JEE Main 2024 — 5 April, Shift 2

Let $f:[-1,2] \rightarrow \mathrm{R}$ be given by $f(\mathrm{x})=2 \mathrm{x}^{2}+\mathrm{x}+\left[\mathrm{x}^{2}\right]-[\mathrm{x}]$, where $[\mathrm{t}]$ denotes the greatest integer less than or

equal to $t$. The number of points, where $f$ is not continuous, is :

The differential equation of the family of circles passing the origin and having center at the line $\mathrm{y}=\mathrm{x}$ is :

Let $S_{1}=\{z \in C:|z| \leq 5\}$, $S_{2}=\left\{z \in C: \operatorname{Im}\left(\frac{z+1-\sqrt{3} i}{1-\sqrt{3} i}\right) \geq 0\right\}$ and $\mathrm{S}_{3}=\{\mathrm{z} \in \mathrm{C}: \operatorname{Re}(\mathrm{z}) \geq 0\}$.

Then

The area enclosed between the curves $y=x|x|$ and $\mathrm{y}=\mathrm{x}-|\mathrm{x}|$ is :

60 words can be made using all the letters of the word BHBJO , with or without meaning. If these words are written as in a

dictionary, then the $50^{\text {th }}$ word is :

Let $\vec{a}=2 \hat{i}+5 \hat{j}-\hat{k}, \vec{b}=2 \hat{i}-2 \hat{j}+2 \hat{k}$ and $\overrightarrow{\mathrm{c}}$ be three vectors such that

$(\vec{c}+\hat{i}) \times(\vec{a}+\vec{b}+\hat{i})=\vec{a} \times(\vec{c}+\hat{i}) \cdot \vec{a} \cdot \vec{c}=-29$, then $\overrightarrow{\mathrm{c}} \cdot(-2 \hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}})$ is equal to

Consider three vectors $\vec{a}, \vec{b}, \vec{c}$. Let $|\vec{a}|=2,|\vec{b}|=3$ and $\vec{a}=\vec{b} \times \vec{c}$. If $\alpha \in\left[0, \frac{\pi}{3}\right]$ is the angle between the vectors $\vec{b}$ and $\vec{c}$, then the minimum value of $27|\overrightarrow{\mathrm{c}}-\overrightarrow{\mathrm{a}}|^{2}$ is equal to :

Let $A(-1,1)$ and $B(2,3)$ be two points and $P$ be a variable point above the line AB such that the area of $\triangle \mathrm{PAB}$ is 10 . If the locus of P is $\mathrm{ax}+\mathrm{by}=15$, then $5 a+2 b$ is :

Let $(\alpha, \beta, \gamma)$ be the image of point $(8,5,7)$ in the line $\frac{x-1}{2}=\frac{y+1}{3}=\frac{z-2}{5}$. Then $\alpha+\beta+\gamma$ is equal to

If the constant term in the expansion of $\left(\frac{\sqrt[5]{3}}{x}+\frac{2 x}{\sqrt[3]{5}}\right)^{12}, x \neq 0$, is $\alpha \times 2^{8} \times \sqrt[5]{3}$, then $25 \alpha$ is equal to :

Let $f, \mathrm{~g}: \mathrm{R} \rightarrow \mathrm{R}$ be defined as : $f(\mathrm{x})=|\mathrm{x}-1|$ and $\text{g}\left( \text{x} \right)=\left\{ \begin{matrix}{{\text{e}}^{\text{x}}}, & \text{x}\ge 0 \\\text{x}+1, & \text{x}\le 0 \\\end{matrix} \right.$. Then the function $f(\mathrm{~g}(\mathrm{x}))$ is

Let the circle $C_{1}: x^{2}+y^{2}-2(x+y)+1=0$ and $C_{2}$ be a circle having centre at $(-1,0)$ and radius 2 .

