JEE Main 2025 (Online) 2nd April Evening Shift

Paper was held on Wed, Apr 2, 2025 9:30 AM

Chemistry

Given below are two statements :

Statement (I) : Neopentane forms only one monosubstituted derivative.

Statement (II) : Melting point of neopentane is higher than n-pentane.

In the light of the above statements, choose the most appropriate answer from the options given below :

Match List - I with List - II.

List - I (Reaction)		List - II (Name of reaction)
(A)		(I)	Lucas reaction
(B)	$$ \mathrm{ArN}_2^{+} \mathrm{X}^{-} \xrightarrow[\mathrm{HCl}]{\mathrm{Cu}} \mathrm{ArCl}+\mathrm{N}_2 \uparrow+\mathrm{CuX} $$	(II)	Finkelstein reaction
(C)	$$ \mathrm{C}_2 \mathrm{H}_5 \mathrm{Br}+\mathrm{NaI} \xrightarrow[\text { Acetone }]{\text { Dry }} \mathrm{C}_2 \mathrm{H}_5 \mathrm{I}+\mathrm{NaBr} $$	(III)	Fittig reaction
(D)	$$ \mathrm{CH}_3 \mathrm{C}(\mathrm{OH})\left(\mathrm{CH}_3\right) \mathrm{CH}_3 \xrightarrow[\mathrm{ZnCl}_2]{\mathrm{HCl}} \mathrm{CH}_3 \mathrm{C}(\mathrm{Cl})\left(\mathrm{CH}_3\right) \mathrm{CH}_3 $$	(IV)	Gatterman reaction

$$ \text { Choose the correct answer from the options given below : } $$

Electronic configuration of four elements A, B, C and D are given below :

(A) $1 s^2 2 s^2 2 p^3$

(B) $1 s^2 2 s^2 2 p^4$

(D) $1 s^2 2 s^2 2 p^2$

Which of the following is the correct order of increasing electronegativity (Pauling's scale)?

A tetrapeptide, " $x$ " on complete hydrolysis produced glycine (Gly), alanine (Ala), valine (Val), leucine (Leu) in equimolar proportion each. The number of tetrapeptides (sequences) possible involving each of these amino acids is :

Which among the following molecules is (a) involved in $\mathrm{sp}^3 \mathrm{~d}$ hybridization, (b) has different bond lengths and (c) has lone pair of electrons on the central atom?

In 3,3-dimethylhex-1-en-4-yne, there are _________$\mathrm{sp}^3$,_________$\mathrm{sp}^2$ and_________ sp hybridised carbon atoms respectively.

In Dumas' method for estimation of nitrogen, 0.5 gram of an organic compound gave 60 mL of nitrogen collected at 300 K temperature and 715 mm Hg pressure. The percentage composition of nitrogen in the compound (Aqueous tension at $300 \mathrm{~K}=15 \mathrm{~mm} \mathrm{Hg}$ ) is___________%.

Which of the following statements are true?

(A) The subsidiary quantum number $l$ describes the shape of the orbital occupied by the electron.

(B) is the boundary surface diagram of the $2 \mathrm{p}_x$ orbital.

(D) The wave function of $2 \mathrm{p}_x$ orbital is zero everywhere in the $x y$ plane.

Choose the correct answer from the options given below :

Arrange the following in order of magnitude of work done by the system/on the system at constant temperature.

(a) $\left|w_{\text {reversible }}\right|$ for expansion in infinite stages.

(b) $\left|w_{\text {irreversible }}\right|$ for expansion in single stage.

(d) $\left|w_{\text {irreversible }}\right|$ for compression in single stage.

Choose the correct answer from the options given below :

When a concentrated solution of sulphanilic acid and 1-naphthylamine is treated with nitrous acid $(273 \mathrm{~K})$ and acidified with acetic acid, the mass $(\mathrm{g})$ of 0.1 mole of product formed is :

(Given molar mass in $\mathrm{g} \mathrm{mol}^{-1} \mathrm{H}: 1, \mathrm{C}: 12, \mathrm{~N}: 14, \mathrm{O}: 16, \mathrm{~S}: 32$ )

Which of the following graphs correctly represents the variation of thermodynamic properties of Haber's process?

Reactant A converts to product D through the given mechanism (with the net evolution of heat):

A → B slow; ΔH = +ve

B → C fast; ΔH = -ve

C → D fast; ΔH = -ve

Which of the following represents the above reaction mechanism?

