Identify the incorrect pair from the following :

Given below are two statements : one is labelled as Assertion $$\mathbf{A}$$ and the other is labelled as Reason $$\mathbf{R}$$ :

Assertion A : The first ionisation enthalpy decreases across a period.

Reason $$\mathbf{R}$$ : The increasing nuclear charge outweighs the shielding across the period.

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

The major product(P) in the following reaction is

Identify product A and product B :

the arenium ion which is not involved in the bromination of Aniline is __________.

Given below are two statements :

Statement I : The electronegativity of group 14 elements from $$\mathrm{Si}$$ to $$\mathrm{Pb}$$, gradually decreases.

Statement II : Group 14 contains non-metallic, metallic, as well as metalloid elements.

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

Chlorine undergoes disproportionation in alkaline medium as shown below :

$$\mathrm{aCl}_{2(\mathrm{~g})}+\mathrm{b} \mathrm{OH}_{(\mathrm{aq})}^{-} \rightarrow \mathrm{c} \mathrm{ClO}_{(\mathrm{aq)}}^{-}+\mathrm{d} \mathrm{Cl}_{(\mathrm{aq})}^{-}+\mathrm{e} \mathrm{H}_2 \mathrm{O}_{(\mathrm{l})}$$

The values of $$a, b, c$$ and $$d$$ in a balanced redox reaction are respectively :

In chromyl chloride test for confirmation of $$\mathrm{Cl}^{-}$$ ion, a yellow solution is obtained. Acidification of the solution and addition of amyl alcohol and $$10 \% \mathrm{~H}_2 \mathrm{O}_2$$ turns organic layer blue indicating formation of chromium pentoxide. The oxidation state of chromium in that is

Type of amino acids obtained by hydrolysis of proteins is :

The correct set of four quantum numbers for the valence electron of rubidium atom $$(\mathrm{Z}=37)$$ is :

The difference in energy between the actual structure and the lowest energy resonance structure for the given compound is

Match List I with List II

Choose the correct answer from the options given below:

The final product A formed in the following multistep reaction sequence is

Which of the following is not correct?

The interaction between $$\pi$$ bond and lone pair of electrons present on an adjacent atom is responsible for

In which one of the following metal carbonyls, $$\mathrm{CO}$$ forms a bridge between metal atoms?

$$\mathrm{KMnO}_4$$ decomposes on heating at $$513 \mathrm{~K}$$ to form $$\mathrm{O}_2$$ along with

Appearance of blood red colour, on treatment of the sodium fusion extract of an organic compound with $$\mathrm{FeSO}_4$$ in presence of concentrated $$\mathrm{H}_2 \mathrm{SO}_4$$ indicates the presence of element/s

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

Assertion A : Aryl halides cannot be prepared by replacement of hydroxyl group of phenol by halogen atom.

Reason R : Phenols react with halogen acids violently.

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

In alkaline medium, $$\mathrm{MnO}_4^{-}$$ oxidises $$\mathrm{I}^{-}$$ to

The mass of zinc produced by the electrolysis of zine sulphate solution with a steady current of $$0.015 \mathrm{~A}$$ for 15 minutes is _________ $$\times 10^{-4} \mathrm{~g}$$.

(Atomic mass of zinc $$=65.4 \mathrm{~amu}$$)

A solution of $$\mathrm{H}_2 \mathrm{SO}_4$$ is $$31.4 \% \mathrm{H}_2 \mathrm{SO}_4$$ by mass and has a density of $$1.25 \mathrm{~g} / \mathrm{mL}$$. The molarity of the $$\mathrm{H}_2 \mathrm{SO}_4$$ solution is _________ $$\mathrm{M}$$ (nearest integer)

[Given molar mass of $$\mathrm{H}_2 \mathrm{SO}_4=98 \mathrm{~g} \mathrm{~mol}^{-1}$$]

Consider the given reaction. The total number of oxygen atom/s present per molecule of the product $$(\mathrm{P})$$ is _________.

For the reaction $$\mathrm{N}_2 \mathrm{O}_{4(\mathrm{~g})} \rightleftarrows 2 \mathrm{NO}_{2(\mathrm{~g})}, \mathrm{K}_{\mathrm{p}}=0.492 \mathrm{~atm}$$ at $$300 \mathrm{~K} . \mathrm{K}_{\mathrm{c}}$$ for the reaction at same temperature is _________ $$\times 10^{-2}$$.

