JEE Main 3 April 2025 Shift 1 Question Paper

Question 1

Let $A$ be a matrix of order $3	imes 3$ and $|A|=5$. If $\left|2\,\mathrm{adj}\big(3A\,\mathrm{adj}(2A)\big)ight|=2^{\alpha}\cdot 3^{\beta}\cdot 5^{\gamma}$, $\alpha,\beta,\gamma\in\mathbb{N}$, then $\alpha+\beta+\gamma$ is equal to:

Accepted Answer

(C) 27

Answer

(A) 25

Answer

(B) 26

Answer

(D) 28

Question 2

Let a line passing through the point $(4,1,0)$ intersect the line $L_1:\dfrac{x-1}{2}=\dfrac{y-2}{3}=\dfrac{z-3}{4}$ at the point $A(\alpha,\beta,\gamma)$ and the line $L_2:x-6=y=-z+4$ at the point $B(a,b,c)$. Then $\begin{vmatrix}1&0&1\\alpha&\beta&\gamma\a&b&c\end{vmatrix}$ is equal to:

Accepted Answer

(A) 8

Answer

(B) 16

Answer

(C) 12

Answer

(D) 6

Question 3

Let $\alpha$ and $\beta$ be the roots of $x^2+\sqrt3\,x-16=0$, and $\gamma$ and $\delta$ be the roots of $x^2+3x-1=0$. If $P_n=\alpha^n+\beta^n$ and $Q_n=\gamma^n+\delta^n$, then $\dfrac{P_{25}+\sqrt3\,P_{24}}{2P_{23}}+\dfrac{Q_{25}-Q_{23}}{Q_{24}}$ is equal to:

Accepted Answer

(C) 5

Answer

(A) 3

Answer

(B) 4

Answer

(D) 7

Question 4

The sum of all rational terms in the expansion of $\left(2+\sqrt3\right)^8$ is:

Accepted Answer

(D) 18817

Answer

(A) 16923

Answer

(B) 3763

Answer

(C) 33845

Question 5

Let $A=\{-3,-2,-1,0,1,2,3\}$. Let $R$ be a relation on $A$ defined by $xRy$ if and only if $0\le x^2+2y\le 4$. Let $l$ be the number of elements in $R$ and $m$ be the minimum number of elements required to be added in $R$ to make it a reflexive relation. Then $l+m$ is equal to:

Accepted Answer

(D) 18

Answer

(A) 19

Answer

(B) 20

Answer

(C) 17

Question 6

A line passing through the point $P(\sqrt5,\sqrt5)$ intersects the ellipse $\dfrac{x^2}{36}+\dfrac{y^2}{25}=1$ at $A$ and $B$ such that $(PA)\cdot(PB)$ is maximum. Then $5(PA^2+PB^2)$ is equal to:

Accepted Answer

(D) 338

Answer

(A) 218

Answer

(B) 377

Answer

(C) 290

Question 7

The sum $1+3+11+25+45+71+\ldots$ upto 20 terms, is equal to:

Accepted Answer

(A) 7240

Answer

(B) 7130

Answer

(C) 6982

Answer

(D) 8124

Question 8

If the domain of the function $f(x)=\log_e\!\left(\dfrac{2x-3}{5+4x}\right)+\sin^{-1}\!\left(\dfrac{4+3x}{2-x}\right)$ is $[\alpha,\beta]$, then $\alpha^2+4\beta$ is equal to:

Accepted Answer

(B) 4

Answer

(A) 5

Answer

(C) 3

Answer

(D) 7

Question 9

If $\displaystyle\sum_{r=1}^{9}\dfrac{r+3}{2^r}\,{}^9C_r=\alpha\left(\dfrac{3}{2}\right)^9-\beta$, $\alpha,\beta\in\mathbb{N}$, then $(\alpha+\beta)^2$ is equal to:

Accepted Answer

(C) 81

Answer

(A) 27

Answer

(B) 9

Answer

(D) 18

Question 10

The number of solutions of the equation $2x+3	an x=\pi$, $x\in[-2\pi,2\pi]-\left\{\pm\dfrac{\pi}{2},\pm\dfrac{3\pi}{2}ight\}$ is:

Accepted Answer

(B) 5

Answer

(A) 6

Answer

(C) 4

Answer

(D) 3

Question 11

If $y(x)=\begin{vmatrix}\sin x & \cos x & \sin x+\cos x+1\27 & 28 & 27\1 & 1 & 1\end{vmatrix}$, $x\in\mathbb{R}$, then $\dfrac{d^2y}{dx^2}+y$ is equal to:

Accepted Answer

(A) $-1$

Answer

(B) 28

Answer

(C) 27

Answer

(D) 1

Question 12

Let $g$ be a differentiable function such that $\displaystyle\int_0^x g(t)\,dt=x-\int_0^x t\,g(t)\,dt$, $x\ge 0$ and let $y=y(x)$ satisfy the differential equation $\dfrac{dy}{dx}-y	an x=2(x+1)\sec x\,g(x)$, $x\in\left[0,\dfrac{\pi}{2}ight)$. If $y(0)=0$, then $y\!\left(\dfrac{\pi}{3}ight)$ is equal to:

Accepted Answer

(B) $\dfrac{4\pi}{3}$

Answer

(A) $\dfrac{2\pi}{3\sqrt3}$

Answer

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

Answer

(D) $\dfrac{4\pi}{3\sqrt3}$

Question 13

A line passes through the origin and makes equal angles with the positive coordinate axes. It intersects the lines $L_1:2x+y+6=0$ and $L_2:4x+2y-p=0$, at the points $A$ and $B$, respectively. If $AB=\dfrac{9}{\sqrt2}$ and the foot of the perpendicular from the point $A$ on the line $L_2$ is $M$, then $\dfrac{AM}{BM}$ is equal to:

Accepted Answer

(D) 3

Answer

(A) 5

Answer

(B) 4

Answer

(C) 2

Question 14

Let $z\in\mathbb{C}$ be such that $\dfrac{z^2+3i}{z-2+i}=2+3i$. Then the sum of all possible values of $z^2$ is:

Accepted Answer

(B) $-19-2i$

Answer

(A) $19-2i$

Answer

(C) $19+2i$

Answer

(D) $-19+2i$

Question 15

Let $f(x)=\displaystyle\int x^3\sqrt{3-x^2}\,dx$. If $5f(\sqrt2)=-4$, then $f(1)$ is equal to:

Accepted Answer

(D) $-\dfrac{6\sqrt2}{5}$

Answer

(A) $-\dfrac{2\sqrt2}{5}$

Answer

(B) $-\dfrac{8\sqrt2}{5}$

Answer

(C) $-\dfrac{4\sqrt2}{5}$

Question 16

Let $a_1,a_2,a_3,\ldots$ be a G.P. of increasing positive numbers. If $a_3a_5=729$ and $a_2+a_4=\dfrac{111}{4}$, then $24(a_1+a_2+a_3)$ is equal to:

Accepted Answer

(C) 129

Answer

(A) 131

Answer

(B) 130

Answer

(D) 128

Question 17

Let the domain of the function $f(x)=\log_2\log_4\log_6(3+4x-x^2)$ be $(a,b)$. If $\displaystyle\int_0^{\,b-a}[x^2]\,dx=p-\sqrt q-\sqrt r$, $p,q,r\in\mathbb{N}$, $\gcd(p,q,r)=1$, where $[\cdot]$ is the greatest integer function, then $p+q+r$ is equal to:

Accepted Answer

(A) 10

Answer

(B) 8

Answer

(C) 11

Answer

(D) 9

Question 18

The radius of the smallest circle which touches the parabolas $y=x^2+2$ and $x=y^2+2$ is:

Accepted Answer

(D) $\dfrac{7\sqrt2}{8}$

Answer

(A) $\dfrac{7\sqrt2}{2}$

Answer

(B) $\dfrac{7\sqrt2}{16}$

Answer

(C) $\dfrac{7\sqrt2}{4}$

Question 19

Let $f(x)=\begin{cases}(1+ax)^{1/x}, & x<0\ 1+b, & x=0\ \dfrac{(x+4)^{1/2}-2}{(x+c)^{1/3}-2}, & x>0\end{cases}$ be continuous at $x=0$. Then $e^a\cdot b\cdot c$ is equal to:

Accepted Answer

(C) 48

Answer

(A) 64

Answer

(B) 72

Answer

(D) 36

Question 20

Line $L_1$ passes through the point $(1,2,3)$ and is parallel to the z-axis. Line $L_2$ passes through the point $(\lambda,5,6)$ and is parallel to the y-axis. Let for $\lambda=\lambda_1,\lambda_2$ $(\lambda_2<\lambda_1)$, the shortest distance between the two lines be 3. Then the square of the distance of the point $(\lambda_1,\lambda_2,2)$ from the line $L_1$ is:

Accepted Answer

(C) 25

Answer

(A) 40

Answer

(B) 32

Answer

(D) 37

Question 21

All five letter words are made using all the letters A, B, C, D, E and arranged as in an English dictionary with serial numbers. Let the word at serial number $n$ be denoted by $W_n$. Let the probability $P(W_n)$ of choosing the word $W_n$ satisfy $P(W_n)=2P(W_{n-1})$, $n>1$. If $P(	ext{CDBEA})=\dfrac{2^{\alpha}}{2^{\beta}-1}$, $\alpha,\beta\in\mathbb{N}$, then $\alpha+\beta$ is equal to __________.

Accepted Answer

183

Question 22

Let the product of the focal distances of the point $P(4,2\sqrt3)$ on the hyperbola $H:\dfrac{x^2}{a^2}-\dfrac{y^2}{b^2}=1$ be 32. Let the length of the conjugate axis of $H$ be $p$ and the length of its latus rectum be $q$. Then $p^2+q^2$ is equal to __________.

Accepted Answer

120

Question 23

Let $\vec a=\hat i+\hat j+\hat k$, $\vec b=3\hat i+2\hat j-\hat k$, $\vec c=\lambda\hat j+\mu\hat k$ and $\hat d$ be a unit vector such that $\vec a	imes\hat d=\vec b	imes\hat d$ and $\vec c\cdot\hat d=1$. If $\vec c$ is perpendicular to $\vec a$, then $\left|3\lambda\hat d+\mu\vec cight|^2$ is equal to __________.

Accepted Answer

5

Question 24

If the number of seven-digit numbers, such that the sum of their digits is even, is $m\cdot n\cdot 10^n$, $m,n\in\{1,2,3,\ldots,9\}$, then $m+n$ is equal to __________.

Accepted Answer

14

Question 25

The area of the region bounded by the curve $y=\max\{|x|,\,x|x-2|\}$, the x-axis and the lines $x=-2$ and $x=4$ is equal to __________.

Accepted Answer

12

Question 26

During the melting of a slab of ice at 273 K at atmospheric pressure:

Accepted Answer

(D) Positive work is done on the ice-water system by the atmosphere.

Answer

(A) Internal energy of ice-water system remains unchanged.

Answer

(B) Positive work is done by the ice-water system on the atmosphere.

Answer

(C) Internal energy of the ice-water system decreases.

Question 27

A completely full cylindrical water tank of height 1.6 m and cross-sectional area $0.5\,	ext{m}^2$ has a small hole in its side at a height 90 cm from the bottom. Assume the cross-sectional area of the hole to be negligibly small compared to that of the tank. If a load of 50 kg is applied at the top surface of the water in the tank, then the velocity of the water coming out at the instant when the hole is opened is: ($g=10\,	ext{m/s}^2$)

Accepted Answer

(D) 4 m/s

Answer

(A) 3 m/s

Answer

(B) 5 m/s

Answer

(C) 2 m/s

Question 28

Choose the correct logic circuit (shown in the figure) for the given truth table having inputs A and B. Truth table — inputs $(A,B)	o$ output $Y$: $(0,0)	o0$, $(0,1)	o0$, $(1,0)	o1$, $(1,1)	o1$.