Formation of $\mathrm{Na}_4\left[\mathrm{Fe}(\mathrm{CN})_5 \mathrm{NOS}\right]$, a purple coloured complex formed by addition of sodium nitroprusside in sodium carbonate extract of salt indicates the presence of :

Consider the following reactions. From these reactions which reaction will give carboxylic acid as a major product ?

(A) $\quad \mathrm{R}-\mathrm{C} \equiv \mathrm{N} \xrightarrow[\text { mild condition }]{\text { (i) } \stackrel{+}{\mathrm{H}} / \mathrm{H}_2 \mathrm{O}}$

(B) $\quad \mathrm{R}-\mathrm{MgX} \xrightarrow[\text { (ii) } \mathrm{H}_3 \mathrm{O}^{+}]{\text {(i) } \mathrm{CO}_2}$

(C) $\mathrm{R}-\mathrm{C} \equiv \mathrm{N} \xrightarrow[\text { (ii) } \mathrm{H}_3 \mathrm{O}^{+}]{\text {(i) } \mathrm{SnCl}_2 / \mathrm{HCl}}$

(D) $\quad \mathrm{R} \cdot \mathrm{CH}_2 \cdot \mathrm{OH} \xrightarrow{\mathrm{PCC}}$

(E)

Choose the correct answer from the options given below :

The nature of oxide $\left(\mathrm{TeO}_2\right)$ and hydride $\left(\mathrm{TeH}_2\right)$ formed by Te , respectively are :

' $x$ ' g of NaCl is added to water in a beaker with a lid. The temperature of the system is raised from $1^{\circ} \mathrm{C}$ to $25^{\circ} \mathrm{C}$. Which out of the following plots, is best suited for the change in the molarity $(\mathrm{M})$ of the solution with respect to temperature ?

[Consider the solubility of NaCl remains unchanged over the temperature range]

The type of hybridization and the magnetic property of $\left[\mathrm{MnCl}_6\right]^{3-}$ are,

$$ \text { Match List - I with List - II. } $$

List - I (Purification technique)		List - II (Mixture of organic compounds)
(A)	$$ \text { Distillation (simple) } $$	(I)	Diesel + Petrol
(B)	$$ \text { Fractional distillation } $$	(II)	Aniline + Water
(C)	$$ \text { Distillation under reduced pressure } $$	(III)	Chloroform + Aniline
(D)	$$ \text { Steam distillation } $$	(IV)	Glycerol + Spent-lye

$$ \text { Choose the correct answer from the options given below : } $$

The d-orbital electronic configuration of the complex among $\left[\mathrm{Co}(\mathrm{en})_3\right]^{3+},\left[\mathrm{CoF}_6\right]^{3-}$, $\left[\mathrm{Mn}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]^{2+}$ and $\left[\mathrm{Zn}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right]^{2+}$ that has the highest CFSE is :

Consider the following chemical equilibrium of the gas phase reaction at a constant temperature : $\mathrm{A}(\mathrm{g}) \rightleftharpoons \mathrm{B}(\mathrm{g})+\mathrm{C}(\mathrm{g})$

If $p$ being the total pressure, $K_p$ is the pressure equilibrium constant and $\alpha$ is the degree of dissociation, then which of the following is true at equilibrium?

For the reaction $\mathrm{A} \rightarrow \mathrm{B}$ the following graph was obtained. The time required (in seconds) for the concentration of A to reduce to $2.5 \mathrm{~g} \mathrm{~L}^{-1}$ (if the initial concentration of A was $50 \mathrm{~g} \mathrm{~L}^{-1}$ ) is $\qquad$ . (Nearest integer)

Given : $\log 2=0.3010$

JEE Main 2025 (Online) 2nd April Evening Shift Chemistry - Chemical Kinetics and Nuclear Chemistry Question 3 English

When 1 g each of compounds AB and $\mathrm{AB}_2$ are dissolved in 15 g of water separately, they increased the boiling point of water by 2.7 K and 1.5 K respectively. The atomic mass of A (in $a m u$ ) is____________ $\times 10^{-1}$ (Nearest integer)

(Given : Molal boiling point elevation constant is $0.5 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$ )

