JEE Main 28 January 2025 Shift 1 Question Paper

Question 1

The number of different 5 digit numbers greater than 50000 that can be formed using the digits 0, 1, 2, 3, 4, 5, 6, 7, such that the sum of their first and last digits should not be more than 8, is

Accepted Answer

(D) 4607

Answer

(A) 4608

Answer

(B) 5720

Answer

(C) 5719

Question 2

Let ABCD be a trapezium whose vertices lie on the parabola $y^2=4x$. Let the sides AD and BC of the trapezium be parallel to y-axis. If the diagonal AC is of length $\frac{25}{4}$ and it passes through the point $(1, 0)$, then the area of ABCD is:

Accepted Answer

(A) $\frac{75}{4}$

Answer

(B) $\frac{25}{2}$

Answer

(C) $\frac{125}{8}$

Answer

(D) $\frac{75}{8}$

Question 3

Two number $k_1$ and $k_2$ are randomly chosen from the set of natural numbers. Then, the probability that the value of $i^{k_1}+i^{k_2}$, $(i=\sqrt{-1})$ is non-zero, equals

Accepted Answer

(C) $\frac{3}{4}$

Answer

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

Answer

(B) $\frac{1}{4}$

Answer

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

Question 4

If $f(x)=\frac{2^x}{2^x+\sqrt{2}}$, $x\in R$, then $\sum_{k=1}^{81} f\left(\frac{k}{82}\right)$ is equal to:

Accepted Answer

(B) $\frac{81}{2}$

Answer

(A) 41

Answer

(C) 82

Answer

(D) $81\sqrt{2}$

Question 5

Let $f:R	o R$ be a function defined by $f(x)=(2+3a)x^2+\frac{a+2}{a-1}x+b$, $a
eq1$. If $f(x+y)=f(x)+f(y)+1-\frac{2}{7}xy$, then the value of $28\sum_{i=1}^{5}|f(i)|$ is:

Accepted Answer

(D) 675

Answer

(A) 715

Answer

(B) 735

Answer

(C) 545

Question 6

Let $A(x, y, z)$ be a point in xy-plane, which is equidistant from three points $(0, 3, 2)$, $(2, 0, 3)$ and $(0, 0, 1)$. Let $B=(1, 4, -1)$ and $C=(2, 0, -2)$. Then among the statements (S1): $	riangle ABC$ is an isosceles right angled triangle and (S2): the area of $	riangle ABC$ is $\frac{9\sqrt{2}}{2}$.

Accepted Answer

(B) only (S1) is true

Answer

(A) both are true

Answer

(C) only (S2) is true

Answer

(D) both are false

Question 7

The relation $R=\{(x, y): x, y\in z$ and $x+y$ is even$\}$ is:

Accepted Answer

(C) an equivalence relation

Answer

(A) reflexive and transitive but not symmetric

Answer

(B) reflexive and symmetric but not transitive

Answer

(D) symmetric and transitive but not reflexive

Question 8

Let the equation of the circle, which touches x-axis at the point $(a, 0)$, $a>0$ and cuts off an intercept of length b on y-axis be $x^2+y^2-\alpha x-\beta y+\gamma=0$. If the circle lies below x-axis, then the ordered pair $(2a, b^2)$ is equal to:

Accepted Answer

(D) $(\alpha, \beta^2-4\gamma)$

Answer

(A) $(\alpha, \beta^2+4\gamma)$

Answer

(B) $(\gamma, \beta^2-4\alpha)$

Answer

(C) $(\gamma, \beta^2+4\alpha)$

Question 9

Let $\langle a_n\rangle$ be a sequence such that $a_0=0$, $a_1=\frac{1}{2}$ and $2a_{n+2}=5a_{n+1}-3a_n$, $n=0, 1, 2, 3, \ldots$ Then $\sum_{k=1}^{100} a_k$ is equal to:

Accepted Answer

(B) $3a_{100}-100$

Answer

(A) $3a_{99}-100$

Answer

(C) $3a_{100}+100$

Answer

(D) $3a_{99}+100$

Question 10

$\cos\left(\sin^{-1}\frac{3}{5}+\sin^{-1}\frac{5}{13}+\sin^{-1}\frac{33}{65}\right)$ is equal to:

Accepted Answer

(B) 0

Answer

(A) 1

Answer

(C) $\frac{33}{65}$

Answer

(D) $\frac{32}{65}$

Question 11

Let $T_r$ be the $r^{th}$ term of an A.P. If for some m, $T_m=\frac{1}{25}$, $T_{25}=\frac{1}{20}$ and $20\sum_{r=1}^{25} T_r=13$, then $5m\sum_{r=m}^{2m} T_r$ is equal to:

Accepted Answer

(B) 126

Answer

(A) 112

Answer

(C) 98

Answer

(D) 142

Question 12

If the image of the point $(4, 4, 3)$ in the line $\frac{x-1}{2}=\frac{y-2}{1}=\frac{z-1}{3}$ is $(\alpha, \beta, \gamma)$, then $\alpha+\beta+\gamma$ is equal to

Accepted Answer

(A) 9

Answer

(B) 12

Answer

(C) 8

Answer

(D) 7

Question 13

If $\int_{-\pi/2}^{\pi/2}\frac{96x^2\cos^2 x}{1+e^x}dx=\pi(\alpha\pi^2+\beta)$, $\alpha, \beta\in Z$, then $(\alpha+\beta)^2$ equals:

Accepted Answer

(C) 100

Answer

(A) 144

Answer

(B) 196

Answer

(D) 64

Question 14

The sum of all local minimum values of the function $f(x)=\begin{cases}1-2x, & x<-1\ \frac{1}{3}(7+2|x|), & -1\le x\le 2\ \frac{11}{18}(x-4)(x-5), & x>2\end{cases}$ is:

Accepted Answer

(C) $\frac{157}{72}$

Answer

(A) $\frac{171}{72}$

Answer

(B) $\frac{131}{72}$

Answer

(D) $\frac{167}{72}$

Question 15

The sum, of the squares of all the roots of the equation $x^2+|2x-3|-4=0$, is:

Accepted Answer

(C) $6(2-\sqrt{2})$

Answer

(A) $3(3-\sqrt{2})$

Answer

(B) $6(3-\sqrt{2})$

Answer

(D) $3(2-\sqrt{2})$

Question 16

Let for some function $y=f(x)$, $\int_0^x t\,f(t)dt=x^2 f(x)$, $x>0$ and $f(2)=3$. Then $f(6)$ is equal to:

Accepted Answer

(A) 1

Answer

(B) 2

Answer

(C) 6

Answer

(D) 3

Question 17

Let $^nC_{r-1}=28$, $^nC_r=56$ and $^nC_{r+1}=70$. Let $A(4\cos t, 4\sin t)$, $B(2\sin t, -2\cos t)$ and $C(3r-n, r^2-n-1)$ be the vertices of a triangle ABC, where t is a parameter. If $(3x-1)^2+(3y)^2=\alpha$, is the locus of the centroid of triangle ABC, then $\alpha$ equals:

Accepted Answer

(A) 20

Answer

(B) 8

Answer

(C) 6

Answer

(D) 18

Question 18

Let O be the origin, the point A be $z_1=\sqrt{3}+2\sqrt{2}i$, the point $B(z_2)$ be such that $\sqrt{3}|z_1|=|z_2|$ and $\arg(z_2)=\arg(z_1)+\frac{\pi}{6}$. Then

Accepted Answer

(D) ABO is an obtuse angled isosceles triangle

Answer

(A) area of triangle ABO is $\frac{11}{\sqrt{3}}$

Answer

(B) ABO is a scalene triangle

Answer

(C) area of triangle ABO is $\frac{11}{4}$

Question 19

Three defective oranges are accidently mixed with seven good ones and on looking at them, it is not possible to differentiate between them. Two oranges are drawn at random from the lot. If x denote the number of defective oranges, then the variance of x is:

Accepted Answer

(A) $\frac{28}{75}$

Answer

(B) $\frac{14}{25}$

Answer

(C) $\frac{26}{75}$

Answer

(D) $\frac{18}{25}$

Question 20

The area (in sq. units) of the region $\{(x, y): 0\le y\le 2|x|+1, 0\le y\le x^2+1, |x|\le 3\}$ is

Accepted Answer

(B) $\frac{64}{3}$

Answer

(A) $\frac{80}{3}$

Answer

(C) $\frac{17}{3}$

Answer

(D) $\frac{32}{3}$

Question 21

Let M denote the set of all real matrices of order $3	imes3$ and let $S=\{-3, -2, -1, 1, 2\}$. Let $S_1=\{A=[a_{ij}]\in M: A=A^T$ and $a_{ij}\in S, \forall i, j\}$, $S_2=\{A=[a_{ij}]\in M: A=-A^T$ and $a_{ij}\in S, \forall i, j\}$, $S_3=\{A=[a_{ij}]\in M: a_{11}+a_{22}+a_{33}=0$ and $a_{ij}\in S, \forall i, j\}$. If $n(S_1\cup S_2\cup S_3)=125\alpha$, then $\alpha$ equals.

