Chemistry
1. The maximum number of electrons present in an orbital with $$n = 4, l = 3$$ is2. 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 and5. The set of molecules in which the central atom is not obeying the octet rule is6. The formal charges of atoms (1), (2) and (3) in the ion is7. 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?
$$\mathrm{SO}_3^{2-}(a q)+10. Observe the following properties :
Volume, enthalpy, density, temperature, heat capacity, pressure and internal energy. 11. Match the following.
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.tg td{border-color:black;border-style:solid;bor12. Which of the following expression is correct?13. The pH of 0.01 N lime water is14. The empirical formula of calgon is15. The pair of elements that form both oxides and nitrides, when burnt in air are16. Among $$\mathrm{P}_4, \mathrm{~S}_8$$ and $$\mathrm{N}_2$$ the elements which undergo disproportionation when heated wit17. Identify the correct statements about the anomalous behaviour of boron.
I. Boron trihalides can form dimeric structures.18. The hybridisations of carbon in graphite, diamond and $$\mathrm{C}_{60}$$ are respectively19. The major product of the following reaction is
20. Identify the ortho and para-directing groups towards aromatic electrophilic substitution reactions from the following li21. Match List I with List II.
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.tg td{border-color:black;border-style:sol22. Which of the following solids is not a molecular solid?23. A solution containing 6.0 g of urea is isotonic with a solution containing 10 g of a non-electrolytic solute $$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$$ solution using platinum electro26. The time required for completion of $$93.75 \%$$ of a first order reaction is $$x$$ minutes. The half-life of it (in min27. The macromolecular colloids of the following are
I. Starch solution
II. Sulphur sol
III. Synthetic detergent
IV. Synthet28. Assertion (A) Animal skins are colloidal in nature.
Reason (R) Animal skin has positively charged particles.29. In the reaction of phosphorus with conc. $$\mathrm{HNO}_3$$, the oxidised and reduced products respectively are30. Which of the following is formed when $$\mathrm{SO}_3$$ is absorbed by concentrated $$\mathrm{H}_2 \mathrm{SO}_4$$ ?31. Assertion (A) Transition metals and their complexes show catalytic activity.
Reason (R) The activation energy of a react32. The crystal field theory is successful in explaining which of the following?
I. Ligands as point charges.
II. Formation 33. Pernicious anemia is caused due to deficiency of which vitamin ?34. Which of the following vitamins cannot be stored in the body?35. Finkelstein reaction is used for the synthesis of36. Which among the following will have highest density?37. Identify the major product (Y) from the following reaction,
38. An aryl carboxylic acid on treatment with sodium hydrogen carbonate liberates a gaseous molecule. Identify the gas molec39. Identify the major product of the following reaction.
40. Identify the major product of the following reaction,
Mathematics
1. $$\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.$$ is3. If $$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}{ccc5. If $$A=\left[\begin{array}{ccc}1 & 0 & 0 \\ a & -1 & 0 \\ b & c & 1\end{array}\right]$$ is such that $$A^2=I$$, then6. 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 $$(\sin \theta, \cos \theta)$$ is8. $$\sum_\limits{k=0}^{440} i^k=x+i y \Rightarrow x^{100}+x^{99} y+x^{242} y^2+x^{97} y^3=$$9. A true statement among the following identities is10. 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 $$|x-2|^2+|x-2|-2=0$$ is13. 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!$$ ends in exactly 1000 zeroes is19. If $$\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)$$ is23. $$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$$ is27. If $$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 is35. In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked randomly. The probability that it is neither red36. For two events $$A$$ and $$B$$, a true statement among the following is37. Five digit numbers are formed by using digits $$1,2,3,4$$ and 5 without repetition. Then, the probability that the rando38. 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 param41. 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 ce43. If the points of intersection of the coordinate axes and $$|x+y|=2$$ form a rhombus, then its area is44. Suppose, in $$\triangle A B C, x-y+5=0, x+2 y=0$$ are respectively the equations of the perpendicular bisectors of the s45. 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, then46. 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 / a48. The area of the circle passing through the points $$(5, \pm 2),(1,2)$$ is49. The ratio of the largest and shortest distances from the point $$(2,-7)$$ to the circle $$x^2+y^2-14 x-10 y-151=0$$ is50. 