JEE Main 23 January 2025 Shift 1 Question Paper

Question 1

The value of $\displaystyle\int_{e^2}^{e^4}\frac{1}{x}\left(\frac{e^{\left((\log_e x)^2+1\right)^{-1}}}{e^{\left((\log_e x)^2+1\right)^{-1}}+e^{\left((6-\log_e x)^2+1\right)^{-1}}}\right)dx$ is

Accepted Answer

(C) $1$

Answer

(A) $\log_e 2$

Answer

(B) $2$

Answer

(D) $e^2$

Question 2

Let $\displaystyle I(x)=\int\frac{dx}{(x-11)^{11/13}(x+15)^{15/13}}$. If $I(37)-I(24)=\frac{1}{4}\left(\frac{1}{b^{1/13}}-\frac{1}{c^{1/13}}\right)$, $b,c\in\mathbb{N}$, then $3(b+c)$ is equal to

Accepted Answer

(B) $39$

Answer

(A) $40$

Answer

(C) $22$

Answer

(D) $26$

Question 3

If the function $f(x)=\begin{cases}\dfrac{2}{x}\{\sin(k_1+1)x+\sin(k_2-1)x\}, & x<0\[2mm] 4, & x=0\[2mm] \dfrac{2}{x}\log_e\left(\dfrac{2+k_1x}{2+k_2x}\right), & x>0\end{cases}$ is continuous at $x=0$, then $k_1^2+k_2^2$ is equal to

Accepted Answer

(D) $10$

Answer

(A) $8$

Answer

(B) $20$

Answer

(C) $5$

Question 4

If the line $3x-2y+12=0$ intersects the parabola $4y=3x^2$ at the points $A$ and $B$, then at the vertex of the parabola, the line segment $AB$ subtends an angle equal to

Accepted Answer

(D) $	an^{-1}\left(\dfrac{9}{7}ight)$

Answer

(A) $	an^{-1}\left(\dfrac{11}{9}ight)$

Answer

(B) $\dfrac{\pi}{2}-	an^{-1}\left(\dfrac{3}{2}ight)$

Answer

(C) $	an^{-1}\left(\dfrac{4}{5}ight)$

Question 5

Let a curve $y=f(x)$ pass through the points $(0,5)$ and $(\log_e 2, k)$. If the curve satisfies the differential equation $2(3+y)e^{2x}dx-(7+e^{2x})dy=0$, then $k$ is equal to

Accepted Answer

(B) $8$

Answer

(A) $16$

Answer

(C) $32$

Answer

(D) $4$

Question 6

Let $f(x)=\log_e x$ and $g(x)=\dfrac{x^4-2x^3+3x^2-2x+2}{2x^2-2x+1}$. Then the domain of $f\circ g$ is

Accepted Answer

(A) $\mathbb{R}$

Answer

(B) $(0,\infty)$

Answer

(C) $[0,\infty)$

Answer

(D) $[1,\infty)$

Question 7

Let the arc $AC$ of a circle subtend a right angle at the centre $O$. If the point $B$ on the arc $AC$ divides the arc $AC$ such that $\dfrac{	ext{length of arc }AB}{	ext{length of arc }BC}=\dfrac{1}{5}$, and $\overrightarrow{OC}=\alpha\,\overrightarrow{OA}+\beta\,\overrightarrow{OB}$, then $\alpha+\sqrt2(\sqrt3-1)\beta$ is equal to

Accepted Answer

(A) $2-\sqrt3$

Answer

(B) $2\sqrt3$

Answer

(C) $5\sqrt3$

Answer

(D) $2+\sqrt3$

Question 8

If the first term of an A.P. is 3 and the sum of its first four terms is equal to one-fifth of the sum of the next four terms, then the sum of the first 20 terms is equal to