Accepted Answer

1613

Question 22

If $\alpha=1+\sum_{r=1}^{6}(-3)^{r-1}\,^{12}C_{2r-1}$, then the distance of the point $(12, \sqrt{3})$ from the line $\alpha x-\sqrt{3}y+1=0$ is ____.

Accepted Answer

5

Question 23

Let $\vec{a}=\hat{i}+\hat{j}+\hat{k}$, $\vec{b}=2\hat{i}+2\hat{j}+\hat{k}$ and $\vec{d}=\vec{a}	imes\vec{b}$. If $\vec{c}$ is a vector such that $\vec{a}\cdot\vec{c}=|\vec{c}|$, $|\vec{c}-2\vec{d}|=8$ and the angle between $\vec{d}$ and $\vec{c}$ is $\frac{\pi}{4}$, then $|10-3\vec{b}\cdot\vec{c}|+|\vec{d}	imes\vec{c}|^2$ is equal to ____.

Accepted Answer

6

Question 24

Let $f(x)=\begin{cases}3x, & x<0\ \min\{1+x+[x], x+2[x]\}, & 0\le x\le 2\ 5, & x>2\end{cases}$ where $[.]$ denotes greatest integer function. If $\alpha$ and $\beta$ are the number of points, where f is not continuous and is not differentiable, respectively, then $\alpha+\beta$ equals____.

Accepted Answer

5

Question 25

Let $E_1:\frac{x^2}{9}+\frac{y^2}{4}=1$ be an ellipse. Ellipses $E_i$'s are constructed such that their centres and eccentricities are same as that of $E_1$, and the length of minor axis of $E_i$ is the length of major axis of $E_{i+1}$ $(i\ge1)$. If $A_i$ is the area of the ellipse $E_i$, then $\frac{5}{\pi}\left(\sum_{i=1}^{\infty} A_i\right)$, is equal to ____.

Accepted Answer

54

Question 26

Two capacitors $C_1$ and $C_2$ are connected in parallel to a battery. Charge-time graph is shown below for the two capacitors. The energy stored with them are $U_1$ and $U_2$, respectively. Which of the given statements is true?

Accepted Answer

(D) $C_2>C_1$, $U_2>U_1$

Answer

(A) $C_1>C_2$, $U_1>U_2$

Answer

(B) $C_2>C_1$, $U_2<U_1$

Answer

(C) $C_1>C_2$, $U_1<U_2$

Question 27

In the experiment for measurement of viscosity '$\eta$' of given liquid with a ball having radius R, consider following statements. A. Graph between terminal velocity V and R will be a parabola. B. The terminal velocities of different diameter balls are constant for a given liquid. C. Measurement of terminal velocity is dependent on the temperature. D. Measurement can be utilized to assess the density of a given liquid. E. If balls are dropped with some initial speed, the value of $\eta$ will change. Choose the correct answer from the options given below:

Accepted Answer

(B) A, C and D only

Answer

(A) B, D and E only

Answer

(C) C, D and E only

Answer

(D) A, B and E only

Question 28

Consider following statements: A. Surface tension arises due to extra energy of the molecules at the interior as compared to the molecules at the surface, of a liquid. B. As the temperature of liquid rises, the coefficient of viscosity increases. C. As the temperature of gas increases, the coefficient of viscosity increases. D. The onset of turbulence is determined by Reynold's number. E. In a steady flow two stream lines never intersect. Choose the correct answer from the options given below:

Accepted Answer

(B) C, D, E only

Answer

(A) A, D, E only

Answer

(C) B, C, D only

Answer

(D) A, B, C only

Question 29

Three infinitely long wires with linear charge density $\lambda$ are placed along the x-axis, y-axis and z-axis respectively. Which of the following denotes an equipotential surface?