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$$-axis. Then, the e53. The focal distances of the point $$\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 $$Q(\theta55. If the vertices and foci of a hyperbola are respectively $$( \pm 3,0)$$ and $$( \pm 4,0)$$, then the parametric equation56. If $$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)$$ and also the mid-point of the58. If the equation of the plane which is at a distance of $$1 / 3$$ units from the origin and perpendicular to a line whose59. If $$[\cdot]$$ denotes greatest integer function, then $$\lim _\limits{x \rightarrow \frac{-3}{5}} \frac{1}{\dot{x}}\lef60. If $$l, m(l61. Let $$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 $$(1,2)$$ is66. 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$$ cut orthogonally is68. A closed cylinder of given volume will have least surface area when the ratio of its height and base radius is69. Two particles $$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)$$ are mo70. If $$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 x78. If $$l$$ and $$m$$ are order and degree of a differential equation of all the straight lines at constant distance of $$P79. If $$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}\right3. A force $$\mathbf{F}_1$$ of magnitude 4 N acts on an object of mass 1 kg , at origin in a direction $$30^{\circ}$$ above4. $$y=\left(P t^2-Q t^3\right) \mathrm{~m}$$ is the vertical displacement of a ball which is moving in vertical plane. The5. 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 th7. A ball of mass 300 g is dropped from a height 10 m above a sandy ground. On reaching the ground, it penetrates through a8. Two balls $$A$$ and $$B$$, of masses $$M$$ and $$2 M$$ respectively collide each other. If the ball $$A$$ moves with a s9. A solid sphere of radius $$R$$ has its outer half removed, so that its radius becomes $$(R / 2)$$. Then its moment of in10. 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 potential12. As shown in the figure, an iron block $$A$$ of volume $$0.25 \mathrm{~m}^3$$ is attached to a spring $$S$$ of unstretche13. 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 sec15. 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 $$0.016. A steady flow of a liquid of density $$\rho$$ is shown in figure. At point 1, the area of cross-section is $$2 A$$ and t17. A metal tape is calibrated at $$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 mode21. Speed of sound in air near room temperature is approximately22. 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 i23. When monochromatic light of wavelength 600 nm is used in Young's double slit experiment, the fifth order bright fringe i24. 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 region26. Statement (A) Inside a charged hollow metal sphere, $$E=0, V \neq 0$$, (where, $$E=$$ electric field, $$V=$$ electric po27. 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 a30. A steel wire of length $$l$$ and magnetic moment $$M$$ is bent into a semicircular arc of radius $$R$$. The new magnetic31. A magnetic needle free to rotate in a vertical plane parallel to the magnetic meridian has its north tip pointing down a32. A circular coil has 100 turns, radius 3 cm and resistance $$4 \Omega$$. This coil is co-axial with a solenoid of 200 tur33. Capacitive reactance of a capacitor in an AC circuit is $$3 \mathrm{k} \Omega$$. If this capacitor is connected to a new34. A light of intensity $$12 \mathrm{Wm}^{-2}$$ incidents on a black surface of area $$4 \mathrm{~cm}^2$$. The radiation pr35. The electric field $$(E)$$ and magnetic field $$(B)$$ of an electromagnetic wave passing through vacuum are given by
$$\36. In a photoelectric experiment light of wavelength 800 nm produces photoelectrons with the smallest de-Broglie wavelength37. A hydrogen atom at the ground level absorbs a photon and is excited n = 4 level. The potential energy of the electron in38. The radius of an atomic nucleus of mass number 64 is 4.8 fermi. Then the mass number of another atomic nucleus of radius39. Consider the statements
In a semiconductor
(A) There are no free electrons at 0 K.
(B) There are no free electrons at an40. A carrier wave is used to transmit a message signal. If the peak voltage of modulating signal and carrier signal are inc
1
AP EAPCET 2022 - 4th July Evening Shift
MCQ (Single Correct Answer)
+1
-0
In a $$\triangle A B C, 2(b c \cos A+a c \cos B+a b \cos C)=$$
A
$$a+b+c$$
B
$$2(a+b+c)$$
C
$$a^2+b^2+c^2$$
D
$$2\left(a^2+b^2+c^2\right)$$
2
AP EAPCET 2022 - 4th July Evening Shift
MCQ (Single Correct Answer)
+1
-0
If $$4+6\left(e^{2 x}+1\right) \tanh x=11 \cosh x+11 \sinh x$$ then $$x=$$
A
$$\log _{10}$$
B
$$\log 4$$
C
$$\log 5$$
D
$$\log 2$$
3
AP EAPCET 2022 - 4th July Evening Shift
MCQ (Single Correct Answer)
+1
-0
In a $$\triangle A B C, \frac{a}{b}=2+\sqrt{3}$$ and $$\angle C=60^{\circ}$$. Then, the measure of $$\angle A$$ is
A
$$95^{\circ}$$
B
$$65^{\circ}$$
C
$$105^{\circ}$$
D
$$115^{\circ}$$
4
AP EAPCET 2022 - 4th July Evening Shift
MCQ (Single Correct Answer)
+1
-0
If $$a=2, b=3, c=4$$ in a $$\triangle A B C$$, then $$\cos C=$$
A
$$\frac{1}{4}$$
B
$$\frac{-1}{4}$$
C
$$\frac{1}{2}$$
D
$$\frac{-1}{2}$$
Paper analysis
Total Questions
Chemistry
40
Mathematics
80
Physics
40
AP EAPCET
Papers
2022