AP EAPCET 2024 - 20th May Evening Shift

Paper was held on Mon, May 20, 2024 9:30 AM

Chemistry

If uncertainty in position and momentum of an electron are equal, then uncertainty in its velocity is

The graph between variation of probability density. $\psi^2(r)$ and distance of the electron from the nucleus, $r$ is shown below. This represents

Match the following.

List I	List II
A. Technicium	I. Non-metal
B. Fluorine	II. Transition metal
C. Tellurium	III. Lanthanoid
D. Dysprosium	IV. Metalloid

Observe the following reactions. Identify the reaction in which the hybridisation of underlined atom is changed

Among the following species, correct set of isostructural pairs are $\mathrm{XeO}_3, \mathrm{CO}_3^{2-}, \mathrm{SO}_3, \mathrm{H}_3 \mathrm{O}^{+}, \mathrm{ClF}_3$

What is the ratio of kinetic energies of 3 g of hydrogen and 4 g of oxygen at a certain temperature?

What is the kinetic energy (in $\mathrm{J} \mathrm{mol}^{-1}$ ) of one mole of an ideal gas (molar mass $=0.1 \mathrm{~kg} \mathrm{~mol}^{-1}$ ) if its rms velocity is $4 \times 10^2 \mathrm{~ms}^{-1}$ at $T(\mathrm{~K})$ ?

At STP ' $x$ ' $g$ of a metal hydrogen carbonate $\left(M \mathrm{HCO}_3\right)$ (molar mass $84 \mathrm{~g} \mathrm{~mol}^{-1}$ ) on heating gives $\mathrm{CO}_2$, which can completely react with 0.2 moles of MOH (molar mass $40 \mathrm{~g} \mathrm{~mol}^{-1}$ ) to give $\mathrm{MHCO}_3$. The value of ' $x^{\prime}$ is

The volume of an ideal gas contracts from 10.0 L to 2.0 L under an applied pressure of 2.0 atm . During contraction the system also evolved 900 J of heat. The change in internal energy (in J ) involved in the system is ( $1 \mathrm{~L} \mathrm{~atm}=101.3 \mathrm{~J}$ )

The molar heat of fusion and vaporisation of benzene are 10.9 and $31.0 \mathrm{~kJ} \mathrm{~mol}^{-1}$ respectively. The changes in entropy for the solid $\rightarrow$ liquid and liquid $\rightarrow$ vapour trasitions for benzene are $x$ and $y, \mathrm{JK}^{-1} \mathrm{~mol}^{-1}$, respectively. The value of $(y-x)$ (in $\mathrm{J} \mathrm{K}^{-1} \mathrm{~mol}^{-1}$ ) is (At 1 atm benzene melts at $5.5^{\circ} \mathrm{C}$ and boils at $80^{\circ} \mathrm{C}$ )

At $T(\mathrm{~K})$, the equilibrium constant for the reaction $\mathrm{H}_2(g)+\mathrm{Br}_2(\mathrm{~g}) \rightleftharpoons 2 \mathrm{HBr}(\mathrm{g})$

is $1.6 \times 10^5$. If 10 bar of HBr is introduced into a sealed vessel at $T(\mathrm{~K})$, the equilibrium pressure of HBr (in bar) is approximately

Which of the following will make a basic buffer solution?

The hydrides of which group elements are examples of electron precise hydrides?

The correct order of density of $\mathrm{Be}, \mathrm{Mg}, \mathrm{Ca}, \mathrm{Sr}$ is

Which of the following orders is not correct against the given property?

Which of the following are correct?

i. Basic structural unit of silicates is $-R_2 \mathrm{SiO}-$

ii. Silicones are biocompatible

iii. Producer gas contains CO and $\mathrm{N}_2$

The correct option is

An metal catalyst $(X)$ is used in the catalytic converter of automobiles. This prevents the release of gas $Y$ into the atmosphere. What are $X$ and $Y$ respectively?

A mixture of substances $A, B, C, D$ is subjected to column chromatography. The degree of adsorption is the order of $D>B>C>A$. The column is eluted with suitable solvent. Identify the correct statement with respect to separation of mixture

What is $X$ in the following reaction?