Accepted Answer

(C) $(x^2+y^2)(y^2+z^2)(z^2+x^2)=$ constant

Answer

(A) $xy+yz+zx=$ constant

Answer

(B) $(x+y)(y+z)(z+x)=$ constant

Answer

(D) $xyz=$ constant

Question 30

A hemispherical vessel is completely filled with a liquid of refractive index $\mu$. A small coin is kept at the lowest point (O) of the vessel as shown in figure. The minimum value of the refractive index of the liquid so that a person can see the coin from point E (at the level of the vessel) is______.

Accepted Answer

(C) $\sqrt{2}$

Answer

(A) $\sqrt{3}$

Answer

(B) $\frac{3}{2}$

Answer

(D) $\frac{\sqrt{3}}{2}$

Question 31

Consider a long thin conducting wire carrying a uniform current I. A particle having mass "M" and charge "q" is released at a distance "a" from the wire with a speed $v_0$ along the direction of current in the wire. The particle gets attracted to the wire due to magnetic force. The particle turns round when it is at distance x from the wire. The value of x is [$\mu_0$ is vacuum permeability]

Accepted Answer

(D) $ae^{-4\pi mv_0/q\mu_0 I}$

Answer

(A) $a\left[1-\frac{mv_0}{2q\mu_0 I}\right]$

Answer

(B) $\frac{a}{2}$

Answer

(C) $a\left[1-\frac{mv_0}{q\mu_0 I}\right]$

Question 32

A Carnot engine (E) is working between two temperatures 473K and 273K. In a new system two engines – engine $E_1$ works between 473K to 373K and engine $E_2$ works between 373K to 273K. If $\eta_{12}$, $\eta_1$ and $\eta_2$ are the efficiencies of the engines E, $E_1$ and $E_2$, respectively, then

Accepted Answer

(A) $\eta_{12}<\eta_1+\eta_2$

Answer

(B) $\eta_{12}=\eta_1\eta_2$

Answer

(C) $\eta_{12}=\eta_1+\eta_2$

Answer

(D) $\eta_{12}\ge\eta_1+\eta_2$

Question 33

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: A sound wave has higher speed in solids than gases.
Reason R: Gases have higher value of Bulk modulus than solids.
In the light of the above statements, choose the correct answer from the options given below

Accepted Answer

(D) A is true but R is false

Answer

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

Answer

(B) A is false but R is true

Answer

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

Question 34

For a particular ideal gas which of the following graphs represents the variation of mean squared velocity of the gas molecules with temperature?

Accepted Answer

(A) (1)

Answer

(B) (2)

Answer

(C) (3)

Answer

(D) (4)

Question 35

A bead of mass "m" slides without friction on the wall of a vertical circular hoop of radius "R" as shown in figure. The bead moves under the combined action of gravity and a massless spring (k) attached to the bottom of the hoop. The equilibrium length of the spring is "R". If the bead is released from top of the hoop with (negligible) zero initial speed, velocity of bead, when the length of spring becomes "R", would be (spring constant is "k", g is acceleration due to gravity)

Accepted Answer

(D) $\sqrt{3Rg+\frac{kR^2}{m}}$

Answer

(A) $\sqrt{2gR+\frac{kR^2}{m}}$

Answer

(B) $\sqrt{2Rg+\frac{4kR^2}{m}}$

Answer

(C) $\sqrt{2Rg+\frac{kR^2}{m}}$

Question 36

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: In a central force field, the work done is independent of the path.
Reason R: Every force encountered in mechanics does not have an associated potential energy.
In the light of the above statements, choose the most appropriate answer from the options given below

Accepted Answer

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

Answer

(A) A is true but R is false

Answer

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

Answer

(D) A is false but R is true

Question 37

Choose the correct nuclear process from the below options [p: proton, n: neutron, $e^-$: electron, $e^+$: positron, $
u$: neutrino, $\bar{
u}$: antineutrino]

Accepted Answer

(A) $n	o p+e^-+\bar{
u}$

Answer

(B) $n	o p+e^-+
u$

Answer

(C) $n	o p+e^++\bar{
u}$

Answer

(D) $n	o p+e^++
u$

Question 38

Which of the following circuits has the same output as that of the given circuit? (The given circuit takes inputs A and B through an inverter and two AND gates feeding a NOR gate to produce output Y.)

