AP EAPCET 2024 - 21th May Evening Shift

Paper was held on Tue, May 21, 2024 9:30 AM

Chemistry

The difference in radii between fourth and third Bohr orbit of $\mathrm{He}^{+}($in m$)$ is

If $\lambda_0$ and $\lambda$ are respectively the threshold wavelength and wavelength of incident light the velocity of photo electrons ejected from the metal surface is

The correct order of atomic radii of $\mathrm{N}, \mathrm{F}, \mathrm{Al}, \mathrm{Si}$ is

The correct order of covalent bond character of $\mathrm{BCl}_3, \mathrm{CCl}_4, \mathrm{BeCl}_2, \mathrm{LiCl}$ is

In which of the following pairs, both molecules possess dipole moment?

At $T(\mathrm{~K})$, the $p, V$ and $u_{\mathrm{rms}}$ of 1 mole of an ideal gas were measured. The following graph is obtained. What is it slope ( $m$ )?

( $x$-axis $=p V: y$-axis $u_{\mathrm{rms}}^2, M=$ Molar mass $)$

AP EAPCET 2024 - 21th May Evening Shift Chemistry - States of Matter Question 1 English

Three layers of liquid are flowing over fixed solid surface as shown below. The correct order of velocity of liquid in these layers is

A flask contains 98 mg of $\mathrm{H}_2 \mathrm{SO}_4$. If $3.01 \times 10^{20}$ molecules of $\mathrm{H}_2 \mathrm{SO}_4$ are removed from the flask. The number of moles of $\mathrm{H}_2 \mathrm{SO}_4$ remained in flask is

$$ \left(N_A=6.02 \times 10^{23}\right) $$

Identify the correct equation relating $\Delta H, \Delta U$ and $\Delta T$ for 1 mole of an ideal gas from the following. ( $R=$ gas constant)

The number of extensive properties in the following list is enthalpy, density, volume, internal energy, temperature.

15 moles of $\mathrm{H}_2$ and 5.2 moles of $\mathrm{I}_2$ are mixed and allowed to attain equilibrium at 773 K . At equilibrium, the number of moles of HI is found to be 10 . The equilibrium constant for the dissociation of HI is

The solubility of barium phosphate of molar mass ' $M$ ' $\mathrm{g} \mathrm{mol}^{-1}$ in water is $x \mathrm{~g}$ per 100 mL at 298 K . Its solubility product is $1.08 \times\left(\frac{x}{M}\right)^a \times(10)^b$. The values of $a$ and $b$ respectively are

Hydrated sodium aluminium silicate is called

Which one of the following statements is not correct about the compounds of alkaline earth metals?

Consider the following standard electrode potentials ( $E^{\circ}$ in volts) in aqueous solution.

$$ \begin{array}{|c|c|c|} \hline \text { Element } & M^{3+} / M & M^{+} / M \\ \hline \mathrm{Al} & -1.66 & +0.55 \\ \hline \mathrm{TI} & +1.26 & -0.34 \\ \hline \end{array} $$

Based on this data. which of the following statements is correct?

Which of the allotropic forms of carbon is aromatic in nature?

The enamel present on teeth becomes much harder due to the conversion of $\left[3 \mathrm{Ca}_3\left(\mathrm{PO}_4\right)_2 \cdot X\right.$ ] into [ $3 \mathrm{Ca}_3\left(\mathrm{PO}_4\right)_2 Y$ ]. What are $X$ and $Y$ ?

Number of deactivating group of the following is $$ -\mathrm{Cl},-\mathrm{SO}_3 \mathrm{H},-\mathrm{OH},-\mathrm{NHC}_2 \mathrm{H}_5,-\mathrm{COOCH}_3,-\mathrm{CH}_3 $$

What are $X$ and $Y$ respectively in the following reaction sequence?

AP EAPCET 2024 - 21th May Evening Shift Chemistry - Hydrocarbons Question 2 English

Identify the incorrect set from the following.

The following graph is obtained for vapour pressure (in atm) (on $Y$-axis) and $T$ (in K) (on $X$-axis) for aqueous urea solution and water. What is the boiling point (in K) of urea solution?

(Atmospheric pressure $=1 \mathrm{~atm}$ )

AP EAPCET 2024 - 21th May Evening Shift Chemistry - Liquid Solution Question 1 English

Given below are two statements.