Accepted Answer

(B) (2)

Answer

(A) (1)

Answer

(C) (3)

Answer

(D) (4)

Question 29

The radiation pressure exerted by a 450 W light source on a perfectly reflecting surface placed at 2 m away from it, is:

Accepted Answer

(C) $6	imes10^{-8}$ Pascals

Answer

(A) $1.5	imes10^{-8}$ Pascals

Answer

(B) $0$

Answer

(D) $3	imes10^{-8}$ Pascals

Question 30

A wire of length 25 m and cross-sectional area $5\,	ext{mm}^2$ having resistivity of $2	imes10^{-7}\,\Omega\,	ext{m}$ is bent into a complete circle. The resistance between diametrically opposite points will be:

Accepted Answer

(D) 25 Ω

Answer

(A) 12.5 Ω

Answer

(B) 50 Ω

Answer

(C) 100 Ω

Question 31

Two blocks of masses $m$ and $M$ $(M>m)$ are placed on a frictionless table, the upper block (mass $m$) resting on the lower block (mass $M$); a massless spring of spring constant $k$ is attached to the lower block, and $\mu$ is the coefficient of friction between the two blocks. If the system is slightly displaced and released then: (A) The time period of small oscillation of the two blocks is $T=2\pi\sqrt{\dfrac{m+M}{k}}$. (B) The acceleration of the blocks is $a=\dfrac{kx}{M+m}$ ($x=$ displacement from the mean position). (C) The magnitude of the frictional force on the upper block is $\dfrac{m\mu|x|}{M+m}$. (D) The maximum amplitude of the upper block, if it does not slip, is $\dfrac{\mu(M+m)g}{k}$. (E) Maximum frictional force can be $\mu(M+m)g$. Choose the correct answer from the options given below:

Accepted Answer

(A) (A), (B), (D) Only

Answer

(B) (B), (C), (D) Only

Answer

(C) (C), (D), (E) Only

Answer

(D) (A), (B), (C) Only

Question 32

Which of the following curves (labelled (A)–(D) in the figure) possibly represent one-dimensional motion of a particle? Choose the correct answer from the options given below:

Accepted Answer

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

Answer

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

Answer

(C) (A) and (B) only

Answer

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

Question 33

A parallel plate capacitor is filled equally (half) with two dielectrics of dielectric constant $\varepsilon_1$ and $\varepsilon_2$, as shown in the figures. The distance between the plates is $d$ and area of each plate is $A$. If the capacitances in the first configuration and the second configuration are $C_1$ and $C_2$ respectively, then $\dfrac{C_1}{C_2}$ is:

Accepted Answer

(B) $\dfrac{4\varepsilon_1\varepsilon_2}{(\varepsilon_1+\varepsilon_2)^2}$

Answer

(A) $\dfrac{\varepsilon_1\varepsilon_2^2}{(\varepsilon_1+\varepsilon_2)^2}$

Answer

(C) $\dfrac{\varepsilon_1\varepsilon_2}{\varepsilon_1+\varepsilon_2}$

Answer

(D) $\dfrac{\varepsilon_0(\varepsilon_1+\varepsilon_2)}{2}$

Question 34

Match the LIST-I (Physical quantity) with LIST-II (Dimensional formula). Choose the correct answer from the options given below:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 35

A force of 49 N acts tangentially at the highest point of a sphere (solid) of mass 20 kg, kept on a rough horizontal plane. If the sphere rolls without slipping, the acceleration of the center of the sphere is:

Accepted Answer

(A) $3.5\,	ext{m/s}^2$

Answer

(B) $0.35\,	ext{m/s}^2$

Answer

(C) $2.5\,	ext{m/s}^2$

Answer

(D) $0.25\,	ext{m/s}^2$

Question 36

A piston of mass M is hung from a massless spring whose restoring force law goes as $F=-kx^3$, where $k$ is the spring constant of appropriate dimension. The piston separates the vertical chamber into two parts, where the bottom part is filled with $n$ moles of an ideal gas. An external work is done on the gas isothermally (at a constant temperature T) with the help of a heating filament (with negligible volume) mounted in the lower part of the chamber, so that the piston goes up from a height $L_0$ to $L_1$. The total energy delivered by the filament is (assume the spring to be at its natural length before heating):

Accepted Answer

(C) $nRT\ln\!\left(\dfrac{L_1}{L_0}\right)+Mg(L_1-L_0)+\dfrac{k}{4}(L_1^4-L_0^4)$

Answer

(A) $3nRT\ln\!\left(\dfrac{L_1}{L_0}\right)+2Mg(L_1-L_0)+\dfrac{k}{3}(L_1^3-L_0^3)$

Answer

(B) $nRT\ln\!\left(\dfrac{L_1^2}{L_0^2}\right)+\dfrac{Mg}{2}(L_1-L_0)+\dfrac{k}{4}(L_1^4-L_0^4)$

