Chemistry
1. The maximum number of electrons present in an orbital with $$n = 4, l = 3$$ is 2. Which quantum number provides information about the shape of an orbital? 3. In which of the following, elements are arranged in the correct order of their electron gain enthalpies? 4. In second period of the long form of the periodic table an element $$X$$ has second lowest first ionisation enthalpy and 5. The set of molecules in which the central atom is not obeying the octet rule is 6. The formal charges of atoms (1), (2) and (3) in the ion is 7. From the following plots, find the correct option.
8. How many grams of Mg is required to completely reduce $$100 \mathrm{~mL}, 0.1 \mathrm{~M} \mathrm{~NO}_3^{-}$$ solution 9. What is the oxidation state of S in the sulphur containing product of the following reaction?
$$\mathrm{SO}_3^{2-}(a q)+ 10. Observe the following properties :
Volume, enthalpy, density, temperature, heat capacity, pressure and internal energy. 11. Match the following.
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.tg td{border-color:black;border-style:solid;bor 12. Which of the following expression is correct? 13. The pH of 0.01 N lime water is 14. The empirical formula of calgon is 15. The pair of elements that form both oxides and nitrides, when burnt in air are 16. Among $$\mathrm{P}_4, \mathrm{~S}_8$$ and $$\mathrm{N}_2$$ the elements which undergo disproportionation when heated wit 17. Identify the correct statements about the anomalous behaviour of boron.
I. Boron trihalides can form dimeric structures. 18. The hybridisations of carbon in graphite, diamond and $$\mathrm{C}_{60}$$ are respectively 19. The major product of the following reaction is
20. Identify the ortho and para-directing groups towards aromatic electrophilic substitution reactions from the following li 21. Match List I with List II.
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.tg td{border-color:black;border-style:sol 22. Which of the following solids is not a molecular solid? 23. A solution containing 6.0 g of urea is isotonic with a solution containing 10 g of a non-electrolytic solute $$X$$. The 24. $$x \%(w / V)$$ solution of urea is isotonic with $$4 \%$$ $$(w / V)$$ solution of a non-volatile solute of molar mass $ 25. 38.6 amperes of current is passed for 100 seconds through an aqueous $$\mathrm{CuSO}_4$$ solution using platinum electro 26. The time required for completion of $$93.75 \%$$ of a first order reaction is $$x$$ minutes. The half-life of it (in min 27. The macromolecular colloids of the following are
I. Starch solution
II. Sulphur sol
III. Synthetic detergent
IV. Synthet 28. Assertion (A) Animal skins are colloidal in nature.
Reason (R) Animal skin has positively charged particles. 29. In the reaction of phosphorus with conc. $$\mathrm{HNO}_3$$, the oxidised and reduced products respectively are 30. Which of the following is formed when $$\mathrm{SO}_3$$ is absorbed by concentrated $$\mathrm{H}_2 \mathrm{SO}_4$$ ? 31. Assertion (A) Transition metals and their complexes show catalytic activity.
Reason (R) The activation energy of a react 32. The crystal field theory is successful in explaining which of the following?
I. Ligands as point charges.
II. Formation 33. Pernicious anemia is caused due to deficiency of which vitamin ? 34. Which of the following vitamins cannot be stored in the body? 35. Finkelstein reaction is used for the synthesis of 36. Which among the following will have highest density? 37. Identify the major product (Y) from the following reaction,
38. An aryl carboxylic acid on treatment with sodium hydrogen carbonate liberates a gaseous molecule. Identify the gas molec 39. Identify the major product of the following reaction.