The density of $\beta-\mathrm{Fe}$ is $7.6 \mathrm{~g} \mathrm{~cm}^{-3}$. It crystallises in cubic lattice with $\mathrm{a}=290 \mathrm{pm}$. What is the value of $Z$ ? $\left(\mathrm{Fe}=56 \mathrm{~g} \mathrm{~mol}^{-1}: N_{\mathrm{A}}=6.022 \times 10^{23} \mathrm{~mol}^{-1}\right)$

The mass % of urea solution is 6 . The total weight of the solution is 1000 g . What is its concentration in $\mathrm{mol} \mathrm{L}^{-1}$ ? (Density of water $=1.0 \mathrm{~g} \mathrm{~mL}^{-1}$ )

( $\mathrm{C}=12 \mathrm{u}, \mathrm{N}=14 \mathrm{u}, \mathrm{O}=16 \mathrm{u}, \mathrm{H}=1 \mathrm{u}$ )

A non- volatile solute is dissolved in water. The $\Delta T_{\mathrm{b}}$ of resultant solution is 0.052 K . What is the freezing point of the solution ( in K )?

( $K_b$ of water $=0.52 \mathrm{~K} \mathrm{kgmol}^{-1}$,

$K_f$ of water $=1.86 \mathrm{~K} \mathrm{kgmol}^{-1}$,

freezing point of water $=273 \mathrm{~K}$ )

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. Observe the following reactions

I. $\mathrm{Zn}+\mathrm{HCI} \rightarrow$

II. $\mathrm{Cu}+\mathrm{HCl} \rightarrow$

III. $\mathrm{Cu}+\mathrm{HNO}_3 \rightarrow$

Which reactions does not liberate $\mathrm{H}_2(g)$ ?

At 298 K the value of $-\frac{\Delta\left[\mathrm{Br}^{-}\right]}{\Delta t}$ for the reaction,

$5 \mathrm{Br}^{-}(a q)+\mathrm{BrO}_3^{-}(a q)+6 \mathrm{H}^{+}(a q) \longrightarrow 3 \mathrm{Br}_2(a q)+3 \mathrm{H}_2 \mathrm{O}(l)$ is $X$ $\mathrm{mol} \mathrm{L} \mathrm{min}^{-1}$. What is the rate (in $\mathrm{mol} \mathrm{L}^{-1} \mathrm{~min}^{-1}$ ) of this reaction?

Which of the following general reaction is an example for heterogeneous catalysis?

Match List I with List II.

List I	List II
A. Aerosol	I. Milk
B. Foam	II. Soap lather
C. Emulsion	III. Cheese
D. Gel	IV. Smoke

The type of iron obtained from blast furnace in the extraction of iron is

$\mathrm{Xe}(g)+2 \mathrm{~F}_2(g) \xrightarrow[7 \text { bar }]{873 \mathrm{~K}} \mathrm{XeF}_4(\mathrm{~s})$

The ratio of $\mathrm{Xe}: \mathrm{F}_2$ required in the above reaction is

The transition metal with highest melting point is

Arrange the following in the increasing order of number of unpaired electrons present in the central metal ion

I. $\left[\mathrm{MnCl}_6\right]^{3-}$

II. $\left[\mathrm{FeF}_6\right]^{3-}$

III. $\left[\mathrm{Mn}(\mathrm{CN})_6\right]^{3-}$

IV. $\left[\mathrm{Fe}(\mathrm{CN})_6\right]^{3-}$

Which of the following polymerisation leads to the formation of neoprene ?

Which of the following represents simplified version of nucleoside?

Which of the following amino acids possess two chiral centres?

Which of the following sweetener use is limited to soft drinks?

Which of the following are general methods for the preparation of 1 -iodopropane?

The product of which of the following reactions undergo hydrolysis by $\mathrm{S}_{\mathrm{N}} 1$ mechanism?

Styrene on reaction with reagent $X$ gave $Y$ which on hydrolysis followed by oxidation gave $Z . Z$ gives positive 2, 4-DNP test but does not give iodoform test. What are $X$ and $Z$ respectively ?