(Given : $$\mathrm{R}=0.082 \mathrm{~L} \mathrm{~atm} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$$)

The number of species from the following which are paramagnetic and with bond order equal to one is _________.

$$\mathrm{H}_2, \mathrm{He}_2^{+}, \mathrm{O}_2^{+}, \mathrm{N}_2^{2-}, \mathrm{O}_2^{2-}, \mathrm{F}_2, \mathrm{Ne}_2^{+}, \mathrm{B}_2$$

For a reaction taking place in three steps at same temperature, overall rate constant $$\mathrm{K}=\frac{\mathrm{K}_1 \mathrm{~K}_2}{\mathrm{~K}_3}$$. If $$\mathrm{Ea}_1, \mathrm{Ea}_2$$ and $$\mathrm{Ea}_3$$ are 40, 50 and $$60 \mathrm{~kJ} / \mathrm{mol}$$ respectively, the overall $$\mathrm{Ea}$$ is ________ $$\mathrm{kJ} / \mathrm{mol}$$.

From the compounds given below, number of compounds which give positive Fehling's test is _________.

Benzaldehyde, Acetaldehyde, Acetone, Acetophenone, Methanal, 4nitrobenzaldehyde, cyclohexane carbaldehyde.

Number of compounds with one lone pair of electrons on central atom amongst following is _________.

$$\mathrm{O}_3, \mathrm{H}_2 \mathrm{O}, \mathrm{SF}_4, \mathrm{ClF}_3, \mathrm{NH}_3, \mathrm{BrF}_5, \mathrm{XeF}_4$$

Number of compounds among the following which contain sulphur as heteroatom is ___________.

Furan, Thiophene, Pyridine, Pyrrole, Cysteine, Tyrosine

The osmotic pressure of a dilute solution is $$7 \times 10^5 \mathrm{~Pa}$$ at $$273 \mathrm{~K}$$. Osmotic pressure of the same solution at $$283 \mathrm{~K}$$ is _________ $$\times 10^4 \mathrm{Nm}^{-2}$$.

Suppose $$f(x)=\frac{\left(2^x+2^{-x}\right) \tan x \sqrt{\tan ^{-1}\left(x^2-x+1\right)}}{\left(7 x^2+3 x+1\right)^3}$$. Then the value of $$f^{\prime}(0)$$ is equal to

Let $$\vec{a}, \vec{b}$$ and $$\vec{c}$$ be three non-zero vectors such that $$\vec{b}$$ and $$\vec{c}$$ are non-collinear. If $$\vec{a}+5 \vec{b}$$ is collinear with $$\vec{c}, \vec{b}+6 \vec{c}$$ is collinear with $$\vec{a}$$ and $$\vec{a}+\alpha \vec{b}+\beta \vec{c}=\overrightarrow{0}$$, then $$\alpha+\beta$$ is equal to

Let $$\left(5, \frac{a}{4}\right)$$ be the circumcenter of a triangle with vertices $$\mathrm{A}(a,-2), \mathrm{B}(a, 6)$$ and $$C\left(\frac{a}{4},-2\right)$$. Let $$\alpha$$ denote the circumradius, $$\beta$$ denote the area and $$\gamma$$ denote the perimeter of the triangle. Then $$\alpha+\beta+\gamma$$ is

If $$\alpha,-\frac{\pi}{2}<\alpha<\frac{\pi}{2}$$ is the solution of $$4 \cos \theta+5 \sin \theta=1$$, then the value of $$\tan \alpha$$ is

A fair die is thrown until 2 appears. Then the probability, that 2 appears in even number of throws, is

In an A.P., the sixth term $$a_6=2$$. If the product $$a_1 a_4 a_5$$ is the greatest, then the common difference of the A.P. is equal to

$$\text { Let } A=\left[\begin{array}{lll} 1 & 0 & 0 \\ 0 & \alpha & \beta \\ 0 & \beta & \alpha \end{array}\right] \text { and }|2 \mathrm{~A}|^3=2^{21} \text { where } \alpha, \beta \in Z \text {, Then a value of } \alpha \text { is }$$