40. Identify the major product of the following reaction,
Mathematics
1. $$\left\{x \in R / \frac{\sqrt{|x|^2-2|x|-8}}{\log \left(2-x-x^2\right)}\right.$$ is a real number $$\}=$$ 2. The domain of the real valued function $$f(x)=\sin \left(\log \left(\frac{\sqrt{4-x^2}}{1-x}\right)\right.$$ is 3. If $$A=\left[\begin{array}{cc}2 & -3 \\ -4 & 1\end{array}\right]$$, then $$\left(A^T\right)^2+(12 A)^T=$$ 4. If $$a, b, c$$ are respectively the 5 th, 8 th, 13 th terms of an arithmetic progression, then $$\left|\begin{array}{ccc 5. If $$A=\left[\begin{array}{ccc}1 & 0 & 0 \\ a & -1 & 0 \\ b & c & 1\end{array}\right]$$ is such that $$A^2=I$$, then 6. Let $$A=\left[\begin{array}{ccc}-2 & x & 1 \\ x & 1 & 1 \\ 2 & 3 & -1\end{array}\right]$$. If the roots of the equation 7. Multiplicative inverse of the complex number $$(\sin \theta, \cos \theta)$$ is 8. $$\sum_\limits{k=0}^{440} i^k=x+i y \Rightarrow x^{100}+x^{99} y+x^{242} y^2+x^{97} y^3=$$ 9. A true statement among the following identities is 10. If $$e^{i \theta}=\operatorname{cis} \theta$$, then $$\sum_\limits{n=0}^{\infty} \frac{\cos (n \theta)}{2^n}=$$ 11. If $$f(f(0))=0$$, where $$f(x)=x^2+a x+b, b \neq 0$$, then $$a+b=$$ 12. The sum of the real roots of the equation $$|x-2|^2+|x-2|-2=0$$ is 13. If the difference between the roots of $$x^2+a x+b=0$$ and that of the roots of $$x^2+b x+a=0$$ is same and $$a \neq b$$ 14. For what values of $$a \in Z$$, the quadratic expression $$(x+a)(x+1991)+1$$ can be factorised as $$(x+b)(x+c)$$, where 15. If a set $$A$$ has $$m$$-elements and the set $$B$$ has $$n$$-elements, then the number of injections from $$A$$ to $$B$ 16. In how many ways can the letters of the word "MULTIPLE" be arranged keeping the position of the vowels fixed? 17. The least value of $$n$$ so that $${ }^{(n-1)} C_3+{ }^{(n-1)} C_4>{ }^n C_3$$ 18. A natural number $$n$$ such that $$n!$$ ends in exactly 1000 zeroes is 19. If $$\frac{13 x+43}{2 x^2+17 x+30}=\frac{A}{2 x+5}+\frac{B}{x+6}$$, then $$A^2+B^2=$$ 20. If $$A+B+C=\pi, \cos B=\cos A \cos C$$, then $$\tan A \tan C=$$ 21. In a $$\triangle A B C,\left(\tan \frac{A}{2} \tan \frac{B}{2} \tan \frac{C}{2}\right)^2 \leq$$ 22. The value of $$\tan \left(\frac{7 \pi}{8}\right)$$ is 23. $$1+\sec ^2 x \sin ^2 x=$$ 24. In a $$\triangle A B C, 2(b c \cos A+a c \cos B+a b \cos C)=$$ 25. If $$4+6\left(e^{2 x}+1\right) \tanh x=11 \cosh x+11 \sinh x$$ then $$x=$$ 26. In a $$\triangle A B C, \frac{a}{b}=2+\sqrt{3}$$ and $$\angle C=60^{\circ}$$. Then, the measure of $$\angle A$$ is 27. If $$a=2, b=3, c=4$$ in a $$\triangle A B C$$, then $$\cos C=$$ 28. In a $$\triangle A B C$$
$$(b+c) \cos A+(c+a) \cos B+(a+b) \cos C=$$ 29. $$D, E, F$$ are respectively the points on the sides $$B C, C A$$ and $$A B$$ of a $$\triangle A B C$$ dividing them in 30. $$O A B C$$ is a tetrahedron. If $$D, E$$ are the mid-points of $$O A$$ and $$B C$$ respectively, then $$\mathbf{D E}=$$ 31. If $$\mathbf{a}+\mathbf{b}+\mathbf{c}=0$$ and $$|\mathbf{a}|=7,|\mathbf{b}|=5,|\mathbf{c}|=3$$ then the angle between $$ 32. If $$P$$ and $$Q$$ are two points on the curve $$y=2^{x+2}$$ in the rectangular cartesian coordinate system such that $$ 33. If the equation of the plane passing through the point $$A(-2,1,3)$$ and perpendicular to the vector $$3 \hat{i}+\hat{j} 34. If the mean of the data $$p, 6,6,7,8,11,15,16$$, is 3 times $$p$$, then the mean deviation of the data from its mean is 35. In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked randomly. The probability that it is neither red 36. For two events $$A$$ and $$B$$, a true statement among the following is 37. Five digit numbers are formed by using digits $$1,2,3,4$$ and 5 without repetition. Then, the probability that the rando 38. A manager decides to distribute ₹ 20000 between two employees $$X$$ and $$Y$$. He knows $$X$$ deserves more than $$Y$$, 39. Which of the following is not a property of a Binomial distribution? 