What are $A$ and $B$ in the following reaction sequence ?

$$ \mathrm{CH}_3 \mathrm{COOH} \xrightarrow{A} X \xrightarrow[\mathrm{H}^{+}]{Y} B \text { (Analgesic drug) } $$

Which of the following sequence of reagents convert propene to 1-chloropropane?

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

Mathematics

$f: R \rightarrow R$ is defined by $f(x+y)=f(x)+12 y, \forall x, y \in R$. If $f(1)=6$, then $\sum_{r=1}^n f(r)=$

The domain of the real valued function $f(x)=\sqrt{2+x}+\sqrt{3-x}$ is

If $2 \cdot 4^{2 n+1}+3^{3 n+1}$ is divisible by $k$ for all $n \in N$, then $k=$

$\left|\begin{array}{ccc}a & b & c \\ a^2 & b^2 & c^2 \\ 1 & 1 & 1\end{array}\right|$ is not equal to

Let $A, B, C, D$ and $E$ be $n \times n$ matrices each with non-zero determinant. If $A B C D E=I$, then $C^{-1}=$

If $A=\left[a_{i j}\right], 1 \leq i, j \leq n$ with $n \geq 2$ and $a_{i j}=i+j$ is a matrix, then the rank of $A$ is

If $z_1=10+6 i, z_2=4+6 i$ and $z$ is any complex number such that the argument of $\frac{\left(z-z_1\right)}{\left(z-z_2\right)}$ is $\frac{\pi}{4}$,

If $\frac{3-2 i \sin \theta}{1+2 i \sin \theta}$ is purely imaginary number, then $\theta=$

If $z=x+i y, x^2+y^2=1$ and $z_1=z e^{i \theta}$, then $\frac{z_1^{2 n}-1}{z_1^{2 n}+1}=$

Let $[r]$ denote the largest integer not exceeditio $r$ and the roots of the equation $3 x^2+6 x+5+\alpha\left(x^2+2 x+2\right)=0$ are complex number when ever $\alpha>L$ and $\alpha

For any real value of $x$. If $\frac{11 x^2+12 x+6}{x^2+4 x+2} \notin(a, b)$, then the value $x$ for which $\frac{11 x^2+12 x+6}{x^2+4 x+2}=b-a+3$ is

If the roots of $\sqrt{\frac{1-y}{y}}+\sqrt{\frac{y}{1-y}}=\frac{5}{2}$ are $\alpha$ and $\beta(\beta>\alpha)$ and the equation $(\alpha+\beta) x^4-25 \alpha \beta x^2+(\gamma+\beta-\alpha)=0$ has real roots, then a possible value of $\gamma$ is

If the roots of the equation $x^3+a x^2+b x+c=0$ are in arithmetic progression. Then,

A test containing 3 objective type of questions is conducted in a class. Each question has 4 options and only one option is the correct answer. No two students of the class have answered identically and no student has written all correct answer. If every students has attempted all the questions, then the maximum possible number of students who has written the test is

The number of numbers lying between 1000 and 10000 such that every number contains the digit 3 and 7 only once without repetition is

The number of ways in which 17 apples can be distributed among four guests such that each guest gets at least 3 apples is .

If the coefficients of $x^5$ and $x^6$ are equal in the expansion of $\left(a+\frac{x}{5}\right)^{65}$, then the coefficient of $x^2$ in the expansion of $\left(a+\frac{x}{5}\right)^4$ is.

If $|x|<\frac{2}{3}$, then the 4th term in the expansion of $(3 x-2)^{\frac{2}{3}}$ is :

If $\frac{x^2+3}{x^4+2 x^2+9}=\frac{A x+B}{x^2+a x+b}+\frac{C x+D}{x^2+c x+b}$, then $a A+b B+c C+D=$

If $\sec \theta+\tan \theta=\frac{1}{3}$, then the quadrant in which $2 \theta$ lies is

If $540^{\circ} < A < 630^{\circ}$ and $|\cos A|=\frac{5}{13}$, then $\tan \frac{A}{2} \tan A=$

If $(\alpha+\beta)$ is not a multiple of $\frac{\pi}{2}$ and $3 \sin (\alpha-\beta)=5 \cos (\alpha+\beta)$, then $\tan \left(\frac{\pi}{4}+\alpha\right)+4 \tan \left(\frac{\pi}{4}+\beta\right)=$

