TS EAMCET 2023 (Online) 13th May Evening Shift | TS EAMCET Year Wise Previous Years Questions

Chemistry

1. What is the approximate angular momentum (in J s ) of electron in hydrogen atom in its ground state? $$ \left(h=6.625 \t 2. The energy of electron in hydrogen atom when present in $n=1, n=2$ and $n=3$ will be in the ratio of 3. What is the correct order with respect to metallic property of Zr, Cd, Sn, Sr? 4. Identify the number of molecules in which the central atom has one lone pair of electrons from the following list. $$ \m 5. In which of the following molecules, the number of lone pairs of electrons on central atom and the number of $d$-orbital 6. 4 g of an ideal gas $A$ (molar mass $=M_A$ ) present in a vessel of volume $V$ litre exerted a pressure of 5 atm at 300 7. The sum of three values $12.0,19.034$ and 2.0143 is equal to $X$. The number of significant figures in $X$ is 8. In. Observe the following properties. Molar volume II. Mass III. Internal energy IV. Volume v. Enthalpy VI. Temperatur 9. 229, $\mathrm{At} T(\mathrm{~K}), K_C$ value for the reaction, $\frac{1}{3} \mathrm{~N}_2(g)+\mathrm{H}_2(g) \rightlefth 10. Identify the correct statements from the following. A. In photosynthesis reaction, water is oxidised to oxygen. B. An ex 11. Which one of the following statements is not correct? 12. Thermal decomposition of lithium nitrate gives 13. Consider the following statements about group 13 elements. A. $\mathrm{AlCl}_3$ gets stability by forming a dimer. B. $\ 14. What is the correct order of melting temperature of $\mathrm{C}, \mathrm{Si}, \mathrm{Ge}$ ? 15. $$ \text { The IUPAC name of the following compound is } $$ 16. The delocalisation of $\sigma$ electrons of C-H bond of an alkyl group with the $\pi$ electrons of benzene is observed i 17. An alkene $X\left(\mathrm{C}_6 \mathrm{H}_{12}\right)$ on ozonolysis gave acetaldehyde and ethyl methyl ketone. What is 18. $$ \text { What is } X \text { in the following reaction sequence? } $$ 19. A compound is formed by elements $A, B$ and O . Atoms of oxygen form ccp lattice. Atoms of $A$ (cation) occupy $\frac{1} 20. Liquids $A$ and $B$ form an ideal solution. The vapour pressures of $A$ and $B$ are 50 and 32 mm Hg respectively at 300 21. $A$ and $B$ are two metals. The standard reduction potential of $A^{+}(a q) / A(s)$ and $B^{+}(a q) / B(s)$ are -0.5 V a 22. For a zero order reaction $A \rightarrow$ product, a plot of $[A]$ (on $y$-axis) and time (on $x$-axis) gave a straight 23. $$ \text { Match the following. } $$ $$ \begin{array}{llll} \hline & \text { List I } & & \text { List II } \\ \hline \t 24. $$ \begin{aligned} 4 \mathrm{Ag}(s)+8 \mathrm{CN}^{-}(a q) & +2 \mathrm{H}_2 \mathrm{O}(a q)+\mathrm{O}_2(g) \longright 25. Which one of the following statements is correct? 26. Which oxo-acid of sulphur contains $\mathrm{S}-\mathrm{O}-\mathrm{S}$ bond? 27. Which of the following reaction gives nitrogen (II) oxides as one of the products? 28. Identify the correct pairs in which the chemical substance given is correctly matched its use Chemical substance 29. Observe the following ions $$ \mathrm{V}^{2+}, \mathrm{Zn}^{2+}, \mathrm{Cu}^{2+}, \mathrm{Fe}^{2+}, \mathrm{Fe}^{3+}, \ 30. Identify the correct set for $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_6\right]^{3+}$ ion. (Hybridisation of $\mathrm 31. Identify the correct statement from the following. A. Glyptal is made from the monomers ethylene glycol and phthalic aci 32. A vitamin $X$ is soluble in fat and its source is egg yolk. Deficiency of $X$ causes the disease 33. Identify the pair of drugs which act as tranquilizers 34. An alkyl halide $X\left(\mathrm{C}_4 \mathrm{H}_9 \mathrm{Br}\right)$ undergoes nucleophilic substitution by $\mathrm{S} 35. Assertion (A) $\mathrm{p} K_a$ of phenol is 4.19 and that of benzoic acid is 10 . Reason (R) Phenoxide ion is stabilised 36. In which of the following pairs reactant is correctly matched with reagent that would form benzaldehyde as product? 37. An alkene $X$ with formula $\mathrm{C}_4 \mathrm{H}_8$ does not exhibit geometrical isomerism. In the conversion of $X$ 38. $$ \text { Which of the following reaction is feasible? } $$ 39. The sequence of reagents which convert $p$-methyl aniline to $p$-methyl benzoic acid are 40. An amine $(X)$ reacts with $p$-toluene sulphonyl chloride to give the product $Y$, which is insoluble in alkali. The pro