40. In a Binomial distribution $$B(n, p)$$, if the mean and variance are 15 and 10 respectively, then the value of the param 41. Suppose $$P$$ and $$Q$$ are the mid-points of the sides $$A B$$ and $$B C$$ of a triangle where $$A(1,3), B(3,7)$$ and $ 42. Suppose $$\triangle A B C$$ is an isosceles triangle with $$\angle C=90^{\circ}, A=(2,3)$$ and $$B=(4,5)$$. Then, the ce 43. If the points of intersection of the coordinate axes and $$|x+y|=2$$ form a rhombus, then its area is 44. Suppose, in $$\triangle A B C, x-y+5=0, x+2 y=0$$ are respectively the equations of the perpendicular bisectors of the s 45. If the pair of straight lines $$9 x^2+a x y+4 y^2+6 x+b y-3=0$$ represents two parallel lines, then 46. A line passing through $$P(2,3)$$ and making an angle of $$30^{\circ}$$ with the positive direction of $$X$$-axis meets 47. For any real number $$t$$, the point $$\left(\frac{8 t}{1+t^2}, \frac{4\left(1-t^2\right)}{1+t^2}\right)$$ lies on a / a 48. The area of the circle passing through the points $$(5, \pm 2),(1,2)$$ is 49. The ratio of the largest and shortest distances from the point $$(2,-7)$$ to the circle $$x^2+y^2-14 x-10 y-151=0$$ is 50. A circle has its centre in the first quadrant and passes through $$(2,3)$$. If this circle makes intercepts of length 3 51. The image of the point $$(3,4)$$ with respect to the radical axis of the circles $$x^2+y^2+8 x+2 y+10=0$$ and $$x^2+y^2+ 52. Suppose a parabola passes through $$(0,4),(1,9)$$ and $$(4,5)$$ and has its axis parallel to the $$Y$$-axis. Then, the e 53. The focal distances of the point $$\left(\frac{4}{\sqrt{5}}, \frac{3}{\sqrt{5}}\right)$$ on the ellipse $$\frac{x^2}{4}+ 54. If the normal to the rectangular hyperbola $$x^2-y^2=1$$ at the point $$P(\pi / 4)$$ meets the curve again at $$Q(\theta 55. If the vertices and foci of a hyperbola are respectively $$( \pm 3,0)$$ and $$( \pm 4,0)$$, then the parametric equation 56. If $$x$$-coordinate of a point $$P$$ on the line joining the points $$Q(2,2,1)$$ and $$R(5,2,-2)$$ is 4, then the $$y$$- 57. If $$(2,3, c)$$ are the direction ratios of a ray passing through the point $$C(5, q, 1)$$ and also the mid-point of the 58. If the equation of the plane which is at a distance of $$1 / 3$$ units from the origin and perpendicular to a line whose 59. If $$[\cdot]$$ denotes greatest integer function, then $$\lim _\limits{x \rightarrow \frac{-3}{5}} \frac{1}{\dot{x}}\lef 60. If $$l, m(l 61. Let $$f(x)=\left\{\begin{array}{cl}\frac{1}{|x|}, & \text { for }|x|>1 \\ a x^2+b, & \text { for }|x| \leq 1\end{array}\ 62. If $$x \neq 0$$ and $$f(x)$$ satisfies $$8 f(x)+6 f(1 / x) =x+5$$, then $$\frac{d}{d x}\left(x^2 f(x)\right)$$ at $$x=1$ 63. $$\frac{d}{d x}\left(\lim _{x \rightarrow 2} \frac{1}{y-2}\left(\frac{1}{x}-\frac{1}{x+y-2}\right)\right)=$$ 64. If $$f(x)=\left\{\begin{array}{cc}\frac{x^2 \log (\cos x)}{\log (1+x)} & , \quad x \neq 0 \\ 0 & , x=0\end{array}\right. 65. The number of those tangents to the curve $$y^2-2 x^3-4 y+8=0$$ which pass through the point $$(1,2)$$ is 66. If the straight line $$x \cos \alpha+y \sin \alpha=p$$ touches the curve $$\left(\frac{x}{a}\right)^n+\left(\frac{y}{b}\ 67. Condition that 2 curves $$y^2=4 a x, x y=c^2$$ cut orthogonally is 68. A closed cylinder of given volume will have least surface area when the ratio of its height and base radius is 69. Two particles $$P$$ and $$Q$$ located at the points $$P\left(t, t^3-16 t-3\right), Q\left(t+1, t^3-6 t-6\right)$$ are mo 70. If $$f(x)=\int x^2 \cos ^2 x\left(2 x \tan ^2 x-2 x-6 \tan x\right) d x$$ and $$f(0)=\pi$$, then $$f(x)=$$ 71. If