The spin-only magnetic moment value of $\mathrm{M}^{\mathrm{n}+}$ ion formed among $\mathrm{Ni}, \mathrm{Zn}, \mathrm{Mn}$ and Cu that has the least enthalpy of atomisation is_________ . (in nearest integer) Here n is equal to the number of diamagnetic complexes among $\mathrm{K}_2\left[\mathrm{NiCl}_4\right],\left[\mathrm{Zn}\left(\mathrm{H}_2 \mathrm{O}\right)_6\right] \mathrm{Cl}_2$, $\mathrm{K}_3\left[\mathrm{Mn}(\mathrm{CN})_6\right]$ and $\left[\mathrm{Cu}\left(\mathrm{PPh}_3\right)_3 \mathrm{I}\right]$

$0.2 \%(\mathrm{w} / \mathrm{v})$ solution of NaOH is measured to have resistivity $870.0 \mathrm{~m} \Omega \mathrm{~m}$. The molar conductivity of the solution will be__________$\times 10^2 \mathrm{mS} \mathrm{dm}^2 \mathrm{~mol}^{-1}$. (Nearest integer)

JEE Main 2025 (Online) 2nd April Evening Shift Chemistry - Haloalkanes and Haloarenes Question 1 English

Consider the above sequence of reactions. 151 g of 2-bromopentane is made to react. Yield of major product P is $80 \%$ whereas Q is $100 \%$.

Mass of product Q obtained is________ g.

(Given molar mass in $\mathrm{g} \mathrm{mol}^{-1} \mathrm{H}: 1, \mathrm{C}: 12, \mathrm{O}: 16, \mathrm{Br}: 80$ )

Mathematics

If the mean and the variance of $6,4, a, 8, b, 12,10,13$ are 9 and 9.25 respectively, then $a+b+a b$ is equal to :

Let $f:[1, \infty) \rightarrow[2, \infty)$ be a differentiable function. If $10 \int_1^1 f(\mathrm{t}) \mathrm{dt}=5 x f(x)-x^5-9$ for all $x \geqslant 1$, then the value of $f(3)$ is :

The number of ways, in which the letters A, B, C, D, E can be placed in the 8 boxes of the figure below so that no row remains empty and at most one letter can be placed in a box, is :

JEE Main 2025 (Online) 2nd April Evening Shift Mathematics - Permutations and Combinations Question 3 English

Let the point P of the focal chord PQ of the parabola $y^2=16 x$ be $(1,-4)$. If the focus of the parabola divides the chord $P Q$ in the ratio $m: n, \operatorname{gcd}(m, n)=1$, then $m^2+n^2$ is equal to :

If the system of equations

$$ \begin{aligned} & 2 x+\lambda y+3 z=5 \\ & 3 x+2 y-z=7 \\ & 4 x+5 y+\mu z=9 \end{aligned} $$

has infinitely many solutions, then $\left(\lambda^2+\mu^2\right)$ is equal to :

Let $A$ be a $3 \times 3$ real matrix such that $A^2(A-2 I)-4(A-I)=O$, where $I$ and $O$ are the identity and null matrices, respectively. If $A^5=\alpha A^2+\beta A+\gamma I$, where $\alpha, \beta$, and $\gamma$ are real constants, then $\alpha+\beta+\gamma$ is equal to :

$$If\,\mathop {\lim }\limits_{x \to 0} {{\cos (2x) + a\cos (4x) - b} \over {{x^4}}}is\,finite,\,then\,(a + b)\,is\,equal\,to:$$

If the image of the point $\mathrm{P}(1,0,3)$ in the line joining the points $\mathrm{A}(4,7,1)$ and $\mathrm{B}(3,5,3)$ is $Q(\alpha, \beta, \gamma)$, then $\alpha+\beta+\gamma$ is equal to :

If $\theta \epsilon\left[-\frac{7 \pi}{6}, \frac{4 \pi}{3}\right]$, then the number of solutions of $\sqrt{3} \operatorname{cosec}^2 \theta-2(\sqrt{3}-1) \operatorname{cosec} \theta-4=0$, is equal to :

Let $A=\{1,2,3, \ldots ., 100\}$ and $R$ be a relation on $A$ such that $R=\{(a, b): a=2 b+1\}$. Let $\left(a_1\right.$, $\left.a_2\right),\left(a_2, a_3\right),\left(a_3, a_4\right), \ldots .,\left(a_k, a_{k+1}\right)$ be a sequence of $k$ elements of $R$ such that the second entry of an ordered pair is equal to the first entry of the next ordered pair. Then the largest integer k , for which such a sequence exists, is equal to :