Mathematics

1. Which one of the following functions is a bijection? 2. The domain of the real valued function $f(x)=\frac{\sqrt{|x|-x}}{\sqrt{x-[x]}}$ is 3. The range of the function defined by $$ f(x)=\left\{\begin{array}{lc} 2 x-3, & \text { if } x1 \end{array}\right. $$ 4. If $A=\left[\begin{array}{lll}b & a & 0 \\ c & 0 & b \\ a & a & b\end{array}\right]$ and $B=\left[\begin{array}{lll}0 & 5. If $A=\left[\begin{array}{lll}1 & a & 3 \\ b & 2 & c \\ 3 & d & 4\end{array}\right]$ is a symmetric matrix and $B=\left[ 6. If the inverse of the matrix $A=\left[\begin{array}{ccc}-1 & -3 & -2 \\ 0 & 1 & 2 \\ 3 & 4 & 5\end{array}\right]$ is $A^ 7. If $x=\alpha, y=\beta, z=\gamma$ is the unique solution of the system of linear equations $2 x-3 y+5 z=12,5 x+2 y+3 z=11 8. If $i^2=-1$, then $(1+\sqrt{3} i)^{2022}-(\sqrt{3}-i)^{2022}=$ 9. If $\left(\frac{\sqrt{3}+i}{\sqrt{3}-i}\right)^4+\left(\frac{\sqrt{3}-i}{\sqrt{3}+i}\right)^4=r$ cis $\theta$, then one 10. If $z=x+i y$ and the point $P$ in the argand plane represents $z$, then the locus of $z$ satisfying the equation $|z-2|+ 11. One of the values of $(\sqrt{3}-i)^{2 / 5}$ is 12. If $\alpha, \beta, \gamma$ and $\delta$ are the roots of the equation $x^4+x^2+1=0$ such that $\alpha+\beta=-1, \gamma+\ 13. Let the equations $a x^2-7 x+c=0$ and $a x^2+5 x-c=0$ have a common root and $a c \neq 0$. If 3 is a root of $a x^2-7 x+ 14. The set of all values of $x$ for which the inequalities $x^2-7 x+10 \geq 0$ and $2 x+3-x^2>0$ hold simultaneously is 15. If $\alpha, \beta, \gamma$ are the roots of the equation $2 x^3+x^2-13 x+6=0$, then $\alpha^3+\beta^3+\gamma^3=$ 16. If $\alpha, \beta, \gamma$ are the real roots of the equation $18 x^3-15 x^2-4 x+4=0$ such that $\alpha=\beta$ and $\alp 17. If $\alpha$ is a multiple root of the equation $x^5-6 x^4+11 x^3-2 x^2-12 x+8=0$, then $3 \alpha^2-2 \alpha+1=$ 18. All the letters of the word 'INDEED' are taken and permuted in all possible ways to form distinct 6 letter strings (word 19. All possible 5-digit numbers each having 5 distinct digits are formed using the digits $1,2,3,5,6,8$. Among them, the nu 20. The total number of ways of forming a committee of 5 members out of 7 Indians, 6 Americans, 5 Russians and 4 Australians 21. The numerically greatest term in the binomial expansion of $(2 x-3 y)^5$, when $x=\frac{3}{2}$ and $y=\frac{2}{3}$ is 22. When $3^{2023}$ is divided by 16 , the remainder obtained is 23. If $3 x=1+\frac{5}{8}+\frac{5}{8} \cdot \frac{9}{13}+\frac{5}{16}+\ldots$, then $x^4+4 x^3+6 x^2+4 x=$ 24. If $\frac{2 x^3+3 x^2+3 x+5}{\left(x^2+1\right)\left(x^2+2\right)}$ is expanded in terms of the powers of $x$, then the 25. $$ \sin 6^{\circ}+\sin 54^{\circ}+\sin 126^{\circ}+\cos 156^{\circ}= $$ 26. If $\tan \alpha=\frac{-12}{5}, \cot \beta=\frac{7}{24}, \alpha$ does not belong to second quadrant and $\beta$ does not 27. $\cos \frac{\pi}{7} \cos \frac{2 \pi}{7} \cos \frac{3 \pi}{7} \cos \frac{\pi}{14} \cos \frac{3 \pi}{14} \cos \frac{5 \pi 28. If $\sinh x=-\frac{4}{3}$, then $\sinh 2 x+\cosh 2 x=$ 29. In $\triangle A B C$, if $b=6, c=7$ and $\tan \frac{A}{2}=\frac{1}{\sqrt{6}}$, then the inradius of $\triangle A B C$ is 30. In $\triangle A B C$, if $a=7, b=8$ and $c=9$, then $\frac{1}{r_1^2}+\frac{1}{r_2^2}+\frac{1}{r_3^2}=$ 31. II. If the points with position vectors $\hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}, 2 \hat{\mathbf{i}}-\hat{\ma 32. Let $\mathbf{a}, \mathbf{b}, \mathbf{c}$ be three non-coplanar vectors and $L$ be the line passing through the points $\ 33. Let $\mathbf{a}=\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}, \mathbf{b}=6 \hat{\mathbf{i}}+2 \hat{\mathbf{j}} 34. Let $\mathbf{a}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}, \mathbf{b}=3 \hat{\mathbf{i}}-\hat{\mathbf{j}}+5 35. The volume of the tetrahedron with $\hat{\mathbf{i}}-\lambda \hat{\mathbf{j}}+\hat{\mathbf{k}}$, $\lambda \hat{\mathbf{i 36. If $M$ and $\sigma^2$ represent respectively the mean deviation from the mean and the variance for the data $1,3,5,7$, $ 37. A bag contains 3 red, 5 black and 7 blue balls. If three balls are drawn at random simultaneously from the bag, then the 38. In a game, two dice are thrown simultaneously by a person $A$ and two cards are drawn at random simultaneously from a pa 39. Two players $A$ and $B$ alternatively toss 3 coins simultaneously. The player who gets 2 heads and 1 tail first, wins th 40. If $X$ is a Poisson variate satisfying the condition $3 P(X=2)=P(X=4)$, then $P(X=6)=$ 41. Let $A=(1,2), B=(2,1), C=(-1,-1)$ be three points. If $P$ is a point such that the area of the quadrilateral $P A B C$ i 42. When the origin is shifted to the point $(h, k)$ by translating the coordinates axes, the equation $S \equiv 2 x^2-x y+y 43. Two points $P(a, 2)$ and $Q(1, b)$ lie on either side of the line $2 x-3 y+1=0$. If $P$ is the point of intersection of 44. Let the angle between the lines $x-2 y+3=0$ and $k x-y+2=0$ be $45^{\circ}$. If $k_1, k_2\left(k_1>k_2\right)$ are two d 45. If the lines $4 x+3 y-k=0,2 x+y+3=0$ and $3 x+2 y+k=0$ are concurrent, then the perpendicular distance from the point of 46. Let $A(1,3)$ and $B(2,5)$ be two points and $C(h, k)$ be a point such that $B C$ is perpendicular to $A C$. If $\angle C 47. Let the line $2 x-3 y-1=0$ intersect the curve $x^2+2 x y+5 y^2+2 x+3 y-1=0$ in distinct points $A$ and $B$. If ' $O$ ' 48. The equation of the circle inscribed in a square formed by the lines $x+y-2=0, x+y-6=0, x-y+1=0$ and $x-y+5=0$ is 49. Let the circle $S \equiv x^2+y^2+2 g x+2 f y+c=0$ touch the positive $X$-axis and the positive $Y$-axis. Let $(2,4)$ be 50. If the equation $2 x-3 y+3=0,2 x+y+1=0$ and $6 x+4 y+1=0$ represent the sides of a triangle, then the equation of the ci 51. If $T_1 T^{\prime}{ }_1$ and $T_2 T_2^{\prime}$ are the common tangents of the