Let $$R$$ be a relation on $$Z \times Z$$ defined by $$(a, b) R(c, d)$$ if and only if $$a d-b c$$ is divisible by 5. Then $$R$$ is

If $$f(x)=\left\{\begin{array}{cc}2+2 x, & -1 \leq x < 0 \\ 1-\frac{x}{3}, & 0 \leq x \leq 3\end{array} ; g(x)=\left\{\begin{array}{cc}-x, & -3 \leq x \leq 0 \\ x, & 0 < x \leq 1\end{array}\right.\right.$$, then range of $$(f o g)(x)$$ is

Let $$O$$ be the origin and the position vectors of $$A$$ and $$B$$ be $$2 \hat{i}+2 \hat{j}+\hat{k}$$ and $$2 \hat{i}+4 \hat{j}+4 \hat{k}$$ respectively. If the internal bisector of $$\angle \mathrm{AOB}$$ meets the line $$\mathrm{AB}$$ at $$\mathrm{C}$$, then the length of $$O C$$ is

In a $$\triangle A B C$$, suppose $$y=x$$ is the equation of the bisector of the angle $$B$$ and the equation of the side $$A C$$ is $$2 x-y=2$$. If $$2 A B=B C$$ and the points $$A$$ and $$B$$ are respectively $$(4,6)$$ and $$(\alpha, \beta)$$, then $$\alpha+2 \beta$$ is equal to

For $$x \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)$$, if $$y(x)=\int \frac{\operatorname{cosec} x+\sin x}{\operatorname{cosec} x \sec x+\tan x \sin ^2 x} d x$$, and $$\lim _\limits{x \rightarrow\left(\frac{\pi}{2}\right)^{-}} y(x)=0$$ then $$y\left(\frac{\pi}{4}\right)$$ is equal to

Let $$\mathrm{A}$$ be a square matrix such that $$\mathrm{AA}^{\mathrm{T}}=\mathrm{I}$$. Then $$\frac{1}{2} A\left[\left(A+A^T\right)^2+\left(A-A^T\right)^2\right]$$ is equal to

If $$z=\frac{1}{2}-2 i$$ is such that $$|z+1|=\alpha z+\beta(1+i), i=\sqrt{-1}$$ and $$\alpha, \beta \in \mathbb{R}$$, then $$\alpha+\beta$$ is equal to

Consider the function $$f:\left[\frac{1}{2}, 1\right] \rightarrow \mathbb{R}$$ defined by $$f(x)=4 \sqrt{2} x^3-3 \sqrt{2} x-1$$. Consider the statements

(I) The curve $$y=f(x)$$ intersects the $$x$$-axis exactly at one point.

(II) The curve $$y=f(x)$$ intersects the $$x$$-axis at $$x=\cos \frac{\pi}{12}$$.

Then

Let $$P Q R$$ be a triangle with $$R(-1,4,2)$$. Suppose $$M(2,1,2)$$ is the mid point of $$\mathrm{PQ}$$. The distance of the centroid of $$\triangle \mathrm{PQR}$$ from the point of intersection of the lines $$\frac{x-2}{0}=\frac{y}{2}=\frac{z+3}{-1}$$ and $$\frac{x-1}{1}=\frac{y+3}{-3}=\frac{z+1}{1}$$ is

$$\mathop {\lim }\limits_{x \to {\pi \over 2}} \left( {{1 \over {{{\left( {x - {\pi \over 2}} \right)}^2}}}\int\limits_{{x^3}}^{{{\left( {{\pi \over 2}} \right)}^3}} {\cos \left( {{t^{{1 \over 3}}}} \right)dt} } \right)$$ is equal to

A function $$y=f(x)$$ satisfies $$f(x) \sin 2 x+\sin x-\left(1+\cos ^2 x\right) f^{\prime}(x)=0$$ with condition $$f(0)=0$$. Then, $$f\left(\frac{\pi}{2}\right)$$ is equal to

If the value of the integral $$\int_\limits{-\frac{\pi}{2}}^{\frac{\pi}{2}}\left(\frac{x^2 \cos x}{1+\pi^x}+\frac{1+\sin ^2 x}{1+e^{\sin x^{2123}}}\right) d x=\frac{\pi}{4}(\pi+a)-2$$, then the value of $$a$$ is

The area (in sq. units) of the part of the circle $$x^2+y^2=169$$ which is below the line $$5 x-y=13$$ is $$\frac{\pi \alpha}{2 \beta}-\frac{65}{2}+\frac{\alpha}{\beta} \sin ^{-1}\left(\frac{12}{13}\right)$$, where $$\alpha, \beta$$ are coprime numbers. Then $$\alpha+\beta$$ is equal to __________.