Accepted Answer

(B) $-1080$

Answer

(A) $-1200$

Answer

(C) $-1020$

Answer

(D) $-120$

Question 9

Let $P$ be the foot of the perpendicular from the point $Q(10,-3,-1)$ on the line $\dfrac{x-3}{7}=\dfrac{y-2}{-1}=\dfrac{z+1}{-2}$. Then the area of the right angled triangle $PQR$, where $R$ is the point $(3,-2,1)$, is

Accepted Answer

(D) $3\sqrt{30}$

Answer

(A) $9\sqrt{15}$

Answer

(B) $\sqrt{30}$

Answer

(C) $8\sqrt{15}$

Question 10

Let $\left|\dfrac{\bar z-i}{2\bar z+i}\right|=\dfrac{1}{3}$, $z\in\mathbb{C}$, be the equation of a circle with center at $C$. If the area of the triangle, whose vertices are at the points $(0,0)$, $C$ and $(\alpha,0)$ is 11 square units, then $\alpha^2$ equals

Accepted Answer

(A) $100$

Answer

(B) $50$

Answer

(C) $\dfrac{121}{25}$

Answer

(D) $\dfrac{81}{25}$

Question 11

Let $R=\{(1,2),(2,3),(3,3)\}$ be a relation defined on the set $\{1,2,3,4\}$. Then the minimum number of elements, needed to be added in $R$ so that $R$ becomes an equivalence relation, is

Accepted Answer

(D) $7$

Answer

(A) $10$

Answer

(B) $8$

Answer

(C) $9$

Question 12

The number of words, which can be formed using all the letters of the word "DAUGHTER", so that all the vowels never come together, is

Accepted Answer

(C) $36000$

Answer

(A) $34000$

Answer

(B) $37000$

Answer

(D) $35000$

Question 13

Let the area of a $	riangle PQR$ with vertices $P(5,4)$, $Q(-2,4)$ and $R(a,b)$ be 35 square units. If its orthocenter and centroid are $O\left(2,\dfrac{14}{5}ight)$ and $C(c,d)$ respectively, then $c+2d$ is equal to

Accepted Answer

(B) $3$

Answer

(A) $\dfrac{7}{3}$

Answer

(C) $2$

Answer

(D) $\dfrac{8}{3}$

Question 14

If $\dfrac{\pi}{2}\le x\le\dfrac{3\pi}{4}$, then $\cos^{-1}\left(\dfrac{12}{13}\cos x+\dfrac{5}{13}\sin x\right)$ is equal to

Accepted Answer

(B) $x-	an^{-1}\dfrac{5}{12}$

Answer

(A) $x-	an^{-1}\dfrac{4}{3}$

Answer

(C) $x+	an^{-1}\dfrac{4}{5}$

Answer

(D) $x+	an^{-1}\dfrac{5}{12}$

Question 15

The value of $(\sin 70^\circ)(\cot 10^\circ\cot 70^\circ-1)$ is

Accepted Answer

(A) $1$

Answer

(B) $0$

Answer

(C) $\dfrac{3}{2}$

Answer

(D) $\dfrac{2}{3}$

Question 16

Marks obtained by all the students of class 12 are presented in a frequency distribution with classes of equal width. Let the median of this grouped data be 14 with median class interval 12-18 and median class frequency 12. If the number of students whose marks are less than 12 is 18, then the total number of students is

Accepted Answer

(B) $44$

Answer

(A) $48$

Answer

(C) $40$

Answer

(D) $52$

Question 17

Let the position vectors of the vertices $A$, $B$ and $C$ of a tetrahedron $ABCD$ be $\hat i+2\hat j+\hat k$, $\hat i+3\hat j-2\hat k$ and $2\hat i+\hat j-\hat k$ respectively. The altitude from the vertex $D$ to the opposite face $ABC$ meets the median line segment through $A$ of the triangle $ABC$ at the point $E$. If the length of $AD$ is $\dfrac{\sqrt{110}}{3}$ and the volume of the tetrahedron is $\dfrac{\sqrt{805}}{6\sqrt2}$, then the position vector of $E$ is

