JEE Main 2 April 2025 Shift 1 Question Paper

Question 1

The largest $n\in N$ such that $3^n$ divides $50!$ is:

Accepted Answer

(B) 22

Answer

(A) 21

Answer

(C) 20

Answer

(D) 23

Question 2

Let one focus of the hyperbola $H:\dfrac{x^2}{a^2}-\dfrac{y^2}{b^2}=1$ be at $(\sqrt{10},0)$ and the corresponding directrix be $x=\dfrac{9}{\sqrt{10}}$. If $e$ and $l$ respectively are the eccentricity and the length of the latus rectum of $H$, then $9(e^2+l)$ is equal to:

Accepted Answer

(C) 16

Answer

(A) 14

Answer

(B) 15

Answer

(D) 12

Question 3

The number of sequences of ten terms, whose terms are either 0 or 1 or 2, that contain exactly five 1s and exactly three 2s, is equal to

Accepted Answer

(C) 2520

Answer

(A) 360

Answer

(B) 45

Answer

(D) 1820

Question 4

Let $f:R	o R$ be a twice differentiable function such that $(\sin x\cos y)(f(2x+2y)-f(2x-2y))=(\cos x\sin y)(f(2x+2y)+f(2x-2y))$, for all $x,y\in R$. If $f'(0)=\dfrac{1}{2}$, then the value of $24\,f''\left(\dfrac{5\pi}{3}ight)$ is:

Accepted Answer

(B) $-3$

Answer

(A) 2

Answer

(C) 3

Answer

(D) $-2$

Question 5

Let $A=\begin{bmatrix}\alpha & -1\ 6 & \beta\end{bmatrix}$, $\alpha>0$, such that $\det(A)=0$ and $\alpha+\beta=1$. If $I$ denotes $2	imes2$ identity matrix, then the matrix $(1+A)^8$ is:

Accepted Answer

(D) $\begin{bmatrix}766 & -255\ 1530 & -509\end{bmatrix}$

Answer

(A) $\begin{bmatrix}4 & -1\ 6 & -1\end{bmatrix}$

Answer

(B) $\begin{bmatrix}257 & -64\ 514 & -127\end{bmatrix}$

Answer

(C) $\begin{bmatrix}1025 & -511\ 2024 & -1024\end{bmatrix}$

Question 6

The term independent of $x$ in the expansion of $\left(\dfrac{(x+1)}{x^{2/3}+1-x^{1/3}}-\dfrac{(x+1)}{x-x^{1/2}}\right)^{10}$, $x>1$ is:

Accepted Answer

(A) 210

Answer

(B) 150

Answer

(C) 240

Answer

(D) 120

Question 7

If $	heta\in[-2\pi,2\pi]$, then the number of solutions of $2\sqrt{2}\cos^2	heta+(2-\sqrt{6})\cos	heta-\sqrt{3}=0$, is equal to:

Accepted Answer

(C) 8

Answer

(A) 12

Answer

(B) 6

Answer

(D) 10

Question 8

Let $a_1, a_2, a_3,\ldots$ be in an A.P. such that $\displaystyle\sum_{k=1}^{12}a_{2k-1}=-\dfrac{72}{5}a_1$, $a_1
e0$. If $\displaystyle\sum_{k=1}^{n}a_k=0$, then $n$ is:

Accepted Answer

(A) 11

Answer

(B) 10

Answer

(C) 18

Answer

(D) 17

Question 9

If the function $f(x)=2x^3-9ax^2+12a^2x+1$, where $a>0$, attains its local maximum and minimum values at $p$ and $q$, respectively, such that $p^2=q$, then $f(3)$ is equal to:

Accepted Answer

(D) 37

Answer

(A) 55

Answer

(B) 10

Answer

(C) 23

Question 10

Let $z$ be a complex number such that $|z|=1$. If $\dfrac{2+k^2z}{k+\bar{z}}=kz$, $k\in R$, then the maximum distance of $k+ik^2$ from the circle $|z-(1+2i)|=1$ is:

Accepted Answer

(A) $\sqrt{5}+1$

Answer

(B) 2

Answer

(C) 3

Answer

(D) $\sqrt{3}+1$

Question 11

If $\vec{a}$ is nonzero vector such that its projections on the vectors $2\hat{i}-\hat{j}+2\hat{k}$, $\hat{i}+2\hat{j}-2\hat{k}$ and $\hat{k}$ are equal, then a unit vector along $\vec{a}$ is:

Accepted Answer

(C) $\dfrac{1}{\sqrt{155}}(7\hat{i}+9\hat{j}+5\hat{k})$

Answer

(A) $\dfrac{1}{\sqrt{155}}(-7\hat{i}+9\hat{j}+5\hat{k})$

Answer

(B) $\dfrac{1}{\sqrt{155}}(-7\hat{i}+9\hat{j}-5\hat{k})$

Answer

(D) $\dfrac{1}{\sqrt{155}}(7\hat{i}+9\hat{j}-5\hat{k})$

Question 12

Let $A$ be the set of all functions $f:Z	o Z$ and $R$ be a relation on $A$ such that $R=\{(f,g):f(0)=g(1)	ext{ and }f(1)=g(0)\}$. Then $R$ is:

Accepted Answer

(B) Symmetric but neither reflexive nor transitive

Answer

(A) Symmetric and transitive but not reflexive

Answer

(C) Reflexive but neither symmetric nor transitive

Answer

(D) Transitive but neither reflexive nor symmetric

Question 13

For $\alpha,\beta,\gamma\in R$, if $\displaystyle\lim_{x	o0}\dfrac{x^2\sin\alpha x+(\gamma-1)e^{x^2}}{\sin 2x-\beta x}=3$, then $\beta+\gamma-\alpha$ is equal to:

Accepted Answer

(A) 7

Answer

(B) 4

Answer

(C) 6

Answer

(D) $-1$

Question 14

If the system of linear equations $3x+y+\beta z=3$; $2x+\alpha y-z=-3$; $x+2y+z=4$ has infinitely many solutions, then the value of $22\beta-9\alpha$ is:

Accepted Answer

(B) 31

Answer

(A) 49

Answer

(C) 43

Answer

(D) 37

Question 15

Let $P_n=\alpha^n+\beta^n$, $n\in N$. If $P_{10}=123$, $P_9=76$, $P_8=47$ and $P_1=1$, then the quadratic equation having roots $\dfrac{1}{\alpha}$ and $\dfrac{1}{\beta}$ is:

Accepted Answer

(B) $x^2+x-1=0$

Answer

(A) $x^2-x+1=0$

Answer

(C) $x^2-x-1=0$

Answer

(D) $x^2+x+1=0$

Question 16

If $S$ and $S'$ are the foci of the ellipse $\dfrac{x^2}{18}+\dfrac{y^2}{9}=1$ and $P$ be a point on the ellipse, then $\min(SP\cdot S'P)+\max(SP\cdot S'P)$ is equal to:

Accepted Answer

(D) 27

Answer

(A) $3(1+\sqrt{2})$

Answer

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

Answer

(C) 9

Question 17

Let the vertices $Q$ and $R$ of the triangle $PQR$ lie on the line $\dfrac{x+3}{5}=\dfrac{y-1}{2}=\dfrac{z+4}{3}$, $QR=5$ and the coordinates of the point $P$ be $(0,2,3)$. If the area of the triangle $PQR$ is $\dfrac{m}{n}$ then:

Accepted Answer

(B) $2m-5\sqrt{21}\,n=0$

Answer

(A) $m-5\sqrt{21}\,n=0$

Answer

(C) $5m-2\sqrt{21}\,n=0$

Answer

(D) $5m-21\sqrt{2}\,n=0$

Question 18

Let $ABCD$ be a tetrahedron such that the edges $AB$, $AC$ and $AD$ are mutually perpendicular. Let the areas of the triangles $ABC$, $ACD$ and $ADB$ be 5, 6 and 7 square units respectively. Then the area (in square units) of the $	riangle BCD$ is equal to:

Accepted Answer

(C) $\sqrt{110}$

Answer

(A) $\sqrt{340}$

Answer

(B) 12

Answer

(D) $7\sqrt{3}$

Question 19

Let $a\in R$ and $A$ be a matrix of order $3	imes3$ such that $\det(A)=-4$ and $A+I=\begin{bmatrix}1 & a & 1\ 2 & 1 & 0\ a & 1 & 2\end{bmatrix}$, where $I$ is the identity matrix of order $3	imes3$. If $\det((a+1)\,\mathrm{adj}((a-1)A))$ is $2^m\,3^n$, $m,n\in\{0,1,2,\ldots,20\}$, then $m+n$ is equal to:

Accepted Answer

(D) 16

Answer

(A) 14

Answer

(B) 17

Answer

(C) 15

Question 20

Let the focal chord $PQ$ of the parabola $y^2=4x$ make an angle of $60^\circ$ with the positive x-axis, where $P$ lies in the first quadrant. If the circle, whose one diameter is $PS$, $S$ being the focus of the parabola, touches the y-axis at the point $(0,\alpha)$, then $5\alpha^2$ is equal to:

Accepted Answer

(A) 15

Answer

(B) 25

Answer

(C) 30

Answer

(D) 20

Question 21

Let $[\cdot]$ denote the greatest integer function. If $\displaystyle\int_0^{e^2}\left[\dfrac{1}{e^{x-1}}\right]dx=\alpha-\log_e 2$, then $\alpha^3$ is equal to ______.

Accepted Answer

8

Question 22

Let $f:R	o R$ be a thrice differentiable odd function satisfying $f''(x)\ge0$, $f''(x)=f(x)$, $f(0)=0$, $f'(0)=3$. Then $9f(\log_e 3)$ is equal to ______.

Accepted Answer

36

Question 23

If the area of the region $\{(x,y):|4-x^2|\le y\le x^2,\ y\le4,\ x\ge0\}$ is $\left(\dfrac{80\sqrt{2}}{\alpha}-\beta\right)$, $\alpha,\beta\in N$, then $\alpha+\beta$ is equal to ______.

Accepted Answer

22

Question 24

Three distinct numbers are selected randomly from the set $\{1,2,3,\ldots,40\}$. If the probability, that the selected numbers are in an increasing G.P. is $\dfrac{m}{n}$, $\gcd(m,n)=1$, then $m+n$ is equal to ______.

Accepted Answer

4949

Question 25

The absolute difference between the squares of the radii of the two circles passing through the point $(-9,4)$ and touching the lines $x+y=3$ and $x-y=3$, is equal to ______.

Accepted Answer

768

Question 26

A light wave is propagating with plane wave fronts of the type $x+y+z=$ constant. The angle made by the direction of wave propagation with the x-axis is:

Accepted Answer

(A) $\cos^{-1}\left(\dfrac{1}{\sqrt{3}}\right)$

Answer

(B) $\cos^{-1}\left(\dfrac{2}{3}\right)$

Answer

(C) $\cos^{-1}\left(\dfrac{1}{3}\right)$

Answer

(D) $\cos^{-1}\left(\sqrt{\dfrac{2}{3}}\right)$

Question 27

The equation for real gas is given by $\left(P+\dfrac{a}{V^2}\right)(V-b)=RT$, where $P,V,T$ and $R$ are the pressure, volume, temperature and gas constant, respectively. The dimension of $ab^{-2}$ is equivalent to that of:

Accepted Answer

(D) Energy density

Answer

(A) Planck’s constant

Answer

(B) Compressibility

Answer

(C) Strain

Question 28

A cord of negligible mass is wound around the rim of a wheel supported by spokes with negligible mass. The mass of wheel is 10 kg and radius is 10 cm and it can freely rotate without any friction. Initially the wheel is at rest. If a steady pull of 20 N is applied on the cord, the angular velocity of the wheel, after the cord is unwound by 1 m, would be:

Accepted Answer

(A) 20 rad/s

Answer

(B) 30 rad/s

Answer

(C) 10 rad/s

Answer

(D) 0 rad/s

Question 29

A slanted object AB is placed on one side of a convex lens as shown in the diagram. The image is formed on the opposite side. Angle made by the image with the principal axis is:

Accepted Answer

(B) $-45^\circ$

Answer

(A) $-\dfrac{\alpha}{2}$

Answer

(C) $+45^\circ$

Answer

(D) $-\alpha$

Question 30

Consider two infinitely large plane parallel conducting plates as shown below. The plates are uniformly charged with a surface charge density $+\sigma$ and $-2\sigma$. The force experienced by a point charge $+q$ placed at the mid point between two plates will be:

Accepted Answer

(B) $\dfrac{3\sigma q}{2\varepsilon_0}$

Answer

(A) $\dfrac{\sigma q}{4\varepsilon_0}$

Answer

(C) $\dfrac{3\sigma q}{4\varepsilon_0}$

Answer

(D) $\dfrac{\sigma q}{2\varepsilon_0}$

Question 31

A river is flowing from west to east direction with speed of 9 km h$^{-1}$. If a boat capable of moving at a maximum speed of 27 km h$^{-1}$ in still water, crosses the river in half a minute, while moving with maximum speed at an angle of $150^\circ$ to direction of river flow, then the width of the river is:

Accepted Answer

(B) 112.5 m

Answer

(A) 300 m

Answer

(C) 75 m

Answer

(D) $112.5	imes\sqrt{3}$ m

Question 32

A point charge $+q$ is placed at the origin. A second point charge $+9q$ is placed at $(d,0,0)$ in Cartesian coordinate system. The point in between them where the electric field vanishes is:

Accepted Answer

(B) $\left(\dfrac{d}{4},0,0\right)$

Answer

(A) $\left(\dfrac{4d}{3},0,0\right)$

Answer

(C) $\left(\dfrac{3d}{4},0,0\right)$

Answer

(D) $\left(\dfrac{d}{3},0,0\right)$

Question 33

The battery of a mobile phone is rated as 4.2 V, 5800 mAh. How much energy is stored in it when fully charged?

Accepted Answer

(C) 87.7 kJ

Answer

(A) 43.8 kJ

Answer

(B) 48.7 kJ

Answer

(D) 24.4 kJ

Question 34

A particle is subjected to two simple harmonic motions as: $x_1=\sqrt{7}\sin 5t$ cm and $x_2=2\sqrt{7}\sin\left(5t+\dfrac{\pi}{3}ight)$ cm, where $x$ is displacement and $t$ is time in seconds. The maximum acceleration of the particle is $x	imes10^{-2}$ ms$^{-2}$. The value of $x$ is:

Accepted Answer

(A) 175

Answer

(B) $25\sqrt{7}$

Answer

(C) $5\sqrt{7}$

Answer

(D) 125

Question 35

The relationship between the magnetic susceptibility ($\chi$) and the magnetic permeability ($\mu$) is given by: ($\mu_0$ is the permeability of free space and $\mu_r$ is relative permeability)

Accepted Answer

(A) $\chi=\dfrac{\mu}{\mu_0}-1$

Answer

(B) $\chi=\dfrac{\mu_r}{\mu_0}+1$

Answer

(C) $\chi=\mu_r+1$

Answer

(D) $\chi=1-\dfrac{\mu}{\mu_0}$

Question 36

A zener diode with 5V zener voltage is used to regulate an unregulated dc voltage input of 25 V. For a 400 $\Omega$ resistor connected in series, the zener current is found to be 4 times load current. The load current ($I_L$) and load resistance ($R_L$) are:

Accepted Answer

(D) $I_L=10$ mA; $R_L=500\ \Omega$

Answer

(A) $I_L=20$ mA; $R_L=250\ \Omega$

Answer

(B) $I_L=10$ mA; $R_L=0.5\ \Omega$

Answer

(C) $I_L=0.02$ mA; $R_L=250\ \Omega$

Question 37

In an adiabatic process, which of the following statements is true?

Accepted Answer

(C) The molar heat capacity is zero

Answer

(A) The molar heat capacity is infinite

Answer

(B) Work done by the gas equals the increase in internal energy

Answer

(D) The internal energy of the gas decreases as the temperature increases

Question 38

A square Lamina OABC of length 10 cm is pivoted at ‘O’. Forces act at the lamina as shown in figure. If the lamina remains stationary, then the magnitude of $F$ is:

Accepted Answer

(C) 10 N

Answer

(A) 20 N

Answer

(B) 0 (zero)

Answer

(D) $10\sqrt{2}$ N

Question 39

Let $B_1$ be the magnitude of magnetic field at the centre of a circular coil of radius $R$ carrying current $I$. Let $B_2$ be the magnitude of magnetic field at an axial distance $x$ from the centre. For $x:R=3:4$, $\dfrac{B_2}{B_1}$ is:

Accepted Answer

(C) 64 : 125

Answer

(A) 4 : 5

Answer

(B) 16 : 25

Answer

(D) 25 : 16

Question 40

Considering Bohr’s atomic model for hydrogen atom: (A) the energy of H atom in ground state is same as energy of He$^+$ ion in its first excited state. (B) The energy of H atom in ground state is same as that for Li$^{2+}$ ion in its second excited state. (C) The energy of H atom in its ground state is same as that of He$^+$ ion for its ground state. (D) the energy of He$^+$ ion in its first excited state is same as that for Li$^{2+}$ ion in its ground state. Choose the correct answer from the options given below:

Accepted Answer

(B) (A), (B) only

Answer

(A) (B), (D) only

Answer

(C) (A), (D) only

Answer

(D) (A), (C) only

Question 41

Moment of inertia of a rod of mass ‘M’ and length ‘L’ about an axis passing through its centre and normal to its length is ‘$\alpha$’. Now the rod is cut into two equal parts and these parts are joined symmetrically to form a cross shape. Moment of inertia of this cross about an axis passing through its centre and normal to the plane containing the cross is:

Accepted Answer

(B) $\dfrac{\alpha}{4}$

Answer

(A) $\alpha$

Answer

(C) $\dfrac{\alpha}{8}$

Answer

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

Question 42

A spherical surface separates two media of refractive indices 1 and 1.5 as shown in the figure. Distance of the image of an object ‘O’, is: ($C$ is the centre of curvature of the spherical surface and $R$ is the radius of curvature)

Accepted Answer

(B) 0.4 m left to the spherical surface

Answer

(A) 0.24 m right to the spherical surface

Answer

(C) 0.24 m left to the spherical surface

Answer

(D) 0.4 m right to the spherical surface

Question 43

Match List-I (physical quantities) with List-II (dimensional formulae). Choose the correct answer from the options given below:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 44

A small bob of mass 100 mg and charge $+10\ \mu C$ is connected to an insulating string of length 1 m. It is brought near to an infinitely long non-conducting sheet of charge density ‘$\sigma$’ as shown in figure. If the string subtends an angle of $45^\circ$ with the sheet at equilibrium, the charge density of the sheet will be: (Given $\varepsilon_0=8.85	imes10^{-12}$ F/m and acceleration due to gravity $g=10$ m/s$^2$)

Accepted Answer

(D) 1.77 nC/m$^2$

Answer

(A) 0.885 nC/m$^2$

Answer

(B) 17.7 nC/m$^2$

Answer

(C) 885 nC/m$^2$

Question 45

A monochromatic light is incident on a metallic plate having work function $\phi$. An electron, emitted normally to the plate from a point A with maximum kinetic energy, enters a constant magnetic field, perpendicular to the initial velocity of the electron. The electron passes through a curve and hits back the plate at a point B. The distance between A and B is: (Given: the magnitude of charge of an electron is $e$ and mass is $m$, $h$ is Planck’s constant, $c$ is velocity of light, magnetic field $B$ exists throughout the path of the electron)

Accepted Answer

(C) $\dfrac{\sqrt{8m\left(\dfrac{hc}{\lambda}-\phi\right)}}{eB}$

Answer

(A) $\dfrac{\sqrt{2m\left(\dfrac{hc}{\lambda}-\phi\right)}}{eB}$

Answer

(B) $\dfrac{\sqrt{m\left(\dfrac{hc}{\lambda}-\phi\right)}}{eB}$

Answer

(D) $\dfrac{2\sqrt{m\left(\dfrac{hc}{\lambda}-\phi\right)}}{eB}$

Question 46

A vessel with square cross-section and height of 6 m is vertically partitioned. A small window of 100 cm$^2$ with a hinged door is fitted at a depth of 3 m in the partition wall. One part of the vessel is filled completely with water and the other side is filled with the liquid having density $1.5	imes10^3$ kg/m$^3$. What force one needs to apply on the hinged door so that it does not get opened? (Acceleration due to gravity $=10$ m/s$^2$)

Accepted Answer

150

Question 47

A steel wire of length 2 m and Young’s modulus $2.0	imes10^{11}$ Nm$^{-2}$ is stretched by a force. If Poisson ratio and transverse strain for the wire are 0.2 and $10^{-3}$ respectively, then the elastic potential energy density of the wire is ______ $	imes10^5$ (in SI units).

