Chemistry
1. Which of the following represents the wavelength of spectral line of Balmer series of $\mathrm{He}^{+}$ion?
$(R=$ Rydber 2. The work functions (in eV ) of $\mathrm{Mg}, \mathrm{Cu}, \mathrm{Ag}, \mathrm{Na}$ respectively are $3.7,4.8,4.3,2.3$. 3. The order of negative electron gain enthalpy of $\mathrm{Li}, \mathrm{Na}$, $\mathrm{S}, \mathrm{Cl}$ is
4. The number of molecules having lone pair of electrons on central atom in the following is
$\mathrm{BF}_3, \mathrm{SF}_4, 5. Observe the following substances.
Ethanol, acetic acid, ethylamine, trimethylamine, salicylic acid. ethanal.
In the abov 6.
Consider the following
Statement I If thermal energy is stronger than intermolecular forces, the substance prefers to 7. At $27^{\circ} \mathrm{C}, 1 \mathrm{~L}$ of $\mathrm{H}_2$ with a pressure of 1 bar is mixed with 2 L of $\mathrm{O}_2$ 8. Two acids $A$ and $B$ are titrated separately, 25 mL of $0.5 \mathrm{M} \mathrm{Na}_2 \mathrm{CO}_3$ solution requires 1 9. If $\Delta_r H^{\ominus}$ and $\Delta_r S^{\ominus}$ are standard enthalpy change and standard entropy change respective 10. The $\mathrm{C}_p$ of $\mathrm{H}_2 \mathrm{O}(l)$ is $75.3 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}$. What is th 11. At $T(\mathrm{~K})$, consider the following gaseous reaction, which is in equilibrium.
$$ \mathrm{N}_2 \mathrm{O}_5 \rig 12. Observe the following molecules/ions $\mathrm{NH}_4^{+}, \mathrm{NH}_3, \mathrm{BF}_3, \mathrm{OH}^{-}, \mathrm{CH}_3^{+ 13. Observe the following reactions
I. $\mathrm{N}_2(g)+3 \mathrm{H}_2(g) \xrightarrow[773 \mathrm{~K}, 200 \mathrm{~atm}]{x 14. Consider the following
Statement - I : Both $\mathrm{BeSO}_4$ and $\mathrm{MgSO}_4$ are readily soluble in water.
Statem 15. Which of the following is not associated with water molecules ?
16. Identify the incorrect statement about silica. 17. Which one of the following statements related to photochemical smog is not correct?
18. In compound $(X)$, hyperconjugation is present and in $(Y)$, resonance effect is present. What are $X$ and $Y$, respecti 19. An alcohol $X\left(\mathrm{C}_4 \mathrm{H}_{10} \mathrm{O}\right)$ on dehydration gave alkene $\left(\mathrm{C}_4 \mathr 20. An element occurs in the body centred cubic structure with edge length of 288 pm . The density of the element is $7.2 \m 21. An aqueous solution containing 0.2 g of a non volatile solute ' $A$ ' in 21.5 g of water freezes at 272.814 K . If the f 22. At $T(\mathrm{~K})$, the vapour pressure of $x$ molal aqueous solution containing a non-volatile solute is $12.078 \math 23. Consider the following cell reaction
$$ 2 \mathrm{Fe}^{3+}(a q)+2 \mathrm{I}^{-}(a q) \rightleftharpoons 2 \mathrm{Fe}^{ 24. For a first order reaction, the ratio between the time taken to complete $\frac{3}{4}$ th of the reaction and time taken 25. What is the indicator used in argentometric titrations?
26. In a Freundlich adsorption isotherm, if the slope is unity and $k$ is 0.1 , the extent of adsorption at 2 atm is ( $\log 27. $$ \text { Match the following } $$
$$ \begin{array}{llll} \hline & \text { List-I (Process) } & & \text { List-II (Meta 28. The number of $\mathrm{P}=\mathrm{O}, \mathrm{P}-\mathrm{P}$ bonds present in oxoacid of phosphorus, prepared by treatin 29. Which one of the following statements is not correct? 30. The coordination number of chromium in $\mathrm{K}\left[\mathrm{Cr}\left(\mathrm{H}_2 \mathrm{O}\right)_2\left(\mathrm{C 31. Consider the following
Statement I Nylon 6 is a condensation copolymer.