If the line of the common chord of $\mathrm{C}_{1}$ and $\mathrm{C}_{2}$ intersects the y -axis at the point P , then the square of the distance of P from

the centre of $\mathrm{C}_{1}$ is :

Let the set $S=\{2,4,8,16, \ldots . ., 512\}$ be partitioned into 3 sets $\mathrm{A}, \mathrm{B}, \mathrm{C}$ with equal number of elements such that

$\mathrm{A} \cup \mathrm{B} \cup \mathrm{C}=\mathrm{S}$ and $\mathrm{A} \cap \mathrm{B}=\mathrm{B} \cap \mathrm{C}=\mathrm{A} \cap \mathrm{C}=\phi$. The maximum number of such possible partitions of $S$ is

equal to :

The values of $m, n$, for which the system of equations $\mathrm{x}+\mathrm{y}+\mathrm{z}=4$ $2 x+5 y+5 z=17$ $x+2 y+m z=n$ has infinitely many solutions, satisfy the equation :

The coefficients $a, b, c$ in the quadratic equation $\mathrm{ax}^{2}+\mathrm{bx}+\mathrm{c}=0$ are from the set $\{1,2,3,4,5,6\}$. If the probability of this equation having one real root bigger than the other is $p$, then 216 p equals :

Let ABCD and AEFG be squares of side 4 and 2 units, respectively. The point E is on the line segment AB and the point F is on the diagonal AC . Then the radius r of the circle passing through the point F and touching the line segments BC and CD satisfies :

Let $\beta(m, n)=\int_{0}^{1} x^{m-1}(1-x)^{n-1} d x, m, n>0$. If $\int_{0}^{1}\left(1-x^{10}\right)^{20} d x=a \times \beta(b, c)$,

then $100(a+b+x)$ equals $\qquad$

Let $\alpha \beta \neq 0$ and $A=\left[ \begin{matrix}\beta & \alpha & 3 \\\alpha & \alpha & \beta \\-\beta & \alpha & 2\alpha \\\end{matrix} \right]$. If $B=\left[ \begin{matrix}3\alpha & -9 & 3\alpha \\-\alpha & 7 & -2\alpha \\-2\alpha & 5 & -2\beta \\\end{matrix} \right]$ is the matrix of cofactors of the elements of $A$, then $\operatorname{det}(A B)$ is equal to :

If $y(\theta)=\frac{2 \cos \theta+\cos 2 \theta}{\cos 3 \theta+4 \cos 2 \theta+5 \cos \theta+2}$, then at $\theta=\frac{\pi}{2}, y^{\prime \prime}+y^{\prime}+\mathrm{y}$ is equal to:

For $x \geq 0$, the least value of $K$, for which $4^{1+x}+4^{1-x}$, $\frac{\mathrm{K}}{2}, 16^{\mathrm{x}}+16^{-\mathrm{x}}$ are three consecutive terms of an A.P. is equal to :

Let the mean and the standard deviation of the probability distribution

be $\mu$ and $\sigma$, respectively. If $\sigma-\mu=2$, then $\sigma+\mu$ is equal to $\qquad$

Let $y=y(x)$ be the solution of the differential equation $\frac{d y}{d x}+\frac{2 x}{\left(1+x^{2}\right)^{2}} y=x e^{\frac{1}{\left(1+x^{2}\right)}} ; y(0)=0$.

Then the area enclosed by the curve $f(\mathrm{x})=\mathrm{y}(\mathrm{x}) \mathrm{e}^{-\frac{1}{\left(1+\mathrm{x}^{2}\right)}}$ and the line $\mathrm{y}-\mathrm{x}=4$ is $\qquad$

The number of solutions of $\sin ^{2} x+\left(2+2 x-x^{2}\right) \sin x-3(x-1)^{2}=0$, where $-\pi \leq \mathrm{x} \leq \pi$, is

Let the point $(-1, \alpha, \beta)$ lie on the line of the shortest distance between the lines

$\frac{x+2}{-3}=\frac{y-2}{4}=\frac{z-5}{2} \quad$ and $\quad \frac{x+2}{-1}=\frac{y+6}{2}=\frac{z-1}{0}$. Then $(\alpha-\beta)^{2}$ is equal to $\qquad$

If $1+\frac{\sqrt{3}-\sqrt{2}}{2 \sqrt{3}}+\frac{5-2 \sqrt{6}}{18}+\frac{9 \sqrt{3}-11 \sqrt{2}}{36 \sqrt{3}}+\frac{49-20 \sqrt{6}}{180}+\ldots$. upto $\infty=2\left(\sqrt{\frac{\mathrm{~b}}{\mathrm{a}}}+1\right) \log _{\mathrm{e}}\left(\frac{\mathrm{a}}{\mathrm{b}}\right)$,

where a and b are integers with $\operatorname{gcd}(a, b)=1$, then $11 \mathrm{a}+18 \mathrm{~b}$ is equal to $\qquad$