The general solution of the equation $\sin ^2 \theta+3 \cos ^2 \theta=$ $5 \sin \theta$ is

If $\cos ^{-1} 2 x+\cos ^{-1} 3 x=\frac{\pi}{3}$ and $4 x^2=\frac{a}{b}$, then $a+b$ is equal to

If $\theta=\sec ^{-1}(\cosh u)$, then $u=$

In $\triangle A B C$, if $4 r_1=5 r_2=6 r_3$, then $\sin ^2 \frac{A}{2}+\sin ^2 \frac{B}{2}+\sin ^2 \frac{C}{2}=$

In $\triangle A B C, r_1 \cot \frac{A}{2}+r_2 \cot \frac{B}{2}+m_3 \cot \frac{C}{2}=$

In $\triangle A B C, b c-r_2 r_3=$

The angle between the diagonals of the parallelogram whose adjacent sides are $2 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}-5 \hat{\mathbf{k}}, \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}$ is

If the points having the position vectors $-i+4 j-4 k_{\text {, }}$, $3 i+2 j-5 k,-3 i+8 j-5 k$ and $-3 i+2 j+\lambda k$ are coplanar, then $\lambda=$

If $|f|=10,|g|=14$ and $|f-g|=15$, then $|f+g|=$

If $\mathbf{a}, \mathbf{b}, \mathbf{c}$ are three vectors such that $|\mathbf{a}|=|\mathbf{b}|=|\mathbf{c}|=\sqrt{3}$ and $(a+b-c)^2+(b+c-a)^2+(c+a-b)^2=36$, then $|2 a-3 b+2 c|=$

The angle between the line with the direction ratios $(2,5,1)$ and the plane $8 x+2 y-z=14$ is

If the mean deviation about the mean is $m$ and variance is $\sigma^2$ for the following data, then $m+\sigma^2=$

$\mathbf{x}$	1	3	5	7	9
$\mathbf{f}$	4	24	28	16	8

If five-digit numbers are formed from the digits $0,1,2,3,4$ using every digit exactly only once. Then, the probability that a randomly chosen number from those numbers is divisible by 4 is

Two natural numbers are chosen at random from 1 to 100 and are multiplied. If $A$ is the event that the product is an even number and $B$ is the event that the product is divisible by 4 , then $P(A \cap \bar{B})=$

A box $P$ contains one white ball, three red ball and two black balls. Another box $Q$ contains two white balls, three red balls and four black balls. If one ball is drawn at random from each one of the two boxes, then the probability that the balls drawn are of different colour is

A person is known to speak false once out of 4 times, If that person picks a card at random from a pack of 52 cards and reports that it is a king, then the probability that it is actually a king is

For a binomial variate $X \sim B(n, p)$ the difference between the mean and variance is 1 and the difference between their square is 11 . If the probability of $P(x=2)=m\left(\frac{5}{6}\right)^n$ and $n=36$, then $m: n$

The probability that a man failing to hit a target is $\frac{1}{3}$. If he fires 4 times, then the probability that he hits the target at least thrice is

$A(2,3), B(-1,1)$ are two points. If $P$ is a variable point such that $\angle A P B=90^{\circ}$, then locus of $P$ is

If the origin is shifted to remove the first degree terms from the equation $2 x^2-3 y^2+4 x y+4 x+4 y-14=0$, then with respect to this new coordinate system the transformed equation of $x^2+y^2-3 x y+4 y+3=0$ is

The circumcentre of the triangle formed by the lines $x+y+2=0,2 x+y+8=0$ and $x-y-2=0$ is

If the line $2 x-3 y+5=0$ is the perpendicular bisector of the line segment joining $(1,-2)$ and $(\alpha, \beta)$, then $\alpha+\beta=$

If the area of the triangle formed by the straight lines $-15 x^2+4 x y+4 y^2=0$ and $x=\alpha$ is 200 sq unit, then $|\alpha|=$

The equation for straight line passing through the point of intersection of the lines represented by $x^2+4 x y+3 y^2-4 x-10 y+3=0$ and the point $(2,2)$ is

