JEE Main 2025 — 24 Jan Shift 1 (Previous Year Paper)

The area of the region $\{(x, y): x^2+4x+2\le y\le|x+2|\}$ is equal to

1. A.7
2. B.20/3✓
3. C.24/5
4. D.5

Correct answer: B

For some $n\neq10$, let the coefficients of the 5th, 6th and 7th terms in the binomial expansion of $(1+x)^{n+4}$ be in A.P. Then the largest coefficient in the expansion of $(1+x)^{n+4}$ is:

1. A.35✓
2. B.70
3. C.10
4. D.20

Correct answer: A

If $I(m, n)=\int_0^1x^{m-1}(1-x)^{n-1}dx$, m, n > 0, then $I(9, 14)+I(10, 13)$ is

1. A.I(9, 13)✓
2. B.I(9, 1)
3. C.I(19, 27)
4. D.I(1, 13)

Correct answer: A

Let $y=y(x)$ be the solution of the differential equation $\left(xy-5x^2\sqrt{1+x^2}\right)dx+(1+x^2)dy=0$, $y(0)=0$. Then $y(\sqrt{3})$ is equal to

1. A.$2\sqrt{2}$
2. B.$\sqrt{\frac{15}{2}}$
3. C.$\frac{5\sqrt{3}}{2}$✓
4. D.$\sqrt{\frac{14}{3}}$

Correct answer: C

Let the lines $3x-4y-\alpha=0$, $8x-11y-33=0$, and $2x-3y+\lambda=0$ be concurrent. If the image of the point (1, 2) in the line $2x-3y+\lambda=0$ is $\left(\frac{57}{13}, \frac{-40}{13}\right)$, then $|\alpha\lambda|$ is equal to

1. A.91✓
2. B.101
3. C.113
4. D.84

Correct answer: A

If $\alpha$ and $\beta$ are the roots of the equation $2z^2-3z-2i=0$, where $i=\sqrt{-1}$, then $16\cdot\mathrm{Re}\left(\frac{\alpha^{19}+\beta^{19}+\alpha^{11}+\beta^{11}}{\alpha^{15}+\beta^{15}}\right)\cdot\mathrm{Im}\left(\frac{\alpha^{19}+\beta^{19}+\alpha^{11}+\beta^{11}}{\alpha^{15}+\beta^{15}}\right)$ is equal to

1. A.441✓
2. B.312
3. C.398
4. D.409

Correct answer: A

If the system of equations $2x-y+z=4$, $5x+\lambda y+3z=12$, $100x-47y+\mu z=212$, has infinitely many solutions, then $\mu-2\lambda$ is equal to

1. A.55
2. B.59
3. C.57✓
4. D.56

Correct answer: C

Let $\vec{a}=\hat{i}+2\hat{j}+3\hat{k}$, $\vec{b}=3\hat{i}+\hat{j}-\hat{k}$ and $\vec{c}$ be three vectors such that $\vec{c}$ is coplanar with $\vec{a}$ and $\vec{b}$. If the vector $\vec{c}$ is perpendicular to $\vec{b}$ and $\vec{a}\cdot\vec{c}=5$, then $|\vec{c}|$ is equal to

1. A.16
2. B.$\sqrt{\frac{11}{6}}$✓
3. C.18
4. D.$\frac{1}{3\sqrt{2}}$

Correct answer: B

For a statistical data $x_1, x_2, \ldots, x_{10}$ of 10 values, a student obtained the mean as 5.5 and $\sum_{i=1}^{10}x_i^2=371$. He later found that he had noted two values in the data incorrectly as 4 and 5, instead of the correct values 6 and 8, respectively. The variance of the corrected data is

1. A.9
2. B.5
3. C.4
4. D.7✓

Correct answer: D

Let the line passing through the points ($-1$, 2, 1) and parallel to the line $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z}{4}$ intersect the line $\frac{x+2}{3}=\frac{y-3}{2}=\frac{z-4}{1}$ at the point P. Then the distance of P from the point Q(4, $-5$, 1) is