Let $\mathrm{a}>0$ be a root of the equation $2 \mathrm{x}^{2}+\mathrm{x}-2=0$. If $\lim _{x \rightarrow \frac{1}{a}} \frac{16\left(1-\cos \left(2+x-2 x^{2}\right)\right)}{\left(1-a x^{2}\right)}=\alpha+\beta \sqrt{17}$,

where $\alpha, \beta \in \mathrm{Z}$ then $\alpha+\beta$ is equal to $\qquad$

If $f(\mathrm{t})=\int_{0}^{\pi} \frac{2 \mathrm{xdx}}{1-\cos ^{2} \mathrm{t} \sin ^{2} \mathrm{x}}, 0<\mathrm{t}<\pi$, then the value of $\int_{0}^{\frac{\pi}{2}} \frac{\pi^{2} \mathrm{dt}}{f(\mathrm{t})}$ equals $\qquad$

Let the maximum and minimum values of $\left(\sqrt{8 x-x^{2}-12}-4\right)^{2}+(x-7)^{2}, x \in R$ be $M$ and $m$ respectively.

Then $M^{2}-m^{2}$ is equal to $\qquad$

Let a line perpendicular to the line $2 \mathrm{x}-\mathrm{y}=10$ touch the parabola $y^{2}=4(x-9)$ at the point $P$. The distance of the

point P from the centre of the circle $x^{2}+y^{2}-14 x-8 y+56=0$ is $\qquad$

The number of real solutions of the equation $x|x+5|+2|x+7|-2=0$ is $\qquad$

Given below are two statements : one is labelled as Statement I and the other is labelled as Statement II :

Statement I : When the white light passed through a prism, the red light bends lesser than yellow and violet.

Statement II : The refractive indices are different for different wavelengths in dispersive medium.

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

Which of the following statement is not true about stopping potential $\left(\mathrm{V}_{0}\right)$ ?

The angular momentum of an electron in a hydrogen atom is proportional to : (Where $r$ is the radius of orbit of electron)

A galvanometer of resistance $100 \Omega$ when connected in series with $400 \Omega$ measures a voltage of upto 10 V . The value of resistance required to convert the galvanometer into ammeter to read upto 10 A is $\mathrm{x} \times 10^{-2} \Omega$. The value of x is :

The vehicles carrying inflammable fluids usually have metallic chains touching the ground :

If n is the number density and d is the diameter of the molecule, then the average distance covered by a molecule between two successive collisions (i.e. mean free path) is represented by :

A particle moves in x-y plane under the influence of a force $\vec{F}$ such that its linear momentum is

$\overrightarrow{\mathrm{P}}(\mathrm{t})=\hat{\mathrm{i}} \cos (\mathrm{kt})-\hat{\mathrm{j}} \sin (\mathrm{kt})$. If k is constant, the angle between $\overrightarrow{\mathrm{F}}$ and $\overrightarrow{\mathrm{P}}$ will be :

The electrostatic force $\left(\overrightarrow{\mathrm{F}}_{1}\right)$ and magnetic force $\left(\overrightarrow{\mathrm{F}}_{2}\right)$ acting on a charge q moving with velocity v can be written :

A man carrying a monkey on his shoulder does cycling smoothly on a circular track of radius 9 m and completes 120 revolutions in 3 minutes. The magnitude of centripetal acceleration of monkey is (in $\mathrm{m} / \mathrm{s}^{2}$ ) :

A series LCR circuit is subjected to an AC signal of $200 \mathrm{~V}, 50 \mathrm{~Hz}$. If the voltage across the inductor $(\mathrm{L}=10 \mathrm{mH})$ is 31.4 V , then the current in this circuit is $\qquad$ :

What is the dimensional formula of $\mathrm{ab}^{-1}$ in the equation $\left(\mathrm{P}+\frac{\mathrm{a}}{\mathrm{V}^{2}}\right)(\mathrm{V}-\mathrm{b})=\mathrm{RT}$, where letters have their usual

meaning.