Statement II Nylon 6, 6 is a condensation polyme 32. $$ \text { Match the following } $$
.tg {border-collapse:collapse;border-spacing:0;}
.tg td{border-color:black;borde 33. The list given below contains essential amino acids that are basic $(X)$ and also non essential amino acids that are neu 34. The artificial sweetener $X$ contains glycosidic linkage and $Y$ contains amide, ester linkages. $X$ and $Y$ respectivel 35. Which one of the following halogen compounds is least reactive towards hydrolysis by $\mathrm{S}_{\mathrm{N}} 1$ mechani 36. $p$-chlorotoluene is the major product in which of the following reactions? 37. Arrange the following in decreasing order of electrophilicity of carbonyl carbon.
$$ \mathrm{CH}_3 \mathrm{CH}_2 \mathrm 38. What is the ratio of $s p^3$ carbons to $s p^2$ carbons in the product ' $P$ ' of the given sequence of reactions? 39. $$ \text { The final product }(C) \text { in the given reaction sequence is } $$
$$ \mathrm{C}_6 \mathrm{H}_5 \mathrm{CO 40. $$ \text { What are } X \text { and } Y \text { in the following reaction sequence? } $$
$$ \mathrm{C}_6 \mathrm{H}_5 \m
Mathematics
1. If $A=\left\{x \in R / \sin ^{-1}\left(\sqrt{x^2+x+1}\right) \in\left(-\frac{\pi}{2}, \frac{\pi}{2}\right)\right\}$ and 2. The domain of the function, $f(x)=\sqrt{\log _e\left(\frac{1}{x^2-4 x+4}\right)}+\sin ^{-1}\left(x^2-2\right)$ is
3. For all $n \in N$, if $n\left(n^2+3\right)$ is divisible by $k$, then the maximum value of $k$ is
4. If $a$ is the determinant of the adjoint of the matrix $\left[\begin{array}{lll}1 & 1 & 2 \\ 1 & 2 & 3 \\ 2 & 3 & 3\end{ 5. Consider two systems of 3 linear equations in 3 unknowns $A X=B$ and $C X=D$. If $A X=B$ has unique solution $D$ and $C 6. $f(x)$ is an $n$th degree polynomial satisfying $f(x)=\frac{1}{2}\left|\begin{array}{cc}f(x) & f\left(\frac{1}{x}\right) 7. If the point $P$ denotes the complex number $z=x+i y$ in the argand plane and $\frac{z-(2-i)}{z+(1+2 i)}$ is purely imag 8. If $(\sqrt{3}-i)^n=2^n, n \in N$, then the least possible value of $n$ is 9. $$ (1+\sqrt{5}+i \sqrt{10-2 \sqrt{5}})^5= $$ 10. The number of solutions of the equation $\sqrt{3 x^2+x+5}=x-3$ is 11. The set of all real values of $x$ for which $\frac{x^2-1}{(x-4)(x-3)} \geq 1$ is 12. If $\alpha, \beta$ and $\gamma$ are the roots of the equation $2 x^3+3 x^2-5 x-7=0$, then $\frac{1}{\alpha^2}+\frac{1}{\ 13. Two roots of the equation, $a x^4+b x^3+c x^2+d x+e=0$ are positive and equal. If the product of the other two real root 14. The number of integers between 10 and 10,000 such that in every integer every digit is greater than its immediate precee 15. All letters of the word 'AGAIN' are permuted in all possible ways and the words so formed (with or without meaning) are 16. The number of ways in which a cricket team of 11 members can be formed out of 6 batsmen, 6 bowlers, 4 all-rounders and 4 17. If $y=\frac{3}{4}+\frac{3 \cdot 5}{4 \cdot 8}+\frac{3 \cdot 5 \cdot 7}{4 \cdot 8 \cdot 12}+\ldots+\infty$, then 18. Sum of the coefficients of $x^4$ and $x^6$ in the expansion of $\left(1+x-x^2\right)^6$ is 19.