1. A.10
2. B.5
3. C.$5\sqrt{6}$
4. D.$5\sqrt{5}$✓

Correct answer: D

Let $f:\mathbf{R}-\{0\}\to\mathbf{R}$ be a function such that $f(x)-6f\left(\frac{1}{x}\right)=\frac{35}{3x}-\frac{5}{2}$. If the $\lim_{x\to0}\left(\frac{1}{\alpha x}+f(x)\right)=\beta$; $\alpha, \beta\in\mathbf{R}$, then $\alpha+2\beta$ is equal to

1. A.6
2. B.4✓
3. C.5
4. D.3

Correct answer: B

Let $f(x)=\frac{2^{x+2}+16}{2^{2x+1}+2^{x+4}+32}$. Then the value of $8\left(f\left(\frac{1}{15}\right)+f\left(\frac{2}{15}\right)+\ldots+f\left(\frac{59}{15}\right)\right)$ is equal to

1. A.102
2. B.92
3. C.118✓
4. D.108

Correct answer: C

$\lim_{x\to0}\mathrm{cosec}\,x\left(\sqrt{2\cos^2x+3\cos x}-\sqrt{\cos^2x+\sin x+4}\right)$ is:

1. A.$\frac{1}{2\sqrt{5}}$
2. B.$-\frac{1}{2\sqrt{5}}$✓
3. C.$\frac{1}{\sqrt{15}}$
4. D.0

Correct answer: B

Let circle C be the image of $x^2+y^2-2x+4y-4=0$ in the line $2x-3y+5=0$ and A be the point on C such that OA is parallel to x-axis and A lies on the right hand side of the centre O of C. If B($\alpha$, $\beta$), with $\beta<4$, lies on C such that the length of the arc AB is $(1/6)^{th}$ of the perimeter of C, then $\beta-\sqrt{3}\alpha$ is equal to

1. A.$4-\sqrt{3}$
2. B.3
3. C.4✓
4. D.$3+\sqrt{3}$

Correct answer: C

Consider the region $R=\left\{(x, y): x\le y\le9-\frac{11}{3}x^2, x\ge0\right\}$. The area, of the largest rectangle of sides parallel to the coordinate axes and inscribed in R, is:

1. A.$\frac{567}{121}$✓
2. B.$\frac{730}{119}$
3. C.$\frac{625}{111}$
4. D.$\frac{821}{123}$

Correct answer: A

Let $S_n=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\ldots$ upto n terms. If the sum of the first six terms of an A.P. with first term −p and common difference p is $\sqrt{2026S_{2025}}$, then the absolute difference between $20^{th}$ and $15^{th}$ terms of the A.P. is

1. A.20
2. B.25✓
3. C.45
4. D.90

Correct answer: B

A and B alternately throw a pair of dice. A wins if he throws a sum of 5 before B throws a sum of 8, and B wins if he throws a sum of 8 before A throws a sum of 5. The probability, that A wins if A makes the first throw, is

1. A.$\frac{9}{17}$
2. B.$\frac{8}{19}$
3. C.$\frac{8}{17}$
4. D.$\frac{9}{19}$✓

Correct answer: D

Let in a $\triangle ABC$, the length of the side AC be 6, the vertex B be (1, 2, 3) and the vertices A, C lie on the line $\frac{x-6}{3}=\frac{y-7}{2}=\frac{z-7}{-2}$. Then the area (in sq. units) of $\triangle ABC$ is:

1. A.42
2. B.21✓
3. C.17
4. D.56

Correct answer: B

The product of all the rational roots of the equation $(x^2-9x+11)^2-(x-4)(x-5)=3$, is equal to

1. A.14✓
2. B.28
3. C.7
4. D.21

Correct answer: A

Let the product of the focal distances of the point $\left(\sqrt{3}, \frac{1}{2}\right)$ on the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$, (a > b), be $\frac{7}{4}$. Then the absolute difference of the eccentricities of two such ellipses is

1. A.$\frac{1-\sqrt{3}}{\sqrt{2}}$
2. B.$\frac{1-2\sqrt{2}}{\sqrt{3}}$
3. C.$\frac{3-2\sqrt{2}}{2\sqrt{3}}$✓
4. D.$\frac{3-2\sqrt{2}}{3\sqrt{2}}$