If the mean and variance of the data $$65,68,58,44,48,45,60, \alpha, \beta, 60$$ where $$\alpha> \beta$$, are 56 and 66.2 respectively, then $$\alpha^2+\beta^2$$ is equal to _________.

Equations of two diameters of a circle are $$2 x-3 y=5$$ and $$3 x-4 y=7$$. The line joining the points $$\left(-\frac{22}{7},-4\right)$$ and $$\left(-\frac{1}{7}, 3\right)$$ intersects the circle at only one point $$P(\alpha, \beta)$$. Then, $$17 \beta-\alpha$$ is equal to _________.

A line with direction ratios $$2,1,2$$ meets the lines $$x=y+2=z$$ and $$x+2=2 y=2 z$$ respectively at the points $$\mathrm{P}$$ and $$\mathrm{Q}$$. If the length of the perpendicular from the point $$(1,2,12)$$ to the line $$\mathrm{PQ}$$ is $$l$$, then $$l^2$$ is __________.

$$\text { If } \frac{{ }^{11} C_1}{2}+\frac{{ }^{11} C_2}{3}+\ldots+\frac{{ }^{11} C_9}{10}=\frac{n}{m} \text { with } \operatorname{gcd}(n, m)=1 \text {, then } n+m \text { is equal to }$$ _______.

If the points of intersection of two distinct conics $$x^2+y^2=4 b$$ and $$\frac{x^2}{16}+\frac{y^2}{b^2}=1$$ lie on the curve $$y^2=3 x^2$$, then $$3 \sqrt{3}$$ times the area of the rectangle formed by the intersection points is _________.

All the letters of the word "GTWENTY" are written in all possible ways with or without meaning and these words are written as in a dictionary. The serial number of the word "GTWENTY" is _________.

Let $$\alpha, \beta$$ be the roots of the equation $$x^2-x+2=0$$ with $$\operatorname{Im}(\alpha)>\operatorname{Im}(\beta)$$. Then $$\alpha^6+\alpha^4+\beta^4-5 \alpha^2$$ is equal to ___________.

Let $$f(x)=2^x-x^2, x \in \mathbb{R}$$. If $$m$$ and $$n$$ are respectively the number of points at which the curves $$y=f(x)$$ and $$y=f^{\prime}(x)$$ intersect the $$x$$-axis, then the value of $$\mathrm{m}+\mathrm{n}$$ is ___________.

If the solution curve $$y=y(x)$$ of the differential equation $$\left(1+y^2\right)\left(1+\log _{\mathrm{e}} x\right) d x+x d y=0, x > 0$$ passes through the point $$(1,1)$$ and $$y(e)=\frac{\alpha-\tan \left(\frac{3}{2}\right)}{\beta+\tan \left(\frac{3}{2}\right)}$$, then $$\alpha+2 \beta$$ is _________.

The resistance $$R=\frac{V}{I}$$ where $$\mathrm{V}=(200 \pm 5) \mathrm{V}$$ and $$I=(20 \pm 0.2) \mathrm{A}$$, the percentage error in the measurement of $$\mathrm{R}$$ is :

The de-Broglie wavelength of an electron is the same as that of a photon. If velocity of electron is $$25 \%$$ of the velocity of light, then the ratio of K.E. of electron and K.E. of photon will be:

A convex mirror of radius of curvature $$30 \mathrm{~cm}$$ forms an image that is half the size of the object. The object distance is :

The deflection in moving coil galvanometer falls from 25 divisions to 5 division when a shunt of $$24 \Omega$$ is applied. The resistance of galvanometer coil will be :

A capacitor of capacitance $$100 \mu \mathrm{F}$$ is charged to a potential of $$12 \mathrm{~V}$$ and connected to a $$6.4 \mathrm{~mH}$$ inductor to produce oscillations. The maximum current in the circuit would be :

At what distance above and below the surface of the earth a body will have same weight. (take radius of earth as $$R$$.)