circles $S \equiv x^2+y^2-2 x-4 y-4=0$ an 52. A circle $S \equiv x^2+y^2+2 g x+2 f y+4=0$ cuts the circle $x^2+y^2-4 x-4 y-4=0$ orthogonally and makes an angle of $60 53. If the circle $S \equiv x^2+y^2+2 g x+2 f y+c=0$ cuts each of the three circles $x^2+y^2+4 x+4 y+7=0$, $x^2+y^2-4 x+4 y+ 54. If the line $2 x+3 y+n=0$ is a tangent to the parabola $y^2=8 x$, then the equation of the normal drawn at the point $(2 55. $a x-y+c=0$ is the equation of the common tangent to the parabola $y^2=8 \sqrt{5} x$ and the circle $x^2+y^2=1$. If this 56. In an ellipse, the distance from one of the foci to its corresponding end of the major axis is $4-\sqrt{7}$ and the dist 57. If the equations $x=1+2 \cos \theta, y=2+\sin \theta, 0 \leq \theta 58. If the equation $x+y+n=0$ represents a normal to the hyperbola $\frac{x^2}{6}-\frac{y^2}{2}=1$, then $n=$ 59. $A(1,2,3), B(2,3,1)$ and $C(3,1,2)$ are three points. If the point $P$ divides $A B$ in the ratio $1: 2$ and the point $ 60. If the image of the point $(1,-2,1)$ with respect to the line passing through the points $B(1,1,2)$ and $C(2,2,1)$ is $( 61. A plane $\pi$ passing through the point $(1,1,1)$ is perpendicular to the line joining the points $(6,3,2)$ and $(1,-4,- 62. $$ \mathop {\lim }\limits_{x \to 2} \frac{\sqrt[3]{6+x}-\sqrt[3]{10-x}}{x-2}= $$ 63. $\mathop {\lim }\limits_{x \to 0} \frac{\tan ^4 x-\sin ^4 x}{x^6}=$ 64. If $f(x)=\sqrt{\log \left(x^2+x+1\right)+\sqrt{\cosh (2 x-3)}}$, then $f^{\prime}(0)=$ 65. If $x=\cos ^3 \theta-\sin ^3 \theta$ and $y=\sqrt[3]{\cos \theta}-\sqrt[3]{\sin \theta}$, then the value of $\frac{d y} 66. If $2 x^2+3 x y-y^2+4 x-5 y+6=0$, then the value of $\frac{d y}{d x}$ at $(x, y)=(1,-2)$ is 67. The diameter of a sphere is measured as 42 cm . If there is an error of $1 / 77 \mathrm{~cm}$ in measuring it, then the 68. For $h, k \in N$, let $P(h, k)$ be the point of intersection of the curves $x^2 y-x^3=8$ and $y^3-x y^2=32$. If $\theta$ 69. If the absolute maximum and absolute minimum values of the function $f(x)=x^3-2 x^2+x-3$ defined on $[0,2]$ are $M$ and 70. $\int \frac{1}{\left(x+\frac{2}{x}\right) \sqrt{x^4+4 x^2+3}} d x=$ 71. If $\frac{3 \pi}{2} 72. If $\int \frac{2 \sin 2 x-3 \cos x}{2 \sin ^2 x-3 \sin x+4} d x=f(x)+C$, where $C$ is the constant of integration, then 73. $\int \frac{2 x+3}{\sqrt{3 x^2-2 x+1}} d x=$ 74. $$ \int_0^\pi \frac{x \cos ^2 x}{1+\sin x} d x= $$ 75. If $[x]$ represents greatest integer function, then $$ \int_{-2}^2[2-x] d x= $$ 76. $$ \int_0^2 \frac{x}{(2-x)^{\frac{3}{4}}} d x= $$ 77. $$ \int_0^2 x^3(2-x)^4 d x= $$ 78. If the slope of the tangent drawn at any point $(x, y)$ to the curve $y=f(x)$ is $3 x^2-5$ and $f(1)=2$, then the tangen 79. The general solution of the differential equation $(3 x-4 y)(d x-3 d y)+(6 d x-4 d y)=0$ is 80. The general solution of the differential equation $(\sec x+\tan x) \frac{d y}{d x}+\left(\sec ^2 x+\sec x \tan x\right)