If $\frac{3 x^3-7 x+1}{(x-2)^5}=\frac{A}{x-2}+\frac{B}{(x-2)^2}+\frac{C}{(x-2)^3}+\frac{D}{(x-2)^4}+\frac{E}{(x-2)^5}, 20. $$ \tan \frac{2 \pi}{7} \cdot \tan \frac{4 \pi}{7}+\tan \frac{4 \pi}{7} \cdot \tan \frac{\pi}{7}+\tan \frac{\pi}{7} \cdo 21. $$ \cos 13^{\circ} \sin 17^{\circ} \sin 21^{\circ} \cos 47^{\circ}= $$ 22. $$
\sin \frac{\pi}{5}+\sin \frac{2 \pi}{5}+\sin \frac{3 \pi}{5}+\sin \frac{4 \pi}{5}=
$$
23. The sum of the solutions of $\cos x \sqrt{16 \sin ^2 x}=1$ in $(0,2 \pi)$ is
24. If $\cot \left(\cos ^{-1} x\right)=\sec \left\{\tan ^{-1}\left(\frac{a}{\sqrt{b^2-a^2}}\right)\right\}, b>a$ then $x=$ 25. If $\sinh ^{-1} x=\log 3$ and $\cosh ^{-1} y=\log \frac{3}{2}$, then $\tanh ^{-1}(x-y)=$ 26. In a $\triangle A B C$, if $a, b, c$ are in arithmetic progression and the angle $A$ is twice the angle $C$, then $\cos 27. In a $\triangle A B C, A, B$ and $C$ are in arithmetic progression, $r r_3=r_1 r_2$ and $c=10$, then $a^2+b^2+c^2=$
28. In a $\triangle A B C, \frac{2\left(r_1+r_3\right)}{a c(1+\cos B)}=$ 29. In a right angled triangle, if the position vector of the vertex having the right angle is $-3 \hat{\mathbf{i}}+5 \hat{\ 30. If the position vectors of the vertices $A, B, C$ of a triangle are $3 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}-\hat{\mathbf{ 31. If the vectors $2 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}-3 \hat{\mathbf{k}},-\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\ma 32. Assertion (A) For the lines $\mathbf{r}=\mathbf{a}+t \mathbf{b}$ and $\mathbf{r}=\mathbf{p}+s \mathbf{q}$, if $(\mathbf{ 33. Let $\mathbf{a}=4 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}$ and $\mathbf{b}$ be two perpendicular vectors in the $X O Y$-plan 34. The mean deviation about the mean for the following data is
$$ \begin{array}{llllll} \hline \text { Class Interval } & 0 35. A basket contains 5 apples and 7 oranges and another basket contains 4 apples and 8 oranges. If one fruit is picked out 36. Two cards are drawn from a pack of 52 playing cards one after the other without replacement. If the first card drawn is 37. An item is tested on a device for its defectiveness. The probability that such an item is defective is 0.3 . The device 38. In a school there are 3 sections $A, B$ and $C$. Section $A$ contains 20 girls and 30 boys, section $B$ contains 40 girl 39. If the probability distribution of a random variable $X$ is as follows, then the mean of $X$ is
$$ \begin{array}{ccccc} 40. If $X$ is a binomial variate with mean $\frac{16}{5}$ and variance $\frac{48}{25}$, then $P(X \leq 2)=$
41. $A(a, 0)$ is a fixed point and $\theta$ is a parameter such that $0 42. The point $P(4,1)$ undergoes the following transformations in succession :
(i) origin is shifted to the point $(1,6)$ by 43. $L_1 \equiv a x-3 y+5=0$ and $L_2 \equiv 4 x-6 y+8=0$ are two parallel lines. If $p, q$ are the intercepts made by $L_1= 44. If $(h, k)$ is the image of the point $(2,-3)$ with respect to the line $5 x-3 y=2$, then $h+k=$