Answer

(D) $nRT\ln\!\left(\dfrac{L_1}{L_0}\right)+Mg(L_1-L_0)+\dfrac{3k}{4}(L_1^4-L_0^4)$

Question 37

A gas is kept in a container having walls which are thermally non-conducting. Initially the gas has a volume of $800\,	ext{cm}^3$ and temperature $27^\circ$C. The change in temperature when the gas is adiabatically compressed to $200\,	ext{cm}^3$ is: (Take $\gamma=1.5$; $\gamma$ is the ratio of specific heats at constant pressure and at constant volume)

Accepted Answer

(D) 300 K

Answer

(A) 327 K

Answer

(B) 600 K

Answer

(C) 522 K

Question 38

Match the LIST-I (Nuclear / chemical reaction) with LIST-II (Type of reaction). Choose the correct answer from the options given below:

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 39

The electrostatic potential on the surface of a uniformly charged spherical shell of radius $R=10$ cm is 120 V. The potential at the centre of the shell, at a distance $r=5$ cm from the centre, and at a distance $r=15$ cm from the centre of the shell respectively, are:

Accepted Answer

(A) 120V, 120V, 80V

Answer

(B) 40V, 40V, 80V

Answer

(C) 0V, 0V, 80V

Answer

(D) 0V, 120V, 40V

Question 40

The work function of a metal is 3 eV. The colour of the visible light that is required to cause emission of photoelectrons is:

Accepted Answer

(B) Blue

Answer

(A) Green

Answer

(C) Red

Answer

(D) Yellow

Question 41

A particle is released from height $S$ above the surface of the earth. At certain height its kinetic energy is three times its potential energy. The height from the surface of the earth and the speed of the particle at that instant are respectively:

Accepted Answer

(D) $\dfrac{S}{4},\ \sqrt{\dfrac{3gS}{2}}$

Answer

(A) $\dfrac{S}{2},\ \sqrt{\dfrac{3gS}{2}}$

Answer

(B) $\dfrac{S}{2},\ \dfrac{3gS}{2}$

Answer

(C) $\dfrac{S}{4},\ \dfrac{3gS}{2}$

Question 42

A person measures the mass of 3 different particles as 435.42 g, 226.3 g and 0.125 g. According to the rules for arithmetic operations with significant figures, the addition of the masses of the 3 particles will be:

Accepted Answer

(C) 661.8 g

Answer

(A) 661.845 g

Answer

(B) 662 g

Answer

(D) 661.84 g

Question 43

The radii of curvature for a thin convex lens are 10 cm and 15 cm respectively. The focal length of the lens is 12 cm. The refractive index of the lens material is:

Accepted Answer

(C) 1.5

Answer

(A) 1.2

Answer

(B) 1.4

Answer

(D) 1.8

Question 44

The angle of projection of a particle is measured from the vertical axis as $\phi$ and the maximum height reached by the particle is $h_m$. Here $h_m$ as a function of $\phi$ can be presented as (choose the correct graph shown in the figure):

Accepted Answer

(C) (3)

Answer

(A) (1)

Answer

(B) (2)

Answer

(D) (4)

Question 45

Consider the following statements for refraction of light through a prism, when the angle of deviation is minimum. (A) The refracted ray inside the prism becomes parallel to the base. (B) Larger angle prisms provide smaller angle of minimum deviation. (C) Angle of incidence and angle of emergence become equal. (D) There are always two sets of angle of incidence for which deviation will be same except at the minimum deviation setting. (E) Angle of refraction becomes double of the prism angle. Choose the correct answer from the options given below:

Accepted Answer

(A) (A), (C) and (D) Only

Answer

(B) (B), (C) and (D) Only

Answer

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

Answer

(D) (B), (D) and (E) Only

Question 46

Three identical spheres of mass $m$ are placed at the vertices of an equilateral triangle of side length $a$. When released, they interact only through gravitational force and collide after a time $T=4$ seconds. If the sides of the triangle are increased to length $2a$ and also the masses of the spheres are made $2m$, then they will collide after __________ seconds.