Accepted Answer

(D) $\dfrac{1}{6}(7\hat i+12\hat j+\hat k)$

Answer

(A) $\dfrac{1}{2}(\hat i+4\hat j+7\hat k)$

Answer

(B) $\dfrac{1}{12}(7\hat i+4\hat j+3\hat k)$

Answer

(C) $\dfrac{1}{6}(12\hat i+12\hat j+\hat k)$

Question 18

If $A$, $B$ and $(\operatorname{adj}(A^{-1})+\operatorname{adj}(B^{-1}))$ are non-singular matrices of same order, then the inverse of $A\big(\operatorname{adj}(A^{-1})+\operatorname{adj}(B^{-1})\big)^{-1}B$, is equal to

Accepted Answer

(C) $\dfrac{1}{|AB|}\big(\operatorname{adj}(B)+\operatorname{adj}(A)\big)$

Answer

(A) $AB^{-1}+A^{-1}B$

Answer

(B) $\operatorname{adj}(B^{-1})+\operatorname{adj}(A^{-1})$

Answer

(D) $\dfrac{AB^{-1}}{|A|}+\dfrac{BA^{-1}}{|B|}$

Question 19

If the system of equations $(\lambda-1)x+(\lambda-4)y+\lambda z=5$ $\lambda x+(\lambda-1)y+(\lambda-4)z=7$ $(\lambda+1)x+(\lambda+2)y-(\lambda+2)z=9$ has infinitely many solutions, then $\lambda^2+\lambda$ is equal to

Accepted Answer

(B) $12$

Answer

(A) $10$

Answer

(C) $6$

Answer

(D) $20$

Question 20

One die has two faces marked 1, two faces marked 2, one face marked 3 and one face marked 4. Another die has one face marked 1, two faces marked 2, two faces marked 3 and one face marked 4. The probability of getting the sum of numbers to be 4 or 5, when both the dice are thrown together, is

Accepted Answer

(A) $\dfrac{1}{2}$

Answer

(B) $\dfrac{3}{5}$

Answer

(C) $\dfrac{2}{3}$

Answer

(D) $\dfrac{4}{9}$

Question 21

If the area of the larger portion bounded between the curves $x^2+y^2=25$ and $y=|x-1|$ is $\dfrac{1}{4}(b\pi+c)$, $b,c\in\mathbb{N}$, then $b+c$ is equal to _______

Accepted Answer

77

Question 22

The sum of all rational terms in the expansion of $(1+2^{1/3}+3^{1/2})^6$ is equal to _______

Accepted Answer

612

Question 23

Let the circle $C$ touch the line $x-y+1=0$, have the centre on the positive x-axis, and cut off a chord of length $\dfrac{4}{\sqrt{13}}$ along the line $-3x+2y=1$. Let $H$ be the hyperbola $\dfrac{x^2}{\alpha^2}-\dfrac{y^2}{\beta^2}=1$, whose one of the foci is the centre of $C$ and the length of the transverse axis is the diameter of $C$. Then $2\alpha^2+3\beta^2$ is equal to _______

Accepted Answer

19

Question 24

If the set of all values of $a$, for which the equation $5x^3-15x-a=0$ has three distinct real roots, is the interval $(\alpha,\beta)$, then $\beta-2\alpha$ is equal to _______

Accepted Answer

30

Question 25

If the equation $a(b-c)x^2+b(c-a)x+c(a-b)=0$ has equal roots, where $a+c=15$ and $b=\dfrac{36}{5}$, then $a^2+c^2$ is equal to _______

Accepted Answer

117

Question 26

Regarding self-inductance : A : The self-inductance of the coil depends on its geometry. B : Self-inductance does not depend on the permeability of the medium. C : Self-induced e.m.f. opposes any change in the current in a circuit. D : Self-inductance is electromagnetic analogue of mass in mechanics. E : Work needs to be done against self-induced e.m.f. in establishing the current. Choose the correct answer from the options given below:

Accepted Answer

(B) A, C, D, E only

Answer

(A) A, B, C, D only

Answer

(C) A, B, C, E only

Answer

(D) B, C, D, E only

Question 27

A light hollow cube of side length 10 cm and mass 10g, is floating in water. It is pushed down and released to execute simple harmonic oscillations. The time period of oscillations is $y\pi	imes10^{-2}$ s, where the value of $y$ is (Acceleration due to gravity, $g=10$ m/s$^2$, density of water $=10^3$ kg/m$^3$)

Accepted Answer

(A) 2

Answer

(B) 6

Answer

(C) 4

Answer

(D) 1

Question 28

Given below are two statements:
Statement-I : The hot water flows faster than cold water.
Statement-II : Soap water has higher surface tension as compared to fresh water.
In the light of the above statements, choose the correct answer from the options given below:

Accepted Answer

(B) Statement-I is true but Statement-II is false

Answer

(A) Statement-I is false but Statement-II is true

Answer

(C) Both Statement-I and Statement-II are true

Answer

(D) Both Statement-I and Statement-II are false

Question 29

A sub-atomic particle of mass $10^{-30}$ kg is moving with a velocity $2.21	imes10^5$ m/s. Under the matter wave consideration, the particle will behave closely like _______ ($h=6.63	imes10^{-34}$ J.s)

Accepted Answer

(B) X-rays

Answer

(A) Infra-red radiation

Answer

(C) Gamma rays

Answer

(D) Visible radiation

Question 30

A spherical surface of radius of curvature $R$, separates air from glass (refractive index $=1.5$). The centre of curvature is in the glass medium. A point object ‘O’ placed in air on the optic axis of the surface, so that its real image is formed at ‘I’ inside glass. The line OI intersects the spherical surface at P and PO = PI. The distance PO equals to-

Accepted Answer

(A) 5R

Answer

(B) 3R

Answer

(C) 2R

Answer

(D) 1.5R

Question 31

A radioactive nucleus $n_2$ has 3 times the decay constant as compared to the decay constant of another radioactive nucleus $n_1$. If initial number of both nuclei are the same, what is the ratio of number of nuclei of $n_2$ to the number of nuclei of $n_1$, after one half-life of $n_1$?

Accepted Answer

(A) $\dfrac{1}{4}$

Answer

(B) $\dfrac{1}{8}$

Answer

(C) 4

Answer

(D) 8

Question 32

Identify the valid statements relevant to the given circuit at the instant when the key is closed. A. There will be no current through resistor R. B. There will be maximum current in the connecting wires. C. Potential difference between the capacitor plates A and B is minimum. D. Charge on the capacitor plates is minimum. Choose the correct answer from the options given below :

Accepted Answer

(B) B, C, D only

Answer

(A) C, D only

Answer

(C) A, C only

Answer

(D) A, B, D only

Question 33

The position of a particle moving on x-axis is given by $x(t)=A\sin t+B\cos^2 t+Ct^2+D$, where $t$ is time. The dimension of $\dfrac{ABC}{D}$ is-

Accepted Answer

(C) $L^2T^{-2}$

Answer

(A) L

Answer

(B) $L^3T^{-2}$

Answer

(D) $L^2$

Question 34

Match List-I (Thermodynamic Process) with List-II (Process Name). Choose the correct answer from the options given below:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 35

Consider a moving coil galvanometer (MCG) : A : The torsional constant in moving coil galvanometer has dimensions $[ML^2T^{-2}]$. B : Increasing the current sensitivity may not necessarily increase the voltage sensitivity. C : If we increase number of turns (N) to its double (2N), then the voltage sensitivity doubles. D : MCG can be converted into an ammeter by introducing a shunt resistance of large value in parallel with galvanometer. E : Current sensitivity of MCG depends inversely on number of turns of coil. Choose the correct answer from the options given below :

Accepted Answer

(A) A, B only

Answer

(B) A, D only

Answer

(C) B, D, E only

Answer

(D) A, B, E only

Question 36

A point particle of charge Q is located at P along the axis of an electric dipole 1 at a distance r as shown in the figure. The point P is also on the equatorial plane of a second electric dipole 2 at a distance r. The dipoles are made of opposite charges q separated by a distance 2a. For the charge particle at P not to experience any net force, which of the following correctly describes the situation?