$$\int \frac{e^{\sqrt{x}}}{\sqrt{x}}(x+\sqrt{x}) d x=e^{\sqrt{x}}[A x+B \sqrt{x}+C]+K$$ then $$A+B+C=$$ 72. If $$\int \frac{1+\sqrt{\tan x}}{\sin 2 x} d x=A \log \tan x+B \tan x+C$$, then $$4 A-2 B=$$ 73. $$\int \frac{1+\tan x \tan (x+a)}{\tan x \tan (x+a)} d x=$$ 74. If $$I_n=\int_0^{\pi / 4} \tan ^n x d x$$, then $$\frac{1}{I_2+I_4}+\frac{1}{I_3+I_5}+\frac{1}{I_4+I_6}=$$ 75. $$\int_0^{\pi / 4} e^{\tan ^2 \theta} \sin ^2 \theta \tan \theta d \theta=$$ 76. $$\int_{\pi / 4}^{5 \pi / 4}(|\cos t| \sin t+|\sin t| \cos t) d t=$$ 77. If $$f(x)=\max \{\sin x, \cos x\}$$ and $$g(x)=\min \{\sin x, \cos x\}$$, then $$\int_0^\pi f(x) d x+\int_0^\pi g(x) d x 78. If $$l$$ and $$m$$ are order and degree of a differential equation of all the straight lines at constant distance of $$P 79. If $$2 x-y+C \log (|x-2 y-4|)=k$$ is the general solution of $$\frac{d y}{d x}=\frac{2 x-4 y-5}{x-2 y+2}$$, then $$C=$$ 80. By eliminating the arbitrary constants from $$y=(a+b) \sin (x+c)-d e^{x+e+f}$$, then differential equation has order of
Physics
1. In SI units, $$\mathrm{kg}-\mathrm{m}^2 \mathrm{~s}^{-2}$$ is equivalent to which of the following? 2. An object moving along $$X$$-axis with a uniform acceleration has velocity $$\mathbf{v}=\left(12 \mathrm{cms}^{-1}\right 3. A force $$\mathbf{F}_1$$ of magnitude 4 N acts on an object of mass 1 kg , at origin in a direction $$30^{\circ}$$ above 4. $$y=\left(P t^2-Q t^3\right) \mathrm{~m}$$ is the vertical displacement of a ball which is moving in vertical plane. The 5. A cricket ball of mass 50 g having velocity $$50 \mathrm{~cm} \mathrm{~s}^{-1}$$ to stopped in 0.5 s. The force applied 6. Two masses $$M_1$$ and $$M_2$$ are arranged as shown in the figure. Let $$a$$ be the magnitude of the acceleration of th 7. A ball of mass 300 g is dropped from a height 10 m above a sandy ground. On reaching the ground, it penetrates through a 8. Two balls $$A$$ and $$B$$, of masses $$M$$ and $$2 M$$ respectively collide each other. If the ball $$A$$ moves with a s 9. A solid sphere of radius $$R$$ has its outer half removed, so that its radius becomes $$(R / 2)$$. Then its moment of in 10. Which of the following is not true about vectors $$\mathbf{A}, \mathbf{B}$$ and $$\mathbf{C}$$ ? 11. A body is executing S.H.M. At a displacement $$x$$ its potential energy is 9 J and at a displacement $$y$$ its potential 12. As shown in the figure, an iron block $$A$$ of volume $$0.25 \mathrm{~m}^3$$ is attached to a spring $$S$$ of unstretche 13. A uniform solid sphere of radius $$R$$ produces a gravitational acceleration of $$a_0$$ on its surface. The distance of 14. In a hydraulic lift, compressed air exerts a force $$F$$ on a small piston of radius 3 cm . Due to this pressure the sec 15. In a $$U$$-shaped tube the radius of one limb is 2 mm and that of other limb is 4 mm . A liquid of surface tension $$0.0 16. A steady flow of a liquid of density $$\rho$$ is shown in figure. At point 1, the area of cross-section is $$2 A$$ and t 17. A metal tape is calibrated at $$25^{\circ} \mathrm{C}$$. On a cold day when the temperature is $$-15^{\circ} \mathrm{C}$ 18. A gas is expanded from an initial state to a final state along a path on a $$p$$-$$V$$ diagram. The path consists of (i) 19. The temperature of the sink of a Carnot engine is 250 K . In order to increase