If the domain of the function $f(x)=\frac{1}{\sqrt{10+3 x-x^2}}+\frac{1}{\sqrt{x+|x|}}$ is $(a, b)$, then $(1+a)^2+b^2$ is equal to :

Let the area of the triangle formed by a straight line $\mathrm{L}: x+\mathrm{b} y+\mathrm{c}=0$ with co-ordinate axes be 48 square units. If the perpendicular drawn from the origin to the line L makes an angle of $45^{\circ}$ with the positive $x$-axis, then the value of $\mathrm{b}^2+\mathrm{c}^2$ is :

The line $\mathrm{L}_1$ is parallel to the vector $\overrightarrow{\mathrm{a}}=-3 \hat{i}+2 \hat{j}+4 \hat{k}$ and passes through the point $(7,6,2)$ and the line $\mathrm{L}_2$ is parallel to the vector $\overrightarrow{\mathrm{b}}=2 \hat{i}+\hat{j}+3 \hat{k}$ and passes through the point $(5,3,4)$. The shortest distance between the lines $L_1$ and $L_2$ is :

The number of terms of an A.P. is even; the sum of all the odd terms is 24 , the sum of all the even terms is 30 and the last term exceeds the first by $\frac{21}{2}$. Then the number of terms which are integers in the A.P. is :

Let $(a, b)$ be the point of intersection of the curve $x^2=2 y$ and the straight line $y-2 x-6=0$ in the second quadrant. Then the integral $\mathrm{I}=\int_{\mathrm{a}}^{\mathrm{b}} \frac{9 x^2}{1+5^x} \mathrm{~d} x$ is equal to :

If the length of the minor axis of an ellipse is equal to one fourth of the distance between the foci, then the eccentricity of the ellipse is :

$$If\,\sum\limits_{r = 0}^{10} {({{{{10}^{r + 1}} - 1} \over {{{10}^r}}}).{}^{11}{C_{r + 1}} = {{{}_\alpha 11 - {{11}^{11}}} \over {{{10}^{10}}}},\,then\,\,\alpha \,\,is\,\,equal\,\,to:} $$

$4 \int_0^1\left(\frac{1}{\sqrt{3+x^2}+\sqrt{1+x^2}}\right) d x-3 \log _e(\sqrt{3})$ is equal to :

Let $\overrightarrow{\mathrm{a}}=2 \hat{i}-3 \hat{j}+\hat{k}, \quad \overrightarrow{\mathrm{~b}}=3 \hat{i}+2 \hat{j}+5 \hat{k}$ and a vector $\overrightarrow{\mathrm{c}}$ be such that $(\vec{a}-\vec{c}) \times \vec{b}=-18 \hat{i}-3 \hat{j}+12 \hat{k}$ and $\vec{a} \cdot \vec{c}=3$. If $\vec{b} \times \vec{c}=\vec{d}$, then $|\vec{a} \cdot \vec{d}|$ is equal to :

$$ \text { Given three indentical bags each containing } 10 \text { balls, whose colours are as follows : } $$

$$ \begin{array}{lccc} & \text { Red } & \text { Blue } & \text { Green } \\ \text { Bag I } & 3 & 2 & 5 \\ \text { Bag II } & 4 & 3 & 3 \\ \text { Bag III } & 5 & 1 & 4 \end{array} $$

A person chooses a bag at random and takes out a ball. If the ball is Red, the probability that it is from bag I is p and if the ball is Green, the probability that it is from bag III is $q$, then the value of $\left(\frac{1}{p}+\frac{1}{q}\right)$ is:

$$ \text { If } y=\cos \left(\frac{\pi}{3}+\cos ^{-1} \frac{x}{2}\right) \text {, then }(x-y)^2+3 y^2 \text { is equal to } $$

If the set of all $\mathrm{a} \in \mathbf{R}-\{1\}$, for which the roots of the equation $(1-\mathrm{a}) x^2+2(\mathrm{a}-3) x+9=0$ are positive is $(-\infty,-\alpha] \cup[\beta, \gamma)$, then $2 \alpha+\beta+\gamma$ is equal to $\qquad$ .