Statement I : Liquids $A$ and $B$ form a non-ideal solution with negative deviation. The interactions between $A$ and $B$ are weaker than $A-A$ and $B-B$ interactions.

Statement II : In reverse osmosis, the applied pressure must be higher than the osmotic pressure of solution

The correct answer is

The standard reduction potentials of $2 \mathrm{H}^{+} / \mathrm{H}_2, \mathrm{Cu}^{2+} / \mathrm{Cu}, \mathrm{Zn}^{2+} / \mathrm{Zn}$ and $\mathrm{NO}_3^{-}, \mathrm{H}^{-} / \mathrm{NO}$ are 0.0 0.34 . -0.76 and 0.97 V respectively. Identify the correct statements from the following.

I. $\mathrm{H}^{+}$does not oxidise Cu to $\mathrm{Cu}^{2+}$

II. Zn reduces $\mathrm{Cu}^{2+}$ to Cu

III. $\mathrm{NO}_3^{-}$oxidises Cu to $\mathrm{Cu}^{2+}$

$A \rightarrow P$ is a zero order reaction. At 298 K the rate constant of the reaction is $1 \times 10^{-3} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}$. Initial concentration of ' $A$ ' is $0.1 \mathrm{~mol} \mathrm{~L}^{-1}$. What is the concentration of ' $A$ after 10 sec ?

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

$$ \begin{array}{llll} \hline & \text { List I } & & \text { List II } \\ \hline \text { I } & \text { Colloidal antimony } & \text { A } & \text { Kalaazar } \\ \hline \text { II } & \text { Silver sol } & \text { B } & \text { Intermuscular injection } \\ \hline \text { III } & \text { Milk of magnesia } & \text { C } & \text { Eye lotion } \\ \hline \text { IV } & \text { Gold sol } & \text { D } & \text { Stomach disorder } \\ \hline \end{array} $$

Identify the method of preparation of a colloidal sol from the following.

The flux used in the preparation of wrought iron from cast iron in reverberatory furnace is

$\mathrm{P}_2 \mathrm{O}_3+\mathrm{H}_2 \mathrm{O} \rightarrow X$, Red $\mathrm{P}_4+$ alkali $\rightarrow Y$

$X, Y$ are oxoacids of phosphorous. The number of $\mathrm{P}-\mathrm{OH}$ bonds in $X, Y$ respectively is

$$ \mathrm{P}_2 \mathrm{O}_3+\mathrm{H}_2 \mathrm{O} \rightarrow X $$

Which of the following occurs with $\mathrm{KMnO}_4$ in neutral medium?

Cobalt (III) chloride forms a green coloured complex ' $X$ ' with $\mathrm{NH}_3$. Number of moles of AgCl formed when excess of $\mathrm{AgNO}_3$ solution is added to 100 mL of 1 M solution of ' $X$ ' is

The correctly matched set of the following is

Identify the correctly matched set from the following.

Given below are two statements.

I. Cytosine and guanine are formed in equal quantities in DNA hydrolysis.

II. Adenine and uracil are formed in equal quantities in RNA hydrolysis.

The correct answer is

$$ \text { Identify the correctly matched pair from the following. } $$

What are $Y$ and $Z$ respectively in the following reaction sequence?

AP EAPCET 2024 - 21th May Evening Shift Chemistry - Haloalkanes and Haloarenes Question 1 English

Hydrolysis of an alkyl bromide $\left(\mathrm{C}_5 \mathrm{H}_{11} \mathrm{Br}\right)$ follows first order kinetics. Reaction of $X$ with Mg in dry ether followed by treatment of $\mathrm{D}_2 \mathrm{O}$ gave $Y$, What is $Y$ ?

An alcohol $X\left(\mathrm{C}_4 \mathrm{H}_{10} \mathrm{O}\right)$ does not give turbidity with conc. HCl and $\mathrm{ZnCl}_2$ at room temperature. $X$ on reaction with reagent $Y$ gives Z . What are $X, Y$ and $Z$ respectively?

Which of the following sets of reagents convert toluene to benzaldehyde?