45. If the pair of lines $a x^2-7 x y-3 y^2=0$ and $2 x^2+x y-6 y^2=0$ have exactly one line in common and ' $a$ ' is an int 46. If the angle between the pair of lines $2 x^2+2 h x y+2 y^2-x+y-1=0$ is $\tan ^{-1}\left(\frac{3}{4}\right)$ and $h$ is 47. If the equation of the circle passing through the point $(8,8)$ and having the lines $x+2 y-2=0$ and $2 x+3 y-1=0$ as it 48. If $2 x-3 y+1=0$ is the equation of the polar of a point $P\left(x_1, y_1\right)$ with respect to the circle $x^2+y^2-2 49. If a unit circle $S \equiv x^2+y^2+2 g x+2 f y+c=0$ touches the circle $S^{\prime} \equiv x^2+y^2-6 x+6 y+2=0$ externall 50. $3 x+4 y-43=0$ is a tangent to the circle $S \equiv x^2+y^2-6 x+8 y+k=0$ at a point $P$. If $C$ is the centre of the cir 51. If the radical axis of the circles $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 52. Tangents are drawn at three points $P\left(t_1\right), Q\left(t_2\right), R\left(t_3\right)$ on the parabola $y^2=x$. Le 53. The area (in sq. units) of the triangle formed by the tangent and normal to the ellipse $9 x^2+4 y^2=72$ at the point $( 54. If $3 \sqrt{2} x-4 y=12$ is a tangent to the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ and $\frac{5}{4}$ is its ecce 55. If the normal drawn to the hyperbola $x y=16$ at $(8,2)$ meets the hyperbola again at a point $(\alpha, \beta)$, then $| 56. The locus of a point at which the line joining the points $(-3,1,2),(1,-2,4)$ subtends a right angle, is 57. If $A(1,2,3), B(2,3,-1), C(3,-1,-2)$ are the vertices of a $\triangle A B C$, then the direction ratios of the bisector 58. Let $A=(2,0,-1), B=(1,-2,0), C=(1,2,-1)$ and $D=(0,-1,-2)$ be four points.
If $\theta$ is the acute angle between the pl 59. $[x]$ represents the greatest integer function. If $\mathop {\lim }\limits_{x \to 0 + } \frac{\cos [x]-\cos (k x-[x])}{x 60. $$ \mathop {\lim }\limits_{x \to 0} \frac{x \tan 2 x-2 x \tan x}{(1-\cos 2 x)^2}= $$ 61. If $f(x)=\left\{\begin{array}{cl}\frac{\left(e^{a x}-1\right) \log (1+x)}{\sin ^2 x}, & \text { if } x>0 \\ 2, & \text { 62. If $y=\tan ^{-1}\left(\frac{3 x-x^3}{1-3 x^2}\right)+\tan ^{-1}\left(\frac{7 x}{1-12 x^2}\right)$, then at $x=0, \frac{d 63. If $y=\sqrt{\frac{x^4 \sqrt{3 x-5}}{\left(x^2-3\right)(2 x-3)}}$, then $\left(\frac{d y}{d x}\right)_{x=2}=$ 64. If $x^2+y^2+\sin y=4$, then the value of $\frac{d^2 y}{d x^2}$ at $x=-2$ is 65. If the surface area of a spherical bubble is increasing at the rate of $4 \mathrm{sq} . \mathrm{cm} / \mathrm{sec}$, the 66. The number of turning points of the curve $f(x)=2 \cos x-\sin 2 x$ in the interval $[-\pi, \pi]$ is 67. The radius and the height of a right circular solid cone are measured as 7 feet each. If there is an error of 0.002 ft f 68. If the slope of the tangent drawn at any point $(x, y)$ on a curve is $(x+y)$, then the equation of that curve is
69. $$ \int(\sqrt{\tan x}+\sqrt{\cot x}) d x= $$ 70. $\int \frac{\sqrt{x-2}}{2 x+4} d x=$ 71. If $\int x^{49}\left[\tan ^{-1} x^{50}+\frac{x^{50}}{1+x^{100}}\right] d x=\frac{x^n}{k} f(x)+c$, then
$$ f(x)-f\left(\s 72. $$ \int \frac{x}{\sqrt{x^2-2 x+5}} d x= $$ 73. For $0 74. $$ \int_{-2 \pi}^{2 \pi} \sin ^4(2 x) \cos ^6(2 x) d x= $$ 75. If $f(t)=\int_0^t \tan ^{(2 n-1)} x d x, n \in N$, then $f(t+\pi)=$ 76. $$ \int_0^2 x^8\left(\frac{4}{x^2}-1\right)^{\frac{5}{2}} d x= $$ 77. The area (in sq. units) of the region bounded by the curves $y=x^2$ and $y=8-x^2$ is 78. The solution of the differential equation $x^2(y+1) \frac{d y}{d x}+y^2(x+1)^2=0$, when $y(1)=2$, is 79. The general solution of the differential equation $\frac{d y}{d x}=\frac{2 x+y-3}{2 y-x+3}$ 80. If $x \log x \frac{d y}{d x}+y=\log x^2$ and $y(e)=0$, then $y\left(e^2\right)=$