A galvanometer having coil resistance $$10 \Omega$$ shows a full scale deflection for a current of $$3 \mathrm{~mA}$$. For it to measure a current of $$8 \mathrm{~A}$$, the value of the shunt should be:

A thermodynamic system is taken from an original state $$\mathrm{A}$$ to an intermediate state $$B$$ by a linear process as shown in the figure. It's volume is then reduced to the original value from $$\mathrm{B}$$ to $$\mathrm{C}$$ by an isobaric process. The total work done by the gas from $$A$$ to $$B$$ and $$B$$ to $$C$$ would be :

Two charges of $$5 Q$$ and $$-2 Q$$ are situated at the points $$(3 a, 0)$$ and $$(-5 a, 0)$$ respectively. The electric flux through a sphere of radius '$$4 a$$' having center at origin is :

A biconvex lens of refractive index 1.5 has a focal length of $$20 \mathrm{~cm}$$ in air. Its focal length when immersed in a liquid of refractive index 1.6 will be:

A block of mass $$100 \mathrm{~kg}$$ slides over a distance of $$10 \mathrm{~m}$$ on a horizontal surface. If the co-efficient of friction between the surfaces is 0.4, then the work done against friction $$(\operatorname{in} J$$) is :

Given below are two statements:

Statement I : If a capillary tube is immersed first in cold water and then in hot water, the height of capillary rise will be smaller in hot water.

Statement II : If a capillary tube is immersed first in cold water and then in hot water, the height of capillary rise will be smaller in cold water.

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

If the radius of curvature of the path of two particles of same mass are in the ratio $$3: 4$$, then in order to have constant centripetal force, their velocities will be in the ratio of :

Match List I with List II

Choose the correct answer from the options given below:

Two vessels $$A$$ and $$B$$ are of the same size and are at same temperature. A contains $$1 \mathrm{~g}$$ of hydrogen and $$B$$ contains $$1 \mathrm{~g}$$ of oxygen. $$\mathrm{P}_{\mathrm{A}}$$ and $$\mathrm{P}_{\mathrm{B}}$$ are the pressures of the gases in $$\mathrm{A}$$ and $$\mathrm{B}$$ respectively, then $$\frac{P_A}{P_B}$$ is:

In the given circuit, the breakdown voltage of the Zener diode is $$3.0 \mathrm{~V}$$. What is the value of $$\mathrm{I}_{\mathrm{z}}$$ ?

A body starts moving from rest with constant acceleration covers displacement $$S_1$$ in first $$(p-1)$$ seconds and $$\mathrm{S}_2$$ in first $$p$$ seconds. The displacement $$\mathrm{S}_1+\mathrm{S}_2$$ will be made in time :

The electric current through a wire varies with time as $$I=I_0+\beta t$$, where $$I_0=20 \mathrm{~A}$$ and $$\beta=3 \mathrm{~A} / \mathrm{s}$$. The amount of electric charge crossed through a section of the wire in $$20 \mathrm{~s}$$ is :

The potential energy function (in $$J$$ ) of a particle in a region of space is given as $$U=\left(2 x^2+3 y^3+2 z\right)$$. Here $$x, y$$ and $$z$$ are in meter. The magnitude of $$x$$-component of force (in $$N$$ ) acting on the particle at point $$P(1,2,3) \mathrm{m}$$ is :

The explosive in a Hydrogen bomb is a mixture of $${ }_1 \mathrm{H}^2,{ }_1 \mathrm{H}^3$$ and $${ }_3 \mathrm{Li}^6$$ in some condensed form. The chain reaction is given by

$$\begin{aligned} & { }_3 \mathrm{Li}^6+{ }_0 \mathrm{n}^1 \rightarrow{ }_2 \mathrm{He}^4+{ }_1 \mathrm{H}^3 \\ & { }_1 \mathrm{H}^2+{ }_1 \mathrm{H}^3 \rightarrow{ }_2 \mathrm{He}^4+{ }_0 \mathrm{n}^1 \end{aligned}$$