Accepted Answer

(D) $\dfrac{a}{r}\sim 3$

Answer

(A) $\dfrac{a}{r}\sim 20$

Answer

(B) $\dfrac{a}{r}\sim 10$

Answer

(C) $\dfrac{a}{r}\sim 0.5$

Question 37

A gun fires a lead bullet of temperature 300K into a wooden block. The bullet having melting temperature of 600 K penetrates into the block and melts down. If the total heat required for the process is 625 J, then the mass of the bullet is _______ grams. (Latent heat of fusion of lead $=2.5	imes10^4$ JKg$^{-1}$ and specific heat capacity of lead $=125$ JKg$^{-1}$K$^{-1}$)

Accepted Answer

(C) 10

Answer

(A) 20

Answer

(B) 15

Answer

(D) 5

Question 38

What is the lateral shift of a ray refracted through a parallel-sided glass slab of thickness ‘h’ in terms of the angle of incidence ‘i’ and angle of refraction ‘r’, if the glass slab is placed in air medium ?

Accepted Answer

(D) $\dfrac{h\sin(i-r)}{\cos r}$

Answer

(A) $\dfrac{h\sin(i-r)}{	an r}$

Answer

(B) $\dfrac{h\cos(i-r)}{\sin r}$

Answer

(C) h

Question 39

A solid sphere of mass ‘m’ and radius ‘r’ is allowed to roll without slipping from the highest point of an inclined plane of length ‘L’ and makes an angle 30° with the horizontal. The speed of the particle at the bottom of the plane is $v_1$. If the angle of inclination is increased to 45° while keeping L constant. Then the new speed of the sphere at the bottom of the plane is $v_2$. The ratio of $v_1^2:v_2^2$ is

Accepted Answer

(A) $1:\sqrt2$

Answer

(B) $1:3$

Answer

(C) $1:2$

Answer

(D) $1:\sqrt3$

Question 40

Refer to the circuit diagram given in the figure, which of the following observation of circuit are correct? A. Total resistance of circuit is 6 Ω. B. Current in Ammeter is 1A. C. Potential across AB is 4 Volts. D. Potential across CD is 4 Volts. E. Total resistance of the circuit is 8Ω. Choose the correct answer from the options given below :

Accepted Answer

(A) A, B and D only

Answer

(B) A, C and D only

Answer

(C) B, C and E only

Answer

(D) A, B and C only

Question 41

The electric flux is $\phi=\alpha\sigma+\beta\lambda$ where $\lambda$ and $\sigma$ are linear and surface charge density, respectively. $\left(\dfrac{\alpha}{\beta}\right)$ represents

Accepted Answer

(C) displacement

Answer

(A) charge

Answer

(B) electric field

Answer

(D) area

Question 42

Given a thin convex lens (refractive index $\mu_2$), kept in a liquid (refractive index $\mu_1$, $\mu_1<\mu_2$) having radii of curvature $|R_1|$ and $|R_2|$. Its second surface is silver polished. Where should an object be placed on the optic axis so that a real and inverted image is formed at the same place ?