A body is moving unidirectionally under the influence of a constant power source. Its displacement in time $t$ is proportional to :

Match List-I with List-II :-

Choose the correct answer from the options given below :

During an adiabatic process, if the pressure of a gas is found to be proportional to the cube of its absolute temperature, then the ratio of $\frac{C_{P}}{C_{V}}$ for the gas is :

Match List-I with List-II :

{l} A force Choose the correct answer from the options given below :

A vernier callipers has 20 divisions on the vernier scale, which coincides with $19^{\text {th }}$ division on the main scale. The least count of the instrument is 0.1 mm . One main scale division is equal to $\qquad$ mm .

A heavy box of mass 50 kg is moving on a horizontal surface. If co-efficient of kinetic friction between the box and horizontal surface is 0.3 then force of kinetic friction is :

A satellite revolving around a planet in stationary orbit has time period 6 hours. The mass of planet is one-fourth the mass of earth. The radius orbit of planet is : $($ Given $=$ Radius of geo-stationary orbit for earth is $4.2 \times 10^{4} \mathrm{~km}$ )

The ratio of heat dissipated per second through the resistance $5 \Omega$ and $10 \Omega$ in the circuit given below is :

A solenoid of length 0.5 m has a radius of 1 cm and is made up of ' $m$ ' number of turns. It carries a current of 5 A . If the magnitude of the magnetic field inside the solenoid is $6.28 \times 10^{-3} \mathrm{~T}$, then the value of $m$ is :

The shortest wavelength of the spectral lines in the Lyman series of hydrogen spectrum is $915 Å.$. The longest wavelength of spectral lines in the Balmer series will be $\qquad$ Å.

In a single slit experiment, a parallel beam of green light of wavelength 550 nm passes through a slit of width 0.20 mm . The transmitted light is collected on a screen 100 cm away. The distance of first order minima from the central maximum will be $x \times 10^{-5} \mathrm{~m}$. The value of $x$ is :

A sonometer wire of resonating length 90 cm has a fundamental frequency of 400 Hz when kept under some tension. The resonating length of the wire with fundamental frequency of 600 Hz under same tension $\qquad$ cm .

A hollow sphere is rolling on a plane surface about its axis of symmetry. The ratio of rotational kinetic energy to its total kinetic energy is $\frac{x}{5}$. The value of $x$ is $\qquad$ .

A hydraulic press containing water has two arms with diameters as mentioned in the figure. A force of 10 N is applied on the surface of water in the thinner arm. The force required to be applied on the surface of water in the thicker arm to maintain equilibrium of water is $\qquad$ N . $\frac{\mathrm{F}_{1}}{\pi(7)^{2}}=\frac{10}{\pi \times(0.7)^{2}}$ $\mathrm{F}_{1}=1000 \mathrm{~N}$ 57. The electric field at point p due to an electric dipole is $E$. The electric field at point $R$ on equitorial line will be $\frac{E}{x}$. The value of $x$ :

The electric field at point p due to an electric dipole is $E$. The electric field at point $R$ on equitorial line will be $\frac{E}{x}$. The value of $x$ :

The maximum height reached by a projectile is 64 m . If the initial velocity is halved, the new maximum height of the projectile is $\qquad$ m .

A wire of resistance $20 \Omega$ is divided into 10 equal parts. A combination of two parts are connected in parallel and so on. Now resulting pairs of parallel combination are connected in series. The equivalent resistance of final combination is $\qquad$ $\Omega$.

The current in an inductor is given by $I=(3 t+8)$ where $t$ is in second. The magnitude of induced emf produced in the inductor is 12 mV . The selfinductance of the inductor $\qquad$ mH .

Match List - I with List - II.

Linear Choose the correct answer from the options given below:

While preparing crystals of Mohr's salt, dil. $\mathrm{H}_{2} \mathrm{SO}_{4}$ is added to a mixture of ferrous sulphate and ammonium sulphate, before dissolving this mixture in water, dil. $\mathrm{H}_{2} \mathrm{SO}_{4}$ is added here to:

Identify the major product in the following reaction.

The correct nomenclature for the following compound is:

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

Assertion (A) : $\mathrm{NH}_{3}$ and $\mathrm{NF}_{3}$ molecule have pyramidal shape with a lone pair of electrons on nitrogen atom. The resultant dipole moment of $\mathrm{NH}_{3}$ is greater than that of $\mathrm{NF}_{3}$.