Accepted Answer

(A) (1)

Answer

(B) (2)

Answer

(C) (3)

Answer

(D) (4)

Question 39

Find the equivalent resistance between two ends of the following circuit.

Accepted Answer

(C) $\frac{r}{9}$

Answer

(A) $r$

Answer

(B) $\frac{r}{6}$

Answer

(D) $\frac{r}{3}$

Question 40

A wire of resistance R is bent into an equilateral triangle and an identical wire is bent into a square. The ratio of resistance between the two end points of an edge of the triangle to that of the square is

Accepted Answer

(D) $\frac{32}{27}$

Answer

(A) $\frac{9}{8}$

Answer

(B) $\frac{8}{9}$

Answer

(C) $\frac{27}{32}$

Question 41

Due to presence of an em-wave whose electric component is given by $E=100\sin(\omega t-kx)$ NC$^{-1}$, a cylinder of length 200 cm holds certain amount of em-energy inside it. If another cylinder of same length but half diameter than previous one holds same amount of em-energy, the magnitude of the electric field of the corresponding em-wave should be modified as

Accepted Answer

(B) $200\sin(\omega t-kx)$ NC$^{-1}$

Answer

(A) $25\sin(\omega t-kx)$ NC$^{-1}$

Answer

(C) $400\sin(\omega t-kx)$ NC$^{-1}$

Answer

(D) $50\sin(\omega t-kx)$ NC$^{-1}$

Question 42

A particle of mass "m" and charge "q" is fastened to one end "A" of a massless string having equilibrium length $\ell$, whose other end is fixed at point "O". The whole system is placed on a frictionless horizontal plane and is initially at rest. If uniform electric field is switched on along the direction as shown in figure, then the speed of the particle when it crosses the x-axis is

Accepted Answer

(C) $\sqrt{\frac{qE\ell}{m}}$

Answer

(A) $\sqrt{\frac{2qE\ell}{m}}$

Answer

(B) $\sqrt{\frac{qE\ell}{4m}}$

Answer

(D) $\sqrt{\frac{qE\ell}{2m}}$

Question 43

A proton of mass "$m_p$" has same energy as that of a photon of wavelength "$\lambda$". If the proton is moving at non-relativistic speed, then ratio of its de Broglie wavelength to the wavelength of photon is.

Accepted Answer

(C) $\frac{1}{c}\sqrt{\frac{E}{2m_p}}$

Answer

(A) $\frac{1}{c}\sqrt{\frac{2E}{m_p}}$

Answer

(B) $\frac{1}{c}\sqrt{\frac{E}{m_p}}$

Answer

(D) $\frac{1}{2c}\sqrt{\frac{E}{m_p}}$

Question 44

The centre of mass of a thin rectangular plate with sides of length a and b, whose mass per unit area $(\sigma)$ varies as $\sigma=\frac{\sigma_0 x}{ab}$ (where $\sigma_0$ is a constant), would be______

Accepted Answer

(A) $\left(\frac{2}{3}a, \frac{b}{2}\right)$

Answer

(B) $\left(\frac{2}{3}a, \frac{2}{3}b\right)$

Answer

(C) $\left(\frac{a}{2}, \frac{b}{2}\right)$

Answer

(D) $\left(\frac{1}{3}a, \frac{b}{2}\right)$

Question 45

A thin prism $P_1$ with angle $4^\circ$ made of glass having refractive index 1.54, is combined with another thin prism $P_2$ made of glass having refractive index 1.72 to get dispersion without deviation. The angle of the prism $P_2$ in degrees is

Accepted Answer

(B) 3

Answer

(A) 4

Answer

(C) $\frac{16}{3}$

Answer

(D) 1.5

Question 46

A tiny metallic rectangular sheet has length and breadth of 5 mm and 2.5 mm, respectively. Using a specially designed screw gauge which has pitch of 0.75 mm and 15 divisions in the circular scale, you are asked to find the area of the sheet. In this measurement, the maximum fractional error will be $\frac{x}{100}$ where x is______

Accepted Answer

3

Question 47

The moment of inertia of a solid disc rotating along its diameter is 2.5 times higher than the moment of inertia of a ring rotating in similar way. The moment of inertia of a solid sphere which has same radius as the disc and rotating in similar way, is n times higher than the moment of inertia of the given ring. Here, n = _______. Consider all the bodies have equal masses.