Accepted Answer

(B) $\dfrac{\mu_1|R_1||R_2|}{\mu_2(|R_1|+|R_2|)-\mu_1|R_2|}$

Answer

(A) $\dfrac{\mu_1|R_1||R_2|}{\mu_2(|R_1|+|R_2|)-\mu_1|R_1|}$

Answer

(C) $\dfrac{\mu_1|R_1||R_2|}{\mu_2(2|R_1|+|R_2|)-\mu_1\sqrt{|R_1||R_2|}}$

Answer

(D) $\dfrac{(\mu_2+\mu_1)|R_1|}{\mu_2-\mu_1}$

Question 43

The electric field of an electromagnetic wave in free space is $\vec E=57\cos[7.5	imes10^6 t-5	imes10^{-3}(3x+4y)](4\hat i-3\hat j)$ N/C. The associated magnetic field in Tesla is-

Accepted Answer

(C) $\vec B=-\dfrac{57}{3	imes10^8}\cos[7.5	imes10^6 t-5	imes10^{-3}(3x+4y)](5\hat k)$

Answer

(A) $\vec B=\dfrac{57}{3	imes10^8}\cos[7.5	imes10^6 t-5	imes10^{-3}(3x+4y)](5\hat k)$

Answer

(B) $\vec B=\dfrac{57}{3	imes10^8}\cos[7.5	imes10^6 t-5	imes10^{-3}(3x+4y)](\hat k)$

Answer

(D) $\vec B=-\dfrac{57}{3	imes10^8}\cos[7.5	imes10^6 t-5	imes10^{-3}(3x+4y)](\hat k)$

Question 44

The motion of an airplane is represented by velocity-time graph as shown below. The distance covered by airplane in the first 30.5 second is _______ km.

Accepted Answer

(D) 12

Answer

(A) 9

Answer

(B) 6

Answer

(C) 3

Question 45

Consider a circular disc of radius 20 cm with centre located at the origin. A circular hole of radius 5 cm is cut from this disc in such a way that the edge of the hole touches the edge of the disc. The distance of centre of mass of residual or remaining disc from the origin will be-

Accepted Answer

(D) 1.0 cm

Answer

(A) 2.0 cm

Answer

(B) 0.5 cm

Answer

(C) 1.5 cm

Question 46

Two particles are located at equal distance from origin. The position vectors of those are represented by $\vec A=2\hat i+3n\hat j+2\hat k$ and $\vec B=2\hat i-2\hat j+4p\hat k$, respectively. If both the vectors are at right angle to each other, the value of $n^{-1}$ is _______.

Accepted Answer

3

Question 47

The element that does not belong to the same period of the remaining elements (modern periodic table) is:

Accepted Answer

(A) Palladium

Answer

(B) Iridium

Answer

(C) Osmium

Answer

(D) Platinum

Question 48

Heat treatment of muscular pain involves radiation of wavelength of about 900 nm. Which spectral line of H atom is suitable for this ? (Given: Rydberg constant $R_H=10^5$ cm$^{-1}$, $h=6.6	imes10^{-34}$ J s, $c=3	imes10^8$ m/s)

Accepted Answer

(A) Paschen series, ∞→3

Answer

(B) Lyman series, ∞→1

Answer

(C) Balmer series, ∞→2

Answer

(D) Paschen series, 5→3

Question 49

The incorrect statement among the following is

Accepted Answer

(D) SO₂ can act as an oxidizing agent, but not as a reducing agent.

Answer

(A) PH₃ shows lower proton affinity than NH₃.

Answer

(B) PF₃ exists but NF₅ does not.

Answer

(C) NO₂ can dimerise easily.