A. $\mathrm{Cl}_2 \mid h v ; \mathrm{H}_2 \mathrm{O}, \Delta$

B. $\mathrm{KMnO}_4 \mid \mathrm{OH}^{-} ; \mathrm{H}^{+}$

C. $\mathrm{Cl}_2 \mid \mathrm{Fe} ; \mathrm{H}_2 \mathrm{O}$

D. $\mathrm{CrO}_2 \mathrm{Cl}_{21} \mid \mathrm{CS}_2 ; \mathrm{H}_3 \mathrm{O}^{+}$

What are $X$ and $Y$ respectively in the following reactions?

AP EAPCET 2024 - 21th May Evening Shift Chemistry - Carboxylic Acids and Its Derivatives Question 1 English

$$ \text { IUPAC names of the following compounds } A \text { and } B $$ are

AP EAPCET 2024 - 21th May Evening Shift Chemistry - IUPAC Nomenclatures Question 1 English

Mathematics

The range of the real valued function $f(x)=\sin ^{-1}\left(\frac{1+x^2}{2 x}\right)+\cos ^{-1}\left(\frac{2 x}{1+x^2}\right)$ is

The real valued function $f: R \rightarrow\left[\frac{5}{2}, \infty\right)$ defined by $f(x)=|2 x+1|+|x-2|$ is

If $1 \cdot 3 \cdot 5+3 \cdot 5 \cdot 7+5 \cdot 7 \cdot 9+\ldots n$ terms $=n(n+1) f(n)-3 n$, then $f(l)=$

If $3 A=\left[\begin{array}{ccc}1 & 2 & 2 \\ 2 & 1 & -2 \\ a & 2 & b\end{array}\right]$ and $A A^T=I$, then $\frac{a}{b}+\frac{b}{a}=$

$\left|\begin{array}{ccc}a+b+2 c & a & b \\ c & b+c+2 a & b \\ c & a & c+a+2 b\end{array}\right|=$

Assertion (A) : If $B$ is a $3 \times 3$ matrix and $|B|=6$, then $|\operatorname{adj}(B)|=36$

Reason (R) : If $B$ is a square matrix of order $n$, then $|\operatorname{adj}(B)|=|B|^n$

Imaginary part of $\frac{(1-i)^3}{(2-i)(3-2 i)}$ is

The square root of $7+24 i$

If $n$ is an integer and $Z=\cos \theta+i \sin \theta, \theta \neq(2 n+1) \frac{\pi}{2}$, then $\frac{1+Z^{2 n}}{1-Z^{2 n}}=$

If $x$ is real and $\alpha, \beta$ are maximum and minimum values of $\frac{x^2-x+1}{x^2+x+1}$ respectively, then $\alpha+\beta=$

If $\alpha$ is a common root of $x^2-5 x+\lambda=0$ and $x^2-8 x-2 \lambda=0(\lambda \neq 0)$ and $\beta, \gamma$ are the other roots of them, then $\alpha+\beta+\gamma+\lambda=$

The equation $x^4-x^3-6 x^2+4 x+8=0$ has two equal roots. If $\alpha, \beta$ are the other two roots of this equation, then $\alpha^2+\beta^2=$

The condition that the roots of $x^3-b x^2+c x-d=0$ are in arithmetic progression is

There are 6 different novels and 3 different poetry books on a table. If 4 novels and 1 poetry book are to be selected and arranged in a row on a shelf such that the poetry book is always in the middle, then the number of such possible arrangements is

If a five-digit number divisible by 3 is to be formed using the numbers $0,1,2,3,4$ and 5 without repetition, then the total number of ways this can be done is

Four-digit numbers with all digits distinct are formed using the digits $1,2,3,4,5,6,7$ in all possible ways.If $p$ is the total number of numbers thus formed and $q$ is the number of numbers greater than 3400 among them, then $p: q=$

If the ratio of the terms equidistant from the middle term in the expansion of $(l+x)^{12}$ is $\frac{1}{256}(x \in N)$, then sum of all the terms of the expansion $(1+x)^{12}$ is

In the expansion of $\frac{2 x+1}{(1+x)(1-2 x)}$ the sum of the coefficients of the first 5 odd powers of $x$ is

If $\frac{x+2}{\left(x^2+3\right)\left(x^4+x^2\right)\left(x^2+2\right)}=\frac{A x+B}{x^2+3}+\frac{C x+D}{x^2+2}$ $+\frac{E x^3+F x^2+G x+H}{x^4+x^2}$, then $(E+F)(C+D)(A)=$