The largest among the distances from the point $P(15,9)$ to the points on the circle $x^2+y^2-6 x-8 y-11=0$ is

The circle $x^2+y^2-8 x-12 y+\alpha=0$ lies in the first quadrant without touching the coordinate axes. If $(6,6)$ is an interior point to the circle, then

The equation of the circle whose diameter is the common chord of the circles $x^2+y^2-6 x-7=0$ and $x^2+y^2-10 x+16=0$ is

If the locus of the mid-point of the chords of the circle $x^2+y^2=25$, which subtend a right angle at the origin is given by $\frac{x^2}{\alpha^2}+\frac{y^2}{\alpha^2}=1$, then $|\alpha|=$

The radical centre of the circles $x^2+y^2+2 x+3 y+1=0$, $x^2+y^2+x-y+3=0, x^2+y^2-3 x+2 y+5=0$

Equation of a tagent line of the parabola $y^2=8 x$, which passes through the point $(1,3)$ is

If the chord of the ellipse $\frac{x^2}{4}+\frac{y^2}{9}=1$ having $(1,1)$ as its middle point is $x+\alpha y=\beta$, then

If a directrix of a hyperbola centred at the origin and passing through the point $(4,-2 \sqrt{3})$ is $\sqrt{5} x=4$ and e is its eccentricity, then $e^2=$

If $l_1$ and $l_2$ are the lengths of the perpendiculars drawn from a point on the hyperbola $5 x^2-4 y^2-20=0$ to its asymptotes, then $\frac{l_1{ }^2 l_2{ }^2}{100}=$

If $O(0,0,0), A(3,0,0)$ and $B(0,4,0)$ form a triangle, then the incentre of $\triangle O A B$ is

The direction cosines of the line of intersection of the planes $x+2 y+z-4=0$ and $2 x-y+z-3=0$ are

If $L_1$ and $L_2$ are two lines which pass through origin and having direction ratios $(3,1,-5)$ and $(2,3,-1)$ respectively, then equation of the plane containing $L_1$ and $L_2$ is

$\lim \limits_{x \rightarrow \frac{\pi}{4}} \frac{4 \sqrt{2}-(\cos x+\sin x)^5}{1-\sin 2 x}=$

If $\lim \limits_{x \rightarrow 0} \frac{e^x-a-\log (1+x)}{\sin x}=0$, then $a=$

The values of $a$ and $b$ for which the function

$ f(x)=\left\{\begin{array}{cl}1+|\sin x|^{\frac{a}{\sin x \mid}} & \frac{-\pi}{6} < x < 0 \\ b, & x=0 \quad \text { is continuous at } x=0 \\ e^{\frac{\tan 2 x}{\tan 3 x},} & 0 < x < \frac{\pi}{6}\end{array}\right. $

are

If $f(x)=\left\{\begin{array}{cc}2 x+3, & x \leq 1 \\ a x^2+b x, & x>1\end{array}\right.$

is differentiable, $\forall x \in R$, then $f^{\prime}(2)=$

If $y=t^2+t^3$ and $x=t-t^4$, then $\frac{d^2 y}{d x^2}$ at $t=1$ is

In the interval $[0,3]$ The function $f(x)=|x-1|+|x-2|$ is

$p_1$ and $p_2$ are the perpendicular distances from the origin to the tangent and normal drawn at any point on the curve $x^{\frac{2}{3}}+y^{\frac{2}{3}}=a^{\frac{2}{3}}$ respectively. If $k_1 p_1^2+k_2 p_2^2=a^2$, then $k_1+k_2=$

The length of the subnormal at any point on the curve $y=\left(\frac{x}{2024}\right)^k$ is constant, if the value of $k$ is

The acute angle between the curves $x^2+y^2=x+y$ and $x^2+y^2=2 y$ is

A' value of $C$ according to the Lagrange's mean value theorem for $f(x)=(x-1)(x-2)(x-3)$ in $[0,4]$ is

$\int \frac{d x}{x\left(x^4+1\right)}=$

$\int \frac{d x}{\sqrt{\sin ^3 x \cos (x-a)}}=$

$\int \frac{e^{2 x}}{\sqrt[4]{e^x+1}} d x=$