Question 50

CrCl₃·xNH₃ can exist as a complex. 0.1 molal aqueous solution of this complex shows a depression in freezing point of 0.558°C. Assuming 100% ionisation of this complex and coordination number of Cr is 6, the complex will be (Given $K_f=1.86$ K kg mol$^{-1}$)

Accepted Answer

(C) [Cr(NH₃)₅Cl]Cl₂

Answer

(A) [Cr(NH₃)₆]Cl₃

Answer

(B) [Cr(NH₃)₄Cl₂]Cl

Answer

(D) [Cr(NH₃)₃Cl₃]

Question 51

In the diagram below, the standard electrode potentials are given in volts (over the arrow). $FeO_4^{2-}\xrightarrow{+2.0V}Fe^{3+}\xrightarrow{0.8V}Fe^{2+}\xrightarrow{-0.5V}Fe^{0}$. The value of $E^{\circ}_{FeO_4^{2-}/Fe^{2+}}$ is

Accepted Answer

(A) 1.7 V

Answer

(B) 1.2 V

Answer

(C) 2.1 V

Answer

(D) 1.4 V

Question 52

Match List-I (Name Reaction) with List-II (Product Obtained). Choose the correct answer from the options given below:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 53

Given below are two statements:
Statement I: Fructose does not contain an aldehydic group but still reduces Tollen's reagent.
Statement II: In the presence of base, fructose undergoes rearrangement to give glucose.
In the light of the above statements, choose the correct answer given below:

Accepted Answer

(B) Both Statement I and Statement II are true

Answer

(A) Statement I is false but Statement II is true

Answer

(C) Both Statement I and Statement II are false

Answer

(D) Statement I is true but Statement II is false

Question 54

$2.8	imes10^{-3}$ mol of CO₂ is left after removing $10^{21}$ molecules from its ‘x’ mg sample. The mass of CO₂ taken initially is (Given : $N_A=6.02	imes10^{23}$ mol$^{-1}$)

Accepted Answer

(A) 196.2 mg

Answer

(B) 98.3 mg

Answer

(C) 150.4 mg

Answer

(D) 48.2 mg

Question 55

Ice at −5°C is heated to become vapor with temperature of 110°C at atmospheric pressure. The entropy change associated with this process can be obtained from :

Accepted Answer

(B) $\int_{268}^{273}\dfrac{C_{p,m}}{T}dT+\dfrac{\Delta H_{m,fusion}}{T_f}+\int_{273}^{373}\dfrac{C_{p,m}}{T}dT+\dfrac{\Delta H_{m,vaporisation}}{T_b}+\int_{373}^{383}\dfrac{C_{p,m}}{T}dT$

Answer

(A) $\int_{268}^{383}C_p\,dT+\dfrac{\Delta H_{melting}}{273}+\dfrac{\Delta H_{boiling}}{373}$

Answer

(C) $\int_{268}^{383}C_p\,dT+\dfrac{q_{rev}}{T}$

Answer

(D) $\int_{268}^{273}C_{p,m}\,dT+\dfrac{\Delta H_{m,fusion}}{T_f}+\dfrac{\Delta H_{m,vaporisation}}{T_b}+\int_{273}^{373}C_{p,m}\,dT+\int_{373}^{383}C_{p,m}\,dT$

Question 56

The d-electronic configuration of an octahedral Co(II) complex having magnetic moment of 3.95 BM is :

Accepted Answer

(C) $t_{2g}^{5}e_{g}^{2}$

Answer

(A) $t_{2g}^{6}e_{g}^{1}$

Answer

(B) $t_{2g}^{5}e_{g}^{0}$

Answer

(D) $e^{4}t_{2}^{3}$

Question 57

The complex that shows Facial – Meridional isomerism is

Accepted Answer

(A) [Co(NH₃)₃Cl₃]

Answer

(B) [Co(NH₃)₄Cl₂]⁺

Answer

(C) [Co(en)₃]³⁺

Answer

(D) [Co(en)₂Cl₂]⁺

Question 58

The major product of the following reaction is : $CH_3CH_2CHO\xrightarrow[	ext{reflux}]{	ext{excess HCHO, alkali}}$ ?