Accepted Answer

25

Question 48

If the measured angular separation between the second minimum to the left of the central maximum and the third minimum to the right of the central maximum is $30^\circ$ in a single slit diffraction pattern recorded using 628 nm light, then the width of the slit is ______ $\mu$m.

Accepted Answer

6

Question 49

$\gamma_A$ is the specific heat ratio of monoatomic gas A having 3 translational degrees of freedom. $\gamma_B$ is the specific heat ratio of polyatomic gas B having 3 translational, 3 rotational degrees of freedom and 1 vibrational mode. If $\dfrac{\gamma_A}{\gamma_B}=\left(1+\dfrac{1}{n}\right)$, then the value of $n$ is ______.

Accepted Answer

3

Question 50

A person travelling on a straight line moves with a uniform velocity $v_1$ for a distance $x$ and with a uniform velocity $v_2$ for the next $\dfrac{3}{2}x$ distance. The average velocity in this motion is $\dfrac{50}{7}$ m/s. If $v_1$ is 5 m/s then $v_2=$ ______ m/s.

Accepted Answer

10

Question 51

Designate whether each of the following compounds (shown in the figure, labelled a–h) is aromatic or not aromatic.

Accepted Answer

(D) a, c, d, e, h aromatic and b, f, g not aromatic

Answer

(A) e, g aromatic and a, b, c, d, f, h not aromatic

Answer

(B) b, e, f, g aromatic and a, c, d, h not aromatic

Answer

(C) a, b, c, d aromatic and e, f, g, h not aromatic

Question 52

An optically active alkyl halide C$_4$H$_9$Br [A] reacts with hot KOH dissolved in ethanol and forms alkene [B] as major product which reacts with bromine to give dibromide [C]. The compound [C] is converted into a gas [D] upon reacting with alcoholic NaOH. During hydration 18 gram of water is added to 1 mole of gas [D] on warming with mercuric sulphate and dilute acid at 333 K to form compound [E]. The IUPAC name of compound [E] is:

Accepted Answer

(C) Butan-2-one

Answer

(A) But-2-yne

Answer

(B) Butan-2-ol

Answer

(D) Butan-1-al

Question 53

The property/properties that show irregularity in the first four elements of group-17 is/are: (A) Covalent radius (B) Electron affinity (C) Ionic radius (D) First ionization energy. Choose the correct answer from the options given below:

Accepted Answer

(C) B only

Answer

(A) B and D only

Answer

(B) A and C only

Answer

(D) A, B, C and D

Question 54

Which of the following graph (shown in the figure) correctly represents the plots of $K_H$ at 1 bar of gases in water versus temperature?

Accepted Answer

(D) (4)

Answer

(A) (1)

Answer

(B) (2)

Answer

(C) (3)

Question 55

According to Bohr’s model of hydrogen atom, which of the following statement is incorrect?

Accepted Answer

(C) Radius of 6th orbit is three times larger than that of 4th orbit.

Answer

(A) Radius of 3rd orbit is nine times larger than that of 1st orbit.

Answer

(B) Radius of 8th orbit is four times larger than that of 4th orbit.

Answer

(D) Radius of 4th orbit is four times larger than that of 2nd orbit.

Question 56

Two vessels A and B are connected via a stopcock. The vessel A is filled with a gas at a certain pressure. The vessel B is empty and is allowed to come to thermal equilibrium with water and no change in temperature is observed in the thermometer. After opening the stopcock the gas from vessel A expands into vessel B and no change in temperature is observed. Which of the following statement is true?

Accepted Answer

(D) The pressure in the vessel B before opening the stopcock is zero.

Answer

(A) $dw
e0$

Answer

(B) $dq
e0$

Answer

(C) $dU
e0$

Question 57

A solution is made by mixing one mole of volatile liquid A with 3 moles of volatile liquid B. The vapour pressure of pure A is 200 mm Hg and that of the solution is 500 mm Hg. The vapour pressure of pure B and the least volatile component of the solution, respectively, are:

Accepted Answer

(D) 600 mm Hg, A

Answer

(A) 1400 mm Hg, A

Answer

(B) 1400 mm Hg, B

Answer

(C) 600 mm Hg, B

Question 58

$CaCO_3(s)+2HCl(aq)	o CaCl_2(aq)+CO_2(g)+H_2O(l)$. Consider the above reaction, what mass of $CaCl_2$ will be formed if 250 mL of 0.76 M HCl reacts with 1000 g of $CaCO_3$? (Given: molar mass of Ca, C, O, H and Cl are 40, 12, 16, 1 and 35.5 g mol$^{-1}$, respectively)