Accepted Answer

4

Question 48

Two iron solid discs of negligible thickness have radii $R_1$ and $R_2$ and moment of inertia $I_1$ and $I_2$, respectively. For $R_2=2R_1$, the ratio of $I_1$ and $I_2$ would be $\frac{1}{x}$, where x = _______.

Accepted Answer

16

Question 49

A double slit interference experiment performed with a light of wavelength 600 nm forms an interference fringe pattern on a screen with $10^{th}$ bright fringe having its centre at a distance of 10 mm from the central maximum. Distance of the centre of the same $10^{th}$ bright fringe from the central maximum when the source of light is replaced by another source of wavelength 660 nm would be_____mm.

Accepted Answer

11

Question 50

The incorrect decreasing order of atomic radii is:

Accepted Answer

(C) $Be>Mg>Al>Si$

Answer

(A) $Mg>Al>C>O$

Answer

(B) $Al>B>N>F$

Answer

(D) $Si>P>Cl>F$

Question 51

Given below are two statements:
Statement I: In oxalic acid v/s KMnO$_4$ (in the presence of dil H$_2$SO$_4$) titration the solution needs to be heated initially to 60°C, but no heating is required in Ferrous ammonium sulphate (FAS) vs KMnO$_4$ titration (in the presence of dil H$_2$SO$_4$).
Statement II: In oxalic acid vs KMnO$_4$ titration, the initial formation of MnSO$_4$ takes place at high temperature, which then acts as catalyst for further reaction. In the case of FAS vs KMnO$_4$, heating oxidizes Fe$^{2+}$ into Fe$^{3+}$ by oxygen of air and error may be introduced in the experiment.
In the light of the above statements, choose the correct answer from the options 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) Statement I is true but Statement II is false

Answer

(D) Both Statement I and Statement II are false

Question 52

Match List-I (Redox Reaction) with List-II (Type of Redox Reaction). Choose the correct answer from the options given below:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 53

Given below are two statements:
Statement I: (the compound shown in the figure) will undergo alkaline hydrolysis at a faster rate than (the second compound shown).
Statement II: (for the compound shown) intramolecular substitution takes place first by involving lone pair of electrons on nitrogen.
In the light of the above statements, choose the most appropriate answer from the options given below:

Accepted Answer

(C) Both Statement I and Statement II are correct

Answer

(A) Both Statement I and Statement II are incorrect

Answer

(B) Statement I is incorrect but statement II is correct

Answer

(D) Statement I is correct but Statement II is incorrect

Question 54

A weak acid HA has degree of dissociation x. Which option gives the correct expression of $pH=pK_a$?

Accepted Answer

(D) $\log\left(\frac{x}{1-x}\right)$

Answer

(A) $\log(1+2x)$

Answer

(B) $\log\left(\frac{1-x}{x}\right)$

Answer

(C) 0

Question 55

Consider 'n' is the number of lone pair of electrons present in the equatorial position of the most stable structure of ClF$_3$. The ions from the following with 'n' number of unpaired electrons are: A. V$^{3+}$ B. Ti$^{3+}$ C. Cu$^{2+}$ D. Ni$^{2+}$ E. Ti$^{2+}$. Choose the correct answer from the options given below:

Accepted Answer

(B) A, D and E only

Answer

(A) A and C only

Answer

(C) B and C only

Answer

(D) B and D only

Question 56

$\begin{array}{cc}[A]_0/molL^{-1} & t_{1/2}/min\ 0.100 & 200\ 0.025 & 100\end{array}$ For a given reaction R $	o$ P, $t_{1/2}$ is related to $[A]_0$ as given in table. Given: $\log 2=0.30$. Which of the following is true? A. The order of the reaction is $\frac{1}{2}$. B. If $[A]_0$ is 1M, $t_{1/2}$ is $200\sqrt{10}$ min. C. The order of the reaction changes to 1 if the concentration of reactant changes from 0.100 M to 0.500 M. D. $t_{1/2}$ is 800 min for $[A]_0=1.6$ M. Choose the correct answer from the options given below:

Accepted Answer

(C) A, B and D only

Answer

(A) A and C only

Answer

(B) A and B only

Answer

(D) C and D only

Question 57

Ice and water are placed in a closed container at a pressure of 1 atm and temperature 273.15 K. If pressure of the system is increased 2 times, keeping temperature constant, then identify correct observation from following:

Accepted Answer

(D) The solid phase (ice) disappears completely.