Accepted Answer

8

Question 47

A 4.0 cm long straight wire carrying a current of 8 A is placed perpendicular to a uniform magnetic field of strength 0.15 T. The magnetic force on the wire is __________ mN.

Accepted Answer

48

Question 48

Two coherent monochromatic light beams of intensities $4I$ and $9I$ are superimposed. The difference between the maximum and minimum intensities in the resulting interference pattern is $xI$. The value of $x$ is __________.

Accepted Answer

24

Question 49

A loop ABCDA, carrying current $I=12$ A, is placed in a plane, consists of two semi-circular segments of radius $R_1=6\pi$ m and $R_2=4\pi$ m (as shown in the figure). The magnitude of the resultant magnetic field at the centre O is $k	imes10^{-7}$ T. The value of $k$ is __________. (Given $\mu_0=4\pi	imes10^{-7}\,	ext{Tm A}^{-1}$)

Accepted Answer

1

Question 50

In the circuit shown in the figure, a resistance of $150.4\,\Omega$ is connected in series to an ammeter A of resistance $240\,\Omega$. A shunt resistance of $10\,\Omega$ is connected in parallel with the ammeter, and the combination is connected across a 20 V source. The reading of the ammeter is __________ mA.

Accepted Answer

125

Question 51

Which of the following postulate of Bohr's model of hydrogen atom is not in agreement with quantum mechanical model of an atom?

Accepted Answer

(D) The electron in a H atom's stationary state moves in a circle around the nucleus.

Answer

(A) An atom in a stationary state does not emit electromagnetic radiation as long as it stays in the same state.

Answer

(B) An atom can take only certain distinct energies $E_1, E_2, E_3$, etc. These allowed states of constant energy are called the stationary states of atom.

Answer

(C) When an electron makes a transition from a higher energy stationary state to a lower energy stationary state, then it emits a photon of light.

Question 52

Given below are two statements.
Statement I: The N-N single bond is weaker and longer than that of P-P single bond.
Statement II: Compounds of group 15 elements in +3 oxidation states readily undergo disproportionation reactions. In the light of above statements, choose the correct answer from the options given below:

Accepted Answer

(B) Both statement I and statement II are false

Answer

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

Answer

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

Answer

(D) Both statement I and Statement II are true

Question 53

Given below are two statements.
Statement I: A catalyst cannot alter the equilibrium constant $(K_{eq})$ of a reaction, temperature remaining constant.
Statement II: A homogenous catalyst can change the equilibrium composition of a system, temperature remaining constant.
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) Statement I is false but Statement II is true

Answer

(B) Both Statement I and Statement II are true

Answer

(C) Both Statement I and Statement II are false

Question 54

The metal ions that have the calculated spin only magnetic moment value of 4.9 B.M. are: (A) $Cr^{2+}$ (B) $Fe^{2+}$ (C) $Fe^{3+}$ (D) $Co^{3+}$ (E) $Mn^{2+}$. Choose the correct answer from the options given below:

Accepted Answer

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

Answer

(A) (A), (C) and (E) only

Answer

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

Answer

(C) (B) and (E) only

Question 55

In a reaction $A+B	o C$, initial concentrations of A and B are related as $[A]_0=8[B]_0$. The half lives of A and B are 10 min and 40 min respectively. If they start to disappear at the same time, both following first order kinetics, after how much time will the concentration of both the reactants be same?

Accepted Answer

(D) 40 min

Answer

(A) 60 min

Answer

(B) 80 min

Answer

(C) 20 min

Question 56

Which of the following is the correct structure of L-fructose? (Choose the correct Fischer projection shown in the figure.)

Accepted Answer

(C) (3)

Answer

(A) (1)

Answer

(B) (2)

Answer

(D) (4)

Question 57

Identify the correct statements from the following (the structures for statements A–D are shown in the figure): A. ...are metamers; B. ...are functional isomers; C. ...are position isomers; D. ...are homologous. Choose the correct answer from the options given below:

Accepted Answer

(C) (A) & (B) only

Answer

(A) (C) & (D) only

Answer

(B) (B) & (C) only

Answer

(D) (A), (B) & (C) only

Question 58

Among $10^{-9}$ g (each) of the following elements, which one will have the highest number of atoms? Element : Pb, Po, Pr and Pt