the efficiency of the Carnot engine from 20. In non-rigid diatomic molecule with an additional vibrational mode 21. Speed of sound in air near room temperature is approximately 22. The radii of curvature of a double convex lens are 4 cm and 8 cm . If the refractive index of the material of the lens i 23. When monochromatic light of wavelength 600 nm is used in Young's double slit experiment, the fifth order bright fringe i 24. A solid sphere of radius $$R$$ carries a positive charge $$Q$$ distributed uniformly throughout its volume. A very thin 25. Assertion (A) In a region of constant potential, the electric field is zero and there can be no charge inside the region 26. Statement (A) Inside a charged hollow metal sphere, $$E=0, V \neq 0$$, (where, $$E=$$ electric field, $$V=$$ electric po 27. The electrons take $$40 \times 10^3$$ s to dirift from one end of a metal wire of length 2 m to its other end. The area 28. The current 'I' in the circuit shown in the figure is
29. A toroid has a non ferromagnetic core of inner radius 24 cm and outer radius 25 cm , around which 4900 turns of a wire a 30. A steel wire of length $$l$$ and magnetic moment $$M$$ is bent into a semicircular arc of radius $$R$$. The new magnetic 31. A magnetic needle free to rotate in a vertical plane parallel to the magnetic meridian has its north tip pointing down a 32. A circular coil has 100 turns, radius 3 cm and resistance $$4 \Omega$$. This coil is co-axial with a solenoid of 200 tur 33. Capacitive reactance of a capacitor in an AC circuit is $$3 \mathrm{k} \Omega$$. If this capacitor is connected to a new 34. A light of intensity $$12 \mathrm{Wm}^{-2}$$ incidents on a black surface of area $$4 \mathrm{~cm}^2$$. The radiation pr 35. The electric field $$(E)$$ and magnetic field $$(B)$$ of an electromagnetic wave passing through vacuum are given by
$$\ 36. In a photoelectric experiment light of wavelength 800 nm produces photoelectrons with the smallest de-Broglie wavelength 37. A hydrogen atom at the ground level absorbs a photon and is excited n = 4 level. The potential energy of the electron in 38. The radius of an atomic nucleus of mass number 64 is 4.8 fermi. Then the mass number of another atomic nucleus of radius 39. Consider the statements
In a semiconductor
(A) There are no free electrons at 0 K.
(B) There are no free electrons at an 40. A carrier wave is used to transmit a message signal. If the peak voltage of modulating signal and carrier signal are inc
1
AP EAPCET 2022 - 4th July Evening Shift
MCQ (Single Correct Answer)
+1
-0
If $$x \neq 0$$ and $$f(x)$$ satisfies $$8 f(x)+6 f(1 / x) =x+5$$, then $$\frac{d}{d x}\left(x^2 f(x)\right)$$ at $$x=1$$ is
A
$$-1 / 14$$
B
$$25 / 14$$
C
$$9 / 14$$
D
$$19 / 14$$
2
AP EAPCET 2022 - 4th July Evening Shift
MCQ (Single Correct Answer)
+1
-0
$$\frac{d}{d x}\left(\lim _{x \rightarrow 2} \frac{1}{y-2}\left(\frac{1}{x}-\frac{1}{x+y-2}\right)\right)=$$
A
$$1 / x^2$$
B
$$2 / x^3$$
C
$$-2 / x^3$$
D
$$1 / x^3$$
3
AP EAPCET 2022 - 4th July Evening Shift
MCQ (Single Correct Answer)
+1
-0
If $$f(x)=\left\{\begin{array}{cc}\frac{x^2 \log (\cos x)}{\log (1+x)} & , \quad x \neq 0 \\ 0 & , x=0\end{array}\right.$$, then at $$x=0, f(x)$$ is
A
not continuous
B
continuous but not differentiable
C
differentiable
D
not continuous, but differentiable
4
AP EAPCET 2022 - 4th July Evening Shift
MCQ (Single Correct Answer)
+1
-0
The number of those tangents to the curve $$y^2-2 x^3-4 y+8=0$$ which pass through the point $$(1,2)$$ is
A
0
B
2
C
1
D
3
Paper analysis
Total Questions
Chemistry
40
Mathematics
80
Physics
40
AP EAPCET
Papers
2022