Answer

(A) Volume of system increases.

Answer

(B) Liquid phase disappears completely.

Answer

(C) The amount of ice decreases.

Question 58

The molecules having square pyramidal geometry are:

Accepted Answer

(A) BrF$_5$ & XeOF$_4$

Answer

(B) SbF$_5$ & XeOF$_4$

Answer

(C) SbF$_5$ & PCl$_5$

Answer

(D) BrF$_5$ & PCl$_5$

Question 59

The metal ion whose electronic configuration is not affected by the nature of the ligand and which gives a violet colour in non-luminous flame under hot condition in borax bead test is

Accepted Answer

(B) Ni$^{2+}$

Answer

(A) Ti$^{3+}$

Answer

(C) Mn$^{2+}$

Answer

(D) Cr$^{3+}$

Question 60

Both acetaldehyde and acetone (individually) undergo which of the following reactions? A. Iodoform Reaction B. Cannizaro Reaction C. Aldol condensation D. Tollen's Test E. Clemmensen Reduction. Choose the correct answer from the options given below:

Accepted Answer

(B) A, C and E only

Answer

(A) A, B and D only

Answer

(C) C and E only

Answer

(D) B, C and D only

Question 61

In a multielectron atom, which of the following orbitals described by three quantum numbers with have same energy in absence of electric and magnetic fields? A. $n=1, l=0, m_l=0$ B. $n=2, l=0, m_l=0$ C. $n=2, l=1, m_l=1$ D. $n=3, l=2, m_l=1$ E. $n=3, l=2, m_l=0$. Choose the correct answer from the options given below:

Accepted Answer

(D) D and E only

Answer

(A) A and B only

Answer

(B) B and C only

Answer

(C) C and D only

Question 62

The products A and B in the following reactions, respectively are: A $\xleftarrow{AgNO_2}$ CH$_3$-CH$_2$-CH$_2$-Br $\xrightarrow{AgCN}$ B

Accepted Answer

(D) CH$_3$-CH$_2$-CH$_2$-NO$_2$, CH$_3$-CH$_2$-CH$_2$-NC

Answer

(A) CH$_3$-CH$_2$-CH$_2$-ONO, CH$_3$-CH$_2$-CH$_2$-NC

Answer

(B) CH$_3$-CH$_2$-CH$_2$-ONO, CH$_3$-CH$_2$-CH$_2$-CN

Answer

(C) CH$_3$-CH$_2$-CH$_2$-NO$_2$, CH$_3$-CH$_2$-CH$_2$-CN

Question 63

What is the freezing point depression constant of a solvent, 50 g of which contain 1 g non volatile solute (molar mass 256 g mol$^{-1}$) and the decrease in freezing point is 0.40 K?

Accepted Answer

(A) 5.12 K kg mol$^{-1}$

Answer

(B) 4.43 K kg mol$^{-1}$

Answer

(C) 1.86 K kg mol$^{-1}$

Answer

(D) 3.72 K kg mol$^{-1}$

Question 64

The correct order of stability of following carbocations is (the carbocations A, B, C, D are shown in the figure):

Accepted Answer

(D) C > A > B > D

Answer

(A) A > B > C > D

Answer

(B) B > C > A > D

Answer

(C) C > B > A > D

List-I (Redox Reaction)	List-II (Type of Redox Reaction)
A.CH $_4$ (g) + 2O $_2$ (g) $\xrightarrow{\Delta}$ CO $_2$ (g) + 2H $_2$ O(l)	I.Disproportionation reaction
B.2NaH(s) $\xrightarrow{\Delta}$ 2Na(s) + H $_2$ (g)	II.Combination reaction
C.V $_2$ O $_5$ (s) + 5Ca(s) $\xrightarrow{\Delta}$ 2V(s) + 5CaO(s)	III.Decomposition reaction
D.2H $_2$ O $_2$ (aq) $\xrightarrow{\Delta}$ 2H $_2$ O(l) + O $_2$ (g)	IV.Displacement reaction

JEE Main 28 January 2025 Shift 1 Question Paper with Answers

Physics — JEE Main 28 January 2025 Shift 1

Chemistry — JEE Main 28 January 2025 Shift 1

Mathematics — JEE Main 28 January 2025 Shift 1

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