Physics
1. If the error in the measurement of the surface area of a sphere is $1.2 \%$, then the error in the determination of the 2. A body starts from rest with uniform acceleration and its velocity at a time of ' $n$ ' seconds is ' $v$ '. The total di 3. If the range of a body projected with a velocity of $60 \mathrm{~ms}^{-1}$ is $180 \sqrt{3} \mathrm{~m}$, then the angle 4. If the height of a projectile at a time of 2 s from the beginning of motion is 60 m , then the time of flight of the pro 5. A disc of mass 0.2 kg is kept floating in air without falling by vertically firing bullets each of mass 0.05 kg on the d 6. Two bodies $A$ and $B$ of masses 1.5 kg and 3 kg are moving with velocities $20 \mathrm{~ms}^{-1}$ and $15 \mathrm{~ms}^ 7. If a force $\mathbf{F}=(3 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}) \mathrm{N}$ acting on a body displaces it from point $(1 8. A body moving along a straight line collides another body of same mass moving in the same direction with half of the vel 9. If a solid sphere is rolling without slipping on a horizontal plane, then the ratio of its rotational and total kinetic 10. As shown in the figure, two thin coplanar circular discs $A$ and $B$ each of mass $M^{\prime}$ and radius ' $r$ ' are at 11. The time period of a simple pendulum on the surface of the Earth is $T$. If the pendulum is taken to a height equal to h 12. A particle is executing simple harmonic motion starting from its mean position. If the time period of the particle is 1. 13. If the escape velocity of a body from the surface of the Earth is $11.2 \mathrm{~km} \mathrm{~s}^{-1}$, then the orbital 14. In a water tank, an air bubble rises from the bottom to the top surface of the water. If the depth of the water in the t 15. A wire of length 0.5 m and area of cross-section $4 \times 10^{-6} \mathrm{~m}^2$ at a temperature of $100^{\circ} \math 16. A wire is stretched 1 mm by a force $F$. If a second wire of same material, same length and 4 times the diameter of the 17. The temperature of water of mass 100 g is rasied from $24^{\circ} \mathrm{C}$ to $90^{\circ} \mathrm{C}$ by adding steam 18. When 80 J of heat is supplied to a gas at constant pressure, if the work done by the gas is 20 J , then the ratio of the 19. A refrigerator of coefficient of performance 5 that extracts heat from the cooling compartment at the rate of 250 J per 20. In a container of volume $16.62 \mathrm{~m}^3$ at $0{ }^{\circ} \mathrm{C}$ temperature, 2 moles of oxygen 5 moles of ni 21. If a travelling wave is given by $y(x, t)=0.5 \sin (70.1 x-10 \pi t)$, where $x$ and $y$ are in metre the time $t$ is in 22. The ratio of the focal lengths of a convex lens when kept in air and when it is immersed in a liquid is $1: 2$. If the r 23. The path difference between two waves given by the equations
$y_1=a_1 \sin \left(\omega t-\frac{2 \pi x}{\lambda}\right) 24. The sum of two point positive charges separated by a distance of 1.5 m in air is $25 \mu \mathrm{C}$. If the electrostat 25. The energy stored in a capacitor of capacitance $10 \mu \mathrm{~F}$ when charged to a potential of 6 kV is