If the sum of the first 10 terms of the series $\frac{4 \cdot 1}{1+4 \cdot 1^4}+\frac{4 \cdot 2}{1+4 \cdot 2^4}+\frac{4 \cdot 3}{1+4 \cdot 3^4}+\ldots .$. is $\frac{\mathrm{m}}{\mathrm{n}}$, where $\operatorname{gcd}(\mathrm{m}, \mathrm{n})=1$, then $\mathrm{m}+\mathrm{n}$ is equal to _______________

Let $y=y(x)$ be the solution of the differential equation $\frac{\mathrm{d} y}{\mathrm{~d} x}+2 y \sec ^2 x=2 \sec ^2 x+3 \tan x \cdot \sec ^2 x$ such that $y(0)=\frac{5}{4}$. Then $12\left(y\left(\frac{\pi}{4}\right)-\mathrm{e}^{-2}\right)$ is equal to_____________________

Let $\mathrm{A}(4,-2), \mathrm{B}(1,1)$ and $\mathrm{C}(9,-3)$ be the vertices of a triangle ABC . Then the maximum area of the parallelogram AFDE, formed with vertices D, E and F on the sides BC, CA and $A B$ of the triangle $A B C$ respectively, is___________

Physics

The moment of inertia of a circular ring of mass M and diameter r about a tangential axis lying in the plane of the ring is :

In a moving coil galvanometer, two moving coils $\mathrm{M}_1$ and $\mathrm{M}_2$ have the following particulars :

$$ \begin{aligned} & \mathrm{R}_1=5 \Omega, \mathrm{~N}_1=15, \mathrm{~A}_1=3.6 \times 10^{-3} \mathrm{~m}^2, \mathrm{~B}_1=0.25 \mathrm{~T} \\ & \mathrm{R}_2=7 \Omega, \mathrm{~N}_2=21, \mathrm{~A}_2=1.8 \times 10^{-3} \mathrm{~m}^2, \mathrm{~B}_2=0.50 \mathrm{~T} \end{aligned} $$

Assuming that torsional constant of the springs are same for both coils, what will be the ratio of voltage sensitivity of $M_1$ and $M_2$ ?

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : Net dipole moment of a polar linear isotropic dielectric substance is not zero even in the absence of an external electric field.

Reason (R) : In absence of an external electric field, the different permanent dipoles of a polar dielectric substance are oriented in random directions.

In the light of the above statements, choose the most appropriate answer from the options given below :

If $\mu_0$ and $\epsilon_0$ are the permeability and permittivity of free space, respectively, then the dimension of $\left(\frac{1}{\mu_0 \epsilon_0}\right)$ is :

A sinusoidal wave of wavelength 7.5 cm travels a distance of 1.2 cm along the $x$-direction in 0.3 sec . The crest P is at $x=0$ at $\mathrm{t}=0 \mathrm{sec}$ and maximum displacement of the wave is 2 cm . Which equation correctly represents this wave?

A solenoid having area A and length ' $l$ ' is filled with a material having relative permeability 2. The magnetic energy stored in the solenoid is :

Two identical objects are placed in front of convex mirror and concave mirror having same radii of curvature of 12 cm , at same distance of 18 cm from the respective mirrors. The ratio of sizes of the images formed by convex mirror and by concave mirror is :

A sportsman runs around a circular track of radius $r$ such that he traverses the path $A B A B$. The distance travelled and displacement, respectively, are

JEE Main 2025 (Online) 2nd April Evening Shift Physics - Circular Motion Question 1 English

$$ \text { In the digital circuit shown in the figure, for the given inputs the } P \text { and } Q \text { values are : } $$

JEE Main 2025 (Online) 2nd April Evening Shift Physics - Semiconductor Question 3 English

An electron with mass ' m ' with an initial velocity $(\mathrm{t}=0) \overrightarrow{\mathrm{v}}=\mathrm{v}_0 \hat{i}\left(\mathrm{v}_0>0\right)$ enters a magnetic field $\overrightarrow{\mathrm{B}}=\mathrm{B}_0 \hat{j}$. If the initial de-Broglie wavelength at $\mathrm{t}=0$ is $\lambda_0$ then its value after time ' t ' would be :

A bi-convex lens has radius of curvature of both the surfaces same as $1 / 6 \mathrm{~cm}$. If this lens is required to be replaced by another convex lens having different radii of curvatures on both sides $\left(R_1 \neq R_2\right)$, without any change in lens power then possible combination of $R_1$ and $R_2$ is :

Two large plane parallel conducting plates are kept 10 cm apart as shown in figure. The potential difference between them is V . The potential difference between the points A and $B$ (shown in the figure) is :

JEE Main 2025 (Online) 2nd April Evening Shift Physics - Electrostatics Question 4 English

Two water drops each of radius ' $r$ ' coalesce to form a bigger drop. If ' $T$ ' is the surface tension, the surface energy released in this process is :