Correct answer: C

Let A be a 3 × 3 matrix such that $X^TAX=O$ for all nonzero 3 × 1 matrices $X=\begin{bmatrix}x\\y\\z\end{bmatrix}$. If $A\begin{bmatrix}1\\1\\1\end{bmatrix}=\begin{bmatrix}1\\4\\-5\end{bmatrix}$, $A\begin{bmatrix}1\\2\\1\end{bmatrix}=\begin{bmatrix}0\\4\\-8\end{bmatrix}$, and $\det(\mathrm{adj}(2(A+I)))=2^\alpha3^\beta5^\gamma$, $\alpha, \beta, \gamma\in\mathbf{N}$, then $\alpha^2+\beta^2+\gamma^2$ is ______.

Correct answer: 44

Let f be a differentiable function such that $2(x+2)^2f(x)-3(x+2)^2=10\int_0^x(t+2)f(t)dt$, $x\ge0$. Then f(2) is equal to ______.

Correct answer: 19

If for some $\alpha, \beta$; $\alpha\le\beta$, $\alpha+\beta=8$ and $\sec^2(\tan^{-1}\alpha)+\mathrm{cosec}^2(\cot^{-1}\beta)=36$, then $\alpha^2+\beta$ is ______.

Correct answer: 14

Let $S=\{p_1, p_2, \ldots, p_{10}\}$ be the set of first ten prime numbers. Let $A=S\cup P$, where P is the set of all possible products of distinct elements of S. Then the number of all ordered pairs (x, y), $x\in S$, $y\in A$, such that x divides y, is ______.

Correct answer: 5120

The number of 3-digit numbers, that are divisible by 2 and 3, but not divisible by 4 and 9, is ______.

Correct answer: 125

For an experimental expression $y=\frac{32.3\times1125}{27.4}$, where all the digits are significant. Then to report the value of y we should write

1. A.y = 1326.19
2. B.y = 1326.2
3. C.y = 1326.186
4. D.y = 1330✓

Correct answer: D

A force $F=\alpha+\beta x^2$ acts on an object in the x–direction. The work done by the force is 5 J when the object is displaced by 1 m. If the constant $\alpha$ = 1N then $\beta$ will be

1. A.12 N/$m^2$✓
2. B.15 N/$m^2$
3. C.8 N/$m^2$
4. D.10 N/$m^2$

Correct answer: A

An ideal gas goes from an initial state to final state. During the process, the pressure of gas increases linearly with temperature. A. The work done by gas during the process is zero. B. The heat added to gas is different from change in its internal energy. C. The volume of the gas is increased. D. The internal energy of the gas is increased. E. The process is isochoric (constant volume process). Choose the correct answer from the options given below:

1. A.A, B, C, D Only
2. B.E Only
3. C.A, C Only
4. D.A, D, E Only✓

Correct answer: D

A uniform solid cylinder of mass 'm' and radius 'r' rolls along an inclined rough plane of inclination 45°. If it starts to roll from rest from the top of the plane then the linear acceleration of the cylinder's axis will be

1. A.$\frac{1}{3\sqrt{2}}g$
2. B.$\frac{1}{\sqrt{2}}g$
3. C.$\sqrt{2}g$
4. D.$\frac{\sqrt{2}g}{3}$✓

Correct answer: D

An air bubble of radius 0.1 cm lies at a depth of 20 cm below the free surface of a liquid of density 1000 kg/$m^3$. If the pressure inside the bubble is 2100 N/$m^2$ greater than the atmospheric pressure, then the surface tension of the liquid in SI unit is (use g = 10m/$s^2$)

1. A.0.05✓
2. B.0.25
3. C.0.1
4. D.0.02

Correct answer: A

Consider the following statements: A. The junction area of solar cell is made very narrow compared to a photo diode. B. Solar cells are not connected with any external bias. C. LED is made of lightly doped p-n junction. D. Increase of forward current results in continuous increase of LED light intensity. E. LEDs have to be connected in forward bias for emission of light. Choose the correct answer from the options given below:

1. A.B, D, E Only
2. B.A, C, E Only
3. C.B, E Only✓
4. D.A, C Only

Correct answer: C

A particle is executing simple harmonic motion with time period 2 s and amplitude 1 cm. If D and d are the total distance and displacement covered by the particle in 12.5 s, then $\frac{D}{d}$ is

1. A.10
2. B.25✓
3. C.$\frac{16}{5}$
4. D.$\frac{15}{4}$

Correct answer: B

A thin plano convex lens made of glass of refractive index 1.5 is immersed in a liquid of refractive index 1.2. When the plane side of the lens is silver coated for complete reflection, the lens immersed in the liquid behaves like a concave mirror of focal length 0.2 m. The radius of curvature of the curved surface of the lens is

1. A.0.15 m
2. B.0.25 m
3. C.0.20 m
4. D.0.10 m✓

Correct answer: D

The amount of work done to break a big water drop of radius 'R' into 27 small drops of equal radius is 10 J. The work done required to break the same big drop into 64 small drops of equal radius will be

1. A.5 J
2. B.15 J✓
3. C.20 J
4. D.10 J

Correct answer: B

Consider a parallel plate capacitor of area A (of each plate) and separation 'd' between the plates. If E is the electric field and $\epsilon_0$ is the permittivity of free space between the plates, then potential energy stored in the capacitor is

1. A.$\frac{1}{2}\epsilon_0E^2Ad$✓
2. B.$\frac{1}{4}\epsilon_0E^2Ad$
3. C.$\epsilon_0E^2Ad$
4. D.$\frac{3}{4}\epsilon_0E^2Ad$

Correct answer: A

An electron of mass 'm' with an initial velocity $\vec{v}=v_0\hat{i}$ ($v_0>0$) enters an electric field $\vec{E}=-E_0\hat{k}$. If the initial de Broglie wavelength is $\lambda_0$, the value after time t would be

1. A.$\lambda_0$
2. B.$\frac{\lambda_0}{\sqrt{1-\frac{e^2E_0^2t^2}{m^2v_0^2}}}$
3. C.$\frac{\lambda_0}{\sqrt{1+\frac{e^2E_0^2t^2}{m^2v_0^2}}}$✓
4. D.$\lambda_0\sqrt{1+\frac{e^2E_0^2t^2}{m^2v_0^2}}$

Correct answer: C

A car of mass 'm' moves on a banked road having radius 'r' and banking angle $\theta$. To avoid slipping from banked road, the maximum permissible speed of the car is $v_0$. The coefficient of friction $\mu$ between the wheels of the car and the banked road is

1. A.$\mu=\frac{v_0^2-rg\tan\theta}{rg+v_0^2\tan\theta}$✓
2. B.$\mu=\frac{v_0^2+rg\tan\theta}{rg-v_0^2\tan\theta}$
3. C.$\mu=\frac{v_0^2+rg\tan\theta}{rg+v_0^2\tan\theta}$
4. D.$\mu=\frac{v_0^2-rg\tan\theta}{rg-v_0^2\tan\theta}$

Correct answer: A

An alternating current is given by $I=I_A\sin\omega t+I_B\cos\omega t$. The r.m.s current will be

1. A.$\frac{|I_A+I_B|}{\sqrt{2}}$
2. B.$\sqrt{I_A^2+I_B^2}$
3. C.$\frac{\sqrt{I_A^2+I_B^2}}{2}$
4. D.$\sqrt{\frac{I_A^2+I_B^2}{2}}$✓

Correct answer: D

A parallel plate capacitor was made with two rectangular plates, each with a length of $l$ = 3 cm and breath of b = 1 cm. The distance between the plates is 3 $\mu$m. Out of the following, which are the ways to increase the capacitance by a factor of 10? A. $l$ = 30 cm, b = 1 cm, d = 1 $\mu$m B. $l$ = 3 cm, b = 1 cm, d = 30 $\mu$m C. $l$ = 6 cm, b = 5 cm, d = 3 $\mu$m D. $l$ = 1 cm, b = 1 cm, d = 10 $\mu$m E. $l$ = 5 cm, b = 2 cm, d = 1 $\mu$m. Choose the correct answer from the options given below:

1. A.A only
2. B.B and D only
3. C.C and E only✓
4. D.C only

Correct answer: C

What is the relative decrease in focal length of a lens for an increase in optical power by 0.1D from 2.5D ? ['D' stands for dioptre]

1. A.0.1
2. B.0.01
3. C.0.04✓
4. D.0.40

Correct answer: C

During the transition of electron from state A to state C of a Bohr atom, the wavelength of emitted radiation is 2000 Å and it becomes 6000 Å when the electron jumps from state B to state C. Then the wavelength of the radiation emitted during the transition of electrons from state A to state B is

1. A.4000 Å
2. B.3000 Å✓
3. C.6000 Å
4. D.2000 Å

Correct answer: B

An object of mass 'm' is projected from origin in a vertical xy plane at an angle 45° with the x–axis with an initial velocity $v_0$. The magnitude and direction of the angular momentum of the object with respect to origin, when it reaches at the maximum height, will be [g is acceleration due to gravity]

1. A.$\frac{mv_0^3}{2\sqrt{2}g}$ along positive z–axis
2. B.$\frac{mv_0^3}{4\sqrt{2}g}$ along positive z–axis
3. C.$\frac{mv_0^3}{4\sqrt{2}g}$ along negative z–axis✓
4. D.$\frac{mv_0^3}{2\sqrt{2}g}$ along negative z–axis

Correct answer: C

A plano-convex lens having radius of curvature of first surface 2 cm exhibits focal length of $f_1$ in air. Another plano-convex lens with first surface radius of curvature 3 cm has focal length of $f_2$ when it is immersed in a liquid of refractive index 1.2. If both the lenses are made of same glass of refractive index 1.5, the ratio of $f_1$ and $f_2$ will be

1. A.3 : 5
2. B.1 : 2
3. C.2 : 3
4. D.1 : 3✓

Correct answer: D

The Young's double slit interference experiment is performed using light consisting of 480 nm and 600 nm wavelengths to form interference patterns. The least number of the bright fringes of 480 nm light that are required for the first coincidence with the bright fringes formed by 600 nm light is

1. A.8
2. B.5✓
3. C.4
4. D.6

Correct answer: B

A satellite is launched into a circular orbit of radius 'R' around the earth. A second satellite is launched into an orbit of radius 1.03 R. The time period of revolution of the second satellite is larger than the first one approximately by

1. A.9%
2. B.4.5%✓
3. C.3%
4. D.2.5%

Correct answer: B

A current of 5A exists in a square loop of side $\frac{1}{\sqrt{2}}$ m. Then the magnitude of the magnetic field B at the centre of the square loop will be $p\times10^{-6}$ T. where, value of p is ______. [Take $\mu_0=4\pi\times10^{-7}$ T m $A^{-1}$].

Correct answer: 8

A square loop of sides a = 1 m is held normally in front of a point charge q = 1C. The flux of the electric field through the shaded region is $\frac{5}{p}\times\frac{1}{\epsilon_0}\frac{Nm^2}{C}$, where the value of p is ______.

Correct answer: 48

A wire of resistance 9 $\Omega$ is bent to form an equilateral triangle. Then the equivalent resistance across any two vertices will be ______ ohm.

Correct answer: 2

The temperature of 1 mole of an ideal monoatomic gas is increased by 50°C at constant pressure. The total heat added and change in internal energy are $E_1$ and $E_2$, respectively. If $\frac{E_1}{E_2}=\frac{x}{9}$ then the value of x is ______

Correct answer: 15

The least count of a screw guage is 0.01 mm. If the pitch is increased by 75% and number of divisions on the circular scale is reduced by 50%, the new least count will be ______ $\times10^{-3}$ mm

Correct answer: 35

Given below are two statements: Statement I: The conversion proceeds well in the less polar medium. $CH_3-CH_2-CH_2-CH_2-Cl\xrightarrow{HO^-}CH_3-CH_2-CH_2-CH_2-OH+Cl^-$ Statement II: The conversion proceeds well in the more polar medium. $CH_3-CH_2-CH_2-CH_2-Cl\xrightarrow{R_3\ddot{N}}CH_3-CH_2-CH_2-CH_2-\overset{+}{N}R_3\ Cl^-$. In the light of the above statements, choose the correct answer from the options given below