During the explosion the energy released is approximately

[Given ; $$\mathrm{M}(\mathrm{Li})=6.01690 \mathrm{~amu}, \mathrm{M}\left({ }_1 \mathrm{H}^2\right)=2.01471 \mathrm{~amu}, \mathrm{M}\left({ }_2 \mathrm{He}^4\right)=4.00388$$ $$\mathrm{amu}$$, and $$1 \mathrm{~amu}=931.5 \mathrm{~MeV}]$$

In a double slit experiment shown in figure, when light of wavelength $$400 \mathrm{~nm}$$ is used, dark fringe is observed at $$P$$. If $$\mathrm{D}=0.2 \mathrm{~m}$$, the minimum distance between the slits $$S_1$$ and $$S_2$$ is _________ $$\mathrm{mm}$$.

A cylinder is rolling down on an inclined plane of inclination $$60^{\circ}$$. It's acceleration during rolling down will be $$\frac{x}{\sqrt{3}} m / s^2$$, where $$x=$$ ________ (use $$\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$$).

An electron is moving under the influence of the electric field of a uniformly charged infinite plane sheet $$\mathrm{S}$$ having surface charge density $$+\sigma$$. The electron at $$t=0$$ is at a distance of $$1 \mathrm{~m}$$ from $$S$$ and has a speed of $$1 \mathrm{~m} / \mathrm{s}$$. The maximum value of $$\sigma$$ if the electron strikes $$S$$ at $$t=1 \mathrm{~s}$$ is $$\alpha\left[\frac{m \epsilon_0}{e}\right] \frac{C}{m^2}$$, the value of $$\alpha$$ is ___________.

When a hydrogen atom going from $$n=2$$ to $$n=1$$ emits a photon, its recoil speed is $$\frac{x}{5} \mathrm{~m} / \mathrm{s}$$. Where $$x=$$ ________. (Use, mass of hydrogen atom $$=1.6 \times 10^{-27} \mathrm{~kg}$$)

A square loop of side $$10 \mathrm{~cm}$$ and resistance $$0.7 \Omega$$ is placed vertically in east-west plane. A uniform magnetic field of $$0.20 T$$ is set up across the plane in north east direction. The magnetic field is decreased to zero in $$1 \mathrm{~s}$$ at a steady rate. Then, magnitude of induced emf is $$\sqrt{x} \times 10^{-3} \mathrm{~V}$$. The value of $$x$$ is __________.

The magnetic potential due to a magnetic dipole at a point on its axis situated at a distance of $$20 \mathrm{~cm}$$ from its center is $$1.5 \times 10^{-5} \mathrm{~T} \mathrm{~m}$$. The magnetic moment of the dipole is _________ $$A \mathrm{~m}^2$$. (Given : $$\frac{\mu_o}{4 \pi}=10^{-7} \mathrm{Tm} A^{-1}$$ )

A $$16 \Omega$$ wire is bend to form a square loop. A $$9 \mathrm{~V}$$ battery with internal resistance $$1 \Omega$$ is connected across one of its sides. If a $$4 \mu F$$ capacitor is connected across one of its diagonals, the energy stored by the capacitor will be $$\frac{x}{2} \mu J$$, where $$x=$$ _________

When the displacement of a simple harmonic oscillator is one third of its amplitude, the ratio of total energy to the kinetic energy is $$\frac{x}{8}$$, where $$x=$$ _________.

A ball rolls off the top of a stairway with horizontal velocity $$u$$. The steps are $$0.1 \mathrm{~m}$$ high and $$0.1 \mathrm{~m}$$ wide. The minimum velocity $$u$$ with which that ball just hits the step 5 of the stairway will be $$\sqrt{x} \mathrm{~ms}^{-1}$$ where $$x=$$ __________ [use $$\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$$ ].

In a test experiment on a model aeroplane in wind tunnel, the flow speeds on the upper and lower surfaces of the wings are $$70 \mathrm{~ms}^{-1}$$ and $$65 \mathrm{~ms}^{-1}$$ respectively. If the wing area is $$2 \mathrm{~m}^2$$, the lift of the wing is _________ $$N$$.

(Given density of air $$=1.2 \mathrm{~kg} \mathrm{~m}^{-3}$$)