If $A, B, C$ are the angles of triangle, then $\sin 2 A-\sin 2 B+\sin 2 C=$

Assertion (A) : If $A=10^{\circ}, B=16^{\circ}$ and $C=19^{\circ}$, then $\tan 2 A \tan 2 B+\tan 2 B \tan 2 C+\tan 2 C \tan 2 A=1$

Reason (R) : If $A+B+C=180^{\circ}, \cot \frac{A}{2}+\cot \frac{B}{2}+\cot \frac{C}{2}$

$$ =\cot \frac{A}{2} \cot \frac{B}{2} \cot \frac{C}{2} $$

Which of the following is correct ?

If $\alpha$ is in the 3rd quadrant, $\beta$ is in the 2nd quadrant such that $\tan \alpha=\frac{1}{7}, \sin \beta=\frac{1}{\sqrt{10}}$, then $\sin (2 \alpha+\beta)=$

Number of solutions of the trigonometric equation $2 \tan 2 \theta-\cot 2 \theta+1=0$ lying in the interval $[0, \pi]$ is

The real values of $x$ that satisfy the equation $\tan ^{-1} x+\tan ^{-1} 2 x=\frac{\pi}{4}$ is

$2 \operatorname{coth}^{-1}(4)+\sec h^{-1}\left(\frac{3}{5}\right)=$

If 7 and 8 are the length of two sides of a triangle and $a^{\prime}$ is the length of its smallest side. The angles of the triangle are in AP and ' $a$ ' has two values $a_1$ and $a_2$ satisfying this condition. If $a_1 < a_2$, then $2 a_1+3 a_2=$

In $\triangle A B C$, if $a=13, b=14$ and $\cos \frac{C}{2}=\frac{3}{\sqrt{13}}$, then $2 r_1=$

In $\triangle A B C$, if $\left(r_2-r_1\right)\left(r_3-r_1\right)=2 r_2 r_3$, then $2(r+R)=$

If $\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}, 2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}-\hat{\mathbf{k}},-3 \hat{\mathbf{i}}-\hat{\mathbf{j}}-2 \hat{\mathbf{k}}$ are the position vectors of three points, $A, B, C$ respectively, then $A, B, C$

If $\mathbf{a}, \mathbf{b}, \mathbf{c}, \mathbf{d}$ are position vectors of 4 points such that $2 a+3 b+5 c-10 d=0$, then the ratio in which the line joining $c$ and $d$ divides the line segment joining $a$ and $\mathbf{b}$ is

If $\mathbf{a}, \mathbf{b}, \mathbf{c}$ are 3 vectors such that $|\mathbf{a}|=5,|\mathbf{b}|=8,|\mathbf{c}|=11$ and $\mathbf{a}+\mathbf{b}+\mathbf{c}=\mathbf{0}$, then the angle between the vectors $\mathbf{a}$ and $\mathbf{b}$ is

Angle between the planes, $\mathbf{r} \cdot(12 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}-3 \hat{\mathbf{k}})=5$ and, $\mathbf{r} \cdot(5 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}})=7$ is

The shortest distance between the skew lines $\mathbf{r}=(2 \hat{\mathbf{i}}-\hat{\mathbf{j}})+t(\hat{\mathbf{i}}+2 \hat{\mathbf{k}})$ and $\mathbf{r}=(-2 \hat{\mathbf{i}}+\hat{\mathbf{k}})+s(\hat{\mathbf{i}}-\hat{\mathbf{j}}-\hat{\mathbf{k}})$ is

The coefficient of variation for the frequency distribution is

$$ \begin{array}{|c|l|l|l|} \hline \boldsymbol{x}_{\boldsymbol{i}} & 4 & 3 & 1 \\ \hline \boldsymbol{f}_{\boldsymbol{i}} & 1 & 3 & 5 \\ \hline \end{array} $$

If all the letters of the word 'SENSELESSNESS' are arranged in all possible ways and an arrangement among them is chosen at random, then the probability that all the E's come together in that arrangement is

If two numbers $x$ and $y$ are chosen one after the other at random with replacement from the set of number $\{1,2,3, \ldots \ldots 10\}$. Then, the probability that $\left|x^2-y^2\right|$ is divisible by 6 is