1. A.Both Statement I and Statement II are true✓
2. B.Statement I is false but Statement II is true
3. C.Both Statement I and Statement II are false
4. D.Statement I is true but Statement II is false

Correct answer: A

Preparation of potassium permanganate from $MnO_2$ involves two step process in which the 1st step is a reaction with KOH and $KNO_3$ to produce

1. A.$K_3MnO_4$
2. B.$KMnO_4$
3. C.$K_2MnO_4$✓
4. D.$K_4[Mn(OH)_6]$

Correct answer: C

Following are the four molecules "P", "Q", "R" and "S". Which one among the four molecules will react with H–Br(aq) at the fastest rate? P: 3,6-dihydro-2H-pyran (ring O not attached to the C=C); Q: 3,4-dihydro-2H-pyran (cyclic enol ether, ring O directly attached to the C=C); R: 1-methylcyclohexene; S: 1,2-dimethylcyclohexene.

1. A.S
2. B.R
3. C.Q✓
4. D.P

Correct answer: C

Consider the given plots of vapour pressure (VP) vs temperature(T/K). Which amongst the following options is correct graphical representation showing $\Delta T_f$, depression in the freezing point of a solvent in a solution?

1. A.Plot 1: curves labelled "Solution" and "Liquid Solvent" rising with T and a dashed horizontal line; $T_f$ and $T_f^\circ$ marked where each curve meets the dashed line
2. B.Plot 2: curves labelled "Solution" and "Frozen Solvent" rising with T, with $T_f$ and $T_f^\circ$ marked at their intersections with a dashed line
3. C.Plot 3: a steep "Frozen solvent" curve crossing the "Liquid Solvent" curve at $T_f^\circ$ and the lower "Solution" curve at $T_f$ (to the left)✓
4. D.Plot 4: "Solution" curve above "Liquid Solvent" curve, with the frozen solvent curve meeting them; $T_f$ to the left of $T_f^\circ$

Correct answer: C

$K_{sp}$ for $Cr(OH)_3$ is $1.6\times10^{-30}$. What is the molar solubility of this salt in water?

1. A.$\sqrt[5]{1.8\times10^{-30}}$
2. B.$\frac{1.8\times10^{-30}}{27}$
3. C.$\sqrt[2]{1.6\times10^{-30}}$
4. D.$\sqrt[4]{\frac{1.6\times10^{-30}}{27}}$✓

Correct answer: D

One mole of the octahedral complex compound $Co(NH_3)_5Cl_3$ gives 3 moles of ions on dissolution in water. One mole of the same complex reacts with excess of $AgNO_3$ solution to yield two moles of $AgCl_{(s)}$. The structure of the complex is:

1. A.$[Co(NH_3)_3Cl_3]\cdot2NH_3$
2. B.$[Co(NH_3)_4Cl]\cdot Cl_2\cdot NH_3$
3. C.$[Co(NH_3)_5Cl]Cl_2$✓
4. D.$[Co(NH_3)_4Cl_2]\cdot Cl\cdot NH_3$

Correct answer: C

The product (A) formed in the following reaction sequence is $CH_3-C\equiv CH\xrightarrow{\text{i) } Hg^{2+}, H_2SO_4;\ \text{ii) HCN;\ iii) } H_2/Ni}$ (A) Product

1. A.$CH_3-CH_2-CH(NH_2)-CH_2-OH$
2. B.$CH_3-C(OH)(CH_3)-CH_2-NH_2$✓
3. C.$CH_3-C(NH_2)(CH_3)-CH_2-OH$
4. D.$CH_3-CH_2-CH(OH)-CH_2-NH_2$

Correct answer: B

Which one of the carbocations from the following is most stable?