Physics

1. The ratio of relative strengths of the gravitational force and the electromagnetic force between two charged particles i 2. The efficiency of an engine is given by $\eta=\frac{\alpha \beta}{\sin \theta} \cdot \log _e \frac{\beta x}{k T}$, where 3. A bird flies with a velocity $(t-2) \mathrm{ms}^{-1}$ along a straight line, where $t$ is the time in seconds. The dista 4. A car is travelling with linear velocity $v$ on a circular road of radius $r$. If its velocity is increasing at a rate o 5. Two blocks of masses $w_1$ and $w_2$ are suspended from the ends of a light string passing over a smooth fixed pulley. I 6. A body is moved along a straight line by an engine which delivers a constant power. The distance moved by the body in ti 7. A body of mass 3 kg is moving under the action of a force which causes a displacement of $\left(t^3 / 3\right) \mathrm{m 8. Two blocks of masses 2 kg and 1 kg are tied to the ends of a string which passes over a light frictionless pulley. The b 9. A particle of mass $m$ is moving along a line $y=x+a$ with a constant velocity $v$. The angular momentum of the particle 10. A force of 6.4 N stretches a vertical spring by 0.1 m . If it were to oscillate with a period of $\pi / 4$, then the mas 11. The ratio of orbital velocity of a body near to the surface of a planet and escape velocity of a body from the surface o 12. The length of a metal rod at $30^{\circ} \mathrm{C}$ is 30 cm . If its temperature is raised to $105^{\circ} \mathrm{C}$ 13. The angle of contact is $120^{\circ}$ when a cylindrical rod is vertically placed in a liquid. If the same rod is placed 14. In a well the pressure at a point 10 m below the surface of water is $\left(g=10 \mathrm{~ms}^{-2}\right)$ 15. The heat energy required to convert 10 kg of ice at $-10^{\circ} \mathrm{C}$ into water at $0^{\circ} \mathrm{C}$ is (sp 16. If the reading in Fahrenheit scale is twice the reading in Celsius scale, then the reading in Fahrenheit scale is 17. When some amount of heat energy is supplied to a monatomic gas, the percentage of heat energy used for increasing the in 18. The average energy possessed by an oscillator at a temperature 300 K is (Boltzmann constant $=1.38 \times 10^{-23} \math 19. A wave is given by $y=5 \times 10^{-3} \sin \left(12.5 \pi x-\frac{\pi}{2} t\right)$. Then its wavelength and time perio 20. A tuning fork $A$ of frequency 250 Hz and another tuning fork $B$ of frequency $x$ produced 5 beats per second when vibr 21. A convex lens forms a real image of a point object placed on its principal axis. If the upper half of the lens is painte 22. Two slits separated by a distance of 1 mm are illuminated with light of wavelength $6.5 \times 10^{-7} \mathrm{~m}$. The 23. Two conducting spheres of radii $r_1$ and $r_2$ are charged to the same surface charge density. The ratio of electric fi 24. Two electric charges $+2 \mu \mathrm{C}$ and $-4 \mu \mathrm{C}$ are separated by a distance 3 m in air. At a point $P$ 25. If the masses of three wires of same material are in the ratio of $1: 2: 3$ and their lengths are in the ratio of $3: 2: 26. As shown in the figure, in a Wheatstone's bridge, three resistances $P, Q$ and $R$ are connected in the three arms and t 27. A current $i$ flows in an infinitely long, straight and thin walled pipe, then 28. A closely wound solenoid of 80 cm long has 5 layers of windings of 400 turns each. The diameter of the solenoid is 1.8 c 29. The period of oscillation of a bar magnet at a place is 2 s . At the same place, the period of oscillation of another id 30. The self inductance of a coil depends on 31. A conducting circular coil is place in a uniform magnetic field with the magnetic field initially directed perpendicular 32. An alternating emf given by the equation $E=200 \sin (50 \pi t)$ (where, $E$ is in volts and $t$ is in seconds) is appli 33. The speed of electromagnetic waves in a medium is $1.5 \times 10^8 \mathrm{~ms}^{-1}$. If relative permittivity of that 34. Consider two black bodies $A$ and $B$ having equal surface area. On the surface of $A, n$ photons of frequency $f$ are i 35. A photon released by the transition of an electron from the second excited state to the ground state of Hydrogen atom is 36. The radius of a nucleus of mass number 27 is $R$. Which of the following is true about a nucleus whose radius is $2 R$ ? 37. The nucleus ${ }_{50}^{120} X$ undergoes the series of reactions given below: $$ { }_Z^A X \xrightarrow{\alpha \text {-d 38. In the logic circuit given below, if $X=1$ and $Y=1$, then the values of $P, Q$ and $R$ are 39. The symbol given below represents 40. A telephonic communication service is working at a carrier frequency of 20 GHz . Only $20 \%$ of it is utilised for tran