Reason (R): In $\mathrm{NH}_{3}$, the orbital dipole due to lone pair is in the same direction as the resultant dipole moment of the $\mathrm{N}-\mathrm{H}$ bonds. F is the most electronegative element.

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

Given below are two statements, one is labelled as Statement I and the other is labelled as Statement II.

Statement I : On passing $\mathrm{HCl}{(\mathrm{g})}$ through a saturated solution of $\mathrm{BaCl}_{2}$, at room temperature white turbidity appears.

Statement II : When HCl gas is passed through a saturated solution of NaCl , sodium chloride is precipitated due to common ion effect.

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

The metal atom present in the complex MABXL (where $\mathrm{A}, \mathrm{B}, \mathrm{X}$ and L are unidentate ligands and M is metal) involves $\mathrm{sp}^{3}$ hybridization. The number of geometrical isomers exhibited by the complex is:

Match List - I with List - II.

The quantity of silver deposited when one coulomb charge is passed through $\mathrm{AgNO}_{3}$ solution:

Which one of the following reactions is NOT possible?

Given below are two statements, one is labelled as Statement I and the other is labelled as Statement II.

Statement I : The metallic radius of Na is $1.86\,\mathrm{\AA}$ and the ionic radius of Na$^+$ is less than $1.86\,\mathrm{\AA}$.

Statement II : Ions are always smaller in size than the corresponding elements.

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

Consider the above reaction sequence and identify the major product P .

Consider the given chemical reaction :

For the electrochemical cell $\mathrm{M \,|\, M^{2+} \,||\, X \,|\, X^{2-}}$, if $E^\circ_{(\mathrm{M^{2+}/M})}=-0.46\,\text{V}$ and $E^\circ_{(\mathrm{X/X^{2-}})}=0.34\,\text{V}$, which of the following is correct?

The number of moles of methane required to produce $11\,\text{g}$ of $\mathrm{CO_2(g)}$ on complete combustion is $\_\_\_\_\_$. (Given: molar mass of methane $= 16\,\text{g mol}^{-1}$).

The number of complexes from the following with no electrons in the $\mathrm{t}_{2}$ orbitals is $\qquad$

$\mathrm{TiCl}_{4},\left[\mathrm{MnO}_{4}\right]^{-},\left[\mathrm{FeO}_{4}\right]^{2-},\left[\mathrm{FeCl}_{4}\right]^{-},\left[\mathrm{CoCl}_{4}\right]^{2-}$

The number of ions from the following [$\mathrm{Ti}^{2+}, \mathrm{Cr}^{2+}$ and $\mathrm{V}^{2+}$] that have the ability to liberate hydrogen from a dilute acid is

The correct statements from the following are :

(A) The decreasing order of atomic radii of group 13 elements is $\mathrm{Tl}>\mathrm{In}>\mathrm{Ga}>\mathrm{Al}>\mathrm{B}$.

(B) Down the group 13 electronegativity decreases from top to bottom.

(C) Al dissolves in dil. HCl and liberate $\mathrm{H}_{2}$ but conc. $\mathrm{HNO}_{3}$ renders Al passive by forming a protective oxide layer on the

surface.

(D) All elements of group 13 exhibits highly stable +1 oxidation state.

(E) Hybridisation of Al in $\left[\mathrm{Al}\left(\mathrm{H}_{2} \mathrm{O}\right)_{6}\right]^{3+}$ ion is $\mathrm{sp}^{3} \mathrm{~d}^{2}$

Choose the correct answer from the options given below :

Coagulation of egg, on heating is because of :

The combustion of 1 mol of benzene is represented as $\mathrm{C_6H_6(l) + \tfrac{15}{2}O_2(g) \rightarrow 6CO_2(g) + 3H_2O(l)}$. The standard enthalpy of combustion of 2 mol of benzene is $-x$ kJ. Calculate the value of $x$, given that :

(1) Standard Enthalpy of formation of 1 mol of $\mathrm{C}_{6} \mathrm{H}_{6}(1)$, for the reaction 6 C (graphite) $+3 \mathrm{H}_{2}(\mathrm{~g}) \rightarrow \mathrm{C}_{6} \mathrm{H}_{6}(1)$ is $48.5 \mathrm{~kJ} \mathrm{~mol}^{-1}$.