Bag $A$ contains 3 white and 4 red balls, bag $B$ contains 4 white and 5 red balls and bag $C$ is contains 5 white and 6 red balls. If one ball is drawn at random from each of these three bags, then the probability of getting one white and two red balls is

Two persons $A$ and $B$ throw a pair of dice alternately until one of them gets the sum of the numbers appeared on the dice as 4 and the person who gets this result first is declared as the winner. If $A$ starts the game, then the probability that $B$ wins the game is

An urn contains 3 black and 5 red balls. If 3 balls are drawn at random from the urn, the mean of the probability distribution of the number of red balls drawn is

If $X \sim B(5, p)$ is a binomial variate such that $P(X=3)=P(X=4)$, then $P(|X-3|<2)=$

The perimeter of the locus of the point $P$ which divides the line segment QA internally in the ratio $1: 2$, where $A=(4,4)$ and $Q$ lies on the circle $x^2+y^2=9$, is

Suppose the axes are to be rotated through an angle $\theta$ so as to remove the $x y$ form from the equation $3 x^2+2 \sqrt{3} x y+y^2=0$. Then, in the new coordinate system the equation $x^2+y^2+2 x y=2$ is transformed to

$P$ is a point on $x+y+5=0$, whose perpendicular distance from $2 x+3 y+3=0$ is $\sqrt{13}$, then the coordinates of $P$ are

For $\lambda, \mu \in R,(x-2 y-1)+\lambda(3 x+2 y-11)=0$ and $(3 x+4 y-11)+\mu(-x+2 y-3)=0$ represent two families of lines. If the equation of the line common to both the families is $a x+b y-5=0$. Then, $2 a+b=$

If the pair of lines represented by $3 x^2-5 x y+P y^2=0$ and $6 x^2-x y-5 y^2=0$ have one line in common, then the sum of all possible value of $P$ is

Area of the region enclosed by the curves $3 x^2-y^2-2 x y+4 x+1=0$ and $3 x^2-y^2-2 x y+6 x+2 y=0$ is

If the equation of the circle whose radius is 3 units and which touches internally the circle $x^2+y^2-4 x-6 y-12=0$ at the point $(-1,-1)$ is $x^2+y^2+p x+q y+r=0$, then $p+q-r=$

The equation of the circle touching the circle $x^2+y^2-6 x+6 y+17=0$ externally and to which the lines $x^2-3 x y-3 x+9 y=0$ are normal is

The pole of the straight line $9 x+y-28=0$ with respect to the circle $2 x^2+2 y^2-3 x+5 y-7=0$ is

The equation of a circle which touches the straight lines $x+y=2, x-y=2$ and also touches the circle $x^2+y^2=1$ is

The radical axis of the circle $x^2+y^2+2 g x+2 f y+c=0$ and $2 x^2+2 y^2+3 x+8 y+2 c=0$ touches the circle $x^2+y^2+2 x+2 y+1=0$. Then,

If the ordinates of points $P$ and $Q$ on the parabola $y^2=12 x$ are in the ratio $1: 2$. Then, the locus of the point of intersection of the normals to the parabola at $P$ and $Q$ is

The product of perpendiculars from the two foci of the ellipse $\frac{x^2}{9}+\frac{y^2}{25}=1$ on the tangent at any point on the ellipse is

The value of $c$ such that the straight line joining the points $(0,3)$ and $(5,-2)$ is tangent to the curve $y=\frac{c}{x+1}$ is

The descending order of magnitude of the eccentricities of the following hyperbolas is A. A hyperbola whose distance between foci is three times the distance between its directrices. B. Hyperbola in which the transverse axis is twice the conjugate axis. C. Hyperbola with asymptotes $x+y+1=0, x-y+3=0$

If the plane $x-y+z+4=0$ divides the line joining the points $P(2,3,-1)$ and $Q(1,4,-2)$ in the ratio $l: m$, then $l+m$ is

If the line with direction ratios $(1, \alpha, \beta)$ is perpendicular to the line with direction ratios $(-1,2,1)$ and parallel to the line with direction ratios $(\alpha, 1, \beta)$ then $(\alpha, \beta)$ is