Energy released when two deuterons $\left({ }_1 \mathrm{H}^2\right)$ fuse to form a helium nucleus $\left({ }_2 \mathrm{He}^4\right)$ is : (Given : Binding energy per nucleon of ${ }_1 \mathrm{H}^2=1.1 \mathrm{MeV}$ and binding energy per nucleon of ${ }_2 \mathrm{He}^4=7.0 \mathrm{MeV}$ )

$$ \text { Match List - I with List - II. } $$

$$ \begin{array}{lll} & \text { List - I } & {List - II }\\ \text { } \\ \text { (A) } & \text { Heat capacity of body } & \text { (I) } \mathrm{J} \mathrm{~kg}^{-1} \\ \text { (B) } & \text { Specific heat capacity of body } & \text { (II) } \mathrm{J} \mathrm{~K}^{-1} \\ \text { (C) } & \text { Latent heat } & \text { (III) } \mathrm{J} \mathrm{~kg}^{-1} \mathrm{~K}^{-1} \\ \text { (D) } & \text { Thermal conductivity } & \text { (IV) } \mathrm{J} \mathrm{~m}^{-1} \mathrm{~K}^{-1} \mathrm{~s}^{-1} \end{array} $$

$$ \text { Choose the correct answer from the options given below : } $$

Consider a circular loop that is uniformly charged and has a radius $\mathrm{a} \sqrt{2}$. Find the position along the positive $z$-axis of the cartesian coordinate system where the electric field is maximum if the ring was assumed to be placed in $x y$ plane at the origin :

A body of mass 1 kg is suspended with the help of two strings making angles as shown in figure. Magnitudes of tensions $\mathrm{T}_1$ and $\mathrm{T}_2$, respectively, are (in N ) :

(Take acceleration due to gravity $10 \mathrm{~m} / \mathrm{s}^2$ )

Identify the characteristics of an adiabatic process in a monoatomic gas. (A) Internal energy is constant. (B) Work done in the process is equal to the change in internal energy. (C) The product of temperature and volume is a constant. (D) The product of pressure and volume is a constant. (E) The work done to change the temperature from $\mathrm{T}_1$ to $\mathrm{T}_2$ is proportional to $\left(\mathrm{T}_2-\mathrm{T}_1\right)$. Choose the correct answer from the options given below :

Given a charge q , current I and permeability of vacuum $\mu_{\mathrm{o}^*}$. Which of the following quantity has the dimension of momentum ?

Assuming the validity of Bohr's atomic model for hydrogen like ions the radius of $\mathrm{Li}^{++}$ ion in its ground state is given by $\frac{1}{X} a_0$, where $X=$ __________ (Where $\mathrm{a}_0$ is the first Bohr's radius.)

A ray of light suffers minimum deviation when incident on a prism having angle of the prism equal to $60^{\circ}$. The refractive index of the prism material is $\sqrt{2}$. The angle of incidence (in degrees) is__________

The length of a light string is 1.4 m when the tension on it is 5 N . If the tension increases to 7 N , the length of the string is 1.56 m . The original length of the string is__________m.

JEE Main 2025 (Online) 2nd April Evening Shift Physics - Rotational Motion Question 3 English

A wheel of radius 0.2 m rotates freely about its center when a string that is wrapped over its rim is pulled by force of 10 N as shown in figure. The established torque produces an angular acceleration of $2 \mathrm{rad} / \mathrm{s}^2$. Moment of intertia of the wheel is___________ $\mathrm{kg} \mathrm{}\,\, \mathrm{m}^2$. (Acceleration due to gravity $=10 \mathrm{~m} / \mathrm{s}^2$ )

The internal energy of air in $4 \mathrm{~m} \times 4 \mathrm{~m} \times 3 \mathrm{~m}$ sized room at 1 atmospheric pressure will be___________________$\times 10^6 \mathrm{~J}$

(Consider air as diatomic molecule)

A satellite of mass 1000 kg is launched to revolve around the earth in an orbit at a height of 270 km from the earth's surface. Kinetic energy of the satellite in this orbit is____________ $\times 10^{10} \mathrm{~J}$.

(Mass of earth $=6 \times 10^{24} \mathrm{~kg}$, Radius of earth $=6.4 \times 10^6 \mathrm{~m}$, Gravitational constant $=6.67 \times 10^{-11} \mathrm{Nm}^2 \mathrm{~kg}^{-2}$ )