Accepted Answer

(B) Pr

Answer

(A) Po

Answer

(C) Pb

Answer

(D) Pt

Question 59

Which of the following statements are correct? A. The process of the addition an electron to a neutral gaseous atom is always exothermic. B. The process of removing an electron from an isolated gaseous atom is always endothermic. C. The 1st ionization energy of the boron is less than that of the beryllium. D. The electronegativity of C is 2.5 in $CH_4$ and $CCl_4$. E. Li is the most electropositive among elements of group I. Choose the correct answer from the options given below:

Accepted Answer

(A) B and C only

Answer

(B) A, C and D only

Answer

(C) B and D only

Answer

(D) B, C and E only

Question 60

Which of the following properties will change when system containing solution 1 will become solution 2? (Solution 1: 10 mol of solute x + 10 L of water; Solution 2: 1 L of solution 1 + 1 mol of solute x + 1 L of water.)

Accepted Answer

(D) Gibbs free energy

Answer

(A) Molar heat capacity

Answer

(B) Density

Answer

(C) Concentration

Question 61

The number of molecules from below which cannot give iodoform reaction is: Ethanol, Isopropyl alcohol, Bromoacetone, 2-Butanol, 2-Butanone, Butanal, 2-Pentanone, 3-Pentanone, Pentanal and 3-Pentanol.

Accepted Answer

(B) 4

Answer

(A) 5

Answer

(C) 3

Answer

(D) 2

Question 62

Identify [A], [B] and [C], respectively in the following reaction sequence (shown in the figure): $[A]\xrightarrow{NaNO_2,\,HCl,\,273	ext{-}278K}[	ext{benzenediazonium chloride}]\xrightarrow{KI}[B]\xrightarrow{2Na,\,	ext{Dry ether}}[C]$. Choose the correct option (the structure sets are shown in the figure):

Accepted Answer

(C) (3)

Answer

(A) (1)

Answer

(B) (2)

Answer

(D) (4)

Question 63

In the following reactions (shown in the figure), which one is NOT correct? Choose the correct option:

Accepted Answer

(A) (1)

Answer

(B) (2)

Answer

(C) (3)

Answer

(D) (4)

Question 64

The correct order of the complexes $[Co(NH_3)_5(H_2O)]^{3+}$ (A), $[Co(NH_3)_6]^{3+}$ (B), $[Co(CN)_6]^{3-}$ (C) and $[CoCl(NH_3)_5]^{2+}$ (D) in terms of wavelength of light absorbed is:

Accepted Answer

(A) D > A > B > C

Answer

(B) C > B > D > A

Answer

(C) D > C > B > A

Answer

(D) C > B > A > D

LIST-I (Physical quantity)	LIST-II (Dimensional formula)
A.Gravitational constant	I. $[LT^{-2}]$
B.Gravitational potential energy	II. $[L^2T^{-2}]$
C.Gravitational potential	III. $[ML^2T^{-2}]$
D.Acceleration due to gravity	IV. $[M^{-1}L^3T^{-2}]$

LIST-I (Nuclear / chemical reaction)	LIST-II (Type of reaction)
A. ${}^{1}_{0}n+{}^{235}_{92}U\to{}^{140}_{54}Xe+{}^{94}_{38}Sr+2{}^{1}_{0}n$	I.Chemical reaction
B. $2H_2+O_2\to 2H_2O$	II.Fusion with +ve Q value
C. ${}^{2}_{1}H+{}^{2}_{1}H\to{}^{3}_{2}He+{}^{1}_{0}n$	III.Fission
D. ${}^{1}_{1}H+{}^{3}_{1}H\to{}^{2}_{1}H+{}^{2}_{1}H$	IV.Fusion with -ve Q value

LIST-I (Molecules/ion)	LIST-II (Hybridisation of central atom)
A. $PF_5$	I. $dsp^2$
B. $SF_6$	II. $sp^3d$
C. $Ni(CO)_4$	III. $sp^3d^2$
D. $[PtCl_4]^{2-}$	IV. $sp^3$

JEE Main 3 April 2025 Shift 1 Question Paper with Answers

Physics — JEE Main 3 April 2025 Shift 1

Chemistry — JEE Main 3 April 2025 Shift 1

Mathematics — JEE Main 3 April 2025 Shift 1

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