm{CrO}_4, \mathrm{CrO}_2 \mathrm{Cl}_2

C)

\mathrm{CrO}_2 \mathrm{Cl}_2, \mathrm{KHSO}_4

D)

\mathrm{CrO}_2 \mathrm{Cl}_2, \mathrm{Na}_2 \mathrm{Cr}_2 \mathrm{O}_7

Question 75

The electronic configuration for Neodymium is:

[Atomic Number for Neodymium 60]

Options:

A)

[\mathrm{Xe}] 4 \mathrm{f}^4 6 \mathrm{~s}^2

B)

[\mathrm{Xe}] 5 \mathrm{f}^4 7 \mathrm{~s}^2

C)

[\mathrm{Xe}] 4 \mathrm{f}^6 6 \mathrm{~s}^2

D)

[\mathrm{Xe}] 4 \mathrm{f}^1 5 \mathrm{~d}^1 6 \mathrm{~s}^2

Numerical TypeQuestion 76

Consider the following data for the given reaction

$2 \mathrm{HI}_{(\mathrm{g})} \rightarrow \mathrm{H}_{2(\mathrm{~g})}+\mathrm{I}_{2(\mathrm{~g})}$

JEE Main 2024 (Online) 27th January Morning Shift Chemistry - Chemical Kinetics and Nuclear Chemistry Question 8 English

The order of the reaction is _________.

Numerical TypeQuestion 77

Among the following, total number of meta directing functional groups is (Integer based)

$-\mathrm{OCH}_3,-\mathrm{NO}_2,-\mathrm{CN},-\mathrm{CH}_3-\mathrm{NHCOCH}_3, -\mathrm{COR},-\mathrm{OH},-\mathrm{COOH},-\mathrm{Cl}$

Numerical TypeQuestion 78

Sum of bond order of CO and NO $^+$ is ________.

Question 79

If

S=\{z \in C:|z-i|=|z+i|=|z-1|\}

, then,

n(S)

is :

Options:

A)

1

B)

2

C)

3

D)

0

Question 80

The portion of the line

4 x+5 y=20

in the first quadrant is trisected by the lines

\mathrm{L}_1

and

\mathrm{L}_2

passing through the origin. The tangent of an angle between the lines

\mathrm{L}_1

and

\mathrm{L}_2

is :

Options:

A)

\frac{30}{41}

B)

\frac{8}{5}

C)

\frac{2}{5}

D)

\frac{25}{41}

Question 81

The number of common terms in the progressions

4,9,14,19, \ldots \ldots

, up to

25^{\text {th }}

term and

3,6,9,12, \ldots \ldots

, up to

37^{\text {th }}

term is :

Options:

A)

9

B)

8

C)

5

D)

7

Numerical TypeQuestion 82

If the solution of the differential equation

(2 x+3 y-2) \mathrm{d} x+(4 x+6 y-7) \mathrm{d} y=0, y(0)=3

, is

\alpha x+\beta y+3 \log _e|2 x+3 y-\gamma|=6

, then

\alpha+2 \beta+3 \gamma

is equal to ____________.

Numerical TypeQuestion 83

Let the set of all

a \in \mathbf{R}

such that the equation

\cos 2 x+a \sin x=2 a-7

has a solution be

[p, q]

and

r=\tan 9^{\circ}-\tan 27^{\circ}-\frac{1}{\cot 63^{\circ}}+\tan 81^{\circ}

, then pqr is equal to ____________.

Numerical TypeQuestion 84

Let for a differentiable function

f:(0, \infty) \rightarrow \mathbf{R}, f(x)-f(y) \geqslant \log _{\mathrm{e}}\left(\frac{x}{y}\right)+x-y, \forall x, y \in(0, \infty)

. Then

\sum\limits_{n=1}^{20} f^{\prime}\left(\frac{1}{n^2}\right)

is equal to ____________.

Numerical TypeQuestion 85

Let

A=\left[\begin{array}{lll}2 & 0 & 1 \\ 1 & 1 & 0 \\ 1 & 0 & 1\end{array}\right], B=\left[B_1, B_2, B_3\right]

, where

B_1, B_2, B_3

are column matrics, and

\mathrm{AB}_1=\left[\begin{array}{l} 1 \\ 0 \\ 0 \end{array}\right], \mathrm{AB}_2=\left[\begin{array}{l} 2 \\ 3 \\ 0 \end{array}\right], \quad \mathrm{AB}_3=\left[\begin{array}{l} 3 \\ 2 \\ 1 \end{array}\right]

If

\alpha=|B|

and

\beta

is the sum of all the diagonal elements of

B

, then

\alpha^3+\beta^3

is equal to ____________.

Question 86

A train is moving with a speed of $12 \mathrm{~m} / \mathrm{s}$ on rails which are $1.5 \mathrm{~m}$ apart. To negotiate a curve radius $400 \mathrm{~m}$ , the height by which the outer rail should be raised with respect to the inner rail is (Given, $g=10 \mathrm{~m} / \mathrm{s}^2)$ :

Options:

A)

6.0 cm

B)

5.4 cm

C)

4.8 cm

D)

4.2 cm

Question 87

Which of the following circuits is reverse - biased?

Options:

A)

JEE Main 2024 (Online) 27th January Morning Shift Physics - Semiconductor Question 8 English Option 1

B)

JEE Main 2024 (Online) 27th January Morning Shift Physics - Semiconductor Question 8 English Option 2

C)

JEE Main 2024 (Online) 27th January Morning Shift Physics - Semiconductor Question 8 English Option 3

D)

JEE Main 2024 (Online) 27th January Morning Shift Physics - Semiconductor Question 8 English Option 4

Question 88

Given below are two statements :

Statement (I) : Planck's constant and angular momentum have same dimensions.

Statement (II) : Linear momentum and moment of force have same dimensions.

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 false

C)

Both Statement I and Statement II are true

D)

Statement I is false but Statement II is true

Numerical TypeQuestion 89

A thin metallic wire having cross sectional area of $10^{-4} \mathrm{~m}^2$ is used to make a ring of radius $30 \mathrm{~cm}$ . A positive charge of $2 \pi \mathrm{~C}$ is uniformly distributed over the ring, while another positive charge of 30 $\mathrm{pC}$ is kept at the centre of the ring. The tension in the ring is ______ $\mathrm{N}$ ; provided that the ring does not get deformed (neglect the influence of gravity). (given, $\frac{1}{4 \pi \epsilon_0}=9 \times 10^9$ SI units)

Numerical TypeQuestion 90

Two immiscible liquids of refractive indices $\frac{8}{5}$ and $\frac{3}{2}$ respectively are put in a beaker as shown in the figure. The height of each column is $6 \mathrm{~cm}$ . A coin is placed at the bottom of the beaker. For near normal vision, the apparent depth of the coin is $\frac{\alpha}{4} \mathrm{~cm}$ . The value of $\alpha$ is _________.

JEE Main 2024 (Online) 27th January Morning Shift Physics - Geometrical Optics Question 8 English