(2) Standard Enthalpy of formation of 1 mol of $\mathrm{CO}_{2}(\mathrm{~g})$, for the reaction $\mathrm{C(graphite) + O_2(g) \rightarrow CO_2(g)}$ is $-393.5 \mathrm{~kJ} \mathrm{~mol}^{-1}$.

(3) Standard and Enthalpy of formation of 1 mol of $\mathrm{H}_{2} \mathrm{O}(1)$, for the reaction $\mathrm{H}_{2}(\mathrm{~g})+\frac{1}{2} \mathrm{O}_{2}(\mathrm{~g}) \rightarrow \mathrm{H}_{2} \mathrm{O}(1)$ is $-286 \mathrm{~kJ} \mathrm{~mol}^{-1}$.

The fusion of chromite ore with sodium carbonate in the presence of air leads to the formation of products $A$ and $B$ along with the evolution of $\mathrm{CO}_{2}$. The sum of spin-only magnetic moment values of $A$ and $B$ is $\_\_\_\_\_\_$B.M. (Nearest integer)

(Given atomic number : $\mathrm{C}=6 ,\mathrm{Na}= 11, \mathrm{O}= 8 , \mathrm{Fe} = 26, \mathrm{Cr}=24$]

$X$ of enthanamine was subjected to reaction with $\mathrm{NaNO}_{2} / \mathrm{HCl}$ followed by hydrolysis to liberate $\mathrm{N}_{2}$ and HCl . The HCl generated was completely neutralised by 0.2 moles of NaOH . X is $\qquad$ g.

In an atom, total number of electrons having quantum numbers $n=4$, $|m_\ell|=1$ and $m_s=-\frac{1}{2}$ is:

Using the given figure, the ratio of $R_{f}$ values of sample $A$ and sample $C$ is $\mathrm{x} \times 10^{-2}$. Value of x is $\qquad$ . Samples (A,B,C)

Fig : Paper chromatography of Samples

In the Claisen-Schmidt reaction to prepare 351 g of dibenzalacetone using 87 g of acetone, the amount of benzaldehyde required is $\_\_\_\_\_\_$ g. (Nearest integer)

Consider the following single step reaction in gas phase at constant temperature.

$2 \mathrm{~A}_{(\mathrm{g})}+\mathrm{B}_{(\mathrm{g})} \rightarrow \mathrm{C}_{(\mathrm{g})}$

The initial rate of the reaction is recorded as $r_{1}$ when the reaction starts with 1.5 atm pressure of A and 0.7 atm pressure of B. After some time, the rate $r_{2}$ is recorded when the pressure of $C$ becomes 0.5 atm. The ratio $r_{1}: r_{2}$ is $\qquad$ $\times 10^{-1}$. (Nearest integer)

The product (C) in the following sequence of reactions has $\_\_\_\_\_\_$ $\pi$ bonds.

Considering acetic acid dissociates in water, its dissociation constant is $6.25 \times 10^{-5}$. If 5 mL of acetic acid is dissolved

in 1 litre water, the solution will freeze at $-\mathrm{x} \times 10^{-2}{ }^{\circ} \mathrm{C}$, provided pure water freezes at $0^{\circ} \mathrm{C}$. $\mathrm{x}=$ (Nearest integer)

Given : $\left(\mathrm{K}_{\mathrm{f}}\right)_{\text {water }}=1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$. density of acetic acid is $1.2 \mathrm{~g} \mathrm{~mol}^{-1}$

molar mass of water $=18 \mathrm{~g} \mathrm{~mol}^{-1}$.

molar mass of acetic acid $=60 \mathrm{~g} \mathrm{~mol}^{-1}$. density of water $=1 \mathrm{~g} \mathrm{~cm}^{-3}$

Acetic acid dissociates as $\mathrm{CH}_{3} \mathrm{COOH} \rightleftharpoons \mathrm{CH}_{3} \mathrm{COO}^{\oplus}+\mathrm{H}^{\oplus}$

Number of compounds from the following with zero dipole moment is $\qquad$ .

$\mathrm{HF}, \mathrm{H}_{2}, \mathrm{H}_{2} \mathrm{~S}, \mathrm{CO}_{2}, \mathrm{NH}_{3}, \mathrm{BF}_{3}, \mathrm{CH}_{4}, \mathrm{CHCl}_{3}, \mathrm{SiF}_{4}$, $\mathrm{H}_{2} \mathrm{O}, \mathrm{BeF}_{2}$