26. A parallel plate capacitor has plates of area $0.4 \pi \mathrm{~m}^2$ and spacing of 0.5 mm . If a slab of thickness 0.5 27. In the given circuit, the potential difference across the plates of the capacitor $C$ in steady state is 28. The potential difference across a conducting wire of length 20 cm is 30 V . If the electron mobility is $2 \times 10^{-6 29. A maximum current of 0.5 mA can pass through a galvanometer of resistance $15 \Omega$. The resistance to be connected in 30. Two charged particles of specific charges in the ratio 2:1 and masses in the ratio $1: 4$ moving with same kinetic energ 31. A sample of paramagnetic salt contains $2 \times 10^{24}$ atomic dipoles each of dipole moment $15 \times 10^{-23} \math 32. A coil of resistance $200 \Omega$ is placed in a magnetic field. If the magnetic flux $\phi$ (in weber) linked with the 33. If the voltage and current in an AC circuit are respectively $50 \sin (50 t) \mathrm{V}$ and $50 \sin \left(50 t+\frac{\ 34. The oscillating electric and magnetic field vectors of an electromagnetic wave are along 35. A laser produces a beam of light of frequency $5 \times 10^{14}$ Hz with an output power of 33 mW . The average number o 36. The ratio of energies of photons produced due to transition of an electron in hydrogen atom from second energy level to 37. The half life of a radioactive substance is 10 minutes. If $n_1$ and $n_2$ are the number of atoms decayed in 20 and 30 38. If $X, Y$ and $Z$ are the sizes of the emitter, base and collector of a transistor respectively, then
39. The logic gate equivalent to the circuit given in the figure is 40. If the ratio of the maximum and minimum amplitudes of an amplitude modulated wave is $7: 3$, then the modulation index i
1
AP EAPCET 2025 - 24th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$\int \frac{\sqrt{x-2}}{2 x+4} d x=$
A
$\sqrt{x-2}-\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{x-2}}{2}\right)+C$
B
$\sqrt{x-2}-2 \tan ^{-1}\left(\frac{\sqrt{x-2}}{2}\right)+C$
C
$\sqrt{x-2}+2 \tan ^{-1}\left(\frac{\sqrt{x-2}}{2}\right)+C$
D
$\sqrt{x-2}+\frac{1}{2} \tan ^{-1}\left(\frac{\sqrt{x-2}}{2}\right)+C$
2
AP EAPCET 2025 - 24th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
If $\int x^{49}\left[\tan ^{-1} x^{50}+\frac{x^{50}}{1+x^{100}}\right] d x=\frac{x^n}{k} f(x)+c$, then
$$ f(x)-f\left(\sqrt[k]{x^n}\right)= $$
A
$k+n$
B
$k-n$
C
$1 / k$
D
$1 / n$
3
AP EAPCET 2025 - 24th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
$$ \int \frac{x}{\sqrt{x^2-2 x+5}} d x= $$
A
$\sqrt{x^2-2 x+5}+\sinh ^{-1}\left(\frac{x-1}{2}\right)+C$
B
$\frac{1}{2} \sqrt{x^2-2 x+5}+\sin ^{-1}\left(\frac{x-1}{2}\right)+C$
C
$2 \sqrt{x^2-2 x+5}+\cosh ^{-1}\left(\frac{x-1}{2}\right)+C$
D
$\sqrt{x^2-2 x+5}-\cos ^{-1}\left(\frac{x-1}{2}\right)+C$
4
AP EAPCET 2025 - 24th May Morning Shift
MCQ (Single Correct Answer)
+1
-0
For $0 < x < 1, \int\left[\tan ^{-1}\left(1-x+x^2\right)+\tan ^{-1}(1-x)\right] d x=$
A
$x \cot ^{-1} x+\log \sqrt{1+x^2}+C$
B
$x \tan ^{-1} x-\log \left(1+x^2\right)+C$
C
$x \cot ^{-1} x+\frac{3}{4} \log \left(1+x^2\right)+C$
D
$x \tan ^{-1} x-\frac{3}{4} \log \sqrt{1+x^2}+C$
Paper Analysis
Total Questions
Chemistry 40
Mathematics 80
Physics 40
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