Accepted Answer

(C) 10.545 g

Answer

(A) 3.908 g

Answer

(B) 2.636 g

Answer

(D) 5.272 g

Question 59

If equal volumes of $AB_2$ and $XY$ (both are salts) aqueous solutions are mixed, which of the following combination will give a precipitate of $AY_2$ at 300 K? (Given $K_{sp}$ at 300 K for $AY_2=5.2	imes10^{-5}$)

Accepted Answer

(C) $2.0	imes10^{-2}$ M $AB_2$, $2.0	imes10^{-2}$ M $XY$

Answer

(A) $3.6	imes10^{-3}$ M $AB_2$, $5.0	imes10^{-4}$ M $XY$

Answer

(B) $2.0	imes10^{-4}$ M $AB_2$, $0.8	imes10^{-4}$ M $XY$

Answer

(D) $1.5	imes10^{-4}$ M $AB_2$, $1.5	imes10^{-3}$ M $XY$

Question 60

Among $SO_2$, $NF_3$, $NH_3$, $XeF_2$, $ClF_3$ and $SF_4$, the hybridization of the molecule with non-zero dipole moment and highest number of lone-pairs of electrons on the central atom is:

Accepted Answer

(D) $sp^3d$

Answer

(A) $sp^3$

Answer

(B) $dsp^2$

Answer

(C) $sp^3d^2$

Question 61

Given below are two statements: Statement (I): Vanillin will react with NaOH and also with Tollen’s reagent. Statement (II): Vanillin will undergo self aldol condensation very easily. In the light of the above statements, choose the most appropriate answer from the options given below:

Accepted Answer

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

Answer

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

Answer

(C) Both Statement I and Statement II are incorrect

Answer

(D) Both Statement I and Statement II are correct

Question 62

Identify the correct statement among the following:

Accepted Answer

(D) Amino acid cysteine easily undergoes dimerization due to the presence of free SH group.

Answer

(A) All naturally occurring amino acids except glycine contain one chiral centre.

Answer

(B) All naturally occurring amino acids are optically active.

Answer

(C) Glutamic acid is the only amino acid that contains a –COOH group at the side chain.

Question 63

The correct order of basic nature in aqueous solution for the bases $NH_3$, $H_2N-NH_2$, $CH_3CH_2NH_2$, $(CH_3CH_2)_2NH$ and $(CH_3CH_2)_3N$ is:

Accepted Answer

(D) $H_2N-NH_2<NH_3<CH_3CH_2NH_2<(CH_3CH_2)_3N<(CH_3CH_2)_2NH$

Answer

(A) $NH_3<H_2N-NH_2<(CH_3CH_2)_2NH<CH_3CH_2NH_2<(CH_3CH_2)_3N$

Answer

(B) $NH_3<H_2N-NH_2<CH_3CH_2NH_2<(CH_3CH_2)_3N<(CH_3CH_2)_2NH$

Answer

(C) $H_2N-NH_2<NH_3<(CH_3CH_2)_3N<CH_3CH_2NH_2<(CH_3CH_2)_2NH$

Question 64

Given below are two statements: Statement (I): The metallic radius of Al is less than that of Ga. Statement (II): The ionic radius of $Al^{3+}$ is less than that of $Ga^{3+}$. In the light of the above statements, choose the most appropriate answer from the options given below:

Accepted Answer

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

Answer

(A) Both Statement I and Statement II are incorrect

Answer

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

Answer

(D) Both Statement I and Statement II are correct

List-I	List-II
A.Coefficient of viscosity	I. $[ML^0T^{-3}]$
B.Intensity of wave	II. $[ML^{-2}T^{-2}]$
C.Pressure gradient	III. $[M^{-1}LT^2]$
D.Compressibility	IV. $[ML^{-1}T^{-1}]$

JEE Main 2 April 2025 Shift 1 Question Paper with Answers

Physics — JEE Main 2 April 2025 Shift 1

Chemistry — JEE Main 2 April 2025 Shift 1

Mathematics — JEE Main 2 April 2025 Shift 1

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