Let $P\left(x_1, y_1, z_1\right)$ be the foot of perpendicular drawn from the point $Q(2,-2,1)$ to the plane $x-2 y+z=1$. If $d$ is the perpendicular from the point $Q$ to the plane and $l=x_1+y_1+z_1$, then $l+3 d^2$ is

$$\mathop {\lim }\limits_{x \to 0} \left( {{{\sin (\pi {{\cos }^2}x} \over {{x^2}}}} \right) = $$

$$\mathop {\lim }\limits_{x \to 1} \left( {{{x + {x^2} + {x^3} + ... + {x^n} - n} \over {x - 1}}} \right) = $$

If the function $f(x)=\frac{\sqrt{1+x}-1}{x}$ is continuous at $x=0$, then $f(0)=$

If $3 f(x)-2 f(1 / x)=x$, then $f(2)=$

If $\frac{d}{d x}\left(\frac{1+x^2+x^4}{1+x+x^2}\right)=a x+b$, then $(a, b)=$

If $y=\sin ^{-1} x$, then $\left(1-x^2\right) y_2-x y_1=$

If the percentage error in the radius of circle is 3 , then the percentage error in its area is

The equation of the tangent to the curve $y=x^3-2 x+7$ at the point $(1,6)$ is

The distance ( s ) travelled by a particle in time $t$ is given by $S=4 t^2+2 t+3$. The velocity of the particle, when $t=3 \mathrm{sec}$ is

If $a^2 x^4+b^2 y^4=c^6$, then maximum value of $x y$ is equal to

$\int \frac{\sin ^6 x}{\cos ^8 x} d x=$

$\int \frac{x^5}{x^2+1} d x=$

$$\int {\left( {\sum\limits_{r = 0}^\infty {{{{x^r}{3^r}} \over {r!}}} } \right)dx = } $$

$\int \frac{x^4+1}{x^6+1} d x=$

$\int e^x(x+1)^2 d x=$

$$\int\limits_0^{\pi /4} {{{{x^2}} \over {{{(x\,\sin \,x + \cos \,x)}^2}}}dx = } $$

$\int_0^1 \frac{x}{(1-x)^{\frac{3}{4}}} d x=$

$$ \int_{-1}^1\left(\sqrt{1+x+x^2}-\sqrt{1-x+x^2}\right) d x= $$

$\int_1^5(|x-3|+|1-x|) d x=$

The differential equation formed by eliminating arbitrary constants $A, B$ from the equation $y=A \cos 3 x+B \sin 3 x$ is

If $\cos x \frac{d y}{d x}-y \sin x=6 x,\left(0 < x < \frac{\pi}{2}\right)$ and $y\left(\frac{\pi}{3}\right)=0$, then $y\left(\frac{\pi}{6}\right)=$

$\frac{d y}{d x}=\frac{y+x \tan \frac{y}{x}}{x} \Rightarrow \sin \frac{y}{x}=$

Physics

The length of the side of a cube is $1.2 \times 10^{-2} \mathrm{~m}$. Its volume up to correct significant figure is

The velocity of a particle is given by the equation $v(x)=3 x^2-4 x$, where $x$ is the distance covered by the particle. The expression for its acceleration is

The acceleration of a particle which moves along the positive $X$-axis varies with its position as shown in the figure. If the velocity of the particle is $0.8 \mathrm{~ms}^{-1}$ at $x=0$ , then its velocity at $x=1.4 \mathrm{~m}$ is $\left(\right.$ in $\left.\mathrm{ms}^{-1}\right)$

AP EAPCET 2024 - 21th May Evening Shift Physics - Motion in a Straight Line Question 1 English

The maximum height attained by projectile is increased by $10 \%$ by keeping the angle of projection constant. What is the percentage increase in the time of flight ?

A light body of momentum $p_L$ and a heavy body of momentum $p_H$ both have the same kinetic energy, then

A block of metal 4 kg is in rest on a frictionless surface. It was targeted by a jet releasing water of $2 \mathrm{~kg} \mathrm{~s}^{-1}$ at a speed of $10 \mathrm{~ms}^{-1}$. The acceleration of the block is

A person climbs up a conveyor belt with a constant acceleration. The speed of the belt is $\sqrt{\frac{g h}{6}}$ and coefficient of friction is $\frac{5}{3 \sqrt{3}}$. The time taken by the person to reach from $A$ to $B$ with maximum possible acceleration is