Accepted Answer

(C) $CH_3-C(CH_2OH)_2-CH_2OH$

Answer

(A) $CH_3-CH_2-CH_2-OH$

Answer

(B) $CH_3-CH(CH_2OH)-CHO$

Answer

(D) $CH_3-C(=CH_2)-CHO$

Question 59

The correct stability order of the following species/molecules is :

Accepted Answer

(A) q > r > p

Answer

(B) r > q > p

Answer

(C) q > p > r

Answer

(D) p > q > r

Question 60

Propane molecule on chlorination under photochemical condition gives two di-chloro products, "x" and "y". Amongst "x" and "y", "x" is an optically active molecule. How many tri-chloro products (consider only structural isomers) will be obtained from "x" when it is further treated with chlorine under the photochemical condition?

Accepted Answer

(D) 3

Answer

(A) 4

Answer

(B) 2

Answer

(C) 5

Question 61

What amount of bromine will be required to convert 2 g of phenol into 2, 4, 6-tribromophenol ? (Given molar mass in g mol$^{-1}$ of C, H, O, Br are 12, 1, 16, 80 respectively)

Accepted Answer

(A) 10.22 g

Answer

(B) 6.0 g

Answer

(C) 4.0 g

Answer

(D) 20.44 g

Question 62

The correct set of ions (aqueous solution) with same colour from the following is :

Accepted Answer

(A) V²⁺, Cr³⁺, Mn³⁺

Answer

(B) Zn²⁺, V³⁺, Fe³⁺

Answer

(C) Ti⁴⁺, V⁴⁺, Mn²⁺

Answer

(D) Sc³⁺, Ti³⁺, Cr²⁺

Question 63

Given below are two statements :
Statement I : In Lassaigne's test, the covalent organic molecules are transformed into ionic compounds.
Statement II : The sodium fusion extract of an organic compound having N and S gives prussian blue colour with FeSO₄ and Na₄[Fe(CN)₆].
In the light of the above statements, choose the correct answer from the options given below

Accepted Answer

(D) Statement I is true but Statement II is false

Answer

(A) Both Statement I and Statement II are true

Answer

(B) Both Statement I and Statement II are false

Answer

(C) Statement I is false but Statement II is true

Question 64

Which of the following happens when NH₄OH is added gradually to the solution containing 1M A³⁺ and 1M B³⁺ ions ? Given : $K_{sp}[A(OH)_3]=9	imes10^{-10}$ and $K_{sp}[B(OH)_3]=27	imes10^{-18}$ at 298 K.

Accepted Answer

(A) B(OH)₃ will precipitate before A(OH)₃

Answer

(B) A(OH)₃ and B(OH)₃ will precipitate together

Answer

(C) A(OH)₃ will precipitate before B(OH)₃

Answer

(D) Both A(OH)₃ and B(OH)₃ do not show precipitation with NH₄OH

List-I (Thermodynamic Process)	List-II (Process Name)
A.Pressure varies inversely with volume of an ideal gas	I.Adiabatic process
B.Heat absorbed goes partly to increase internal energy and partly to do work	II.Isochoric process
C.Heat is neither absorbed nor released by a system	III.Isothermal process
D.No work is done on or by a gas	IV.Isobaric process

List-I (Name Reaction)	List-II (Product Obtained)
A.Swarts reaction	I.Ethyl benzene
B.Sandmeyer's reaction	II.Ethyl iodide
C.Wurtz Fittig reaction	III.Cyanobenzene
D.Finkelstein reaction	IV.Ethyl fluoride

List-I (Octet Behaviour)	List-II (Example Molecules)
A.Molecules obeying octet rule	I.NO, NO₂
B.Molecules with incomplete octet	II.BCl₃, AlCl₃
C.Molecules with incomplete octet with odd electron	III.H₂SO₄, PCl₅
D.Molecules with expanded octet	IV.CCl₄, CO₂

JEE Main 23 January 2025 Shift 1 Question Paper with Answers

Physics — JEE Main 23 January 2025 Shift 1

Chemistry — JEE Main 23 January 2025 Shift 1

Mathematics — JEE Main 23 January 2025 Shift 1

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