1. A.$\overset{+}{C}H_2-CH=CH-O-CH_2-CO-CH_3$
2. B.$\overset{+}{C}H_2-CH=CH-CH_2-O-CH_3$
3. C.$\overset{+}{C}H_2-CH=CH-O-CH_2CH_3$✓
4. D.$\overset{+}{C}H_2-CH=CH-F$

Correct answer: C

Which of the following ions is the strongest oxidizing agent? (Atomic Number of Ce = 58, Eu = 63, Tb = 65, Lu = 71)

1. A.$Eu^{2+}$
2. B.$Lu^{3+}$
3. C.$Tb^{4+}$✓
4. D.$Ce^{3+}$

Correct answer: C

Let us consider an endothermic reaction which is non-spontaneous at the freezing point of water. However, the reaction is spontaneous at boiling point of water. Choose the correct option.

1. A.Both ΔH and ΔS are (−ve)
2. B.ΔH is (−ve) but ΔS is (+ve)
3. C.Both ΔH and ΔS are (+ve)✓
4. D.ΔH is (+ve) but ΔS is (−ve)

Correct answer: C

For a reaction, $N_2O_{5(g)}\to2NO_{2(g)}+\frac{1}{2}O_{2(g)}$ in a constant volume container, no products were present initially. The final pressure of the system when 50% of reaction gets completed is

1. A.7/2 times of initial pressure
2. B.5/2 times of initial pressure
3. C.5 times of initial pressure
4. D.7/4 times of initial pressure✓

Correct answer: D

For the given cell $Fe^{2+}_{(aq)}+Ag^+_{(aq)}\to Fe^{3+}_{(aq)}+Ag_{(s)}$. The standard cell potential of the above reaction is Given: $Ag^++e^-\to Ag$ $E^\ominus=x$ V; $Fe^{2+}+2e^-\to Fe$ $E^\ominus=y$ V; $Fe^{3+}+3e^-\to Fe$ $E^\ominus=z$ V

1. A.x + 2y
2. B.x + y − z
3. C.x + 2y − 3z✓
4. D.y − 2x

Correct answer: C

Aman has been asked to synthesise the molecule 1-acetylcyclopentene (x). He thought of preparing the molecule using an aldol condensation reaction. He found a few cyclic alkenes in his laboratory. He thought of performing ozonolysis reaction on alkene to produce a dicarbonyl compound followed by aldol reaction to prepare "x". Predict the suitable alkene that can lead to the formation of "x".

1. A.4-Methylcyclohexene (CH3 on the carbon para to the C=C)
2. B.1-Methylcyclohexene (CH3 on a double-bond carbon)✓
3. C.Methylenecyclohexane (exocyclic =CH2)
4. D.3-Methylcyclohexene (CH3 on the allylic carbon)

Correct answer: B

The large difference between the melting and boiling points of oxygen and sulphur may be explained on the basis of

1. A.Atomicity✓
2. B.Atomic size
3. C.Electron gain enthalpy
4. D.Electronegativity

Correct answer: A

Which of the following statement is true with respect to $H_2O$, $NH_3$ and $CH_4$ ? A. The central atoms of all the molecules are $sp^3$ hybridized. B. The H–O–H, H–N–H and H–C–H angles in the above molecules are 104.5°, 107.5° and 109.5°, respectively. C. The increasing order of dipole moment is $CH_4<NH_3<H_2O$. D. Both $H_2O$ and $NH_3$ are Lewis acids and $CH_4$ is a Lewis base. E. A solution of $NH_3$ in $H_2O$ is basic. In this solution $NH_3$ and $H_2O$ act as Lowry-Bronsted acid and base respectively. Choose the correct answer from the options given below:

1. A.A, D and E Only
2. B.A, B, C and E Only
3. C.A, B and C Only✓
4. D.C, D and E Only

Correct answer: C

Which of the following statements are NOT true about the periodic table? A. The properties of elements are function of atomic weights. B. The properties of elements are function of atomic numbers. C. Elements having similar outer electronic configurations are arranged in same period. D. An element's location reflects the quantum numbers of the last filled orbital. E. The number of elements in a period is same as the number of atomic orbitals available in energy level that is being filled. Choose the correct answer from the options given below:

1. A.A, C and E Only✓
2. B.A and E Only
3. C.D and E Only
4. D.B, C and E Only

Correct answer: A

Which of the following linear combination of atomic orbitals will lead to formation of molecular orbitals in homonuclear diatomic molecules [internuclear axis in z- direction] ? A. $2p_z$ and $2p_x$ B. 2s and $2p_x$ C. $3d_{xy}$ and $3d_{x^2-y^2}$ D. 2s and $2p_z$ E. $2p_z$ and $3d_{x^2-y^2}$. Choose the correct answer from the options given below:

1. A.D Only✓
2. B.A and B Only
3. C.E Only
4. D.C and D Only

Correct answer: A

Given below are two statements I and II. Statement I: Dumas method is used for estimation of "Nitrogen" in an organic compound. Statement II: Dumas method involves the formation of ammonium sulphate by heating the organic compound with conc $H_2SO_4$. In the light of the above statements, choose the correct answer from the options given below

1. A.Both Statement I and Statement II are false
2. B.Statement I is true but Statement II is false✓
3. C.Both Statement I and Statement II are true
4. D.Statement I is false but Statement II is true

Correct answer: B

Which of the following arrangements with respect to their reactivity in nucleophilic addition reaction is correct?

1. A.p- nitrobenzaldehyde < benzaldehyde < p-tolualdehyde < acetophenone
2. B.acetophenone < benzaldehyde < p-tolualdehyde < p- nitrobenzaldehyde
3. C.benzaldehyde < acetophenone < p- nitrobenzaldehyde < p-tolualdehyde
4. D.acetophenone < p-tolualdehyde < benzaldehyde < p- nitrobenzaldehyde✓

Correct answer: D

The carbohydrate "Ribose" present in DNA, is A. A pentose sugar B. present in pyranose from C. in "D" configuration D. a reducing sugar, when free E. in $\alpha$–anomeric form. Choose the correct answer from the options given below:

1. A.A, C and D Only✓
2. B.B, D and E Only
3. C.A, D and E Only
4. D.A, B and E Only

Correct answer: A

37.8 g $N_2O_5$ was taken in a 1 L reaction vessel and allowed to undergo the following reaction at 500 K $2N_2O_{5(g)}\rightleftharpoons2N_2O_{4(g)}+O_{2(g)}$. The total pressure at equilibrium was found to be 18.65 bar. Then, Kp = ______ $\times10^{-2}$ [nearest integer] Assume $N_2O_5$ to behave ideally under these conditions. Given: R = 0.082 bar L $mol^{-1}$ $K^{-1}$

Correct answer: 962

Consider the following reaction occurring in the blast furnace: $Fe_3O_{4(s)}+4CO_{(g)}\to3Fe_{(l)}+4CO_{2(g)}$. 'x' kg of iron is produced when $2.32\times10^3$ kg $Fe_3O_4$ and $2.8\times10^2$ kg CO are brought together in the furnace. The value of 'x' is ______. (nearest integer) {Given: molar mass of $Fe_3O_4$ = 232 g $mol^{-1}$, molar mass of CO = 28 g $mol^{-1}$, molar mass of Fe = 56 g $mol^{-1}$}

Correct answer: 420

Xg of benzoic acid on reaction with aq $NaHCO_3$ released $CO_2$ that occupied 11.2 L volume at STP. X is ______ g.

Correct answer: 61

Among the following cations, the number of cations which will give characteristic precipitate in their identification tests with $K_4[Fe(CN)_6]$ is ______. $Cu^{2+}$, $Fe^{3+}$, $Ba^{2+}$, $Ca^{2+}$, $NH_4^+$, $Mg^{2+}$, $Zn^{2+}$

Correct answer: 3

Standard entropies of $X_2$, $Y_2$ and $XY_5$ are 70, 50 and 110 J $K^{-1}$ $mol^{-1}$ respectively. The temperature in Kelvin at which the reaction $\frac{1}{2}X_2+\frac{5}{2}Y_2\rightleftharpoons XY_5$ $\Delta H^\ominus=-35$ kJ $mol^{-1}$ will be at equilibrium is ______ (Nearest integer)