TS EAMCET 2023 (Online) 13th May Evening Shift

MCQ (Single Correct Answer)

-0

$$ \text { Which of the following reaction is feasible? } $$

TS EAMCET 2023 (Online) 13th May Evening Shift Chemistry - Alcohol, Phenols and Ethers Question 24 English Option 1

$$ \mathrm{H}_3 \mathrm{CCH}=\mathrm{CHCH}_2 \mathrm{OH} \xrightarrow{\mathrm{PCC}} \mathrm{H}_3 \mathrm{CCH}=\mathrm{CHCHO} $$

TS EAMCET 2023 (Online) 13th May Evening Shift Chemistry - Alcohol, Phenols and Ethers Question 24 English Option 3

$$ \mathrm{CH}_3 \mathrm{CH}_2 \mathrm{CH}_2 \mathrm{OH} \xrightarrow[\mathrm{H}^{+}]{\mathrm{KMnO}_4} \mathrm{H}_3 \mathrm{CCH}_2 \mathrm{CHO} $$

TS EAMCET 2023 (Online) 13th May Evening Shift

MCQ (Single Correct Answer)

-0

The sequence of reagents which convert $p$-methyl aniline to $p$-methyl benzoic acid are

$\mathrm{KMnO}_4 / \mathrm{H}^{+} ; \mathrm{NaNO}_2+\mathrm{HCl} ; \mathrm{Cu} / \mathrm{HCl}$

$\mathrm{NaNO}_2+\mathrm{HCl} / 273 \mathrm{~K} ; \mathrm{Cu} / \mathrm{HCl} ; \mathrm{KMnO}_4 / \mathrm{H}^{+}$

$\mathrm{NaNO}_2+\mathrm{HCl} / 273 \mathrm{~K}$; $\mathrm{CuCN} / \mathrm{KCN}$; $\mathrm{H}_3 \mathrm{O}^{+}$

$\mathrm{NaNO}_2+\mathrm{HCl} / 285 \mathrm{~K} ; \mathrm{KCN} ; \mathrm{H}_3 \mathrm{O}^{+}$

TS EAMCET 2023 (Online) 13th May Evening Shift

MCQ (Single Correct Answer)

-0

An amine $(X)$ reacts with $p$-toluene sulphonyl chloride to give the product $Y$, which is insoluble in alkali. The product of $X$ with benzoyl chloride is

TS EAMCET 2023 (Online) 13th May Evening Shift Chemistry - Compounds Containing Nitrogen Question 18 English Option 1

TS EAMCET 2023 (Online) 13th May Evening Shift Chemistry - Compounds Containing Nitrogen Question 18 English Option 2

$$ \mathrm{CH}_3 \mathrm{CH}_2 \mathrm{NHCOC}_6 \mathrm{H}_5 $$

TS EAMCET 2023 (Online) 13th May Evening Shift Chemistry - Compounds Containing Nitrogen Question 18 English Option 4

TS EAMCET 2023 (Online) 13th May Evening Shift

MCQ (Single Correct Answer)

-0

Which one of the following functions is a bijection?

$f: R-Z \rightarrow[0,1]$ defined by $f(x)=\sqrt{x-[x]}$. (Here $[x]$ represents the greatest integer function)

$f: R \rightarrow(-\infty, 2)$ defined by $f(x)=4 x-x^2-3$

$f:(5, \infty) \rightarrow R-\{0\}$ defined by $f(x)=\frac{1}{\sqrt{x-5}}$

$f:[0,4] \rightarrow[0,4]$ defined by $f(x)=\sqrt{16-x^2}$

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